Trace-Based Sparsity Order Estimation With Sparsely Sampled Random Matrices

Abstract

In most of compressed sensing (CS) contributions, the sparsity of interesting signals is usually assumed to be prior. It may incur performance degradation of CS in such environments, where the sparsity order of channel occupancy changes dynamically. Therefore, sparsity order estimation (SOE) is vital, so that the sampling rate can be adjusted adaptively to exploit fully CS techniques. This paper studies the SOE problem for wideband cognitive radio. To investigate this issue, at first, the theoretical expression of sparsity order of the considered signals is derived via random matrix theory. The theoretical analysis shows that the sparsity order can be expressed with the ratio, which consists of the trace of measured signals' covariance matrix, compression sampling ratio, signal-to-noise ratio, and so on. And then, according to the theoretical expressions, a novel SOE approach is presented. In the proposed method, the trace of measured signals' covariance matrix is first calculated, and second, the sparsity order is estimated based on the trace. Compared with the previous work, the proposed algorithm, besides the lower computational complexity, has some superior performance, such as better robustness, smaller SOE error, and so on. Theoretical analysis and simulation results demonstrate the performance of the proposed approach.