Coherent MAP detection of DQPSK bits

Both IS-136 and PDC digital cellular systems employ forward error correction (FEC) encoding followed by a form of DQPSK modulation. In this letter, we derive the maximum a posteriori (MAP) bit detector for DQPSK modulation in non-ISI channels for a coherent receiver with one or more antennas. The MAP detector forms a bit log-likelihood ratio, which provides the optimal "soft information" for MLSE or MAP convolutional decoding. MAP detection requires exponentiation and logarithm operations, as well as knowledge of the noise covariance. To avoid these operations, two approximate forms are developed, which do not require the noise covariance value under certain assumptions. Both approximate approaches, when used with soft FEC decoding, are within 0.5 dB of the optimal approach.