Research Article On the Eigenvalue Based Detection for ...downloads.hindawi.com/journals/misy/2016/3848734.pdf · Research Article On the Eigenvalue Based Detection for Multiantenna

Research ArticleOn the Eigenvalue Based Detection for MultiantennaCognitive Radio System

Syed Sajjad Ali1 Chang Liu1 Jialong Liu1 Minglu Jin1 and Jae Moung Kim2

1School of Information and Communication Engineering Dalian University of Technology Dalian 116024 China2Department of Information and Communication Engineering INHA University Incheon 402-751 Republic of Korea

Correspondence should be addressed to Jae Moung Kim jaekiminhaackr

Received 29 December 2015 Revised 4 April 2016 Accepted 5 May 2016

Academic Editor Yunfei Chen

Copyright copy 2016 Syed Sajjad Ali 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

Eigenvalue based spectrum sensing can make detection by catching correlation features in space and time domains which can notonly reduce the effect of noise uncertainty but also achieve high detection probability Hence the eigenvalue based detection isalways a hot topic in spectrum sensing area However most existing algorithms only consider part of eigenvalues rather than allthe eigenvalues which does not make full use of correlation of eigenvalues Motivated by this this paper focuses on multiantennasystem and makes all the eigenvalues weighted for detection Through the analysis of system model we transfer the eigenvalueweighting issue to an optimal problem and derive the theoretical expression of detection threshold and probability of false alarmand obtain the close form expression of optimal solution Finally we propose new weighting schemes to give promotions of thedetection performance Simulations verify the efficiency of the proposed algorithms

1 Introduction

The rapid development of wireless services leads to thescarcity of the public radio spectrum becoming more andmore serious Traditionally licensed spectrum is allocatedover relatively long time periods and is intended to be usedonly by legitimate users Cognitive radio (CR) technologywasproposed to handle the contradiction between the shortage ofspectrum resource and the underutilization of licensed spec-trum [1 2] Spectrum sensing which is a fundamental task ofCR is aimed at obtaining the awareness of licensed spectrumusage and existence of primary users (PUs) in a specificgeographical location [3ndash7] The main function of spectrumsensing is to frequently explore the spectrum holes for thesecondary users (SUs) by detecting the presence of primaryusers so that the SUs can share the licensed spectrumThere-fore spectrum sensing becomes critical in cognitive radiosystem

There have been many discussions and proposed solu-tions for spectrum sensing [8] Of these methods likelihoodratio test (LRT) [9] cyclostationary detection (CSD) [10 11]

and matched filtering (MF) detection [12 13] can achieveoptimal performance while requiring both source signal andnoise power information which is not available in practiceHence semiblind methods such as energy detection (ED)[9 14] and maximum eigenvalue detection (MED) [15] areproposed Among these ED is the most commonly chosenscheme for study and implementation due to its relatively lowcomplexity and satisfactory performance under low signal-to-noise ratio (SNR) environmentHowever EDheavily relieson the accuracy of the knowledge of noise power which isgenerally changing over time This so-called noise uncer-tainty problem [16] can significantly degrade the perfor-mance of ED algorithm

To overcome these shortcomings blind detection algo-rithms which require no information on source signal ornoise power have been intensively studied recently [17ndash21]The classical blind detection algorithms are the eigenvaluebased methods For example maximum-minimum eigen-value (MME) detection [22] arithmetic to geometric mean(AGM) detection [23] and signal-subspace eigenvalues (SSE)method [23] can overcome the shortcoming of ED and

Hindawi Publishing CorporationMobile Information SystemsVolume 2016 Article ID 3848734 8 pageshttpdxdoiorg10115520163848734

2 Mobile Information Systems

achieve outstanding performance On the other hand eigen-value basedmethods have also been studied in new scenariossuch as cooperative adaptive versions [24] and MultiplePrimary Transmit Power (MPTP) scenario [25]

However most algorithms only consider part of eigenval-ues such as maximum minimum and mean value whichdoes not make full use of all the eigenvalues to make detec-tionMotivated by this we focus on the problemof eigenvalueweighting in multiantenna system and analyze the relatedproblems By analyzing the model of eigenvalue weightingwe transfer the weighting problem to an optimal problemUsing the latest random matrix theory (RMT) [26 27] wederive the close form expression of probability of detectionand probability of false alarm and obtain the optimal solutionFinally we propose new weighting schemes to give promo-tions of the detection performance Simulations verify theefficiency of the proposed algorithms The main contribu-tions of this paper include the following

(i) Different from the traditional eigenvalue based detec-tion we consider making detection by utilizing allof the eigenvalues in the multiantenna system Bytransferring the weighting problem to an optimalproblem we analyze and derive an energy basedmaximum ratio combination (EN-MRC) method

(ii) Considering the case of correlated signals is commonin applications we use the idea of MRC weightingin EN-MRC method to design an eigenvalue basedMRC (EIG-MRC) scheme signal eigenvalue weight-ing (SEW) based detection which needs the a prioriinformation of signalsrsquo covariance matrix and noisepower

(iii) To make the detection more practical we use themaximum likelihood estimation (MLE) approach todesign a method of signal eigenvalue approximationweighting (SEAW) based detection in which only thenoise power is needed

The rest of the paper is organized as follows Section 2explains the system model The eigenvalue weighting baseddetection is studied in Section 3 Section 4 presents simula-tion results and conclusion is presented in Section 5 Somenotations used in the paper are listed as follows superscripts119879 and 119867 stand for transpose and Hermitian transpose(transpose-conjugate) respectively

2 System Model

Figure 1 illustrates a classical multiantenna spectrum sensingscenario with 119863 randomly distributed primary users (PU infigure) and 119875 randomly distributed secondary users (SU infigure) Once PUs begin to communicate the surroundingSUs can receive the PU signals and then capture the samplesto operate the spectrum sensing

According to Figure 1 the SUs are equipped with 119872

receiving antennas and there are 119863 PU signals arriving

in the antenna array In this case the sensing problem inmultiantenna cognitive radio system can be written as

1198670 119909119894(119896) = 119899

119894(119896)

1198671 119909119894(119896) =

119863

sum

119895=1

ℎ119894119895119904119895(119896) + 119899

119894(119896)

(1)

where 119894 = 1 2 119872 represents the 119894th receiving antennaand 119896 = 0 1 119873 minus 1 is the 119896th sample 119909

119894(119896) is the sample

of the 119894th receiving antenna ℎ119894119895is the channel gain between

the 119895th PU signal 119904119895(119896) and the 119894th receiving antenna 119899

119894(119896) is

the additive white Gaussian noise (AWGN) with 0 mean 1205902119899

varianceStacking the samples at the same time we can get the

following receiving vector of antenna array

x (119896) = [1199091 (119896) 1199092 (119896) 119909119872 (119896)]119879

s (119896) = [1199041(119896) 1199042(119896) 119904

119863(119896)]119879

n (119896) = [1198991(119896) 119899

2(119896) 119899

119872(119896)]119879

(2)

Hence formula (1) can be rewritten as the matrix form

1198670 X = N

1198671 X = HS + N

(3)

where X = [x(0) x(1) x(119873 minus 1)]119879 and N = [n(0)n(1)

n(119873 minus 1)]119879 are the antenna receiving matrix and noise

matrix respectivelyH isin C119872times119863 is the channel gain matrix ofthe signal matrix S = [s(0) s(1) s(119873 minus 1)]

119879

3 Eigenvalue Weighting Based Detection

31 Fundamental of Eigenvalue Weighting Based DetectionBased on (3) the corresponding covariance matrix can bewritten as

RX = 119864 (XX119867)

RS = 119864 (SS119867)

RN = 119864 (NN119867)

(4)

Hence we can rewrite RX as

RX = HRSH119867+ RN (5)

Let 1205821ge 1205822ge sdot sdot sdot ge 120582

119872and 1205881ge 1205882ge sdot sdot sdot ge 120588

119863represent the

eigenvalues ofRX andHRSH119867 respectively Obviously whenPUs are present we can get 120582

119894= 120588119894+1205902

119899 when PUs are absent

that is RX = RN we can have 1205821= 1205822= sdot sdot sdot = 120582

119872= 1205902

119899

Based on the analysis above we can make detection byweighting the eigenvalues Considering the number of sam-ples is finite in reality we can get the following test statistic

119879 =

119872

sum

119894=1

119908119894120582119894(RX (119873)) (6)

Mobile Information Systems 3

Licensed PU channels


Sensing wireless channels

Sensing wirelesschannels

SU4

SU3

SU2

PU2

SU1

PU1

SUP

PUD

Primary user (PU)Secondary user (SU)with multiantenna

Figure 1 Scenario of spectrum sensing for multiantenna cognitiveradio system

where 120582(sdot) is the eigenvalues and 119908119894is the weighting coeffi-

cient RX(119873) = (1119873)XX119867 is the samples covariance matrixObviously if 119879 gt 120574 (120574 is the test threshold) then PUs arepresent otherwise PUs are absent

Finally we summarize the general eigenvalue weightingalgorithm steps as follows

Eigenvalue Weighting Based Spectrum Sensing Algorithm forMultiantenna Cognitive Radio System

Step 1 (compute the sample covariance matrix of the receivedsignal) Since the number of samples is finite we can only usethe sample covariance matrix RX(119873) = (1119873)XX119867

Step 2 (obtain the eigenvalues of sample covariance matrix)Make eigenvalue decomposition (EVD) of RX(119873) obtain119872eigenvalues and sort them in a descending order 120582

1ge 1205822ge

sdot sdot sdot ge 120582119872

Step 3 (calculate the test statistic of the eigenvalue weighting)Let all the eigenvalues be weighted by 119908

119894and compute the

sum of them Thus we can obtain the test statistic in (6)

Step 4 (decision) If119879 gt 120574 then signal exists (ldquoyesrdquo decision)otherwise signal does not exist (ldquonordquo decision) where 120574 is athreshold

32 Theoretical Analysis of Eigenvalue Weighting Based Detec-tion Note that how to select weights 119908

119894is of great impor-

tance which can affect the performance of the algorithmdirectly Based on the Neyman-Pearson rule we can expressthe weighting selection problem as the following optimalproblem [28 29]

maxw

119875119889= int

infin

119903

119891119879|1198671(119909w) 119889119909

st 119875119891119886= int

infin

119903

119891119879|1198670(119909w) 119889119909

(7)

where w = [1199081 1199082 119908

119872]119879 is the weighting coefficient

vector 119875119889and 119875

119891119886represent the probability of detection and

the probability of false alarm 119891119879|1198671

(sdot) and 119891119879|1198670

(sdot) are theprobability density function of test statistic under119867

1and119867

0

respectivelyBased on (6) we find that it is possible to analyze the

distribution of the test statistic whereas the joint probabilitydensity function is rather complex whose close form expres-sion is not available However we can transfer the problem ofeigenvalue weighting of the matrix to a problem of the traceof a new matrix and the analysis of distribution of the traceis a simple problem The detailed analysis is showed in thefollowing

Let Y = GX isin C119872times119873 and G = diag[1198921 1198922 119892

119872] =

diag[radic1199081 radic1199082 radic119908119872]119879 Hence

WY = YY119867 = GWXG119867 (8)

whereWX = XX119867 When the number of samples119873 tends toinfinite theWX tends to a diagonal matrix and we can get thefollowing

EVD (WY) = EVD (GWXG119867) asymp GEVD (WX)G

119867 (9)

where EVD(sdot) represents the diagonal matrix of eigenvaluesand the equality holds when the number of samples119873 tendsto infinite Hence if we make eigenvalue weighting ofWX byw = [119908

1 1199082 119908

119872]119879 and calculate the sum of the eigen-

values after weighting then it is equivalent to compute thetrace ofWY SinceWX = 119873RX(119873) we can rewrite (6) as thefollowing

119879 =

119872

sum

119894=1

119908119894120582119894(RX (119873)) asymp

119872

sum

119894=1

120582119894(RY (119873))

= Trace (RY (119873)) = Trace (GRX (119873)G119867)

=1

119873

119872

sum

119894=1

119873minus1

sum

119896=0

119908119894

1003816100381610038161003816119903X119894 (119896)1003816100381610038161003816

2

(10)

where 119903X119894(119896) is the 119894th row (119896 + 1)th element of RX(119873) Let119886119894= sum119873minus1

119896=0|119903X119894(119896)|

2 and thus the test statistic 119879 can be writtenas

1198791015840= 119873119879 =

119872

sum

119894=1

119908119894119886119894 (11)

For simplification we assume the noise variance 1205902119899= 1

When the number of samples is large enough we can get thefollowing expression based on central limit theorem (CRT)

119886119894

sim

N(119873

119872

sum

119894=1

119908119894 2119873

119872

sum

119894=1

1199082

119894) 119867

0

N(119873

119872

sum

119894=1

119908119894(1 + 119903

119894) 2119873

119872

sum

119894=1

1199082

119894(1 + 2119903

119894)) 119867

1

(12)


where 119903119894= 119864|sum

119863

119895=1ℎ119894119895119904119895(119896)|2 is the power of the PU signals

Therefore we can obtain the expressions of 119875119891119886

and 119875119889

respectively

119875119891119886= 119875 119879

1015840gt 120574 | 119867

0 = 119876(

120574 minus 119873sum119872

119894=1119908119894

radic2119873sum119872

119894=11199082

119894

) (13)

119875119889= 119875 119879

1015840gt 120574 | 119867

1

= 119876(120574 minus 119873sum

119872

119894=1119908119894(1 + 119903

119894)

radic2119873sum119872

119894=11199082

119894(1 + 2119903

119894)

)

(14)

where119876(119909) = int+infin119909

(1radic2120587)119890minus11990522119889119905 Hence based on (13) and

(14) we can finally get the expression as

119875119889= 119876(

119876minus1(119875119891119886) minus radic(1198732)sum

119872

119894=1120572119894119903119894

radicsum119872

119894=11205722

119894(1 + 2119903

119894)

) (15)

where 120572119894= 119908119894radicsum119872

119894=11199082

119894and sum119872

119894=11205722

119894= 1 Since the SNR

of spectrum sensing is rather low (minus20 dB) which leads to119903119894≪ 1 we can get sum119872

119894=11205722

119894(1 + 2119903

119894) asymp 1 Hence (15) can be

approximated as

119875119889asymp 119876(119876

minus1(119875119891119886) minus radic

119873

2

119872

sum

119894=1

120572119894119903119894) (16)

Therefore problem (7) can be rewritten as

max120572

119872

sum

119894=1

120572119894119903119894

st119872

sum

119894=1

1205722

119894= 1

(17)

Note that this problem can be solved by Lagrangianmultipliermethod and the solution is written as

120572lowast

119894=

119903119894

radicsum119872

119894=11199032

119894

(18)

Let sum119872119894=11199082

119894= 1 and we can finally get the weighting coef-

ficient119908lowast

119894= 120572lowast

119894 1 le 119894 le 119872 (19)

Note that this weighting scheme is exactly identical to themaximal ratio combination (MRC) weighting scheme in [2829] and we call it energy based MRC (EN-MRC) detectionHence by studying the idea of MRC weighting scheme weapply this idea into eigenvalueweighting and finally develop akind of energy basedMRC algorithmThe test statistic can bewritten as

119879EN-MRC =119872

sum

119894=1

119903119894

radicsum119872

119894=11199032

119894

120582119894 (20)

where 119903119894= 119864|sum

119863


33 Eigenvalue Weighting Based Detection Note that thetransformation from eigenvalue to energy in (9) is approx-imately equivalent and the equality holds when 119873 tends toinfinite Hence the corresponding analysis should be moreaccurate when the number of samples tends to be very largeOn the other hand the analysis under this case is based onthe assumption that the received signals are independent andidentically distributed (iid) for each other which is not veryaccurate for the case of highly correlated signals For exampleas for (12) the distribution of 119886

119894under 119867

1is considered as

a linear combination of Gaussian variables with (1 + 119903119894)-

variance which is based on the assumption that the receivedsignals under 119867

1are iid for each other However this

assumption is only available under a cooperative spectrumsensing model whose samples are collected from differentsensing nodes Hence the weighting coefficient in (20) is notan appropriate weighting scheme especially for the case ofhighly correlated signals and thus it needs to be improved forbetter catching the signalsrsquo correlation

Motivated by this we try to analyze the weightingcoefficients from the aspect of eigenvalue directly Since 119903

119894=

119864|ℎ119894119895119904119895(119896)|2 is the power of the PU signals and 119864[|ℎ

119894119895|2] =

1 we can then replace the power of the PU signals 119903119894in

(20) with the eigenvalues of signal covariance matrix 120588119894=

[EVD(HRSH119867)]119894In this case the test statistic can further capture the

correlation among signals and may achieve better perfor-mance especially when there are highly correlated PU signalsHence we propose a signal eigenvalue weighting (SEW)based detection and the test statistic is given as

119879SEW =

119872

sum

119894=1

120588119894

radicsum119872

119894=11205882

119894

120582119894 (21)

where 120582119894and 120588

119894are the eigenvalues of sample and signalsrsquo

covariance matrix respectively Although the SEW baseddetection may perform better performance it is not availablein practice as it needs the a priori information of the channelsignal and noise Hence we try to use the maximum likeli-hood estimation (MLE) of these parameters to design semi-blind detection in which only noise power is needed Hencewe will analyze and derive the MLE of eigenvalues of thePU signalsrsquo covariance matrix in the following

According to the analysis in [23] the MLE of signalsrsquocovariance matrix Rs can be expressed as

Rs = UxDiag ((1205821 minus 1205902

119899)+

(1205822minus 1205902

119899)+

(120582119872minus 1205902

119899)+

)U119867x (22)

where Ux is the eigenvector of sample covariance Rx(119873) and(119909)+= max(0 119909) represents the maximum between 119909 and

0 Hence the MLE of eigenvalues of PU signalsrsquo covariancematrix can be written as

119894= (120582119894minus 1205902

119899)+

(23)


Optimal eigenvalue weighting problem

Joint PDF of eigenvalues is intractable

Loose the constraint conditionsiid signal model

Large number of samples

Transfer the eigenvalue weighting tothe energy weighting

Inaccuracy solutionEN-MRC

The idea of MRC is introduced

Tighten the constraint conditionscorrelated signals

Consider the assumption of iid signalmodel is not valid in practice andeigenvalues can further capture thecorrelations of signals

Model modifyingThe idea of MRC from EN-MRCReplacing energy with eigenvalue

Improved solutionEN-MRC rarr EIG-MRC

SEW and SEAW are proposed

lowastldquoENrdquo and ldquoEIGrdquo are represented energy and eigenvalue respectively

Figure 2 Illustration of how to obtain the eigenvalue weighting schemes

Substituting the MLE of signal eigenvalue into (21) we canobtain the test statistic of signal eigenvalue approximationweighting (SEAW) based detection as

119879SEAW =

119872

sum

119894=1

(120582119894minus 1205902

119899)+

radicsum119872

119895=1((120582119895minus 1205902119899)+

)

2

120582119894 (24)

As a summary we propose three weighting schemes oneis traditional MRC based detection (ie EN-MRC) and theother two are improvement eigenvalue weighting schemesthat is SEW based detection and SEAW based detection Forthe convenience of comparison we summarize these threemethods in Table 1

Remark Since eigenvalue weighting problem can not besolved directly we first loose the constraint conditions andassume that the PU signals follow the iid model and thenumber of samples is very large In this case we can obtain aninaccuracy solution EN-MRC Based on theMRC weightingscheme we then tighten the constraint conditions and mod-ify the assumption to make it satisfy the requirements of thepractical system that is correlated signalmodel Consideringthe eigenvalues can further capture the correlations of signalswe finally replace the energies with eigenvalues and designthe eigenvalue based MRC (EIG-MRC) schemes SEW and

SEAW based detection The corresponding illustration isshown in Figure 2

4 Simulations and Discussions

This section provides some simulation results for multi-antenna cognitive radio systems in the MATLAB environ-ment Since this paper focuses the eigenvalue weightingschemes for spectrum sensing we will compare the proposedEN-MRC SEW and SEAW based detection with eigenvaluebased methods including MED MME and AGM detectionWe assume there is 1 PU or 2 PUs transmitting signal over theNakagami-119898 (119898 = 1) channel in presence of AWGNThe SUsare equipped with 4-element antenna arrayThe stopping cri-terion set is at 10 000 iterations and the119875

119891119886is set as 01 (this has

been specified as the maximum allowable 119875119891119886

by the WRAN80222 working group)

The simulation results of detection performance in termsof number of samples119873 = 100 with 1 PU and 2 PUs are pre-sented in Figures 3 and 4 respectively It is shown that whencompared with eigenvalue based methods such as MEDMME and AGM the proposed SEW and SEAWbased detec-tion perform much higher probability of detection with dif-ferent SNRs while the EN-MRC performs a relatively lowerdetection probability when compared with MED MME andAGM detection It is because algorithms SEW and SEAWare regarded as ldquoEIG-MRCrdquo weighting scheme andMED and


Table 1 Promotion schemes of eigenvalue weighting based spectrum sensing algorithm

Algorithm Test statistic Priori conditions

Energy based maximum ratiocombination (EN-MRC)

119879EN-MRC =119872

sum

119894=1

119903119894

radicsum119872

119894=11199032

119894

120582119894

where 120582119894and 119903119894are the eigenvalues of sample and

the power of the PU signals respectively

PU signalsrsquo energy and noise power

Signal eigenvalue weighting(SEW) based detection

119879SEW =

119872

sum

119894=1

120588119894

radicsum119872

119894=11205882

119894

120582119894

where 120582119894and 120588

119894are the eigenvalues of sample and

PU signalsrsquo covariance matrix respectively

Eigenvalues of PU signalsrsquo covariance matrixand noise power

Signal eigenvalue approximationweighting (SEAW) baseddetection

119879SEAW =

119872

sum

119894=1

(120582119894minus 1205902

119899)+

radicsum119872

119895=1((120582119895minus 1205902119899)+)2

120582119894

where 120582119894is the eigenvalues of sample covariance

matrix 1205902119899is the noise power at receiver

Noise power at receiver

0

01

02

03

04

05

06

07

08

09

1

Prob

abili

ty o

f det

ectio

n

minus30minus35 minus20 minus15 minus10minus25 minus5 0SNR (dB)

EN-MRCSEWSEAW

MEDMMEAGM

Figure 3 Detection performance under119873 = 100 with 1 PU

AGM belong to the selection combination (SC) and equalgain combination (EGC) weighting schemes for eigenvaluesrespectively As for EN-MRC it is the energy based weightingcoefficients which can not fully capture the correlations Inaddition the MME is just a kind of partial eigenvalue basednonweighting detection and thus it has limited detectionperformance However since low SNR approximation hasbeen adopted to derive the EN-MRC scheme the EN-MRCis able to achieve a relatively higher detection probability Forexample the EN-MRC is slightly better thanMME andAGMwhen the SNR is ranging from minus35 dB to minus13 dB On the otherhand when the SNR increases the probability of detection ofEN-MRC drops a little and presents a slightly worse perfor-mance (since the number of eigenvalues for the simulation

0

01

02

03

04

05

06

07

08

09

1

Prob

abili

ty o

f det

ectio

n


EN-MRCSEWSEAW

MEDMMEAGM

Figure 4 Detection performance under119873 = 100 with 2 PUs

is very small the advantages of making detection by using allthe eigenvalues or the energies are not obvious which meansthe AGM or EN-MRCmay not achieve a better performancethan MME) When comparing Figure 3 with Figure 4 wecan find that the performance increases with the increasingnumber of PUs such as a nearly 30 detection probabilityimprovement in terms of minus15 dB

Similarly Figures 5 and 6 present the simulation resultsof probability of detection in terms of number of samples119873 = 1000with 1 PU and 2 PUs Again the proposed SEWandSEAWmethods achieve a higher detection performance andthe EN-MRC outperformsMME and AGM under low SNRsHence the simulation results can further verify that it is just


0

01

02

03

04

05

06

07

08

09

1

Prob

abili

ty o

f det

ectio

n


EN-MRCSEWSEAW

MEDMMEAGM


0

01

02

03

04

05

06

07

08

09

1

Prob

abili

ty o

f det

ectio

n


EN-MRCSEWSEAW

MEDMMEAGM


the replacement of energy with eigenvalue that leads to thehigh improvements in terms of detection probability

In addition as for the three new methods we can findthat SEW performs the best among these proposed methodsEN-MRC performs the worst and the performance of SEAWis between these two methods For example the probabilityof detection of SEAW with 2 PUs (ie SEAW in Figure 3) is

05 in terms of SNR = minus15 dB which is in the middle of 119875119889of

SEW (ie 1) and 119875119889of EN-MRC (ie 02)

According to Figures 3ndash6 a more interesting phe-nomenon can be found that is the SEAWrsquos performanceshifts from the lower 119875

119889area (close to EN-MRC) to a higher

119875119889area (close to SEW) with the increasing of number of

samples and number of PUs which is like a kind of lower andupper bounds of the performance of SEAW If we considerthe performance-complexity tradeoff the proposed SEAWcan be selected as an alternative for its low complexity andrelatively better performance Hence the SEAWmay bemoresuitable for the application in reality

5 Conclusion

This paper focuses on the problem of the eigenvalue weight-ing based spectrum sensing in multiantenna cognitive radiosystem Through the analysis of system model we transferthe eigenvalue weighting issue to the energy based weightingproblem and derive the theoretical expression of detectionthreshold and probability of false alarm and finally obtainthe close form expression Considering the case of correlatedsignals is common in applications we then design the signaleigenvalue based detection methods and they can achievemore higher detection probability Simulation results verifythe efficiency of the proposed algorithms

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

This research was supported by the MSIP (Ministry ofScience ICT and Future Planning) Korea under the ITRC(Information Technology Research Center) support program(IITP-2016-H8501-16-1019) supervised by the IITP (Institutefor Information amp Communications Technology Promo-tion)

References

[1] Federal Communications Commission ldquoNotice of proposedrule making and order facilitating opportunities for flexibleefficient and reliable spectrum use employing cognitive radiotechnologiesrdquo ET Docket 03-108 Federal CommunicationsCommission Washington Wash USA 2005

[2] 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

[3] T Yucek and H Arslan ldquoA survey of spectrum sensing algo-rithms for cognitive radio applicationsrdquo IEEE CommunicationsSurveys and Tutorials vol 11 no 1 pp 116ndash130 2009

[4] E Axell G Leus E G Larsson andH V Poor ldquoSpectrum sens-ing for cognitive radio state-of-the-art and recent advancesrdquoIEEE Signal ProcessingMagazine vol 29 no 3 pp 101ndash116 2012

[5] M T Masonta M Mzyece and N Ntlatlapa ldquoSpectrumdecision in cognitive radio networks a surveyrdquo IEEECommuni-cations Surveys and Tutorials vol 15 no 3 pp 1088ndash1107 2013


[6] H Sun A Nallanathan C-X Wang and Y Chen ldquoWidebandspectrum sensing for cognitive radio networks a surveyrdquo IEEEWireless Communications vol 20 no 2 pp 74ndash81 2013

[7] X Huang T Han and N Ansari ldquoOn green-energy-poweredcognitive radio networksrdquo IEEE Communications Surveys andTutorials vol 17 no 2 pp 827ndash842 2015

[8] Y Zeng Y-C Liang A T Hoang and R Zhang ldquoA review onspectrum sensing for cognitive radio challenges and solutionsrdquoEURASIP Journal on Advances in Signal Processing vol 2010Article ID 381465 15 pages 2010

[9] S M Kay Fundamentals of Statistical Signal Processing Detec-tion Theory Prentice Hall 1998

[10] W A Gardner ldquoExploitation of spectral redundancy in cyclo-stationary signalsrdquo IEEE Signal Processing Magazine vol 8 no2 pp 14ndash36 1991

[11] NHan SH Shon J O Joo and JMKim ldquoSpectral correlationbased signal detection method for spectrum sensing in IEEE80222 WRAN systemsrdquo in Proceedings of the 8th InternationalConference Advanced Communication Technology pp 1765ndash1770 Dublin Ireland February 2006

[12] A Sahai and D Cabric ldquoSpectrum sensing fundamental limitsand practical challengesrdquo in Proceedings of the IEEE Interna-tional Symposium onNew Frontiers in Dynamic SpectrumAccessNetworks (DySPAN rsquo05) Baltimore Md USA November 2005

[13] H-S ChenW Gao andD G Daut ldquoSignature based spectrumsensing algorithms for IEEE 80222 WRANrdquo in Proceedingsof the IEEE International Conference on Communications (ICCrsquo07) pp 6487ndash6492 Glasgow UK June 2007

[14] H Urkowitz ldquoEnergy detection of unknown deterministicsignalsrdquo Proceedings of the IEEE vol 55 no 4 pp 523ndash531 1967

[15] Y Zeng C L Koh and Y-C Liang ldquoMaximum eigenvaluedetection theory and applicationrdquo in Proceedings of the IEEEInternational Conference on Communications (ICC rsquo08) pp4160ndash4164 Beijing China May 2008

[16] R Tandra and A Sahai ldquoSNR walls for signal detectionrdquo IEEEJournal on Selected Topics in Signal Processing vol 2 no 1 pp4ndash17 2008

[17] Y Zeng and Y C Liang ldquoCovariance based signal detectionsfor cognitive radiordquo in Proceedings of the 2nd IEEE InternationalSymposium on New Frontiers in Dynamic Spectrum AccessNetworks (DySPAN rsquo07) pp 202ndash207 Dublin Ireland April2007

[18] C Liu M Li and M-L Jin ldquoBlind energy-based detection forspatial spectrum sensingrdquo IEEE Wireless Communications Let-ters vol 4 no 1 pp 98ndash101 2015

[19] C Liu and M Jin ldquoMaximum-minimum spatial spectrumdetection for cognitive radio using parasitic antenna arraysrdquo inProceedings of the IEEECIC International Conference on Com-munications in China (ICCC rsquo14) pp 365ndash369 Shanghai ChinaOctober 2014

[20] C Liu H Li andM Jin ldquoBlind central symmetry-based featuredetection for spatial spectrumsensingrdquo IEEE Transactions onVehicular Technology 2016

[21] C Liu S S Ali R Zhang S-Y Li J Wang andM-L Jin ldquoSpa-tial spectrum based blind spectrum sensing for multi-antennacognitive radio systemrdquo Journal on Communications vol 36no 4 Article ID 2015087 10 pages 2015

[22] Y Zeng and Y-C Liang ldquoEigenvalue-based spectrum sensingalgorithms for cognitive radiordquo IEEE Transactions on Commu-nications vol 57 no 6 pp 1784ndash1793 2009

[23] R Zhang T J Lim Y-C Liang and Y Zeng ldquoMulti-antennabased spectrum sensing for cognitive radios a GLRT approachrdquoIEEE Transactions on Communications vol 58 no 1 pp 84ndash882010

[24] 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

[25] Z Li D Wang P Qi and B Hao ldquoMaximum eigenvalue basedsensing and power recognition for multi-antenna cognitiveradio systemrdquo IEEE Transactions on Vehicular Technology 2015

[26] A M Tulino and S Verd Random Matrix Theory and WirelessCommunivations Now Publishers Hanover Mass USA 2004

[27] I M Johnstone ldquoOn the distribution of the largest eigenvaluein principal components analysisrdquo The Annals of Statistics vol29 no 2 pp 295ndash327 2001

[28] Y-C Liang Y Zeng E C Y Peh and A T Hoang ldquoSensing-throughput tradeoff for cognitive radio networksrdquo IEEE Trans-actions onWireless Communications vol 7 no 4 pp 1326ndash13372008

[29] J Ma G Zhao and Y Li ldquoSoft combination and detectionfor cooperative spectrum sensing in cognitive radio networksrdquoIEEETransactions onWireless Communications vol 7 no 11 pp4502ndash4507 2008

Submit your manuscripts athttpwwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Distributed Sensor Networks


Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014


ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014


Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

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Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications


Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia


Biomedical Imaging


ArtificialNeural Systems

Advances in


RoboticsJournal of



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Industrial EngineeringJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in



achieve outstanding performance On the other hand eigen-value basedmethods have also been studied in new scenariossuch as cooperative adaptive versions [24] and MultiplePrimary Transmit Power (MPTP) scenario [25]

However most algorithms only consider part of eigenval-ues such as maximum minimum and mean value whichdoes not make full use of all the eigenvalues to make detec-tionMotivated by this we focus on the problemof eigenvalueweighting in multiantenna system and analyze the relatedproblems By analyzing the model of eigenvalue weightingwe transfer the weighting problem to an optimal problemUsing the latest random matrix theory (RMT) [26 27] wederive the close form expression of probability of detectionand probability of false alarm and obtain the optimal solutionFinally we propose new weighting schemes to give promo-tions of the detection performance Simulations verify theefficiency of the proposed algorithms The main contribu-tions of this paper include the following

(i) Different from the traditional eigenvalue based detec-tion we consider making detection by utilizing allof the eigenvalues in the multiantenna system Bytransferring the weighting problem to an optimalproblem we analyze and derive an energy basedmaximum ratio combination (EN-MRC) method

(ii) Considering the case of correlated signals is commonin applications we use the idea of MRC weightingin EN-MRC method to design an eigenvalue basedMRC (EIG-MRC) scheme signal eigenvalue weight-ing (SEW) based detection which needs the a prioriinformation of signalsrsquo covariance matrix and noisepower

(iii) To make the detection more practical we use themaximum likelihood estimation (MLE) approach todesign a method of signal eigenvalue approximationweighting (SEAW) based detection in which only thenoise power is needed

The rest of the paper is organized as follows Section 2explains the system model The eigenvalue weighting baseddetection is studied in Section 3 Section 4 presents simula-tion results and conclusion is presented in Section 5 Somenotations used in the paper are listed as follows superscripts119879 and 119867 stand for transpose and Hermitian transpose(transpose-conjugate) respectively

2 System Model

Figure 1 illustrates a classical multiantenna spectrum sensingscenario with 119863 randomly distributed primary users (PU infigure) and 119875 randomly distributed secondary users (SU infigure) Once PUs begin to communicate the surroundingSUs can receive the PU signals and then capture the samplesto operate the spectrum sensing

According to Figure 1 the SUs are equipped with 119872

receiving antennas and there are 119863 PU signals arriving

in the antenna array In this case the sensing problem inmultiantenna cognitive radio system can be written as

1198670 119909119894(119896) = 119899

119894(119896)

1198671 119909119894(119896) =

119863

sum

119895=1

ℎ119894119895119904119895(119896) + 119899

119894(119896)

(1)

where 119894 = 1 2 119872 represents the 119894th receiving antennaand 119896 = 0 1 119873 minus 1 is the 119896th sample 119909

119894(119896) is the sample

of the 119894th receiving antenna ℎ119894119895is the channel gain between

the 119895th PU signal 119904119895(119896) and the 119894th receiving antenna 119899

119894(119896) is

the additive white Gaussian noise (AWGN) with 0 mean 1205902119899

varianceStacking the samples at the same time we can get the

following receiving vector of antenna array

x (119896) = [1199091 (119896) 1199092 (119896) 119909119872 (119896)]119879

s (119896) = [1199041(119896) 1199042(119896) 119904

119863(119896)]119879

n (119896) = [1198991(119896) 119899

2(119896) 119899

119872(119896)]119879

(2)

Hence formula (1) can be rewritten as the matrix form

1198670 X = N

1198671 X = HS + N

(3)

where X = [x(0) x(1) x(119873 minus 1)]119879 and N = [n(0)n(1)

n(119873 minus 1)]119879 are the antenna receiving matrix and noise

matrix respectivelyH isin C119872times119863 is the channel gain matrix ofthe signal matrix S = [s(0) s(1) s(119873 minus 1)]

119879

3 Eigenvalue Weighting Based Detection

31 Fundamental of Eigenvalue Weighting Based DetectionBased on (3) the corresponding covariance matrix can bewritten as

RX = 119864 (XX119867)

RS = 119864 (SS119867)

RN = 119864 (NN119867)

(4)

Hence we can rewrite RX as

RX = HRSH119867+ RN (5)

Let 1205821ge 1205822ge sdot sdot sdot ge 120582

119872and 1205881ge 1205882ge sdot sdot sdot ge 120588

119863represent the

eigenvalues ofRX andHRSH119867 respectively Obviously whenPUs are present we can get 120582

119894= 120588119894+1205902

119899 when PUs are absent

that is RX = RN we can have 1205821= 1205822= sdot sdot sdot = 120582

119872= 1205902

119899

Based on the analysis above we can make detection byweighting the eigenvalues Considering the number of sam-ples is finite in reality we can get the following test statistic

119879 =

119872

sum

119894=1

119908119894120582119894(RX (119873)) (6)






SU4

SU3

SU2

PU2

SU1

PU1

SUP

PUD









1ge 1205822ge









maxw

119875119889= int

infin

119903

119891119879|1198671(119909w) 119889119909

st 119875119891119886= int

infin

119903

119891119879|1198670(119909w) 119889119909

(7)

where w = [1199081 1199082 119908


vector 119875119889and 119875



(sdot) and 119891119879|1198670


1and119867

0




119872] =


WY = YY119867 = GWXG119867 (8)



119867 (9)


1 1199082 119908



119879 =

119872

sum

119894=1

119908119894120582119894(RX (119873)) asymp

119872

sum

119894=1

120582119894(RY (119873))


=1

119873

119872

sum

119894=1

119873minus1

sum

119896=0

119908119894

1003816100381610038161003816119903X119894 (119896)1003816100381610038161003816

2

(10)


119896=0|119903X119894(119896)|


1198791015840= 119873119879 =

119872

sum

119894=1

119908119894119886119894 (11)



119886119894

sim

N(119873

119872

sum

119894=1

119908119894 2119873

119872

sum

119894=1

1199082

119894) 119867

0

N(119873

119872

sum

119894=1

119908119894(1 + 119903

119894) 2119873

119872

sum

119894=1

1199082

119894(1 + 2119903

119894)) 119867

1

(12)


where 119903119894= 119864|sum

119863



and 119875119889

respectively

119875119891119886= 119875 119879

1015840gt 120574 | 119867

0 = 119876(

120574 minus 119873sum119872

119894=1119908119894

radic2119873sum119872

119894=11199082

119894

) (13)

119875119889= 119875 119879

1015840gt 120574 | 119867

1

= 119876(120574 minus 119873sum

119872

119894=1119908119894(1 + 119903

119894)

radic2119873sum119872

119894=11199082

119894(1 + 2119903

119894)

)

(14)

where119876(119909) = int+infin119909



119875119889= 119876(


119872

119894=1120572119894119903119894

radicsum119872

119894=11205722

119894(1 + 2119903

119894)

) (15)

where 120572119894= 119908119894radicsum119872

119894=11199082

119894and sum119872

119894=11205722



119894=11205722

119894(1 + 2119903


approximated as

119875119889asymp 119876(119876


119873

2

119872

sum

119894=1

120572119894119903119894) (16)


max120572

119872

sum

119894=1

120572119894119903119894

st119872

sum

119894=1

1205722

119894= 1

(17)


120572lowast

119894=

119903119894

radicsum119872

119894=11199032

119894

(18)

Let sum119872119894=11199082


ficient119908lowast

119894= 120572lowast

119894 1 le 119894 le 119872 (19)


119879EN-MRC =119872

sum

119894=1

119903119894

radicsum119872

119894=11199032

119894

120582119894 (20)

where 119903119894= 119864|sum

119863



119894under 119867

1is considered as






119894=


119894119895|2] =





119879SEW =

119872

sum

119894=1

120588119894

radicsum119872

119894=11205882

119894

120582119894 (21)

where 120582119894and 120588




Rs = UxDiag ((1205821 minus 1205902

119899)+

(1205822minus 1205902

119899)+

(120582119872minus 1205902

119899)+

)U119867x (22)



119894= (120582119894minus 1205902

119899)+

(23)

















119879SEAW =

119872

sum

119894=1

(120582119894minus 1205902

119899)+

radicsum119872

119895=1((120582119895minus 1205902119899)+

)

2

120582119894 (24)














119879EN-MRC =119872

sum

119894=1

119903119894

radicsum119872

119894=11199032

119894

120582119894





119879SEW =

119872

sum

119894=1

120588119894

radicsum119872

119894=11205882

119894

120582119894

where 120582119894and 120588





119879SEAW =

119872

sum

119894=1

(120582119894minus 1205902

119899)+

radicsum119872

119895=1((120582119895minus 1205902119899)+)2

120582119894




0

01

02

03

04

05

06

07

08

09

1

Prob

abili

ty o

f det

ectio

n


EN-MRCSEWSEAW

MEDMMEAGM



0

01

02

03

04

05

06

07

08

09

1

Prob

abili

ty o

f det

ectio

n


EN-MRCSEWSEAW

MEDMMEAGM





0

01

02

03

04

05

06

07

08

09

1

Prob

abili

ty o

f det

ectio

n


EN-MRCSEWSEAW

MEDMMEAGM


0

01

02

03

04

05

06

07

08

09

1

Prob

abili

ty o

f det

ectio

n


EN-MRCSEWSEAW

MEDMMEAGM










5 Conclusion


Competing Interests


Acknowledgments


References






































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in








SU4

SU3

SU2

PU2

SU1

PU1

SUP

PUD









1ge 1205822ge









maxw

119875119889= int

infin

119903

119891119879|1198671(119909w) 119889119909

st 119875119891119886= int

infin

119903

119891119879|1198670(119909w) 119889119909

(7)

where w = [1199081 1199082 119908


vector 119875119889and 119875



(sdot) and 119891119879|1198670


1and119867

0




119872] =


WY = YY119867 = GWXG119867 (8)



119867 (9)


1 1199082 119908



119879 =

119872

sum

119894=1

119908119894120582119894(RX (119873)) asymp

119872

sum

119894=1

120582119894(RY (119873))


=1

119873

119872

sum

119894=1

119873minus1

sum

119896=0

119908119894

1003816100381610038161003816119903X119894 (119896)1003816100381610038161003816

2

(10)


119896=0|119903X119894(119896)|


1198791015840= 119873119879 =

119872

sum

119894=1

119908119894119886119894 (11)



119886119894

sim

N(119873

119872

sum

119894=1

119908119894 2119873

119872

sum

119894=1

1199082

119894) 119867

0

N(119873

119872

sum

119894=1

119908119894(1 + 119903

119894) 2119873

119872

sum

119894=1

1199082

119894(1 + 2119903

119894)) 119867

1

(12)


where 119903119894= 119864|sum

119863



and 119875119889

respectively

119875119891119886= 119875 119879

1015840gt 120574 | 119867

0 = 119876(

120574 minus 119873sum119872

119894=1119908119894

radic2119873sum119872

119894=11199082

119894

) (13)

119875119889= 119875 119879

1015840gt 120574 | 119867

1

= 119876(120574 minus 119873sum

119872

119894=1119908119894(1 + 119903

119894)

radic2119873sum119872

119894=11199082

119894(1 + 2119903

119894)

)

(14)

where119876(119909) = int+infin119909



119875119889= 119876(


119872

119894=1120572119894119903119894

radicsum119872

119894=11205722

119894(1 + 2119903

119894)

) (15)

where 120572119894= 119908119894radicsum119872

119894=11199082

119894and sum119872

119894=11205722



119894=11205722

119894(1 + 2119903


approximated as

119875119889asymp 119876(119876


119873

2

119872

sum

119894=1

120572119894119903119894) (16)


max120572

119872

sum

119894=1

120572119894119903119894

st119872

sum

119894=1

1205722

119894= 1

(17)


120572lowast

119894=

119903119894

radicsum119872

119894=11199032

119894

(18)

Let sum119872119894=11199082


ficient119908lowast

119894= 120572lowast

119894 1 le 119894 le 119872 (19)


119879EN-MRC =119872

sum

119894=1

119903119894

radicsum119872

119894=11199032

119894

120582119894 (20)

where 119903119894= 119864|sum

119863



119894under 119867

1is considered as






119894=


119894119895|2] =





119879SEW =

119872

sum

119894=1

120588119894

radicsum119872

119894=11205882

119894

120582119894 (21)

where 120582119894and 120588




Rs = UxDiag ((1205821 minus 1205902

119899)+

(1205822minus 1205902

119899)+

(120582119872minus 1205902

119899)+

)U119867x (22)



119894= (120582119894minus 1205902

119899)+

(23)

















119879SEAW =

119872

sum

119894=1

(120582119894minus 1205902

119899)+

radicsum119872

119895=1((120582119895minus 1205902119899)+

)

2

120582119894 (24)














119879EN-MRC =119872

sum

119894=1

119903119894

radicsum119872

119894=11199032

119894

120582119894





119879SEW =

119872

sum

119894=1

120588119894

radicsum119872

119894=11205882

119894

120582119894

where 120582119894and 120588





119879SEAW =

119872

sum

119894=1

(120582119894minus 1205902

119899)+

radicsum119872

119895=1((120582119895minus 1205902119899)+)2

120582119894




0

01

02

03

04

05

06

07

08

09

1

Prob

abili

ty o

f det

ectio

n


EN-MRCSEWSEAW

MEDMMEAGM



0

01

02

03

04

05

06

07

08

09

1

Prob

abili

ty o

f det

ectio

n


EN-MRCSEWSEAW

MEDMMEAGM





0

01

02

03

04

05

06

07

08

09

1

Prob

abili

ty o

f det

ectio

n


EN-MRCSEWSEAW

MEDMMEAGM


0

01

02

03

04

05

06

07

08

09

1

Prob

abili

ty o

f det

ectio

n


EN-MRCSEWSEAW

MEDMMEAGM










5 Conclusion


Competing Interests


Acknowledgments


References






































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




where 119903119894= 119864|sum

119863



and 119875119889

respectively

119875119891119886= 119875 119879

1015840gt 120574 | 119867

0 = 119876(

120574 minus 119873sum119872

119894=1119908119894

radic2119873sum119872

119894=11199082

119894

) (13)

119875119889= 119875 119879

1015840gt 120574 | 119867

1

= 119876(120574 minus 119873sum

119872

119894=1119908119894(1 + 119903

119894)

radic2119873sum119872

119894=11199082

119894(1 + 2119903

119894)

)

(14)

where119876(119909) = int+infin119909



119875119889= 119876(


119872

119894=1120572119894119903119894

radicsum119872

119894=11205722

119894(1 + 2119903

119894)

) (15)

where 120572119894= 119908119894radicsum119872

119894=11199082

119894and sum119872

119894=11205722



119894=11205722

119894(1 + 2119903


approximated as

119875119889asymp 119876(119876


119873

2

119872

sum

119894=1

120572119894119903119894) (16)


max120572

119872

sum

119894=1

120572119894119903119894

st119872

sum

119894=1

1205722

119894= 1

(17)


120572lowast

119894=

119903119894

radicsum119872

119894=11199032

119894

(18)

Let sum119872119894=11199082


ficient119908lowast

119894= 120572lowast

119894 1 le 119894 le 119872 (19)


119879EN-MRC =119872

sum

119894=1

119903119894

radicsum119872

119894=11199032

119894

120582119894 (20)

where 119903119894= 119864|sum

119863



119894under 119867

1is considered as






119894=


119894119895|2] =





119879SEW =

119872

sum

119894=1

120588119894

radicsum119872

119894=11205882

119894

120582119894 (21)

where 120582119894and 120588




Rs = UxDiag ((1205821 minus 1205902

119899)+

(1205822minus 1205902

119899)+

(120582119872minus 1205902

119899)+

)U119867x (22)



119894= (120582119894minus 1205902

119899)+

(23)

















119879SEAW =

119872

sum

119894=1

(120582119894minus 1205902

119899)+

radicsum119872

119895=1((120582119895minus 1205902119899)+

)

2

120582119894 (24)














119879EN-MRC =119872

sum

119894=1

119903119894

radicsum119872

119894=11199032

119894

120582119894





119879SEW =

119872

sum

119894=1

120588119894

radicsum119872

119894=11205882

119894

120582119894

where 120582119894and 120588





119879SEAW =

119872

sum

119894=1

(120582119894minus 1205902

119899)+

radicsum119872

119895=1((120582119895minus 1205902119899)+)2

120582119894




0

01

02

03

04

05

06

07

08

09

1

Prob

abili

ty o

f det

ectio

n


EN-MRCSEWSEAW

MEDMMEAGM



0

01

02

03

04

05

06

07

08

09

1

Prob

abili

ty o

f det

ectio

n


EN-MRCSEWSEAW

MEDMMEAGM





0

01

02

03

04

05

06

07

08

09

1

Prob

abili

ty o

f det

ectio

n


EN-MRCSEWSEAW

MEDMMEAGM


0

01

02

03

04

05

06

07

08

09

1

Prob

abili

ty o

f det

ectio

n


EN-MRCSEWSEAW

MEDMMEAGM










5 Conclusion


Competing Interests


Acknowledgments


References






































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in



















119879SEAW =

119872

sum

119894=1

(120582119894minus 1205902

119899)+

radicsum119872

119895=1((120582119895minus 1205902119899)+

)

2

120582119894 (24)














119879EN-MRC =119872

sum

119894=1

119903119894

radicsum119872

119894=11199032

119894

120582119894





119879SEW =

119872

sum

119894=1

120588119894

radicsum119872

119894=11205882

119894

120582119894

where 120582119894and 120588





119879SEAW =

119872

sum

119894=1

(120582119894minus 1205902

119899)+

radicsum119872

119895=1((120582119895minus 1205902119899)+)2

120582119894




0

01

02

03

04

05

06

07

08

09

1

Prob

abili

ty o

f det

ectio

n


EN-MRCSEWSEAW

MEDMMEAGM



0

01

02

03

04

05

06

07

08

09

1

Prob

abili

ty o

f det

ectio

n


EN-MRCSEWSEAW

MEDMMEAGM





0

01

02

03

04

05

06

07

08

09

1

Prob

abili

ty o

f det

ectio

n


EN-MRCSEWSEAW

MEDMMEAGM


0

01

02

03

04

05

06

07

08

09

1

Prob

abili

ty o

f det

ectio

n


EN-MRCSEWSEAW

MEDMMEAGM










5 Conclusion


Competing Interests


Acknowledgments


References






































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in







119879EN-MRC =119872

sum

119894=1

119903119894

radicsum119872

119894=11199032

119894

120582119894





119879SEW =

119872

sum

119894=1

120588119894

radicsum119872

119894=11205882

119894

120582119894

where 120582119894and 120588





119879SEAW =

119872

sum

119894=1

(120582119894minus 1205902

119899)+

radicsum119872

119895=1((120582119895minus 1205902119899)+)2

120582119894




0

01

02

03

04

05

06

07

08

09

1

Prob

abili

ty o

f det

ectio

n


EN-MRCSEWSEAW

MEDMMEAGM



0

01

02

03

04

05

06

07

08

09

1

Prob

abili

ty o

f det

ectio

n


EN-MRCSEWSEAW

MEDMMEAGM





0

01

02

03

04

05

06

07

08

09

1

Prob

abili

ty o

f det

ectio

n


EN-MRCSEWSEAW

MEDMMEAGM


0

01

02

03

04

05

06

07

08

09

1

Prob

abili

ty o

f det

ectio

n


EN-MRCSEWSEAW

MEDMMEAGM










5 Conclusion


Competing Interests


Acknowledgments


References






































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




0

01

02

03

04

05

06

07

08

09

1

Prob

abili

ty o

f det

ectio

n


EN-MRCSEWSEAW

MEDMMEAGM


0

01

02

03

04

05

06

07

08

09

1

Prob

abili

ty o

f det

ectio

n


EN-MRCSEWSEAW

MEDMMEAGM










5 Conclusion


Competing Interests


Acknowledgments


References






































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in



































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in










Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in



Documents

Research Article On the Eigenvalue Based Detection for ...downloads.hindawi.com/journals/misy/2016/3848734.pdf · Research Article On the Eigenvalue Based Detection for Multiantenna