Multiple-symbol Differential Sphere Decoding for Network Coding

In order to shorten 3dB performance gap between the conventional differential detection and correlation detection in network coding, we consider multiple-symbol differential detection (MSDD) for two-way relay channel (TWRC) model. MSDD, which makes use of continuously N symbols to jointly detect N-1 symbols. However, the complexity of the maximum likelihood differential detection increases exponentially with the detection group length and the modulation constellation points. In this paper, we propose multiple-symbol differential sphere decoding (MSDSD) to circumvent this excessive computational complexity. Simulation results show that the combination of MSDSD and differential network coding can not only reduce the computational complexity, but also overcome error platform caused by High-Doppler frequency offset at high signal-to-noise ratio, and obtain the optimum detection performance simultaneously. Hence, MSDSD can be regarded as a low complexity detection algorithm in differential network coding scheme.