Soft Combination for Cooperative Spectrum Sensing in Fading Channels

Abstract

In this paper, we study the distributed energy-based detectors for spectrum sensing in cognitive radio networks. We assume that the sensing channel includes both small-scale and large-scale fading. The small-scale fading is modeled as Nakagami- $m$ and independent for different cooperating cognitive users, while the large-scale fading is assumed to be known (or can be estimated) by the cognitive users, due to their slowly changing nature. Furthermore, we assume that the channel gains are constant in one observation interval and vary independently in different intervals. Based on the Bayesian rule, we derive the optimal energy combining rule, i.e., the average likelihood ratio (ALR) detector. We also suggest two solutions: 1) mixture of gamma (MoG)-based ALR detector and 2) generalized Gauss–Laguerre formula (GLF)-based ALR detector, to overcome the problem of the intractable integrals in the optimal rule, and we propose two novel suboptimal but practical combining rules: 1) GLF-based linear combining detector, which can be implemented by linear functions and a comparator with negligible performance degradation and 2) GLF-based weighted-energy detector applicable for the low SNR regime. The simulation results reveal that with MoG and GLF detectors, the ALR detector can be implemented almost precisely with lower complexity. Moreover, all the proposed detectors outperform the conventional ones, especially when large-scale channel gains differ for different cognitive users.