M-BCJR algorithm with channel shortening based on ungerboeck observation model for faster-than-Nyquist signaling

The M-BCJR algorithm based on the Ungerboeck observation model is a recent study to reduce the computational complexity for faster-than-Nyquist (FTN) signaling [1]. In this paper, we propose a method that can further reduce the complexity with the approximately same or better bit error rate (BER) performance compared to [1]. The information rate (IR) loss for the proposed method is less than 1% compared to the true achievable IR (AIR). The proposed improvement is mainly by introducing channel shortening (CS) before the M-BCJR equalizer. In our proposal, the Ungerboeck M-BCJR algorithm and CS can work together to defeat severe inter-symbol interference (ISI) introduced by FTN signaling. The ISI length for the M-BCJR algorithm with CS is optimized based on the criterion of the IR maximization. For the two cases τ = 0.5 and τ = 0.35, compared to Ungerboeck M-BCJR without CS benchmark [1], the computational complexities of Ungerboeck M-BCJR with CS are reduced by 75%. Moreover, for the case τ = 0.35, the BER performance of Ungerboeck M-BCJR with CS outperforms that of the conventional M-BCJR in [1] at the low signal to noise ratio region.