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In this paper, we describe linear turbo equalizers (TEQ) and investigate their practical application to underwater acoustic communications. Owing to the ability to achieve a good performance-complexity trade-off, linear TEQ is a good candidate for long reverberant channels, which usually demand high computational complexity. First, we reveal a relationship between two different TEQ structures; channel estimate (CE)-based minimum mean square error (MMSE) TEQ versus direct-adaptive linear TEQ. We show that without inclusion of the second-order a priori statistics, the coefficients of direct-adaptive TEQ converge to linear time-invariant form, though an optimal MMSE solution derived from a priori information is time-variant. Nevertheless, the direct-adaptive TEQ yields performance comparable to the CE-based MMSE TEQ while maintaining lower complexity. This was confirmed through real experiments conducted off the coast of Martha’s Vinyard, MA (“SPACE 08”). We also discuss a practical design of a multi-channel least mean square (LMS) TEQ and experiments show that the LMS-TEQ successfully decodes data achieving up to 19.53 kbit/s for 1000 meter distance.
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