New measurement matrix for compressive sensing in cognitive radio networks

Abstract

Cognitive radio (CR) is a promising solution for an efficient usage of both wideband and narrowband spectrum. Compressive sensing (CS) paradigm is one of the methods that can assist CR to sense the wideband sparse spectrum using a small number of measurements. The implementation of CS depends on utilising a suitable random or structured measurement matrix. To fully enhance CS performance, the measurement matrix should be a full rank and has a small mutual coherence with the basis matrix. According to these necessities, this study introduces a new measurement matrix called the modified regular parity check (RPC) matrix. RPC matrix that is first designed by Gallager technique suffers from the missing of the previous requirements. Thus, a new algorithm is proposed to convert this matrix to a semi-orthogonal one using the gradient-descent method with a variable step size. The modified RPC matrix has fixed values for all entries regardless of the number of active CR users relative to the maximum expected number of CR users. The results show that the proposed matrix has a low recovery error without increasing the recovery time compared with Gaussian matrix. Moreover, it achieves a higher probability of detection and smaller probability of false alarm.