Iterative Sparse Channel Estimation and Data Detection for Underwater Acoustic Communications Using Partial Interval Demodulation

We present an iterative scheme for sparse channel recovery and data detection in cyclic-prefix orthogonal frequency division multiplex communication over doubly spread underwater acoustic channels. We consider the sequence of observations from partial interval demodulators (PIDs), and cast them into an observation model amenable for sparse channel recovery. We propose a two-stage iterative algorithm for channel estimation and data detection. In the first stage, we recover the channel from pilot-only observations and estimate the unknown data symbols from the postcombined PID outputs. In the second stage, we use the data symbols estimated in the first stage to reconstruct the dictionary matrix corresponding to a full interval demodulator, re-estimate the channel using the entire observations including the data subcarriers, and use it to detect the unknown data symbols from the PID outputs. Theoretically, we show that the PID outputs help in tracking the time-varying channel better by providing additional measurements to estimate the intercarrier interference due to Doppler spread compared to full interval demodulation. Also, we derive the Cramér-Rao lower bound on the mean squared error in channel estimation, and empirically show that the proposed two-stage algorithm meets the bound at high signal-to-noise ratio. Numerical studies on simulated channels and publicly available experimental channel data in Watermark show that the proposed algorithm considerably improves data detection performance, in terms of bit error rate, over that from a traditional full length demodulator output, in highly Doppler distorted scenarios.