Performance Analysis and Optimal Design of Multichannel Equalizer for Underwater Acoustic Communications

Adaptive equalization is a widely used method of mitigating the effects of multipath propagation and Doppler spreading in underwater acoustic communication channels. While the structure of a multichannel equalizer and least-squares-based adaptation algorithm are extensively used in practice, little is known in how to choose the number of sensors, separation between them, and lengths of the constituent filters such that the equalization performance is optimized. This paper studies the problem of optimal multichannel equalizer design in the context of time-varying underwater acoustic communication channels. In the first part, the paper presents a theoretical characterization of the equalization performance when the number of symbols that can be received in the time period over which the channel can be considered time invariant is limited. This result is then used to develop an understanding that the optimal number of equalizer coefficients is a tradeoff between the minimum mean squared error (MMSE) requirement for longer constituent filters and the insight that the limit on the number of stationary observations also limits the number of filter coefficients that can be effectively adapted. In the second part, the paper develops a theoretical model for wideband arrivals impinging upon an array of sensors of the multichannel equalizer. This model is used to develop an understanding that the optimal sensor separation is a tradeoff between the requirement for long aperture which improves resolution, and the fact that the grating lobes, caused by spatial undersampling, limit the equalizer's ability to estimate the transmitted signal from the received signal.