Exploiting Spatial–Temporal Joint Sparsity for Underwater Acoustic Multiple-Input–Multiple-Output Communications

Multiple-input-multiple-output (MIMO) system offers a promising way for high data rate communication over bandwidth-limited underwater acoustic channels. However, MIMO communication not only suffers from intersymbol interference, but also introduces the additional co-channel interference, which brings challenge for underwater acoustic MIMO channel estimation and for channel equalization. In this article, we propose novel interference cancellation (IC) methods for handling this co-channel interference problem in the design of both channel estimation and channel equalization. Our method for channel estimation utilizes the spatial joint sparsity and the temporal joint sparsity in the multipath structure to estimate sparse channels with common delays under distributed compressed sensing framework. In this way, we enhance channel estimates with common delays, thus, suppress co-channel interference. Meanwhile, to address the case of multipath arrivals with different delays, which are estimated as noise under simultaneous orthogonal matching pursuit (SOMP) algorithm, we introduce forward-reverse strategy to SOMP algorithm, which is referred to as the FRSOMP algorithm. Our proposed FRSOMP algorithm performs the SOMP algorithm to achieve the initial channel estimates, performs the forward-add process, which attempts to add promising candidates into support sets, and performs the reverse-fetch process to check if the candidates in the support set are retained or removed. The purpose of channel estimation is to directly calculate the filter coefficients for channel-estimation-based decision feedback equalization (CE-DFE). In this article, we also propose a novel CE-DFE receiver with IC component. We design IC filters based on the traditional CE-DFE, and we derive the coefficients of the feedforward filters, feedback filters, and IC filters based on the channel estimate metric obtained by the FRSOMP algorithm, so the co-channel interference will be suppressed both in channel estimation and channel equalization. We demonstrate the performance of our approach by numerical simulation, lake experiment, and sea experiment. Results are provided to demonstrate the effectiveness of the proposed methods, which show that the proposed methods obtain higher output signal-to-noise ratio, lower bit error rate, and more separated constellations compared with the traditional compressed sensing channel estimation method and the traditional CE-DFE method.