A Novel Spectrum Sensing Algorithm Based on MED for Cognitive Radio*

WANG Hanrui,LI Manjiang,TANG Pengcheng,YANG Xi,LEI Kejun

(College of Information Science and Engineering,Jishou University,Jishou 416000,Hunan China)

1 Introduction

With the development of the wireless communication,the demand for greater speed,more reliability and wider coverage is increasing.Thus,the demand for wireless spectrum resources is becoming more and more vigorous.However,the conventional fixed spectrum allocation policy leads to low spectrum usage in many of the frequency bands.Cognitive radio is a promising technology to exploit the under-used spectrum by detecting the spectrum holes before the secondary user uses the frequecy band[1-2].Obviously,the design of spectrum sensing algorithm which is adopted to reliably find out the unused spectrum resources is a key issue for cognitive radio.

There have been several spectrum sensing algorithms,including the energy detector (ED),matched filter (MF) and cyclostationary detection (CD).Each of them has advantages and disadvantages.Among them,ED is optimal for sensing independent and identically distributed primary user signal[3].However,ED is not optimal for sensing correlated primary user signal[4].To overcome shortcomings of the ED method,a spectrum sensing method based on the maximum eigenvalues detection (MED) has been firstly introduced in ref.[4],which uses the ratio of the maximum eigenvalue of the sample covariance matrix and the noise variance as the decision variable.The results have showed that the MED method performs better ED when the primary user signal is correlated.However,it is very hard for us to calculate the theoretical decision threshold for MED algorithm because the accurate expression of the statistical distribution function is very complicated.In ref.[4],an approximated decision threshold was obtained by using the large dimensional random matrix theory (LDRMT)[5-7].However,the approximated threshold cannot yield reliable sensing results and leads to suboptimal detection performance.

In this paper,a new MED method based on a more accurate decision threshold has been proposed.The new MED algorithm can yield more reliable detection results than the traditional MED method.Simulation results verify the effectiveness of the proposed method.

2 Spectrum Sensing Algorithm Based on Maximum Eigenvalue

In this paper,a multiple antenna spectrum sensing scenario is considered.Assume that the sensor node is equipped withLantennas andMconsecutive samples can be utilized for the statistical decision.StackNreceived signal samples into a column vectory(m),i.e.,

y(m)=(y1(m)y2(m)...yL(m))T.

Similarly,we respectively define the primary signal vector and the noise vector as follows:

x(m)=(x1(m)x2(m)...xL(m))T,

and

n(m)=(n1(m)n2(m)...nL(m))T,

wherey(m)=x(m)+n(m),m=1,2,…,M.In the following,the hypothesisH0indicates that the primary signal does not exist,and the hypothesisH1indicates that the primary signal exists.Correspondingly,the binary hypothesis testing model for the multi-antenna spectrum sensing problem can be expressed as

Note thatx(m)=Hs(m) is the received primary user signal vector whereHis the channel gain.Without loss of generality,we assume thatn(m) is the zero mean white Gaussian process with statistical covariance matrixpI.Here,pdenotes the noise variance.Assuming that the received primary signal and the background noise are statistically independent,the statistical covariance matrices of the received signal can then be written as

whereRx=E(x(n)xT(n)) denotes the statistical covariance matrix of the primary signal,superscript (·)Tstands for transpose,andE(·) stands for expectation operation.Note that the maximum eigenvalue ofRyunderH1is usually greater than the noise variance;however,the maximum eigenvalue ofRyunderH0is equal to the noise variancep.Thus,the ratio between the maximum eigenvalue ofRyandpcan be selected as a decision statistic to detect the unused channel.

DenoteTas the decision threshold.IfD>T,then the primary signal exists.Other,only the background noise exists.BecauseDis a random variable,the statistical distribution ofDunderH0should be determined to obtain the decision threshold.

3 Analysis of False-Alarm Probability and Decision Threshold

Pf=P(lmax>pT).

(1)

Denotelminas the minimum eigenvalue ofR.According to the recent results of LDRMT,lminandlmaxrespectively converge to a definite value[5]:

(2)

and

(3)

Combining (2) and (3),we have

(4)

Substituting (4) into (1) yields

Correspondingly,we have

where the normalized parametersaandbin the above relational expression are defined as

4 Simulation Results

In this section,the performance of the novel multiple antenna spectrum sensing algorithm based on the maximum eigenvalue detection is demonstrated.All simulation results are obtained via 10 000 Monte Carlo trials.In the simulations,the number of antennaL=5,the number of samplesM=100,and the target false-alarm probabilityPFA=0.1.

Table 1 shows the practical output false-alarm probabilities under different signal-to-noise ratios (SNR) whenPFA=0.1.Note that the theoretical decision thresholds,which are obtained by using the traditional method in ref.[4] and the new method proposed in this paper,are used for the multiple antenna spectrum sensing.The results clearly show that the traditional MED method cannot produce accurate enough theoretical threshold for the decision process,which results in suboptimal false-alarm performance.On the other hand,the simulation results also clearly indicate that our new method can produce reliable theoretical decision threshold because the practical output false-alarm probabilities match well with the target valuePFA=0.1.Obviously,the proposed MED algorithm can produce more reliable sensing results than the traditional one in ref.[4].

Table1PracticalOutputFalse-AlarmProbabilitiesUnderDifferentSNR

MethodSNR/dB-12-11-10-9-8-7-6-5-4-3-2ProposedMED0．09450．10300．09550．09100．10300．09300．08500．08800．09600．08250．1040TraditionalMED[4]0．06600．07300．06350．06150．06500．06200．05750．05700．06350．05100．0635

Fig.1 shows the detection probabilities of the above two MED algorithms under different SNR conditions whenPFA=0.1.The simulation results clearly illustrate that the new MED method achieves a higher detection probability compared with the traditional method in the low SNR region.For instant,whenPFA=0.1,the detection probability of our algorithm is about 63.7%,while the detection probability of the traditional algorithm is about 56% when SNR was -10 dB.In other words,the detection probability is increased by 7.7% when SNR was -10 dB.To further verify the performance of the algorithm,Fig.2 shows the detection probabilities whenPFA=0.05.The simulation results in Fig.2 illustrate the superiority of the algorithm again.

Fig.1 Probability of Detection Versus SNR When PFA=0.1

Fig.2 Probability of Detection Versus SNR When PFA=0.05

5 Conclusions

In this paper,a novel maximum eigenvalue based spectrum sensing algorithm for cognitive radio has been proposed.Using the recent results of the large dimensional random matrix theory,a new theoretical decision threshold has been derived for MED algorithm.The new decision threshold has more reliable sensing performance and a higher detection probability.Simulation results verify the effectiveness of the new MED algorithm.

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