A Very Low Complexity Successive Symbol-by-Symbol Sequence Estimator for Faster-than-Nyquist Signaling

In this paper, we investigate the sequence estimation problem of binary and quadrature phase shift keying faster-than-Nyquist (FTN) signaling and propose two novel low-complexity sequence estimation techniques based on concepts of successive interference cancellation. To the best of our knowledge, this is the first approach in the literature to detect FTN signaling on a symbol-by-symbol basis. In particular, based on the structure of the self-interference inherited in FTN signaling, we first find the operating region boundary---defined by the root-raised cosine (rRC) pulse shape, its roll-off factor, and the time acceleration parameter of the FTN signaling---where perfect estimation of the transmit data symbols on a symbol-by-symbol basis is guaranteed, assuming noise-free transmission. For noisy transmission, we then propose a novel low-complexity technique that works within the operating region and is capable of estimating the transmit data symbols on a symbol-by-symbol basis. To reduce the error propagation of the proposed successive symbol-by-symbol sequence estimator (SSSSE), we propose a successive symbol-by-symbol with go-back-$K$ sequence estimator (SSSgb$K$SE) that goes back to re-estimate up to $K$ symbols, and subsequently improves the estimation accuracy of the current data symbol. Simulation results show that the proposed sequence estimation techniques perform well for low intersymbol interference (ISI) scenarios and can significantly increase the data rate and spectral efficiency. Additionally, results reveal that choosing the value of $K$ as low as $2$ or $3$ data symbols is sufficient to significantly improve the bit-error-rate performance. Results also show that the performance of the proposed SSSgb$K$SE, with $K = 1$ or $2$, surpasses the performance of the lowest complexity equalizers reported in the literature, with reduced computational complexity.