Differential MPSK with n-Bit phase quantization

This paper derives the optimum detection rule for communication systems with n-bit phase quantization when data is differentially encoded at the transmitter. The proposed approach avoids the channel estimation problem at the receiver. First, a maximum likelihood detection rule for block-2 detectors utilizing only two consecutive quantized observations at the channel output is obtained. Second, it is shown that the derived maximum likelihood detection rule continues to be optimum for the class of block-L detectors for L = 3 when n = log₂ M, where M is the input alphabet size. Finally, utilizing the structure of the derived optimum detector, a message error probability expression is obtained for Rayleigh fading wireless channels. A simulation study is performed to illustrate the performance of the optimum detectors as well as the performance loss due to the lack of channel knowledge at the receiver. The proposed approach and the solutions presented in this paper provide an initial step to communicate with low-resolution ADCs without requiring receiver-side channel knowledge.