Coherent MAP detection of DQPSK bits

Both IS-136 and PDC digital cellular systems employ forward error correctio n (FEC) encoding followed by a form of DQPSK modulation. In this letter, me derive the maximum a posteriori (MAP) bit detector for DQPSK modulation in non-ISI channels for a coherent receiver with one or mote antennas, The MA P detector forms a bit log-likelihood ratio, which provides the optimal "so ft information" for MLSE or MAP convolutional decoding. MAP detection requi res exponentiation and logarithm operations, as well as knowledge of the no ise covariance. To avoid these operations, two approximate forms are develo ped, which do not require the noise covariance value under certain assumpti ons. Both approximate approaches, when used with soft FEC decoding, are wit hin 0.5 dB of the optimal approach.