Eigenvalue Decomposition Precoded Faster-Than-Nyquist Transmission of Index Modulated Symbols

In this paper, we propose a precoded faster-than-Nyquist (FTN) signaling technique for time-domain single-carrier index modulated (IM) symbol transmission. More precisely, eigenvalue decomposition precoding is adopted for the FTN transmission of data bits modulated by single-carrier time-domain IM. While the FTN scheme increases the spectral efficiency and data rate by packing more transmit symbols per block duration than those defined in the Nyquist criterion, time-domain IM works towards the same objective while maintaining symbol sparsity. We analytically derive the constrained capacity of the proposed system. Our simulation results show that the proposed scheme has better bit error ratio (BER) performance over the conventional FTN-IM scheme, particularly for the scenario of a higher packing ratio. In the proposed scheme, 2.5-dB performance gain is observed at the BER of = 10⁻⁴, employing the packing ratio of 0.7 and the roll-off factor of 0.5 in a channel-uncoded scenario.

I. Introduction

The scarcity of communication bandwidth, as well as the demand for higher spectral efficiency, is at a record high [1], [2]. For the sake of increasing spectral efficiency, faster-than-Nyquist (FTN) signaling [3] packs signal pulses tighter in time than in Nyquist signaling. Such packing of signals with high density by violating Nyquist's zero inter-symbol interference (ISI) criterion, and hence requiring advanced signal processing techniques to mitigate the deliberately introduced ISI has gained increased attention. After the original introduction of FTN signaling in [4], [5], Mazo [6] showed in his seminal work that the minimum Euclidean distance (MED) remains unaffected if the signal packing ratio satisfies for sinc pulses, hence capable of transmitting 25% faster than the rate of Nyquist signaling. In [7], the capacity of FTN signaling was derived to show that the FTN signaling is capable of the excess bandwidth. In [8], the FTN concept was extended to the frequency-domain counterpart as well as both the time-frequency domain one [9], outperforming orthogonal frequency-division multiplexing (OFDM).