Detection and Estimation of multiple far-field primary users using sensor array in Cognitive Radio Networks

7/30/2019 Detection and Estimation of multiple far-field primary users using sensor array in Cognitive Radio Networks

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Detection and Estimation of multiple far-fieldprimary users using sensor array in Cognitive

Radio NetworksKiran Sultan, Ijaz Mansoor Qureshi, Muhammad Zubair

Abstract The field of spectrum sensing faces a lot of challenges in terms of reliability and accuracy in gathering information for detection

and estimation of primary transmissions in Cognitive Radio Networks (CRNs). We propose an efficient, reliable and low-complexity spectrum

sensing scheme for CRNs which not only detects the number of sources but also estimates their parameters such as frequency, Direction-of-

Arrival (DOA) and power strength. It is based on Genetic Algorithm (GA) as global optimizer hybridized with Pattern Search (PS) as local

optimizer. Fitness function is derived from Maximum Likelihood (ML) principle and defines the MSE between actual and estimated signals. Its

effectiveness under low SNR conditions is proved. Our proposed system model constitutes a uniform linear array (ULA) of sensors. Best

estimates of the parameters of the active primary users are obtained by minimizing the fitness function. We detect signals in the frequency

band of 80MHz-108MHz and assume far-field approximation and the snapshots are available to us after 10-15 seconds.

Index Terms Cognitive Radio Network, Direction-of-Arrival, Spectrum Sensing

1 INTRODUCTION

Spectrum sensing [1] is a process conducted to becomeaware of the status of the spectrum usage which involves

detection of active signals then estimation of the signal

parameters, followed by decision but it has revamped as a

very active area of research with the advent of cognitive

radio technology [2]. In Cognitive Radio (CR), spectrum

sensing is a decision making technique in which secondary

users (SUs) are required to dynamically detect spectrum

holes to become aware of the presence of the primary users

(PUs) which have high priority being the licensed users. Being

the core component of Cognitive Radio Network (CRN),

spectrum sensing faces many challenges [3] in terms of

hardware requirements, hidden terminal problem, detection

of spread spectrum primary users, data/decision fusion in

scenarios of cooperative sensing, multipath fading, noise

power uncertainty, implementation complexity, security etc.

In order to meet these challenges efficiently, spectrum

sensing requires innovative techniques for not only

detecting the number of PUs but also estimating their

amplitudes, DOAs and frequencies to avoid interference

between primary and secondary transmissions. A number o

spectrum sensing methods to detect spectrum holes in CRs

have been proposed in literature which have been broadly

categorized into three main classes: Non-cooperative

spectrum sensing [4], cooperative spectrum sensing [5]-[6

and interference based spectrum sensing [7].

Non-cooperative spectrum sensing also known astransmitter detection is further classified into Energy

Detection (ED), Matched Filter Detection (MFD) and

Cyclostationary based Detection (CBD). Energy Detector [8

is the most widely studied spectrum sensing technique

because of its less complexity and no requirement of prior

knowledge of PU signal, but it is accompanied by a number

of shortcomings which include noise power uncertainty

poor performance under low SNR and inefficient to detec

spread spectrum signals. MFD [9] is considered as the

optimum method of signal detection when perfect

knowledge of PU is available otherwise it performs poorly

Implementation complexity of MF is impractically large

because it demands CR to have dedicated receivers for al

signal types. CBD [10] relies on the prior knowledge of PU

signals and exploits cyclostationary features of the received

signals, hence it is capable of differentiating PU signals and

noise. Its implementation complexity lies between energy

detector and matched filter.

Kiran Sultan, Department of Electrical Engineering, Air University,

Islamabad, Pakistan, 46000. Ijaz Mansoor Qureshi, Department of Electrical Engineering, Air

University, Islamabad, Pakistan, 46000.Muhammad Zubair, Department of Electronics Engineering, International

Islamic University, Islamabad, Pakistan, 46000.

JOURNAL OF COMPUTING, VOLUME 5, ISSUE 2, FEBRUARY 2013, ISSN (Online) 2151-9617

https://sites.google.com/site/journalofcomputing

WWW.JOURNALOFCOMPUTING.ORG 7


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The focus of interference-based spectrum sensing is to

design the CRNs to operate in underlay spectrum sharing

environment. In this method, SUs do not perform spectrum

sensing to find spectrum opportunities rather they identify

spectrum occupancy status of PUs and an interference

power threshold is set up for SUs towards PUs for a

particular frequency band and location. In cooperativespectrum sensing, SUs collaborate and share sensing

information to solve problems like hidden terminal problem,

receiver uncertainty and multipath fading at the cost of

increased detection delay and high implementation

complexity due to requirement of control channels efficient

information sharing algorithms.

With new challenges and dimensions in CRNs, sensing

frequency only may not be enough. Thus it requires

exploration of new dimensions of direction of arrival (DOA),

frequency, strength of signal, range and a critical parameter

which is number of active PUs. All these parameters

formulate a hyperspace which may be called as transmission

hyperspace [11] or radio spectrum space. Knowledge of this

hyperspace will provide more comprehensive view of the

radio environment which has to be shared by multiple users.

In order to ensure secure, reliable and efficient

communication keeping in view the privilege of PUs,

advanced spectrum sensing algorithms capable of

identifying occupancy in all of the above dimensions of

spectrum space to locate spectrum holes need to be

developed which have not been considered simultaneously

in CRNs yet according to the best of our knowledge.

Source localization by means of sensor arrays has been one

of the fundamental and effective ways to estimate

amplitude, frequency, DOA and range estimation of both far

and near field sources upto high accuracy in many systems

including radar, navigation and wireless communication

systems. In order to achieve optimum performance of a

sensor array [12], array geometry, the number of sensors and

the physical separation between the sensors are critical

design parameters in addition to the number of other factors

including signal-to-noise ratio. Many algorithms have

already been proposed in array signal processing for source

localization which can be categorized into far-field source

localization and near-field source localization on the basis of

range between the radiating source and the array of sensors.

Far-field source localization algorithms make assumption

that sources are located in the far-field region of the array.

Thus each signal arriving at the array has planar wavefront.

ESPRIT algorithm [13] and MUSIC algorithm [14] are among

the widely studied far-field source localization algorithms.

However, the far-field assumption is no longer valid when

the sources are located close to the array and are described

by spherical wavefront assumption, thus range parameter is

also included in addition to amplitude, DOA and frequency

to characterize the sources. A number of techniques have

been proposed in this area such as 2-D MUSIC [15], Linear

Prediction method [16], higher order ESPRIT-method [17

etc but most of these algorithms are computationally

complex.This paper addresses the problem of detecting the number of

active PU signals and then estimating their signa

parameters to ensure interference free communication in

CRNs. Most of the existing techniques to determine the

number of sources are based on the Singular Value

Decomposition SVD of the covariance matrix of the

snapshots which yields M distinct eigenvalues, where M is

the number of signals present and the remaining

eigenvalues are either zero or non-zero repeated eigenvalues

[18] or non-zero eigenvalues less than threshold. However,SVD has high uncertainty in terms of decisions about setting

of the threshold and so different schemes [19] have been

proposed for threshold setting to detect the presence of

signals. These include Maximum Eigenvalue Detection

(MED), Maximum Minimum Eigenvalue (MME), Maximum

Eigenvalue to Trace (MET) etc. Unfortunately, most of the

existing methods are either problem specific or

computationally complex due to exhaustive comparisons of

test hypothesis involved to achieve high accuracy. In [20], a

technique is proposed to detect number of signals in order to

solve problem of DOA.

In this paper, we propose a generalized method to firs

detect the number of possibly active primary users located in

the far field region of the array and then estimate their

amplitudes, DOAs and frequencies. Our proposed spectrum

sensing scheme is not application specific. It can be used for

cooperative as well as non-cooperative spectrum sensing

We use Mean Square Error (MSE) as fitness function which

defines an error between actual and estimated signals a

different sensors of the uniform linear array ULA and is

derived from Maximum Likelihood (ML) Principle. MSE isone of the easy and optimum fitness functions to be

minimized using array of sensors and fairly good results are

obtained even in the scenario of low signal to noise ratio

(SNR). We employed heuristic optimization techniques to

minimize the error in which Genetic Algorithm (GA) [21

being one of the most popular evolutionary algorithm

because of its reliability, efficiency and robustness is used as





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global optimizer hybridized with Pattern Search (PS) as local

optimizer. This simple and elegant technique simply

demands a passive sensor array whose snapshots should be

readily available to us for calculation after every 10-20

seconds.

2 SYSTEM MODEL AND PROBLEM FORMULATION

We have an array of sensors that is sensing the signals from

different base stations of primary users. If the array is almost

at the same height as that of the base station transmitters, we

do not have to detect the elevation angle . So, consider a

uniform linear array as shown in fig.1 consisting of L

omnidirectional sensors observing M far-field primary

signals radiating with different unknown carrier frequencies.

The distance dbetween two consecutive elements is kept

one-quarter of the minimum wavelength of received signals

i.e.4

min .

Fig.1. The System Model

The composite signali

received by thethi sensor is

expressed as,

i

M

m

idjk

mi zeamm

1

sin)1( Li 1 )1(

where ma and m represent the amplitude and DOA of thethm source impinging on the array, mk is the propagation

constant and cfk mmm /2/2 with m

representing the frequency of thethm signal incident on the

array and iz is the AWGN added to the output ofth

i

sensor. Thus the parameters to be estimated for M incident

sources are expresses in a vector as,

where M is the number of active PUs and is also unknown

and has to be detected first.

The received signal vector at the L-element ULA is

expressed as,

LLixxxxx ],.,,..................,,[

121

where superscript T denotes the transpose.

Thus the problem in hand is to develop a novel technique for

two purposes, first detecting the number of active PU signals

impinging on ULA and second, performing joint estimation

of amplitude, DOA and frequency of the detected sources

considering the sensor array as reference. We also consider

the effect of variation in SNR on the detection and estimation

results. The fitness function can be expressed mathematically

as,2

,,,

min XXfag

)2(

where defines the estimated signal vector at the sensor

array and is given as,

LLi xxxxx ],.,,..................,,[ 121

i is the estimated output at the ith sensor and is expressed

as,

g

mm

M

m

idkj

miea

1

sin)1(

'

''

'

Li 1 )3(

whereg

is the number of sources randomly selected to

detect the possibly active PUs.

Thus the elements of the estimated vector ' obtainedthrough optimization algorithm are given by,

3 Proposed Algorithm for Detection

In this section, we give an overview of the procedural steps

carried out in GA optimization, parameter settings for GA

and hybrid scheme PS, and pseudo code for the proposed

algorithm. We solve the problem of detection first. To

achieve this purpose, we randomly select g number o

sources in the estimated signal vector and calculate mean

square error MSE given in eq. (2). The value of gis then

increased or decreased aiming to decrease the MSE in each

selection. This process is repeated until minimum mean,......,,,......,,,......, 111 MMMaa

],......,,,......,,,......,[' 111 ggg MMM ffaa





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square error MMSE is obtained withg

corresponding to

MMSE indicating the number of active PUs. After detection

of the number of sources is done, we perform joint

estimation of amplitude, DOA and frequency of the detected

signals by further refining the MMSE. We solve our

optimization problem given in eq. (2) through GeneticAlgorithm (GA) hybridized with Pattern Search (PS). GA has

been widely used to solve optimization problems in

communication and array signal processing because of being

simple in concept, reliable, ease in implementation and with

less probability of getting stuck in local minima [22].

Efficiency, accuracy and reliability of GA can be

considerably improved by hybridization with any other

competent computational technique such as Interior Point

Algorithm (IPA), Pattern Search (PS) etc. In [23],

performance of GA, PS and Simulated Annealing (SA) is

compared with GA-PS and SA-PS in the joint estimation of

amplitude and DOA of multiple far-field sources incident onL-type array considering Mean Square Error (MSE) as fitness

function.

The steps followed in GA-PS optimization are summarized

below.

______________________________________________________

Algorithm: GA hybridized with PS

______________________________________________________

Step (i): Initialization

Randomly generate P number of chromosomes

(potential solutions). Lower and upper bounds are

specified for the genes.

Step (ii): Fitness Function Evaluation

Fitness of each chromosome in the population is

computed using mean square error MSE derived

from Maximum Likelihood (ML) Principle as fitness

function and is given in eq (2). The chromosomes

are sorted on the basis of their fitness values.

Step (iii): Termination Criteria

The algorithm terminates if any of the following

two criteria are met, i.e. reaching the maximum

number of cycles or achieving the predefined fitnessvalue.

Step (iv): Create New Generations

Select the best chromosome depending on the value

of its fitness and create next generation by

employing mutation and crossover.

Step (v): Fine-Tuning via Local Search

The PS algorithm takes the best chromosome

obtained from GA as a starting point for further

improvement and refinement of results.

Step (vi): Storage:

Store the global best and to achieve better results

repeat the steps 2 to 5 for sufficient numbers ofiterations for better statistical analysis.

______________________________________________________

MATLAB optimization toolbox is used for this purpose and

parameter settings for GA and PS are shown in table 1

Pseudo code of the proposed algorithm to solve the

detection and estimation problem is provided in table 2.

Table1. PARAMETER SETTINGS FOR GA-PS

GA PS

Parameters Settings Parameters Settings

Populationsize

300 Start point Optimal valuesfrom GA

No. ofgenerations

2000 Poll method GPS positivebasis 2N

Selection Stochasticuniform

Polling order consecutive

Mutationfunction

Adaptivefeasible

Maximumiterations

1000

Crossoverfunction

Heuristic Maximumfunction

evaluation

10000

CrossoverFraction

0.2 FunctionTolerance

1e-18

Hybridization PSNo. of

generations3000 Expansion

Factor2.0

FunctionTolerance

1e-15 ContractionFactor

2.5

MigrationDirection

Both Way Penalty Factor 100

ScalingFunction

Rank

Elite Count 8





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Table 2: PSEUDO CODE OF THE PROPOSED

ALGORITHM FOR DETECTION OF NUMBER OF

SOURCES

.1,,,: MmwherefadInputs mmm

MforguessaasMChoose g

.1

M

m

idjk

mimmea

1

sin)1(

Li 1

.2

g

mm

M

m

idkj

miea

1

sin)1(

'

''

'

Li 1

.3 compute0

gMMXXE

rrorquareean

.4 et 1 gnew

g M sourceoneadd

.5 compute

newg

mm

M

m

idkj

mieax

1

sin)1(

'

''

'

Li 1

.6 compute2

'

0

newgM

MXXE

.7 i )( 0'

0 EE

.i Mofvaluepo ssibleaasMsavean dEE newg00

.iinew

gMupdate updatelastportingMM newg

new

g sup1// .iii

new

gMlastofrecordkeepingwhiletostepsrepeat 75

gincreastartsuntiacquire s n

e se .i 1 g

newg M

.ii 75 tostepsrepeat

iend

min00.8 EaroundEofvaluesthreeatleastObserve

0gMthatgconsiderindirectionsbothin

orincreasesMasEinincreaseensureto newg0

min0EtocorrespondwhichMarounddecreases newg

min0..Re: EeiMMSEtocorrespondthatMturnOutput

new

g

4 SIMULATION RESUTS AND DISCUSSIONS

In this section, we evaluate the performance of our proposed

technique in terms of accuracy for two purposes, first, to

detect of number of far-field sources impinging on ULA, and

second, for joint estimation of amplitude, DOA and

frequency of the detected signals. Inter-element spacing in

the array is kept4

min

. We perform spectrum sensing in the

frequency band of 81MHz 108MHz. The signals received a

the array were polluted by AWGN. Different cases are

discussed on the basis of different number of sources M

impinging on ULA, different number of sensors L, and fordifferent SNR levels, with SNR to be as high as 35dB and as

low as 15dB. All the values of DOA and signal to noise ratio

(SNR) are taken in degrees and dB respectively.

Fig. (2) illustrates the performance of GA for two incoming

sources i.e. M = 2 under different SNR conditions. A ULA

with L = 20 sensors is employed for this purpose. The

amplitude , DOA and frequency of the incoming

signals are taken as ,5.4,0.3 21 A

,145,75 21oo

MHzfMHz 100,85 21 where

111,, correspond to the first PU and

222,,

correspond to the second PU. The obtained results areaveraged over 20 snapshots. Fig. 2(a) illustrates the detection

of sources with g ranging from 1 to 7. Minimum Mean

square error (MMSE) is plotted against the number of

sources g in the estimated signal vector which clearly

gives the minimum value wheng

coincides with M. The

figure also indicates that increase in error is less significant

in the case when g > M as compared to the case when

g< M which represents an under-determined system i.e

number of solutions are less than the number of unknownsAfter the detection of active sources, table 3 provides the

estimates of amplitudes, DOAs and frequencies of both PUs

for different values of SNR. Fig. 2(b) and fig. 2(c) plot error

in DOA and frequency of the incident signals versus SNR

respectively and it is obvious from the figures that

estimation accuracy increases to 99.87% in DOA and 99.77%

in frequency as the SNR increases from 15dB to 35dB.

TABLE 3Amplitude, DOA and frequency estimation for different SNR

levels with M = 2, L = 20

SNR 1 2

o

1

o

2

)(1 z

(2 z

35dB 3.00 4.50 75.04 144.97 84.89 100.1030dB 3.00 4.50 74.95 144.96 85.13 100.12

25dB 2.99 4.51 75.07 145.06 84.84 99.85

20dB 2.98 4.52 74.91 145.08 84.82 100.1915dB 3.02 4.48 74.90 144.89 85.19 100.21





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Fig 2. (a). Detection of M = 2 PUs

Fig. 2(b). Error in DOA vs SNR for M = 2, L = 20

Fig. 2(c). Error in frequency vs SNR for M = 2, L = 20

In fig. (3) illustrates the performance of GA-PS with M = 4

primary users. ULA with L = 25 sensors is used for this

purpose. The values of amplitude, DOA and frequency of

the sources are taken as },81,60,2{ MHzo

},88,90,5.2{ MHzo

},95,135,3{ MHzo

and }.105,160,5.3{ MHzo Fig 3(a) plots MMSE versus g to

detect the number of active sources by setting g in the

range of 1 to 7 and it is obvious from the figure that error is

minimum when Mg giving a clear indication of 4

active PUs. Fig 3(b) and (c) plot error in DOA and frequency

estimates of the detected users versus different SNR levels

with SNR raised from 15dB to 35dB. The values estimated by

GA are tabulated in table 4. The results are averaged over 20

snapshots. Table 4 provides the amplitude, DOA and

frequency estimates obtained. Fig.3 proves the validity of the

proposed technique when the number of signals incident on

the array increases and it can still simultaneously estimate

amplitudes, DOAs and frequencies with high estimationaccuracy.

Fig 3. (a). Detection of M = 4 PUs

Fig. 3(b). Error in DOA vs SNR for M = 4, L = 25

Fig. 3(c). Error in frequency vs SNR for M = 4, L = 25

15 20 25 30 350.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

0.11

0.12

0.13

SNR (dB)

rrorn

egrees

delta fi1

delta fi2

15 20 25 30 350.1

0.12

0.14

0.16

0.18

0.2

0.22

SNR (dB)

E

rrorinf(MHz)

delta f1

delta f2

1 2 3 4 5 610

-4

10-3

10-2

10-1

100

101

102

Mg

MeanSquareError

SNR = 30dB

SNR = 25dB

SNR = 20dB

15 20 25 30 35

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

SNR (dB)

Errorin

fi(Degrees)

delta fi1

delta fi2

delta fi3

delta fi4

1 2 3 4 5 6 710

-4

10-3

10-2

10-1

100

101

10

M'

ean

quare

rror

SNR = 30dB

SNR = 25dB

SNR = 20dB

15 20 25 30 350.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

0.11

0.12

0.13

SNR (dB)

rrorn

egrees

delta fi1

delta fi2

15 20 25 30 350.1

0.12

0.14

0.16

0.18

0.2

0.22

SNR (dB)

E

rrorinf(MHz)

delta f1

delta f2

15 20 25 30 350.2

0.25

0.3

0.35

0.4

0.45

SNR (dB)

rrorin

z

delta f1

delta f2

delta f3

delta f4





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In fig. (4) we evaluate the performance of our proposed

scheme with different number of sensors L in the array as

the SNR is raised from 15dB to 35dB. Number of PUs and

the values of amplitudes, DOAs and frequencies of the PUs

are kept the same as in the case of fig. (2). The values

estimated by GA-PS are tabulated in table 5. The results are

averaged over 20 snapshots. It is obvious from figures 4(a)and 4(b) that the greater the number of sensors in the array,

the higher is the accuracy in the estimated values with

further improvement achieved at high SNR levels.

Fig. 4(a). Error in DOA estimation for different SNR levels and differentnumber of sensors in the array considering M = 2

Fig. 4(b). Error in frequency estimation for different SNR levels anddifferent number of sensors in the array considering M = 2

CONCLUSION

In this paper, we present a novel idea based on Genetic

Algorithm (GA) hybridized with Pattern Search (PS) fordetecting the number of active primary users and estimation

of joint amplitudes, DOAs and frequencies of the detected

users for cognitive radio networks. Our proposed method is

not application specific and the signal parameters are paired

automatically and estimated with high accuracy. Moreover,

the proposed algorithm has less computation burden and

offers satisfactory results even when number of users

increases. The simulation results verify the validity and

effectiveness of the proposed algorithm in AWGN

environment.

REFERENCES

[1] S. Haykin, "Cognitive radio: brain-empowered wireles

communications", IEEE J. Sel. Areas Comm., vol. 23, no. 2, pp. 201-2202005.

[2]J. Mitola, Cognitive Radio Architecture Evolution, Proceedings o

the IEEE, pp. 626641, 2009.

[3] A. Ghasemi, E. S. Sousa, Spectrum Sensing in Cognitive Radio

Networks: Requirements, Challenges and Design Trade-offs, IEEE

Comm. Magazine, Vol. 46, pp. 32-39, 2008.

[4] S. Kapoor, G. Singh, Cooperative Spectrum Sensing: A Hybrid

Model Approach, ICDECom IEEE, pp. 1-5, 2011.

[5] S. Hussain, X. Fernando, Spectrum Sensing in Cognitive Radio

Networks: up-to-date techniques and future challenges, TIC-STH IEEE

pp. 736-741, 2009.

[6] N. Pratas, N. R. Prasad, A. Rodrigues and R. Prasad, Cooperative

Spectrum Sensing: State of the Art Review, Wireless VITAE IEEE, pp.1

6, 2011.[7] M. Subhedar and G. Birajdar, Spectrum Sensing Techniques in

Cognitive Radio Networks: A Survey, IJNGN, Vol.3, 2011.

[8] A. Chandran, A. Karthik, A. Kumar, R. Naidu, S. Siva, U. S. Iyer, R

Ramanathan, Evaluation of Energy Detector based Spectrum Sensing

for OFDM Based Cognitive Radio, INCOCCI, IEEE, pp. 163-167, 2010.

[9] S. M. Kay, Fundamentals of Statistical Signal Processing: Detection

Theory, vol. 2, Prentice Hall, Upper Saddle River, NJ, USA, 1998.

[10] W. A. Gardner, Exploitation of spectral redundancy in

cyclostationary signals, IEEE Signal Processing Magazine, vol. 8, pp

1436, 1991.

[11] T. Yucek and H. Arslan, A Survey of Spectrum Sensing

Algorithms for Cognitive Radio Applications, Comm. Surveys and

Tutorials, IEEE Vol. 11, pp. 116-130, 2009.

[12] L. Gupta, R. P. Singh, Array Signal Processing: DOA Estimationfor Missing Sensors, ICPCES IEEE, pp. 1-4, 2010.

[13] ESPRIT-estimation of signal parameters via rotational invarianc

techniques, IEEE Trans. Acoust., Speech, Signal Process., vol. 37, no. 7

pp. 984995, 1989.

[14] R. Schmidt, Multiple emitter location and signal paramete

estimation, IEEE Trans. Antennas Propagation, vol. 34, no. 3, pp. 276

280, 1986.

[15] Y. D. Huang and M. Barkat, Near-field multiple source localization

by passive sensor array. IEEE Trans. Antennas Propag., vol 39, pp

968975, 1991.

[16] K. A. Meraim, Y. Hua and A. Belouchrani, Second-order near-field

source localization: method and performance analysis, Conferenc

Record of the Thirtieth Asilomar Conference on Signals, Systems and

Computers, Vol. 1, pp. 723727, 1996.

[17] N. Yuen and B. Friedlander, Performance analysis of higher orde

ESPRIT for localization of near-field sources, IEEE Trans. Signa

Process., vol. 46, no. 3, 1998, pp. 709719. [18] N. Pillay, H. J. Xu, Blind

eigenvalue-based spectrum sensing for cognitive radio networks, IET

Commun., Vol 6, pp. 1388-1396, 2012.

[18] Q.T. Zhang and K.M. Wong, A new information-theoretic criterion

for detection of the number of signals in spatially correlated noise with

covariance matrix, ICASSP IEEE, Vol. 5, pp. 381-384, 1992.

[19] U. Konda, Y. Cheng, T. Singh, P. D. Scott, Source Identification o

Puff-Based Dispersion Models Using Convex Optimization, IEEE 13t

6 8 10 12 14 16 18 20 220.06

0.08

0.1

0.12

0.14

0.16

0.18

L

rrorn

egrees

SNR = 30dB

SNR = 25dB

SNR = 20dB

SNR = 15dB

6 8 10 12 14 16 18 20 22

0.16

0.18

0.2

0.22

0.24

0.26

0.28

L

Errorinf1(MHz)

SNR = 30dB

SNR = 25dB

SNR = 20dB

SNR = 15dB



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conference on Computing & Processing

(Hardware/Software) ;Engineered Materials, Dielectrics &

Plasmas ; Nuclear Engineering, pp. 1-6, 2010.

[20] C. Candan and S. Koc, Beamspace Approach for Detection of the

Number of Coherent Sources, Radar Conference IEEE, pp. 913-918,

2012.

[21] D. E. Goldberg, Genetic algorithms in search, optimization and

machine learning", Addison Wesley, Jan. 1989.

[22] J. Zhang, H. S. Chung, and W. L. Lo, Clustering-based adaptive

crossover and mutation probabilities for genetic algorithms," IEEE

Trans. on Evol. Comput. Vol. 11, pp. 326-335, 2007.

[23] F. Zaman, I. M. Qureshi, A. Naveed, J. A. Khan, and M. A. Z. Raja,

Amplitude and Direction of Arrival Estimation: Comparison between

different Techniques, Progress In Electromagnetics Research B, Vol. 39

pp. 319-335, 2012.

TABLE 4Amplitude, DOA and frequency estimation for different SNR levels with M = 4, L = 25

TABLE 5Amplitude, DOA and frequency estimation for different SNR levels and different number of sensors in the array with M = 2

SNR1 2 3 4

o

1

o

2

o

3

o

4 1 MHz

2 MHz

(3 MHz

4 MHz

35dB 2.00 2.50 3.00 3.50 60.20 90.18 135.19 159.84 81.23 88.24 94.79 104.7730dB 1.99 2.51 3.00 3.48 59.78 90.24 134.75 159.79 80.71 88.28 94.74 104.7225dB 1.98 2.41 3.01 3.47 59.72 90.31 134.73 160.28 80.68 87.67 95.33 104.69

20dB 2.02 2.52 2.99 3.53 59.62 89.66 135.37 160.34 80.63 88.35 95.39 105.38

15dB 2.03 2.47 2.98 3.54 60.40 90.34 134.59 159.63 81.45 87.39 95.43 105.42

SNR L1

2

o

1

o

2 1 MHz 2 MHz

30dB

6 3.04 4.54 75.12 144.88 85.22 100.23

10 3.03 4.53 75.11 144.90 85.21 100.2214 3.02 4.53 74.91 144.93 84.83 100.19

18 2.98 4.49 75.07 145.05 85.16 99.8222 3.00 4.50 74.94 144.96 85.15 100.16

25dB

6 2.96 4.55 75.13 145.12 85.23 99.7710 2.95 4.46 75.12 145.11 85.22 100.22

14 2.95 4.48 74.91 145.09 84.81 100.1818 3.02 4.48 74.91 145.07 84.82 100.1722 2.99 4.51 74.92 144.93 85.17 99.83

20dB

6 3.06 4.57 75.15 144.84 85.25 99.76

10 3.05 4.56 75.13 145.15 84.77 99.7514 3.03 4.53 75.12 145.12 84.80 100.23

18 2.98 4.51 74.90 145.09 84.82 99.8022 2.99 4.49 74.91 144.92 85.17 100.18

15dB

6 3.07 4.42 75.17 144.82 85.27 100.26

10 2.96 4.57 74.83 144.84 84.78 99.75

14 3.03 4.45 74.86 145.12 85.79 100.2318 2.98 4.46 74.88 145.08 85.81 99.79

22 2.98 4.47 75.10 145.09 84.82 99.80



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Documents

Detection and Estimation of multiple far-field primary users using sensor array in Cognitive Radio Networks