Low-Complexity Near-Optimal Presence Detection of a Linearly Modulated Signal

Spectrum sensing is an activity of a cognitive radio to detect the presence of a primary user in the frequency band of interest. In this paper, we consider under the Neyman-Pearson criterion the detection of a primary-user signal that linearly modulates codeword symbols from a Gaussian codebook. To reduce the complexity in computing the likelihood ratio, a simple method based on the approximation of signal covariance matrices is presented. By invoking the Central Limit Theorem, the approximate probability distribution of the decision statistic, the threshold for decision, and the performance of the proposed detector are computed and parameterized only by the overall pulse shape and noise variance. Numerical results show that the proposed detector with much lower computational complexity performs almost the same as the optimal detector. The signal-to-noise ratio wall of the proposed detector is also investigated to quantify the performance limit under uncertainty in the noise variance.