Soft Symbol Decoding in Sweep-Spread-Carrier Underwater Acoustic Communications: A Novel Variational Bayesian Algorithm and Its Analysis

Abstract

Sweep spread carrier (S2C) based underwater acoustic (UWA) communications is a practically attractive but less explored modulation scheme in the published literature. In this paper, we present a rigorous treatment of the S2C communication receiver design and propose a data detection scheme that can handle challenging UWA channels. State-of-the-art S2C receivers based on the gradient heterodyne processing are only effective when the path delay and Doppler spread are moderate. We develop a new variational soft symbol decoding (VSSD) algorithm based on the principle of variational Bayes’ inference for a general linear channel model. In channels with moderate delay and Doppler spreads, we show that the VSSD algorithm is equivalent to the existing gradient heterodyne receivers for S2C communications. We apply the VSSD algorithm to the i.i.d. Gaussian multiple-input multiple-output channel and show, through numerical simulations, that it far outperforms the minimum mean squared error (MMSE) data detection. We illustrate the dramatic improvement in the performance of the VSSD based S2C receiver in two different models of simulated UWA channels and two contrasting measured UWA environments publicly available in the Watermark channel dataset. The proposed VSSD algorithm recovers data symbols at a signal-to-noise ratio (SNR) which is at least 10 dB (8 dB) lower than the MMSE decoder for uncoded (rate 2/3 LDPC coded) communications over UWA channels where the existing receivers either fail completely or must compromise on the data rate to maintain the bit error rate (BER) performance.