Asymptotic detection performance of energy detector in fixed-gain cooperative relay networks

Energy detectors are preferred choice for spectrum sensing in cognitive radio networks due to their low implementation complexity. Recently, there is a lot of work being done to analyze the energy detectors in both diversity and cooperative relay networks. In this work, detection performance of energy detector is analyzed in a fixed-gain cooperative relay network with maximum-ratio combiner (MRC) at the destination. Upper and lower bounds on instantaneous signal-to-noise ratio (SNR) of the relay path are used in this work to mathematically tract the analyses. Probability density function (PDF) is derived for these asymptotic instantaneous SNR bounds to obtain upper and lower bound expressions of average detection probability (P_d) for the relay path transmission. Similarly, PDF is derived for the combined signal from direct and relay path at destination with MRC, which is then used to derive asymptotic bounds on average P_d of the cooperative system. The derived upper and lower bounds are tight approximations of the exact average P_d which is also validated through simulations.