In this paper, a generalized likelihood ratio test (GLRT) is proposed for cyclostationary multiantenna spectrum sensing in cognitive radio systems, which takes into account the cyclic autocorrelations obtained from all the receiver antennas and the cyclic crosscorrelations 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 multiantenna systems than those employed by the DandawatéGiannakis 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 DandawatéGiannakis algorithm and its extension for multiantenna cases.
1. Introduction
R
ecently, cognitive radio (CR) has drawn significant attention from academic and industrial communities to meet the evergrowing 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. Cyclostationaritybased 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 autocorrelation for the detection of licensed user, which are nonzero at particular cyclic frequencies for the licensed user signal
[9]
,
[10]
.
Many existing cyclostationaritybased spectrum sensing methods
[11]

[21]
have employed the DandawateGiannakis algorithm
[22]
due to its constant false alarm rate (CFAR) property and robustness in the low signaltonoise ratio (SNR) regime. The DandawateGiannakis 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 autocorrelation 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, multiantenna 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 DandawateGiannakis algorithm to allow multiantenna spectrum sensing, which takes into account the cyclic autocorrelations obtained from all receiver antennas and the cyclic crosscorrelations 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 multiantenna spectrum sensing, which drops the cyclic crosscorrelations in detection.
In this paper, we propose a novel GLRT for cyclostationary multiantenna spectrum sensing. The framework of the proposed algorithm is similar to that in
[20]
, i.e., taking into account all the achievable cyclic autocorrelations and cyclic crosscorrelations. However, it is different with
[20]
in hypotheses problem formulation and asymptotic covariance estimation. More specifically, the the asymptotic covariances among the cyclic crosscorrelations and autocorrelations under the null hypothesis are assumed to different from those under the alternative hypothesis, while they are assumed to be the same in the DandawatéGiannakis algorithm and its extension
[20]
. We use an example, where the additive noise is lowpass zeromean 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 fourantenna system. The necessity of taking into account the cyclic crosscorrelations is also demonstrated via simulation experiments.
The rest of this paper is organized as follows: In Section 2, the multiantenna spectrum sensing model is presented. In Section 3, we propose the GLRT for cyclostationary multiantenna spectrum sensing, and then demonstrate how to construct the proposed GLRT under the assumption that the additive noise is lowpass zeromean 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 MultiAntenna 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.
Multiantenna spectrum sensing model.
At each sensing period, the CR tries to distinguish between the following two hypotheses:
where
s
(
t
) is the signal transmitted by the licensed user;
i
denotes the index of antenna;
x_{i}
(
t
) and
w_{i}
(
t
) denote the received signal and the lowpass zeromean complex Gaussian noise at the
i
th antenna, respectively;
h_{i}
denotes the channel response for the
i
th antenna, which can be further expressed as
where
γ_{i}
is Rayleigh distributed with the probability density function (PDF) as
and
θ_{i}
denotes the phase offset of the channel response, which is uniformly distributed with the PDF as
Throughout this paper, we assume that
h_{i}
is invariant over the sensing period, and both
w_{i}
(
t
) and
h_{i}
are independent for different antennas.
3. CyclostationarityBased MultiAntenna Spectrum Sensing
 3.1 Cyclostationarity
A continuoustime random process
x
(
t
) is a wide sense secondorder cyclostationary process, if its mean and autocorrelation are periodical with some periods
[10]
. Define the time varying autocorrelation of
x
(
t
) as
where
τ
denotes the lag. Then, due to its periodicity,
R_{xx}
(
t
,
τ
) can be represented as a Fourier series as
where
τ
is called the cyclic frequency and the Fourier coefficients are called the cyclic autocorrelation functions, which are given by
Another useful function that can characterize the secondorder cyclostationary process
x
(
t
) is called the conjugated cyclic autocorrelation (CCA) function, which is given by
where
In the rest of this paper, we focus on the case using the CCA functions, while the one concerning cyclic autocorrelation functions can be derived similarly.
The discrete time version of the CCA estimation,
can be calculated as
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
(
mT_{s}
), where
T_{s}
denotes the sampling period.
As for the multiantenna spectrum sensing problem where there are
N
antennas at the CR receiver,
N
CCA functions and
N
(
N
−1)/2 conjugated cyclic crosscorrelation (CCC) functions can be obtained, which can be defined together as follows:
where
Note that when
i
=
j
,
denotes the CCA functions, and when
denotes the CCC functions. Also note that we only take into account
and neglect
since it is easy to verify that
Similar to (8), a discrete time version estimation of
with
M
samples is given by
 3.2 GLRT for the MultiAntenna Cyclostationary Spectrum Sensing
Taking into account all CCA and CCC estimations, we can define a vector
as
where
By using
, the hypotheses problem for multiantenna spectrum sensing is now formulated as follows:
where
r
_{mul}
is the asymptotic value of
under
H
_{1}
,
is the estimation error vector resulted from
W_{i}
(
t
) and
is the estimation error vector resulted from both
W_{i}
(
t
) and
s
(
t
), which are asymptotically distributed as
respectively. Different from the DandawatéGiannakis 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
w_{i}
(
t
) contributes to the asymptotic covariance matrix under
H
_{1}
, whereas only
w_{i}
(
t
) contributes to
H
_{0}
. We will use an example, where the additive noise is the lowpass zeromean 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
By substituting
for
θ
_{1}
and
0
for
θ
_{0}
, we can obtain that
Taking the logarithm transformation of the GLR gives the test statistic as follows:
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
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 lowpass zeromean 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
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,
calculated from the recent detection is a good approximation of current
Σ
_{mul,0}
. The test statistic of DandawatéGiannakis algorithm employs current
, whereas our proposed method suggests using the
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 lowpass zeromean 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 lowpass zeromean complex Gaussian noise, the power spectral density (PSD) of
w
(
t
) is given by
where
B
is the bandwidth of the equivalent bandpass signal of
w
(
t
) and
N
_{0}
is assumed to be unknown due to noise power uncertainty. The autocorrelation function and the conjugated autocorrelation function of
w
(
t
) are defined as
and
respectively, whose discrete time versions are given by
and
where
T_{s}
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
(
mT_{s}
),.
Theorem 1:
Suppose the PSD of
w_{i}
(
t
) is
Then, when
i
<
j
, the asymptotic covariance of
is given by
Proof:
Following the procedure presented in the proof of Theorem 1 of
[22]
, and applying the PSD of
w_{i}
(
t
), (23) and (24) are proved.
Theorem 2:
When
i
=
j
, the asymptotic covariance of
is given by
Proof:
Similar to that of Theorem 1.
It can be seen from (23) to (26) that only
N_{i}
needs to be estimated to calculate the asymptotic covariance of
and
, since the cyclic frequency of interest and the lag parameters are given in prior, and the bandwidth
B
and the sampling period
T_{s}
are available as for a specific CR receiver. Under
H
_{0}
, when
x_{i}
(
t
)=
w_{i}
(
t
),
N_{i}
can be consistently estimated by
Under
H
_{1}
, using (27) to estimate
N_{i}
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
and
can be estimated. Actually, this covariance estimation method can be viewed as a special case of that in the DandawatéGiannakis algorithm
[22]
. No matter it is under
H
_{0}
or
H
_{1}
,
N_{i}
is estimated as the energy of
x_{i}
(
t
). This approximation is essentially equivalent to the assumption in the DandawatéGiannakis 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
N_{i}
.
Theorem 3:
The asymptotic covariance between
is given by
Proof:
Similar to that of Theorem 1, omitted due to space limit.
Theorem 3 indicates that under
H
_{0}
the asymptotic covariance between
can be simply and correctly estimated as zero under the lowpass zeromean complex Gaussian noise. Apparently, the asymptotic covariance between
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
and
This also demonstrate the necessity to formulate the hypotheses of cyclostationary multiantenna spectrum sensing as in (14).
Denote
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
:
where
is the asymptotic covariance matrix between
under
H
_{0}
, which can be calculated as
where
Q
_{ij,ab}
is a
P
×
P
matrix with the(
p
,
q
)th entry defined as follows:
According to Theorem 3,
with (
i
,
j
)≠(
a
,
b
) is a 2
P
×2
P
zero matrix, thus, we can rewrite
Σ
_{mul,0}
as
Combining (24), (26) and the equations from (31) to (33), the estimator of
Σ
_{mul,0}
,
can be calculated.
In summary, the proposed algorithm for cyclostationary multiantenna spectrum sensing, under lowpass zeromean 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
as in (12).
Step 3 Calculate
by using (24), (26), and (31) to (33).
Step 4 Substitute
for
Σ
_{mul,0}
in (17) and calculate the test statistic as
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 chisquare 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
μ
=0,
V
=
Σ
_{mul,0}
and
Since
is a meansquare sense consistent estimation of
N_{i}
under
H
_{0}
and
is only determined by
is also meansquare sense consistent under
H
_{0}
. Thus,
i.e., the matrix product,
AV
, is asymptotically idempotent. The convergence in probability
follows from application of a CramerWold device
[26]
and from the fact that convergence in the meansquare implies convergence in probability. Hence, from Theorem 4, it follows that under
H
_{0}
where
N_{mul}
=(
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. 6788 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 chisquare distribution.
As for the proposed test statistic under
H
_{1}
,
Under
thus, the test statistic
is asymptotically generalized chisquare distributed.
 5.2 Computational Complexity
Denote the test static of the extended DandawatéGiannakis algorithm proposed in
[20]
as T
_{mul,Dan}
. The computational complexity of T
_{mul,Dan}
focuses on the calculation of the estimated asymptotic covariance
, which is given as follows when only multiplication is considered:
where
M
_{FFT}
is the length of the FastFourier transform (FFT), which is employed for the calculation of
(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
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
where
I_{k}
is the
k
th data symbol, and
I_{k}
∈{−1,1};
h_{m}
=0.5 is the modulation index;
g
(
t
) is the impulse function given by
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
where
P_{N}
is the average power of the lowpass zeromean complex Gaussian noise. The bandwidth of the equivalent bandpass 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.,
f_{s}
=10
f
_{GSM}
and
T_{s}
=
T
_{GSM}
/10.
For the estimation of the asymptotic covariance matrix with the DandawatéGiannakis algorithm, a length2049 Kaiser window with
β
parameter of 10 is used
[11]
.
We mainly use the false alarm rate,
P_{f}
, and the detection probability,
P_{d}
, to measure the detector performance, which are defined respectively as
and
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.
Distributions of the proposed test statistics under H_{0}.
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 MultiAntenna Cyclostationary Spectrum Sensing
We investigate the detection performance of the proposed multiantenna 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 DandawatéGiannakis algorithm for singleantenna sensing, whose test statistic is denoted as T
_{Dan}
, and the one simply extending the DandawatéGiannakis algorithm for multiantenna 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 DandawatéGiannakis 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 fourantenna 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
under
H
_{0}
, i.e.,
Σ
_{mul,0}
, than the DandawatéGiannakis algorithm does, and the improvement increases as the number of antennas and the dimension of the matrices increase, which are verified in
Fig. 5
.
P_{d} vs. P_{f} with an average SNR of 5dB and a sample size of 4000, under Rayleigh fading channel.
P_{d} vs. average SNR with a false alarm rate P_{f}=0.01 and a sample size of 4000, under Rayleigh fading channel.
Normalized Estimation Error (normalized with antenna number N) vs. average SNR for the estimation of Σ_{mul,0}, with a sample size of 4000, under Rayleigh fading channel.
To demonstrate the contribution of CCCs, we simulate the performance of the multiantenna cyclostationary spectrum sensing algorithms excluding all CCCs, which uses
as following instead of
in the proposed algorithm:
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 multiantenna 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 DandawateGiannakis 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 DandawateGiannakis algorithm fails to take full advantages of the CCCs due to the false assumption that the asymptotic covariance matrix of
is the same under
H
_{0}
and
H
_{1}
for spectrum sensing.
P_{d} vs. P_{f} for the proposed multiantenna cyclostationary spectrum sensing algorithms, with an average SNR of 5dB and a sample size of 4000, under Rayleigh fading channel.
P_{d} vs. average SNR for the proposed multiantenna cyclostationary spectrum sensing algorithms, with a false alarm rate P_{f}=0.01 and a sample size of 4000, under Rayleigh fading channel.
Zoom of the important region of Fig. 7. P_{d} vs. average SNR for the proposed multiantenna cyclostationary spectrum sensing algorithms, with a false alarm rate P_{f}=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 multiantenna spectrum sensing. Using an example where the additive noise is lowpass zeromean 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 DandawatéGiannakis 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 DandawatéGiannakis algorithm and its extension. Moreover, simulation results also verified the necessity of taking into account the CCCs in multiantenna 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 CoChair 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.
View Fulltext
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: brainempowered 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
“Multiantenna 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
“Multiantennaassisted 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
FontSegura J.
,
Wang X.
2010
“GLRTBased 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
KieuXuan 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
PrenticcHall
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 MultiSources 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 SpaceTime 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
“CyclostationarityBased 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 OFDMBased 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 CyclostationarityBased 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 MultiAntenna 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 CorrelationBased MultiAntenna 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