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In this paper, the sparse direct adaptive equalization based on the recently developed proportionate recursive least squares (PRLS) adaptive filtering algorithm is investigated for multiple-input multiple-output (MIMO) underwater acoustic (UWA) communications. First, performance analysis is made for the PRLS, and simulation results show its gain over a standard recursive least squares algorithm under sparse systems. The fast implementation of the PRLS, named the proportionate stable fast transversal filters (PSFTF), is revisited to impl
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