Analysis of Error Probability with Maximum Likelihood Detection over Discrete-Time Memoryless Noncoherent Rayleigh Fading Channels

It is known that the capacity of the discrete-time memoryless noncoherent Rayleigh fading channels (DTM-NRFC) is achieved by a discrete constellation with finite number of mass points and when one of the mass points is located at the origin [1]. In this paper, we present the maximum likelihood detection (MLD) error performance on DTM-NRFC for a discrete constellation with coding and spatial diversity. In the absence of outer coding, the error probability with MLD is derived in a surprisingly simple closed-form. On the other hand, with coding and diversity, our error probability expressions can be evaluated via saddle-point approximation techniques.