Homotopy reconstruction for compressive sensing based cooperative transmissions in cognitive radio network

Compressive sensing (CS) based cooperative transmissions is investigated in cognitive radio networks (CRN). Energy efficiency based optimal relay selection is implemented to determine the measurement numbers in CS. Homotopy reconstruction method that solves a bound constrained quadratic programming (BCQP) problem is studied for signal sparse reconstruction at secondary user destination (SUD) in CRN. Based on the determined measurement numbers, binary phase shift keying (BPSK) modulation signal is sparsely sampled by analog-to-information converters (AICs) equipped at the selected secondary user relays (SURs). The corresponding measurement matrix is constructed in CS-based cooperative transmissions. Homotopy reconstruction method is implemented to obtain dynamic update of the solution for BCQP problem. The updating critical value of homotopy parameter and the updating solution of the reconstructed signals´ autocorrelation vector can be both achieved via iteration. Simulation results are presented to validate the effectiveness of the proposed approach. It is shown that, homotopy method recovers original signal approximately in low signal-to-noise ratio (SNR) region. Compared with orthogonal matching pursuit (OMP) reconstruction approach, it provides a balanced solution considering normalized mean square error (NMSE) performance versus computational complexity. Moreover, spectrum sensing overhead plays significant role in CS based cooperative transmissions.