Low-Complexity SVD Precoding for Faster-Than-Nyquist Signaling Using High-Order Modulations

To address the low spectrum efficiency of satellite communications, faster-than-Nyquist (FTN) signaling has proven a promising technology to improve the spectrum efficiency without requiring additional bandwidth or antennas. However, FTN signaling violates the Nyquist criterion, thereby resulting in intersymbol interference (ISI). While existing singular value decomposition (SVD) precoding can eliminate FTN-induced ISI, it ignores interblock interference, leading to low estimation accuracy. Besides, existing SVD precoding requires high complexity due to the lack of efficient and convenient implementation method. Replacing the linear convolution in FTN shaping by the circular convolution, we construct the circular FTN (CFTN) signaling and propose a CFTN-SVD precoding, which offers several advantages over the existing SVD precoding. First, the proposed CFTN-SVD precoding does not require the transmitter to acquire any accurate information about the receiver, streamlining the transmission process. Second, the proposed CFTN-SVD precoding is designed with low implementation complexity, leveraging fast Fourier transform (FFT) and inverse FFT (IFFT) to facilitate the practical implementation. Last but not least, the proposed CFTN-SVD precoding takes all FTN-induced ISI into consideration, resulting in improved estimation accuracy and making it suitable for high-order modulations. Simulation results show that compared with the bit error rate (BER) of Nyquist signaling, the BER loss of the proposed CFTN-SVD precoding is about 0.8 and 0.25 dB for uncoded and coded FTN signaling, respectively, when adopting 256-amplitude phase shift keying.