Affine projection algorithm for oversampled subband adaptive filters

The performance of the Normalized Least Mean Square (NLMS) algorithm for adaptive filtering is dependent on the spectral flatness of the reference input. Thus, the standard NLMS algorithm does not perform well in Over-Sampled Subband Adaptive Filters (OS-SAFs) because colored subband signals are generated even for white input signals. Thus we propose the use of the Affine Projection Algorithm (APA) to adapt the individual subband filters in OS-SAF systems. The OS-SAF using APA for adaptation is implemented on a fast, low-resource over-sampled filterbank. Through both theoretical and experimental analyses, it is demonstrated that a low order APA will significantly improve the convergence behavior, offering a low computational complexity compared to the Recursive Least Squares (RLS) method. We employ a recursive method of calculating the correlation matrix to further decrease the computation cost without affecting the performance.