  This paper investigates doubly-selective (i.e., time- and
frequency-selective) channel estimation in faster-than-Nyquist (FTN) signaling
HF communications. In particular, we propose a novel IM-based channel
estimation algorithm for FTN signaling HF communications including pilot
sequence placement (PSP) and pilot sequence location identification (PSLI)
algorithms. At the transmitter, we propose the PSP algorithm that utilizes the
locations of pilot sequences to carry additional information bits, thereby
improving the SE of HF communications. HF channels have two non-zero
independent fading paths with specific fixed delay spread and frequency spread
characteristics as outlined in the Union Radio communication Sector (ITU-R)
F.1487 and F.520. Having said that, based on the aforementioned properties of
the HF channels and the favorable auto-correlation characteristics of the
optimal pilot sequence, we propose a novel PSLI algorithm that effectively
identifies the pilot sequence location within a given frame at the receiver.
This is achieved by showing that the square of the absolute value of the
cross-correlation between the received symbols and the pilot sequence consists
of a scaled version of the square of the absolute value of the auto-correlation
of the pilot sequence weighted by the gain of the corresponding HF channel
path. Simulation results show very low pilot sequence location identification
errors for HF channels. Our simulation results show a 6 dB improvement in the
MSE of the channel estimation as well as about 3.5 dB BER improvement of FTN
signaling along with an enhancement in SE compared to the method in [1]. We
also achieved an enhancement in SE compared to the work in [2] while
maintaining comparable MSE of the channel estimation and BER performance.
