Transient Analysis of a Selective Partial-Update LMS Algorithm

In applications where large-order filters are needed, the computational load of adaptive filtering algorithms can become prohibitively expensive. In this paper, a comprehensive analysis of a selective partial-update least mean squares, named SPU-LMS-M-min, is developed. By employing the partial-update strategy for a non-normalized adaptive scheme, the designer can choose an appropriate number of update blocks considering a trade-off between convergence rate and computational complexity, which can result in a more than 40% reduction in the number of multiplications in some configurations compared to the traditional LMS algorithm. Based on the principle of minimum distortion, a selection criterion is proposed that is based on the input signal’s blocks with the lowest energy, whereas typical Selective Partial Update (SPU) algorithms use a selection criterion based on blocks with highest energy. Stochastic models are developed for the mean weights and mean and mean squared behaviour of the proposed algorithm, which are further extended to accommodate scenarios involving time-varying dynamics and suboptimal filter lengths. Simulation results show that the theoretical predictions are in good agreement with the experimental outcomes. Furthermore, it is demonstrated that the proposed selection criterion can be easily extended to active noise cancellation algorithms as well as algorithms utilizing variable filter length. This allows for the reduction of computational costs for these algorithms without compromising their asymptotic performance.