A Neural Network-Assisted Variable Step-Size NLMS Algorithm

The traditional normalized least-mean-square (NLMS) algorithm faces an inherent trade-off between convergence rate and steady-state error, and its adaptability is limited in non-stationary environments. This paper proposes a neural network-assisted variable step-size NLMS algorithm (NN-VSS-NLMS). An analytically motivated reference step size is first derived under a zero-mean statistically symmetric signal assumption to characterize the desired step-size trend. Based on this reference, an eight-dimensional feature vector composed of input signal power, error energy, and related statistical descriptors is constructed to describe the instantaneous signal state, and a two-layer fully connected neural network (NN) is introduced as an auxiliary tool to provide data-driven correction to the reference step size. In addition, dynamic modulation, step-size constraints, and smoothing operations are incorporated to regulate the predicted step size and enhance its controllability under time-varying conditions. Through simulations with stationary and non-stationary inputs as well as time-invariant and time-varying systems, the proposed algorithm achieves up to a fourfold improvement in convergence rate and more than 8 dB reduction in steady-state error compared with the classical NLMS algorithm, while maintaining improved tracking ability.