Low-Complexity Detection of M-ary PSK Faster-than-Nyquist Signaling

TL;DR

This paper introduces a polynomial-time algorithm for detecting M-ary PSK FTN signaling, balancing performance and complexity, and demonstrating significant spectral efficiency gains over Nyquist signaling.

Contribution

A novel semidefinite relaxation and Gaussian randomization-based detection algorithm for M-ary PSK FTN signaling that is computationally efficient and improves spectral efficiency.

Findings

Achieves around 17% spectral efficiency increase over Nyquist signaling.

Balances detection performance with low computational complexity.

Outperforms existing schemes in spectral efficiency at the same error rate.

Abstract

Faster-than-Nyquist (FTN) signaling is a promising non-orthogonal physical layer transmission technique to improve the spectral efficiency of future communication systems but at the expense of intersymbol-interference (ISI). In this paper, we investigate the detection problem of FTN signaling and formulate the sequence estimation problem of any $M$-ary phase shift keying (PSK) FTN signaling as an optimization problem that turns out to be non-convex and nondeterministic polynomial time (NP)-hard to solve. We propose a novel algorithm, based on concepts from semidefinite relaxation (SDR) and Gaussian randomization, to detect any $M$-ary PSK FTN signaling in polynomial time complexity regardless of the constellation size $M$ or the ISI length. Simulation results show that the proposed algorithm strikes a balance between the achieved performance and the computational complexity. Additionally, results show the merits of the proposed algorithm in improving the spectral efficiency when compared to Nyquist signaling and the state-of-the-art schemes from the literature. In particular, when compared to Nyquist signaling at the same error rate and signal-to-noise ratio, our scheme provides around $17\%$ increase in the spectral efficiency at a roll-off factor of 0.3.