Selective partial-update augmented complex-valued LMS algorithm and its performance analysis

Adaptive filtering applications such as acoustic echo cancellation may require a large number of filter weights in order to estimate the unknown system with a long response, leading to high computational complexity. Using partial-update techniques is an effective method to alleviate this issue, and two partial-update augmented complex-valued LMS (PU-ACLMS) algorithms have been recently proposed. However, their convergence rates severely deteriorate due to using a stochastic or sequential weight update manner. This paper proposes a new PU-ACLMS, which selects the weights corresponding to the M largest moduli of input samples to update, with M less than the number of all weights. The mean and mean-square performance of the proposed algorithm is then analyzed to predict its stochastic behavior. In order to achieve this goal, the values of two scale factors are derived by using multiple integrals, which play an important role in our performance analysis. Finally, the performance of the proposed algorithm is compared with that of the sequential PU-ACLMS and stochastic PU-ACLMS, and the theoretical findings are verified by extensive simulations.