A review on spectrum sensing for cognitive radio: challenges and solutions <s> Exploiting Spatial Correlation of Multiple Received Signals <s> In this letter, we consider cooperative spectrum sensing based on energy detection in cognitive radio networks. Soft combination of the observed energies from different cognitive radio users is investigated. Based on the Neyman-Pearson criterion, we obtain an optimal soft combination scheme that maximizes the detection probability for a given false alarm probability. Encouraged by the performance gain of soft combination, we further propose a new softened hard combination scheme with two-bit overhead for each user and achieve a good tradeoff between detection performance and complexity. <s> BIB001 </s> A review on spectrum sensing for cognitive radio: challenges and solutions <s> Exploiting Spatial Correlation of Multiple Received Signals <s> Sensing (signal detection) is a fundamental problem in cognitive radio. In this paper, a new method is proposed based on the eigenvalues of the covariance matrix of the received signal. It is shown that the ratio of the maximum eigenvalue to the minimum eigenvalue can be used to detect the signal existence. Based on some latest random matrix theories (RMT), we can quantize the ratio and find the threshold. The probability of false alarm is also found by using the RMT. The proposed method overcomes the noise uncertainty difficulty while keeps the advantages of the energy detection. The method can be used for various sensing applications without knowledge of the signal, the channel and noise power. Simulations based on randomly generated signals and captured ATSC DTV signals are presented to verify the methods. <s> BIB002 </s> A review on spectrum sensing for cognitive radio: challenges and solutions <s> Exploiting Spatial Correlation of Multiple Received Signals <s> In this letter, a method is proposed to optimally combine the received signal samples in space and time based on the principle of maximizing the signal-to-noise ratio (SNR). After the combining, energy detection (ED) is used. However, optimal combining needs information of the source signal and channel, which is usually unknown. To overcome this difficulty, a method is proposed to blindly combine the signal samples. Similar to energy detection, blindly combined energy detection (BCED) does not need any information of the source signal and the channel a priori. BCED can be much better than ED for highly correlated signals, and most importantly, it does not need noise power estimation and overcomes ED's susceptibility to noise uncertainty. Also, perfect synchronization is not required. Simulations based on wireless microphone signals and randomly generated signals are presented to verify the methods. <s> BIB003 </s> A review on spectrum sensing for cognitive radio: challenges and solutions <s> Exploiting Spatial Correlation of Multiple Received Signals <s> Spectrum sensing is a fundamental component in a cognitive radio. In this paper, we propose new sensing methods based on the eigenvalues of the covariance matrix of signals received at the secondary users. In particular, two sensing algorithms are suggested, one is based on the ratio of the maximum eigenvalue to minimum eigenvalue; the other is based on the ratio of the average eigenvalue to minimum eigenvalue. Using some latest random matrix theories (RMT), we quantify the distributions of these ratios and derive the probabilities of false alarm and probabilities of detection for the proposed algorithms. We also find the thresholds of the methods for a given probability of false alarm. The proposed methods overcome the noise uncertainty problem, and can even perform better than the ideal energy detection when the signals to be detected are highly correlated. The methods can be used for various signal detection applications without requiring the knowledge of signal, channel and noise power. Simulations based on randomly generated signals, wireless microphone signals and captured ATSC DTV signals are presented to verify the effectiveness of the proposed methods. <s> BIB004 </s> A review on spectrum sensing for cognitive radio: challenges and solutions <s> Exploiting Spatial Correlation of Multiple Received Signals <s> In this contribution, we propose a new technique for collaborative sensing based on the analysis of the normalized (by the trace) largest eigenvalues of the sample covariance matrix. Assuming that several base stations are cooperating and without the knowledge of the noise variance, the test is able to determine the presence of mobile users in a network when only few samples are available. Unlike previous heuristic techniques, we show that the test has roots within the Generalized Likelihood Ratio Test and provide an asymptotic random matrix analysis enabling to determine adequate threshold detection values (probability of false alarm). Simulations sustain our theoretical claims. <s> BIB005 </s> A review on spectrum sensing for cognitive radio: challenges and solutions <s> Exploiting Spatial Correlation of Multiple Received Signals <s> Recent advances in random matrix theory have spurred the adoption of eigenvalue-based detection techniques for cooperative spectrum sensing in cognitive radio. These techniques use the ratio between the largest and the smallest eigenvalues of the received signal covariance matrix to infer the presence or absence of the primary signal. The results derived so far are based on asymptotical assumptions, due to the difficulties in characterizing the exact eigenvalues ratio distribution. By exploiting a recent result on the limiting distribution of the smallest eigenvalue in complex Wishart matrices, in this paper we derive an expression for the limiting eigenvalue ratio distribution, which turns out to be much more accurate than the previous approximations also in the non-asymptotical region. This result is then applied to calculate the decision sensing threshold as a function of a target probability of false alarm. Numerical simulations show that the proposed detection rule provides a substantial improvement compared to the other eigenvalue-based algorithms. <s> BIB006
The received signal samples at different antennas/receivers are usually correlated, because all s i (n)'s are generated from the same source signal s k (n)'s. As mentioned previously, the energy detection defined in (8) is not optimal for this case. Furthermore, it is difficult to realize the LRT in practice. Hence, we consider suboptimal sensing methods as follows. If M > 1, K = 1, and assuming that the propagation channels are flat-fading (q ik = 0, ∀i, k) and known to the receiver, the energy at different antennas can be coherently combined to obtain a nearly optimal detection BIB001   . This is also called maximum ratio combining (MRC). However, in practice, the channel coefficients are unknown at the receiver. As a result, the coherent combining may not be applicable and the equal gain combining (EGC) is used in practice BIB001  , which is the same as the energy detection defined in (8) . In general, we can choose a matrix B with M rows to combine the signals from all antennas as The combining matrix should be chosen such that the resultant signal has the largest SNR. It is obvious that the SNR after combining is where E(·) denotes the mathematical expectation. Hence, the optimal combining matrix should maximize the value of function Γ(B). be the statistical covariance matrix of the primary signals. It can be verified that where Tr(·) denotes the trace of a matrix. Let λ max be the maximum eigenvalue of R s and let β 1 be the corresponding eigenvector. It can be proved that the optimal combining matrix degrades to the vector β 1 BIB003 . Upon substituting β 1 into (13), the test statistic for the energy detection becomes EURASIP Journal on Advances in Signal Processing 5 The resulting detection method is called optimally combined energy detection (OCED) BIB003 . It is easy to show that this test statistic is better than T ED (x) in terms of SNR. The OCED needs an eigenvector of the received source signal covariance matrix, which is usually unknown. To overcome this difficulty, we provide a method to estimate the eigenvector using the received signal samples only. Considering the statistical covariance matrix of the signal defined as we can verify that Since R x and R s have the same eigenvectors, the vector β 1 is also the eigenvector of R x corresponding to its maximum eigenvalue. However, in practice, we do not know the statistical covariance matrix R x either, and therefore we cannot obtain the exact vector β 1 . An approximation of the statistical covariance matrix is the sample covariance matrix defined as Let β 1 (normalized to β 1 2 = 1) be the eigenvector of the sample covariance matrix corresponding to its maximum eigenvalue. We can replace the combining vector β 1 by β 1 , that is, Then, the test statistics for the resulting blindly combined energy detection (BCED) BIB003 becomes It can be verified that where λ max (N) is the maximum eigenvalue of R x (N). Thus, T BCED (x) can be taken as the maximum eigenvalue of the sample covariance matrix. Note that this test is a special case of the eigenvalue-based detection (EBD)  BIB002 BIB004 BIB005  BIB006 .