This paper addresses multi-input multi-output (MIMO) communications over sparse acoustic channels suffering from frequency modulations. An extension of the recently introduced SLIM algorithm, which stands for sparse learning via iterative minimization, is presented to estimate the sparse and frequency modulated acoustic channels. The extended algorithm is referred to as generalization of SLIM (GoSLIM). The sparseness is exploited through a hierarchical Bayesian model, and because GoSLIM is user parameter free, it is easy to use in practical applications. Moreover this paper considers channel equalization and symbol detection for various MIMO transmission schemes, including both space-time block coding and spatial multiplexing, under the challenging channel conditions. The effectiveness of the proposed approaches is demonstrated using in-water experimental measurements recently acquired during WHOI09 and ACOMM10 experiments.