  Being capable of enhancing the spectral efficiency (SE), faster-than-Nyquist
(FTN) signaling is a promising approach for wireless communication systems.
This paper investigates the doubly-selective (i.e., time- and
frequency-selective) channel estimation and data detection of FTN signaling. We
consider the intersymbol interference (ISI) resulting from both the FTN
signaling and the frequency-selective channel and adopt an efficient frame
structure with reduced overhead. We propose a novel channel estimation
technique of FTN signaling based on the least sum of squared errors (LSSE)
approach to estimate the complex channel coefficients at the pilot locations
within the frame. In particular, we find the optimal pilot sequence that
minimizes the mean square error (MSE) of the channel estimation. To address the
time-selective nature of the channel, we use a low-complexity linear
interpolation to track the complex channel coefficients at the data symbols
locations within the frame. To detect the data symbols of FTN signaling, we
adopt a turbo equalization technique based on a linear soft-input soft-output
(SISO) minimum mean square error (MMSE) equalizer. Simulation results show that
the MSE of the proposed FTN signaling channel estimation employing the designed
optimal pilot sequence is lower than its counterpart designed for conventional
Nyquist transmission. The bit error rate (BER) of the FTN signaling employing
the proposed optimal pilot sequence shows improvement compared to the FTN
signaling employing the conventional Nyquist pilot sequence. Additionally, for
the same SE, the proposed FTN signaling channel estimation employing the
designed optimal pilot sequence shows better performance when compared to
competing techniques from the literature.
