Energy Detection for Spatial Receive Diversity and On-Off Keying in Rayleigh Fading with Channel Norm Estimation

Energy detection for single-input multiple-output (SIMO) systems using perfect estimates of the channel norm has been shown to exhibit the same diversity order as that of a coherent system. In this work, we analyze the performance of energy detection for SIMO when only least squares estimates of the channel norm are available. The configuration of on-off keying in a flat Rayleigh fading environment is considered. A closed form expression for the approximate conditional symbol error probability (SEP), conditioned on the normalized channel norm and its estimate, is derived. A Gaussian approximation for the received signal energy is applied in the derivation. Furthermore, a closed form approximation of the SEP at high signal-to-noise ratio is obtained. Numerical results are presented to show SEP variation with system parameters and comparison of error performance with that of fully noncoherent energy detection.