A low-complexity error-feedback lattice-equalizer with phase tracking for underwater acoustic communications.

Recursive least squares (RLS)-based equalizers are hindered by their high complexity in underwater acoustic (UWA) communications. This article proposes an adaptive equalizer with a phase tracking method for the UWA communication, named the error-feedback lattice-equalizer (EFLE). First, we derive the algorithm for recursively solving the least squares problem from EFLE, introducing a lattice structure using time and order updates, thereby reducing the complexity to be linearly related to its length. The error-feedback mechanism used in computing reflection coefficients ensures the numerical stability of the algorithm. By focusing on the rapid tap rotation in time-varying channels, we design phase tracking in EFLE to further improve equalization performance. To verify the bit error rate (BER) performance of the proposed EFLE, we study the UWA communication system and conduct UWA simulations and at-sea experiments. Comparisons include linear complexity equalizers such as least mean square (LMS), leaky LMS, least mean mixed-norm, and ϵ-normalized LMS equalizers, and quadratic complexity RLS equalizers. At-sea experiment results show that the BER performance of EFLE significantly outperforms its counterparts.