J. Cent. South Univ. (2018) 25: 2451-2461
DOI: https://doi.org/10.1007/s11771-018-3928-z
A K-means clustering based blind multiband spectrum sensing algorithm for cognitive radio
LEI Ke-jun(雷可君)1, TAN Yang-hong(谭阳红)1, YANG Xi(杨喜)2, 3, WANG Han-rui(王韩瑞)2
1. College of Electrical and Information Engineering, Hunan University, Changsha 410082, China;
2. College of Information Science and Engineering, Jishou University, Jishou 416000, China;
3. National Mobile Communications Research Laboratory, Southeast University, Nanjing 210096, China
Central South University Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018
Abstract:
In this paper, a blind multiband spectrum sensing (BMSS) method requiring no knowledge of noise power, primary signal and wireless channel is proposed based on the K-means clustering (KMC). In this approach, the KMC algorithm is used to identify the occupied subband set (OSS) and the idle subband set (ISS), and then the location and number information of the occupied channels are obtained according to the elements in the OSS. Compared with the classical BMSS methods based on the information theoretic criteria (ITC), the new method shows more excellent performance especially in the low signal-to-noise ratio (SNR) and the small sampling number scenarios, and more robust detection performance in noise uncertainty or unequal noise variance applications. Meanwhile, the new method performs more stablely than the ITC-based methods when the occupied subband number increases or the primary signals suffer multi-path fading. Simulation result verifies the effectiveness of the proposed method.
Key words:
Cite this article as:
LEI Ke-jun, TAN Yang-hong, YANG Xi, WANG Han-rui. A K-means clustering based blind multiband spectrum sensing algorithm for cognitive radio [J]. Journal of Central South University, 2018, 25(10): 2451–2461.
DOI:https://dx.doi.org/https://doi.org/10.1007/s11771-018-3928-z1 Introduction
With the rapid growth of wireless communication, the spectrum resources become more and more scarce. Thus the effective use of spectrum resources has become an important problem in the wireless communication fields [1–3]. According to a survey report provided by the US Federal Communications Commission (FCC), the utilization ratio of the licensed band fluctuate between 15% to 85%, which means that many licensed spectrum has not been fully utilized, namely, the spectrum holes exist. Cognitive radio (CR) is one of the most promising technologies to effectively utilize the spectrum hole, but a key of realizing CR technology is how to sense the spectrum hole.
In cognitive radio networks, spectrum sensing is a key functionality that enables secondary users (SUs) to detect the under-used licensed frequency bands and opportunistically utilize them without interfering with the primary users (PUs). Up to now, various spectrum sensing algorithms have been proposed, such as the matched filter method, energy detection method, cyclostationary feature detection method, eigenvalue method, covariance matrix method, trace-based method [3–7]. Meanwhile, various collaborative sensing algorithms have also been proposed to enhance the sensing performance [3, 8]. These algorithms have their own advantages and disadvantages, and can be used in different situations. However, all of these algorithms have been previously designed to detect narrowband channels.
In order to improve spectrum sensing efficiency, the wideband spectrum sensing technology, which can detect different frequency subbands simultaneously, has gradually become a new research hotspot. In Ref. [9], a wideband spectrum sensing method based on wavelet algorithm was proposed, which tests the channels according to the phenomenon that the different frequency bands have different power spectrum densities. But its detection performance is easy to be affected by noise. In Ref. [10], an optimal multiband joint detection framework for wideband sensing was presented, in which the sensing decision is jointly made over all of the under- detected subbands. Furthermore, a multiband sensing-time-adaptive joint detection framework by maximizing the achievable opportunistic throughput was proposed in Ref. [11]. Considering the non-convex nature of the problem considered in Ref. [10], an alternative optimization technique based on genetic algorithms was proposed in Ref. [12]. However, the performance of the above optimal multiband spectrum sensing algorithms heavily depends on the estimation accuracy of the noise variance because energy detection is used as a basic building block in them.
To overcome the shortcomings of those methods, the blind multiband spectrum sensing (BMSS) methods are widely studied. Recently, the information theoretic criteria (ITC) based BMSS methods have attracted extensive attention. For example, the ITC-based BMSS algorithms using Akaike information criterion (AIC), minimum description length (MDL) criterion and Hunnan- Quinn (HQ) criterion were introduced in Refs. [13–15]. In addition, the sensing performance of the ITC-based methods was theoretically analyzed in Ref. [16]. The main advantage of the ITC-based methods lies in that their sensing procedures are independent of the prior knowledge of noise variance, PU signal and wireless channel. However, the ITC-based methods have three drawbacks: Firstly, the ITC-based methods require the eigenvalue decomposition of the sample covariance matrix, which is too time-consuming for real-time applications in cognitive radio networks. Secondly, the sensing performance of the ITC- based methods in low signal-to-noise ratio (SNR) environments is unsatisfactory. Finally, the ITC- based methods assure equal noise variances across all subbands, however, the noise variances across different subbands may be slightly changed due to different channel conditions and calibration errors [17, 18].
In this work, the K-means clustering (KMC) algorithm is investigated to significantly improve multiband spectrum sensing method. Our contributions include: a) the multiband detection is formulated into a clustering problem in which the channels are divided into the occupied subband set (OSS) and the idle subband set (ISS) according to the sample powers of subbands; b) the K-means algorithm is applied to attacking blind multiband sensing problem, which not only improves the sensing efficiency, but also achieves excellent detection performance; c) the proposed BMSS algorithm shows better detection performance than the classical ITC-based BMSS algorithms in case of noise uncertainty, unequal noise variances and low received SNR. Additionally, when the occupied subband number is changing or the primary signals suffer multi-path fading, the new method always maintains stable detection performance.
The remainder of the paper is organized as follows. In Section 2, the basic system models are present. In Section 3, the principle of the ITC-based BMSS algorithm is reviewed simply. The proposed KMC-based BMSS algorithm for cognitive radio is introduced in detail in Section 4. In Section 5, it is evaluated that the sensing performance of the proposed algorithm， and finally conclusions are drawn in Section 6.
2 System model
Suppose that the total investigated spectrum covers frequency range from Flow to Fhigh Hz, and the bandwidth of each subband is B Hz, then the entire frequency band is divided into M=(Fhigh–Flow)/B subbands. Use Q={1, 2, …, M} to denote the index set of all subbands, and Q1={q1, q2, …, qL}, Q1
Q, to denote the index set of the occupied subbands. Correspondingly, the task of the multiband spectrum sesing problem is to correctly find the number and the locations of the occupied subbands. The multiband frequency spectrum usage model is depicted in Figure 1, in which the white rectangles denote the idle subbands, and the occupied subbands are shown as grey rectangles [13].
Figure 1 Multiband frequency spectrum usage model
Assume there are M subands to be detected and N observations can be used for the multiband sensing problem. Respectively, denote the received signal vector, the received PU signal vector and the noise vector as
(1)
(2)
(3)
Note that the above vectors are composed of samples from M subbands at the k-th time instant with k∈[1, N]. Following the multiband sensing model of [13], sm(k)’s are the statistically independent Gaussian received PU signal samples in the m-th subband with zero mean and power (variance) 
and nm(k)’s are the additive white Gaussian noise (AWGN) with variance σ2for m∈[1, M]. Without loss of generality, sm(k) and nm(k) are assumed to be statistically independent. Denote the received data matrix as Y=[y(1) y(2) … y(N)]. Define the sample covariance matrix of the received signal vector as
(4)
Then the probability density function (PDF) of Y can be written as
(5)
where the statistical covariance matrix R of the received signal vectors y(k) under H0 can be written as
(6)
with I being an M×M identity matrix, and R of y(k)=s(k)+n(k) under H1 can be written as
(7)
where diag{·} denotes a diagonal matrix, and λm is the eigenvalue of R under H1 which can be written as
(8)
3 Traditional ITC-based BMSS algorithm
Before starting to discuss our proposed scheme, we shall make a brief review of the ITC-based BMSS methods. Note that the multiplicity of the smallest eigenvalues of R is precisely the number of the under-used subchannels. Based on this fact, the problem of estimating the number of occupied channels can be transformed as a problem of estimating the number of signal sources [13]. Therefore, the ITC-based methods were introduced to perform the multiband spectrum sensing in cognitive radios. The sensing statistic based on the information theoretic criteria is correspondingly defined as
(9)
where 
is the log-likelihood of the received data matrix Y, 
is the maximum likelihood estimation (MLE) of R in the L-th hypothesis, and 
is the ITC penalty term. It is necessary to point out that different penalty terms would lead to different decision criteria for the multiband spectrum sensing problem. The popular ITC-based criteria include AIC criterion, MDL criterion and HQ criterion [13–15].
Denote
as the eigenvalues of 
The expressions for the above three criteria can then be respectively written as
(10)
(11)
(12)
According to the principle of the ITC-based BMSS methods, the number of the occupied subbands can be obtained by minimizing the criteria defined in Eqs. (10)–(12). Once the number of the occupied subbands is determined, the ITC-based BMSS algorithms select the corresponding number of subbands with maximum sample power as the occupied ones.
4 Proposed KMC-based BMSS algorithm
Different from the classical ITC-based BMSS methods, the multiband spectrum sensing problem is performed from another angle in this paper. From Eq. (8), it is not difficult to find that, when the primary signals are present in channels, λm (
) are the sum of the variances of the received signals and the noise, while the rest eigenvalues λm 
are equal to the noise variance. Therefore, the eigenvalues of the statistical matrix R can be naturally grouped into two clusters as
(13)
and
(14)
As analyzed above, S1 is closely related to the occupied subband set, while S2 is closely related to the idle subband set. This means that, once S1 and S2 are determined, the information on the occupied and the idle subbands can also be obtained. Note that the signal eigenvalues λm() are strictly greater than the noise eigenvalues λm . So S1 and S2 can be distinguishable as long as the received SNR is not too low. As a result, the multiband detection problem can be effectively solved via clustering analysis, which is widely used to group a set of observations into multiple clusters such that the observations within a cluster have high similarity, but are very dissimilar to observations in other clusters [19, 20]. Because KMC is well known for its simplicity, robustness and high effectiveness among various clustering methods, it is adopted to find the two subsets in this paper. In the next subsections, the basic idea of KMC is firstly briefly reviewed, some results about the sample eigenvalues and sample powers are then discussed, and the proposed KMC-based BMSS algorithm is introduced in detail at last.
4.1 Basic idea of KMC
KMC is a prototype-based clustering method that attempts to find K non-overlapping clusters Dk (1≤k≤K). These clusters are represented by their centroids, which is usually the mean of the points in that cluster [21]. Suppose D={x1, x2, …, xn} is the data set to be grouped and xi (1≤i≤n) denote finite-dimensional vectors. KMC can be expressed as an optimization problem as follows
(15)
where wx assigns the weight of data vector x,|Dk| and 
respectively denote the
cardinality and the centroid of cluster Dk, and the function “dist” computes the distance between x and xk. Usually, the squared Euclidean distance is selected to measure the distance, and K initial centroids are selected in some way, for example to random selected values in D={x1, x2, …, xn}. KMC is then an iterative two-step algorithm, including the assignment step and the update step. In the assignment step, every point in D is assigned to the closest centroid, and all of the points assigned to a centroid forms a cluster. In the update step, the centroid of each cluster is re-calculated according to the points assigned to that cluster. This process is repeated until no point changes clusters.
4.2 Sample eigenvalue and sample power
Note that computing R requires the statistical characteristics of PU signals and background noise. However, it is usually difficult to obtain them in practical sensing applications. Therefore, directly performing clustering analysis on the set of eigenvalues of R, i.e., {λ1, λ2, λ3, …, λM}, is not feasible in many applications. In traditional ITC-based BMSS algorithms, the eigenvalues are approximated by the sample eigenvalues
(1≤m≤M), i.e., the eigenvalues of 
. However, computingand its eigenvalues will be time-consuming, which is undesirable in the real-time sensing scenarios. On the other hand, the large dimensional random matrix theory shows that the fluctuation of the sample eigenvalues usually leads to the situation where the smallest signal eigenvalue is not necessarily distinctly larger than the largest noise eigenvalue [22]. This means that the traditional methods based on the sample eigenvalues fail to distinguish PU signals from background noise.
To effectively address the above problems, a new strategy by performing clustering analysis on the sample powers is proposed in this paper. The sample power is the time-average over the limited samples. The sample power of the m-th subband is defined as
(16)
It is necessary to point out that φm is the m-th diagonal element of . Before starting to discuss our new scheme, we shall introduce the following theorem.
Theorem 1: The maximum likelihood estimation (MLE) of λm is φm.
Proof: Combining Eq. (5) with Eq. (7), we have
and
Therefore, it is easy to show that
(17)
Substituting Eq. (17) into Eq. (5), we obtain the likelihood function (LF) of Y as
(18)
Taking the natural logarithm on both sides of Eq. (18) yields
(19)
Letting
(20)
it can be easily obtained that the MLE of λm is φm.
The results of Theorem 1 indicate that the sample powers of subbands can be used to well approximate the corresponding eigenvalues of R when N is large enough. Correspondingly, the clustering analysis for the proposed KMC-based BMSS algorithm is carried out on the sample power set Φ={φ1, φ2, …, φM} instead of the eigenvalues of the statistical covariance matrix in this work.
4.3 Proposed KMC-based BMSS algorithm
As analyzed above, the eigenvalues should be divided into two clusters in the multiband sensing scenarios. As a result, the sample powers set Φ is partitioned into K=2 clusters, say Φ1 and Φ2. In addition, the same weights are assigned to all of the sample powers in the clustering process. Correspondingly, the objective function for clustering analysis can then be written as
(21)
(22)
where i=1, 2, 
is the mean of elements in Φi and |Φi| denotes the cardinality of Φi. Randomly choosing two elements in Φ as the initial means, the clustering proceeds by alternating between two steps:
Assignment step: Using Eq. (23) and Eq. (24) to assign each sample power to the cluster mean of which yields the least within-cluster sum of squares for the t-th iteration
(23)
(24)
Update step: Using Eq. (25) and Eq. (26) to calculate new means as the centroids of the sample powers in the new clusters
(25)
(26)
Repeat the assignment step and update step until the assignments do not change. Once Φ1 and Φ2 are obtained, the set with the larger mean is selected as the OSS, and the set with the smaller mean as the ISS.
In summary, the detailed steps of the proposed algorithm are shown as follows.
Step 1: Calculate the sample powers φm’s using Eq. (16) for M subbands, and then initialize the set of the sample powers 
where f denotes the empty set;
Step 2: Randomly choose two elements in Φ as the initial means 
and 
Step 3: Assign each sample power to the specific cluster using Eq. (23) and Eq. (24);
Step 4: Update the centroids of the current two clusters using Eq. (25) and Eq. (26);
Step 5: Repeat Step 3 and Step 4 until the assignment does not change;
Step 6: Select the subset with the larger mean as the OSS and the rest set as the ISS;
Step 7: Determine the number and the locations of the occupied subbands according to the cardinality of the OSS and the indexes of the elements in the OSS, respectively. The rest subbands are identified as the idle ones.
Remark 1: The proposed KMC-based scheme is robust to noise uncertainty because it is not involved with the estimation of noise power in the sensing decision process. At the same time, the new scheme is suitable for blind sensing scenarios, which does not require the prior knowledge of noise variance, PU signal, wireless channel and the determination of the decision threshold.
Remark 2: The ITC-based BMSS schemes utilize the multiplicity of the smallest eigenvalues to identify the OSS and the ISS, which in essence requires that the noise variances in idle subbands are equal. By contrast, the proposed scheme identifies the OSS and the ISS via the sample powers instead of the eigenvalues of the statistical covariance matrix. Hence, the new scheme can be theoretically used for the scenarios with unequal noise variances in different subbands when the distance between the above two subsets is large enough.
Remark 3: The main complexity of the proposed scheme lies in the K-means clustering analysis, which requires 
operations [20]. By contrast, the ITC-based schemes require 
operations to perform sample covariance matrix computation and eigenvalue decomposition. Obviously, our scheme is more suitable for real-time applications considering the fact that usually N>>M in practical applications.
5 Simulation results and analysis
In this section, the performance of the proposed KMC-based method is numerically evaluated in detail by different sensing scenarios. The probability of detection Pd and the probability of false-alarm Pf are used to scale the sensing performance. Numerical results are obtained via 5000 simulation trials.
5.1 Performance comparison among proposed KMC-based method and ITC-based methods
In the simulation experiments, the performance of the new KMC-based method is compared with ITC-based methods. Assume that all of the PU signals have the same transmission power and consider a multiband detection problem with N=200, and PU signals are present in L=4 subbands among the total M=10 subbands.
Figure 2 shows the probabilities of detection and false-alarm against SNR without noise uncertainty. It can be seen that the proposed KMC-based scheme outperforms the other three ITC-based methods in terms of Pd especially in low SNR environments. For instant, the Pd’s of the four schemes based on the KMC, HQ, AIC, and MDL criteria are respectively equal to 89.3%, 9.52%, 1.50% and 0% when SNR=–14 dB. Furthermore, the false-alarm performance of the above four BMSS algorithms is investigated. From Table 1, it can be seen that both the proposed method and the MDL-based method achieve the lowest and most stable false-alarm probabilities throughout the whole SNR region.
The noise variances in subbands cannot be accurately obtained in real multiband spectrum sensing applications due to the noise uncertainty phenomenon [13]. In order to comprehensively investigate the detection performance of the proposed algorithm, the noise variance followed a uniform distribution in [10–α/10, 10α/10]σ2, is used to replace the true one in each Monte-Carlo experiment, where α [dB] is the noise uncertainty factor and indicates the size of noise uncertainty. The probability of detection curves of the four schemes for α=1 dB and α=3 dB are described in Figure 3, respectively. It can be seen that all of them exhibit robust detection performance, but the new KMC-based BMSS method shows the best detection performance among all methods.
Figure 2 Pd against SNR without noise uncertainty
Table 1 Actual false-alarm probabilities for different SNR’s without noise uncertainty
Figure 4 shows the sensing performance of the above methods in multiband detection scenario with unequal noise variances. In the simulations, the noise variances in M = 10 subbands are set as [0.8 1 1 1 0.9 1.1 1.2 1 0.85 1.15]. As expected, the new KMC-based method performs robust sensing performance in the unequal noise variance case. From Figure 4, it can be seen that the proposed method consistently performs better, even in high SNR region, than the HQ-based method and the AIC-based method, meanwhile shows better detection performance than the MDL-based method in low SNR region. At the same time, it can also be seen from Table 2 that the proposed method achieves excellent false-alarm performance again, while the false-alarm performance of both the HQ-based method and the AIC-based method further deteriorate due to the unequal noise variances in different subbands.
Figure 3 Pd against SNR with noise uncertainty
Figure 4 Pd against SNR with unequal noise variances
Table 2 Actual false-alarm probabilities for different SNR’s with unequal noise variances
5.2 Case study with different numbers of samples
Considering that the number of samples N also affects the detection performance of BMSS, we further investigate the sensing performance of the proposed method and ITC-based methods against different N’s at a fixed SNR.
Figure 5 depicts the probabilities of detection and false-alarm of the above four BMSS methods at SNR=–15 dB. Here, set L=4 and M=10. The simulation results clearly show that with the increase of sampling number, the detection probabilities of the AIC-based, HQ-based and KMC-based BMSS methods increase quickly, while the MDL-based method cannot work efficiently due to the low SNR. Meanwhile, it also can be seen that the proposed KMC-based BMSS method always has more obvious advantages than the ITC-based methods especially for small sampling numbers, and the probability of detection of our method quickly reaches 100% when the number of samples N increases from 100 to 1000. For instant, it can be seen from Figure 5(a) that in the case of N=300 the Pd’s of HQ-based and AIC-based methods are below 10%, however the Pd of our KMC-based method is about 90%. On the other hand, in Figure 5(b) both the proposed KMC-based method and the MDL-based method have the best false- alarm performance, the AIC-based method shows the suboptimal one, while the HQ-based method performs the worst false-alarm performance. Furthermore, comparing Figure 6 with Figure 5 it can be seen that the detection probability enhances with the increase of the SNR, however, our method obtains the best performance again.
Figure 5 Sensing performance against number of samples N (SNR=–15 dB):
Figure 6 Sensing performance against number of samples N (SNR=–13 dB):
5.3 Case study with different numbers of occupied subbands
To comprehensively evaluate the performance of the proposed method, we investigate the impact of the occupied subband number on the detection performance. When fix N=200, M=30, the probabilities of detection against SNR are sketched in Figures 7(a)–(c) by setting L=4, 15 and 20, respectively. It is obvious that the detection performance of the HQ-based, AIC-based and MDL-based methods decrease significantly with the increase of the occupied subband numbers, and especially the MDL-based method becomes completely unable to correctly detect the occupied subbands when L is large. On the contrary, the proposed KMC-based BMSS method always maintains stable detection performance. For example, when SNR=–10 dB and L increases from 4 to 15, the Pd’s of the KMC-based, HQ-based and AIC-based methods respectively decrease from 99.76% to 99.60%, 74.38% to 1.44%, and 35.48% to 0%, while the MDL-based method cannot work properly. Furthermore, when L continues to increase to 20, except the proposed method, the other three ITC-based BMSS methods are unable to work effectively. So it can be said that the detection performance of the KMC-based BMSS method is only slightly influenced by the number of the occupied subbands, but the performance of ITC-based methods is sensitive to it.
Figure 7 Detection probability against SNR for different numbers of occupied subbands:
5.4 Performance comparison of BMSS methods in multi-path fading environment
In the above simulation trials, we suppose the signal transmission channels are AGWN channels. But in the real sensing environment, considering the influences of multi-path fading is necessary. So among this experiment, let the signals pass through the Rayleigh fading channel and set N=200, L=4, M=10.
Comparing Figure 8 with Figure 2 and Table 1,the influences of multi-path fading to sensing performance can be seen. When SNR=–10 dB, the Pd’s of the KMC-based, HQ-based, AIC-based and MDL-based methods decrease from 99.6% to 96.3%, 98% to 47.1%, 99.6% to 20%, and 5.5% to zero respectively, in the same time the maximal Pf’sof HQ-based and AIC-based methods increase from 0.42% to 1.8%, 0.1% to 0.2%, while the Pf’sof KMC-based and MDL-based methods always equal zero. The simulation results demonstrate that the sensing performance of the proposed KMC-based method has the stability in multi-path fading environment.
Figure 8 Performance comparison of sensing methods in Rayleigh fading environment:
6 Conclusions
A new multiband detection method based on the K-means clustering has been proposed in this paper. The proposed KMC-based method is simple to be implemented by using the sample powers to avoid the complex calculation of the sample covariance matrix and eigenvalue decomposition. Additionally, the new method belongs to a blind multiband detection scheme which does not require knowledge of the noise power, the PU signal and the propagation channel. The simulation results show that the new method is superior to the classical ITC-based schemes especially in the low SNR, the small sampling number and multi-path fading environments, and can perform better in both noise uncertainty and unequal noise variance scenarios. Meanwhile, the results also indicate that the new method is more robust in the sensing applications with large number of the occupied subbands.
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(Edited by HE Yun-bin)
中文导读
一种基于K均值聚类的认知无线电盲多带频谱感知算法
摘要：提出了基于K均值聚类(KMC)的盲多带频谱感知（BMSS）方法。该方法不需要知道噪声方差、主信号和无线信道的先验知识，利用KMC算法区分被占用子带集合(OSS)和空闲子带集合 (ISS)，然后再根据OSS中的元素获得被占用信道的数量和位置信息。与基于信息理论准则（ITC）的BMSS方法相比的结果为：在低信噪比和小样本场景中，新方法表现出更好的检测性能；在噪声方差不确定或不一致的应用中，其检测性能具有鲁棒性；当被占用的子带数增加或信号经过多径衰落时，其检测性能更优。仿真结果验证了所提方法的有效性和优越性。
关键词：认知无线电；盲多带频谱感知；K均值聚类；被占用子带集合；空闲子带集合；信息论准则；噪声不确定
Foundation item: Projects(61362018, 61861019) supported by the National Natural Science Foundation of China; Project(1402041B) supported by the Jiangsu Province Postdoctoral Scientific Research Project, China; Project(16A174) supported by the Scientific Research Fund of Hunan Provincial Education Department, China; Project([2016]283) supported by the Research Study and Innovative Experiment Project of College Students, China
Received date: 2017-07-18; Accepted date: 2017-12-05
Corresponding author: TAN Yang-hong, PhD, Professor; Tel: +86-731–87202461; E-mail: 809677326@qq.com; ORCID: 0000-0002- 6713-5618
Abstract: In this paper, a blind multiband spectrum sensing (BMSS) method requiring no knowledge of noise power, primary signal and wireless channel is proposed based on the K-means clustering (KMC). In this approach, the KMC algorithm is used to identify the occupied subband set (OSS) and the idle subband set (ISS), and then the location and number information of the occupied channels are obtained according to the elements in the OSS. Compared with the classical BMSS methods based on the information theoretic criteria (ITC), the new method shows more excellent performance especially in the low signal-to-noise ratio (SNR) and the small sampling number scenarios, and more robust detection performance in noise uncertainty or unequal noise variance applications. Meanwhile, the new method performs more stablely than the ITC-based methods when the occupied subband number increases or the primary signals suffer multi-path fading. Simulation result verifies the effectiveness of the proposed method.
