On the Optimality of MAP Bit Detection of Coded M-PSK Signals

The optimality of the maximum a posteriori probability(MAP) bit detection for differentially encoded M-PSK signals over static non-ISI channels is emphasized, in which the demodulator computes loglikelihood ratio (LLR) of individual coded bits directly, but not via transforming those successive detected symbolspsila LLR into bitspsila LLR as the conventional methods. As a representative, the designs and analyses focus on the convolutionally encoded pi/4-DQPSK signal. In order to demonstrate the optimality comparatively, the other two types of soft demodulators derived under the MAP symbol detection criterion and the MAP sequence detection criterion are also addressed. Through simulations the noticeable performance of the MAP bit detection are illustrated, especially in low SNR scenarios.