Eigenvalue-based spectrum sensing for multiple received signals under the non-reconstruction framework of compressed sensing

Eigenvalue-based algorithm is generally acknowledged to be a promising method for spectrum sensing. However, it possesses high computational complexity, because the sampled covariance matrix and the corresponding eigenvalues are calculated. Furthermore, the detection performance of eigenvalue-based algorithms experiences a huge decline when the received signals are uncorrelated. Therefore, compressed sensing is adopted to reduce the computational complexity and introduce the relevance for multiple received signals. First, the sampled covariance matrix and its eigenvalues are calculated under the non-reconstruction framework of compressed sensing. The corresponding standard condition number of the eigenvalues is employed as test statistic to perform spectrum sensing. Then, the impact of the measurement matrix on the detection performance is discussed, and the computational complexity is analyzed. Next, the measurement matrix is optimized to improve the detection performance. In addition, a novel method of setting decision threshold is proposed to maintain a stable false alarm probability for the proposed spectrum sensing algorithm, and its computational complexity is compared with some existing methods. Finally, the corresponding simulations are performed to testify the theoretical results. Theoretical analysis and simulation results certify the effectiveness and validity of the proposed method.