Revisiting Non-Coherent Detection of Differential PSK: A Factor Graph Perspective

For non-coherent differential modulated communications, the multiple-symbol differential detection (MSDD) may approach the coherent detection performance by jointly detecting a block of symbols. However, MSDD cannot support large-size block detection due to its complexity exponentially increasing with the block size. Moreover, MSDD assumes that the channel phase is constant over the symbols in a block, which is not realistic. In this letter, we propose to formulate the signal model of non-coherent differential modulated communications by means of a factor graph. Based on the factor graph, we develop a sum-product message-passing algorithm to enable the maximum a posteriori probability detection. Compared with MSDD, the detection complexity of our proposed scheme is linearly proportional to the block size. Simulation results show that the proposed scheme can not only achieve the performance of MSDD over the constant-phase channel, but also outperform it over the random-walk phase channel.