Block-based fuzzy step size nlms algorithms for subband adaptive channel equalisation

Judicious selection of the step size parameter is crucial for adaptive algorithms to strike a good balance between convergence speed and misadjustment. The fuzzy step size (FSS) technique has been shown to improve the performance of the classical fixed step size and variable step size (VSS) normalised least mean square (NLMS) algorithms. The performance of the FSS technique in the context of subband adaptive equalisation is analysed and two novel block-based fuzzy step size (BFSS) strategies for the NLMS algorithm, namely fixed block fuzzy step size (FBFSS) and adaptive block fuzzy step size (ABFSS) are proposed. By exploiting the nature of gradient noise inherent in stochastic gradient algorithms, these strategies are shown to substantially reduce the computational complexity of the conventional FSS technique without sacrificing the convergence speed and steady-state performance. Instead of updating the step size at every iteration, the proposed techniques adjust the step size based on the instantaneous squared error once over a block length. Design methodology and guidelines that lead to good performance for the algorithms are given.