research article on the eigenvalue based detection for...
Post on 21-Jun-2020
1 Views
Preview:
TRANSCRIPT
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
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)
4 Mobile Information Systems
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
119895=1ℎ119894119895119904119895(119896)|2 is the power of the PU signals
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)
Mobile Information Systems 5
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
6 Mobile Information Systems
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
minus30minus35 minus20 minus15 minus10minus25 minus5 0SNR (dB)
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
Mobile Information Systems 7
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 5 Detection performance under119873 = 1000 with 1 PU
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 6 Detection performance under119873 = 1000 with 2 PUs
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
8 Mobile Information Systems
[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
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Distributed Sensor Networks
International Journal of
Advances in
FuzzySystems
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014
International Journal of
ReconfigurableComputing
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied Computational Intelligence and Soft Computing
thinspAdvancesthinspinthinsp
Artificial Intelligence
HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014
Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Journal of
Computer Networks and Communications
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation
httpwwwhindawicom Volume 2014
Advances in
Multimedia
International Journal of
Biomedical Imaging
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ArtificialNeural Systems
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Computational Intelligence and Neuroscience
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Human-ComputerInteraction
Advances in
Computer EngineeringAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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
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)
4 Mobile Information Systems
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
119895=1ℎ119894119895119904119895(119896)|2 is the power of the PU signals
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)
Mobile Information Systems 5
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
6 Mobile Information Systems
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
minus30minus35 minus20 minus15 minus10minus25 minus5 0SNR (dB)
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
Mobile Information Systems 7
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 5 Detection performance under119873 = 1000 with 1 PU
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 6 Detection performance under119873 = 1000 with 2 PUs
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
8 Mobile Information Systems
[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
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Distributed Sensor Networks
International Journal of
Advances in
FuzzySystems
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014
International Journal of
ReconfigurableComputing
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied Computational Intelligence and Soft Computing
thinspAdvancesthinspinthinsp
Artificial Intelligence
HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014
Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Journal of
Computer Networks and Communications
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation
httpwwwhindawicom Volume 2014
Advances in
Multimedia
International Journal of
Biomedical Imaging
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ArtificialNeural Systems
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Computational Intelligence and Neuroscience
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Human-ComputerInteraction
Advances in
Computer EngineeringAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mobile Information Systems 3
Licensed PU channels
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)
4 Mobile Information Systems
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
119895=1ℎ119894119895119904119895(119896)|2 is the power of the PU signals
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)
Mobile Information Systems 5
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
6 Mobile Information Systems
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
minus30minus35 minus20 minus15 minus10minus25 minus5 0SNR (dB)
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
Mobile Information Systems 7
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 5 Detection performance under119873 = 1000 with 1 PU
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 6 Detection performance under119873 = 1000 with 2 PUs
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
8 Mobile Information Systems
[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
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Distributed Sensor Networks
International Journal of
Advances in
FuzzySystems
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014
International Journal of
ReconfigurableComputing
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied Computational Intelligence and Soft Computing
thinspAdvancesthinspinthinsp
Artificial Intelligence
HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014
Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Journal of
Computer Networks and Communications
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation
httpwwwhindawicom Volume 2014
Advances in
Multimedia
International Journal of
Biomedical Imaging
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ArtificialNeural Systems
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Computational Intelligence and Neuroscience
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Human-ComputerInteraction
Advances in
Computer EngineeringAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
4 Mobile Information Systems
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
119895=1ℎ119894119895119904119895(119896)|2 is the power of the PU signals
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)
Mobile Information Systems 5
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
6 Mobile Information Systems
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
minus30minus35 minus20 minus15 minus10minus25 minus5 0SNR (dB)
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
Mobile Information Systems 7
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 5 Detection performance under119873 = 1000 with 1 PU
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 6 Detection performance under119873 = 1000 with 2 PUs
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
8 Mobile Information Systems
[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
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Distributed Sensor Networks
International Journal of
Advances in
FuzzySystems
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014
International Journal of
ReconfigurableComputing
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied Computational Intelligence and Soft Computing
thinspAdvancesthinspinthinsp
Artificial Intelligence
HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014
Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Journal of
Computer Networks and Communications
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation
httpwwwhindawicom Volume 2014
Advances in
Multimedia
International Journal of
Biomedical Imaging
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ArtificialNeural Systems
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Computational Intelligence and Neuroscience
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Human-ComputerInteraction
Advances in
Computer EngineeringAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mobile Information Systems 5
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
6 Mobile Information Systems
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
minus30minus35 minus20 minus15 minus10minus25 minus5 0SNR (dB)
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
Mobile Information Systems 7
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 5 Detection performance under119873 = 1000 with 1 PU
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 6 Detection performance under119873 = 1000 with 2 PUs
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
8 Mobile Information Systems
[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
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Distributed Sensor Networks
International Journal of
Advances in
FuzzySystems
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014
International Journal of
ReconfigurableComputing
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied Computational Intelligence and Soft Computing
thinspAdvancesthinspinthinsp
Artificial Intelligence
HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014
Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Journal of
Computer Networks and Communications
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation
httpwwwhindawicom Volume 2014
Advances in
Multimedia
International Journal of
Biomedical Imaging
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ArtificialNeural Systems
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Computational Intelligence and Neuroscience
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Human-ComputerInteraction
Advances in
Computer EngineeringAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
6 Mobile Information Systems
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
minus30minus35 minus20 minus15 minus10minus25 minus5 0SNR (dB)
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
Mobile Information Systems 7
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 5 Detection performance under119873 = 1000 with 1 PU
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 6 Detection performance under119873 = 1000 with 2 PUs
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
8 Mobile Information Systems
[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
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Distributed Sensor Networks
International Journal of
Advances in
FuzzySystems
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014
International Journal of
ReconfigurableComputing
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied Computational Intelligence and Soft Computing
thinspAdvancesthinspinthinsp
Artificial Intelligence
HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014
Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Journal of
Computer Networks and Communications
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation
httpwwwhindawicom Volume 2014
Advances in
Multimedia
International Journal of
Biomedical Imaging
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ArtificialNeural Systems
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Computational Intelligence and Neuroscience
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Human-ComputerInteraction
Advances in
Computer EngineeringAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mobile Information Systems 7
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 5 Detection performance under119873 = 1000 with 1 PU
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 6 Detection performance under119873 = 1000 with 2 PUs
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
8 Mobile Information Systems
[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
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Distributed Sensor Networks
International Journal of
Advances in
FuzzySystems
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014
International Journal of
ReconfigurableComputing
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied Computational Intelligence and Soft Computing
thinspAdvancesthinspinthinsp
Artificial Intelligence
HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014
Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Journal of
Computer Networks and Communications
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation
httpwwwhindawicom Volume 2014
Advances in
Multimedia
International Journal of
Biomedical Imaging
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ArtificialNeural Systems
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Computational Intelligence and Neuroscience
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Human-ComputerInteraction
Advances in
Computer EngineeringAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
8 Mobile Information Systems
[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
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Distributed Sensor Networks
International Journal of
Advances in
FuzzySystems
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014
International Journal of
ReconfigurableComputing
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied Computational Intelligence and Soft Computing
thinspAdvancesthinspinthinsp
Artificial Intelligence
HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014
Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Journal of
Computer Networks and Communications
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation
httpwwwhindawicom Volume 2014
Advances in
Multimedia
International Journal of
Biomedical Imaging
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ArtificialNeural Systems
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Computational Intelligence and Neuroscience
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Human-ComputerInteraction
Advances in
Computer EngineeringAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Submit your manuscripts athttpwwwhindawicom
Computer Games Technology
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Distributed Sensor Networks
International Journal of
Advances in
FuzzySystems
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014
International Journal of
ReconfigurableComputing
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied Computational Intelligence and Soft Computing
thinspAdvancesthinspinthinsp
Artificial Intelligence
HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014
Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Journal of
Computer Networks and Communications
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation
httpwwwhindawicom Volume 2014
Advances in
Multimedia
International Journal of
Biomedical Imaging
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ArtificialNeural Systems
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Computational Intelligence and Neuroscience
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Human-ComputerInteraction
Advances in
Computer EngineeringAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
top related