Error analysis for nonuniform signaling over Rayleigh fading channels

We investigate the error performance of a communication system where a nonuniform memoryless binary source is transmitted via Gray-mapped M-ary phase-shift keying or quadrature amplitude modulation over memoryless Rayleigh fading channels, and demodulated via optimal maximum a posteriori detection. Using recently derived upper and lower bounds on the probability of a general union of events, which are tight and can be efficiently computed, the system symbol-error (P_s) and bit-error (P_b) rates are evaluated for a wide range of channel conditions. Since for nonuniform signaling, Gray mapping is not necessarily optimal for minimizing P_s or P_b (as was recently shown by Takahara et al.), we also evaluate the system performance under the map obtained by Takahara et al. and compare it with a Gray-mapped system.