Advanced
Generalized Likelihood Ratio Test For Cyclostationary Multi-Antenna Spectrum Sensing
Generalized Likelihood Ratio Test For Cyclostationary Multi-Antenna Spectrum Sensing
KSII Transactions on Internet and Information Systems (TIIS). 2014. Aug, 8(8): 2763-2782
Copyright © 2014, Korean Society For Internet Information
  • Received : December 19, 2013
  • Accepted : June 21, 2014
  • Published : August 28, 2014
Download
PDF
e-PUB
PubReader
PPT
Export by style
Share
Article
Author
Metrics
Cited by
TagCloud
About the Authors
Guohui Zhong
Jiaming Guo
Daiming Qu
Tao Jiang
Jingchao Sun

Abstract
In this paper, a generalized likelihood ratio test (GLRT) is proposed for cyclostationary multi-antenna spectrum sensing in cognitive radio systems, which takes into account the cyclic autocorrelations obtained from all the receiver antennas and the cyclic cross-correlations obtained from all pairs of receiver antennas. The proposed GLRT employs a different hypotheses problem formulation and a different asymptotic covariance estimation method, which are proved to be more suitable for multi-antenna systems than those employed by the Dandawaté-Giannakis algorithm. Moreover, we derive the asymptotic distributions of the proposed test statistics, and prove the constant false alarm rate property of the proposed algorithm. Extensive simulations are conducted, showing that the proposed GLRT can achieve better detection performance than the Dandawaté-Giannakis algorithm and its extension for multi-antenna cases.
Keywords
1. Introduction
R ecently, cognitive radio (CR) has drawn significant attention from academic and industrial communities to meet the ever-growing needs for spectrum resources [1] - [4] . In CR systems, cognitive unlicensed users are allowed to identify and exploit the local and instantaneous spectrum white space where no licensed user is present. A CR user is required to perform spectrum sensing [5] - [8] periodically to avoid significant interference to the licensed systems. If an idle channel is detected, the CR user can transmit or receive data on the channel; whereas, if a licensed user is detected, the CR user avoids data transmission on the channel and tunes to another idle channel. Cyclostationarity-based signal detection is one of the widely considered spectrum sensing techniques for CR systems, due to its capability of differentiating noise from licensed user signals. The cyclostationary spectrum sensing methods exploit the cyclic statistics such as cyclic auto-correlation for the detection of licensed user, which are nonzero at particular cyclic frequencies for the licensed user signal [9] , [10] .
Many existing cyclostationarity-based spectrum sensing methods [11] - [21] have employed the Dandawate-Giannakis algorithm [22] due to its constant false alarm rate (CFAR) property and robustness in the low signal-to-noise ratio (SNR) regime. The Dandawate-Giannakis algorithm can be viewed as the generalized likelihood ratio test (GLRT) for the presence of cyclostationarity. It has assumed that the distributions of the cyclic auto-correlation estimations under the null hypothesis and the alternative hypothesis have the same asymptotic covariance and differ only in mean. Based on this, the asymptotic covariance estimation can be generalized regardless of the hypothesis, which leads to a final test statistic having a squared Mahalanobis distance form.
The performance of spectrum sensing can be seriously degraded in Rayleigh fading situations. To remedy this problem, multi-antenna spectrum sensing that exploits spatial diversity could be employed. Recently, how to improve the performance of cyclostationary spectrum sensing by using multiple antennas has also been studied by researchers. In [20] , we have extended the Dandawate-Giannakis algorithm to allow multi-antenna spectrum sensing, which takes into account the cyclic auto-correlations obtained from all receiver antennas and the cyclic cross-correlations obtained from all pairs of receiver antennas. Maximum radio combining was proposed in [21] , which requires the channel state information as a priori information. In [23] , the spectral correlation function (SCF) is used to estimate the phase difference between the channel responses of different antennas, and the test statistic is formed by combining the SCFs of the received signals from all the antennas. Collaborative spectrum sensing [11] can be viewed as a special case of multi-antenna spectrum sensing, which drops the cyclic cross-correlations in detection.
In this paper, we propose a novel GLRT for cyclostationary multi-antenna spectrum sensing. The framework of the proposed algorithm is similar to that in [20] , i.e., taking into account all the achievable cyclic auto-correlations and cyclic cross-correlations. However, it is different with [20] in hypotheses problem formulation and asymptotic covariance estimation. More specifically, the the asymptotic covariances among the cyclic cross-correlations and auto-correlations under the null hypothesis are assumed to different from those under the alternative hypothesis, while they are assumed to be the same in the Dandawaté-Giannakis algorithm and its extension [20] . We use an example, where the additive noise is low-pass zero-mean Gaussian noise, to illustrate the validity and necessity of this difference and conduct the proposed GLRT. The distribution and the computational complexity of the proposed test statistic are also derived. The proposed algorithm maintains the CFAR property and has better detection performance and much lower computational complexity than those of [20] . For example, a performance gain of 1.7dB is achieved for a four-antenna system. The necessity of taking into account the cyclic cross-correlations is also demonstrated via simulation experiments.
The rest of this paper is organized as follows: In Section 2, the multi-antenna spectrum sensing model is presented. In Section 3, we propose the GLRT for cyclostationary multi-antenna spectrum sensing, and then demonstrate how to construct the proposed GLRT under the assumption that the additive noise is low-pass zero-mean Gaussian noise with uncertain power. An example is presented in Section 4 to further illustrate the proposed test. In section 5, asymptotic distribution and computational complexity of the proposed test statistic are given. Simulation results and discussions are presented in Section 6. Finally, conclusions are drawn in Section 7.
2. System Model of Multi-Antenna Spectrum Sensing
As shown in Fig. 1 , we consider a CR receiver with N ( N ≥2) antennas. We assume an independent flat Rayleigh fading channel [24] for each pair of antennas between the transmitter and receiver in the following derivations.
PPT Slide
Lager Image
Multi-antenna spectrum sensing model.
At each sensing period, the CR tries to distinguish between the following two hypotheses:
PPT Slide
Lager Image
where s ( t ) is the signal transmitted by the licensed user; i denotes the index of antenna; xi ( t ) and wi ( t ) denote the received signal and the low-pass zero-mean complex Gaussian noise at the i -th antenna, respectively; hi denotes the channel response for the i -th antenna, which can be further expressed as
PPT Slide
Lager Image
where γi is Rayleigh distributed with the probability density function (PDF) as
PPT Slide
Lager Image
and θi denotes the phase offset of the channel response, which is uniformly distributed with the PDF as
PPT Slide
Lager Image
Throughout this paper, we assume that hi is invariant over the sensing period, and both wi ( t ) and hi are independent for different antennas.
3. Cyclostationarity-Based Multi-Antenna Spectrum Sensing
- 3.1 Cyclostationarity
A continuous-time random process x ( t ) is a wide sense second-order cyclostationary process, if its mean and auto-correlation are periodical with some periods [10] . Define the time varying auto-correlation of x ( t ) as
PPT Slide
Lager Image
where τ denotes the lag. Then, due to its periodicity, Rxx ( t , τ ) can be represented as a Fourier series as
PPT Slide
Lager Image
where τ is called the cyclic frequency and the Fourier coefficients are called the cyclic auto-correlation functions, which are given by
PPT Slide
Lager Image
Another useful function that can characterize the second-order cyclostationary process x ( t ) is called the conjugated cyclic auto-correlation (CCA) function, which is given by
PPT Slide
Lager Image
where
PPT Slide
Lager Image
In the rest of this paper, we focus on the case using the CCA functions, while the one concerning cyclic auto-correlation functions can be derived similarly.
The discrete time version of the CCA estimation,
PPT Slide
Lager Image
can be calculated as
PPT Slide
Lager Image
where M is the number of available signal samples, ν is the discrete version of the lag parameter, and m is the discrete time index, i.e., x [ m ]= x ( mTs ), where Ts denotes the sampling period.
As for the multi-antenna spectrum sensing problem where there are N antennas at the CR receiver, N CCA functions and N ( N −1)/2 conjugated cyclic cross-correlation (CCC) functions can be obtained, which can be defined together as follows:
PPT Slide
Lager Image
where
PPT Slide
Lager Image
Note that when i = j ,
PPT Slide
Lager Image
denotes the CCA functions, and when
PPT Slide
Lager Image
denotes the CCC functions. Also note that we only take into account
PPT Slide
Lager Image
and neglect
PPT Slide
Lager Image
since it is easy to verify that
PPT Slide
Lager Image
Similar to (8), a discrete time version estimation of
PPT Slide
Lager Image
with M samples is given by
PPT Slide
Lager Image
- 3.2 GLRT for the Multi-Antenna Cyclostationary Spectrum Sensing
Taking into account all CCA and CCC estimations, we can define a vector
PPT Slide
Lager Image
as
PPT Slide
Lager Image
where
PPT Slide
Lager Image
By using
PPT Slide
Lager Image
, the hypotheses problem for multi-antenna spectrum sensing is now formulated as follows:
PPT Slide
Lager Image
where r mul is the asymptotic value of
PPT Slide
Lager Image
under H 1 ,
PPT Slide
Lager Image
is the estimation error vector resulted from Wi ( t ) and
PPT Slide
Lager Image
is the estimation error vector resulted from both Wi ( t ) and s ( t ), which are asymptotically distributed as
PPT Slide
Lager Image
respectively. Different from the Dandawaté-Giannakis algorithm and its extension proposed in [20] , we do not assume that the asymptotic covariance matrix under H 0 and H 1 is the same, i.e., we assume Σ mul,0 Σ mul,1 in our hypotheses problem. Our hypotheses problem is more realistic, due to the fact that both s ( t ) and wi ( t ) contributes to the asymptotic covariance matrix under H 1 , whereas only wi ( t ) contributes to H 0 . We will use an example, where the additive noise is the low-pass zero-mean complex Gaussian noise, to illustrate its validity and necessity in the next subsection.
According to the binary hypotheses given in (14), the generalized likelihood ratio (GLR) for the test problem is given by
PPT Slide
Lager Image
By substituting
PPT Slide
Lager Image
for θ 1 and 0 for θ 0 , we can obtain that
PPT Slide
Lager Image
Taking the logarithm transformation of the GLR gives the test statistic as follows:
PPT Slide
Lager Image
Since the second term of this test statistic is of the same value under H 1 and H 0 , it has no contribution to the detection and can be eliminated, which yields the final test statistic as
PPT Slide
Lager Image
Remark 1: The GLR test statistic only uses the asymptotic covariance matrix under H 0 , Σ mul,0 , and it is unrelated to the asymptotic covariance matrix under H 1 , Σ mul,1 .
Remark 2: The GLR test statistic suggests that knowledge or partial knowledge of the statistics and distributions of the additive noise can be exploited to improve the detection performance. In the next section, it is shown in an example that if the additive noise is low-pass zero-mean complex Gaussian, and its bandwidth and power spectral density is known, Σ mul,0 can be calculated.
Remark 3: If no assumption about the additive noise can be made in the detection, the estimated
PPT Slide
Lager Image
calculated from the most recent detection that was decided to be under H 0 can be employed as a good approximation of Σ mul,0 of the current detection. Since the noise statistic does not change rapidly in practical situations,
PPT Slide
Lager Image
calculated from the recent detection is a good approximation of current Σ mul,0 . The test statistic of Dandawaté-Giannakis algorithm employs current
PPT Slide
Lager Image
, whereas our proposed method suggests using the
PPT Slide
Lager Image
calculated from the most recent detection that was decided to be under H 0 .
4. An Example ofΣmul,0Estimation and the Corresponding Test
In this section, we demonstrate how to estimate Σ mul,0 and construct the GLRT, with the partial knowledge that the noise is a low-pass zero-mean complex Gaussian noise with uncertain power, which is a typical and practical scenario for wireless communication (it models the equivalent baseband signal of bandpass additive white Gaussian noise). Moreover, we demonstrate the necessity of assuming Σ mul,0 Σ mul,1 during the derivation of the covariance matrix estimation.
With the assumption that w ( t ) is a low-pass zero-mean complex Gaussian noise, the power spectral density (PSD) of w ( t ) is given by
PPT Slide
Lager Image
where B is the bandwidth of the equivalent band-pass signal of w ( t ) and N 0 is assumed to be unknown due to noise power uncertainty. The auto-correlation function and the conjugated auto-correlation function of w ( t ) are defined as
PPT Slide
Lager Image
and
PPT Slide
Lager Image
respectively, whose discrete time versions are given by
PPT Slide
Lager Image
and
PPT Slide
Lager Image
where Ts denotes the sampling period, ν is the discrete time version of lag, and w [ m ] is the discrete time version of w ( t ), i.e., w [ m ]= w ( mTs ),.
Theorem 1: Suppose the PSD of wi ( t ) is
PPT Slide
Lager Image
Then, when i < j , the asymptotic covariance of
PPT Slide
Lager Image
is given by
PPT Slide
Lager Image
PPT Slide
Lager Image
Proof: Following the procedure presented in the proof of Theorem 1 of [22] , and applying the PSD of wi ( t ), (23) and (24) are proved.
Theorem 2: When i = j , the asymptotic covariance of
PPT Slide
Lager Image
is given by
PPT Slide
Lager Image
PPT Slide
Lager Image
Proof: Similar to that of Theorem 1.
It can be seen from (23) to (26) that only Ni needs to be estimated to calculate the asymptotic covariance of
PPT Slide
Lager Image
and
PPT Slide
Lager Image
, since the cyclic frequency of interest and the lag parameters are given in prior, and the bandwidth B and the sampling period Ts are available as for a specific CR receiver. Under H 0 , when xi ( t )= wi ( t ), Ni can be consistently estimated by
PPT Slide
Lager Image
Under H 1 , using (27) to estimate Ni tends to yield a larger result. However, in the regime of low SNR, which is the critical situation in spectrum sensing, the error introduced is not significant. Since this approximation error only happens under H 1 , it has no impact on the CFAR property of the proposed algorithm.
By substituting (27) into (24) and (26), the asymptotic covariance of
PPT Slide
Lager Image
and
PPT Slide
Lager Image
can be estimated. Actually, this covariance estimation method can be viewed as a special case of that in the Dandawaté-Giannakis algorithm [22] . No matter it is under H 0 or H 1 , Ni is estimated as the energy of xi ( t ). This approximation is essentially equivalent to the assumption in the Dandawaté-Giannakis algorithm that the cyclic correlation estimation has the same asymptotic covariance under H 0 and H 1 . It cannot be avoided, since under H 1 it is impossible to consistently estimate Ni .
Theorem 3: The asymptotic covariance between
PPT Slide
Lager Image
is given by
PPT Slide
Lager Image
PPT Slide
Lager Image
Proof: Similar to that of Theorem 1, omitted due to space limit.
Theorem 3 indicates that under H 0 the asymptotic covariance between
PPT Slide
Lager Image
can be simply and correctly estimated as zero under the low-pass zero-mean complex Gaussian noise. Apparently, the asymptotic covariance between
PPT Slide
Lager Image
can not be guaranteed to be equal to zero under H 1 . Therefore, it is necessary to assume that the asymptotic covariance is different under H 0 and H 1 .
As for the estimation of Σ mul,0 , which contains all the asymptotic covariance among the CCA and CCC estimations, the covariance matrix estimator [20] with the Dandawaté- Giannakis algorithm is not valid, since under H 1 it fails to give good approximations for the entries of Σ mul,0 corresponding to the asymptotic covariance between
PPT Slide
Lager Image
and
PPT Slide
Lager Image
This also demonstrate the necessity to formulate the hypotheses of cyclostationary multi-antenna spectrum sensing as in (14).
Denote
PPT Slide
Lager Image
as the estimation of the asymptotic covariance matrix Σ mul,0 , which is of size (( N 2 + N ) P )×(( N 2 + N ) P ), and can be divided into (( N 2 + N )/2)×(( N 2 + N )/2) blocks as follows, one block for each pair of (( i , j ),( a , b )), where i j N and a b N :
PPT Slide
Lager Image
where
PPT Slide
Lager Image
is the asymptotic covariance matrix between
PPT Slide
Lager Image
under H 0 , which can be calculated as
PPT Slide
Lager Image
where Q ij,ab is a P × P matrix with the( p , q )-th entry defined as follows:
PPT Slide
Lager Image
According to Theorem 3,
PPT Slide
Lager Image
with ( i , j )≠( a , b ) is a 2 P ×2 P zero matrix, thus, we can rewrite Σ mul,0 as
PPT Slide
Lager Image
Combining (24), (26) and the equations from (31) to (33), the estimator of Σ mul,0 ,
PPT Slide
Lager Image
can be calculated.
In summary, the proposed algorithm for cyclostationary multi-antenna spectrum sensing, under low-pass zero-mean complex Gaussian noise with uncertain power, can be implemented using the following steps:
Step 1 Declare a cyclic frequency α and a set of lags.
Step 2 Compute the CCA and CCC estimations as in (11) and construct
PPT Slide
Lager Image
as in (12).
Step 3 Calculate
PPT Slide
Lager Image
by using (24), (26), and (31) to (33).
Step 4 Substitute
PPT Slide
Lager Image
for Σ mul,0 in (17) and calculate the test statistic as
PPT Slide
Lager Image
Step 5 Let Γ denote the threshold that satisfies the required detection performance. If T mul,Prop >Γ, accept H 1 ; if T mul,Prop ≤Γ, accept H 0 .
5. Asymptotic Distribution and Computational Complexity of the Proposed Test Statistic
- 5.1 Asymptotic Distribution of Tmul,Prop
To derive the asymptotic distribution of T mul,Prop , we follow [11] and borrow the following theorem from [25] :
Theorem 4: Let x ~N( μ , V ), where V is L × L nonsingular, suppose that the real L × L matrix A is symmetric, and let r ( A ) denote its rank. Then the quadratic form xAx T follows a chi-square distribution if and only if AV is idempotent, in which case xAx T has r ( A ) degrees of freedom and noncentrality parameter μAμ T .
As for the proposed test statistic under H 0 , let
PPT Slide
Lager Image
μ =0, V = Σ mul,0 and
PPT Slide
Lager Image
Since
PPT Slide
Lager Image
is a mean-square sense consistent estimation of Ni under H 0 and
PPT Slide
Lager Image
is only determined by
PPT Slide
Lager Image
is also mean-square sense consistent under H 0 . Thus,
PPT Slide
Lager Image
i.e., the matrix product, AV , is asymptotically idempotent. The convergence in probability
PPT Slide
Lager Image
follows from application of a Cramer-Wold device [26] and from the fact that convergence in the mean-square implies convergence in probability. Hence, from Theorem 4, it follows that under H 0
PPT Slide
Lager Image
where Nmul =( N 2 + N )/2. Clearly, this distribution is not related to the noise power, so uncertainty of the noise power has no impact on the CFAR property of the proposed algorithm. Deriving the distribution of the proposed test statistic under H 1 needs to introduce the following definition (See p. 67-88 of [27] ):
Definition 1: If x has a multivariate normal distribution, N( μ , V ), then the value of the following form ( x + a ) A ( x + a ) T + b T x , where A is a square matrix, has a generalized chi-square distribution.
As for the proposed test statistic under H 1 ,
PPT Slide
Lager Image
Under
PPT Slide
Lager Image
thus, the test statistic
PPT Slide
Lager Image
is asymptotically generalized chi-square distributed.
- 5.2 Computational Complexity
Denote the test static of the extended Dandawaté-Giannakis algorithm proposed in [20] as T mul,Dan . The computational complexity of T mul,Dan focuses on the calculation of the estimated asymptotic covariance
PPT Slide
Lager Image
, which is given as follows when only multiplication is considered:
PPT Slide
Lager Image
where M FFT is the length of the Fast-Fourier transform (FFT), which is employed for the calculation of
PPT Slide
Lager Image
(Refer to [20] and [22] for details). Note that M FFT must not be less than the sample size, i.e., M FFT M .
As for the proposed test statistic given in (34), the computational complexity is
PPT Slide
Lager Image
Apparently, the calculation of T mul,Prop has a lower complexity compared with T mul,Dan .
6. Simulation Results
The licensed communication system considered in the following simulations is a simplified GSM system with GMSK modulated signal of symbol rate f GSM =1/ T GSM =270.833kbit/sf. The baseband GMSK modulated signal is given by
PPT Slide
Lager Image
where Ik is the k th data symbol, and Ik ∈{−1,1}; hm =0.5 is the modulation index; g ( t ) is the impulse function given by
PPT Slide
Lager Image
where rect( t ) is the rectangular pulse function of unit length, and p ( t ) is a Gaussian impulse function with the time bandwidth product B Gaussion T GSM =0.3. We assume that all the time slots of the simplified GSM system are occupied. It has been derived in [13] that a GMSK signal exhibits cyclostationarity at the cyclic frequency α = f GSM and the lag τ =0, which are employed in the following simulations as the cyclic frequency and lag of interest, respectively.
We assume flat Rayleigh fading channels in the simulations of Fig. 3 to Fig. 8 , and the average SNR in dB of the received signal is defined by
PPT Slide
Lager Image
where PN is the average power of the low-pass zero-mean complex Gaussian noise. The bandwidth of the equivalent band-pass Gaussian noise is B =223.437kHz. The sampling rate of the CR receiver is set to be 10 times the symbol rate of the GSM system, i.e., fs =10 f GSM and Ts = T GSM /10.
For the estimation of the asymptotic covariance matrix with the Dandawaté-Giannakis algorithm, a length-2049 Kaiser window with β parameter of 10 is used [11] .
We mainly use the false alarm rate, Pf , and the detection probability, Pd , to measure the detector performance, which are defined respectively as
PPT Slide
Lager Image
and
PPT Slide
Lager Image
where T is the test statistic.
- 6.1 Distributions of the Proposed Test Statistics under H0
To verify the distributions of the proposed test statistics given in (35), we plot in Fig. 2 the simulated cumulative distribution functions (CDFs) of T mul,Prop for different numbers of antennas under H 0 . The theoretical CDFs of χ 2 distribution with corresponding degrees of freedom are also presented for comparison. The sample size is M =4000.
PPT Slide
Lager Image
Distributions of the proposed test statistics under H0.
It is observed from Fig. 2 that the curves of the simulated CDFs and the theoretical CDFs nearly coincide, which confirms that the proposed test statistics given in (34) are χ 2 distributed as (35) under H 0 . Moreover, since these distributions are not related to the noise power, the CFAR property can be guaranteed for spectrum sensing based on the proposed test statistics.
- 6.2 Multi-Antenna Cyclostationary Spectrum Sensing
We investigate the detection performance of the proposed multi-antenna cyclostationary spectrum sensing with flat Rayleigh fading channel in this subsection. We first compare the proposed algorithm using the test statistic T mul,Prop with the Dandawaté-Giannakis algorithm for single-antenna sensing, whose test statistic is denoted as T Dan , and the one simply extending the Dandawaté-Giannakis algorithm for multi-antenna sensing, which was given in [20] and whose test statistic is denoted as T mul,Dan . Next, we show the necessity of taking into account the CCCs by comparing the proposed algorithm with the one excluding all the CCCs.
Fig. 3 plots the curves of detection probability vs. false alarm rate for an average SNR of -5dB and different numbers of antennas, and Fig. 4 plots the curves of detection probability vs. average SNR with a false alarm rate of 0.01 and different numbers of antennas. The sample size of both figures is 4000. From Fig. 3 and Fig. 4 , it observed that as the number of antennas increases, the detection performance increases significantly. These two figures also demonstrate that our proposed algorithm has better detection performance than the extended Dandawaté-Giannakis algorithm, i.e., the detection probability using ,T mul,Prop is larger than the one using T mul,Dan under the same number of antennas. Most importantly, the performance gap becomes more significant as the number of antennas increases. For a four-antenna system, the performance gain is about 1.7dB, which is much more significant than that for a single- antenna system. The reason is that the proposed algorithm gives better estimation of the asymptotic covariance matrices of
PPT Slide
Lager Image
under H 0 , i.e., Σ mul,0 , than the Dandawaté-Giannakis algorithm does, and the improvement increases as the number of antennas and the dimension of the matrices increase, which are verified in Fig. 5 .
PPT Slide
Lager Image
Pd vs. Pf with an average SNR of -5dB and a sample size of 4000, under Rayleigh fading channel.
PPT Slide
Lager Image
Pd vs. average SNR with a false alarm rate Pf=0.01 and a sample size of 4000, under Rayleigh fading channel.
PPT Slide
Lager Image
Normalized Estimation Error (normalized with antenna number N) vs. average SNR for the estimation of Σmul,0, with a sample size of 4000, under Rayleigh fading channel.
To demonstrate the contribution of CCCs, we simulate the performance of the multi-antenna cyclostationary spectrum sensing algorithms excluding all CCCs, which uses
PPT Slide
Lager Image
as following instead of
PPT Slide
Lager Image
in the proposed algorithm:
PPT Slide
Lager Image
Fig. 6 plots the curves of detection probability vs. false alarm rate for the proposed algorithm without the CCCs with an average SNR of -5dB and different numbers of antennas ( N =2 and N =4). It shows that the multi-antenna spectrum sensing algorithms that take into account all CCAs and CCCs outperform the ones excluding the CCCs, which reveals the contribution of CCCs. Fig. 7 plots the curves of detection probability vs. average SNR for the proposed algorithm without CCCs with a false alarm rate of 0.01 and different numbers of antennas ( N =2 and N =4), and Fig. 8 shows a zoom of the important area illustrating the differences in performance more clearly. From Fig. 8 , it is observed that the proposed algorithm obtains a performance gain of nearly 2.0dB over the one excluding the CCCs for four antennas. Moreover, it is observed that the performance gain provided by the CCCs is more significant for the proposed algorithm than that for the extended Dandawate-Giannakis algorithm. As the number of antennas increases, the performance gain provided by CCCs also increases for the proposed algorithm, but stays unchanged for the extended Dandawate- Giannakis algorithm. This demonstrates that the extended Dandawate-Giannakis algorithm fails to take full advantages of the CCCs due to the false assumption that the asymptotic covariance matrix of
PPT Slide
Lager Image
is the same under H 0 and H 1 for spectrum sensing.
PPT Slide
Lager Image
Pd vs. Pf for the proposed multi-antenna cyclostationary spectrum sensing algorithms, with an average SNR of -5dB and a sample size of 4000, under Rayleigh fading channel.
PPT Slide
Lager Image
Pd vs. average SNR for the proposed multi-antenna cyclostationary spectrum sensing algorithms, with a false alarm rate Pf=0.01 and a sample size of 4000, under Rayleigh fading channel.
PPT Slide
Lager Image
Zoom of the important region of Fig. 7. Pd vs. average SNR for the proposed multi-antenna cyclostationary spectrum sensing algorithms, with a false alarm rate Pf=0.01 and a sample size of 4000, under Rayleigh fading channel.
7. Conclusion
In this paper, we proposed a novel GLRT algorithm for cyclostationary multi-antenna spectrum sensing. Using an example where the additive noise is low-pass zero-mean Gaussian noise, we verified that the proposed GLRT has a more reasonable hypotheses problem formulation and employs a more suitable asymptotic covariance estimator than those of the Dandawaté-Giannakis algorithm and its extension. We have also derived the asymptotic distributions of the proposed test statistics, and proved the CFAR property of the proposed algorithm. Theoretical analysis and simulation results showed that the proposed algorithm has better performance of detection probability and lower computational complexity compared with the Dandawaté-Giannakis algorithm and its extension. Moreover, simulation results also verified the necessity of taking into account the CCCs in multi-antenna cyclostationary spectrum sensing.
BIO
Guohui Zhong received his B.S. degree and M.S. degree from Huazhong University of Science and Technology. He is currently a Lecturer with the Department of Electronics and Information Engineering, Huazhong University of Science and Technology. His current research interests include signal processing, and dynamic spectrum techniques for wireless communications.
Jiaming Guo received his B.E. degree in telecommunication engineering from Huazhong University of Science and Technology in 2010. He is now a PhD student at National University of Singapore in the department of ECE. His research interests include signal processing, video segmentation, pattern recognition and machine learning.
Daiming Qu received the Ph.D. degree in information and communication engineering from Huazhong University of Science and Technology, Wuhan, P. R. China, in 2003.
He is currently a Full Professor with the Department of Electronics and Information Engineering, Huazhong University of Science and Technology. His current research interests include signal processing, coding, and dynamic spectrum techniques for wireless communications.
Tao Jiang received the B.S. and M.S. degrees in applied geophysics from China University of Geosciences, Wuhan, in 1997 and 2000, respectively, and the Ph.D. degree in information and communication engineering from Huazhong University of Science and Technology,Wuhan, P. R. China, in April 2004.
He is currently a Full Professor at Wuhan National Laboratory for Optoelectronics, Department of Electronics and Information Engineering, Huazhong University of Science and Technology, Wuhan. From August 2004 to December 2007, he worked in some universities, such as Brunel University, U.K., and the University of Michigan, respectively. He has authored or coauthored more than 100 technical papers in major journals and conferences and five books/chapters in the areas of communications. His current research interests include the areas of wireless communications and corresponding signal processing, especially for cognitive wireless access, vehicular technology, OFDM, UWB and MIMO, cooperative networks, smart grid and wireless sensor networks.
Dr. Jiang was invited to serve as TPC Symposium Chair for the IEEE GLOBECOM 2013 and IEEE WCNC 2013, and as a General Co-Chair for the workshop of M2M Communications and Networking in conjunction with IEEE INFOCOM 2011. He served or is serving as Symposium Technical Program committee membership of many major IEEE conferences, including INFOCOM, ICC, and GLOBECOM, etc. He served or is serving as Associate Editor of some technical journals in communications, including the IEEE COMMUNICATIONS SURVEYS AND TUTORIALS, IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, etc. He is a recipient of Best Paper Awards in IEEE CHINACOM09 and WCSP09. He is a Member of the IEEE Communication Society, IEEE Vehicular Technology Society, IEEE Broadcasting Society, IEEE Signal Processing Society, and IEEE Circuits and Systems Society.
Jingchao Sun received the B.E. in Electronics and Information Engineering and the M.E. in Communication and Information System from Huazhong University of Science and Technology, China, respectively. He is currently a Ph.D. student in School of Electrical, Computer, and Energy Engineering at Arizona State University. His primary research interests are network and distributed system security and privacy, wireless networking, and mobile computing.
References
Mitola J. , Maguire G. Q. 1999 “Cognitive radio: Making software radios more personal” IEEE Personal Communications Magazine Article(CrossRefLink). 6 (4) 13 - 18    DOI : 10.1109/98.788210
Haykin S. 2005 “Cognitive radio: brain-empowered wireless communications” IEEE Journal Selected Areas in Communications Article(CrossRefLink). 23 (2) 201 - 220    DOI : 10.1109/JSAC.2004.839380
Akyildiz I. F. , Lee W.-Y. , Vuran M. C. , Mohanty S. 2006 “NeXt Generation/ Dynamic Spectrum Access/Cognitive Radio Wireless Networks: A Survey” Computer Networks Article(CrossRefLink). 50 (13) 2127 - 2159    DOI : 10.1016/j.comnet.2006.05.001
Hassan Walid A. , Jo Han Shin , Nekovee Maziar 2012 “Spectrum Sharing Method for Cognitive Radio in TV White Spaces: Enhancing Spectrum Sensing and Geolocation Database” KSII Transactions on Internet and Information Systems Article(CrossRefLink). 6 (8) 1894 - 1912
Zhang R. , Lim T. , Liang Y. C. , Zeng Y. 2010 “Multi-antenna based spectrum sensing for cognitive radios: A GLRT approach” IEEE Transactions on Communications Article(CrossRefLink). 58 (1) 84 - 88    DOI : 10.1109/TCOMM.2010.01.080158
Wang P. , Fang J. , Han N. , Li H. 2010 “Multiantenna-assisted spectrum sensing for cognitive radio” IEEE Transactions on Vehicular Technology Special Issue Achievements and the Road Ahead: The First Decade of Cognitive Radio. Article(CrossRefLink). 59 (4) 1791 - 1800    DOI : 10.1109/TVT.2009.2037912
Font-Segura J. , Wang X. 2010 “GLRT-Based Spectrum Sensing for Cogntive Radio with Prior Information” IEEE Transactions on Communications Article(CrossRefLink). 58 (7) 2137 - 2146    DOI : 10.1109/TCOMM.2010.07.090556
Kieu-Xuan Thuc , Koo Insoo 2010 “A Cooperative Spectrum Sensing Scheme Using Fuzzy Logic for Cognitive Radio Networks” KSII Transactions on Internet and Information Systems Article(CrossRefLink). 4 (3) 289 - 304
Gardner W. A. 1987 Statsitcal Spectral Analysis: A Nonprobabilistic Theory Prenticc-Hall Upper Saddle River, NJ
Gardner W. A. 1988 “Signal interception: a unifying theoretical framework for feature detection” IEEE Transactions on Communications Article(CrossRefLink). 36 (8) 897 - 906    DOI : 10.1109/26.3769
Lundén J. , Koivunen V. , Huttune A. , Poor H. V. 2009 “Collaborative Cyclostationary Spectrum Sensing for Cognitive Radio Systems” IEEE Transactions on Signal Processing Article(CrossRefLink). 57 (11) 4182 - 4195    DOI : 10.1109/TSP.2009.2025152
Lundén J. , Kassam S. A. , Koivunen V. 2010 “On the Extraction of the Channel Allocation Information in Spectrum Pooling Systems” IEEE Journal on Selected Areas in Communications Article(CrossRefLink). 58 (1) 38 - 52
Öner M. , Jondral F. 2007 “On the Extraction of the Channel Allocation Information in Spectrum Pooling Systems” IEEE Journal on Selected Areas in Communications Article(CrossRefLink). 25 (3) 558 - 565    DOI : 10.1109/JSAC.2007.070406
Duval O. , Punchihewa A. , Gagnon F. , Despins C. , Bhargava V. K. 2008 “Blind Multi-Sources Detection and Localization for Cognitive Radio” in Proc. of Proceedings of Global Telecommunications Conference, New Orleans New Orleans, LO Nov. Article(CrossRefLink). 2962 - 2966
DeYoung M. R. , Heath R. W. , Evans B. L. 2008 “Using Higher Order Cyclostationarity to Identify Space-Time Block Codes” in Proc. of Proceedings of Global Telecommunications Conference New Orleans, LO Nov. Article(CrossRefLink). 3370 - 3374
Zhao Z. , Zhong G. , Qu D. , Jiang T. 2009 “Cyclostationarity-Based Spectrum Sensing with Subspace Projection” Proceedings of Personal, Indoor and Mobile Radio Communications Tokyo Sep. Article(CrossRefLink). 2300 - 2304
Guo H. , Hu H. , Yang Y. 2009 “Cyclostationary Signatures in OFDM-Based Cognitive Radios with Cyclic Delay Diversity” in Proc. of Proceedings of IEEE International Conference on Communications Dresden June Article(CrossRefLink). 3499 - 3504
Ma J. , Li G. Y. , Juang G. H. 2009 “Signal Processing in Cognitive Radio” Proceedings of IEEE Article(CrossRefLink). 97 (5) 805 - 823    DOI : 10.1109/JPROC.2009.2015707
Harada H. , Fujii H. , Furuno T. , Miura S. , Ohya T. 2010 “Iterative Cyclostationarity-Based Feature Detection of Multiple Primary Signals for Spectrum Sharing Scenarios” in Proc. of Proceedings of 2010 IEEE Symposium on New Frontiers in Dynamic Spectrum Singapore Apr. Article(CrossRefLink). 492 - 499
Zhong G. , Guo J. , Zhao Z. , Qu D. 2010 “Cyclostationarity Based Multi-Antenna Spectrum Sensing in Cognitive Radio Networks” in Proc. of Proceedings of IEEE Vehicular Technology Conference Taipei, Taiwan May vol. 3, Article(CrossRefLink). 2339 - 2344
Mahapatra R. , Krusheel M. 2008 “Cyclostationary Detection for Cognitive Radio with Multiple Receivers” Proceedings of IEEE International Symposium on Wireless Communications Systems Reykjavik Oct. Article(CrossRefLink). 493 - 497
Dandawaté A. V. , Giannakis G. B. 1994 “Statistical Tests for Presence of Cyclostationarity” IEEE Transactions on Signal Processing Article(CrossRefLink). 42 (9) 2355 - 2369    DOI : 10.1109/78.317857
Chen X. , Xu W. , He Z. , Tao X. 2008 “Spectral Correlation-Based Multi-Antenna Spectrum Sensing Technique” in Proc. of Proceedings of IEEE Wireless Communications and Networking Conference Las Vegas, NV Mar. Article(CrossRefLink). 735 - 740
Goldsmith A. 2005 Wireless Communications Cambridge University Press
Driscoll M. F. 1999 “An Improved Result Relating Quadratic Forms and Chi- Square Distributions” The American Statistician Article(CrossRefLink). 53 (3) 273 - 275
Knight K. 2000 Mathematical Statistics, Texts in Statistical Science Chapman & Hall/CRC Press Boca Raton, FL
Jones D. A. 1983 Statistical analysis of empirical models fitted by optimisation Biometrika Article(CrossRefLink). 70 (1) 67 - 68    DOI : 10.1093/biomet/70.1.67