An iterative message passing approach for compressive spectrum sensing

Abstract

In compressive spectrum sensing (CS), a high-dimensional sparse signal is undersampled. This is achieved using linear projections of the sparse signal onto a small number of basis vectors that form a measurement matrix. This matrix has a smaller number of rows compared to the columns and it represents an under-determined system of linear equations. In CS, this matrix system is typically inverted using convex optimization or a greedy pursuit approach (e.g., in which the sparse signal is recovered from the measurements by minimization of an L 1 cost function). In this paper, we describe an alternative approach based on iterative message passing. We apply the concept of belief propagation on Tanner graphs to the problem of CS sparsity pattern detection. The unknown sparsity pattern to be determined, which we model in this paper as a vector of binary random variables, is mapped to the variable nodes of a Tanner graph, and vector of non-binary and noisy measurements are mapped to its check nodes. The check nodes and the variable nodes are connected by a set of edges that define a binary, and sparse, measurement matrix. An iterative message passing algorithm is developed and applied to the problem of detecting the unknown binary-valued variable nodes given the noisy measurements at the check nodes. A simulation based verification and performance evaluation of this algorithm is conducted. The proposed approach is used for blind spectrum sensing in wideband communication systems with sparse frequency domain occupancy. A method of implementing the proposed CS measurement matrix in the analog front-end of communication receivers is described. Compared to alternate methods for compressive spectrum sensing, our approach, due to the sparse nature of CS measurement matrix, has a smaller noise enhancement due to spectrum folding in sub-Nyquist domain.