Robust Estimators for Faster-Than-Nyquist Signaling

Abstract

Novel, robust, and computationally attractive non-data-aided (NDA) and data-aided (DA) single and joint parameter estimators for faster-than-Nyquist (FTN) signaling are presented. By using the sixth moment alongside the second and fourth, it is possible to formulate an estimator (hence termed M2M4M6), allowing the joint blind estimation of the FTN symbol-packing ratio (SPR) (speed-up parameter) as well as the signal-to-noise ratio (SNR). The proposed estimators are robust in that they are based on uniformly spaced samples of the FTN signal taken at a fairly arbitrary FTN rate, insensitive to carrier and timing phase errors. While avoided in Nyquist signaling, the inter-symbol interference (ISI) term deliberately introduced in FTN signals is advantageously utilized for the estimation of SNR and SPR. The derivations are performed on a general complex base-signaling pulse and are illustrated for the commonly used root-raised cosine (RRC). Novel FTN Cramer-Rao lower bounds (CRLB) are derived to benchmark the efficiency of the proposed estimators. Extensive simulations are provided to illustrate the performance of the proposed estimators with respect to variations in all the relevant parameters and indicate that the estimators work best for the practical range of lower-intermediate values of SPR and SNR. The computational features of the proposed estimators, in addition to their robustness against carrier and sampling errors, make them valuable in many practical applications that incorporate cognitive radio (CR) alongside FTN.