Precoded Faster-than-Nyquist Signaling with Optimal Power Allocation in Frequency-Selective Channel

In this paper, we propose eigendecomposition-precoded faster-than-Nyquist (FTN) signaling with power allocation in a frequency-selective fading channel. More specifically, we derive mutual information associated with the proposed FTN signaling. Then, the optimal power coefficients are calculated such that the derived mutual information is maximized. Our analytical performance results show that the proposed FTN signaling scheme achieves a higher information rate than the conventional FTN signaling scheme without relying on power allocation and the classic Nyquist-based signaling scheme, under the assumption that all the schemes employ a root-raised cosine shaping filter. Moreover, our numerical simulation results of the bit error ratio performance and the power spectral density demonstrate that the proposed FTN scheme outperforms the conventional Nyquist-based signaling scheme without sacrificing any bandwidth broadening.

I. Introduction

The classic Nyquist criterion has played an essential role in bandlimited communication systems, having finite bandwidth 2W Hz, since it achieves intersymbol interference (ISI)-free information transmission. In the Nyquist criterion, a minimum symbol interval is limited to T₀ = 1/(2W) [s], and hence the achievable symbol rate is upper-bounded by 1/T₀. To overcome this limitation, the concept of faster-than-Nyquist (FTN) signaling has been studied [1], [2]. In FTN signaling, a symbol interval is defined by T = τT₀ (0 < τ ≤ 1), where τ is a symbol’s packing ratio. Therefore, FTN signaling has the potential of achieving a higher transmission rate than the conventional Nyquist-based ISI-free counterpart without imposing any extra bandwidth. Several properties of FTN signaling have been revealed in the literature [1], [3]–[10]. In [1], it was shown that the minimum Euclidean distance (MED) of FTN signaling is the same as that of Nyquist-based signaling for τ ≥ 0.802 under the assumption of the ideal rectangular shaping filter (sinc pulse). In [3], the capacity of FTN signaling was derived for the first time, where the use of a root raised-cosine (RRC) shaping filter having a roll-off factor β was assumed. It was revealed that FTN signaling achieves a higher capacity than the conventional Nyquist-based counterpart employing the same RRC shaping filter, owing to the exploitation of the excess bandwidth. In [5], an achievable information rate of FTN signaling for a finite block-length was analyzed.