Relay Selections for Security and Reliability in Mobile ...downloads.hindawi.com/journals/scn/2017/2569239.pdfRelay Selections for Security and Reliability in Mobile Communication

Research ArticleRelay Selections for Security and Reliability in MobileCommunication Networks over Nakagami-m Fading Channels

Hongji Huang Wanyou Sun Jie Yang and Guan Gui

College of Telecommunication and Information Nanjing University of Posts and Telecommunications Nanjing China

Correspondence should be addressed to Guan Gui guiguannjupteducn

Received 5 July 2017 Accepted 15 August 2017 Published 17 September 2017

Academic Editor Guangjie Han

Copyright copy 2017 Hongji Huang et al This 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

This paper studies the relay selection schemes inmobile communication system over Nakagami-m channel Tomake efficient use oflicensed spectrum both single relay selection (SRS) scheme andmultirelays selection (MRS) scheme over the Nakagami-m channelare proposed Also the intercept probability (IP) and outage probability (OP) of the proposed SRS andMRS for the communicationlinks depending on realistic spectrum sensing are derived Furthermore this paper assesses the manifestation of conventionaldirect transmission scheme to compare with the proposed SRS andMRS ones based on the Nakagami-m channel and the security-reliability trade-off (SRT) performance of the proposed schemes and the conventional schemes is well investigated Additionally theSRT of the proposed SRS and MRS schemes is demonstrated better than that of direct transmission scheme over the Nakagami-mchannel which can protect the communication transmissions against eavesdropping attacks Additionally simulation results showthat our proposed relay selection schemes achieve better SRT performance than that of conventional direct transmission over theNakagami-m channel

1 Introduction

Cognitive radio (CR) [1] is considered as one of the mostpromising technologies to significantly improve spectrumutilization [2] According to obtained information in differentenvironments transmission parameters such as frequencytransmission power modulation and bandwidth can beadaptively changed in CR networks [3] Based on the highlydynamic nature existing in architecture of CRnetworks how-ever legitimate CR devices expose themselves to both inter-nal and external attackers The security problem is urgentto solve in order to devise dependable CR networks Hencethe security problems of CR network [4ndash6] have attractedgreat attention in both academia and industry Security andreliability are two vital indexes of communication systemsbut they fail to have good performance simultaneously inmany cases Therefore it is of great significance to enhancethe security-reliability trade-off (SRT) [7] performance basedon the CR network

Physical-layer security is regarded as one of effectiveapproaches to improve the security of the wireless communi-cations On the one hand point-to-point (P2P) transmission

techniques such as MIMO diversity [8] jamming [9] andbeamforming [10] have been developed in order to improvedependable wireless links Also since localization providesfundamental support for many location-aware protocols andapplications in the communication networks it is one of thekey technologies inwireless sensor networks (WSNs) [11] Forthe purpose of improving localization accuracy and energyconsumption aspects which are essential factors of designingmobile communication network a novel algorithm consid-ering the aftermath of disasters based on wireless sensornetworks (WSNs) was provided by Han and his colleagues[12] As observed in many literatures about physical-layersecurity some scholars employ signal processing techniquessuch as the precoding and beaming to settle relevant issuesaiming at obtaining better performance Recently an agileconfidential transmission strategy combining big data drivencluster and opportunistic beamforming was well investigated[13] On the other hand the author in [14] explored a scenariowhere an eavesdropper appears to tap the transmissions of thesource and the relays Also node cooperation is employed toovercome eavesdroppingwithout upper layer data encryption

HindawiSecurity and Communication NetworksVolume 2017 Article ID 2569239 8 pageshttpsdoiorg10115520172569239

2 Security and Communication Networks

ST

MUR

MT

PU

PBS

PU

E

Figure 1 Model of a mobile communication network

and improve the performance of secure wireless communica-tions in the physical-layer security aspect [15] In additionrelays selection schemes over the Rayleigh fading channelwere proposed to improve the SRT performance of the CRnetworks [16] However the Rayleigh channel fails to becorresponding to the characteristics of many actual channels

TheNakagami-m channel ismore accordant with channelcharacteristics in realistic communication systems comparedwith that of Rayleigh fading channel and Ricean channelIn addition it is widely used for modeling wireless fadingchannels including Rayleigh and the one-sided Gaussiandistribution as special cases [17ndash19] However few scholarshave employed this kind of channels in SRT analysis Thiscauses the failure of previous SRT analysis to meet theperformance in realistic mobile communication system ingeneral Motivated by the above considerations a mobilecommunication network based on the Nakagami-m channelis conducted as a branch of CR networks This networkcomprises one primary base station (PBS) eavesdropper (119864)some primary users (PUs) multiple mobile terminals (MT)multiple relays (MUR) and a secondary transmitter (ST)Different from [16] we propose a scenario that investigatesthe SRT performance over the Nakagami-m channel whichcan better capture the characteristics of the physical channel[20ndash23] Specifically relay selection schemes in mobile com-munication systems over the Nakagami-m channel are wellinvestigated and mathematical SRT analysis of the proposedSRS and MRS schemes over the Nakagami-m channel is firstprovided Furthermore simulation results show limpidly thatthe proposed SRS and MRS schemes over the Nakagami-mchannel generally outperform the direct transmission schemein their SRT

The remainder of this paper is organized as belowSection 2 develops the system model And the relay selectionschemes over the Nakagami-m channel and mathematical

analysis are provided in Section 3 In Section 4 simulationresults and analysis are presented which is followed by theconclusions in Section 5

2 System Model

A typical mobile communication system is considered in Fig-ure 1 As we know the ST should detect by spectrum sensingwhether the PBS occupies the licensed spectrum In caseof this situation the ST cannot transmit randomly to avoidinterference within the PUs On the contrary the licensedspectrum is not occupied Meanwhile 119864 tries to interceptthe secondary transmission process For convenience wedefine 1198670 and 1198671 respectively as the cases in which thelicensed spectrum is unoccupied and occupied by the PBSin a special time slot Additionally represents the statusthat the licensed spectrum is detected by spectrum sensingHence the status of the spectrum is given as

= 1198670 unoccupied

1198671 occupied (1)

where the probability 119875119889 of the correct detection of thepresence of PBS and the associated false alarm probability 119875119891are noted as119875119889 = 119875( = 1198671 | 1198671) and119875119891 = 119875( = 1198671 | 1198670)respectively To ensure that the interference exerted on thePUs is below a tolerable level we set 119875119889 = 099 and 119875119891 = 001according to the IEEE 80222 standard [14]

3 SRT Analysis over Nakagami-m Channel

In this section we present the SRT analysis about thedirect transmission and the SRS and MRS schemes over theNakagami-m channel As is analyzed in [14] IP and OP

Security and Communication Networks 3

respectively represent the security and reliability which areexperienced by the eavesdropper and destination Hence thechannel capacities at the destination and eavesdropper areassumed as 119862119863 and 119862119864 and the OP and IP can be expressedas

119875out = 119875 (119862119863 lt 119877 | = 1198670) (2)

119875int = 119875 (119862119864 gt 119877 | = 1198670) (3)

31 Direct Transmission Scheme In this section we con-sider a conventional direct transmission scheme over theNakagami-m channel Let 119875119904 and 119875119877 denote the transmitpowers of the ST and PBS respectively For the licensedspectrum is considered to be unoccupied by the ST (ie =1198670) the signal received at the PBS can be expressed as

119910ST = ℎMURradic119875119904119909119904 + ℎPBSradic120572119875119877119909119877 + 1198990 (4)

Here119909119904 and119909119877 represent the random symbols transmitted bythe ST and the PBS at a special time instance Also withoutloss of generality assume that 119864[|119909119904|2] = 119864[|119909119877|2] = 1where 119864[sdot] is the expected value operator At the same timeℎMUR and ℎPBS are noted as the fading coefficients of thechannel spanning from ST to MT and from PBS to MTrespectively Furthermore 1198990 is the additive white Gaussiannoise (AWGN) Then the random variable 120572 can be given by

120572 = 0 11986701 1198671 (5)

However for that thewirelessmediumhas a broadcast naturethe signal of the ST which will be overheard by 119864 can bewritten by

119910SE = ℎMTradic119875119904119909119904 + ℎ119864radic120572119875119877119909119877 + 1198990 (6)

Supposing that a spectrum hole has been detected from (5)we obtain

119875directout = 119875 (119862ST lt 1198771198670 | = 1198670)

+ 119875 (119862ST lt 1198771198671 | = 1198670)= 1205820119875 (1003816100381610038161003816ℎST10038161003816100381610038162 lt Δ)+ 1205821119875 (1003816100381610038161003816ℎST10038161003816100381610038162 minus 1003816100381610038161003816ℎPBS10038161003816100381610038162 120574119901Δ lt Δ)

(7)

where Δ = (2119877 minus 1)120574119904 120574119904 = 1198751199041198730 and 120574119901 = 1198751198771198730 In (7)119875(|ℎST|2 lt Δ) and 119875(|ℎST|2 minus |ℎPBS|2120574119901Δ lt Δ) can be obtainedas

119875 (1003816100381610038161003816ℎST10038161003816100381610038162 lt Δ)= 1 minus 1198981minus1sum

119896=1

11989811198981minus119896 exp (minus1198981Δ)Γ (1198981 minus 119896 + 1)minus exp (minus1198981Δ)119875 (1003816100381610038161003816ℎST10038161003816100381610038162 minus 1003816100381610038161003816ℎPBS10038161003816100381610038162 120574119901Δ lt Δ)

= 1 + 1198982minus1sum119896=1

11989821198982minus119896 exp (1198982120574119901)Γ (1198982)minus 11989821198982Γ (1198982) exp (minus1198981Δ)times (1198981Δ120574119901 + 1198982)minus1198982 Γ(1198982 1198981Δ120574119901 + 1198982120574119901 )times (1198981minus1sum119896=1

11989811198981minus119896Γ (1198981) + 1)

(8)

Furthermore we can observe from (3) that when the capacityof the ST-119864 channel exceeds the data rate an intercept eventwill occur Hence the corresponding IP is given by

119875directint = 1205820119875 (1003816100381610038161003816ℎMT

10038161003816100381610038162 gt Δ)+ 1205821119875 (1003816100381610038161003816ℎMT

10038161003816100381610038162 minus 1003816100381610038161003816ℎPBS10038161003816100381610038162 120574119901Δ gt Δ) (9)

To be specific 119875(|ℎMT|2 gt Δ) and 119875(|ℎMT|2 minus |ℎPBS|2120574119901Δ gt Δ)are written as

119875 (1003816100381610038161003816ℎMT10038161003816100381610038162 gt Δ)

= 1198981minus1sum119896=1

11989811198981minus119896 exp (minus1198981Δ)Γ (1198981 minus 119896 + 1)+ exp (minus1198981Δ)119875 (1003816100381610038161003816ℎMT

10038161003816100381610038162 minus 1003816100381610038161003816ℎPBS10038161003816100381610038162 120574119901Δ gt Δ)= minus1198982minus1sum119896=1

11989821198982minus119896 exp (1198982120574119901)Γ (1198982)+ 11989821198982Γ (1198982) exp (minus1198981Δ)times (1198981Δ120574119901 + 1198982)minus1198982 Γ(1198982 1198981Δ120574119901 + 1198982120574119901 )times (1198981minus1sum119896=1

11989811198981minus119896Γ (1198981) + 1)

(10)

32 Single Relay Selection The SRS scheme over theNakagami-m channel is investigated in this section Specif-ically once the licensed spectrum is deemed to be unoc-cupied the ST first broadcasts its signal to the 119873 MURwhich attempts to decode 119909119904 from their received signals Forconvenience Θ is denoted as the set of MUR that succeedin decoding 119909119904119873MUR are assumed in this network which


consist of 2119873 possible subsets Θ and the sample space of Θcan be formulated as

Θ = 0 1205791 1205792 120579119894 1205792119873minus1 (11)

where 0 and 120579119894 represent the empty set and the 119894th nonemptysubset of the 119873 relays If the set Θ is empty no MURsuccessfully decodes 119909119904 By contrast a specific MUR isselected from Θ to decode the signal and transmit it to theMT Hence given that = 1198670 we can work out the signalreceived at a specific MUR-119894

119910119894 = ℎ119877119894radic120572119875119904119909119904 + ℎ119875119894radic119875119877119909119877 + 1198990 (12)

To make SRT analysis noting that = 1198670 the OP of thecognitive transmission depending on SRS can be denoted as

119875singleout = 119875 (119862ST lt 119877 120579 = 0 | = 1198670) + 2119873minus1sum

119899=1

119875 (119862ST

lt 119877 120579 = 120579119899 | = 1198670) = 1205820 119873prod119894=1

119875 (1003816100381610038161003816ℎ11987811989410038161003816100381610038162 lt Λ)+ 1205821 119873prod119894=1

119875 (1003816100381610038161003816ℎ11987811989410038161003816100381610038162 lt 1003816100381610038161003816ℎ11987711989410038161003816100381610038162 120574119901Λ + Λ)+ 12058202119873minus1sum119899=1

prod119894isinΘ

119875 (1003816100381610038161003816ℎ11987811989410038161003816100381610038162 gt Λ)sdotprod119895isinΘ

119875(10038161003816100381610038161003816ℎ119878119895100381610038161003816100381610038162 lt Λ)119875(max119894isinΘ

1003816100381610038161003816ℎ11987711989410038161003816100381610038162 lt Λ)

+ 12058212119873minus1sum119899=1

prod119894isinΘ

119875 (1003816100381610038161003816ℎ11987811989410038161003816100381610038162 gt 1003816100381610038161003816ℎ11987711989410038161003816100381610038162 120574119901Λ + Λ)sdotprod119895isinΘ

119875(10038161003816100381610038161003816ℎ119878119895100381610038161003816100381610038162 lt 1003816100381610038161003816ℎ11987711989410038161003816100381610038162 120574119901Λ + Λ) times 119875(max119894isinΘ

1003816100381610038161003816ℎ11987711989410038161003816100381610038162lt 1003816100381610038161003816ℎPBS10038161003816100381610038162 120574119901Λ + Λ)

(13)

whereΛ = (22119877minus1)120574119904 Specifically (13) consists of the follow-ing parts

119875 (1003816100381610038161003816ℎ11987811989410038161003816100381610038162 lt Λ)= 1 minus 1198983minus1sum

119896=1

11989831198983minus119896 exp (minus1198983Λ)Γ (1198983 minus 119896 + 1)minus exp (minus1198983Λ)119875 (1003816100381610038161003816ℎ11987811989410038161003816100381610038162 minus 1003816100381610038161003816ℎ11987711989410038161003816100381610038162 120574119901Λ lt Λ)

= 1 + 1198984minus1sum119896=1

11989841198982minus119896 exp (1198984120574119901)Γ (1198984)minus 11989841198984Γ (1198984) exp (minus1198983Λ) (1198983Λ120574119901 + 1198984)minus1198984times Γ(1198984 1198983Λ120574119901 + 1198984120574119901 )times (1198983minus1sum119896=1

11989831198983minus119896Γ (1198983) + 1)119875(max119894isinΘ

1003816100381610038161003816ℎ11987711989410038161003816100381610038162 lt Λ)= prod119894isinΘ

[1 minus 119898119894minus1sum119896=1

119898119894119898119894minus119896 exp (minus119898119894Λ)Γ (119898119894 minus 119896 + 1) minus exp (minus119898119894Λ)] (14)

Also we discuss the IP of the SRS scheme From (6) the IPcan be given by

119875singleint = 12058202119873minus1sum

119899=1

prod119894isinΘ


119875(10038161003816100381610038161003816ℎ119878119895100381610038161003816100381610038162 lt Λ)119875(max119894isinΘ

1003816100381610038161003816ℎbest10038161003816100381610038162 gt Λ)

+ 12058212119873minus1sum119899=1

prod119894isinΘ

119875 (1003816100381610038161003816ℎ11987811989410038161003816100381610038162 gt 1003816100381610038161003816ℎ11987711989410038161003816100381610038162 120574119901Λ + Λ)timesprod119895isinΘ

119875(10038161003816100381610038161003816ℎ119878119895100381610038161003816100381610038162 lt 1003816100381610038161003816ℎ11987711989410038161003816100381610038162 120574119901Λ + Λ) times 119875 (1003816100381610038161003816ℎbest10038161003816100381610038162gt 1003816100381610038161003816ℎ11986410038161003816100381610038162 120574119901Λ + Λ)

(15)

Here with the aids of functional analysis theory andmultivariate integral theory we express 119875(max119894isinΘ|ℎ119877119894|2 lt|ℎPBS|2120574119901Λ + Λ) 119875(max119894isinΘ|ℎbest|2 gt Λ) and119875(max119894isinΘ|ℎbest|2 gt |ℎPBS|2120574119901Λ + Λ) as below

119875(max119894isinΘ

1003816100381610038161003816ℎ11987711989410038161003816100381610038162 lt 1003816100381610038161003816ℎPBS10038161003816100381610038162 120574119901Λ + Λ)= prod119894isinΘ

prod119895isinΘ

[[1 +119898119895minus1sum119896=1

119898119895119898119895minus119896 exp (119898119895120574119901)Γ (119898119895) ]]minus 119898119894119898119895Γ (119898119895) exp (minus119898119894Λ) times (119898119894Λ120574119901 + 119898119895)

minus119898119895

sdot Γ (119898119895 119898119894Λ120574119901 + 119898119895120574119901 ) times (119898119894minus1sum119896=1

1198981119898119894minus119896Γ (119898119894) + 1)


119875(max119894isinΘ

1003816100381610038161003816ℎbest10038161003816100381610038162 gt Λ) = prod119894isinΘ

1 minus [1minus 119898119894minus1sum119896=1

119898119894119898119894minus119896 exp (minus119898119894Λ)Γ (119898119894 minus 119896 + 1) minus exp (minus119898119894Λ)]119875(max119894isinΘ

1003816100381610038161003816ℎbest10038161003816100381610038162 gt 1003816100381610038161003816ℎPBS10038161003816100381610038162 120574119901Λ + Λ)= prod119894isinΘ

prod119895isinΘ

[[minus1 minus119898119895minus1sum119896=1

119898119895119898119895minus119896 exp (119898119895120574119901)Γ (119898119895) ]]+ 119898119894119898119895Γ (119898119895) exp (minus119898119894Λ) times (119898119894Λ120574119901 + 119898119895)

minus119898119895

sdot Γ (119898119895 119898119894Λ120574119901 + 119898119895120574119901 )(119898119894minus1sum119896=1

1198981119898119894minus119896Γ (119898119895) + 1)

(16)

33 Multirelays Selection Scheme We provide the SRT analy-sis which is based on the MRS scheme over the Nakagami-mchannel in this subsection Specifically 119909119904 is first transmittedto 119873 MUR over a detected spectrum hole As is mentionedin Section 32 we denote Θ by the set of SRS with successfuldecoding If it is empty all MUR fail to decode 119909119904 and willnot pass the source signal forward leading to the difficulty indecoding of MT and 119864 If it is not empty all MUR within Θwill be utilized for simultaneously transmitting119909119904 toMTThisis different from the SRS scheme When it comes to powerconsumption a fair comparison with the SRS scheme can bemade under the conditions that the overall transmit poweracross all MUR is constrained to 119875119904 For the sake of makinggood use of MRS we define the weight vector as

119908 = [1199081 1199082 119908|Θ|]119879 119908 = 1 (17)

And the signals received at MT and 119864 are expressed as

119910multi119863 = radic119875119904119908119879119867119863119909119904 + radic120572119875119877ℎPBS119909119877 + 1198990119910multi119864 = radic119875119904119908119879119867MT119909119904 + radic120572119875119877ℎ119864119909119877 + 1198990 (18)

where 119867119863 = [ℎ1119863 ℎ2119863 ℎΘ119863] Then based on theNakagami-m channel we study the SRT performance of theMRS scheme Similar to (7) the OP analysis is obtained as

119875multiout = 119875 (120579 = 0 | = 1198670)+ 2119873minus1sum119899=1

119875 (119862multi119863 lt 119877 120579 = 120579119899 | = 1198670)

= 1205820 119873prod119894=1

119875 (1003816100381610038161003816ℎ11987811989410038161003816100381610038162 lt Λ)+ 1205821 119873prod119894=1

119875 (1003816100381610038161003816ℎ11987811989410038161003816100381610038162 lt 1003816100381610038161003816ℎ11987711989410038161003816100381610038162 120574119901Λ + Λ)+ 12058202119873minus1sum119899=1

prod119894isinΘ

119875 (1003816100381610038161003816ℎ11987811989410038161003816100381610038162 gt Λ)prod119895isinΘ

119875(10038161003816100381610038161003816ℎ119878119895100381610038161003816100381610038162 lt Λ)sdot 119875(sum119894isinΘ

1003816100381610038161003816ℎ11987711989410038161003816100381610038162 lt Λ)+ 12058212119873minus1sum119899=1

prod119894isinΘ


119875(10038161003816100381610038161003816ℎ119878119895100381610038161003816100381610038162 lt 1003816100381610038161003816ℎ11987711989410038161003816100381610038162 120574119901Λ + Λ) times 119875(sum119894isinΘ

1003816100381610038161003816ℎ11987711989410038161003816100381610038162

lt 1003816100381610038161003816ℎPBS10038161003816100381610038162 120574119901Λ + Λ) (19)

The IP analysis of the MRS scheme can be given as follows

119875multiint = 12058202119873minus1sum

119899=1

prod119894isinΘ

119875 (1003816100381610038161003816ℎ11987811989410038161003816100381610038162 gt Λ)prod119895isinΘ

119875(10038161003816100381610038161003816ℎ119878119895100381610038161003816100381610038162 lt Λ)

times 119875(10038161003816100381610038161003816119867MT119867119867119889 100381610038161003816100381610038162100381610038161003816100381611986711986310038161003816100381610038162 gt Λ)+ 12058212119873minus1sum119899=1

prod119894isinΘ


119875(10038161003816100381610038161003816ℎ119878119895100381610038161003816100381610038162 lt 1003816100381610038161003816ℎ11987711989410038161003816100381610038162 120574119901Λ + Λ)

sdot 119875(10038161003816100381610038161003816119867MT119867119867119889 100381610038161003816100381610038162100381610038161003816100381611986711986310038161003816100381610038162 gt 1003816100381610038161003816ℎ11986410038161003816100381610038162 120574119901Λ + Λ)

(20)

To find a general closed-form OP and IP expression for theMRS scheme is quite a challenge and thus we use computersimulations to get the numerical SRT performance of theMRS scheme Clearly when ℎ119877119894 is given as the fading coef-ficients of the channel spanning fromMUR-119894 to PBS we havesum |ℎ119877119894|2 gt max |ℎ119877119894|2 119894 isin Θ This leads to a performancegain for the MRS over that of SRS in terms of maximizingthe legitimate transmission capacity Furthermore for a fixedoutage requirement the MRS scheme can in comparisonwith the SRS scheme realize a better intercept performanceover the Nakagami-m channel This is due to the fact thatan outage reduction achieved by the capacity enhancementof the legitimate transmission relaying on MRS would beconverted into an intercept improvement Meanwhile in the


Theoretical results of direct transmissionSimulation results of direct transmissionTheoretical results of SRSSimulation results of SRSSimulation results of MRS

10minus2

10minus1

100

10minus3

10minus3

10minus2

10minus1

100

Outage probability

Inte

rcep

t pro

babi

lity

Figure 2 OP versus IP when119898 = 2 and119873 = 5 when 119875119889 = 099 and119875119891 = 001MRS schemewhen simultaneously transmitting toMT it willrequire a high-complexity symbol-level synchronization formultiple distributed relays whereas the SRS does not requiresuch a complex synchronization process Therefore we canachieve a better performance of MRS over SRS at the expenseof a higher implementation

4 Numerical Results and Discussion

We give a numerical analysis of our expressions using differ-ent types of parameters in this section Specifically the OPand the IP in the direct transmission schemes SRS schemesandMRS schemes are investigatedTheoretical results and thesimulation results are presented in the case under differentconditions in the Nakagami-m channel model Initially 119875119889 isset to119875119889 = 099 while119875119891 is 001 Also we set the initial signal-to-noise ratio (SNR) 120574119901 as 10 dB and data rate is employed as119877 = 1 bitsHz in this simulation

Figure 2 shows the simulation results when 119898 = 2 and119873 = 5 the IP and OP of the direct transmission along withthe SRS and MRS schemes Here the solid lines and discretemarker symbols each represent the theoretical and simulatedresults As is shown in the figure the proposed SRS andMRSschemes both attain lower OP (reliability) and IP (security)than the direct transmission scheme over the Nakagami-mchannel Also the OP and IP of the MRS are lower thanthose of SRS scheme Hence we can conclude that the SRSand MRS schemes have better SRT performance than thedirect transmission scheme However considering that theMRS scheme needs to work with very complex and high-costsymbol-level synchronization system it is inappropriate forus to assert that the MRS scheme outweighs the SRS scheme

Figure 3 illustrates the simulation results in the caseof 119898 = 2 and 119873 = 2 Compared with the simulation


10minus2

10minus1

100

10minus3

10minus3

10minus2

10minus1

100

Outage probability

Inte

rcep

t pro

babi

lity

Figure 3 OP versus IP when119898 = 2 and119873 = 2 when 119875119889 = 099 and119875119891 = 001results shown in Figure 2 we can observe that with theincreasing number of the relays theOP and IP are decreasingMeanwhile the performance of the SRS and MRS schemessignificantly improves when the number of relays increasesFurthermore similar to the analysis given in Figure 2 thesuperiority of the MRS over the SRS shows when elaboratesymbol-level synchronization is required among the multiplerelays for simultaneously transmitting to the relays or basestations

In Figure 4 the simulation results under different fadingexponents 119898 are presented in which case 119898 = 3 isconsidered Figure 4 shows that the proposed SRS andMRS schemes generally outstrip the conventional directtransmission in terms of IP and OP in the case that 119898 = 3Moreover compared with the results depicted in Figure 2the SRT of the SRS and MRS schemes rises as the fadingexponent 119898 increases from 2 to 3 Additionally the MRSschemes outperform the SRS approach in the IP and OPanalysis which further confirms the strength of the MRS forprotecting theMUR-PBS links against eavesdropping attacks

In Figure 5 119875119889 and 119875119891 are set 09 and 01 respectivelyFrom Figures 2 and 5 we observe the proposed SRS andMRS schemes perform better than the direct transmissionin terms of OP and IP aspect and the SRT performanceimproves when 119875119889 = 099 It illustrates that the SRTperformance of the SRS andMRS schemes improveswhen thecorrect detection probability increases Additionally theMRSschemes outperform the SRS approach in the SRT analysiswhich implies the strength of the MRS for protecting theMUR-PBS links against eavesdropping attacks although itneeds complex synchronization system



10minus2

10minus1

100

10minus3

10minus3

10minus2

10minus1

100

Outage probability

Inte

rcep

t pro

babi

lity

Figure 4 OP versus IP when119898 = 3 and119873 = 5 when 119875119889 = 099 and119875119891 = 001


10minus2

10minus1

100

10minus3

10minus3

10minus2

10minus1

100

Outage probability

Inte

rcep

t pro

babi

lity

Figure 5 OP versus IP when 119898 = 2 and119873 = 5 when 119875119889 = 09 and119875119891 = 01

5 Conclusion

We propose new relay selection schemes over the Nakagami-m channel in the mobile communication system in thispaper SRS and MRS schemes are presented to assess thesecurity and reliability of the communication links Mean-while simulation results indicate a better performance of

the SRS and MRS schemes than the direct transmissionscheme over theNakagami-m channel Additionally with theincreasing number of the relays the SRT performance of boththe SRS and the MRS schemes improves remarkably whichdemonstrates their benefits in enhancing both the securityand reliability of the mobile communication system

Conflicts of Interest

The authors declare no conflicts of interest

Authorsrsquo Contributions

Hongji Huang and Wanyou Sun derived the performancebound and designed the experiments Hongji Huang andGuan Gui performed the experiments Hongji Huang and JieYang analyzed the data Hongji Huang and Guan Gui wrotethe paper

Acknowledgments

This work is supported by National Natural Science Foun-dation of China Grants (no 61401069 no 61671252 no61471202 and no 61322112) Jiangsu Specially AppointedProfessor Grant (RK002STP16001) high-level talent startupgrant ofNanjingUniversity of Posts andTelecommunications(XK0010915026) and ldquo1311 Talent Planrdquo ofNanjingUniversityof Posts and Telecommunications

References

[1] G Han L Liu S Chan R Yu and Y Yang ldquoHySense ahybrid mobile crowd sensing framework for sensing opportu-nities compensation under dynamic coverage constraintrdquo IEEECommunications Magazine vol 55 no 3 pp 93ndash99 2017

[2] Y Zhang Y Xie Y Liu Z Feng P Zhang and Z Wei ldquoOutageprobability analysis of cognitive relay networks in nakagami-m fading channelsrdquo in Proceedings of the 76th IEEE VehicularTechnology Conference (VTC Fall rsquo12) 5 1 pages Quebec CityCanada September 2012

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

[4] J Mitola and G Q Maguire ldquoCognitive radio making softwareradios more personalrdquo IEEE Personal Communications vol 6no 4 pp 13ndash18 1999

[5] H Chen M Zhou L Xie and J Li ldquoCooperative spectrumsensing with M-ary quantized data in cognitive radio networksunder SSDF attacksrdquo IEEE Transactions on Wireless Communi-cations vol 16 no 8 pp 5244ndash5257 2017

[6] G Baldini T Sturman A R Biswas R Leschhorn G Godorand M Street ldquoSecurity aspects in software defined radio andcognitive radio networks a survey and a way aheadrdquo IEEECommunications Surveys and Tutorials vol 14 no 2 pp 355ndash379 2012

[7] R Yin S Wei J Yuan X Shan and X Wang ldquoTradeoffbetween reliability and security in block ciphering systems withphysical channel errorsrdquo in Proceedings of the IEEE MilitaryCommunications Conference (MILCOM rsquo10) pp 2156ndash2161 SanJose Claif USA November 2010


[8] J Huang and A L Swindlehurst ldquoCooperative jamming forsecure communications in MIMO relay networksrdquo IEEE Trans-actions on Signal Processing vol 59 no 10 pp 4871ndash4884 2011

[9] H LongW Xiang JWang Y Zhang andWWang ldquoCoopera-tive jamming and power allocation with untrusty two-way relaynodesrdquo IET Communications vol 8 no 13 pp 2290ndash2297 2014

[10] C Jeong I-M Kim and D I Kim ldquoJoint secure beamformingdesign at the source and the relay for an amplify-and-forwardMIMO untrusted relay systemrdquo IEEE Transactions on SignalProcessing vol 60 no 1 pp 310ndash325 2012

[11] G Han J Jiang C Zhang T Q Duong M Guizani and GK Karagiannidis ldquoA survey on mobile anchor node assistedlocalization inwireless sensor networksrdquo IEEECommunicationsSurveys amp Tutorials vol 18 no 3 pp 2220ndash2243 2016

[12] G Han X Yang L Liu M Guizani and W Zhang ldquoAdisastermanagement-oriented path planning formobile anchornode-based localization in wireless sensor networksrdquo IEEETransactions on Emerging Topics in Computing no 99 article1 2017

[13] S Han S Xu W Meng and C Li ldquoAn agile confidentialtransmission strategy combining big data driven cluster andOBFrdquo IEEE Transactions on Vehicular Technology no 99 article1 2017

[14] Y Zou X Wang W Shen and L Hanzo ldquoSecurity versusreliability analysis of opportunistic relayingrdquo IEEE Transactionson Vehicular Technology vol 63 no 6 pp 2653ndash2661 2014

[15] L Dong Z Han A P Petropulu and H V Poor ldquoImprovingwireless physical layer security via cooperating relaysrdquo IEEETransactions on Signal Processing vol 58 no 3 pp 1875ndash18882010

[16] Y Zou B Champagne W-P Zhu and L Hanzo ldquoRelay-selection improves the security-reliability trade-off in cognitiveradio systemsrdquo IEEE Transactions on Communications vol 63no 1 pp 215ndash228 2015

[17] H Lei C Gao I S Ansari et al ldquoSecrecy outage performanceof transmit antenna selection for MIMO underlay cognitiveradio systems over nakagami-m channelsrdquo IEEE Transactionson Vehicular Technology vol 66 no 3 pp 2237ndash2250 2017

[18] Z Shi S Ma G Yang K Tam and M Xia ldquoAsymptotic outageanalysis of HARQ-IR over time-correlated nakagami-m fadingchannelsrdquo IEEE Transactions on Wireless Communications no99 article 1 2017

[19] M O Hasna and M-S Alouini ldquoOutage probability of mul-tihop transmission over Nakagami fading channelsrdquo IEEECommunications Letters vol 7 no 5 pp 216ndash218 2003

[20] IEEE 80222Working Group IEEE P80222D10 draft standardfor wireless regional area networks part 22 Cognitive wirelessRAN medium access control (MAC) and physical layer (PHY)specifications Policies and procedures for operation in the TVbands Apr 2008

[21] J Zhang Y Zhang Y Yu R Xu Q Zheng and P Zhang ldquo3-D MIMO how much does it meet our expectations observedfrom channel measurementsrdquo IEEE Journal on Selected Areasin Communications vol 35 no 8 pp 1887ndash1903 2017

[22] J Zhang P Tang L Tian Z Hu T Wang and H Wangldquo6ndash100GHz research progress and challenges from a channelperspective for fifth generation (5G) and future wireless com-municationrdquo Science China Information Sciences vol 60 no 82017

[23] T S Rappaport Y Xing G R MacCartney A F Molisch EMellios and J Zhang ldquoOverview of millimeter wave communi-cations for fifth-generation (5G) wireless networks-with a focus

on propagation modelsrdquo IEEE Transactions on Antennas andPropagation no 99 article 1 2017

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of


International Journal of

RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal of

Volume 201

Submit your manuscripts athttpswwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



ST

MUR

MT

PU

PBS

PU

E

Figure 1 Model of a mobile communication network

and improve the performance of secure wireless communica-tions in the physical-layer security aspect [15] In additionrelays selection schemes over the Rayleigh fading channelwere proposed to improve the SRT performance of the CRnetworks [16] However the Rayleigh channel fails to becorresponding to the characteristics of many actual channels

TheNakagami-m channel ismore accordant with channelcharacteristics in realistic communication systems comparedwith that of Rayleigh fading channel and Ricean channelIn addition it is widely used for modeling wireless fadingchannels including Rayleigh and the one-sided Gaussiandistribution as special cases [17ndash19] However few scholarshave employed this kind of channels in SRT analysis Thiscauses the failure of previous SRT analysis to meet theperformance in realistic mobile communication system ingeneral Motivated by the above considerations a mobilecommunication network based on the Nakagami-m channelis conducted as a branch of CR networks This networkcomprises one primary base station (PBS) eavesdropper (119864)some primary users (PUs) multiple mobile terminals (MT)multiple relays (MUR) and a secondary transmitter (ST)Different from [16] we propose a scenario that investigatesthe SRT performance over the Nakagami-m channel whichcan better capture the characteristics of the physical channel[20ndash23] Specifically relay selection schemes in mobile com-munication systems over the Nakagami-m channel are wellinvestigated and mathematical SRT analysis of the proposedSRS and MRS schemes over the Nakagami-m channel is firstprovided Furthermore simulation results show limpidly thatthe proposed SRS and MRS schemes over the Nakagami-mchannel generally outperform the direct transmission schemein their SRT

The remainder of this paper is organized as belowSection 2 develops the system model And the relay selectionschemes over the Nakagami-m channel and mathematical

analysis are provided in Section 3 In Section 4 simulationresults and analysis are presented which is followed by theconclusions in Section 5

2 System Model

A typical mobile communication system is considered in Fig-ure 1 As we know the ST should detect by spectrum sensingwhether the PBS occupies the licensed spectrum In caseof this situation the ST cannot transmit randomly to avoidinterference within the PUs On the contrary the licensedspectrum is not occupied Meanwhile 119864 tries to interceptthe secondary transmission process For convenience wedefine 1198670 and 1198671 respectively as the cases in which thelicensed spectrum is unoccupied and occupied by the PBSin a special time slot Additionally represents the statusthat the licensed spectrum is detected by spectrum sensingHence the status of the spectrum is given as

= 1198670 unoccupied

1198671 occupied (1)

where the probability 119875119889 of the correct detection of thepresence of PBS and the associated false alarm probability 119875119891are noted as119875119889 = 119875( = 1198671 | 1198671) and119875119891 = 119875( = 1198671 | 1198670)respectively To ensure that the interference exerted on thePUs is below a tolerable level we set 119875119889 = 099 and 119875119891 = 001according to the IEEE 80222 standard [14]

3 SRT Analysis over Nakagami-m Channel

In this section we present the SRT analysis about thedirect transmission and the SRS and MRS schemes over theNakagami-m channel As is analyzed in [14] IP and OP



119875out = 119875 (119862119863 lt 119877 | = 1198670) (2)

119875int = 119875 (119862119864 gt 119877 | = 1198670) (3)




120572 = 0 11986701 1198671 (5)




119875directout = 119875 (119862ST lt 1198771198670 | = 1198670)


(7)



119896=1


= 1 + 1198982minus1sum119896=1


11989811198981minus119896Γ (1198981) + 1)

(8)


119875directint = 1205820119875 (1003816100381610038161003816ℎMT

10038161003816100381610038162 gt Δ)+ 1205821119875 (1003816100381610038161003816ℎMT

10038161003816100381610038162 minus 1003816100381610038161003816ℎPBS10038161003816100381610038162 120574119901Δ gt Δ) (9)


119875 (1003816100381610038161003816ℎMT10038161003816100381610038162 gt Δ)

= 1198981minus1sum119896=1




11989811198981minus119896Γ (1198981) + 1)

(10)




Θ = 0 1205791 1205792 120579119894 1205792119873minus1 (11)


119910119894 = ℎ119877119894radic120572119875119904119909119904 + ℎ119875119894radic119875119877119909119877 + 1198990 (12)



119899=1

119875 (119862ST

lt 119877 120579 = 120579119899 | = 1198670) = 1205820 119873prod119894=1

119875 (1003816100381610038161003816ℎ11987811989410038161003816100381610038162 lt Λ)+ 1205821 119873prod119894=1

119875 (1003816100381610038161003816ℎ11987811989410038161003816100381610038162 lt 1003816100381610038161003816ℎ11987711989410038161003816100381610038162 120574119901Λ + Λ)+ 12058202119873minus1sum119899=1

prod119894isinΘ


119875(10038161003816100381610038161003816ℎ119878119895100381610038161003816100381610038162 lt Λ)119875(max119894isinΘ

1003816100381610038161003816ℎ11987711989410038161003816100381610038162 lt Λ)

+ 12058212119873minus1sum119899=1

prod119894isinΘ



1003816100381610038161003816ℎ11987711989410038161003816100381610038162lt 1003816100381610038161003816ℎPBS10038161003816100381610038162 120574119901Λ + Λ)

(13)



119896=1


= 1 + 1198984minus1sum119896=1


11989831198983minus119896Γ (1198983) + 1)119875(max119894isinΘ

1003816100381610038161003816ℎ11987711989410038161003816100381610038162 lt Λ)= prod119894isinΘ

[1 minus 119898119894minus1sum119896=1




119899=1

prod119894isinΘ


119875(10038161003816100381610038161003816ℎ119878119895100381610038161003816100381610038162 lt Λ)119875(max119894isinΘ

1003816100381610038161003816ℎbest10038161003816100381610038162 gt Λ)

+ 12058212119873minus1sum119899=1

prod119894isinΘ



(15)


119875(max119894isinΘ


prod119895isinΘ

[[1 +119898119895minus1sum119896=1


minus119898119895


1198981119898119894minus119896Γ (119898119894) + 1)


119875(max119894isinΘ





prod119895isinΘ



minus119898119895

sdot Γ (119898119895 119898119894Λ120574119901 + 119898119895120574119901 )(119898119894minus1sum119896=1

1198981119898119894minus119896Γ (119898119895) + 1)

(16)


119908 = [1199081 1199082 119908|Θ|]119879 119908 = 1 (17)





119875 (119862multi119863 lt 119877 120579 = 120579119899 | = 1198670)

= 1205820 119873prod119894=1

119875 (1003816100381610038161003816ℎ11987811989410038161003816100381610038162 lt Λ)+ 1205821 119873prod119894=1

119875 (1003816100381610038161003816ℎ11987811989410038161003816100381610038162 lt 1003816100381610038161003816ℎ11987711989410038161003816100381610038162 120574119901Λ + Λ)+ 12058202119873minus1sum119899=1

prod119894isinΘ

119875 (1003816100381610038161003816ℎ11987811989410038161003816100381610038162 gt Λ)prod119895isinΘ


1003816100381610038161003816ℎ11987711989410038161003816100381610038162 lt Λ)+ 12058212119873minus1sum119899=1

prod119894isinΘ



1003816100381610038161003816ℎ11987711989410038161003816100381610038162

lt 1003816100381610038161003816ℎPBS10038161003816100381610038162 120574119901Λ + Λ) (19)



119899=1

prod119894isinΘ

119875 (1003816100381610038161003816ℎ11987811989410038161003816100381610038162 gt Λ)prod119895isinΘ

119875(10038161003816100381610038161003816ℎ119878119895100381610038161003816100381610038162 lt Λ)


prod119894isinΘ


119875(10038161003816100381610038161003816ℎ119878119895100381610038161003816100381610038162 lt 1003816100381610038161003816ℎ11987711989410038161003816100381610038162 120574119901Λ + Λ)

sdot 119875(10038161003816100381610038161003816119867MT119867119867119889 100381610038161003816100381610038162100381610038161003816100381611986711986310038161003816100381610038162 gt 1003816100381610038161003816ℎ11986410038161003816100381610038162 120574119901Λ + Λ)

(20)




10minus2

10minus1

100

10minus3

10minus3

10minus2

10minus1

100

Outage probability

Inte

rcep

t pro

babi

lity







10minus2

10minus1

100

10minus3

10minus3

10minus2

10minus1

100

Outage probability

Inte

rcep

t pro

babi

lity






10minus2

10minus1

100

10minus3

10minus3

10minus2

10minus1

100

Outage probability

Inte

rcep

t pro

babi

lity



10minus2

10minus1

100

10minus3

10minus3

10minus2

10minus1

100

Outage probability

Inte

rcep

t pro

babi

lity


5 Conclusion







Acknowledgments


References


























RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











119875out = 119875 (119862119863 lt 119877 | = 1198670) (2)

119875int = 119875 (119862119864 gt 119877 | = 1198670) (3)




120572 = 0 11986701 1198671 (5)




119875directout = 119875 (119862ST lt 1198771198670 | = 1198670)


(7)



119896=1


= 1 + 1198982minus1sum119896=1


11989811198981minus119896Γ (1198981) + 1)

(8)


119875directint = 1205820119875 (1003816100381610038161003816ℎMT

10038161003816100381610038162 gt Δ)+ 1205821119875 (1003816100381610038161003816ℎMT

10038161003816100381610038162 minus 1003816100381610038161003816ℎPBS10038161003816100381610038162 120574119901Δ gt Δ) (9)


119875 (1003816100381610038161003816ℎMT10038161003816100381610038162 gt Δ)

= 1198981minus1sum119896=1




11989811198981minus119896Γ (1198981) + 1)

(10)




Θ = 0 1205791 1205792 120579119894 1205792119873minus1 (11)


119910119894 = ℎ119877119894radic120572119875119904119909119904 + ℎ119875119894radic119875119877119909119877 + 1198990 (12)



119899=1

119875 (119862ST

lt 119877 120579 = 120579119899 | = 1198670) = 1205820 119873prod119894=1

119875 (1003816100381610038161003816ℎ11987811989410038161003816100381610038162 lt Λ)+ 1205821 119873prod119894=1

119875 (1003816100381610038161003816ℎ11987811989410038161003816100381610038162 lt 1003816100381610038161003816ℎ11987711989410038161003816100381610038162 120574119901Λ + Λ)+ 12058202119873minus1sum119899=1

prod119894isinΘ


119875(10038161003816100381610038161003816ℎ119878119895100381610038161003816100381610038162 lt Λ)119875(max119894isinΘ

1003816100381610038161003816ℎ11987711989410038161003816100381610038162 lt Λ)

+ 12058212119873minus1sum119899=1

prod119894isinΘ



1003816100381610038161003816ℎ11987711989410038161003816100381610038162lt 1003816100381610038161003816ℎPBS10038161003816100381610038162 120574119901Λ + Λ)

(13)



119896=1


= 1 + 1198984minus1sum119896=1


11989831198983minus119896Γ (1198983) + 1)119875(max119894isinΘ

1003816100381610038161003816ℎ11987711989410038161003816100381610038162 lt Λ)= prod119894isinΘ

[1 minus 119898119894minus1sum119896=1




119899=1

prod119894isinΘ


119875(10038161003816100381610038161003816ℎ119878119895100381610038161003816100381610038162 lt Λ)119875(max119894isinΘ

1003816100381610038161003816ℎbest10038161003816100381610038162 gt Λ)

+ 12058212119873minus1sum119899=1

prod119894isinΘ



(15)


119875(max119894isinΘ


prod119895isinΘ

[[1 +119898119895minus1sum119896=1


minus119898119895


1198981119898119894minus119896Γ (119898119894) + 1)


119875(max119894isinΘ





prod119895isinΘ



minus119898119895

sdot Γ (119898119895 119898119894Λ120574119901 + 119898119895120574119901 )(119898119894minus1sum119896=1

1198981119898119894minus119896Γ (119898119895) + 1)

(16)


119908 = [1199081 1199082 119908|Θ|]119879 119908 = 1 (17)





119875 (119862multi119863 lt 119877 120579 = 120579119899 | = 1198670)

= 1205820 119873prod119894=1

119875 (1003816100381610038161003816ℎ11987811989410038161003816100381610038162 lt Λ)+ 1205821 119873prod119894=1

119875 (1003816100381610038161003816ℎ11987811989410038161003816100381610038162 lt 1003816100381610038161003816ℎ11987711989410038161003816100381610038162 120574119901Λ + Λ)+ 12058202119873minus1sum119899=1

prod119894isinΘ

119875 (1003816100381610038161003816ℎ11987811989410038161003816100381610038162 gt Λ)prod119895isinΘ


1003816100381610038161003816ℎ11987711989410038161003816100381610038162 lt Λ)+ 12058212119873minus1sum119899=1

prod119894isinΘ



1003816100381610038161003816ℎ11987711989410038161003816100381610038162

lt 1003816100381610038161003816ℎPBS10038161003816100381610038162 120574119901Λ + Λ) (19)



119899=1

prod119894isinΘ

119875 (1003816100381610038161003816ℎ11987811989410038161003816100381610038162 gt Λ)prod119895isinΘ

119875(10038161003816100381610038161003816ℎ119878119895100381610038161003816100381610038162 lt Λ)


prod119894isinΘ


119875(10038161003816100381610038161003816ℎ119878119895100381610038161003816100381610038162 lt 1003816100381610038161003816ℎ11987711989410038161003816100381610038162 120574119901Λ + Λ)

sdot 119875(10038161003816100381610038161003816119867MT119867119867119889 100381610038161003816100381610038162100381610038161003816100381611986711986310038161003816100381610038162 gt 1003816100381610038161003816ℎ11986410038161003816100381610038162 120574119901Λ + Λ)

(20)




10minus2

10minus1

100

10minus3

10minus3

10minus2

10minus1

100

Outage probability

Inte

rcep

t pro

babi

lity







10minus2

10minus1

100

10minus3

10minus3

10minus2

10minus1

100

Outage probability

Inte

rcep

t pro

babi

lity






10minus2

10minus1

100

10minus3

10minus3

10minus2

10minus1

100

Outage probability

Inte

rcep

t pro

babi

lity



10minus2

10minus1

100

10minus3

10minus3

10minus2

10minus1

100

Outage probability

Inte

rcep

t pro

babi

lity


5 Conclusion







Acknowledgments


References


























RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











Θ = 0 1205791 1205792 120579119894 1205792119873minus1 (11)


119910119894 = ℎ119877119894radic120572119875119904119909119904 + ℎ119875119894radic119875119877119909119877 + 1198990 (12)



119899=1

119875 (119862ST

lt 119877 120579 = 120579119899 | = 1198670) = 1205820 119873prod119894=1

119875 (1003816100381610038161003816ℎ11987811989410038161003816100381610038162 lt Λ)+ 1205821 119873prod119894=1

119875 (1003816100381610038161003816ℎ11987811989410038161003816100381610038162 lt 1003816100381610038161003816ℎ11987711989410038161003816100381610038162 120574119901Λ + Λ)+ 12058202119873minus1sum119899=1

prod119894isinΘ


119875(10038161003816100381610038161003816ℎ119878119895100381610038161003816100381610038162 lt Λ)119875(max119894isinΘ

1003816100381610038161003816ℎ11987711989410038161003816100381610038162 lt Λ)

+ 12058212119873minus1sum119899=1

prod119894isinΘ



1003816100381610038161003816ℎ11987711989410038161003816100381610038162lt 1003816100381610038161003816ℎPBS10038161003816100381610038162 120574119901Λ + Λ)

(13)



119896=1


= 1 + 1198984minus1sum119896=1


11989831198983minus119896Γ (1198983) + 1)119875(max119894isinΘ

1003816100381610038161003816ℎ11987711989410038161003816100381610038162 lt Λ)= prod119894isinΘ

[1 minus 119898119894minus1sum119896=1




119899=1

prod119894isinΘ


119875(10038161003816100381610038161003816ℎ119878119895100381610038161003816100381610038162 lt Λ)119875(max119894isinΘ

1003816100381610038161003816ℎbest10038161003816100381610038162 gt Λ)

+ 12058212119873minus1sum119899=1

prod119894isinΘ



(15)


119875(max119894isinΘ


prod119895isinΘ

[[1 +119898119895minus1sum119896=1


minus119898119895


1198981119898119894minus119896Γ (119898119894) + 1)


119875(max119894isinΘ





prod119895isinΘ



minus119898119895

sdot Γ (119898119895 119898119894Λ120574119901 + 119898119895120574119901 )(119898119894minus1sum119896=1

1198981119898119894minus119896Γ (119898119895) + 1)

(16)


119908 = [1199081 1199082 119908|Θ|]119879 119908 = 1 (17)





119875 (119862multi119863 lt 119877 120579 = 120579119899 | = 1198670)

= 1205820 119873prod119894=1

119875 (1003816100381610038161003816ℎ11987811989410038161003816100381610038162 lt Λ)+ 1205821 119873prod119894=1

119875 (1003816100381610038161003816ℎ11987811989410038161003816100381610038162 lt 1003816100381610038161003816ℎ11987711989410038161003816100381610038162 120574119901Λ + Λ)+ 12058202119873minus1sum119899=1

prod119894isinΘ

119875 (1003816100381610038161003816ℎ11987811989410038161003816100381610038162 gt Λ)prod119895isinΘ


1003816100381610038161003816ℎ11987711989410038161003816100381610038162 lt Λ)+ 12058212119873minus1sum119899=1

prod119894isinΘ



1003816100381610038161003816ℎ11987711989410038161003816100381610038162

lt 1003816100381610038161003816ℎPBS10038161003816100381610038162 120574119901Λ + Λ) (19)



119899=1

prod119894isinΘ

119875 (1003816100381610038161003816ℎ11987811989410038161003816100381610038162 gt Λ)prod119895isinΘ

119875(10038161003816100381610038161003816ℎ119878119895100381610038161003816100381610038162 lt Λ)


prod119894isinΘ


119875(10038161003816100381610038161003816ℎ119878119895100381610038161003816100381610038162 lt 1003816100381610038161003816ℎ11987711989410038161003816100381610038162 120574119901Λ + Λ)

sdot 119875(10038161003816100381610038161003816119867MT119867119867119889 100381610038161003816100381610038162100381610038161003816100381611986711986310038161003816100381610038162 gt 1003816100381610038161003816ℎ11986410038161003816100381610038162 120574119901Λ + Λ)

(20)




10minus2

10minus1

100

10minus3

10minus3

10minus2

10minus1

100

Outage probability

Inte

rcep

t pro

babi

lity







10minus2

10minus1

100

10minus3

10minus3

10minus2

10minus1

100

Outage probability

Inte

rcep

t pro

babi

lity






10minus2

10minus1

100

10minus3

10minus3

10minus2

10minus1

100

Outage probability

Inte

rcep

t pro

babi

lity



10minus2

10minus1

100

10minus3

10minus3

10minus2

10minus1

100

Outage probability

Inte

rcep

t pro

babi

lity


5 Conclusion







Acknowledgments


References


























RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










119875(max119894isinΘ





prod119895isinΘ



minus119898119895

sdot Γ (119898119895 119898119894Λ120574119901 + 119898119895120574119901 )(119898119894minus1sum119896=1

1198981119898119894minus119896Γ (119898119895) + 1)

(16)


119908 = [1199081 1199082 119908|Θ|]119879 119908 = 1 (17)





119875 (119862multi119863 lt 119877 120579 = 120579119899 | = 1198670)

= 1205820 119873prod119894=1

119875 (1003816100381610038161003816ℎ11987811989410038161003816100381610038162 lt Λ)+ 1205821 119873prod119894=1

119875 (1003816100381610038161003816ℎ11987811989410038161003816100381610038162 lt 1003816100381610038161003816ℎ11987711989410038161003816100381610038162 120574119901Λ + Λ)+ 12058202119873minus1sum119899=1

prod119894isinΘ

119875 (1003816100381610038161003816ℎ11987811989410038161003816100381610038162 gt Λ)prod119895isinΘ


1003816100381610038161003816ℎ11987711989410038161003816100381610038162 lt Λ)+ 12058212119873minus1sum119899=1

prod119894isinΘ



1003816100381610038161003816ℎ11987711989410038161003816100381610038162

lt 1003816100381610038161003816ℎPBS10038161003816100381610038162 120574119901Λ + Λ) (19)



119899=1

prod119894isinΘ

119875 (1003816100381610038161003816ℎ11987811989410038161003816100381610038162 gt Λ)prod119895isinΘ

119875(10038161003816100381610038161003816ℎ119878119895100381610038161003816100381610038162 lt Λ)


prod119894isinΘ


119875(10038161003816100381610038161003816ℎ119878119895100381610038161003816100381610038162 lt 1003816100381610038161003816ℎ11987711989410038161003816100381610038162 120574119901Λ + Λ)

sdot 119875(10038161003816100381610038161003816119867MT119867119867119889 100381610038161003816100381610038162100381610038161003816100381611986711986310038161003816100381610038162 gt 1003816100381610038161003816ℎ11986410038161003816100381610038162 120574119901Λ + Λ)

(20)




10minus2

10minus1

100

10minus3

10minus3

10minus2

10minus1

100

Outage probability

Inte

rcep

t pro

babi

lity







10minus2

10minus1

100

10minus3

10minus3

10minus2

10minus1

100

Outage probability

Inte

rcep

t pro

babi

lity






10minus2

10minus1

100

10minus3

10minus3

10minus2

10minus1

100

Outage probability

Inte

rcep

t pro

babi

lity



10minus2

10minus1

100

10minus3

10minus3

10minus2

10minus1

100

Outage probability

Inte

rcep

t pro

babi

lity


5 Conclusion







Acknowledgments


References


























RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











10minus2

10minus1

100

10minus3

10minus3

10minus2

10minus1

100

Outage probability

Inte

rcep

t pro

babi

lity







10minus2

10minus1

100

10minus3

10minus3

10minus2

10minus1

100

Outage probability

Inte

rcep

t pro

babi

lity






10minus2

10minus1

100

10minus3

10minus3

10minus2

10minus1

100

Outage probability

Inte

rcep

t pro

babi

lity



10minus2

10minus1

100

10minus3

10minus3

10minus2

10minus1

100

Outage probability

Inte

rcep

t pro

babi

lity


5 Conclusion







Acknowledgments


References


























RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











10minus2

10minus1

100

10minus3

10minus3

10minus2

10minus1

100

Outage probability

Inte

rcep

t pro

babi

lity



10minus2

10minus1

100

10minus3

10minus3

10minus2

10minus1

100

Outage probability

Inte

rcep

t pro

babi

lity


5 Conclusion







Acknowledgments


References


























RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation



























RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









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