Optimal decoding of coded PSK and QAM signals in correlated fast fading channels and AWGN: a combined envelope, multiple differential and coherent detection approach

The maximum likelihood sequence estimator for the reception of coded digital phase modulated signals with single or multiamplitude constellations, transmitted over a multiplicative, frequency-nonselective (i.e., flat) correlated fast fading Rayleigh or Rician channel and corrupted by additive white Gaussian noise (AWGN), is derived. Due to this correlation, the errors caused by fading tend to occur in bursts. In the analysis, no assumption simplifying the problem is made. For fast fading the authors consider the most general case where both phase and amplitude distortion resulting from the fading process could change significantly and thus cannot be assumed to be constant over a number of transmitted symbols. It is shown that the estimator´s hardware structure consists of a combination of envelope, multiple differential and coherent detectors. With multiple differential detectors they define a receiver structure consisting of a combination of more than one distinct differential detectors each of them employing a progressively increasing (by the symbol duration) time-delay element. The outputs of these detectors are jointly processed by means of an algorithm which is presented in a recursive form. The derivation of this new receiver is general enough to accommodate trellis coded phase shift keying (PSK) and quadrature amplitude modulated (QAM) systems. Differentially encoded signals, such as the π/4-shift differential quadrature phase shift keying (DQPSK) scheme can also be incorporated. In order to reduce the overall receiver implementation complexity, several reduced complexity, near-optimal versions of the algorithm are presented. These reduced complexity receivers are based on the use of only a few multiple differential detectors. Performance evaluation results for reduced complexity trellis coded π/4-shift DQPSK, π/4-shift 8-DQAM (differential quadrature amplitude modulation) and 8-DPSK (differential phase shift keying) systems have demonstrated that the proposed receivers significantly reduce the error floors caused by fading