Stability and Convergence Analysis of Transform-Domain LMS Adaptive Filters With Second-Order Autoregressive Process

• Published in: IEEE transactions on signal processing 2009-01, Vol.57 (1), p.119-130
• Main Authors: Shengkui Zhao, Shengkui Zhao, Zhihong Man, Zhihong Man, Suiyang Khoo, Suiyang Khoo, Hong Ren Wu, Hong Ren Wu
• Format: Article
• Language: English
• Subjects: Adaptive filters; Applied sciences; Asymptotic properties; Autoregressive processes; Convergence; Detection, estimation, filtering, equalization, prediction; discrete cosine transform (DCT); Discrete cosine transforms; discrete Fourier transform (DFT); Discrete Fourier transforms; discrete Hartley transform (DHT); Discrete wavelet transforms; Eigenvalues; Eigenvalues and eigenfunctions; Exact sciences and technology; Fourier transforms; Information, signal and communications theory; Least squares approximation; Mathematical analysis; Miscellaneous; Queuing theory; Signal and communications theory; Signal processing; Signal, noise; Stability; Stability analysis; Studies; system identification; Telecommunications and information theory; Transforms
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2008.2007618

In this paper, the stability and convergence properties of the class of transform-domain least mean square (LMS) adaptive filters with second-order autoregressive (AR) process are investigated. It is well known that this class of adaptive filters improve convergence property of the standard LMS adaptive filters by applying the fixed data-independent orthogonal transforms and power normalization. However, the convergence performance of this class of adaptive filters can be quite different for various input processes, and it has not been fully explored. In this paper, we first discuss the mean-square stability and steady-state performance of this class of adaptive filters. We then analyze the effects of the transforms and power normalization performed in the various adaptive filters for both first-order and second-order AR processes. We derive the input asymptotic eigenvalue distributions and make comparisons on their convergence performance. Finally, computer simulations on AR process as well as moving-average (MA) process and autoregressive-moving-average (ARMA) process are demonstrated for the support of the analytical results.