Error performance of PAM systems using energy detection with optimal and suboptimal decision thresholds

In this paper, we consider the error probability for multilevel pulse amplitude modulated (PAM) signals, which are used with a multipath diversity combiner based on energy detection (ED). A distinctive feature of ED combined with nonconstant envelope signals is that the symbol decision thresholds need to be determined from a non-Gaussian distributed decision variable. We first present a novel theoretical analysis framework which provides a basis to predict the error performance of ED-PAM systems with optimal maximum likelihood decision thresholds in general multipath fading channels with arbitrary number of degrees of freedom. We then use frequency-selective lognormal fading channels as a case example and evaluate simple approximations for the error probability. Moreover, the analysis is extended to include the joint effect of systematic and random threshold deviation on the error probability with suboptimal but practical data-aided threshold estimation.