Practical application of turbo equalization to underwater acoustic communications

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.