Modified Gram Schmidt Based Chaotic Matrix for Compressive Sensing in Cognitive Radio

Cognitive Radio (CR) is a wireless technology for solving the spectrum scarcity problem. Wideband Spectrum sensing is a first step to be done and the most challenging in the next generation CR. Compressive sensing (CS) can be used as a spectrum sensing technique in CR for wideband spectrum. CS consists of three stages: sparse representation, encoding and recovery based on one of recovery algorithms. Sensing matrix used by encoding stage has an important role in CS performance. Best performance of CS can be produced when the sensing matrix is designed to have low mutual coherence. In this paper, a sensing matrix using Modified Gram Schmidt (MGS) algorithm based on chaotic matrix created from logistic map is proposed. The proposed sensing matrix has low reconstruction error, high compression ratio, and high immunity to attackers from outside the network due to sensitivity of chaotic matrix used to slight changes in control parameters and initial values. The performance of CS based on the proposed matrix is measured using absolute error and MSE and evaluated through comparisons with existing chaotic matrices using CoSaMP as recovery algorithm. The simulation results show that CS based on proposed sensing matrix significantly reduces absolute and MSE errors at low SNR values. Furthermore, it provides high compression under AWGN and Rayleigh multipath fading channels compared to existing sensing matrices.