Log-Likelihood Ratio Test for Spectrum Sensing With Truncated Covariance Matrix

Conventional autocorrelation-based detectors often require the knowledge of a covariance matrix, which is usually replaced with its corresponding sample covariance matrix by dividing the received signal vector into a number of subvectors. This can lead to performance loss due to the deviation of the sample covariance matrix from the population covariance matrix. In this work, the received signal is used as a single signal vector and the use of sample covariance matrices is avoided. Taking advantage of oversampling, we obtain a truncated approximate covariance matrix of primary signals, which leads to a new approximate log-likelihood-ratio-test (aLLRT) detector with low complexity. In addition, a noise power estimator is also proposed by exploiting oversampling, which is incorporated into the new detector for practical implementation. Theoretical analyses for the false-alarm and detection probabilities of the proposed detector are conducted, and their accurate expressions are obtained via performing a nonlinear transformation to the test statistic of the proposed detector. Numerical results show that, compared to state-of-the-art detectors, the proposed detector improves the detection probability by at least 10%.