A simplified decision feedback Chebyshev function link neural network with intelligent initialization for underwater acoustic channel equalization

IntroductionIn shallow-water environments, the reliability of underwater communication links is often compromised by significant multipath effects. Some equalization techniques such as decision feedback equalizer, and deep neural network equalizer suffer from slow convergence and high computational complexity.MethodsTo address this challenge, this paper proposes a simplified decision feedback Chebyshev function link neural network equalizer (SDF-CFLNNE). The structure of the SDF-CFLNNE employs Chebyshev polynomial function expansion modules to directly and non-linearly transform the input signals into the output layer, without the inclusion of hidden layers. Additionally, it feeds the decision signal back to the input layer rather than the function expansion module, which significantly reduces computational complexity. Considering that, in the training phase of neural networks, the random initialization of weights and biases can substantially impact the training process and the ultimate performance of the network, this paper proposes a chaotic sparrow search algorithm combining the osprey optimization algorithm and Cauchy mutation (OCCSSA) to optimize the initial weights and thresholds of the proposed equalizer. The OCCSSA utilizes the Piecewise chaotic population initialization and combines the exploration strategy of the ospreywith the Cauchy mutation strategy to enhance both global and local search capabilities.RseultsSimulations were conducted using underwater multipath signals generated by the Bellhop Acoustic Toolbox. The results demonstrate that the performance of the SDFCFLNNE initialized by OCCSSA surpasses that of CFLNN-based and traditional nonlinear equalizers, with a notable improvement of 2-6 dB in terms of signal-to-noise ratio at a bit error rate (BER) of 10-4 and a reduced mean square error (MSE). Furthermore, the effectiveness of the proposed equalizer was validated using the lake experimental data, demonstrating lower BER and MSE with improved stability.DiscussionThis underscores thepromise of employing the SDFCFLNNE initialized by OCCSSA as a promising solution to enhance the robustness of underwater communication in challenging environments.