Simulation of precoding algorithms based on matrix decomposition for faster-than-Nyquist signaling

The communication system based on the faster-than-Nyquist (FTN) signaling is a bandwidth-efficient technology which has drawn much attention recently. Since FTN uses faster symbol rate than Nyquist signaling, inter-symbol interference (ISI) is generated inevitably in the receiver. Partial Decision Feedback Equalization (PDFE) cancellation is an efficient interference cancellation and signal detection schemes for FTN system. However, the noise is only partial considered and its computational complexity is very high. In fact, precoding technique can reduce the interference effectively as well as further improve the detection performance. So we introduce three precoding algorithms in FTN signaling, including: singular value decomposition (SVD), geometric mean decomposition (GMD) and unified channel decomposition (UCD). This paper presents the performance of three precoding methods, PDFE and directly hard decision(HD) without FTN signaling. Simulation results show that UCD precoding can perform better than GMD precoding at any SNR value, SVD precoding and PDFE can perform worse than GMD precoding at higher SNR, only the performance of SVD precoding is slightly worse than directly HD.