FFT-Spread Faster-Than-Nyquist Signaling in Frequency-Selective Fading Channel

In this paper, we propose novel reduced-complexity fast Fourier transform (FFT)-spread faster-than-Nyquist (FTN) signaling with optimal power allocation for a frequency-selective fading channel. The information rate of the proposed FTN signaling is approximately derived by relying on the circulant approximation of the FTN-specific intersymbol interference matrix and noise covariance matrix. This allows us to constitute efficient calculations of precoding and weighting matrices. The power allocation coefficients are optimized such that the approximated information rate is maximized. Our simulation results demonstrate that the proposed scheme achieves the bit error ratio performance close to the conventional eigenvalue-decomposition (EVD)-precoded FTN signaling counterpart that is optimal in terms of an achievable information rate while significantly reducing the computational complexity as low as the order of ${\mathcal{O}}(N\log N)$.

I. Introduction

Conventional wireless communication systems are designed based on the Nyquist criterion, which defines a minimum symbol interval by T₀ = 1/(2W), where 2W represents the bandwidth of an ideal rectangular shaping filter, and the associated maximum symbol rate is 1/T₀. The excess bandwidth of 2W (1+β) is induced when employing a realistic root raised cosine (RRC) shaping filter having a roll-off factor β > 0. Hence, the achievable spectral efficiency of Nyquist signaling based on an RRC shaping filter becomes (1 + β)-times lower than that of an idealistic rectangular shaping filter (β = 0). To overcome this limitation, the concept of faster-than-Nyquist (FTN) signaling has been explored for more than 50 years [1]–[3]. In FTN signaling, a symbol interval is set lower than that of Nyquist signaling, i.e., T = τT₀, where τ (0 < τ ≤ 1) represents a symbol packing ratio, hence achieving a higher symbol rate than the Nyquist signaling counterpart, which is, naturally, achieved at the cost of the detrimental intersymbol interference (ISI) effects.