Factor Graph Aided Multiple-Symbol Differential Detection in the Broadcasting Phase of a Network Coding Based UWB Relay System

A factor-graph-aided multiple-symbol differential detection (FG-MSDD) is proposed and its performance is analyzed and evaluated in the broadcasting phase (i.e., the downlink phase) of an ultra-wideband (UWB) two-way relay system (TWRS). In the downlink of the TWRS, the relay is transmitting network-coded information to the sources, and each source node aims to calculate a posteriori probabilities (APPs) of the information symbols from the relay node. A sampling method based on the modified autocorrelation receiver is proposed for FG-MSDD, which has a trellis structure. The trellis can be decomposed into multiple subtrellises depending on the FG factorization. Then, a methodology for APPs is derived when the forward-and-backward message passing is performed on the subtrellises. The main advantage of FG-MSDD is that it exploits soft information accurately with the aid of the bidirectional message passing. In addition, the proposed FG-MSDD, in conjunction with any soft-input soft-output (SISO) decoding scheme, is capable of obtaining an iterative detection algorithm. Various performance evaluation results obtained by means of computer simulations have verified that the proposed algorithm improves detection performance for the noncoherent UWB TWRS.