Simulation Results for the Decision-Directed MAP Receiver for M-ary Signals in Mulitiplicative and Additive Gaussian Noise

Simulation results are presented for the error-rate performance of the recursive digital maximum a posteriori probability (MAP) detector for knownM-ary signals in multiplicative and additive Gaussian noise. The structure of the digital simulation of the optimum detector is generally described, with specific results obtained for a quaternary signal and 2500 digit per second transmission rate. The simulation is focused on the aeronautical multipath communication problem. Plots of detection error rate versus additive signal-to-noise ratio are given, with the power ratio of multiplicative process to desired signal as a parameter. Results are presented for the cases where the detector has perfect knowledge of the first- and second-order statistics of the multiplicative and additive processes and also where these statistics are estimated in near real time. For comparison, the error rates of conventional coherent and noncoherent digital MAP detectors are also obtained. It is shown that with nonzero multiplicative noise, the error rates of the conventional detectors saturate at a level that is irreducible for increasing additive signal-to-noise ratio. The error rate of the optimum detector having perfect statistical knowledge continues to decrease rapidly with increasing additive signal-to-noise ratio. In the absence of multiplicative noise, the conventional coherent detector and the optimum detector are shown to exhibit identical performance. Suboptimum detectors, having less than perfect statistical knowledge, yield error rates bounded below by the optimum detector rates and bounded above by the conventional detector rates.