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MIMO-OFDM has been actively studied for high data rate communications over the bandwidth-limited underwater acoustic (UWA) channels. Unlike existing receivers that treat the intercarrier interference (ICI) as additive noise, in this paper we deal with ICI explicitly together with the co-channel interference (CCI) due to parallel transmissions in MIMO-OFDM. The proposed receiver has the following components: 1) compressed-sensing (CS) based sparse channel estimation, 2) soft-input-soft-output MMSE/Markov Chain Monte Carlo (MCMC) detector for interference mitigation, and 3) nonbinary LDPC decoding. These components are integrated under a progressive receiver framework, where the receiver starts with low-compleixty ICI-ignorant processing, and then progresses to ICI-aware processing with increasing ICI levels. In addition to simulation, we use real data from the MACE10 experiment, in which the transmitter was slowly moving, to verify the system performance. Simulation and experimental results show that explicitly addressing ICI and CCI significantly improves the performance of MIMO-OFDM in underwater acoustic systems.