  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.
