A review on spectrum sensing for cognitive radio: challenges and solutions <s> Combining Space and Time Correlation <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> BIB001 </s> A review on spectrum sensing for cognitive radio: challenges and solutions <s> Combining Space and Time Correlation <s> Sensing (signal detection) is a fundamental problem in cognitive radio. The statistical covariances of signal and noise are usually different. In this paper, this property is used to differentiate signal from noise. The sample covariance matrix of the received signal is computed and transformed based on the receiving filter. Then two detection methods are proposed based on the transformed sample covariance matrix. One is the covariance absolute value (CAV) detection and the other is the covariance Frobenius norm (CFN) detection. Theoretical analysis and threshold setting for the algorithms are discussed. Both methods do not need any information of the signal, the channel and noise power as a priori. Simulations based on 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> Combining Space and Time Correlation <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> BIB003 </s> A review on spectrum sensing for cognitive radio: challenges and solutions <s> Combining Space and Time Correlation <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> BIB004 </s> A review on spectrum sensing for cognitive radio: challenges and solutions <s> Combining Space and Time Correlation <s> Spectrum sensing, i.e., detecting the presence of primary users in a licensed spectrum, is a fundamental problem in cognitive radio. Since the statistical covariances of the received signal and noise are usually different, they can be used to differentiate the case where the primary user's signal is present from the case where there is only noise. In this paper, spectrum-sensing algorithms are proposed based on the sample covariance matrix calculated from a limited number of received signal samples. Two test statistics are then extracted from the sample covariance matrix. A decision on the signal presence is made by comparing the two test statistics. Theoretical analysis for the proposed algorithms is given. Detection probability and the associated threshold are found based on the statistical theory. The methods do not need any information about the signal, channel, and noise power a priori. In addition, no synchronization is needed. Simulations based on narrow-band signals, captured digital television (DTV) signals, and multiple antenna signals are presented to verify the methods. <s> BIB005 </s> A review on spectrum sensing for cognitive radio: challenges and solutions <s> Combining Space and Time Correlation <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
In addition to being spatially correlated, the received signal samples are usually correlated in time due to the following reasons. (1) The received signal is oversampled. Let Δ 0 be the Nyquist sampling period of continuous-time signal s c (t) and let s c (nΔ 0 ) be the sampled signal based on the Nyquist sampling rate. Thanks to the Nyquist theorem, the signal s c (t) can be expressed as where g(t) is an interpolation function. Hence, the signal samples s(n) = s c (nΔ s ) are only related to s c (nΔ 0 ), where Δ s is the actual sampling period. If the sampling rate at the receiver is An example of this is the wireless microphone signal specified in the IEEE 802.22 standard   , which occupies about 200 KHz in a 6-MHz TV band. In this example, if we sample the received signal with sampling rate no lower than 6 MHz, the wireless microphone signal is actually oversampled and the resulting signal samples are highly correlated in time. (2) The propagation channel is time-dispersive. In this case, the received signal can be expressed as where s 0 (t) is the transmitted signal and h(t) is the response of the time-dispersive channel. Since the sampling period Δ s is usually very small, the integration (24) can be approximated as Hence, where (3) The transmitted signal is correlated in time. In this case, even if the channel is flat-fading and there is no oversampling at the receiver, the received signal samples are correlated. The above discussions suggest that the assumption of independent (in time) received signal samples may be invalid in practice, such that the detection methods relying on this assumption may not perform optimally. However, additional correlation in time may not be harmful for signal detection, while the problem is how we can exploit this property. For the multi-antenna/receiver case, the received signal samples are also correlated in space. Thus, to use both the space and time correlations, we may stack the signals from the M 6 EURASIP Journal on Advances in Signal Processing antennas and over L sampling periods all together and define the corresponding ML × 1 signal/noise vectors: Then, by replacing x(n) by x L (n), we can directly extend the previously introduced OCED and BCED methods to incorporate joint space-time processing. Similarly, the eigenvaluebased detection methods BIB001 BIB003 BIB004  can also be modified to work for correlated signals in both time and space. Another approach to make use of space-time signal correlation is the covariance based detection BIB002 BIB005  briefly described as follows. Defining the space-time statistical covariance matrices for the signal and noise as respectively, we can verify that If the signal is not present, R L,s = 0, and thus the off-diagonal elements in R L,x are all zeros. If there is a signal and the signal samples are correlated, R L,s is not a diagonal matrix. Hence, the nonzero off-diagonal elements of R L,x can be used for signal detection. In practice, the statistical covariance matrix can only be computed using a limited number of signal samples, where R L,x can be approximated by the sample covariance matrix defined as Based on the sample covariance matrix, we could develop the covariance absolute value (CAV) test BIB002 BIB005 defined as where r nm (N) denotes the (n, m)th element of the sample covariance matrix R L,x (N). There are other ways to utilize the elements in the sample covariance matrix, for example, the maximum value of the nondiagonal elements, to form different test statistics. Especially, when we have some prior information on the source signal correlation, we may choose a corresponding subset of the elements in the sample covariance matrix to form a more efficient test. Another effective usage of the covariance matrix for sensing is the eigenvalue based detection (EBD)  BIB001 BIB003 BIB004  BIB006 , which uses the eigenvalues of the covariance matrix as test statistics.