Low Computational Complexity RLS-Based Decision-Feedback Equalization in Underwater Acoustic Communications

The adaptive recursive least squares (RLS) algorithm plays a crucial role in underwater acoustic (UWA) communications because of its robustness and fast convergence. However, the high computational complexity of the RLS algorithm has limited its application in UWA channels with long delay spreads. Two strategies can be developed to reduce the complexity of the RLS algorithm. The first one is to directly reduce the complexity considering the algorithm itself. Here, we exploit the dichotomous coordinate descent (DCD) algorithm to achieve low complexity. Since the received signals from multiple hydrophones are compensated with fluctuating phase increments at each instant, the shift structure of the input sequence, which enables a significant reduction in the complexity of updating the correlation matrix of the input vector in the DCD algorithm, is no longer applicable in UWA channels. To make the DCD algorithm compatible with the nonshifted structure of input sequence, a partial updating approach is employed for the correlation matrix of the input sequence over time in the RLS algorithm. This approach skips cases with small phase variations and only updates the cross-correlation submatrix. In this way, constant and full-scale phase compensation is avoided. The other strategy is to shorten the channel length. Here, we exploit the iterative frequency-domain equalization (FDE) to suppress the intersymbol interference from multipaths. The received signal is first partitioned into overlapping subblocks for iterative FDE. A weighting processing with a subblock forgetting factor is designed to make the mean squared error continuous across subblocks and iterations in the RLS algorithm. Both the strategies were adopted in the decision-feedback equalization (DFE) and examined by simulations and experiments. Results demonstrate that the proposed algorithms approximate or outperform the traditional RLS-based DFE with much lower computational overheads in channels with small delay spreads and fluctuation rates. For the improved DCD-RLS-based DFE, a threshold provides a tradeoff between the performance and complexity. For the FDE-RLS-based DFE, the mean squared error and computational complexity induced by long equalizer taps can be kept at low levels due to channel shortening. The latter algorithm remains effective even as channel delays and fluctuation rates increase.