Sequential LMS for low-resource subband adaptive filtering: Oversampled implementation and polyphase analysis

The periodic and sequential partial update normalized LMS (P-NLMS and S-NLMS) algorithms and their variants are often used to reduce the computation cost of NLMS. In this paper, S-NLMS is employed in a low-resource subband adaptive filter implemented on an oversampled DFT filterbank. To analyze the system performance, we present a polyphase filterbank model for the P-NLMS and S-NLMS algorithms. It is shown that implicitly both algorithms employ perfect reconstruction delay chain analysis/synthesis filterbanks. As a result, the decimation involved in partial filter update does not introduce any steady-state performance degradation. The presented model can be employed to further predict and justify the convergence behavior of the partial update algorithms more accurately. Implementation of the S-NLMS algorithm on subband adaptive filters employing oversampled filterbanks is next described. Evaluation of the adaptive system performance shows that for stationary inputs, the S-NLMS algorithm (with proper step-size scaling) performs very similarly for moderate decimation factors of the S-NLMS.