Optimization for faster‐than‐Nyquist signaling based combining under multi‐path channel

Abstract

SummaryWe propose a faster‐than‐Nyquist (FTN) signaling based combining scheme to increase the achievable rate for the single‐input‐single‐output (SISO) system and the single‐carrier system under the multi‐path channel, where the combining scheme aims to combine the signals received at all symbol periods during the channel length for each transmitted symbol. An important feature of the FTN signaling based combining scheme is that the transmitter ceases the transmission for b symbol periods after transmitting each symbol. By proposing the optimization algorithm for finding the optimum b that maximizes the achievable (information) rate, we propose in this paper the optimal FTN signaling based combining scheme. We first establish the optimization problem and then present a theorem for proving the existence of the optimum b that maximizes the lower bound of the average achievable (information) rate. On the basis of this theorem, we present the steps of the proposed optimization algorithm. Numerical results are provided, and they confirm that the proposed optimization algorithm can find the optimum b.