Research ArticleCooperative Spectrum Sensing for Cognitive HeterogeneousNetworking Using Iterative Gauss-Seidel Process

Haleh Hosseini1 Kaamran Raahemifar1

Sharifah Kamilah Syed Yusof2 and Alagan Anpalagan1

1Department of Electrical Engineering Ryerson University Toronto Canada M5B 2K32Universiti Teknologi Malaysia 81310 Johor Malaysia

Correspondence should be addressed to Alagan Anpalagan alaganeeryersonca

Received 9 June 2015 Revised 14 September 2015 Accepted 29 September 2015

Academic Editor Qingqi Pei

Copyright copy 2015 Haleh Hosseini et alThis is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Heterogeneous networks with dense deployment of small cells can employ cognitive features to efficiently utilize the availablespectrum resources Spectrum sensing is the key enabler for cognitive radio to detect the unoccupied channels for data transmissionIn order to deal with shadowing and multipath fading in sensing channels cooperative spectrum sensing is designed to increasethe accuracy of the sensed signal In this paper an optimized local decision rule is implemented for the case that the received datafrom primary users are possibly correlated due to the sensing channel impairments Since the prior information is unavailable inthe real systems Neyman-Pearson criterion is used as the cost functionThen a discrete iterative algorithm based on Gauss-Seidelprocess is applied to optimize the local cognitive user decision rules under a fixed fusion rule This method with low complexitycan minimize the cost using the golden section search method in a finite number of iterations ROC curves are depicted usingthe achieved probability of detection and false alarm by numerical examples to illustrate the efficiency of the proposed algorithmSimulation results also confirm the superiority of the proposed method compared to the conventional topologies and decisionrules

1 Introduction

Heterogeneous networks are the next generation of cellu-lar networks with densely deployed low power small cellsthat may reuse spectrum resources across the space Sinceheterogeneous networks may experience spectral crowd-ing the main challenge is to coexist efficiently with otherlicensed users According to the Federal CommunicationCommissions (FCC) frequency allocation chart the spec-trum bands dedicated to the licensed or primary user (PU)are highly underutilized [1] Cognitive radio features mayequip heterogeneous networks with spectrum sensing withinthe small cells to acquire available channels and enhance theiroperations [2] Cognitive radio can provide opportunisticspectrum access for unlicensed or secondary users andoptimize the spectral efficiency [3 4] The most criticalrequirement of cognitive radio is the sensing mechanism

to exploit the spectrum holes while suppressing the mutualinterference with PUs [4ndash6]

An optimal spectrum sensingmechanism is necessary forcognitive radios tomaximize detection probability of the PUsrsquosignal subject to the constraint of the limited probability offalse alarm Among various signal detection schemes energydetection has been recognized with low computational com-plexity to be used for spectrum sensingThis method is basedon measuring and comparing the received signal strengthfrom the PUs with a threshold within the channels and acertain sensing time [7] However the performance of energydetector is degraded with sensing channel impairmentswhich leads to attenuation and variations of the sensed signalMultipath fading path loss shadowing and hidden nodeproblem inevitably compromise the sensing reliability Aneffective approach to overcoming these uncertainty problemsand improving the performance is cooperative sensing [8ndash11]

Hindawi Publishing CorporationInternational Journal of Distributed Sensor NetworksVolume 2015 Article ID 319164 9 pageshttpdxdoiorg1011552015319164

2 International Journal of Distributed Sensor Networks

Cooperative sensing can be used to acquire informationof an intelligent wireless network with various applicationsincluding radar and sensor networks [12 13] The designof cooperative sensing can increase the reliability flexibilityspeed and coverage area of the sensing network In a cogni-tive radio with large number of sensing nodes cooperativespectrum sensing can increase the detection probabilityof primary users and the channel utilization Cooperativespectrum sensing can enhance the sensing performance byexploiting the spatial diversity in the observations of spatiallylocated secondary users which transmit their sensing infor-mation to a fusion center for final decision It has been shownthat increasing the number of cooperative users can decreasethe required detector sensitivity and sensing time Moreovera cooperative approach needs lower communication band-width and is more robust to channel fading [14ndash16]

The drawback of the feedback overhead of spectrumsensing is overcome in [14] by using a fixed number ofcommon feedback channels so that each node compares thesensing result with a threshold and selects the appropriatedata to be sent to the fusion center In [15] a sensor selectionstrategy is proposed to minimize the energy consumptionfor cooperative spectrum sensing under satisfactory pri-mary user detection performance A decentralized spectrumsensing approach is proposed in [16] to reduce the overalloverhead and power consumption of the network by elim-inating the need for fusion center node In this schemeeach secondary user communicates only with its adjacentnodes via one-hop transmissions within several rounds toreach global convergence The performance of cooperativespectrum sensing over Rayleigh fading channel is improvedin [17] using an adaptive linear combiner with weights tosecondary user decisions

In this paper a cooperative spectrum sensing is deployedfor cognitive heterogeneous network with a parallel approachinstead of centralized topology that needs wideband chan-nels With correlated local sensing observations a numericalalgorithm is proposed to optimize the local decisions oflocal cognitive users (LCUs) and send the information to acommon cognitive user (CCU) as fusion center The designof parallel topology increases the reliability flexibility speedand coverage area of the sensing network Based on Bayesianoptimality criteria with independent observations the opti-mized rule for decision making of each LCU is likelihoodratio test (LRT) [18ndash20] Since the prior probabilities ofhypotheses and accurate illustration of cost coefficients arenot available in real systems common Bayesian method formaximizing LRT is not practicalThereforeNeyman-Pearsoncriterion is adopted for optimum local decision rule (OLDR)so that the probability of false alarm is limited to a desiredvalue while the probability of missed detection is minimized[21]

The rest of this paper is organized as follows Section 2describes cooperative sensing schemes and Section 3 illus-trates the systemmodelThe proposed iterative algorithm fordecision making at LCUs is described in Section 4Then thismethod is simulated and the results are analyzed in Section 5The paper is concluded in Section 6 and the open issues forfuture researches are addressed

2 Cooperative Sensing Schemes

Various cooperative sensing schemes by LCUs depending onthe decision making methods of the fusion center can beused to carry out PU detection In a centralized networkapproach local sensors send the raw sensing information to afusion center which decides on the presence or absence of thePUHowever the transmission of these unprocessed observa-tions does not efficiently utilize the bandwidth Cooperativesensing methods perform some preliminary data processingat each sensor to condense the information [21] The majorcooperative configurations include parallel serial and treetopologies as shown in Figure 1

In a parallel sensing model each LCU can decide inde-pendently based on its sensed information and pass thequantized local decision to a CCU whose role as a fusioncenter is to make a final decision on PU existence accordingto the spatially collected results Even though extensive inves-tigations have been done for cooperative sensing schemes toincrease the sensing accuracy most of the research assumedthat the sensed information is independent and identicallydistributed within the local sensors [22] This assumption ispractically unrealistic as shadowing is highly correlated whenseveral cognitive users are geographically proximate withsimilar shadowing effects Spatially correlated shadowingwhich exponentially depends on the distance can bound theachievable gain of cooperative sensing [23]

For optimal PU detection Bayesian criterion with maxi-mizing LRT is the most common method in signal detectiontheory For a given set of observations119884 = [119910

1 119910

119873] it has

been shown that when the prior information of probabilitiesis known LRT is the optimized detection method in whichthe likelihood ratio is calculated for the received signals andcompared to a threshold 120579 as Λ(119884) = 119875(119884 | 119867

1)119875(119884 |

1198670) lt 120579 where 120579 is a function of prior probabilities of 119901

0

and 1199011and the cost function 119888

119894119895of 119867119894decision while 119867

119895has

been true so we have 120579 = (11988810

minus 11988800

)1199010(11988801

minus 11988811

)1199011 In

many cases it is difficult to know these cost coefficients andprior probabilities Instead Neyman-Pearson cost function 119865

is replaced under a condition that false alarmprobability119875119891is

less than a certain value 120572 as119865 = 120582(119875119891

minus120572)+119875119898 where 120582 is the

Lagrange multiplier 119875119891is the probability of false alarm and

119875119898is the probability of detection respectively To provide the

final relations for119875119889and119875119891 note that119875

119889= 1minusint

Ω119875(119884 | 119867

1)119889119884

and 119875119891

= 1 minus intΩ

119875(119884 | 1198670)119889119884 where Ω is decision region

of 1198670determined due to the type of local decision rules and

fusion rulesIn the case of Bayesian criterion for centralized network

as shown in Figure 1(a) there are 119873 sensors that send theirobservations directly to one fusion center before processingand the final decision 119880

119891is made based on a fusion rule as

119866(119884) while

119880119891

=

0 1198670decision if 119866 (119884) le 0

1 1198670decision if 119866 (119884) gt 0

(1)

The region of final decision based on 1198670is ΩCN = 119884

119866(119884) le 0 The fusion rule 119866(119884) is defined while minimizing

International Journal of Distributed Sensor Networks 3

Observations

Final decision

FC

middot middot middot

(a) Centralized topology

Observations

Final decision

FC

middot middot middotS1 S2SN

(b) Parallel topology

Observations

Final decisionmiddot middot middot SNS1 S2

(c) Serial topology

Observations

Obs

erva

tions

Final decision

S2 S3 S4

S1

S0

(d) Tree topology

Figure 1 Major topologies of cooperative sensing networks

the cost function of 119865 = 119888 + intΩCN

119891(119884)119889119884 where 119888 = (119901011988810

+

119901111988811

) 119891(119884) = 1198861119875(119884 | 119867

1) minus 1198860119875(119884 | 119867

0) with 119886

1= (11988801

minus

11988811

)1199011 and 119886

0= (11988810

minus11988800

)1199010Therefore the optimumdecision

region of centralized network is ΩCN = 119910119894

Λ(119884) lt 120579CN 119894 =

1 119873 where Λ(119884) = 119875(119884 | 1198671)119875(119884 | 119867

0) 120579CN is the

threshold of decision making for centralized network and 119873

is the number of sensorsIn parallel topology with distributed local observations

as shown in Figure 1(b) Bayesian criterion leads to LRT forlocal decision rule For a network with 119873 receivers and ORfusion rule it can be written that ΩLRTOR = 119910

119894 Λ(119910

119894) le

120579119894 119894 = 1 119873 where 120579

119894is the threshold for the 119894th receiver

Meanwhile for AND fusion rule it is given that ΩLRTAND =

119878 minus 119910119894

Λ(119910119894) gt 120579

119894 119894 = 1 119873 where 119878 is the whole

decision region Based on Neyman-Pearson criterion thevalues of thresholds 120579

119894can be achieved byminimizing the cost

function of 119865 which in the case of OR fusion rule is

119865LRTOR = 120574 + intΩLRTOR

119891 (119884) 119889119884 (2)

and for AND fusion rule is

119865LRTAND = 120574 + intΩLRTAND

119891 (119884) 119889119884 (3)

where 120574 = 120582(1 minus 120572) 119891(119884) = 119875(119884 | 1198671) minus 120582119875(119884 | 119867

0)

The region of decision making for parallel sensingapproach under cognitive radio channels is discussed in thenext section The local decision rules of local cognitive usersand fusion rule are formulated to design an optimal algorithmwith Neyman-Pearson criterion

3 System Model

In this work a cellular network scenario so called as hetero-geneous network is considered for densely populated areassuch that macrocells are mixed with low power cells Thesmall cells of heterogeneous networks can increase the signalcoverage for the areas that are not accessible by macrobasestations to optimize the reliability and data rate However in

4 International Journal of Distributed Sensor Networks

Primarynetwork

PU

PU

Tx

Rx

Heterogeneous network

Macro-eNB

H-UE

H-UEH-UE

H-eNB(CCU)

M-UE

(LCU1)

(LCU3)

(LCU2)

Figure 2 A heterogeneous network overlapping with primarynetwork

CCU (fusion center)

PU

Sensing channels

Reporting channels

LCU1 LCU2LCUN

middot middot middot

Figure 3 Parallel cooperative spectrum sensing

this network the coverage areas of small cells and primarysystems can be overlapped This mutual interference occurswhen they are using the same time-frequency resources whilespatially located in a certain distance apart from each otheras shown in Figure 2 The frequency reusing of adjacentmacrocell user equipment (M-UE) or other primary systemsby small cells can create interferences to heterogeneoususer equipment (H-UE) Hence H-UE which operates assecondary users needs to transmit under a certain powerlevel which is acceptable by the licensed users PUs and atthe same time mitigates the interference from the primarysystem

The decision making on the presence or absence of PUsignals is a critical part of spectrum sensing procedure atcognitive H-UE In practice each cognitive piece of H-UEplays a role same as distributed LCUs that is equipped withspectrum sensing by energy detection to locally measurethe PU signal transmission power and frequencies Thelocal decisions are the output of certain local rules at thesedistributed pieces of H-UEs that will be sent to H-eNB withthe capability of a CCU to process the received informationand produce the final decision based on the embedded fusionrule Then in the presence of PU signals pieces of H-UEadapt their configurations to avoid mutual interferences withprimary network Since the channel impairments affect theinput observations of each energy detector at H-UE theassumption of independency is not correct any more anda cooperative decision making is required as the solution

Cognitive features enable the secondary users to analyzeinterference using the spectrum sensing mechanism that ismainly performed in LCUs whereas the decision is made forthe cooperative network Let us consider 119873 distributed LCUsas shown in Figure 3 In this figure the 119894th LCU is shownas LCU

119894that receives the observation signals 119910

119894 from the

PU through the sensing channels Each LCU119894sends its local

binary decision 119906119894 to the fusion center the CCU tomake the

final decision using the fusion ruleThemetrics of probabilityof detection 119875

119889119894 and probability of false alarm 119875

119891119894 for

local decision at the 119894th LCU119894are derived to be employed

for the performance evaluation Assuming that during thesensing time CUs do not broadcast and there is no mutualinterference between them the vector of the received signalthrough the sensing channels is defined as

119884 = 119867 sdot 119878119901

+ 119881 (4)

where 119878119901denotes PUrsquos transmitted signal 119867 = [ℎ

1

ℎ119894 ℎ

119873] states the sensing channel gain vector and 119884 =

[1199101 119910

119894 119910

119873] shows the observation vector in which

119910119894denotes the received signal at LCU

119894 The vector of addi-

tive white Gaussian noise (AWGN) at LCU receivers is119881 = [V

1 V

119894 V

119873] The observations of PUrsquos signal

are received through the sensing channels at LCU119894 In this

scenario the correlated channels lead to correlated sensingobservations at the LCU receivers that analyze the data asa binary hypothesis testing form 119867

0and 119867

1are the binary

hypotheses which define the absence and presence of PUrespectively Then the general form of the received signal atthe spectrum sensing part of LCU is

1198671

1199101

= ℎ1

sdot 119878119901

+ V1 119910

119873

= ℎ119873

sdot 119878119901

+ V119873

1198670

1199101

= V1 119910

119873= V119873

(5)

Given that 119910119894denotes the available observation of PU

signal at LCU119894receiver the local decision rule 119892

119894(119910119894) is

employed by LCU119894to make a binary decision 119906

119894about the

existence of PU signal Based on a set of local decision rulesas 119866(119884) = [119892

1(1199101) 119892

119894(119910119894) 119892

119873(119910119873

)] the fusion centerCCU receives the local decision as

119906119894

= 0 119892

119894(119910119894) le 0

1 119892119894(119910119894) gt 0

(6)

TheCCU follows a fusion rule as119876(119880)which is a Booleanfunction and whenever 119876(119880) = 0 the final decision is takenas 1198670 otherwise it is 119867

1 The local decision rule maps the

observation set 119884 = 1199101 119910

119873to a local decision set 119880 =

1199061 119906

119894 119906

119873 where 119906

119894isin 0 1 119894 = 1 119873 The

combination of local binary decisions 119906119894results in 2

119873 statesThus the 2

2119873

is the total number of states for final decision119906119891

= 119876(119880) and

119876 (119880) = 119876119899 119906119894

= mod (119899 minus 1

2(119894minus1) 2) 1

le 119899 le 2119873

(7)

International Journal of Distributed Sensor Networks 5

where mod(119860 2) is the division remaining of 1198602 and 119906119894

=

mod((119899 minus 1)2(119894minus1)

2) is the 119894th bit of 119899 Hence 119876(119880) =

119876119899 119899 = sum

119873

119894=11199061198942119894minus1

+ 1 Consider two different sets as1198780

= 119899 119876119899

= 0 and 1198781

= 119899 119876119899

= 1 such that1198780

cup 1198781

= 1 2 2119873

then ΩOLDR = 119910119894

119876119899

= 0 119899 isin 1198780

where ΩOLDR defines the region of optimal decision makingfor parallel cooperative cognitive network which leads to thefinal decision of 119867

0 With a given set of 119878

0 the fusion rule

119876(119880) is deterministic and constant and for every 119899 belongingto 1198780 119899th composition will result in a decision on 119867

0 For

a fixed fusion rule the region of final decision is ΩOLDR =

⋃119899isin1198780

Ω119899 where Ω

119899denotes the region of 119899th combination of

119876 as

Ω119899

= 119884 119906119894

= mod (119899 minus 1

2(119894minus1) 2) 119876

= 119876119899

(8)

In the next section the optimization problem for parallellocal decision rules is reduced to solve a set of fixed pointintegral equations that minimizes the Neyman-Pearson costfunction The decision rules are digitized for simplicity andGauss-Seidel algorithm [24] and Golden Section search [25]are applied to find the final solutions

4 OLDR Algorithm with Gauss-Seidel Process

Each distributedH-UELCU119894performs the spectrum sensing

by energy detection to detect the initial PU signal obser-vation 119910

119894 This distributed information from all LCUs is

used by the OLDR algorithm to cooperatively optimize localdecision rules 119892

119894 according to the fix central fusion rule at

H-eNBCCU ANDOR and achieve the final minimized 119875119891

with Gauss-Seidel process Based on the Neyman-Pearsoncriterion the optimum local decision rule is defined tominimize the corresponding cost function 119865

119865 (119866 119876) = 120582 (1 minus 120572) + intΩOLDR

119891 (119884) 119889119884 (9)

where 119876 is the Boolean fusion function 119884 denotes localobservations and 119891(119884) = 119875(119884 | 119867

1) minus 120582119875(119884 | 119867

0) Given

that 120574 = 120582(1 minus 120572) according to the above relations it can beconcluded that

119865 (119866 119876) = 120574 + int119884isinΩOLDR

119891 (119884) 119889119884 = 120574

+ (int119892119894(119910119894)le0

(int⋃119899isin11987801119894

Ω119899119894

minus int⋃119899isin11987802119894

Ω119899119894

) + int119910119894

int⋃119899isin11987802119894

Ω119899119894

)

sdot 119891 (119884) 119889119884

(10)

where Ω119899119894

is Ω119899excluding 119910

119894 11987801119894

11987802119894

are two subsetsof 1198780such that 119878

01119894cup 11987802119894

= 1198780 11987801119894

is a subset of 119899

belonging to 1198780with 119906

119894= 0 119878

01119894= 119899 119876

119899=

0 119906119894

= 0 and similarly 11987802119894

is a subset of 119899 belongingto 1198780with 119906

119894= 1 119878

02119894= 119899 119876

119899= 0 119906

119894= 1

The set of optimum local decision rules that minimizes the119865 function in (10) can be defined as 119866 = (119892

1 119892

119873)

[26]

119892119894(119910119894) = (int

⋃119899isin11987801119894

Ω119899119894

minus int⋃119899isin11987802119894

Ω119899119894

)

sdot119891 (119884) 119889119884

119889119910119894

(11)

where Ω119899119894

= (1199101 119910

119894minus1 119910119894+1

119910119873

) 120601(119892119894 119906119894) le 0

and 120601(119892119894 119906119894) = (12 minus 119906

119894)119892119894 Consequently each set of

optimum local decisions is derived by solving several fixedpoint integral equations as

Γ119876

(119866) =

[[[[[[[[[[[[[[[[[[[[

[

(intcup119899isin119878011

Ω1198991

minus intcup119899isin119878021

Ω1198991

)119891 (119884) 119889119884

1198891199101

(intcup119899isin11987801119894

Ω119899119894

minus intcup119899isin11987802119894

Ω119899119894

)119891 (119884) 119889119884

119889119910119894

(intcup119899isin11987801119873

Ω119899119873

minus intcup119899isin11987802119873

Ω119899119873

)119891 (119884) 119889119884

119889119910119873

]]]]]]]]]]]]]]]]]]]]

]

(12)

Therefore the problem of optimum cooperative sensingis essentially reduced to optimizing a set of 119866 = (119892

1 119892

119873)

that satisfies the integral equations An iterative algorithmbased on Gauss-Seidel process can approximate the solutionof the above equations [26] This method is used for solvinga matrix of linear equations when the number of systemparameters is too high to find a solution by common PLUtechniques The initial requirement is that the diagonalelements of the matrix of equations must be nonzero andconvergence is provided when this matrix is either diagonallydominant or symmetric and positive definite [24] Let usconsider the local decision rule in 119895th iteration stage of thealgorithm as 119866

(119895) and the initial set as 119866(0) Gauss-Seidel

process for optimum local decision rules can be definedas

119866(119895+1)

= Γ119876

(119866(119895)

) forall119895 = 0 1 2 (13)

6 International Journal of Distributed Sensor Networks

where

119892119894

(119895+1)(119910119894)

= (int⋃119899isin11987801119894

Ω119899119894

minus int⋃119899isin11987802119894

Ω119899119894

)

sdot119891 (119884) 119889119884

119889119910119894

(14)

To reduce the computation complexity the discrete vari-ables 119905

119894are extracted from 119910

119894as 119879 = 119905

1 119905

119894 119905

119873 and

(14) can be described as

119892119895+1

119894(119905119894)

= ( sum

⋃119899isin11987801119894

Ω119899119894

minus sum

⋃119899isin11987802119894

Ω119899119894

)119891 (119879) Δ119879

Δ119905119894

(15)

Hence the discrete local decision rules are defined as

119885119894(119905119894) = 119868 (119892

119894(119905119894))

119868 (119909) = 0 119909 le 0

1 119909 gt 0

(16)

Accordingly the cost function 119865 is approximated as

119865 (119885 119876) = 120574

+ sum

119899isin1198780

( sum

11990511198851=1199061

sum

119905119894119885119894=119906119894

sum

119905119873119885119873=119906119873

119891 (119879) Δ119879)

(17)

Therefore

119892119895+1

119894(119905119894) = ( sum

119899isin11987801119894

minus sum

119899isin11987802119894

)

sum

1199051

sdot sdot sdot sum

119905119894minus1

sum

119905119894+1

sdot sdot sdot sum

119905119873

119894minus1

prod

119871=1

(1 minus

1003816100381610038161003816100381610038161003816mod (

119899 minus 1

2(119871minus1) 2) minus 119885

119871

(119895+1)(119905119871)

1003816100381610038161003816100381610038161003816)

119873

prod

119871=119894+1

(1 minus

1003816100381610038161003816100381610038161003816mod (

119899 minus 1

2(119871minus1) 2) minus 119885

119871

(119895)(119905119871)

1003816100381610038161003816100381610038161003816)

119891 (119879) Δ119879

Δ119910119894

(18)

For the simplicity of computations discrete local decisionrules 119885

119894(119905119894) are substituted instead of 119892

119894(119905119894) as both of them

have the same region of decision making Note that the iter-ative process converges when absolute relative approximateerror |(119885

119894

(119895+1)(119905119894) minus 119885

119894

(119895)(119905119894))119885119894

(119895+1)(119905119894)| times 100 ≪ 120576 where

120576 gt 0 is prespecified tolerance parameter For each positivevalue of Δ119905

119894and initial selection of 119885

0

119894 the algorithm is

converged after a certain number of iterations to a set of119885119895

119894that satisfies the convergence condition Figure 4 presents

the flowchart of the developed optimization algorithm basedon the golden section search method for Neyman-Pearsoncriterion Golden section ratio of golden section search isapplied with 120593 = 0618 or symmetrically (1 minus 0618) = 0382

to condense the width of the range in each step [25]

5 Simulation and Discussion

For the performance evaluation of the proposed OLDRalgorithm and compared to the other methods the receiveroperating characteristic (ROC) curve is depicted as a graph of119875119889versus 119875

119891 To depict ROC curves for the OLDR algorithm

in each iteration the values of 119875119889and 119875

119891are provided based

on the OLDR rules As a benchmark the simulation resultsare compared to centralized network and parallel networkwith LRT local decision rule

When normal pdf is assumed for the sensed signalsthe conditional pdf rsquos under both hypotheses 119867

0and

1198671are defined as 119901(119910

1 1199102 119910

119873| 1198670) = 119873(120583

0 1198620)

and 119901(1199101 1199102 119910

119873| 1198671) = 119873(120583

1 1198621) where 119862

0

and 1198621are the covariance matrices under 119867

0and 119867

1

respectively With correlation coefficient minus1 le 120588 le 1the covariance matrix is written as 119862(119910

1 1199102 119910

119873) =

[1205902

1 12058812

12059011205902 120588

11198731205901120590119873

1205881198731

120590119873

1205901 1205881198732

120590119873

1205902 120590

2

119873]

The performance of OLDR algorithm for cooperativespectrum sensing is shown in this section Centralizednetwork (CN) with a fusion center is considered as theoptimum benchmark for the evaluation of the proposedmethod Numerical results are analyzed for both OLDRand LRT local decision rules with ANDOR fusion rulesThen the effect of various correlation coefficients (120588)on ROC curves is investigated with correlated sensedsignals

In the first case a cooperative spectrum sensing with twolocal cognitive users is considered Given that the receivedobservations from PU are random Gaussian signal 119867 sdot 119878

119901

with mean 120583119867sdot119878119901

= 2 and variance 1205902

119867sdot119878119901

= 1 added to 1198991

and 1198992as independent zero mean Gaussian noises such that

1205902

1198991

= 2 and 1205902

1198992

= 1 then the conditional pdf rsquos under bothhypotheses 119867

0and 119867

1 are 119901(119910

1 1199102

| 1198670) = 119873(120583

0 1198620) and

119901(1199101 1199102

| 1198671) = 119873(120583

1 1198621) Therefore 120583

0= [0 0] 119862

0= [2 0

0 1] 1205831

= [2 2] 1198621

= [3 1 1 2]Figure 5 compares the performance of OLDR and LRT

with centralized network As illustrated in this figure OLDRwithAND fusion rule outperforms the other techniques since

International Journal of Distributed Sensor Networks 7

Start

Yes NoYesNo

Yes

No

End

Initializing of 120582(j) and Δ120582 j = 0

P(j)

flt 120572 P

(j)

fgt 120572

P(j)

flt 120572 P

(j)

fgt 120572

120582(j+1) = 120582(j) minus Δ120582j = j + 1 j = j + 1

j = j + 1

120582(j+1) = 120582(j) + Δ120582

120582(j+1) = 120582(j) + Δ120582

Δ120582 =

120593 times Δ120582 if P(j)

fgt 120572

minus120593 times Δ120582 otherwise

Pf(120582(j)) minus 120572 le 120576

P(j)

f(120582(j)) = 1 minusint

ΩOLDR(g1g119873)P(y1 yN |H0)dy1middot middot middot dyN

Figure 4 The proposed optimization algorithm (OLDR)

it is closer to the CN curve Meanwhile OLDR performsbetter than LRT with the same fusion rules for example at119875119891

= 002 OLDR shows 4 improvement in 119875119889compared to

the LRT with the same fusion rulesIn the second case parallel spectrum sensing with two

local cognitive users are considered with correlated receivedsignals as 120583

0= [0 0] 120583

1= [2 2] 119862

0= 1198621

= [1205902

1 12058812059011205902

12058812059011205902 1205902

2] The results of simulations with 120588 = 01 are

presented in Figure 6 which illustrates that the OLDR withAND fusion rule is more proximate to the CN curve andachieves a better performance than OR fusion rule forinstance at 119875

119891= 002 the improvement is about 4

The performance of the same network for various valuesof correlation coefficient (120588) is shown in Figure 7 Accordingto these results the performance is enhanced by the reductionof the correlation coefficient (120588)

Now a network of three local cognitive users with Gaus-sian signal observations is considered with mean 120583

119867sdot119878119901

= 2

and variance 1205902

119867sdot119878119901

= 1 added to zero mean independentnoises with 120590

2

1198991

= 3 12059021198992

= 2 and 1205902

1198993

= 1Thus the covariance

0 002 004 006 008 01 012 014 016 018 0203

04

05

06

07

08

09

1

CN-2 LCUOLDR-AND 2 LCUOLDR-OR 2 LCU

LRT-AND 2 LCULRT-OR 2 CU

Pf

Pd

Figure 5 ROC comparison forGaussian received signal in indepen-dent Gaussian noise with two LCUs

03

04

05

06

07

08

09

1

CN 2 LCUOLDR-AND 2 LCUOLDR-OR 2 LCU

LRT-AND 2 LCULRT-OR 2 LCU

0 002 004 006 008 01 012 014 016 018 02Pf

Pd

Figure 6 ROC comparison for deterministic received signal incorrelated Gaussian noises with two LCUs

matrices under 1198670and 119867

1are described as 119862

0= [3 0 0

0 2 0 0 0 1] and 1198621

= [4 1 1 1 3 1 1 1 2]Figures 8 and 9 show that increasing the number of local

cognitive users enhances the performance of the network ForGaussian received signals with independentGaussian noise at119875119891

= 002 the 119875119889is enhanced about 3 for OLDR with three

LCUs comparing to OLDR with two LCUsFrom these results it is concluded that for a fixed fusion

rule OLDR algorithm shows a superior performance oflocal decision rules to detect primary users compared toLRT method Apparently the probability of primary userdetection is increased with the number of cooperative localcognitive users equipped with spectrum sensing When thesensing channels are correlated results show performancedegradation in higher correlation coefficients

8 International Journal of Distributed Sensor Networks

03

04

05

06

07

08

09

1

0 002 004 006 008 01 012 014 016 018 02Pf

Pd

OLDR-AND 120588 = minus03

OLDR-AND 120588 = minus01

OLDR-AND 120588 = 0

OLDR-AND 120588 = 01

OLDR-AND 120588 = 03

Figure 7 ROC comparison for deterministic received signal incorrelated Gaussian noise with different correlation coefficients (120588)

CN 3 LCUOLDR-AND 3 LCU

OLDR-AND 2 LCUCN 2 LCU

0 002 004 006 008 01 012 014 016 018 02Pf

03

04

05

06

07

08

09

1

Pd

Figure 8 ROC comparison for Gaussian received signal in inde-pendent Gaussian noises with different numbers of LCUs

OLDR method is a low complexity solution for theproblem of (11) which is reduced to optimizing a set of localdecision rules 119866 = (119892

1 119892

119873) that satisfies the integral

equations (12) In addition the computation complexity of(14) has been reduced by considering discrete variables forthe observations 119910

119894 as well as local decision rules 119892

119894 to 119905119894

and 119885119894 respectively For the centralized network there is

no local decision rule and the local decision rule of LRTmethod is defined as Λ(119910

119894) le 120579

119894 where 120579

119894is the threshold

for the 119894th receiver In each iteration of the algorithm withLRTΛ(119884

119894) is calculated for all observations119910

119894 and compared

with threshold 120579119894 For the initial threshold within a range

of 119872 levels the time complexity of each local decision rulecan be written as 119874(119872) According to (18) the local decision

CN 3 LCUOLDR-AND 3 LCU

CN 2 LCUOLDR-AND 2 LCU

03

04

05

06

07

08

09

1

Pd

004 018 02008 01 012 014 016002 0060Pf

Figure 9 ROC comparison for deterministic signal in correlatedGaussian noises with different numbers of LCUs

Number of LCUs1 2 3 4 5 6 7 8

CNOLDRLRT

0

10

20

30

40

50

60

70Ti

me c

ompl

exity

Figure 10 Time complexity comparison of local decision rules

rule of OLDR algorithm 119892119895+1

119894 has to be updated at each

iteration with the time complexity of 119874(1198732) compared to the

other local decision rulesThe time complexity comparison oflocal decision rules for 119872 = 20 is shown in Figure 10 whichdescribes the increase of the calculations number propor-tional to the number of the receivers 119873 However since CNmethod consumes too large bandwidths for sending the datato the fusion center and LRT method assumes independentobservations they cannot be considered as optimum solutionfor cooperative cognitive users with correlated sensed signals

6 Conclusion

In this paper the cooperative spectrum sensing for cognitiveheterogeneous network has been designed with a parallelconfiguration An optimum algorithm for local decision

International Journal of Distributed Sensor Networks 9

rule based on Neyman-Pearson criterion with correlatedobservations from PUs has been proposed This schemebased on a discrete Gauss-Seidel iterative algorithm leads toa low complexity method of finding an optimum solution forLCUrsquos decision rules The performance evaluation shows theefficiency of this algorithm with fixed fusion rules in whichAND rule outperforms the OR fusion rule Furthermorewith lower correlation coefficients a better performance isachieved The experimental measurements and implemen-tation of OLDR algorithm for a distributed heterogeneouscognitive network are a challenging open area for the futurework Meanwhile optimizing the fusion rule simultaneouslywith the local decision rules study of different topologiesof cooperative cognitive networks the performance analysisof multilevel decision rules and shadowing in reportingchannels are among the other suggestions for the futureexploration

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] Federal Communications Commission ldquoSpectrum policy taskforcerdquo Report ET Docket 02-135 2002

[2] O B Akan O B Karli and O Ergul ldquoCognitive radio sensornetworksrdquo IEEE Network vol 23 no 4 pp 34ndash40 2009

[3] J Mitola III and G Q Maguire Jr ldquoCognitive radio makingsoftware radios more personalrdquo IEEE Personal Communica-tions vol 6 no 4 pp 13ndash18 1999

[4] S Haykin ldquoCognitive radio brain-empowered wireless com-municationsrdquo IEEE Journal on Selected Areas in Communica-tions vol 23 no 2 pp 201ndash220 2005

[5] H Arslan and M E Shin ldquoUWB cognitive radiordquo in CognitiveRadio Software Defined Radio and Adaptive Wireless Systemschapter 6 pp 355ndash381 Springer Dordrecht The Netherlands2007

[6] A A El-Saleh M Ismail M A M Ali and A N H AlnuaimyldquoCapacity optimization for local and cooperative spectrumsensing in cognitive radio networksrdquoWorld Academy of ScienceEngineering and Technology vol 4 no 11 pp 679ndash685 2009

[7] H Hosseini N Fisal and S K Syed-Yusof ldquoEnhanced FCMEthresholding for wavelet-based cognitive UWB over fadingchannelsrdquo ETRI Journal vol 33 no 6 pp 961ndash964 2011

[8] I F Akyildiz B F Lo and R Balakrishnan ldquoCooperative spec-trum sensing in cognitive radio networks a surveyrdquo PhysicalCommunication vol 4 no 1 pp 40ndash62 2011

[9] H Du Z XWei YWang andD C Yang ldquoDetection reliabilityand throughput analysis for cooperative spectrum sensing incognitive radio networksrdquo Advanced Materials and EngineeringMaterials vol 457-458 pp 668ndash674 2012

[10] Q-T Vien G B Stewart H Tianfield and H X NguyenldquoEfficient cooperative spectrum sensing for three-hop cognitivewireless relay networksrdquo IET Communications vol 7 no 2 pp119ndash127 2013

[11] X Liu M Jia and X Tan ldquoThreshold optimization of coop-erative spectrum sensing in cognitive radio networksrdquo RadioScience vol 48 no 1 pp 23ndash32 2013

[12] H Chen S Ta and B Sun ldquoCooperative game approach topower allocation for target tracking in distributedMIMO radarsensor networksrdquo IEEE Sensors Journal vol 15 no 10 pp 5423ndash5432 2015

[13] R M Vaghefi and R M Buehrer ldquoCooperative joint synchro-nization and localization in wireless sensor networksrdquo IEEETransactions on Signal Processing vol 63 no 14 pp 3615ndash36272015

[14] S Jaewoo and R Srikant ldquoImproving channel utilization viacooperative spectrum sensing with opportunistic feedback incognitive radio networksrdquo IEEECommunications Letters vol 19no 6 pp 1065ndash1068 2015

[15] M Najimi A Ebrahimzadeh S M H Andargoli and AFallahi ldquoEnergy-efficient sensor selection for cooperative spec-trum sensing in the lack or partial informationrdquo IEEE SensorsJournal vol 15 no 7 pp 3807ndash3818 2015

[16] C G Tsinos and K Berberidis ldquoDecentralized adaptiveeigenvalue-based spectrum sensing for multiantenna cognitiveradio systemsrdquo IEEE Transactions onWireless Communicationsvol 14 no 3 pp 1703ndash1715 2015

[17] G Loganathan G Padmavathi and S Shanmugavel ldquoAn effi-cient adaptive fusion scheme for cooperative spectrum sensingin cognitive radios over fading channelsrdquo in Proceedings ofthe International Conference on Information Communicationand Embedded Systems (ICICES rsquo14) pp 1ndash5 Chennai IndiaFeburary 2014

[18] I Y Hoballah and P K Varshney ldquoDistributed Bayesian signaldetectionrdquo IEEETransactions on InformationTheory vol 35 no5 pp 995ndash1000 1989

[19] W A Hashlamoun and P K Varshney ldquoAn approach tothe design of distributed Bayesian detection structuresrdquo IEEETransactions on Systems Man and Cybernetics vol 21 no 5 pp1206ndash1211 1991

[20] W A Hashlamoun and P K Varshney ldquoFurther results ondistributed Bayesian signal detectionrdquo IEEE Transactions onInformation Theory vol 39 no 5 pp 1660ndash1661 1993

[21] R Viswanathan and P K Varshney ldquoDistributed detectionwithmultiple sensors Part Imdashfundamentalsrdquo Proceedings of theIEEE vol 85 no 1 pp 54ndash63 1997

[22] V R Kanchumarthy R Viswanathan and M MadishettyldquoImpact of channel errors on decentralized detection perfor-mance of wireless sensor networks a study of binary modu-lations Rayleigh-fading and nonfading channels and fusion-combinersrdquo IEEE Transactions on Signal Processing vol 56 no5 pp 1761ndash1769 2008

[23] S M Mishra A Sahai and R W Brodersen ldquoCooperativesensing among cognitive radiosrdquo in Proceedings of the IEEEInternational Conference on Communications (ICC rsquo06) pp1658ndash1663 Istanbul Turkey July 2006

[24] A W Al-Khafaji and J R Tooley Numerical Methods inEngineering Practice Holt Rinehart and Winston New YorkNY USA 1986

[25] X Li J Cao Q Ji and Y Hei ldquoEnergy efficient techniques withsensing time optimization in cognitive radio networksrdquo in Pro-ceedings of the IEEE Wireless Communications and NetworkingConference (WCNC rsquo13) pp 25ndash28 Shanghai China April 2013

[26] Y Zhu R S Blum Z-Q Luo and K M Wong ldquoUnex-pected properties and optimum-distributed sensor detectors fordependent observation casesrdquo IEEE Transactions on AutomaticControl vol 45 no 1 pp 62ndash72 2000

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Navigation and Observation

International Journal of

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DistributedSensor Networks

International Journal of

2 International Journal of Distributed Sensor Networks

Cooperative sensing can be used to acquire informationof an intelligent wireless network with various applicationsincluding radar and sensor networks [12 13] The designof cooperative sensing can increase the reliability flexibilityspeed and coverage area of the sensing network In a cogni-tive radio with large number of sensing nodes cooperativespectrum sensing can increase the detection probabilityof primary users and the channel utilization Cooperativespectrum sensing can enhance the sensing performance byexploiting the spatial diversity in the observations of spatiallylocated secondary users which transmit their sensing infor-mation to a fusion center for final decision It has been shownthat increasing the number of cooperative users can decreasethe required detector sensitivity and sensing time Moreovera cooperative approach needs lower communication band-width and is more robust to channel fading [14ndash16]

The drawback of the feedback overhead of spectrumsensing is overcome in [14] by using a fixed number ofcommon feedback channels so that each node compares thesensing result with a threshold and selects the appropriatedata to be sent to the fusion center In [15] a sensor selectionstrategy is proposed to minimize the energy consumptionfor cooperative spectrum sensing under satisfactory pri-mary user detection performance A decentralized spectrumsensing approach is proposed in [16] to reduce the overalloverhead and power consumption of the network by elim-inating the need for fusion center node In this schemeeach secondary user communicates only with its adjacentnodes via one-hop transmissions within several rounds toreach global convergence The performance of cooperativespectrum sensing over Rayleigh fading channel is improvedin [17] using an adaptive linear combiner with weights tosecondary user decisions

In this paper a cooperative spectrum sensing is deployedfor cognitive heterogeneous network with a parallel approachinstead of centralized topology that needs wideband chan-nels With correlated local sensing observations a numericalalgorithm is proposed to optimize the local decisions oflocal cognitive users (LCUs) and send the information to acommon cognitive user (CCU) as fusion center The designof parallel topology increases the reliability flexibility speedand coverage area of the sensing network Based on Bayesianoptimality criteria with independent observations the opti-mized rule for decision making of each LCU is likelihoodratio test (LRT) [18ndash20] Since the prior probabilities ofhypotheses and accurate illustration of cost coefficients arenot available in real systems common Bayesian method formaximizing LRT is not practicalThereforeNeyman-Pearsoncriterion is adopted for optimum local decision rule (OLDR)so that the probability of false alarm is limited to a desiredvalue while the probability of missed detection is minimized[21]

The rest of this paper is organized as follows Section 2describes cooperative sensing schemes and Section 3 illus-trates the systemmodelThe proposed iterative algorithm fordecision making at LCUs is described in Section 4Then thismethod is simulated and the results are analyzed in Section 5The paper is concluded in Section 6 and the open issues forfuture researches are addressed

2 Cooperative Sensing Schemes

Various cooperative sensing schemes by LCUs depending onthe decision making methods of the fusion center can beused to carry out PU detection In a centralized networkapproach local sensors send the raw sensing information to afusion center which decides on the presence or absence of thePUHowever the transmission of these unprocessed observa-tions does not efficiently utilize the bandwidth Cooperativesensing methods perform some preliminary data processingat each sensor to condense the information [21] The majorcooperative configurations include parallel serial and treetopologies as shown in Figure 1

In a parallel sensing model each LCU can decide inde-pendently based on its sensed information and pass thequantized local decision to a CCU whose role as a fusioncenter is to make a final decision on PU existence accordingto the spatially collected results Even though extensive inves-tigations have been done for cooperative sensing schemes toincrease the sensing accuracy most of the research assumedthat the sensed information is independent and identicallydistributed within the local sensors [22] This assumption ispractically unrealistic as shadowing is highly correlated whenseveral cognitive users are geographically proximate withsimilar shadowing effects Spatially correlated shadowingwhich exponentially depends on the distance can bound theachievable gain of cooperative sensing [23]

For optimal PU detection Bayesian criterion with maxi-mizing LRT is the most common method in signal detectiontheory For a given set of observations119884 = [119910

1 119910

119873] it has

been shown that when the prior information of probabilitiesis known LRT is the optimized detection method in whichthe likelihood ratio is calculated for the received signals andcompared to a threshold 120579 as Λ(119884) = 119875(119884 | 119867

1)119875(119884 |

1198670) lt 120579 where 120579 is a function of prior probabilities of 119901

0

and 1199011and the cost function 119888

119894119895of 119867119894decision while 119867

119895has

been true so we have 120579 = (11988810

minus 11988800

)1199010(11988801

minus 11988811

)1199011 In

many cases it is difficult to know these cost coefficients andprior probabilities Instead Neyman-Pearson cost function 119865

is replaced under a condition that false alarmprobability119875119891is

less than a certain value 120572 as119865 = 120582(119875119891

minus120572)+119875119898 where 120582 is the

Lagrange multiplier 119875119891is the probability of false alarm and

119875119898is the probability of detection respectively To provide the

final relations for119875119889and119875119891 note that119875

119889= 1minusint

Ω119875(119884 | 119867

1)119889119884

and 119875119891

= 1 minus intΩ

119875(119884 | 1198670)119889119884 where Ω is decision region

of 1198670determined due to the type of local decision rules and

fusion rulesIn the case of Bayesian criterion for centralized network

as shown in Figure 1(a) there are 119873 sensors that send theirobservations directly to one fusion center before processingand the final decision 119880

119891is made based on a fusion rule as

119866(119884) while

119880119891

=

0 1198670decision if 119866 (119884) le 0

1 1198670decision if 119866 (119884) gt 0

(1)

The region of final decision based on 1198670is ΩCN = 119884

119866(119884) le 0 The fusion rule 119866(119884) is defined while minimizing

International Journal of Distributed Sensor Networks 3

Observations

Final decision

FC

middot middot middot

(a) Centralized topology

Observations

Final decision

FC

middot middot middotS1 S2SN

(b) Parallel topology

Observations

Final decisionmiddot middot middot SNS1 S2

(c) Serial topology

Observations

Obs

erva

tions

Final decision

S2 S3 S4

S1

S0

(d) Tree topology

Figure 1 Major topologies of cooperative sensing networks

the cost function of 119865 = 119888 + intΩCN

119891(119884)119889119884 where 119888 = (119901011988810

+

119901111988811

) 119891(119884) = 1198861119875(119884 | 119867

1) minus 1198860119875(119884 | 119867

0) with 119886

1= (11988801

minus

11988811

)1199011 and 119886

0= (11988810

minus11988800

)1199010Therefore the optimumdecision

region of centralized network is ΩCN = 119910119894

Λ(119884) lt 120579CN 119894 =

1 119873 where Λ(119884) = 119875(119884 | 1198671)119875(119884 | 119867

0) 120579CN is the

threshold of decision making for centralized network and 119873

is the number of sensorsIn parallel topology with distributed local observations

as shown in Figure 1(b) Bayesian criterion leads to LRT forlocal decision rule For a network with 119873 receivers and ORfusion rule it can be written that ΩLRTOR = 119910

119894 Λ(119910

119894) le

120579119894 119894 = 1 119873 where 120579

119894is the threshold for the 119894th receiver

Meanwhile for AND fusion rule it is given that ΩLRTAND =

119878 minus 119910119894

Λ(119910119894) gt 120579

119894 119894 = 1 119873 where 119878 is the whole

decision region Based on Neyman-Pearson criterion thevalues of thresholds 120579

119894can be achieved byminimizing the cost

function of 119865 which in the case of OR fusion rule is

119865LRTOR = 120574 + intΩLRTOR

119891 (119884) 119889119884 (2)

and for AND fusion rule is

119865LRTAND = 120574 + intΩLRTAND

119891 (119884) 119889119884 (3)

where 120574 = 120582(1 minus 120572) 119891(119884) = 119875(119884 | 1198671) minus 120582119875(119884 | 119867

0)

The region of decision making for parallel sensingapproach under cognitive radio channels is discussed in thenext section The local decision rules of local cognitive usersand fusion rule are formulated to design an optimal algorithmwith Neyman-Pearson criterion

3 System Model

In this work a cellular network scenario so called as hetero-geneous network is considered for densely populated areassuch that macrocells are mixed with low power cells Thesmall cells of heterogeneous networks can increase the signalcoverage for the areas that are not accessible by macrobasestations to optimize the reliability and data rate However in

4 International Journal of Distributed Sensor Networks

Primarynetwork

PU

PU

Tx

Rx

Heterogeneous network

Macro-eNB

H-UE

H-UEH-UE

H-eNB(CCU)

M-UE

(LCU1)

(LCU3)

(LCU2)

Figure 2 A heterogeneous network overlapping with primarynetwork

CCU (fusion center)

PU

Sensing channels

Reporting channels

LCU1 LCU2LCUN

middot middot middot

Figure 3 Parallel cooperative spectrum sensing

this network the coverage areas of small cells and primarysystems can be overlapped This mutual interference occurswhen they are using the same time-frequency resources whilespatially located in a certain distance apart from each otheras shown in Figure 2 The frequency reusing of adjacentmacrocell user equipment (M-UE) or other primary systemsby small cells can create interferences to heterogeneoususer equipment (H-UE) Hence H-UE which operates assecondary users needs to transmit under a certain powerlevel which is acceptable by the licensed users PUs and atthe same time mitigates the interference from the primarysystem

The decision making on the presence or absence of PUsignals is a critical part of spectrum sensing procedure atcognitive H-UE In practice each cognitive piece of H-UEplays a role same as distributed LCUs that is equipped withspectrum sensing by energy detection to locally measurethe PU signal transmission power and frequencies Thelocal decisions are the output of certain local rules at thesedistributed pieces of H-UEs that will be sent to H-eNB withthe capability of a CCU to process the received informationand produce the final decision based on the embedded fusionrule Then in the presence of PU signals pieces of H-UEadapt their configurations to avoid mutual interferences withprimary network Since the channel impairments affect theinput observations of each energy detector at H-UE theassumption of independency is not correct any more anda cooperative decision making is required as the solution

Cognitive features enable the secondary users to analyzeinterference using the spectrum sensing mechanism that ismainly performed in LCUs whereas the decision is made forthe cooperative network Let us consider 119873 distributed LCUsas shown in Figure 3 In this figure the 119894th LCU is shownas LCU

119894that receives the observation signals 119910

119894 from the

PU through the sensing channels Each LCU119894sends its local

binary decision 119906119894 to the fusion center the CCU tomake the

final decision using the fusion ruleThemetrics of probabilityof detection 119875

119889119894 and probability of false alarm 119875

119891119894 for

local decision at the 119894th LCU119894are derived to be employed

for the performance evaluation Assuming that during thesensing time CUs do not broadcast and there is no mutualinterference between them the vector of the received signalthrough the sensing channels is defined as

119884 = 119867 sdot 119878119901

+ 119881 (4)

where 119878119901denotes PUrsquos transmitted signal 119867 = [ℎ

1

ℎ119894 ℎ

119873] states the sensing channel gain vector and 119884 =

[1199101 119910

119894 119910

119873] shows the observation vector in which

119910119894denotes the received signal at LCU

119894 The vector of addi-

tive white Gaussian noise (AWGN) at LCU receivers is119881 = [V

1 V

119894 V

119873] The observations of PUrsquos signal

are received through the sensing channels at LCU119894 In this

scenario the correlated channels lead to correlated sensingobservations at the LCU receivers that analyze the data asa binary hypothesis testing form 119867

0and 119867

1are the binary

hypotheses which define the absence and presence of PUrespectively Then the general form of the received signal atthe spectrum sensing part of LCU is

1198671

1199101

= ℎ1

sdot 119878119901

+ V1 119910

119873

= ℎ119873

sdot 119878119901

+ V119873

1198670

1199101

= V1 119910

119873= V119873

(5)

Given that 119910119894denotes the available observation of PU

signal at LCU119894receiver the local decision rule 119892

119894(119910119894) is

employed by LCU119894to make a binary decision 119906

119894about the

existence of PU signal Based on a set of local decision rulesas 119866(119884) = [119892

1(1199101) 119892

119894(119910119894) 119892

119873(119910119873

)] the fusion centerCCU receives the local decision as

119906119894

= 0 119892

119894(119910119894) le 0

1 119892119894(119910119894) gt 0

(6)

TheCCU follows a fusion rule as119876(119880)which is a Booleanfunction and whenever 119876(119880) = 0 the final decision is takenas 1198670 otherwise it is 119867

1 The local decision rule maps the

observation set 119884 = 1199101 119910

119873to a local decision set 119880 =

1199061 119906

119894 119906

119873 where 119906

119894isin 0 1 119894 = 1 119873 The

combination of local binary decisions 119906119894results in 2

119873 statesThus the 2

2119873

is the total number of states for final decision119906119891

= 119876(119880) and

119876 (119880) = 119876119899 119906119894

= mod (119899 minus 1

2(119894minus1) 2) 1

le 119899 le 2119873

(7)

International Journal of Distributed Sensor Networks 5

where mod(119860 2) is the division remaining of 1198602 and 119906119894

=

mod((119899 minus 1)2(119894minus1)

2) is the 119894th bit of 119899 Hence 119876(119880) =

119876119899 119899 = sum

119873

119894=11199061198942119894minus1

+ 1 Consider two different sets as1198780

= 119899 119876119899

= 0 and 1198781

= 119899 119876119899

= 1 such that1198780

cup 1198781

= 1 2 2119873

then ΩOLDR = 119910119894

119876119899

= 0 119899 isin 1198780

where ΩOLDR defines the region of optimal decision makingfor parallel cooperative cognitive network which leads to thefinal decision of 119867

0 With a given set of 119878

0 the fusion rule

119876(119880) is deterministic and constant and for every 119899 belongingto 1198780 119899th composition will result in a decision on 119867

0 For

a fixed fusion rule the region of final decision is ΩOLDR =

⋃119899isin1198780

Ω119899 where Ω

119899denotes the region of 119899th combination of

119876 as

Ω119899

= 119884 119906119894

= mod (119899 minus 1

2(119894minus1) 2) 119876

= 119876119899

(8)

In the next section the optimization problem for parallellocal decision rules is reduced to solve a set of fixed pointintegral equations that minimizes the Neyman-Pearson costfunction The decision rules are digitized for simplicity andGauss-Seidel algorithm [24] and Golden Section search [25]are applied to find the final solutions

4 OLDR Algorithm with Gauss-Seidel Process

Each distributedH-UELCU119894performs the spectrum sensing

by energy detection to detect the initial PU signal obser-vation 119910

119894 This distributed information from all LCUs is

used by the OLDR algorithm to cooperatively optimize localdecision rules 119892

119894 according to the fix central fusion rule at

H-eNBCCU ANDOR and achieve the final minimized 119875119891

with Gauss-Seidel process Based on the Neyman-Pearsoncriterion the optimum local decision rule is defined tominimize the corresponding cost function 119865

119865 (119866 119876) = 120582 (1 minus 120572) + intΩOLDR

119891 (119884) 119889119884 (9)

where 119876 is the Boolean fusion function 119884 denotes localobservations and 119891(119884) = 119875(119884 | 119867

1) minus 120582119875(119884 | 119867

0) Given

that 120574 = 120582(1 minus 120572) according to the above relations it can beconcluded that

119865 (119866 119876) = 120574 + int119884isinΩOLDR

119891 (119884) 119889119884 = 120574

+ (int119892119894(119910119894)le0

(int⋃119899isin11987801119894

Ω119899119894

minus int⋃119899isin11987802119894

Ω119899119894

) + int119910119894

int⋃119899isin11987802119894

Ω119899119894

)

sdot 119891 (119884) 119889119884

(10)

where Ω119899119894

is Ω119899excluding 119910

119894 11987801119894

11987802119894

are two subsetsof 1198780such that 119878

01119894cup 11987802119894

= 1198780 11987801119894

is a subset of 119899

belonging to 1198780with 119906

119894= 0 119878

01119894= 119899 119876

119899=

0 119906119894

= 0 and similarly 11987802119894

is a subset of 119899 belongingto 1198780with 119906

119894= 1 119878

02119894= 119899 119876

119899= 0 119906

119894= 1

The set of optimum local decision rules that minimizes the119865 function in (10) can be defined as 119866 = (119892

1 119892

119873)

[26]

119892119894(119910119894) = (int

⋃119899isin11987801119894

Ω119899119894

minus int⋃119899isin11987802119894

Ω119899119894

)

sdot119891 (119884) 119889119884

119889119910119894

(11)

where Ω119899119894

= (1199101 119910

119894minus1 119910119894+1

119910119873

) 120601(119892119894 119906119894) le 0

and 120601(119892119894 119906119894) = (12 minus 119906

119894)119892119894 Consequently each set of

optimum local decisions is derived by solving several fixedpoint integral equations as

Γ119876

(119866) =

[[[[[[[[[[[[[[[[[[[[

[

(intcup119899isin119878011

Ω1198991

minus intcup119899isin119878021

Ω1198991

)119891 (119884) 119889119884

1198891199101

(intcup119899isin11987801119894

Ω119899119894

minus intcup119899isin11987802119894

Ω119899119894

)119891 (119884) 119889119884

119889119910119894

(intcup119899isin11987801119873

Ω119899119873

minus intcup119899isin11987802119873

Ω119899119873

)119891 (119884) 119889119884

119889119910119873

]]]]]]]]]]]]]]]]]]]]

]

(12)

Therefore the problem of optimum cooperative sensingis essentially reduced to optimizing a set of 119866 = (119892

1 119892

119873)

that satisfies the integral equations An iterative algorithmbased on Gauss-Seidel process can approximate the solutionof the above equations [26] This method is used for solvinga matrix of linear equations when the number of systemparameters is too high to find a solution by common PLUtechniques The initial requirement is that the diagonalelements of the matrix of equations must be nonzero andconvergence is provided when this matrix is either diagonallydominant or symmetric and positive definite [24] Let usconsider the local decision rule in 119895th iteration stage of thealgorithm as 119866

(119895) and the initial set as 119866(0) Gauss-Seidel

process for optimum local decision rules can be definedas

119866(119895+1)

= Γ119876

(119866(119895)

) forall119895 = 0 1 2 (13)

6 International Journal of Distributed Sensor Networks

where

119892119894

(119895+1)(119910119894)

= (int⋃119899isin11987801119894

Ω119899119894

minus int⋃119899isin11987802119894

Ω119899119894

)

sdot119891 (119884) 119889119884

119889119910119894

(14)

To reduce the computation complexity the discrete vari-ables 119905

119894are extracted from 119910

119894as 119879 = 119905

1 119905

119894 119905

119873 and

(14) can be described as

119892119895+1

119894(119905119894)

= ( sum

⋃119899isin11987801119894

Ω119899119894

minus sum

⋃119899isin11987802119894

Ω119899119894

)119891 (119879) Δ119879

Δ119905119894

(15)

Hence the discrete local decision rules are defined as

119885119894(119905119894) = 119868 (119892

119894(119905119894))

119868 (119909) = 0 119909 le 0

1 119909 gt 0

(16)

Accordingly the cost function 119865 is approximated as

119865 (119885 119876) = 120574

+ sum

119899isin1198780

( sum

11990511198851=1199061

sum

119905119894119885119894=119906119894

sum

119905119873119885119873=119906119873

119891 (119879) Δ119879)

(17)

Therefore

119892119895+1

119894(119905119894) = ( sum

119899isin11987801119894

minus sum

119899isin11987802119894

)

sum

1199051

sdot sdot sdot sum

119905119894minus1

sum

119905119894+1

sdot sdot sdot sum

119905119873

119894minus1

prod

119871=1

(1 minus

1003816100381610038161003816100381610038161003816mod (

119899 minus 1

2(119871minus1) 2) minus 119885

119871

(119895+1)(119905119871)

1003816100381610038161003816100381610038161003816)

119873

prod

119871=119894+1

(1 minus

1003816100381610038161003816100381610038161003816mod (

119899 minus 1

2(119871minus1) 2) minus 119885

119871

(119895)(119905119871)

1003816100381610038161003816100381610038161003816)

119891 (119879) Δ119879

Δ119910119894

(18)

For the simplicity of computations discrete local decisionrules 119885

119894(119905119894) are substituted instead of 119892

119894(119905119894) as both of them

have the same region of decision making Note that the iter-ative process converges when absolute relative approximateerror |(119885

119894

(119895+1)(119905119894) minus 119885

119894

(119895)(119905119894))119885119894

(119895+1)(119905119894)| times 100 ≪ 120576 where

120576 gt 0 is prespecified tolerance parameter For each positivevalue of Δ119905

119894and initial selection of 119885

0

119894 the algorithm is

converged after a certain number of iterations to a set of119885119895

119894that satisfies the convergence condition Figure 4 presents

the flowchart of the developed optimization algorithm basedon the golden section search method for Neyman-Pearsoncriterion Golden section ratio of golden section search isapplied with 120593 = 0618 or symmetrically (1 minus 0618) = 0382

to condense the width of the range in each step [25]

5 Simulation and Discussion

For the performance evaluation of the proposed OLDRalgorithm and compared to the other methods the receiveroperating characteristic (ROC) curve is depicted as a graph of119875119889versus 119875

119891 To depict ROC curves for the OLDR algorithm

in each iteration the values of 119875119889and 119875

119891are provided based

on the OLDR rules As a benchmark the simulation resultsare compared to centralized network and parallel networkwith LRT local decision rule

When normal pdf is assumed for the sensed signalsthe conditional pdf rsquos under both hypotheses 119867

0and

1198671are defined as 119901(119910

1 1199102 119910

119873| 1198670) = 119873(120583

0 1198620)

and 119901(1199101 1199102 119910

119873| 1198671) = 119873(120583

1 1198621) where 119862

0

and 1198621are the covariance matrices under 119867

0and 119867

1

respectively With correlation coefficient minus1 le 120588 le 1the covariance matrix is written as 119862(119910

1 1199102 119910

119873) =

[1205902

1 12058812

12059011205902 120588

11198731205901120590119873

1205881198731

120590119873

1205901 1205881198732

120590119873

1205902 120590

2

119873]

The performance of OLDR algorithm for cooperativespectrum sensing is shown in this section Centralizednetwork (CN) with a fusion center is considered as theoptimum benchmark for the evaluation of the proposedmethod Numerical results are analyzed for both OLDRand LRT local decision rules with ANDOR fusion rulesThen the effect of various correlation coefficients (120588)on ROC curves is investigated with correlated sensedsignals

In the first case a cooperative spectrum sensing with twolocal cognitive users is considered Given that the receivedobservations from PU are random Gaussian signal 119867 sdot 119878

119901

with mean 120583119867sdot119878119901

= 2 and variance 1205902

119867sdot119878119901

= 1 added to 1198991

and 1198992as independent zero mean Gaussian noises such that

1205902

1198991

= 2 and 1205902

1198992

= 1 then the conditional pdf rsquos under bothhypotheses 119867

0and 119867

1 are 119901(119910

1 1199102

| 1198670) = 119873(120583

0 1198620) and

119901(1199101 1199102

| 1198671) = 119873(120583

1 1198621) Therefore 120583

0= [0 0] 119862

0= [2 0

0 1] 1205831

= [2 2] 1198621

= [3 1 1 2]Figure 5 compares the performance of OLDR and LRT

with centralized network As illustrated in this figure OLDRwithAND fusion rule outperforms the other techniques since

International Journal of Distributed Sensor Networks 7

Start

Yes NoYesNo

Yes

No

End

Initializing of 120582(j) and Δ120582 j = 0

P(j)

flt 120572 P

(j)

fgt 120572

P(j)

flt 120572 P

(j)

fgt 120572

120582(j+1) = 120582(j) minus Δ120582j = j + 1 j = j + 1

j = j + 1

120582(j+1) = 120582(j) + Δ120582

120582(j+1) = 120582(j) + Δ120582

Δ120582 =

120593 times Δ120582 if P(j)

fgt 120572

minus120593 times Δ120582 otherwise

Pf(120582(j)) minus 120572 le 120576

P(j)

f(120582(j)) = 1 minusint

ΩOLDR(g1g119873)P(y1 yN |H0)dy1middot middot middot dyN

Figure 4 The proposed optimization algorithm (OLDR)

it is closer to the CN curve Meanwhile OLDR performsbetter than LRT with the same fusion rules for example at119875119891

= 002 OLDR shows 4 improvement in 119875119889compared to

the LRT with the same fusion rulesIn the second case parallel spectrum sensing with two

local cognitive users are considered with correlated receivedsignals as 120583

0= [0 0] 120583

1= [2 2] 119862

0= 1198621

= [1205902

1 12058812059011205902

12058812059011205902 1205902

2] The results of simulations with 120588 = 01 are

presented in Figure 6 which illustrates that the OLDR withAND fusion rule is more proximate to the CN curve andachieves a better performance than OR fusion rule forinstance at 119875

119891= 002 the improvement is about 4

The performance of the same network for various valuesof correlation coefficient (120588) is shown in Figure 7 Accordingto these results the performance is enhanced by the reductionof the correlation coefficient (120588)

Now a network of three local cognitive users with Gaus-sian signal observations is considered with mean 120583

119867sdot119878119901

= 2

and variance 1205902

119867sdot119878119901

= 1 added to zero mean independentnoises with 120590

2

1198991

= 3 12059021198992

= 2 and 1205902

1198993

= 1Thus the covariance

0 002 004 006 008 01 012 014 016 018 0203

04

05

06

07

08

09

1

CN-2 LCUOLDR-AND 2 LCUOLDR-OR 2 LCU

LRT-AND 2 LCULRT-OR 2 CU

Pf

Pd

Figure 5 ROC comparison forGaussian received signal in indepen-dent Gaussian noise with two LCUs

03

04

05

06

07

08

09

1

CN 2 LCUOLDR-AND 2 LCUOLDR-OR 2 LCU

LRT-AND 2 LCULRT-OR 2 LCU

0 002 004 006 008 01 012 014 016 018 02Pf

Pd

Figure 6 ROC comparison for deterministic received signal incorrelated Gaussian noises with two LCUs

matrices under 1198670and 119867

1are described as 119862

0= [3 0 0

0 2 0 0 0 1] and 1198621

= [4 1 1 1 3 1 1 1 2]Figures 8 and 9 show that increasing the number of local

cognitive users enhances the performance of the network ForGaussian received signals with independentGaussian noise at119875119891

= 002 the 119875119889is enhanced about 3 for OLDR with three

LCUs comparing to OLDR with two LCUsFrom these results it is concluded that for a fixed fusion

rule OLDR algorithm shows a superior performance oflocal decision rules to detect primary users compared toLRT method Apparently the probability of primary userdetection is increased with the number of cooperative localcognitive users equipped with spectrum sensing When thesensing channels are correlated results show performancedegradation in higher correlation coefficients

8 International Journal of Distributed Sensor Networks

03

04

05

06

07

08

09

1

0 002 004 006 008 01 012 014 016 018 02Pf

Pd

OLDR-AND 120588 = minus03

OLDR-AND 120588 = minus01

OLDR-AND 120588 = 0

OLDR-AND 120588 = 01

OLDR-AND 120588 = 03

Figure 7 ROC comparison for deterministic received signal incorrelated Gaussian noise with different correlation coefficients (120588)

CN 3 LCUOLDR-AND 3 LCU

OLDR-AND 2 LCUCN 2 LCU

0 002 004 006 008 01 012 014 016 018 02Pf

03

04

05

06

07

08

09

1

Pd

Figure 8 ROC comparison for Gaussian received signal in inde-pendent Gaussian noises with different numbers of LCUs

OLDR method is a low complexity solution for theproblem of (11) which is reduced to optimizing a set of localdecision rules 119866 = (119892

1 119892

119873) that satisfies the integral

equations (12) In addition the computation complexity of(14) has been reduced by considering discrete variables forthe observations 119910

119894 as well as local decision rules 119892

119894 to 119905119894

and 119885119894 respectively For the centralized network there is

no local decision rule and the local decision rule of LRTmethod is defined as Λ(119910

119894) le 120579

119894 where 120579

119894is the threshold

for the 119894th receiver In each iteration of the algorithm withLRTΛ(119884

119894) is calculated for all observations119910

119894 and compared

with threshold 120579119894 For the initial threshold within a range

of 119872 levels the time complexity of each local decision rulecan be written as 119874(119872) According to (18) the local decision

CN 3 LCUOLDR-AND 3 LCU

CN 2 LCUOLDR-AND 2 LCU

03

04

05

06

07

08

09

1

Pd

004 018 02008 01 012 014 016002 0060Pf

Figure 9 ROC comparison for deterministic signal in correlatedGaussian noises with different numbers of LCUs

Number of LCUs1 2 3 4 5 6 7 8

CNOLDRLRT

0

10

20

30

40

50

60

70Ti

me c

ompl

exity

Figure 10 Time complexity comparison of local decision rules

rule of OLDR algorithm 119892119895+1

119894 has to be updated at each

iteration with the time complexity of 119874(1198732) compared to the

other local decision rulesThe time complexity comparison oflocal decision rules for 119872 = 20 is shown in Figure 10 whichdescribes the increase of the calculations number propor-tional to the number of the receivers 119873 However since CNmethod consumes too large bandwidths for sending the datato the fusion center and LRT method assumes independentobservations they cannot be considered as optimum solutionfor cooperative cognitive users with correlated sensed signals

6 Conclusion

In this paper the cooperative spectrum sensing for cognitiveheterogeneous network has been designed with a parallelconfiguration An optimum algorithm for local decision

International Journal of Distributed Sensor Networks 9

rule based on Neyman-Pearson criterion with correlatedobservations from PUs has been proposed This schemebased on a discrete Gauss-Seidel iterative algorithm leads toa low complexity method of finding an optimum solution forLCUrsquos decision rules The performance evaluation shows theefficiency of this algorithm with fixed fusion rules in whichAND rule outperforms the OR fusion rule Furthermorewith lower correlation coefficients a better performance isachieved The experimental measurements and implemen-tation of OLDR algorithm for a distributed heterogeneouscognitive network are a challenging open area for the futurework Meanwhile optimizing the fusion rule simultaneouslywith the local decision rules study of different topologiesof cooperative cognitive networks the performance analysisof multilevel decision rules and shadowing in reportingchannels are among the other suggestions for the futureexploration

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] Federal Communications Commission ldquoSpectrum policy taskforcerdquo Report ET Docket 02-135 2002

[2] O B Akan O B Karli and O Ergul ldquoCognitive radio sensornetworksrdquo IEEE Network vol 23 no 4 pp 34ndash40 2009

[3] J Mitola III and G Q Maguire Jr ldquoCognitive radio makingsoftware radios more personalrdquo IEEE Personal Communica-tions vol 6 no 4 pp 13ndash18 1999

[4] S Haykin ldquoCognitive radio brain-empowered wireless com-municationsrdquo IEEE Journal on Selected Areas in Communica-tions vol 23 no 2 pp 201ndash220 2005

[5] H Arslan and M E Shin ldquoUWB cognitive radiordquo in CognitiveRadio Software Defined Radio and Adaptive Wireless Systemschapter 6 pp 355ndash381 Springer Dordrecht The Netherlands2007

[6] A A El-Saleh M Ismail M A M Ali and A N H AlnuaimyldquoCapacity optimization for local and cooperative spectrumsensing in cognitive radio networksrdquoWorld Academy of ScienceEngineering and Technology vol 4 no 11 pp 679ndash685 2009

[7] H Hosseini N Fisal and S K Syed-Yusof ldquoEnhanced FCMEthresholding for wavelet-based cognitive UWB over fadingchannelsrdquo ETRI Journal vol 33 no 6 pp 961ndash964 2011

[8] I F Akyildiz B F Lo and R Balakrishnan ldquoCooperative spec-trum sensing in cognitive radio networks a surveyrdquo PhysicalCommunication vol 4 no 1 pp 40ndash62 2011

[9] H Du Z XWei YWang andD C Yang ldquoDetection reliabilityand throughput analysis for cooperative spectrum sensing incognitive radio networksrdquo Advanced Materials and EngineeringMaterials vol 457-458 pp 668ndash674 2012

[10] Q-T Vien G B Stewart H Tianfield and H X NguyenldquoEfficient cooperative spectrum sensing for three-hop cognitivewireless relay networksrdquo IET Communications vol 7 no 2 pp119ndash127 2013

[11] X Liu M Jia and X Tan ldquoThreshold optimization of coop-erative spectrum sensing in cognitive radio networksrdquo RadioScience vol 48 no 1 pp 23ndash32 2013

[12] H Chen S Ta and B Sun ldquoCooperative game approach topower allocation for target tracking in distributedMIMO radarsensor networksrdquo IEEE Sensors Journal vol 15 no 10 pp 5423ndash5432 2015

[13] R M Vaghefi and R M Buehrer ldquoCooperative joint synchro-nization and localization in wireless sensor networksrdquo IEEETransactions on Signal Processing vol 63 no 14 pp 3615ndash36272015

[14] S Jaewoo and R Srikant ldquoImproving channel utilization viacooperative spectrum sensing with opportunistic feedback incognitive radio networksrdquo IEEECommunications Letters vol 19no 6 pp 1065ndash1068 2015

[15] M Najimi A Ebrahimzadeh S M H Andargoli and AFallahi ldquoEnergy-efficient sensor selection for cooperative spec-trum sensing in the lack or partial informationrdquo IEEE SensorsJournal vol 15 no 7 pp 3807ndash3818 2015

[16] C G Tsinos and K Berberidis ldquoDecentralized adaptiveeigenvalue-based spectrum sensing for multiantenna cognitiveradio systemsrdquo IEEE Transactions onWireless Communicationsvol 14 no 3 pp 1703ndash1715 2015

[17] G Loganathan G Padmavathi and S Shanmugavel ldquoAn effi-cient adaptive fusion scheme for cooperative spectrum sensingin cognitive radios over fading channelsrdquo in Proceedings ofthe International Conference on Information Communicationand Embedded Systems (ICICES rsquo14) pp 1ndash5 Chennai IndiaFeburary 2014

[18] I Y Hoballah and P K Varshney ldquoDistributed Bayesian signaldetectionrdquo IEEETransactions on InformationTheory vol 35 no5 pp 995ndash1000 1989

[19] W A Hashlamoun and P K Varshney ldquoAn approach tothe design of distributed Bayesian detection structuresrdquo IEEETransactions on Systems Man and Cybernetics vol 21 no 5 pp1206ndash1211 1991

[20] W A Hashlamoun and P K Varshney ldquoFurther results ondistributed Bayesian signal detectionrdquo IEEE Transactions onInformation Theory vol 39 no 5 pp 1660ndash1661 1993

[21] R Viswanathan and P K Varshney ldquoDistributed detectionwithmultiple sensors Part Imdashfundamentalsrdquo Proceedings of theIEEE vol 85 no 1 pp 54ndash63 1997

[22] V R Kanchumarthy R Viswanathan and M MadishettyldquoImpact of channel errors on decentralized detection perfor-mance of wireless sensor networks a study of binary modu-lations Rayleigh-fading and nonfading channels and fusion-combinersrdquo IEEE Transactions on Signal Processing vol 56 no5 pp 1761ndash1769 2008

[23] S M Mishra A Sahai and R W Brodersen ldquoCooperativesensing among cognitive radiosrdquo in Proceedings of the IEEEInternational Conference on Communications (ICC rsquo06) pp1658ndash1663 Istanbul Turkey July 2006

[24] A W Al-Khafaji and J R Tooley Numerical Methods inEngineering Practice Holt Rinehart and Winston New YorkNY USA 1986

[25] X Li J Cao Q Ji and Y Hei ldquoEnergy efficient techniques withsensing time optimization in cognitive radio networksrdquo in Pro-ceedings of the IEEE Wireless Communications and NetworkingConference (WCNC rsquo13) pp 25ndash28 Shanghai China April 2013

[26] Y Zhu R S Blum Z-Q Luo and K M Wong ldquoUnex-pected properties and optimum-distributed sensor detectors fordependent observation casesrdquo IEEE Transactions on AutomaticControl vol 45 no 1 pp 62ndash72 2000

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Submit your manuscripts athttpwwwhindawicom

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Electrical and Computer Engineering

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Advances inOptoElectronics

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Volume 2014

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Chemical EngineeringInternational Journal of Antennas and

Propagation

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DistributedSensor Networks

International Journal of

International Journal of Distributed Sensor Networks 3

Observations

Final decision

FC

middot middot middot

(a) Centralized topology

Observations

Final decision

FC

middot middot middotS1 S2SN

(b) Parallel topology

Observations

Final decisionmiddot middot middot SNS1 S2

(c) Serial topology

Observations

Obs

erva

tions

Final decision

S2 S3 S4

S1

S0

(d) Tree topology

Figure 1 Major topologies of cooperative sensing networks

the cost function of 119865 = 119888 + intΩCN

119891(119884)119889119884 where 119888 = (119901011988810

+

119901111988811

) 119891(119884) = 1198861119875(119884 | 119867

1) minus 1198860119875(119884 | 119867

0) with 119886

1= (11988801

minus

11988811

)1199011 and 119886

0= (11988810

minus11988800

)1199010Therefore the optimumdecision

region of centralized network is ΩCN = 119910119894

Λ(119884) lt 120579CN 119894 =

1 119873 where Λ(119884) = 119875(119884 | 1198671)119875(119884 | 119867

0) 120579CN is the

threshold of decision making for centralized network and 119873

is the number of sensorsIn parallel topology with distributed local observations

as shown in Figure 1(b) Bayesian criterion leads to LRT forlocal decision rule For a network with 119873 receivers and ORfusion rule it can be written that ΩLRTOR = 119910

119894 Λ(119910

119894) le

120579119894 119894 = 1 119873 where 120579

119894is the threshold for the 119894th receiver

Meanwhile for AND fusion rule it is given that ΩLRTAND =

119878 minus 119910119894

Λ(119910119894) gt 120579

119894 119894 = 1 119873 where 119878 is the whole

decision region Based on Neyman-Pearson criterion thevalues of thresholds 120579

119894can be achieved byminimizing the cost

function of 119865 which in the case of OR fusion rule is

119865LRTOR = 120574 + intΩLRTOR

119891 (119884) 119889119884 (2)

and for AND fusion rule is

119865LRTAND = 120574 + intΩLRTAND

119891 (119884) 119889119884 (3)

where 120574 = 120582(1 minus 120572) 119891(119884) = 119875(119884 | 1198671) minus 120582119875(119884 | 119867

0)

The region of decision making for parallel sensingapproach under cognitive radio channels is discussed in thenext section The local decision rules of local cognitive usersand fusion rule are formulated to design an optimal algorithmwith Neyman-Pearson criterion

3 System Model

In this work a cellular network scenario so called as hetero-geneous network is considered for densely populated areassuch that macrocells are mixed with low power cells Thesmall cells of heterogeneous networks can increase the signalcoverage for the areas that are not accessible by macrobasestations to optimize the reliability and data rate However in

4 International Journal of Distributed Sensor Networks

Primarynetwork

PU

PU

Tx

Rx

Heterogeneous network

Macro-eNB

H-UE

H-UEH-UE

H-eNB(CCU)

M-UE

(LCU1)

(LCU3)

(LCU2)

Figure 2 A heterogeneous network overlapping with primarynetwork

CCU (fusion center)

PU

Sensing channels

Reporting channels

LCU1 LCU2LCUN

middot middot middot

Figure 3 Parallel cooperative spectrum sensing

this network the coverage areas of small cells and primarysystems can be overlapped This mutual interference occurswhen they are using the same time-frequency resources whilespatially located in a certain distance apart from each otheras shown in Figure 2 The frequency reusing of adjacentmacrocell user equipment (M-UE) or other primary systemsby small cells can create interferences to heterogeneoususer equipment (H-UE) Hence H-UE which operates assecondary users needs to transmit under a certain powerlevel which is acceptable by the licensed users PUs and atthe same time mitigates the interference from the primarysystem

The decision making on the presence or absence of PUsignals is a critical part of spectrum sensing procedure atcognitive H-UE In practice each cognitive piece of H-UEplays a role same as distributed LCUs that is equipped withspectrum sensing by energy detection to locally measurethe PU signal transmission power and frequencies Thelocal decisions are the output of certain local rules at thesedistributed pieces of H-UEs that will be sent to H-eNB withthe capability of a CCU to process the received informationand produce the final decision based on the embedded fusionrule Then in the presence of PU signals pieces of H-UEadapt their configurations to avoid mutual interferences withprimary network Since the channel impairments affect theinput observations of each energy detector at H-UE theassumption of independency is not correct any more anda cooperative decision making is required as the solution

Cognitive features enable the secondary users to analyzeinterference using the spectrum sensing mechanism that ismainly performed in LCUs whereas the decision is made forthe cooperative network Let us consider 119873 distributed LCUsas shown in Figure 3 In this figure the 119894th LCU is shownas LCU

119894that receives the observation signals 119910

119894 from the

PU through the sensing channels Each LCU119894sends its local

binary decision 119906119894 to the fusion center the CCU tomake the

final decision using the fusion ruleThemetrics of probabilityof detection 119875

119889119894 and probability of false alarm 119875

119891119894 for

local decision at the 119894th LCU119894are derived to be employed

for the performance evaluation Assuming that during thesensing time CUs do not broadcast and there is no mutualinterference between them the vector of the received signalthrough the sensing channels is defined as

119884 = 119867 sdot 119878119901

+ 119881 (4)

where 119878119901denotes PUrsquos transmitted signal 119867 = [ℎ

1

ℎ119894 ℎ

119873] states the sensing channel gain vector and 119884 =

[1199101 119910

119894 119910

119873] shows the observation vector in which

119910119894denotes the received signal at LCU

119894 The vector of addi-

tive white Gaussian noise (AWGN) at LCU receivers is119881 = [V

1 V

119894 V

119873] The observations of PUrsquos signal

are received through the sensing channels at LCU119894 In this

scenario the correlated channels lead to correlated sensingobservations at the LCU receivers that analyze the data asa binary hypothesis testing form 119867

0and 119867

1are the binary

hypotheses which define the absence and presence of PUrespectively Then the general form of the received signal atthe spectrum sensing part of LCU is

1198671

1199101

= ℎ1

sdot 119878119901

+ V1 119910

119873

= ℎ119873

sdot 119878119901

+ V119873

1198670

1199101

= V1 119910

119873= V119873

(5)

Given that 119910119894denotes the available observation of PU

signal at LCU119894receiver the local decision rule 119892

119894(119910119894) is

employed by LCU119894to make a binary decision 119906

119894about the

existence of PU signal Based on a set of local decision rulesas 119866(119884) = [119892

1(1199101) 119892

119894(119910119894) 119892

119873(119910119873

)] the fusion centerCCU receives the local decision as

119906119894

= 0 119892

119894(119910119894) le 0

1 119892119894(119910119894) gt 0

(6)

TheCCU follows a fusion rule as119876(119880)which is a Booleanfunction and whenever 119876(119880) = 0 the final decision is takenas 1198670 otherwise it is 119867

1 The local decision rule maps the

observation set 119884 = 1199101 119910

119873to a local decision set 119880 =

1199061 119906

119894 119906

119873 where 119906

119894isin 0 1 119894 = 1 119873 The

combination of local binary decisions 119906119894results in 2

119873 statesThus the 2

2119873

is the total number of states for final decision119906119891

= 119876(119880) and

119876 (119880) = 119876119899 119906119894

= mod (119899 minus 1

2(119894minus1) 2) 1

le 119899 le 2119873

(7)

International Journal of Distributed Sensor Networks 5

where mod(119860 2) is the division remaining of 1198602 and 119906119894

=

mod((119899 minus 1)2(119894minus1)

2) is the 119894th bit of 119899 Hence 119876(119880) =

119876119899 119899 = sum

119873

119894=11199061198942119894minus1

+ 1 Consider two different sets as1198780

= 119899 119876119899

= 0 and 1198781

= 119899 119876119899

= 1 such that1198780

cup 1198781

= 1 2 2119873

then ΩOLDR = 119910119894

119876119899

= 0 119899 isin 1198780

where ΩOLDR defines the region of optimal decision makingfor parallel cooperative cognitive network which leads to thefinal decision of 119867

0 With a given set of 119878

0 the fusion rule

119876(119880) is deterministic and constant and for every 119899 belongingto 1198780 119899th composition will result in a decision on 119867

0 For

a fixed fusion rule the region of final decision is ΩOLDR =

⋃119899isin1198780

Ω119899 where Ω

119899denotes the region of 119899th combination of

119876 as

Ω119899

= 119884 119906119894

= mod (119899 minus 1

2(119894minus1) 2) 119876

= 119876119899

(8)

In the next section the optimization problem for parallellocal decision rules is reduced to solve a set of fixed pointintegral equations that minimizes the Neyman-Pearson costfunction The decision rules are digitized for simplicity andGauss-Seidel algorithm [24] and Golden Section search [25]are applied to find the final solutions

4 OLDR Algorithm with Gauss-Seidel Process

Each distributedH-UELCU119894performs the spectrum sensing

by energy detection to detect the initial PU signal obser-vation 119910

119894 This distributed information from all LCUs is

used by the OLDR algorithm to cooperatively optimize localdecision rules 119892

119894 according to the fix central fusion rule at

H-eNBCCU ANDOR and achieve the final minimized 119875119891

with Gauss-Seidel process Based on the Neyman-Pearsoncriterion the optimum local decision rule is defined tominimize the corresponding cost function 119865

119865 (119866 119876) = 120582 (1 minus 120572) + intΩOLDR

119891 (119884) 119889119884 (9)

where 119876 is the Boolean fusion function 119884 denotes localobservations and 119891(119884) = 119875(119884 | 119867

1) minus 120582119875(119884 | 119867

0) Given

that 120574 = 120582(1 minus 120572) according to the above relations it can beconcluded that

119865 (119866 119876) = 120574 + int119884isinΩOLDR

119891 (119884) 119889119884 = 120574

+ (int119892119894(119910119894)le0

(int⋃119899isin11987801119894

Ω119899119894

minus int⋃119899isin11987802119894

Ω119899119894

) + int119910119894

int⋃119899isin11987802119894

Ω119899119894

)

sdot 119891 (119884) 119889119884

(10)

where Ω119899119894

is Ω119899excluding 119910

119894 11987801119894

11987802119894

are two subsetsof 1198780such that 119878

01119894cup 11987802119894

= 1198780 11987801119894

is a subset of 119899

belonging to 1198780with 119906

119894= 0 119878

01119894= 119899 119876

119899=

0 119906119894

= 0 and similarly 11987802119894

is a subset of 119899 belongingto 1198780with 119906

119894= 1 119878

02119894= 119899 119876

119899= 0 119906

119894= 1

The set of optimum local decision rules that minimizes the119865 function in (10) can be defined as 119866 = (119892

1 119892

119873)

[26]

119892119894(119910119894) = (int

⋃119899isin11987801119894

Ω119899119894

minus int⋃119899isin11987802119894

Ω119899119894

)

sdot119891 (119884) 119889119884

119889119910119894

(11)

where Ω119899119894

= (1199101 119910

119894minus1 119910119894+1

119910119873

) 120601(119892119894 119906119894) le 0

and 120601(119892119894 119906119894) = (12 minus 119906

119894)119892119894 Consequently each set of

optimum local decisions is derived by solving several fixedpoint integral equations as

Γ119876

(119866) =

[[[[[[[[[[[[[[[[[[[[

[

(intcup119899isin119878011

Ω1198991

minus intcup119899isin119878021

Ω1198991

)119891 (119884) 119889119884

1198891199101

(intcup119899isin11987801119894

Ω119899119894

minus intcup119899isin11987802119894

Ω119899119894

)119891 (119884) 119889119884

119889119910119894

(intcup119899isin11987801119873

Ω119899119873

minus intcup119899isin11987802119873

Ω119899119873

)119891 (119884) 119889119884

119889119910119873

]]]]]]]]]]]]]]]]]]]]

]

(12)

Therefore the problem of optimum cooperative sensingis essentially reduced to optimizing a set of 119866 = (119892

1 119892

119873)

that satisfies the integral equations An iterative algorithmbased on Gauss-Seidel process can approximate the solutionof the above equations [26] This method is used for solvinga matrix of linear equations when the number of systemparameters is too high to find a solution by common PLUtechniques The initial requirement is that the diagonalelements of the matrix of equations must be nonzero andconvergence is provided when this matrix is either diagonallydominant or symmetric and positive definite [24] Let usconsider the local decision rule in 119895th iteration stage of thealgorithm as 119866

(119895) and the initial set as 119866(0) Gauss-Seidel

process for optimum local decision rules can be definedas

119866(119895+1)

= Γ119876

(119866(119895)

) forall119895 = 0 1 2 (13)

6 International Journal of Distributed Sensor Networks

where

119892119894

(119895+1)(119910119894)

= (int⋃119899isin11987801119894

Ω119899119894

minus int⋃119899isin11987802119894

Ω119899119894

)

sdot119891 (119884) 119889119884

119889119910119894

(14)

To reduce the computation complexity the discrete vari-ables 119905

119894are extracted from 119910

119894as 119879 = 119905

1 119905

119894 119905

119873 and

(14) can be described as

119892119895+1

119894(119905119894)

= ( sum

⋃119899isin11987801119894

Ω119899119894

minus sum

⋃119899isin11987802119894

Ω119899119894

)119891 (119879) Δ119879

Δ119905119894

(15)

Hence the discrete local decision rules are defined as

119885119894(119905119894) = 119868 (119892

119894(119905119894))

119868 (119909) = 0 119909 le 0

1 119909 gt 0

(16)

Accordingly the cost function 119865 is approximated as

119865 (119885 119876) = 120574

+ sum

119899isin1198780

( sum

11990511198851=1199061

sum

119905119894119885119894=119906119894

sum

119905119873119885119873=119906119873

119891 (119879) Δ119879)

(17)

Therefore

119892119895+1

119894(119905119894) = ( sum

119899isin11987801119894

minus sum

119899isin11987802119894

)

sum

1199051

sdot sdot sdot sum

119905119894minus1

sum

119905119894+1

sdot sdot sdot sum

119905119873

119894minus1

prod

119871=1

(1 minus

1003816100381610038161003816100381610038161003816mod (

119899 minus 1

2(119871minus1) 2) minus 119885

119871

(119895+1)(119905119871)

1003816100381610038161003816100381610038161003816)

119873

prod

119871=119894+1

(1 minus

1003816100381610038161003816100381610038161003816mod (

119899 minus 1

2(119871minus1) 2) minus 119885

119871

(119895)(119905119871)

1003816100381610038161003816100381610038161003816)

119891 (119879) Δ119879

Δ119910119894

(18)

For the simplicity of computations discrete local decisionrules 119885

119894(119905119894) are substituted instead of 119892

119894(119905119894) as both of them

have the same region of decision making Note that the iter-ative process converges when absolute relative approximateerror |(119885

119894

(119895+1)(119905119894) minus 119885

119894

(119895)(119905119894))119885119894

(119895+1)(119905119894)| times 100 ≪ 120576 where

120576 gt 0 is prespecified tolerance parameter For each positivevalue of Δ119905

119894and initial selection of 119885

0

119894 the algorithm is

converged after a certain number of iterations to a set of119885119895

119894that satisfies the convergence condition Figure 4 presents

the flowchart of the developed optimization algorithm basedon the golden section search method for Neyman-Pearsoncriterion Golden section ratio of golden section search isapplied with 120593 = 0618 or symmetrically (1 minus 0618) = 0382

to condense the width of the range in each step [25]

5 Simulation and Discussion

For the performance evaluation of the proposed OLDRalgorithm and compared to the other methods the receiveroperating characteristic (ROC) curve is depicted as a graph of119875119889versus 119875

119891 To depict ROC curves for the OLDR algorithm

in each iteration the values of 119875119889and 119875

119891are provided based

on the OLDR rules As a benchmark the simulation resultsare compared to centralized network and parallel networkwith LRT local decision rule

When normal pdf is assumed for the sensed signalsthe conditional pdf rsquos under both hypotheses 119867

0and

1198671are defined as 119901(119910

1 1199102 119910

119873| 1198670) = 119873(120583

0 1198620)

and 119901(1199101 1199102 119910

119873| 1198671) = 119873(120583

1 1198621) where 119862

0

and 1198621are the covariance matrices under 119867

0and 119867

1

respectively With correlation coefficient minus1 le 120588 le 1the covariance matrix is written as 119862(119910

1 1199102 119910

119873) =

[1205902

1 12058812

12059011205902 120588

11198731205901120590119873

1205881198731

120590119873

1205901 1205881198732

120590119873

1205902 120590

2

119873]

The performance of OLDR algorithm for cooperativespectrum sensing is shown in this section Centralizednetwork (CN) with a fusion center is considered as theoptimum benchmark for the evaluation of the proposedmethod Numerical results are analyzed for both OLDRand LRT local decision rules with ANDOR fusion rulesThen the effect of various correlation coefficients (120588)on ROC curves is investigated with correlated sensedsignals

In the first case a cooperative spectrum sensing with twolocal cognitive users is considered Given that the receivedobservations from PU are random Gaussian signal 119867 sdot 119878

119901

with mean 120583119867sdot119878119901

= 2 and variance 1205902

119867sdot119878119901

= 1 added to 1198991

and 1198992as independent zero mean Gaussian noises such that

1205902

1198991

= 2 and 1205902

1198992

= 1 then the conditional pdf rsquos under bothhypotheses 119867

0and 119867

1 are 119901(119910

1 1199102

| 1198670) = 119873(120583

0 1198620) and

119901(1199101 1199102

| 1198671) = 119873(120583

1 1198621) Therefore 120583

0= [0 0] 119862

0= [2 0

0 1] 1205831

= [2 2] 1198621

= [3 1 1 2]Figure 5 compares the performance of OLDR and LRT

with centralized network As illustrated in this figure OLDRwithAND fusion rule outperforms the other techniques since

International Journal of Distributed Sensor Networks 7

Start

Yes NoYesNo

Yes

No

End

Initializing of 120582(j) and Δ120582 j = 0

P(j)

flt 120572 P

(j)

fgt 120572

P(j)

flt 120572 P

(j)

fgt 120572

120582(j+1) = 120582(j) minus Δ120582j = j + 1 j = j + 1

j = j + 1

120582(j+1) = 120582(j) + Δ120582

120582(j+1) = 120582(j) + Δ120582

Δ120582 =

120593 times Δ120582 if P(j)

fgt 120572

minus120593 times Δ120582 otherwise

Pf(120582(j)) minus 120572 le 120576

P(j)

f(120582(j)) = 1 minusint

ΩOLDR(g1g119873)P(y1 yN |H0)dy1middot middot middot dyN

Figure 4 The proposed optimization algorithm (OLDR)

it is closer to the CN curve Meanwhile OLDR performsbetter than LRT with the same fusion rules for example at119875119891

= 002 OLDR shows 4 improvement in 119875119889compared to

the LRT with the same fusion rulesIn the second case parallel spectrum sensing with two

local cognitive users are considered with correlated receivedsignals as 120583

0= [0 0] 120583

1= [2 2] 119862

0= 1198621

= [1205902

1 12058812059011205902

12058812059011205902 1205902

2] The results of simulations with 120588 = 01 are

presented in Figure 6 which illustrates that the OLDR withAND fusion rule is more proximate to the CN curve andachieves a better performance than OR fusion rule forinstance at 119875

119891= 002 the improvement is about 4

The performance of the same network for various valuesof correlation coefficient (120588) is shown in Figure 7 Accordingto these results the performance is enhanced by the reductionof the correlation coefficient (120588)

Now a network of three local cognitive users with Gaus-sian signal observations is considered with mean 120583

119867sdot119878119901

= 2

and variance 1205902

119867sdot119878119901

= 1 added to zero mean independentnoises with 120590

2

1198991

= 3 12059021198992

= 2 and 1205902

1198993

= 1Thus the covariance

0 002 004 006 008 01 012 014 016 018 0203

04

05

06

07

08

09

1

CN-2 LCUOLDR-AND 2 LCUOLDR-OR 2 LCU

LRT-AND 2 LCULRT-OR 2 CU

Pf

Pd

Figure 5 ROC comparison forGaussian received signal in indepen-dent Gaussian noise with two LCUs

03

04

05

06

07

08

09

1

CN 2 LCUOLDR-AND 2 LCUOLDR-OR 2 LCU

LRT-AND 2 LCULRT-OR 2 LCU

0 002 004 006 008 01 012 014 016 018 02Pf

Pd

Figure 6 ROC comparison for deterministic received signal incorrelated Gaussian noises with two LCUs

matrices under 1198670and 119867

1are described as 119862

0= [3 0 0

0 2 0 0 0 1] and 1198621

= [4 1 1 1 3 1 1 1 2]Figures 8 and 9 show that increasing the number of local

cognitive users enhances the performance of the network ForGaussian received signals with independentGaussian noise at119875119891

= 002 the 119875119889is enhanced about 3 for OLDR with three

LCUs comparing to OLDR with two LCUsFrom these results it is concluded that for a fixed fusion

rule OLDR algorithm shows a superior performance oflocal decision rules to detect primary users compared toLRT method Apparently the probability of primary userdetection is increased with the number of cooperative localcognitive users equipped with spectrum sensing When thesensing channels are correlated results show performancedegradation in higher correlation coefficients

8 International Journal of Distributed Sensor Networks

03

04

05

06

07

08

09

1

0 002 004 006 008 01 012 014 016 018 02Pf

Pd

OLDR-AND 120588 = minus03

OLDR-AND 120588 = minus01

OLDR-AND 120588 = 0

OLDR-AND 120588 = 01

OLDR-AND 120588 = 03

Figure 7 ROC comparison for deterministic received signal incorrelated Gaussian noise with different correlation coefficients (120588)

CN 3 LCUOLDR-AND 3 LCU

OLDR-AND 2 LCUCN 2 LCU

0 002 004 006 008 01 012 014 016 018 02Pf

03

04

05

06

07

08

09

1

Pd

Figure 8 ROC comparison for Gaussian received signal in inde-pendent Gaussian noises with different numbers of LCUs

OLDR method is a low complexity solution for theproblem of (11) which is reduced to optimizing a set of localdecision rules 119866 = (119892

1 119892

119873) that satisfies the integral

equations (12) In addition the computation complexity of(14) has been reduced by considering discrete variables forthe observations 119910

119894 as well as local decision rules 119892

119894 to 119905119894

and 119885119894 respectively For the centralized network there is

no local decision rule and the local decision rule of LRTmethod is defined as Λ(119910

119894) le 120579

119894 where 120579

119894is the threshold

for the 119894th receiver In each iteration of the algorithm withLRTΛ(119884

119894) is calculated for all observations119910

119894 and compared

with threshold 120579119894 For the initial threshold within a range

of 119872 levels the time complexity of each local decision rulecan be written as 119874(119872) According to (18) the local decision

CN 3 LCUOLDR-AND 3 LCU

CN 2 LCUOLDR-AND 2 LCU

03

04

05

06

07

08

09

1

Pd

004 018 02008 01 012 014 016002 0060Pf

Figure 9 ROC comparison for deterministic signal in correlatedGaussian noises with different numbers of LCUs

Number of LCUs1 2 3 4 5 6 7 8

CNOLDRLRT

0

10

20

30

40

50

60

70Ti

me c

ompl

exity

Figure 10 Time complexity comparison of local decision rules

rule of OLDR algorithm 119892119895+1

119894 has to be updated at each

iteration with the time complexity of 119874(1198732) compared to the

other local decision rulesThe time complexity comparison oflocal decision rules for 119872 = 20 is shown in Figure 10 whichdescribes the increase of the calculations number propor-tional to the number of the receivers 119873 However since CNmethod consumes too large bandwidths for sending the datato the fusion center and LRT method assumes independentobservations they cannot be considered as optimum solutionfor cooperative cognitive users with correlated sensed signals

6 Conclusion

In this paper the cooperative spectrum sensing for cognitiveheterogeneous network has been designed with a parallelconfiguration An optimum algorithm for local decision

International Journal of Distributed Sensor Networks 9

rule based on Neyman-Pearson criterion with correlatedobservations from PUs has been proposed This schemebased on a discrete Gauss-Seidel iterative algorithm leads toa low complexity method of finding an optimum solution forLCUrsquos decision rules The performance evaluation shows theefficiency of this algorithm with fixed fusion rules in whichAND rule outperforms the OR fusion rule Furthermorewith lower correlation coefficients a better performance isachieved The experimental measurements and implemen-tation of OLDR algorithm for a distributed heterogeneouscognitive network are a challenging open area for the futurework Meanwhile optimizing the fusion rule simultaneouslywith the local decision rules study of different topologiesof cooperative cognitive networks the performance analysisof multilevel decision rules and shadowing in reportingchannels are among the other suggestions for the futureexploration

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] Federal Communications Commission ldquoSpectrum policy taskforcerdquo Report ET Docket 02-135 2002

[2] O B Akan O B Karli and O Ergul ldquoCognitive radio sensornetworksrdquo IEEE Network vol 23 no 4 pp 34ndash40 2009

[3] J Mitola III and G Q Maguire Jr ldquoCognitive radio makingsoftware radios more personalrdquo IEEE Personal Communica-tions vol 6 no 4 pp 13ndash18 1999

[4] S Haykin ldquoCognitive radio brain-empowered wireless com-municationsrdquo IEEE Journal on Selected Areas in Communica-tions vol 23 no 2 pp 201ndash220 2005

[5] H Arslan and M E Shin ldquoUWB cognitive radiordquo in CognitiveRadio Software Defined Radio and Adaptive Wireless Systemschapter 6 pp 355ndash381 Springer Dordrecht The Netherlands2007

[6] A A El-Saleh M Ismail M A M Ali and A N H AlnuaimyldquoCapacity optimization for local and cooperative spectrumsensing in cognitive radio networksrdquoWorld Academy of ScienceEngineering and Technology vol 4 no 11 pp 679ndash685 2009

[7] H Hosseini N Fisal and S K Syed-Yusof ldquoEnhanced FCMEthresholding for wavelet-based cognitive UWB over fadingchannelsrdquo ETRI Journal vol 33 no 6 pp 961ndash964 2011

[8] I F Akyildiz B F Lo and R Balakrishnan ldquoCooperative spec-trum sensing in cognitive radio networks a surveyrdquo PhysicalCommunication vol 4 no 1 pp 40ndash62 2011

[9] H Du Z XWei YWang andD C Yang ldquoDetection reliabilityand throughput analysis for cooperative spectrum sensing incognitive radio networksrdquo Advanced Materials and EngineeringMaterials vol 457-458 pp 668ndash674 2012

[10] Q-T Vien G B Stewart H Tianfield and H X NguyenldquoEfficient cooperative spectrum sensing for three-hop cognitivewireless relay networksrdquo IET Communications vol 7 no 2 pp119ndash127 2013

[11] X Liu M Jia and X Tan ldquoThreshold optimization of coop-erative spectrum sensing in cognitive radio networksrdquo RadioScience vol 48 no 1 pp 23ndash32 2013

[12] H Chen S Ta and B Sun ldquoCooperative game approach topower allocation for target tracking in distributedMIMO radarsensor networksrdquo IEEE Sensors Journal vol 15 no 10 pp 5423ndash5432 2015

[13] R M Vaghefi and R M Buehrer ldquoCooperative joint synchro-nization and localization in wireless sensor networksrdquo IEEETransactions on Signal Processing vol 63 no 14 pp 3615ndash36272015

[14] S Jaewoo and R Srikant ldquoImproving channel utilization viacooperative spectrum sensing with opportunistic feedback incognitive radio networksrdquo IEEECommunications Letters vol 19no 6 pp 1065ndash1068 2015

[15] M Najimi A Ebrahimzadeh S M H Andargoli and AFallahi ldquoEnergy-efficient sensor selection for cooperative spec-trum sensing in the lack or partial informationrdquo IEEE SensorsJournal vol 15 no 7 pp 3807ndash3818 2015

[16] C G Tsinos and K Berberidis ldquoDecentralized adaptiveeigenvalue-based spectrum sensing for multiantenna cognitiveradio systemsrdquo IEEE Transactions onWireless Communicationsvol 14 no 3 pp 1703ndash1715 2015

[17] G Loganathan G Padmavathi and S Shanmugavel ldquoAn effi-cient adaptive fusion scheme for cooperative spectrum sensingin cognitive radios over fading channelsrdquo in Proceedings ofthe International Conference on Information Communicationand Embedded Systems (ICICES rsquo14) pp 1ndash5 Chennai IndiaFeburary 2014

[18] I Y Hoballah and P K Varshney ldquoDistributed Bayesian signaldetectionrdquo IEEETransactions on InformationTheory vol 35 no5 pp 995ndash1000 1989

[19] W A Hashlamoun and P K Varshney ldquoAn approach tothe design of distributed Bayesian detection structuresrdquo IEEETransactions on Systems Man and Cybernetics vol 21 no 5 pp1206ndash1211 1991

[20] W A Hashlamoun and P K Varshney ldquoFurther results ondistributed Bayesian signal detectionrdquo IEEE Transactions onInformation Theory vol 39 no 5 pp 1660ndash1661 1993

[21] R Viswanathan and P K Varshney ldquoDistributed detectionwithmultiple sensors Part Imdashfundamentalsrdquo Proceedings of theIEEE vol 85 no 1 pp 54ndash63 1997

[22] V R Kanchumarthy R Viswanathan and M MadishettyldquoImpact of channel errors on decentralized detection perfor-mance of wireless sensor networks a study of binary modu-lations Rayleigh-fading and nonfading channels and fusion-combinersrdquo IEEE Transactions on Signal Processing vol 56 no5 pp 1761ndash1769 2008

[23] S M Mishra A Sahai and R W Brodersen ldquoCooperativesensing among cognitive radiosrdquo in Proceedings of the IEEEInternational Conference on Communications (ICC rsquo06) pp1658ndash1663 Istanbul Turkey July 2006

[24] A W Al-Khafaji and J R Tooley Numerical Methods inEngineering Practice Holt Rinehart and Winston New YorkNY USA 1986

[25] X Li J Cao Q Ji and Y Hei ldquoEnergy efficient techniques withsensing time optimization in cognitive radio networksrdquo in Pro-ceedings of the IEEE Wireless Communications and NetworkingConference (WCNC rsquo13) pp 25ndash28 Shanghai China April 2013

[26] Y Zhu R S Blum Z-Q Luo and K M Wong ldquoUnex-pected properties and optimum-distributed sensor detectors fordependent observation casesrdquo IEEE Transactions on AutomaticControl vol 45 no 1 pp 62ndash72 2000

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DistributedSensor Networks

International Journal of

4 International Journal of Distributed Sensor Networks

Primarynetwork

PU

PU

Tx

Rx

Heterogeneous network

Macro-eNB

H-UE

H-UEH-UE

H-eNB(CCU)

M-UE

(LCU1)

(LCU3)

(LCU2)

Figure 2 A heterogeneous network overlapping with primarynetwork

CCU (fusion center)

PU

Sensing channels

Reporting channels

LCU1 LCU2LCUN

middot middot middot

Figure 3 Parallel cooperative spectrum sensing

this network the coverage areas of small cells and primarysystems can be overlapped This mutual interference occurswhen they are using the same time-frequency resources whilespatially located in a certain distance apart from each otheras shown in Figure 2 The frequency reusing of adjacentmacrocell user equipment (M-UE) or other primary systemsby small cells can create interferences to heterogeneoususer equipment (H-UE) Hence H-UE which operates assecondary users needs to transmit under a certain powerlevel which is acceptable by the licensed users PUs and atthe same time mitigates the interference from the primarysystem

The decision making on the presence or absence of PUsignals is a critical part of spectrum sensing procedure atcognitive H-UE In practice each cognitive piece of H-UEplays a role same as distributed LCUs that is equipped withspectrum sensing by energy detection to locally measurethe PU signal transmission power and frequencies Thelocal decisions are the output of certain local rules at thesedistributed pieces of H-UEs that will be sent to H-eNB withthe capability of a CCU to process the received informationand produce the final decision based on the embedded fusionrule Then in the presence of PU signals pieces of H-UEadapt their configurations to avoid mutual interferences withprimary network Since the channel impairments affect theinput observations of each energy detector at H-UE theassumption of independency is not correct any more anda cooperative decision making is required as the solution

Cognitive features enable the secondary users to analyzeinterference using the spectrum sensing mechanism that ismainly performed in LCUs whereas the decision is made forthe cooperative network Let us consider 119873 distributed LCUsas shown in Figure 3 In this figure the 119894th LCU is shownas LCU

119894that receives the observation signals 119910

119894 from the

PU through the sensing channels Each LCU119894sends its local

binary decision 119906119894 to the fusion center the CCU tomake the

final decision using the fusion ruleThemetrics of probabilityof detection 119875

119889119894 and probability of false alarm 119875

119891119894 for

local decision at the 119894th LCU119894are derived to be employed

for the performance evaluation Assuming that during thesensing time CUs do not broadcast and there is no mutualinterference between them the vector of the received signalthrough the sensing channels is defined as

119884 = 119867 sdot 119878119901

+ 119881 (4)

where 119878119901denotes PUrsquos transmitted signal 119867 = [ℎ

1

ℎ119894 ℎ

119873] states the sensing channel gain vector and 119884 =

[1199101 119910

119894 119910

119873] shows the observation vector in which

119910119894denotes the received signal at LCU

119894 The vector of addi-

tive white Gaussian noise (AWGN) at LCU receivers is119881 = [V

1 V

119894 V

119873] The observations of PUrsquos signal

are received through the sensing channels at LCU119894 In this

scenario the correlated channels lead to correlated sensingobservations at the LCU receivers that analyze the data asa binary hypothesis testing form 119867

0and 119867

1are the binary

hypotheses which define the absence and presence of PUrespectively Then the general form of the received signal atthe spectrum sensing part of LCU is

1198671

1199101

= ℎ1

sdot 119878119901

+ V1 119910

119873

= ℎ119873

sdot 119878119901

+ V119873

1198670

1199101

= V1 119910

119873= V119873

(5)

Given that 119910119894denotes the available observation of PU

signal at LCU119894receiver the local decision rule 119892

119894(119910119894) is

employed by LCU119894to make a binary decision 119906

119894about the

existence of PU signal Based on a set of local decision rulesas 119866(119884) = [119892

1(1199101) 119892

119894(119910119894) 119892

119873(119910119873

)] the fusion centerCCU receives the local decision as

119906119894

= 0 119892

119894(119910119894) le 0

1 119892119894(119910119894) gt 0

(6)

TheCCU follows a fusion rule as119876(119880)which is a Booleanfunction and whenever 119876(119880) = 0 the final decision is takenas 1198670 otherwise it is 119867

1 The local decision rule maps the

observation set 119884 = 1199101 119910

119873to a local decision set 119880 =

1199061 119906

119894 119906

119873 where 119906

119894isin 0 1 119894 = 1 119873 The

combination of local binary decisions 119906119894results in 2

119873 statesThus the 2

2119873

is the total number of states for final decision119906119891

= 119876(119880) and

119876 (119880) = 119876119899 119906119894

= mod (119899 minus 1

2(119894minus1) 2) 1

le 119899 le 2119873

(7)

International Journal of Distributed Sensor Networks 5

where mod(119860 2) is the division remaining of 1198602 and 119906119894

=

mod((119899 minus 1)2(119894minus1)

2) is the 119894th bit of 119899 Hence 119876(119880) =

119876119899 119899 = sum

119873

119894=11199061198942119894minus1

+ 1 Consider two different sets as1198780

= 119899 119876119899

= 0 and 1198781

= 119899 119876119899

= 1 such that1198780

cup 1198781

= 1 2 2119873

then ΩOLDR = 119910119894

119876119899

= 0 119899 isin 1198780

where ΩOLDR defines the region of optimal decision makingfor parallel cooperative cognitive network which leads to thefinal decision of 119867

0 With a given set of 119878

0 the fusion rule

119876(119880) is deterministic and constant and for every 119899 belongingto 1198780 119899th composition will result in a decision on 119867

0 For

a fixed fusion rule the region of final decision is ΩOLDR =

⋃119899isin1198780

Ω119899 where Ω

119899denotes the region of 119899th combination of

119876 as

Ω119899

= 119884 119906119894

= mod (119899 minus 1

2(119894minus1) 2) 119876

= 119876119899

(8)

In the next section the optimization problem for parallellocal decision rules is reduced to solve a set of fixed pointintegral equations that minimizes the Neyman-Pearson costfunction The decision rules are digitized for simplicity andGauss-Seidel algorithm [24] and Golden Section search [25]are applied to find the final solutions

4 OLDR Algorithm with Gauss-Seidel Process

Each distributedH-UELCU119894performs the spectrum sensing

by energy detection to detect the initial PU signal obser-vation 119910

119894 This distributed information from all LCUs is

used by the OLDR algorithm to cooperatively optimize localdecision rules 119892

119894 according to the fix central fusion rule at

H-eNBCCU ANDOR and achieve the final minimized 119875119891

with Gauss-Seidel process Based on the Neyman-Pearsoncriterion the optimum local decision rule is defined tominimize the corresponding cost function 119865

119865 (119866 119876) = 120582 (1 minus 120572) + intΩOLDR

119891 (119884) 119889119884 (9)

where 119876 is the Boolean fusion function 119884 denotes localobservations and 119891(119884) = 119875(119884 | 119867

1) minus 120582119875(119884 | 119867

0) Given

that 120574 = 120582(1 minus 120572) according to the above relations it can beconcluded that

119865 (119866 119876) = 120574 + int119884isinΩOLDR

119891 (119884) 119889119884 = 120574

+ (int119892119894(119910119894)le0

(int⋃119899isin11987801119894

Ω119899119894

minus int⋃119899isin11987802119894

Ω119899119894

) + int119910119894

int⋃119899isin11987802119894

Ω119899119894

)

sdot 119891 (119884) 119889119884

(10)

where Ω119899119894

is Ω119899excluding 119910

119894 11987801119894

11987802119894

are two subsetsof 1198780such that 119878

01119894cup 11987802119894

= 1198780 11987801119894

is a subset of 119899

belonging to 1198780with 119906

119894= 0 119878

01119894= 119899 119876

119899=

0 119906119894

= 0 and similarly 11987802119894

is a subset of 119899 belongingto 1198780with 119906

119894= 1 119878

02119894= 119899 119876

119899= 0 119906

119894= 1

The set of optimum local decision rules that minimizes the119865 function in (10) can be defined as 119866 = (119892

1 119892

119873)

[26]

119892119894(119910119894) = (int

⋃119899isin11987801119894

Ω119899119894

minus int⋃119899isin11987802119894

Ω119899119894

)

sdot119891 (119884) 119889119884

119889119910119894

(11)

where Ω119899119894

= (1199101 119910

119894minus1 119910119894+1

119910119873

) 120601(119892119894 119906119894) le 0

and 120601(119892119894 119906119894) = (12 minus 119906

119894)119892119894 Consequently each set of

optimum local decisions is derived by solving several fixedpoint integral equations as

Γ119876

(119866) =

[[[[[[[[[[[[[[[[[[[[

[

(intcup119899isin119878011

Ω1198991

minus intcup119899isin119878021

Ω1198991

)119891 (119884) 119889119884

1198891199101

(intcup119899isin11987801119894

Ω119899119894

minus intcup119899isin11987802119894

Ω119899119894

)119891 (119884) 119889119884

119889119910119894

(intcup119899isin11987801119873

Ω119899119873

minus intcup119899isin11987802119873

Ω119899119873

)119891 (119884) 119889119884

119889119910119873

]]]]]]]]]]]]]]]]]]]]

]

(12)

Therefore the problem of optimum cooperative sensingis essentially reduced to optimizing a set of 119866 = (119892

1 119892

119873)

that satisfies the integral equations An iterative algorithmbased on Gauss-Seidel process can approximate the solutionof the above equations [26] This method is used for solvinga matrix of linear equations when the number of systemparameters is too high to find a solution by common PLUtechniques The initial requirement is that the diagonalelements of the matrix of equations must be nonzero andconvergence is provided when this matrix is either diagonallydominant or symmetric and positive definite [24] Let usconsider the local decision rule in 119895th iteration stage of thealgorithm as 119866

(119895) and the initial set as 119866(0) Gauss-Seidel

process for optimum local decision rules can be definedas

119866(119895+1)

= Γ119876

(119866(119895)

) forall119895 = 0 1 2 (13)

6 International Journal of Distributed Sensor Networks

where

119892119894

(119895+1)(119910119894)

= (int⋃119899isin11987801119894

Ω119899119894

minus int⋃119899isin11987802119894

Ω119899119894

)

sdot119891 (119884) 119889119884

119889119910119894

(14)

To reduce the computation complexity the discrete vari-ables 119905

119894are extracted from 119910

119894as 119879 = 119905

1 119905

119894 119905

119873 and

(14) can be described as

119892119895+1

119894(119905119894)

= ( sum

⋃119899isin11987801119894

Ω119899119894

minus sum

⋃119899isin11987802119894

Ω119899119894

)119891 (119879) Δ119879

Δ119905119894

(15)

Hence the discrete local decision rules are defined as

119885119894(119905119894) = 119868 (119892

119894(119905119894))

119868 (119909) = 0 119909 le 0

1 119909 gt 0

(16)

Accordingly the cost function 119865 is approximated as

119865 (119885 119876) = 120574

+ sum

119899isin1198780

( sum

11990511198851=1199061

sum

119905119894119885119894=119906119894

sum

119905119873119885119873=119906119873

119891 (119879) Δ119879)

(17)

Therefore

119892119895+1

119894(119905119894) = ( sum

119899isin11987801119894

minus sum

119899isin11987802119894

)

sum

1199051

sdot sdot sdot sum

119905119894minus1

sum

119905119894+1

sdot sdot sdot sum

119905119873

119894minus1

prod

119871=1

(1 minus

1003816100381610038161003816100381610038161003816mod (

119899 minus 1

2(119871minus1) 2) minus 119885

119871

(119895+1)(119905119871)

1003816100381610038161003816100381610038161003816)

119873

prod

119871=119894+1

(1 minus

1003816100381610038161003816100381610038161003816mod (

119899 minus 1

2(119871minus1) 2) minus 119885

119871

(119895)(119905119871)

1003816100381610038161003816100381610038161003816)

119891 (119879) Δ119879

Δ119910119894

(18)

For the simplicity of computations discrete local decisionrules 119885

119894(119905119894) are substituted instead of 119892

119894(119905119894) as both of them

have the same region of decision making Note that the iter-ative process converges when absolute relative approximateerror |(119885

119894

(119895+1)(119905119894) minus 119885

119894

(119895)(119905119894))119885119894

(119895+1)(119905119894)| times 100 ≪ 120576 where

120576 gt 0 is prespecified tolerance parameter For each positivevalue of Δ119905

119894and initial selection of 119885

0

119894 the algorithm is

converged after a certain number of iterations to a set of119885119895

119894that satisfies the convergence condition Figure 4 presents

the flowchart of the developed optimization algorithm basedon the golden section search method for Neyman-Pearsoncriterion Golden section ratio of golden section search isapplied with 120593 = 0618 or symmetrically (1 minus 0618) = 0382

to condense the width of the range in each step [25]

5 Simulation and Discussion

For the performance evaluation of the proposed OLDRalgorithm and compared to the other methods the receiveroperating characteristic (ROC) curve is depicted as a graph of119875119889versus 119875

119891 To depict ROC curves for the OLDR algorithm

in each iteration the values of 119875119889and 119875

119891are provided based

on the OLDR rules As a benchmark the simulation resultsare compared to centralized network and parallel networkwith LRT local decision rule

When normal pdf is assumed for the sensed signalsthe conditional pdf rsquos under both hypotheses 119867

0and

1198671are defined as 119901(119910

1 1199102 119910

119873| 1198670) = 119873(120583

0 1198620)

and 119901(1199101 1199102 119910

119873| 1198671) = 119873(120583

1 1198621) where 119862

0

and 1198621are the covariance matrices under 119867

0and 119867

1

respectively With correlation coefficient minus1 le 120588 le 1the covariance matrix is written as 119862(119910

1 1199102 119910

119873) =

[1205902

1 12058812

12059011205902 120588

11198731205901120590119873

1205881198731

120590119873

1205901 1205881198732

120590119873

1205902 120590

2

119873]

The performance of OLDR algorithm for cooperativespectrum sensing is shown in this section Centralizednetwork (CN) with a fusion center is considered as theoptimum benchmark for the evaluation of the proposedmethod Numerical results are analyzed for both OLDRand LRT local decision rules with ANDOR fusion rulesThen the effect of various correlation coefficients (120588)on ROC curves is investigated with correlated sensedsignals

In the first case a cooperative spectrum sensing with twolocal cognitive users is considered Given that the receivedobservations from PU are random Gaussian signal 119867 sdot 119878

119901

with mean 120583119867sdot119878119901

= 2 and variance 1205902

119867sdot119878119901

= 1 added to 1198991

and 1198992as independent zero mean Gaussian noises such that

1205902

1198991

= 2 and 1205902

1198992

= 1 then the conditional pdf rsquos under bothhypotheses 119867

0and 119867

1 are 119901(119910

1 1199102

| 1198670) = 119873(120583

0 1198620) and

119901(1199101 1199102

| 1198671) = 119873(120583

1 1198621) Therefore 120583

0= [0 0] 119862

0= [2 0

0 1] 1205831

= [2 2] 1198621

= [3 1 1 2]Figure 5 compares the performance of OLDR and LRT

with centralized network As illustrated in this figure OLDRwithAND fusion rule outperforms the other techniques since

International Journal of Distributed Sensor Networks 7

Start

Yes NoYesNo

Yes

No

End

Initializing of 120582(j) and Δ120582 j = 0

P(j)

flt 120572 P

(j)

fgt 120572

P(j)

flt 120572 P

(j)

fgt 120572

120582(j+1) = 120582(j) minus Δ120582j = j + 1 j = j + 1

j = j + 1

120582(j+1) = 120582(j) + Δ120582

120582(j+1) = 120582(j) + Δ120582

Δ120582 =

120593 times Δ120582 if P(j)

fgt 120572

minus120593 times Δ120582 otherwise

Pf(120582(j)) minus 120572 le 120576

P(j)

f(120582(j)) = 1 minusint

ΩOLDR(g1g119873)P(y1 yN |H0)dy1middot middot middot dyN

Figure 4 The proposed optimization algorithm (OLDR)

it is closer to the CN curve Meanwhile OLDR performsbetter than LRT with the same fusion rules for example at119875119891

= 002 OLDR shows 4 improvement in 119875119889compared to

the LRT with the same fusion rulesIn the second case parallel spectrum sensing with two

local cognitive users are considered with correlated receivedsignals as 120583

0= [0 0] 120583

1= [2 2] 119862

0= 1198621

= [1205902

1 12058812059011205902

12058812059011205902 1205902

2] The results of simulations with 120588 = 01 are

presented in Figure 6 which illustrates that the OLDR withAND fusion rule is more proximate to the CN curve andachieves a better performance than OR fusion rule forinstance at 119875

119891= 002 the improvement is about 4

The performance of the same network for various valuesof correlation coefficient (120588) is shown in Figure 7 Accordingto these results the performance is enhanced by the reductionof the correlation coefficient (120588)

Now a network of three local cognitive users with Gaus-sian signal observations is considered with mean 120583

119867sdot119878119901

= 2

and variance 1205902

119867sdot119878119901

= 1 added to zero mean independentnoises with 120590

2

1198991

= 3 12059021198992

= 2 and 1205902

1198993

= 1Thus the covariance

0 002 004 006 008 01 012 014 016 018 0203

04

05

06

07

08

09

1

CN-2 LCUOLDR-AND 2 LCUOLDR-OR 2 LCU

LRT-AND 2 LCULRT-OR 2 CU

Pf

Pd

Figure 5 ROC comparison forGaussian received signal in indepen-dent Gaussian noise with two LCUs

03

04

05

06

07

08

09

1

CN 2 LCUOLDR-AND 2 LCUOLDR-OR 2 LCU

LRT-AND 2 LCULRT-OR 2 LCU

0 002 004 006 008 01 012 014 016 018 02Pf

Pd

Figure 6 ROC comparison for deterministic received signal incorrelated Gaussian noises with two LCUs

matrices under 1198670and 119867

1are described as 119862

0= [3 0 0

0 2 0 0 0 1] and 1198621

= [4 1 1 1 3 1 1 1 2]Figures 8 and 9 show that increasing the number of local

cognitive users enhances the performance of the network ForGaussian received signals with independentGaussian noise at119875119891

= 002 the 119875119889is enhanced about 3 for OLDR with three

LCUs comparing to OLDR with two LCUsFrom these results it is concluded that for a fixed fusion

rule OLDR algorithm shows a superior performance oflocal decision rules to detect primary users compared toLRT method Apparently the probability of primary userdetection is increased with the number of cooperative localcognitive users equipped with spectrum sensing When thesensing channels are correlated results show performancedegradation in higher correlation coefficients

8 International Journal of Distributed Sensor Networks

03

04

05

06

07

08

09

1

0 002 004 006 008 01 012 014 016 018 02Pf

Pd

OLDR-AND 120588 = minus03

OLDR-AND 120588 = minus01

OLDR-AND 120588 = 0

OLDR-AND 120588 = 01

OLDR-AND 120588 = 03

Figure 7 ROC comparison for deterministic received signal incorrelated Gaussian noise with different correlation coefficients (120588)

CN 3 LCUOLDR-AND 3 LCU

OLDR-AND 2 LCUCN 2 LCU

0 002 004 006 008 01 012 014 016 018 02Pf

03

04

05

06

07

08

09

1

Pd

Figure 8 ROC comparison for Gaussian received signal in inde-pendent Gaussian noises with different numbers of LCUs

OLDR method is a low complexity solution for theproblem of (11) which is reduced to optimizing a set of localdecision rules 119866 = (119892

1 119892

119873) that satisfies the integral

equations (12) In addition the computation complexity of(14) has been reduced by considering discrete variables forthe observations 119910

119894 as well as local decision rules 119892

119894 to 119905119894

and 119885119894 respectively For the centralized network there is

no local decision rule and the local decision rule of LRTmethod is defined as Λ(119910

119894) le 120579

119894 where 120579

119894is the threshold

for the 119894th receiver In each iteration of the algorithm withLRTΛ(119884

119894) is calculated for all observations119910

119894 and compared

with threshold 120579119894 For the initial threshold within a range

of 119872 levels the time complexity of each local decision rulecan be written as 119874(119872) According to (18) the local decision

CN 3 LCUOLDR-AND 3 LCU

CN 2 LCUOLDR-AND 2 LCU

03

04

05

06

07

08

09

1

Pd

004 018 02008 01 012 014 016002 0060Pf

Figure 9 ROC comparison for deterministic signal in correlatedGaussian noises with different numbers of LCUs

Number of LCUs1 2 3 4 5 6 7 8

CNOLDRLRT

0

10

20

30

40

50

60

70Ti

me c

ompl

exity

Figure 10 Time complexity comparison of local decision rules

rule of OLDR algorithm 119892119895+1

119894 has to be updated at each

iteration with the time complexity of 119874(1198732) compared to the

other local decision rulesThe time complexity comparison oflocal decision rules for 119872 = 20 is shown in Figure 10 whichdescribes the increase of the calculations number propor-tional to the number of the receivers 119873 However since CNmethod consumes too large bandwidths for sending the datato the fusion center and LRT method assumes independentobservations they cannot be considered as optimum solutionfor cooperative cognitive users with correlated sensed signals

6 Conclusion

In this paper the cooperative spectrum sensing for cognitiveheterogeneous network has been designed with a parallelconfiguration An optimum algorithm for local decision

International Journal of Distributed Sensor Networks 9

rule based on Neyman-Pearson criterion with correlatedobservations from PUs has been proposed This schemebased on a discrete Gauss-Seidel iterative algorithm leads toa low complexity method of finding an optimum solution forLCUrsquos decision rules The performance evaluation shows theefficiency of this algorithm with fixed fusion rules in whichAND rule outperforms the OR fusion rule Furthermorewith lower correlation coefficients a better performance isachieved The experimental measurements and implemen-tation of OLDR algorithm for a distributed heterogeneouscognitive network are a challenging open area for the futurework Meanwhile optimizing the fusion rule simultaneouslywith the local decision rules study of different topologiesof cooperative cognitive networks the performance analysisof multilevel decision rules and shadowing in reportingchannels are among the other suggestions for the futureexploration

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] Federal Communications Commission ldquoSpectrum policy taskforcerdquo Report ET Docket 02-135 2002

[2] O B Akan O B Karli and O Ergul ldquoCognitive radio sensornetworksrdquo IEEE Network vol 23 no 4 pp 34ndash40 2009

[3] J Mitola III and G Q Maguire Jr ldquoCognitive radio makingsoftware radios more personalrdquo IEEE Personal Communica-tions vol 6 no 4 pp 13ndash18 1999

[4] S Haykin ldquoCognitive radio brain-empowered wireless com-municationsrdquo IEEE Journal on Selected Areas in Communica-tions vol 23 no 2 pp 201ndash220 2005

[5] H Arslan and M E Shin ldquoUWB cognitive radiordquo in CognitiveRadio Software Defined Radio and Adaptive Wireless Systemschapter 6 pp 355ndash381 Springer Dordrecht The Netherlands2007

[6] A A El-Saleh M Ismail M A M Ali and A N H AlnuaimyldquoCapacity optimization for local and cooperative spectrumsensing in cognitive radio networksrdquoWorld Academy of ScienceEngineering and Technology vol 4 no 11 pp 679ndash685 2009

[7] H Hosseini N Fisal and S K Syed-Yusof ldquoEnhanced FCMEthresholding for wavelet-based cognitive UWB over fadingchannelsrdquo ETRI Journal vol 33 no 6 pp 961ndash964 2011

[8] I F Akyildiz B F Lo and R Balakrishnan ldquoCooperative spec-trum sensing in cognitive radio networks a surveyrdquo PhysicalCommunication vol 4 no 1 pp 40ndash62 2011

[9] H Du Z XWei YWang andD C Yang ldquoDetection reliabilityand throughput analysis for cooperative spectrum sensing incognitive radio networksrdquo Advanced Materials and EngineeringMaterials vol 457-458 pp 668ndash674 2012

[10] Q-T Vien G B Stewart H Tianfield and H X NguyenldquoEfficient cooperative spectrum sensing for three-hop cognitivewireless relay networksrdquo IET Communications vol 7 no 2 pp119ndash127 2013

[11] X Liu M Jia and X Tan ldquoThreshold optimization of coop-erative spectrum sensing in cognitive radio networksrdquo RadioScience vol 48 no 1 pp 23ndash32 2013

[12] H Chen S Ta and B Sun ldquoCooperative game approach topower allocation for target tracking in distributedMIMO radarsensor networksrdquo IEEE Sensors Journal vol 15 no 10 pp 5423ndash5432 2015

[13] R M Vaghefi and R M Buehrer ldquoCooperative joint synchro-nization and localization in wireless sensor networksrdquo IEEETransactions on Signal Processing vol 63 no 14 pp 3615ndash36272015

[14] S Jaewoo and R Srikant ldquoImproving channel utilization viacooperative spectrum sensing with opportunistic feedback incognitive radio networksrdquo IEEECommunications Letters vol 19no 6 pp 1065ndash1068 2015

[15] M Najimi A Ebrahimzadeh S M H Andargoli and AFallahi ldquoEnergy-efficient sensor selection for cooperative spec-trum sensing in the lack or partial informationrdquo IEEE SensorsJournal vol 15 no 7 pp 3807ndash3818 2015

[16] C G Tsinos and K Berberidis ldquoDecentralized adaptiveeigenvalue-based spectrum sensing for multiantenna cognitiveradio systemsrdquo IEEE Transactions onWireless Communicationsvol 14 no 3 pp 1703ndash1715 2015

[17] G Loganathan G Padmavathi and S Shanmugavel ldquoAn effi-cient adaptive fusion scheme for cooperative spectrum sensingin cognitive radios over fading channelsrdquo in Proceedings ofthe International Conference on Information Communicationand Embedded Systems (ICICES rsquo14) pp 1ndash5 Chennai IndiaFeburary 2014

[18] I Y Hoballah and P K Varshney ldquoDistributed Bayesian signaldetectionrdquo IEEETransactions on InformationTheory vol 35 no5 pp 995ndash1000 1989

[19] W A Hashlamoun and P K Varshney ldquoAn approach tothe design of distributed Bayesian detection structuresrdquo IEEETransactions on Systems Man and Cybernetics vol 21 no 5 pp1206ndash1211 1991

[20] W A Hashlamoun and P K Varshney ldquoFurther results ondistributed Bayesian signal detectionrdquo IEEE Transactions onInformation Theory vol 39 no 5 pp 1660ndash1661 1993

[21] R Viswanathan and P K Varshney ldquoDistributed detectionwithmultiple sensors Part Imdashfundamentalsrdquo Proceedings of theIEEE vol 85 no 1 pp 54ndash63 1997

[22] V R Kanchumarthy R Viswanathan and M MadishettyldquoImpact of channel errors on decentralized detection perfor-mance of wireless sensor networks a study of binary modu-lations Rayleigh-fading and nonfading channels and fusion-combinersrdquo IEEE Transactions on Signal Processing vol 56 no5 pp 1761ndash1769 2008

[23] S M Mishra A Sahai and R W Brodersen ldquoCooperativesensing among cognitive radiosrdquo in Proceedings of the IEEEInternational Conference on Communications (ICC rsquo06) pp1658ndash1663 Istanbul Turkey July 2006

[24] A W Al-Khafaji and J R Tooley Numerical Methods inEngineering Practice Holt Rinehart and Winston New YorkNY USA 1986

[25] X Li J Cao Q Ji and Y Hei ldquoEnergy efficient techniques withsensing time optimization in cognitive radio networksrdquo in Pro-ceedings of the IEEE Wireless Communications and NetworkingConference (WCNC rsquo13) pp 25ndash28 Shanghai China April 2013

[26] Y Zhu R S Blum Z-Q Luo and K M Wong ldquoUnex-pected properties and optimum-distributed sensor detectors fordependent observation casesrdquo IEEE Transactions on AutomaticControl vol 45 no 1 pp 62ndash72 2000

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Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

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DistributedSensor Networks

International Journal of

International Journal of Distributed Sensor Networks 5

where mod(119860 2) is the division remaining of 1198602 and 119906119894

=

mod((119899 minus 1)2(119894minus1)

2) is the 119894th bit of 119899 Hence 119876(119880) =

119876119899 119899 = sum

119873

119894=11199061198942119894minus1

+ 1 Consider two different sets as1198780

= 119899 119876119899

= 0 and 1198781

= 119899 119876119899

= 1 such that1198780

cup 1198781

= 1 2 2119873

then ΩOLDR = 119910119894

119876119899

= 0 119899 isin 1198780

where ΩOLDR defines the region of optimal decision makingfor parallel cooperative cognitive network which leads to thefinal decision of 119867

0 With a given set of 119878

0 the fusion rule

119876(119880) is deterministic and constant and for every 119899 belongingto 1198780 119899th composition will result in a decision on 119867

0 For

a fixed fusion rule the region of final decision is ΩOLDR =

⋃119899isin1198780

Ω119899 where Ω

119899denotes the region of 119899th combination of

119876 as

Ω119899

= 119884 119906119894

= mod (119899 minus 1

2(119894minus1) 2) 119876

= 119876119899

(8)

In the next section the optimization problem for parallellocal decision rules is reduced to solve a set of fixed pointintegral equations that minimizes the Neyman-Pearson costfunction The decision rules are digitized for simplicity andGauss-Seidel algorithm [24] and Golden Section search [25]are applied to find the final solutions

4 OLDR Algorithm with Gauss-Seidel Process

Each distributedH-UELCU119894performs the spectrum sensing

by energy detection to detect the initial PU signal obser-vation 119910

119894 This distributed information from all LCUs is

used by the OLDR algorithm to cooperatively optimize localdecision rules 119892

119894 according to the fix central fusion rule at

H-eNBCCU ANDOR and achieve the final minimized 119875119891

with Gauss-Seidel process Based on the Neyman-Pearsoncriterion the optimum local decision rule is defined tominimize the corresponding cost function 119865

119865 (119866 119876) = 120582 (1 minus 120572) + intΩOLDR

119891 (119884) 119889119884 (9)

where 119876 is the Boolean fusion function 119884 denotes localobservations and 119891(119884) = 119875(119884 | 119867

1) minus 120582119875(119884 | 119867

0) Given

that 120574 = 120582(1 minus 120572) according to the above relations it can beconcluded that

119865 (119866 119876) = 120574 + int119884isinΩOLDR

119891 (119884) 119889119884 = 120574

+ (int119892119894(119910119894)le0

(int⋃119899isin11987801119894

Ω119899119894

minus int⋃119899isin11987802119894

Ω119899119894

) + int119910119894

int⋃119899isin11987802119894

Ω119899119894

)

sdot 119891 (119884) 119889119884

(10)

where Ω119899119894

is Ω119899excluding 119910

119894 11987801119894

11987802119894

are two subsetsof 1198780such that 119878

01119894cup 11987802119894

= 1198780 11987801119894

is a subset of 119899

belonging to 1198780with 119906

119894= 0 119878

01119894= 119899 119876

119899=

0 119906119894

= 0 and similarly 11987802119894

is a subset of 119899 belongingto 1198780with 119906

119894= 1 119878

02119894= 119899 119876

119899= 0 119906

119894= 1

The set of optimum local decision rules that minimizes the119865 function in (10) can be defined as 119866 = (119892

1 119892

119873)

[26]

119892119894(119910119894) = (int

⋃119899isin11987801119894

Ω119899119894

minus int⋃119899isin11987802119894

Ω119899119894

)

sdot119891 (119884) 119889119884

119889119910119894

(11)

where Ω119899119894

= (1199101 119910

119894minus1 119910119894+1

119910119873

) 120601(119892119894 119906119894) le 0

and 120601(119892119894 119906119894) = (12 minus 119906

119894)119892119894 Consequently each set of

optimum local decisions is derived by solving several fixedpoint integral equations as

Γ119876

(119866) =

[[[[[[[[[[[[[[[[[[[[

[

(intcup119899isin119878011

Ω1198991

minus intcup119899isin119878021

Ω1198991

)119891 (119884) 119889119884

1198891199101

(intcup119899isin11987801119894

Ω119899119894

minus intcup119899isin11987802119894

Ω119899119894

)119891 (119884) 119889119884

119889119910119894

(intcup119899isin11987801119873

Ω119899119873

minus intcup119899isin11987802119873

Ω119899119873

)119891 (119884) 119889119884

119889119910119873

]]]]]]]]]]]]]]]]]]]]

]

(12)

Therefore the problem of optimum cooperative sensingis essentially reduced to optimizing a set of 119866 = (119892

1 119892

119873)

that satisfies the integral equations An iterative algorithmbased on Gauss-Seidel process can approximate the solutionof the above equations [26] This method is used for solvinga matrix of linear equations when the number of systemparameters is too high to find a solution by common PLUtechniques The initial requirement is that the diagonalelements of the matrix of equations must be nonzero andconvergence is provided when this matrix is either diagonallydominant or symmetric and positive definite [24] Let usconsider the local decision rule in 119895th iteration stage of thealgorithm as 119866

(119895) and the initial set as 119866(0) Gauss-Seidel

process for optimum local decision rules can be definedas

119866(119895+1)

= Γ119876

(119866(119895)

) forall119895 = 0 1 2 (13)

6 International Journal of Distributed Sensor Networks

where

119892119894

(119895+1)(119910119894)

= (int⋃119899isin11987801119894

Ω119899119894

minus int⋃119899isin11987802119894

Ω119899119894

)

sdot119891 (119884) 119889119884

119889119910119894

(14)

To reduce the computation complexity the discrete vari-ables 119905

119894are extracted from 119910

119894as 119879 = 119905

1 119905

119894 119905

119873 and

(14) can be described as

119892119895+1

119894(119905119894)

= ( sum

⋃119899isin11987801119894

Ω119899119894

minus sum

⋃119899isin11987802119894

Ω119899119894

)119891 (119879) Δ119879

Δ119905119894

(15)

Hence the discrete local decision rules are defined as

119885119894(119905119894) = 119868 (119892

119894(119905119894))

119868 (119909) = 0 119909 le 0

1 119909 gt 0

(16)

Accordingly the cost function 119865 is approximated as

119865 (119885 119876) = 120574

+ sum

119899isin1198780

( sum

11990511198851=1199061

sum

119905119894119885119894=119906119894

sum

119905119873119885119873=119906119873

119891 (119879) Δ119879)

(17)

Therefore

119892119895+1

119894(119905119894) = ( sum

119899isin11987801119894

minus sum

119899isin11987802119894

)

sum

1199051

sdot sdot sdot sum

119905119894minus1

sum

119905119894+1

sdot sdot sdot sum

119905119873

119894minus1

prod

119871=1

(1 minus

1003816100381610038161003816100381610038161003816mod (

119899 minus 1

2(119871minus1) 2) minus 119885

119871

(119895+1)(119905119871)

1003816100381610038161003816100381610038161003816)

119873

prod

119871=119894+1

(1 minus

1003816100381610038161003816100381610038161003816mod (

119899 minus 1

2(119871minus1) 2) minus 119885

119871

(119895)(119905119871)

1003816100381610038161003816100381610038161003816)

119891 (119879) Δ119879

Δ119910119894

(18)

For the simplicity of computations discrete local decisionrules 119885

119894(119905119894) are substituted instead of 119892

119894(119905119894) as both of them

have the same region of decision making Note that the iter-ative process converges when absolute relative approximateerror |(119885

119894

(119895+1)(119905119894) minus 119885

119894

(119895)(119905119894))119885119894

(119895+1)(119905119894)| times 100 ≪ 120576 where

120576 gt 0 is prespecified tolerance parameter For each positivevalue of Δ119905

119894and initial selection of 119885

0

119894 the algorithm is

converged after a certain number of iterations to a set of119885119895

119894that satisfies the convergence condition Figure 4 presents

the flowchart of the developed optimization algorithm basedon the golden section search method for Neyman-Pearsoncriterion Golden section ratio of golden section search isapplied with 120593 = 0618 or symmetrically (1 minus 0618) = 0382

to condense the width of the range in each step [25]

5 Simulation and Discussion

For the performance evaluation of the proposed OLDRalgorithm and compared to the other methods the receiveroperating characteristic (ROC) curve is depicted as a graph of119875119889versus 119875

119891 To depict ROC curves for the OLDR algorithm

in each iteration the values of 119875119889and 119875

119891are provided based

on the OLDR rules As a benchmark the simulation resultsare compared to centralized network and parallel networkwith LRT local decision rule

When normal pdf is assumed for the sensed signalsthe conditional pdf rsquos under both hypotheses 119867

0and

1198671are defined as 119901(119910

1 1199102 119910

119873| 1198670) = 119873(120583

0 1198620)

and 119901(1199101 1199102 119910

119873| 1198671) = 119873(120583

1 1198621) where 119862

0

and 1198621are the covariance matrices under 119867

0and 119867

1

respectively With correlation coefficient minus1 le 120588 le 1the covariance matrix is written as 119862(119910

1 1199102 119910

119873) =

[1205902

1 12058812

12059011205902 120588

11198731205901120590119873

1205881198731

120590119873

1205901 1205881198732

120590119873

1205902 120590

2

119873]

The performance of OLDR algorithm for cooperativespectrum sensing is shown in this section Centralizednetwork (CN) with a fusion center is considered as theoptimum benchmark for the evaluation of the proposedmethod Numerical results are analyzed for both OLDRand LRT local decision rules with ANDOR fusion rulesThen the effect of various correlation coefficients (120588)on ROC curves is investigated with correlated sensedsignals

In the first case a cooperative spectrum sensing with twolocal cognitive users is considered Given that the receivedobservations from PU are random Gaussian signal 119867 sdot 119878

119901

with mean 120583119867sdot119878119901

= 2 and variance 1205902

119867sdot119878119901

= 1 added to 1198991

and 1198992as independent zero mean Gaussian noises such that

1205902

1198991

= 2 and 1205902

1198992

= 1 then the conditional pdf rsquos under bothhypotheses 119867

0and 119867

1 are 119901(119910

1 1199102

| 1198670) = 119873(120583

0 1198620) and

119901(1199101 1199102

| 1198671) = 119873(120583

1 1198621) Therefore 120583

0= [0 0] 119862

0= [2 0

0 1] 1205831

= [2 2] 1198621

= [3 1 1 2]Figure 5 compares the performance of OLDR and LRT

with centralized network As illustrated in this figure OLDRwithAND fusion rule outperforms the other techniques since

International Journal of Distributed Sensor Networks 7

Start

Yes NoYesNo

Yes

No

End

Initializing of 120582(j) and Δ120582 j = 0

P(j)

flt 120572 P

(j)

fgt 120572

P(j)

flt 120572 P

(j)

fgt 120572

120582(j+1) = 120582(j) minus Δ120582j = j + 1 j = j + 1

j = j + 1

120582(j+1) = 120582(j) + Δ120582

120582(j+1) = 120582(j) + Δ120582

Δ120582 =

120593 times Δ120582 if P(j)

fgt 120572

minus120593 times Δ120582 otherwise

Pf(120582(j)) minus 120572 le 120576

P(j)

f(120582(j)) = 1 minusint

ΩOLDR(g1g119873)P(y1 yN |H0)dy1middot middot middot dyN

Figure 4 The proposed optimization algorithm (OLDR)

it is closer to the CN curve Meanwhile OLDR performsbetter than LRT with the same fusion rules for example at119875119891

= 002 OLDR shows 4 improvement in 119875119889compared to

the LRT with the same fusion rulesIn the second case parallel spectrum sensing with two

local cognitive users are considered with correlated receivedsignals as 120583

0= [0 0] 120583

1= [2 2] 119862

0= 1198621

= [1205902

1 12058812059011205902

12058812059011205902 1205902

2] The results of simulations with 120588 = 01 are

presented in Figure 6 which illustrates that the OLDR withAND fusion rule is more proximate to the CN curve andachieves a better performance than OR fusion rule forinstance at 119875

119891= 002 the improvement is about 4

The performance of the same network for various valuesof correlation coefficient (120588) is shown in Figure 7 Accordingto these results the performance is enhanced by the reductionof the correlation coefficient (120588)

Now a network of three local cognitive users with Gaus-sian signal observations is considered with mean 120583

119867sdot119878119901

= 2

and variance 1205902

119867sdot119878119901

= 1 added to zero mean independentnoises with 120590

2

1198991

= 3 12059021198992

= 2 and 1205902

1198993

= 1Thus the covariance

0 002 004 006 008 01 012 014 016 018 0203

04

05

06

07

08

09

1

CN-2 LCUOLDR-AND 2 LCUOLDR-OR 2 LCU

LRT-AND 2 LCULRT-OR 2 CU

Pf

Pd

Figure 5 ROC comparison forGaussian received signal in indepen-dent Gaussian noise with two LCUs

03

04

05

06

07

08

09

1

CN 2 LCUOLDR-AND 2 LCUOLDR-OR 2 LCU

LRT-AND 2 LCULRT-OR 2 LCU

0 002 004 006 008 01 012 014 016 018 02Pf

Pd

Figure 6 ROC comparison for deterministic received signal incorrelated Gaussian noises with two LCUs

matrices under 1198670and 119867

1are described as 119862

0= [3 0 0

0 2 0 0 0 1] and 1198621

= [4 1 1 1 3 1 1 1 2]Figures 8 and 9 show that increasing the number of local

cognitive users enhances the performance of the network ForGaussian received signals with independentGaussian noise at119875119891

= 002 the 119875119889is enhanced about 3 for OLDR with three

LCUs comparing to OLDR with two LCUsFrom these results it is concluded that for a fixed fusion

rule OLDR algorithm shows a superior performance oflocal decision rules to detect primary users compared toLRT method Apparently the probability of primary userdetection is increased with the number of cooperative localcognitive users equipped with spectrum sensing When thesensing channels are correlated results show performancedegradation in higher correlation coefficients

8 International Journal of Distributed Sensor Networks

03

04

05

06

07

08

09

1

0 002 004 006 008 01 012 014 016 018 02Pf

Pd

OLDR-AND 120588 = minus03

OLDR-AND 120588 = minus01

OLDR-AND 120588 = 0

OLDR-AND 120588 = 01

OLDR-AND 120588 = 03

Figure 7 ROC comparison for deterministic received signal incorrelated Gaussian noise with different correlation coefficients (120588)

CN 3 LCUOLDR-AND 3 LCU

OLDR-AND 2 LCUCN 2 LCU

0 002 004 006 008 01 012 014 016 018 02Pf

03

04

05

06

07

08

09

1

Pd

Figure 8 ROC comparison for Gaussian received signal in inde-pendent Gaussian noises with different numbers of LCUs

OLDR method is a low complexity solution for theproblem of (11) which is reduced to optimizing a set of localdecision rules 119866 = (119892

1 119892

119873) that satisfies the integral

equations (12) In addition the computation complexity of(14) has been reduced by considering discrete variables forthe observations 119910

119894 as well as local decision rules 119892

119894 to 119905119894

and 119885119894 respectively For the centralized network there is

no local decision rule and the local decision rule of LRTmethod is defined as Λ(119910

119894) le 120579

119894 where 120579

119894is the threshold

for the 119894th receiver In each iteration of the algorithm withLRTΛ(119884

119894) is calculated for all observations119910

119894 and compared

with threshold 120579119894 For the initial threshold within a range

of 119872 levels the time complexity of each local decision rulecan be written as 119874(119872) According to (18) the local decision

CN 3 LCUOLDR-AND 3 LCU

CN 2 LCUOLDR-AND 2 LCU

03

04

05

06

07

08

09

1

Pd

004 018 02008 01 012 014 016002 0060Pf

Figure 9 ROC comparison for deterministic signal in correlatedGaussian noises with different numbers of LCUs

Number of LCUs1 2 3 4 5 6 7 8

CNOLDRLRT

0

10

20

30

40

50

60

70Ti

me c

ompl

exity

Figure 10 Time complexity comparison of local decision rules

rule of OLDR algorithm 119892119895+1

119894 has to be updated at each

iteration with the time complexity of 119874(1198732) compared to the

other local decision rulesThe time complexity comparison oflocal decision rules for 119872 = 20 is shown in Figure 10 whichdescribes the increase of the calculations number propor-tional to the number of the receivers 119873 However since CNmethod consumes too large bandwidths for sending the datato the fusion center and LRT method assumes independentobservations they cannot be considered as optimum solutionfor cooperative cognitive users with correlated sensed signals

6 Conclusion

In this paper the cooperative spectrum sensing for cognitiveheterogeneous network has been designed with a parallelconfiguration An optimum algorithm for local decision

International Journal of Distributed Sensor Networks 9

rule based on Neyman-Pearson criterion with correlatedobservations from PUs has been proposed This schemebased on a discrete Gauss-Seidel iterative algorithm leads toa low complexity method of finding an optimum solution forLCUrsquos decision rules The performance evaluation shows theefficiency of this algorithm with fixed fusion rules in whichAND rule outperforms the OR fusion rule Furthermorewith lower correlation coefficients a better performance isachieved The experimental measurements and implemen-tation of OLDR algorithm for a distributed heterogeneouscognitive network are a challenging open area for the futurework Meanwhile optimizing the fusion rule simultaneouslywith the local decision rules study of different topologiesof cooperative cognitive networks the performance analysisof multilevel decision rules and shadowing in reportingchannels are among the other suggestions for the futureexploration

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] Federal Communications Commission ldquoSpectrum policy taskforcerdquo Report ET Docket 02-135 2002

[2] O B Akan O B Karli and O Ergul ldquoCognitive radio sensornetworksrdquo IEEE Network vol 23 no 4 pp 34ndash40 2009

[3] J Mitola III and G Q Maguire Jr ldquoCognitive radio makingsoftware radios more personalrdquo IEEE Personal Communica-tions vol 6 no 4 pp 13ndash18 1999

[4] S Haykin ldquoCognitive radio brain-empowered wireless com-municationsrdquo IEEE Journal on Selected Areas in Communica-tions vol 23 no 2 pp 201ndash220 2005

[5] H Arslan and M E Shin ldquoUWB cognitive radiordquo in CognitiveRadio Software Defined Radio and Adaptive Wireless Systemschapter 6 pp 355ndash381 Springer Dordrecht The Netherlands2007

[6] A A El-Saleh M Ismail M A M Ali and A N H AlnuaimyldquoCapacity optimization for local and cooperative spectrumsensing in cognitive radio networksrdquoWorld Academy of ScienceEngineering and Technology vol 4 no 11 pp 679ndash685 2009

[7] H Hosseini N Fisal and S K Syed-Yusof ldquoEnhanced FCMEthresholding for wavelet-based cognitive UWB over fadingchannelsrdquo ETRI Journal vol 33 no 6 pp 961ndash964 2011

[8] I F Akyildiz B F Lo and R Balakrishnan ldquoCooperative spec-trum sensing in cognitive radio networks a surveyrdquo PhysicalCommunication vol 4 no 1 pp 40ndash62 2011

[9] H Du Z XWei YWang andD C Yang ldquoDetection reliabilityand throughput analysis for cooperative spectrum sensing incognitive radio networksrdquo Advanced Materials and EngineeringMaterials vol 457-458 pp 668ndash674 2012

[10] Q-T Vien G B Stewart H Tianfield and H X NguyenldquoEfficient cooperative spectrum sensing for three-hop cognitivewireless relay networksrdquo IET Communications vol 7 no 2 pp119ndash127 2013

[11] X Liu M Jia and X Tan ldquoThreshold optimization of coop-erative spectrum sensing in cognitive radio networksrdquo RadioScience vol 48 no 1 pp 23ndash32 2013

[12] H Chen S Ta and B Sun ldquoCooperative game approach topower allocation for target tracking in distributedMIMO radarsensor networksrdquo IEEE Sensors Journal vol 15 no 10 pp 5423ndash5432 2015

[13] R M Vaghefi and R M Buehrer ldquoCooperative joint synchro-nization and localization in wireless sensor networksrdquo IEEETransactions on Signal Processing vol 63 no 14 pp 3615ndash36272015

[14] S Jaewoo and R Srikant ldquoImproving channel utilization viacooperative spectrum sensing with opportunistic feedback incognitive radio networksrdquo IEEECommunications Letters vol 19no 6 pp 1065ndash1068 2015

[15] M Najimi A Ebrahimzadeh S M H Andargoli and AFallahi ldquoEnergy-efficient sensor selection for cooperative spec-trum sensing in the lack or partial informationrdquo IEEE SensorsJournal vol 15 no 7 pp 3807ndash3818 2015

[16] C G Tsinos and K Berberidis ldquoDecentralized adaptiveeigenvalue-based spectrum sensing for multiantenna cognitiveradio systemsrdquo IEEE Transactions onWireless Communicationsvol 14 no 3 pp 1703ndash1715 2015

[17] G Loganathan G Padmavathi and S Shanmugavel ldquoAn effi-cient adaptive fusion scheme for cooperative spectrum sensingin cognitive radios over fading channelsrdquo in Proceedings ofthe International Conference on Information Communicationand Embedded Systems (ICICES rsquo14) pp 1ndash5 Chennai IndiaFeburary 2014

[18] I Y Hoballah and P K Varshney ldquoDistributed Bayesian signaldetectionrdquo IEEETransactions on InformationTheory vol 35 no5 pp 995ndash1000 1989

[19] W A Hashlamoun and P K Varshney ldquoAn approach tothe design of distributed Bayesian detection structuresrdquo IEEETransactions on Systems Man and Cybernetics vol 21 no 5 pp1206ndash1211 1991

[20] W A Hashlamoun and P K Varshney ldquoFurther results ondistributed Bayesian signal detectionrdquo IEEE Transactions onInformation Theory vol 39 no 5 pp 1660ndash1661 1993

[21] R Viswanathan and P K Varshney ldquoDistributed detectionwithmultiple sensors Part Imdashfundamentalsrdquo Proceedings of theIEEE vol 85 no 1 pp 54ndash63 1997

[22] V R Kanchumarthy R Viswanathan and M MadishettyldquoImpact of channel errors on decentralized detection perfor-mance of wireless sensor networks a study of binary modu-lations Rayleigh-fading and nonfading channels and fusion-combinersrdquo IEEE Transactions on Signal Processing vol 56 no5 pp 1761ndash1769 2008

[23] S M Mishra A Sahai and R W Brodersen ldquoCooperativesensing among cognitive radiosrdquo in Proceedings of the IEEEInternational Conference on Communications (ICC rsquo06) pp1658ndash1663 Istanbul Turkey July 2006

[24] A W Al-Khafaji and J R Tooley Numerical Methods inEngineering Practice Holt Rinehart and Winston New YorkNY USA 1986

[25] X Li J Cao Q Ji and Y Hei ldquoEnergy efficient techniques withsensing time optimization in cognitive radio networksrdquo in Pro-ceedings of the IEEE Wireless Communications and NetworkingConference (WCNC rsquo13) pp 25ndash28 Shanghai China April 2013

[26] Y Zhu R S Blum Z-Q Luo and K M Wong ldquoUnex-pected properties and optimum-distributed sensor detectors fordependent observation casesrdquo IEEE Transactions on AutomaticControl vol 45 no 1 pp 62ndash72 2000

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

6 International Journal of Distributed Sensor Networks

where

119892119894

(119895+1)(119910119894)

= (int⋃119899isin11987801119894

Ω119899119894

minus int⋃119899isin11987802119894

Ω119899119894

)

sdot119891 (119884) 119889119884

119889119910119894

(14)

To reduce the computation complexity the discrete vari-ables 119905

119894are extracted from 119910

119894as 119879 = 119905

1 119905

119894 119905

119873 and

(14) can be described as

119892119895+1

119894(119905119894)

= ( sum

⋃119899isin11987801119894

Ω119899119894

minus sum

⋃119899isin11987802119894

Ω119899119894

)119891 (119879) Δ119879

Δ119905119894

(15)

Hence the discrete local decision rules are defined as

119885119894(119905119894) = 119868 (119892

119894(119905119894))

119868 (119909) = 0 119909 le 0

1 119909 gt 0

(16)

Accordingly the cost function 119865 is approximated as

119865 (119885 119876) = 120574

+ sum

119899isin1198780

( sum

11990511198851=1199061

sum

119905119894119885119894=119906119894

sum

119905119873119885119873=119906119873

119891 (119879) Δ119879)

(17)

Therefore

119892119895+1

119894(119905119894) = ( sum

119899isin11987801119894

minus sum

119899isin11987802119894

)

sum

1199051

sdot sdot sdot sum

119905119894minus1

sum

119905119894+1

sdot sdot sdot sum

119905119873

119894minus1

prod

119871=1

(1 minus

1003816100381610038161003816100381610038161003816mod (

119899 minus 1

2(119871minus1) 2) minus 119885

119871

(119895+1)(119905119871)

1003816100381610038161003816100381610038161003816)

119873

prod

119871=119894+1

(1 minus

1003816100381610038161003816100381610038161003816mod (

119899 minus 1

2(119871minus1) 2) minus 119885

119871

(119895)(119905119871)

1003816100381610038161003816100381610038161003816)

119891 (119879) Δ119879

Δ119910119894

(18)

For the simplicity of computations discrete local decisionrules 119885

119894(119905119894) are substituted instead of 119892

119894(119905119894) as both of them

have the same region of decision making Note that the iter-ative process converges when absolute relative approximateerror |(119885

119894

(119895+1)(119905119894) minus 119885

119894

(119895)(119905119894))119885119894

(119895+1)(119905119894)| times 100 ≪ 120576 where

120576 gt 0 is prespecified tolerance parameter For each positivevalue of Δ119905

119894and initial selection of 119885

0

119894 the algorithm is

converged after a certain number of iterations to a set of119885119895

119894that satisfies the convergence condition Figure 4 presents

the flowchart of the developed optimization algorithm basedon the golden section search method for Neyman-Pearsoncriterion Golden section ratio of golden section search isapplied with 120593 = 0618 or symmetrically (1 minus 0618) = 0382

to condense the width of the range in each step [25]

5 Simulation and Discussion

For the performance evaluation of the proposed OLDRalgorithm and compared to the other methods the receiveroperating characteristic (ROC) curve is depicted as a graph of119875119889versus 119875

119891 To depict ROC curves for the OLDR algorithm

in each iteration the values of 119875119889and 119875

119891are provided based

on the OLDR rules As a benchmark the simulation resultsare compared to centralized network and parallel networkwith LRT local decision rule

When normal pdf is assumed for the sensed signalsthe conditional pdf rsquos under both hypotheses 119867

0and

1198671are defined as 119901(119910

1 1199102 119910

119873| 1198670) = 119873(120583

0 1198620)

and 119901(1199101 1199102 119910

119873| 1198671) = 119873(120583

1 1198621) where 119862

0

and 1198621are the covariance matrices under 119867

0and 119867

1

respectively With correlation coefficient minus1 le 120588 le 1the covariance matrix is written as 119862(119910

1 1199102 119910

119873) =

[1205902

1 12058812

12059011205902 120588

11198731205901120590119873

1205881198731

120590119873

1205901 1205881198732

120590119873

1205902 120590

2

119873]

The performance of OLDR algorithm for cooperativespectrum sensing is shown in this section Centralizednetwork (CN) with a fusion center is considered as theoptimum benchmark for the evaluation of the proposedmethod Numerical results are analyzed for both OLDRand LRT local decision rules with ANDOR fusion rulesThen the effect of various correlation coefficients (120588)on ROC curves is investigated with correlated sensedsignals

In the first case a cooperative spectrum sensing with twolocal cognitive users is considered Given that the receivedobservations from PU are random Gaussian signal 119867 sdot 119878

119901

with mean 120583119867sdot119878119901

= 2 and variance 1205902

119867sdot119878119901

= 1 added to 1198991

and 1198992as independent zero mean Gaussian noises such that

1205902

1198991

= 2 and 1205902

1198992

= 1 then the conditional pdf rsquos under bothhypotheses 119867

0and 119867

1 are 119901(119910

1 1199102

| 1198670) = 119873(120583

0 1198620) and

119901(1199101 1199102

| 1198671) = 119873(120583

1 1198621) Therefore 120583

0= [0 0] 119862

0= [2 0

0 1] 1205831

= [2 2] 1198621

= [3 1 1 2]Figure 5 compares the performance of OLDR and LRT

with centralized network As illustrated in this figure OLDRwithAND fusion rule outperforms the other techniques since

International Journal of Distributed Sensor Networks 7

Start

Yes NoYesNo

Yes

No

End

Initializing of 120582(j) and Δ120582 j = 0

P(j)

flt 120572 P

(j)

fgt 120572

P(j)

flt 120572 P

(j)

fgt 120572

120582(j+1) = 120582(j) minus Δ120582j = j + 1 j = j + 1

j = j + 1

120582(j+1) = 120582(j) + Δ120582

120582(j+1) = 120582(j) + Δ120582

Δ120582 =

120593 times Δ120582 if P(j)

fgt 120572

minus120593 times Δ120582 otherwise

Pf(120582(j)) minus 120572 le 120576

P(j)

f(120582(j)) = 1 minusint

ΩOLDR(g1g119873)P(y1 yN |H0)dy1middot middot middot dyN

Figure 4 The proposed optimization algorithm (OLDR)

it is closer to the CN curve Meanwhile OLDR performsbetter than LRT with the same fusion rules for example at119875119891

= 002 OLDR shows 4 improvement in 119875119889compared to

the LRT with the same fusion rulesIn the second case parallel spectrum sensing with two

local cognitive users are considered with correlated receivedsignals as 120583

0= [0 0] 120583

1= [2 2] 119862

0= 1198621

= [1205902

1 12058812059011205902

12058812059011205902 1205902

2] The results of simulations with 120588 = 01 are

presented in Figure 6 which illustrates that the OLDR withAND fusion rule is more proximate to the CN curve andachieves a better performance than OR fusion rule forinstance at 119875

119891= 002 the improvement is about 4

The performance of the same network for various valuesof correlation coefficient (120588) is shown in Figure 7 Accordingto these results the performance is enhanced by the reductionof the correlation coefficient (120588)

Now a network of three local cognitive users with Gaus-sian signal observations is considered with mean 120583

119867sdot119878119901

= 2

and variance 1205902

119867sdot119878119901

= 1 added to zero mean independentnoises with 120590

2

1198991

= 3 12059021198992

= 2 and 1205902

1198993

= 1Thus the covariance

0 002 004 006 008 01 012 014 016 018 0203

04

05

06

07

08

09

1

CN-2 LCUOLDR-AND 2 LCUOLDR-OR 2 LCU

LRT-AND 2 LCULRT-OR 2 CU

Pf

Pd

Figure 5 ROC comparison forGaussian received signal in indepen-dent Gaussian noise with two LCUs

03

04

05

06

07

08

09

1

CN 2 LCUOLDR-AND 2 LCUOLDR-OR 2 LCU

LRT-AND 2 LCULRT-OR 2 LCU

0 002 004 006 008 01 012 014 016 018 02Pf

Pd

Figure 6 ROC comparison for deterministic received signal incorrelated Gaussian noises with two LCUs

matrices under 1198670and 119867

1are described as 119862

0= [3 0 0

0 2 0 0 0 1] and 1198621

= [4 1 1 1 3 1 1 1 2]Figures 8 and 9 show that increasing the number of local

cognitive users enhances the performance of the network ForGaussian received signals with independentGaussian noise at119875119891

= 002 the 119875119889is enhanced about 3 for OLDR with three

LCUs comparing to OLDR with two LCUsFrom these results it is concluded that for a fixed fusion

rule OLDR algorithm shows a superior performance oflocal decision rules to detect primary users compared toLRT method Apparently the probability of primary userdetection is increased with the number of cooperative localcognitive users equipped with spectrum sensing When thesensing channels are correlated results show performancedegradation in higher correlation coefficients

8 International Journal of Distributed Sensor Networks

03

04

05

06

07

08

09

1

0 002 004 006 008 01 012 014 016 018 02Pf

Pd

OLDR-AND 120588 = minus03

OLDR-AND 120588 = minus01

OLDR-AND 120588 = 0

OLDR-AND 120588 = 01

OLDR-AND 120588 = 03

Figure 7 ROC comparison for deterministic received signal incorrelated Gaussian noise with different correlation coefficients (120588)

CN 3 LCUOLDR-AND 3 LCU

OLDR-AND 2 LCUCN 2 LCU

0 002 004 006 008 01 012 014 016 018 02Pf

03

04

05

06

07

08

09

1

Pd

Figure 8 ROC comparison for Gaussian received signal in inde-pendent Gaussian noises with different numbers of LCUs

OLDR method is a low complexity solution for theproblem of (11) which is reduced to optimizing a set of localdecision rules 119866 = (119892

1 119892

119873) that satisfies the integral

equations (12) In addition the computation complexity of(14) has been reduced by considering discrete variables forthe observations 119910

119894 as well as local decision rules 119892

119894 to 119905119894

and 119885119894 respectively For the centralized network there is

no local decision rule and the local decision rule of LRTmethod is defined as Λ(119910

119894) le 120579

119894 where 120579

119894is the threshold

for the 119894th receiver In each iteration of the algorithm withLRTΛ(119884

119894) is calculated for all observations119910

119894 and compared

with threshold 120579119894 For the initial threshold within a range

of 119872 levels the time complexity of each local decision rulecan be written as 119874(119872) According to (18) the local decision

CN 3 LCUOLDR-AND 3 LCU

CN 2 LCUOLDR-AND 2 LCU

03

04

05

06

07

08

09

1

Pd

004 018 02008 01 012 014 016002 0060Pf

Figure 9 ROC comparison for deterministic signal in correlatedGaussian noises with different numbers of LCUs

Number of LCUs1 2 3 4 5 6 7 8

CNOLDRLRT

0

10

20

30

40

50

60

70Ti

me c

ompl

exity

Figure 10 Time complexity comparison of local decision rules

rule of OLDR algorithm 119892119895+1

119894 has to be updated at each

iteration with the time complexity of 119874(1198732) compared to the

other local decision rulesThe time complexity comparison oflocal decision rules for 119872 = 20 is shown in Figure 10 whichdescribes the increase of the calculations number propor-tional to the number of the receivers 119873 However since CNmethod consumes too large bandwidths for sending the datato the fusion center and LRT method assumes independentobservations they cannot be considered as optimum solutionfor cooperative cognitive users with correlated sensed signals

6 Conclusion

In this paper the cooperative spectrum sensing for cognitiveheterogeneous network has been designed with a parallelconfiguration An optimum algorithm for local decision

International Journal of Distributed Sensor Networks 9

rule based on Neyman-Pearson criterion with correlatedobservations from PUs has been proposed This schemebased on a discrete Gauss-Seidel iterative algorithm leads toa low complexity method of finding an optimum solution forLCUrsquos decision rules The performance evaluation shows theefficiency of this algorithm with fixed fusion rules in whichAND rule outperforms the OR fusion rule Furthermorewith lower correlation coefficients a better performance isachieved The experimental measurements and implemen-tation of OLDR algorithm for a distributed heterogeneouscognitive network are a challenging open area for the futurework Meanwhile optimizing the fusion rule simultaneouslywith the local decision rules study of different topologiesof cooperative cognitive networks the performance analysisof multilevel decision rules and shadowing in reportingchannels are among the other suggestions for the futureexploration

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] Federal Communications Commission ldquoSpectrum policy taskforcerdquo Report ET Docket 02-135 2002

[2] O B Akan O B Karli and O Ergul ldquoCognitive radio sensornetworksrdquo IEEE Network vol 23 no 4 pp 34ndash40 2009

[3] J Mitola III and G Q Maguire Jr ldquoCognitive radio makingsoftware radios more personalrdquo IEEE Personal Communica-tions vol 6 no 4 pp 13ndash18 1999

[4] S Haykin ldquoCognitive radio brain-empowered wireless com-municationsrdquo IEEE Journal on Selected Areas in Communica-tions vol 23 no 2 pp 201ndash220 2005

[5] H Arslan and M E Shin ldquoUWB cognitive radiordquo in CognitiveRadio Software Defined Radio and Adaptive Wireless Systemschapter 6 pp 355ndash381 Springer Dordrecht The Netherlands2007

[6] A A El-Saleh M Ismail M A M Ali and A N H AlnuaimyldquoCapacity optimization for local and cooperative spectrumsensing in cognitive radio networksrdquoWorld Academy of ScienceEngineering and Technology vol 4 no 11 pp 679ndash685 2009

[7] H Hosseini N Fisal and S K Syed-Yusof ldquoEnhanced FCMEthresholding for wavelet-based cognitive UWB over fadingchannelsrdquo ETRI Journal vol 33 no 6 pp 961ndash964 2011

[8] I F Akyildiz B F Lo and R Balakrishnan ldquoCooperative spec-trum sensing in cognitive radio networks a surveyrdquo PhysicalCommunication vol 4 no 1 pp 40ndash62 2011

[9] H Du Z XWei YWang andD C Yang ldquoDetection reliabilityand throughput analysis for cooperative spectrum sensing incognitive radio networksrdquo Advanced Materials and EngineeringMaterials vol 457-458 pp 668ndash674 2012

[10] Q-T Vien G B Stewart H Tianfield and H X NguyenldquoEfficient cooperative spectrum sensing for three-hop cognitivewireless relay networksrdquo IET Communications vol 7 no 2 pp119ndash127 2013

[11] X Liu M Jia and X Tan ldquoThreshold optimization of coop-erative spectrum sensing in cognitive radio networksrdquo RadioScience vol 48 no 1 pp 23ndash32 2013

[12] H Chen S Ta and B Sun ldquoCooperative game approach topower allocation for target tracking in distributedMIMO radarsensor networksrdquo IEEE Sensors Journal vol 15 no 10 pp 5423ndash5432 2015

[13] R M Vaghefi and R M Buehrer ldquoCooperative joint synchro-nization and localization in wireless sensor networksrdquo IEEETransactions on Signal Processing vol 63 no 14 pp 3615ndash36272015

[14] S Jaewoo and R Srikant ldquoImproving channel utilization viacooperative spectrum sensing with opportunistic feedback incognitive radio networksrdquo IEEECommunications Letters vol 19no 6 pp 1065ndash1068 2015

[15] M Najimi A Ebrahimzadeh S M H Andargoli and AFallahi ldquoEnergy-efficient sensor selection for cooperative spec-trum sensing in the lack or partial informationrdquo IEEE SensorsJournal vol 15 no 7 pp 3807ndash3818 2015

[16] C G Tsinos and K Berberidis ldquoDecentralized adaptiveeigenvalue-based spectrum sensing for multiantenna cognitiveradio systemsrdquo IEEE Transactions onWireless Communicationsvol 14 no 3 pp 1703ndash1715 2015

[17] G Loganathan G Padmavathi and S Shanmugavel ldquoAn effi-cient adaptive fusion scheme for cooperative spectrum sensingin cognitive radios over fading channelsrdquo in Proceedings ofthe International Conference on Information Communicationand Embedded Systems (ICICES rsquo14) pp 1ndash5 Chennai IndiaFeburary 2014

[18] I Y Hoballah and P K Varshney ldquoDistributed Bayesian signaldetectionrdquo IEEETransactions on InformationTheory vol 35 no5 pp 995ndash1000 1989

[19] W A Hashlamoun and P K Varshney ldquoAn approach tothe design of distributed Bayesian detection structuresrdquo IEEETransactions on Systems Man and Cybernetics vol 21 no 5 pp1206ndash1211 1991

[20] W A Hashlamoun and P K Varshney ldquoFurther results ondistributed Bayesian signal detectionrdquo IEEE Transactions onInformation Theory vol 39 no 5 pp 1660ndash1661 1993

[21] R Viswanathan and P K Varshney ldquoDistributed detectionwithmultiple sensors Part Imdashfundamentalsrdquo Proceedings of theIEEE vol 85 no 1 pp 54ndash63 1997

[22] V R Kanchumarthy R Viswanathan and M MadishettyldquoImpact of channel errors on decentralized detection perfor-mance of wireless sensor networks a study of binary modu-lations Rayleigh-fading and nonfading channels and fusion-combinersrdquo IEEE Transactions on Signal Processing vol 56 no5 pp 1761ndash1769 2008

[23] S M Mishra A Sahai and R W Brodersen ldquoCooperativesensing among cognitive radiosrdquo in Proceedings of the IEEEInternational Conference on Communications (ICC rsquo06) pp1658ndash1663 Istanbul Turkey July 2006

[24] A W Al-Khafaji and J R Tooley Numerical Methods inEngineering Practice Holt Rinehart and Winston New YorkNY USA 1986

[25] X Li J Cao Q Ji and Y Hei ldquoEnergy efficient techniques withsensing time optimization in cognitive radio networksrdquo in Pro-ceedings of the IEEE Wireless Communications and NetworkingConference (WCNC rsquo13) pp 25ndash28 Shanghai China April 2013

[26] Y Zhu R S Blum Z-Q Luo and K M Wong ldquoUnex-pected properties and optimum-distributed sensor detectors fordependent observation casesrdquo IEEE Transactions on AutomaticControl vol 45 no 1 pp 62ndash72 2000

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

International Journal of Distributed Sensor Networks 7

Start

Yes NoYesNo

Yes

No

End

Initializing of 120582(j) and Δ120582 j = 0

P(j)

flt 120572 P

(j)

fgt 120572

P(j)

flt 120572 P

(j)

fgt 120572

120582(j+1) = 120582(j) minus Δ120582j = j + 1 j = j + 1

j = j + 1

120582(j+1) = 120582(j) + Δ120582

120582(j+1) = 120582(j) + Δ120582

Δ120582 =

120593 times Δ120582 if P(j)

fgt 120572

minus120593 times Δ120582 otherwise

Pf(120582(j)) minus 120572 le 120576

P(j)

f(120582(j)) = 1 minusint

ΩOLDR(g1g119873)P(y1 yN |H0)dy1middot middot middot dyN

Figure 4 The proposed optimization algorithm (OLDR)

it is closer to the CN curve Meanwhile OLDR performsbetter than LRT with the same fusion rules for example at119875119891

= 002 OLDR shows 4 improvement in 119875119889compared to

the LRT with the same fusion rulesIn the second case parallel spectrum sensing with two

local cognitive users are considered with correlated receivedsignals as 120583

0= [0 0] 120583

1= [2 2] 119862

0= 1198621

= [1205902

1 12058812059011205902

12058812059011205902 1205902

2] The results of simulations with 120588 = 01 are

presented in Figure 6 which illustrates that the OLDR withAND fusion rule is more proximate to the CN curve andachieves a better performance than OR fusion rule forinstance at 119875

119891= 002 the improvement is about 4

The performance of the same network for various valuesof correlation coefficient (120588) is shown in Figure 7 Accordingto these results the performance is enhanced by the reductionof the correlation coefficient (120588)

Now a network of three local cognitive users with Gaus-sian signal observations is considered with mean 120583

119867sdot119878119901

= 2

and variance 1205902

119867sdot119878119901

= 1 added to zero mean independentnoises with 120590

2

1198991

= 3 12059021198992

= 2 and 1205902

1198993

= 1Thus the covariance

0 002 004 006 008 01 012 014 016 018 0203

04

05

06

07

08

09

1

CN-2 LCUOLDR-AND 2 LCUOLDR-OR 2 LCU

LRT-AND 2 LCULRT-OR 2 CU

Pf

Pd

Figure 5 ROC comparison forGaussian received signal in indepen-dent Gaussian noise with two LCUs

03

04

05

06

07

08

09

1

CN 2 LCUOLDR-AND 2 LCUOLDR-OR 2 LCU

LRT-AND 2 LCULRT-OR 2 LCU

0 002 004 006 008 01 012 014 016 018 02Pf

Pd

Figure 6 ROC comparison for deterministic received signal incorrelated Gaussian noises with two LCUs

matrices under 1198670and 119867

1are described as 119862

0= [3 0 0

0 2 0 0 0 1] and 1198621

= [4 1 1 1 3 1 1 1 2]Figures 8 and 9 show that increasing the number of local

cognitive users enhances the performance of the network ForGaussian received signals with independentGaussian noise at119875119891

= 002 the 119875119889is enhanced about 3 for OLDR with three

LCUs comparing to OLDR with two LCUsFrom these results it is concluded that for a fixed fusion

rule OLDR algorithm shows a superior performance oflocal decision rules to detect primary users compared toLRT method Apparently the probability of primary userdetection is increased with the number of cooperative localcognitive users equipped with spectrum sensing When thesensing channels are correlated results show performancedegradation in higher correlation coefficients

8 International Journal of Distributed Sensor Networks

03

04

05

06

07

08

09

1

0 002 004 006 008 01 012 014 016 018 02Pf

Pd

OLDR-AND 120588 = minus03

OLDR-AND 120588 = minus01

OLDR-AND 120588 = 0

OLDR-AND 120588 = 01

OLDR-AND 120588 = 03

Figure 7 ROC comparison for deterministic received signal incorrelated Gaussian noise with different correlation coefficients (120588)

CN 3 LCUOLDR-AND 3 LCU

OLDR-AND 2 LCUCN 2 LCU

0 002 004 006 008 01 012 014 016 018 02Pf

03

04

05

06

07

08

09

1

Pd

Figure 8 ROC comparison for Gaussian received signal in inde-pendent Gaussian noises with different numbers of LCUs

OLDR method is a low complexity solution for theproblem of (11) which is reduced to optimizing a set of localdecision rules 119866 = (119892

1 119892

119873) that satisfies the integral

equations (12) In addition the computation complexity of(14) has been reduced by considering discrete variables forthe observations 119910

119894 as well as local decision rules 119892

119894 to 119905119894

and 119885119894 respectively For the centralized network there is

no local decision rule and the local decision rule of LRTmethod is defined as Λ(119910

119894) le 120579

119894 where 120579

119894is the threshold

for the 119894th receiver In each iteration of the algorithm withLRTΛ(119884

119894) is calculated for all observations119910

119894 and compared

with threshold 120579119894 For the initial threshold within a range

of 119872 levels the time complexity of each local decision rulecan be written as 119874(119872) According to (18) the local decision

CN 3 LCUOLDR-AND 3 LCU

CN 2 LCUOLDR-AND 2 LCU

03

04

05

06

07

08

09

1

Pd

004 018 02008 01 012 014 016002 0060Pf

Figure 9 ROC comparison for deterministic signal in correlatedGaussian noises with different numbers of LCUs

Number of LCUs1 2 3 4 5 6 7 8

CNOLDRLRT

0

10

20

30

40

50

60

70Ti

me c

ompl

exity

Figure 10 Time complexity comparison of local decision rules

rule of OLDR algorithm 119892119895+1

119894 has to be updated at each

iteration with the time complexity of 119874(1198732) compared to the

other local decision rulesThe time complexity comparison oflocal decision rules for 119872 = 20 is shown in Figure 10 whichdescribes the increase of the calculations number propor-tional to the number of the receivers 119873 However since CNmethod consumes too large bandwidths for sending the datato the fusion center and LRT method assumes independentobservations they cannot be considered as optimum solutionfor cooperative cognitive users with correlated sensed signals

6 Conclusion

In this paper the cooperative spectrum sensing for cognitiveheterogeneous network has been designed with a parallelconfiguration An optimum algorithm for local decision

International Journal of Distributed Sensor Networks 9

rule based on Neyman-Pearson criterion with correlatedobservations from PUs has been proposed This schemebased on a discrete Gauss-Seidel iterative algorithm leads toa low complexity method of finding an optimum solution forLCUrsquos decision rules The performance evaluation shows theefficiency of this algorithm with fixed fusion rules in whichAND rule outperforms the OR fusion rule Furthermorewith lower correlation coefficients a better performance isachieved The experimental measurements and implemen-tation of OLDR algorithm for a distributed heterogeneouscognitive network are a challenging open area for the futurework Meanwhile optimizing the fusion rule simultaneouslywith the local decision rules study of different topologiesof cooperative cognitive networks the performance analysisof multilevel decision rules and shadowing in reportingchannels are among the other suggestions for the futureexploration

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] Federal Communications Commission ldquoSpectrum policy taskforcerdquo Report ET Docket 02-135 2002

[2] O B Akan O B Karli and O Ergul ldquoCognitive radio sensornetworksrdquo IEEE Network vol 23 no 4 pp 34ndash40 2009

[3] J Mitola III and G Q Maguire Jr ldquoCognitive radio makingsoftware radios more personalrdquo IEEE Personal Communica-tions vol 6 no 4 pp 13ndash18 1999

[4] S Haykin ldquoCognitive radio brain-empowered wireless com-municationsrdquo IEEE Journal on Selected Areas in Communica-tions vol 23 no 2 pp 201ndash220 2005

[5] H Arslan and M E Shin ldquoUWB cognitive radiordquo in CognitiveRadio Software Defined Radio and Adaptive Wireless Systemschapter 6 pp 355ndash381 Springer Dordrecht The Netherlands2007

[6] A A El-Saleh M Ismail M A M Ali and A N H AlnuaimyldquoCapacity optimization for local and cooperative spectrumsensing in cognitive radio networksrdquoWorld Academy of ScienceEngineering and Technology vol 4 no 11 pp 679ndash685 2009

[7] H Hosseini N Fisal and S K Syed-Yusof ldquoEnhanced FCMEthresholding for wavelet-based cognitive UWB over fadingchannelsrdquo ETRI Journal vol 33 no 6 pp 961ndash964 2011

[8] I F Akyildiz B F Lo and R Balakrishnan ldquoCooperative spec-trum sensing in cognitive radio networks a surveyrdquo PhysicalCommunication vol 4 no 1 pp 40ndash62 2011

[9] H Du Z XWei YWang andD C Yang ldquoDetection reliabilityand throughput analysis for cooperative spectrum sensing incognitive radio networksrdquo Advanced Materials and EngineeringMaterials vol 457-458 pp 668ndash674 2012

[10] Q-T Vien G B Stewart H Tianfield and H X NguyenldquoEfficient cooperative spectrum sensing for three-hop cognitivewireless relay networksrdquo IET Communications vol 7 no 2 pp119ndash127 2013

[11] X Liu M Jia and X Tan ldquoThreshold optimization of coop-erative spectrum sensing in cognitive radio networksrdquo RadioScience vol 48 no 1 pp 23ndash32 2013

[12] H Chen S Ta and B Sun ldquoCooperative game approach topower allocation for target tracking in distributedMIMO radarsensor networksrdquo IEEE Sensors Journal vol 15 no 10 pp 5423ndash5432 2015

[13] R M Vaghefi and R M Buehrer ldquoCooperative joint synchro-nization and localization in wireless sensor networksrdquo IEEETransactions on Signal Processing vol 63 no 14 pp 3615ndash36272015

[14] S Jaewoo and R Srikant ldquoImproving channel utilization viacooperative spectrum sensing with opportunistic feedback incognitive radio networksrdquo IEEECommunications Letters vol 19no 6 pp 1065ndash1068 2015

[15] M Najimi A Ebrahimzadeh S M H Andargoli and AFallahi ldquoEnergy-efficient sensor selection for cooperative spec-trum sensing in the lack or partial informationrdquo IEEE SensorsJournal vol 15 no 7 pp 3807ndash3818 2015

[16] C G Tsinos and K Berberidis ldquoDecentralized adaptiveeigenvalue-based spectrum sensing for multiantenna cognitiveradio systemsrdquo IEEE Transactions onWireless Communicationsvol 14 no 3 pp 1703ndash1715 2015

[17] G Loganathan G Padmavathi and S Shanmugavel ldquoAn effi-cient adaptive fusion scheme for cooperative spectrum sensingin cognitive radios over fading channelsrdquo in Proceedings ofthe International Conference on Information Communicationand Embedded Systems (ICICES rsquo14) pp 1ndash5 Chennai IndiaFeburary 2014

[18] I Y Hoballah and P K Varshney ldquoDistributed Bayesian signaldetectionrdquo IEEETransactions on InformationTheory vol 35 no5 pp 995ndash1000 1989

[19] W A Hashlamoun and P K Varshney ldquoAn approach tothe design of distributed Bayesian detection structuresrdquo IEEETransactions on Systems Man and Cybernetics vol 21 no 5 pp1206ndash1211 1991

[20] W A Hashlamoun and P K Varshney ldquoFurther results ondistributed Bayesian signal detectionrdquo IEEE Transactions onInformation Theory vol 39 no 5 pp 1660ndash1661 1993

[21] R Viswanathan and P K Varshney ldquoDistributed detectionwithmultiple sensors Part Imdashfundamentalsrdquo Proceedings of theIEEE vol 85 no 1 pp 54ndash63 1997

[22] V R Kanchumarthy R Viswanathan and M MadishettyldquoImpact of channel errors on decentralized detection perfor-mance of wireless sensor networks a study of binary modu-lations Rayleigh-fading and nonfading channels and fusion-combinersrdquo IEEE Transactions on Signal Processing vol 56 no5 pp 1761ndash1769 2008

[23] S M Mishra A Sahai and R W Brodersen ldquoCooperativesensing among cognitive radiosrdquo in Proceedings of the IEEEInternational Conference on Communications (ICC rsquo06) pp1658ndash1663 Istanbul Turkey July 2006

[24] A W Al-Khafaji and J R Tooley Numerical Methods inEngineering Practice Holt Rinehart and Winston New YorkNY USA 1986

[25] X Li J Cao Q Ji and Y Hei ldquoEnergy efficient techniques withsensing time optimization in cognitive radio networksrdquo in Pro-ceedings of the IEEE Wireless Communications and NetworkingConference (WCNC rsquo13) pp 25ndash28 Shanghai China April 2013

[26] Y Zhu R S Blum Z-Q Luo and K M Wong ldquoUnex-pected properties and optimum-distributed sensor detectors fordependent observation casesrdquo IEEE Transactions on AutomaticControl vol 45 no 1 pp 62ndash72 2000

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

8 International Journal of Distributed Sensor Networks

03

04

05

06

07

08

09

1

0 002 004 006 008 01 012 014 016 018 02Pf

Pd

OLDR-AND 120588 = minus03

OLDR-AND 120588 = minus01

OLDR-AND 120588 = 0

OLDR-AND 120588 = 01

OLDR-AND 120588 = 03

Figure 7 ROC comparison for deterministic received signal incorrelated Gaussian noise with different correlation coefficients (120588)

CN 3 LCUOLDR-AND 3 LCU

OLDR-AND 2 LCUCN 2 LCU

0 002 004 006 008 01 012 014 016 018 02Pf

03

04

05

06

07

08

09

1

Pd

Figure 8 ROC comparison for Gaussian received signal in inde-pendent Gaussian noises with different numbers of LCUs

OLDR method is a low complexity solution for theproblem of (11) which is reduced to optimizing a set of localdecision rules 119866 = (119892

1 119892

119873) that satisfies the integral

equations (12) In addition the computation complexity of(14) has been reduced by considering discrete variables forthe observations 119910

119894 as well as local decision rules 119892

119894 to 119905119894

and 119885119894 respectively For the centralized network there is

no local decision rule and the local decision rule of LRTmethod is defined as Λ(119910

119894) le 120579

119894 where 120579

119894is the threshold

for the 119894th receiver In each iteration of the algorithm withLRTΛ(119884

119894) is calculated for all observations119910

119894 and compared

with threshold 120579119894 For the initial threshold within a range

of 119872 levels the time complexity of each local decision rulecan be written as 119874(119872) According to (18) the local decision

CN 3 LCUOLDR-AND 3 LCU

CN 2 LCUOLDR-AND 2 LCU

03

04

05

06

07

08

09

1

Pd

004 018 02008 01 012 014 016002 0060Pf

Figure 9 ROC comparison for deterministic signal in correlatedGaussian noises with different numbers of LCUs

Number of LCUs1 2 3 4 5 6 7 8

CNOLDRLRT

0

10

20

30

40

50

60

70Ti

me c

ompl

exity

Figure 10 Time complexity comparison of local decision rules

rule of OLDR algorithm 119892119895+1

119894 has to be updated at each

iteration with the time complexity of 119874(1198732) compared to the

other local decision rulesThe time complexity comparison oflocal decision rules for 119872 = 20 is shown in Figure 10 whichdescribes the increase of the calculations number propor-tional to the number of the receivers 119873 However since CNmethod consumes too large bandwidths for sending the datato the fusion center and LRT method assumes independentobservations they cannot be considered as optimum solutionfor cooperative cognitive users with correlated sensed signals

6 Conclusion

In this paper the cooperative spectrum sensing for cognitiveheterogeneous network has been designed with a parallelconfiguration An optimum algorithm for local decision

International Journal of Distributed Sensor Networks 9

rule based on Neyman-Pearson criterion with correlatedobservations from PUs has been proposed This schemebased on a discrete Gauss-Seidel iterative algorithm leads toa low complexity method of finding an optimum solution forLCUrsquos decision rules The performance evaluation shows theefficiency of this algorithm with fixed fusion rules in whichAND rule outperforms the OR fusion rule Furthermorewith lower correlation coefficients a better performance isachieved The experimental measurements and implemen-tation of OLDR algorithm for a distributed heterogeneouscognitive network are a challenging open area for the futurework Meanwhile optimizing the fusion rule simultaneouslywith the local decision rules study of different topologiesof cooperative cognitive networks the performance analysisof multilevel decision rules and shadowing in reportingchannels are among the other suggestions for the futureexploration

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] Federal Communications Commission ldquoSpectrum policy taskforcerdquo Report ET Docket 02-135 2002

[2] O B Akan O B Karli and O Ergul ldquoCognitive radio sensornetworksrdquo IEEE Network vol 23 no 4 pp 34ndash40 2009

[3] J Mitola III and G Q Maguire Jr ldquoCognitive radio makingsoftware radios more personalrdquo IEEE Personal Communica-tions vol 6 no 4 pp 13ndash18 1999

[4] S Haykin ldquoCognitive radio brain-empowered wireless com-municationsrdquo IEEE Journal on Selected Areas in Communica-tions vol 23 no 2 pp 201ndash220 2005

[5] H Arslan and M E Shin ldquoUWB cognitive radiordquo in CognitiveRadio Software Defined Radio and Adaptive Wireless Systemschapter 6 pp 355ndash381 Springer Dordrecht The Netherlands2007

[6] A A El-Saleh M Ismail M A M Ali and A N H AlnuaimyldquoCapacity optimization for local and cooperative spectrumsensing in cognitive radio networksrdquoWorld Academy of ScienceEngineering and Technology vol 4 no 11 pp 679ndash685 2009

[7] H Hosseini N Fisal and S K Syed-Yusof ldquoEnhanced FCMEthresholding for wavelet-based cognitive UWB over fadingchannelsrdquo ETRI Journal vol 33 no 6 pp 961ndash964 2011

[8] I F Akyildiz B F Lo and R Balakrishnan ldquoCooperative spec-trum sensing in cognitive radio networks a surveyrdquo PhysicalCommunication vol 4 no 1 pp 40ndash62 2011

[9] H Du Z XWei YWang andD C Yang ldquoDetection reliabilityand throughput analysis for cooperative spectrum sensing incognitive radio networksrdquo Advanced Materials and EngineeringMaterials vol 457-458 pp 668ndash674 2012

[10] Q-T Vien G B Stewart H Tianfield and H X NguyenldquoEfficient cooperative spectrum sensing for three-hop cognitivewireless relay networksrdquo IET Communications vol 7 no 2 pp119ndash127 2013

[11] X Liu M Jia and X Tan ldquoThreshold optimization of coop-erative spectrum sensing in cognitive radio networksrdquo RadioScience vol 48 no 1 pp 23ndash32 2013

[12] H Chen S Ta and B Sun ldquoCooperative game approach topower allocation for target tracking in distributedMIMO radarsensor networksrdquo IEEE Sensors Journal vol 15 no 10 pp 5423ndash5432 2015

[13] R M Vaghefi and R M Buehrer ldquoCooperative joint synchro-nization and localization in wireless sensor networksrdquo IEEETransactions on Signal Processing vol 63 no 14 pp 3615ndash36272015

[14] S Jaewoo and R Srikant ldquoImproving channel utilization viacooperative spectrum sensing with opportunistic feedback incognitive radio networksrdquo IEEECommunications Letters vol 19no 6 pp 1065ndash1068 2015

[15] M Najimi A Ebrahimzadeh S M H Andargoli and AFallahi ldquoEnergy-efficient sensor selection for cooperative spec-trum sensing in the lack or partial informationrdquo IEEE SensorsJournal vol 15 no 7 pp 3807ndash3818 2015

[16] C G Tsinos and K Berberidis ldquoDecentralized adaptiveeigenvalue-based spectrum sensing for multiantenna cognitiveradio systemsrdquo IEEE Transactions onWireless Communicationsvol 14 no 3 pp 1703ndash1715 2015

[17] G Loganathan G Padmavathi and S Shanmugavel ldquoAn effi-cient adaptive fusion scheme for cooperative spectrum sensingin cognitive radios over fading channelsrdquo in Proceedings ofthe International Conference on Information Communicationand Embedded Systems (ICICES rsquo14) pp 1ndash5 Chennai IndiaFeburary 2014

[18] I Y Hoballah and P K Varshney ldquoDistributed Bayesian signaldetectionrdquo IEEETransactions on InformationTheory vol 35 no5 pp 995ndash1000 1989

[19] W A Hashlamoun and P K Varshney ldquoAn approach tothe design of distributed Bayesian detection structuresrdquo IEEETransactions on Systems Man and Cybernetics vol 21 no 5 pp1206ndash1211 1991

[20] W A Hashlamoun and P K Varshney ldquoFurther results ondistributed Bayesian signal detectionrdquo IEEE Transactions onInformation Theory vol 39 no 5 pp 1660ndash1661 1993

[21] R Viswanathan and P K Varshney ldquoDistributed detectionwithmultiple sensors Part Imdashfundamentalsrdquo Proceedings of theIEEE vol 85 no 1 pp 54ndash63 1997

[22] V R Kanchumarthy R Viswanathan and M MadishettyldquoImpact of channel errors on decentralized detection perfor-mance of wireless sensor networks a study of binary modu-lations Rayleigh-fading and nonfading channels and fusion-combinersrdquo IEEE Transactions on Signal Processing vol 56 no5 pp 1761ndash1769 2008

[23] S M Mishra A Sahai and R W Brodersen ldquoCooperativesensing among cognitive radiosrdquo in Proceedings of the IEEEInternational Conference on Communications (ICC rsquo06) pp1658ndash1663 Istanbul Turkey July 2006

[24] A W Al-Khafaji and J R Tooley Numerical Methods inEngineering Practice Holt Rinehart and Winston New YorkNY USA 1986

[25] X Li J Cao Q Ji and Y Hei ldquoEnergy efficient techniques withsensing time optimization in cognitive radio networksrdquo in Pro-ceedings of the IEEE Wireless Communications and NetworkingConference (WCNC rsquo13) pp 25ndash28 Shanghai China April 2013

[26] Y Zhu R S Blum Z-Q Luo and K M Wong ldquoUnex-pected properties and optimum-distributed sensor detectors fordependent observation casesrdquo IEEE Transactions on AutomaticControl vol 45 no 1 pp 62ndash72 2000

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

International Journal of Distributed Sensor Networks 9

rule based on Neyman-Pearson criterion with correlatedobservations from PUs has been proposed This schemebased on a discrete Gauss-Seidel iterative algorithm leads toa low complexity method of finding an optimum solution forLCUrsquos decision rules The performance evaluation shows theefficiency of this algorithm with fixed fusion rules in whichAND rule outperforms the OR fusion rule Furthermorewith lower correlation coefficients a better performance isachieved The experimental measurements and implemen-tation of OLDR algorithm for a distributed heterogeneouscognitive network are a challenging open area for the futurework Meanwhile optimizing the fusion rule simultaneouslywith the local decision rules study of different topologiesof cooperative cognitive networks the performance analysisof multilevel decision rules and shadowing in reportingchannels are among the other suggestions for the futureexploration

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] Federal Communications Commission ldquoSpectrum policy taskforcerdquo Report ET Docket 02-135 2002

[2] O B Akan O B Karli and O Ergul ldquoCognitive radio sensornetworksrdquo IEEE Network vol 23 no 4 pp 34ndash40 2009

[3] J Mitola III and G Q Maguire Jr ldquoCognitive radio makingsoftware radios more personalrdquo IEEE Personal Communica-tions vol 6 no 4 pp 13ndash18 1999

[4] S Haykin ldquoCognitive radio brain-empowered wireless com-municationsrdquo IEEE Journal on Selected Areas in Communica-tions vol 23 no 2 pp 201ndash220 2005

[5] H Arslan and M E Shin ldquoUWB cognitive radiordquo in CognitiveRadio Software Defined Radio and Adaptive Wireless Systemschapter 6 pp 355ndash381 Springer Dordrecht The Netherlands2007

[6] A A El-Saleh M Ismail M A M Ali and A N H AlnuaimyldquoCapacity optimization for local and cooperative spectrumsensing in cognitive radio networksrdquoWorld Academy of ScienceEngineering and Technology vol 4 no 11 pp 679ndash685 2009

[7] H Hosseini N Fisal and S K Syed-Yusof ldquoEnhanced FCMEthresholding for wavelet-based cognitive UWB over fadingchannelsrdquo ETRI Journal vol 33 no 6 pp 961ndash964 2011

[8] I F Akyildiz B F Lo and R Balakrishnan ldquoCooperative spec-trum sensing in cognitive radio networks a surveyrdquo PhysicalCommunication vol 4 no 1 pp 40ndash62 2011

[9] H Du Z XWei YWang andD C Yang ldquoDetection reliabilityand throughput analysis for cooperative spectrum sensing incognitive radio networksrdquo Advanced Materials and EngineeringMaterials vol 457-458 pp 668ndash674 2012

[10] Q-T Vien G B Stewart H Tianfield and H X NguyenldquoEfficient cooperative spectrum sensing for three-hop cognitivewireless relay networksrdquo IET Communications vol 7 no 2 pp119ndash127 2013

[11] X Liu M Jia and X Tan ldquoThreshold optimization of coop-erative spectrum sensing in cognitive radio networksrdquo RadioScience vol 48 no 1 pp 23ndash32 2013

[12] H Chen S Ta and B Sun ldquoCooperative game approach topower allocation for target tracking in distributedMIMO radarsensor networksrdquo IEEE Sensors Journal vol 15 no 10 pp 5423ndash5432 2015

[13] R M Vaghefi and R M Buehrer ldquoCooperative joint synchro-nization and localization in wireless sensor networksrdquo IEEETransactions on Signal Processing vol 63 no 14 pp 3615ndash36272015

[14] S Jaewoo and R Srikant ldquoImproving channel utilization viacooperative spectrum sensing with opportunistic feedback incognitive radio networksrdquo IEEECommunications Letters vol 19no 6 pp 1065ndash1068 2015

[15] M Najimi A Ebrahimzadeh S M H Andargoli and AFallahi ldquoEnergy-efficient sensor selection for cooperative spec-trum sensing in the lack or partial informationrdquo IEEE SensorsJournal vol 15 no 7 pp 3807ndash3818 2015

[16] C G Tsinos and K Berberidis ldquoDecentralized adaptiveeigenvalue-based spectrum sensing for multiantenna cognitiveradio systemsrdquo IEEE Transactions onWireless Communicationsvol 14 no 3 pp 1703ndash1715 2015

[17] G Loganathan G Padmavathi and S Shanmugavel ldquoAn effi-cient adaptive fusion scheme for cooperative spectrum sensingin cognitive radios over fading channelsrdquo in Proceedings ofthe International Conference on Information Communicationand Embedded Systems (ICICES rsquo14) pp 1ndash5 Chennai IndiaFeburary 2014

[18] I Y Hoballah and P K Varshney ldquoDistributed Bayesian signaldetectionrdquo IEEETransactions on InformationTheory vol 35 no5 pp 995ndash1000 1989

[19] W A Hashlamoun and P K Varshney ldquoAn approach tothe design of distributed Bayesian detection structuresrdquo IEEETransactions on Systems Man and Cybernetics vol 21 no 5 pp1206ndash1211 1991

[20] W A Hashlamoun and P K Varshney ldquoFurther results ondistributed Bayesian signal detectionrdquo IEEE Transactions onInformation Theory vol 39 no 5 pp 1660ndash1661 1993

[21] R Viswanathan and P K Varshney ldquoDistributed detectionwithmultiple sensors Part Imdashfundamentalsrdquo Proceedings of theIEEE vol 85 no 1 pp 54ndash63 1997

[22] V R Kanchumarthy R Viswanathan and M MadishettyldquoImpact of channel errors on decentralized detection perfor-mance of wireless sensor networks a study of binary modu-lations Rayleigh-fading and nonfading channels and fusion-combinersrdquo IEEE Transactions on Signal Processing vol 56 no5 pp 1761ndash1769 2008

[23] S M Mishra A Sahai and R W Brodersen ldquoCooperativesensing among cognitive radiosrdquo in Proceedings of the IEEEInternational Conference on Communications (ICC rsquo06) pp1658ndash1663 Istanbul Turkey July 2006

[24] A W Al-Khafaji and J R Tooley Numerical Methods inEngineering Practice Holt Rinehart and Winston New YorkNY USA 1986

[25] X Li J Cao Q Ji and Y Hei ldquoEnergy efficient techniques withsensing time optimization in cognitive radio networksrdquo in Pro-ceedings of the IEEE Wireless Communications and NetworkingConference (WCNC rsquo13) pp 25ndash28 Shanghai China April 2013

[26] Y Zhu R S Blum Z-Q Luo and K M Wong ldquoUnex-pected properties and optimum-distributed sensor detectors fordependent observation casesrdquo IEEE Transactions on AutomaticControl vol 45 no 1 pp 62ndash72 2000

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of