Cooperative spectrum sensing over correlated Rayleigh fading channels in cognitive radio using factor graph

Modelling of the cooperative spectrum sensing in cognitive radio networks in presence of correlated multipath-fading is an important issue. It deals with complex dependencies of large number of random variables. Earlier developments on decision fusion consider correlated local decisions, correlated shadowing, spatial correlation and independent fading channels. This paper presents likelihood ratio test (LRT) based new fusion rule using normal factor graph (NFG) and Sum-Product-Algorithm (SPA) model for cooperative spectrum sensing in presence of correlated multipath-fading channels. The proposed approach requires exact channel statistics instead of instantaneous channel state information (CSI). It leads to Neyman-Pearson (N-P) criteria based optimal sensing. We assume SUs are aligned in a linear fashion and each channel is correlated only with its adjacent channels with identical fading correlation coefficients. In this respect, we derive a new tri-variate Rayleigh probability density function using Miller´s [1] approach. Moreover, closed form solutions for local probabilities of detection and false alarm are also derived by assuming that all secondary users employ energy detection. The decision fusion is performed using SPA as message passing strategy over the NFG. Simulation results are provided to validate the performance of the proposed approach.