A sparse reconstruction algorithm with hierarchical Bayesian analysis for wideband spectrum detection

Bayesian Compressive Sensing (BCS) theory with hierarchical Bayesian analysis model is investigated in the process of wideband spectrum detection and data fusion for Cognitive Wireless Sensor Network (C-WSN). A sparse Bayesian reconstruction method is proposed, which is based on the spatial-temporal correlation structure of real non-stationary spectrum signals sensed by multiple cognitive sensor nodes. Novel wideband spectrum detection and data recovery algorithm are implemented by hierarchical Bayesian analysis model, with higher detection probability and lower reconstruction Mean-Square Errors (MSE). Numerical results confirm our theoretical derivations. It is indicated that, compared with Orthogonal Matched Pursuit (OMP) reconstruction algorithm which is based on greedy algorithm, the proposed Tree Structured Wavelet (TSW) BCS reconstruction scheme has advanced detection performance and lower MSE during data recovery process. Meanwhile, fast convergence could be realized in lower compression rate, which provides the effectiveness of our algorithm and proves that it is suitable for wideband spectrum sensing and data sparse reconstruction in large-scale Cognitive WSN.