Challenges and analysis of adaptive multichannel equalization for large-N arrays

Hydrophone arrays with large numbers of elements (Large-N) offer the potential for significantly increasing the capabilities of underwater acoustic communications systems. However, the use of such arrays poses challenges. In the context of adaptive equalization in underwater acoustic communications, these challenges include the computational complexity of the adaptation algorithms and the long averaging intervals (memory) required by algorithms to effectively estimate optimal equalizer filter coefficients. Empirical results have shown that partitioning an array into subarrays, independently processing there signals received on each subarray, and then combining the outputs of the processors for each subarray can result in both improved performance and reduced computational complexity. Here, the performance trade-off associated with choosing the number of subarrays, or equivalently, choosing the number of elements (hydrophones) per subarray, is analyzed using tools from Asymptotic Random Matrix Theory and a numerical underwater acoustic propagation model. The results show that the optimal number of subarrays depends on both the length of the observation interval over which the adaptive equalizer weights are computed and the received signal SNR. Long averaging intervals or higher SNRs favor larger subarrays (fewer number of subarrays) while short averaging intervals or low SNRs favor small subarrays. In addition, the performance of linear equalizers (LE) and decision feedback equalizers (DFE) is compared and the relative performance is shown to depend on subarray size, SNR, and the averaging window length.