Convergence properties of affine projection and normalized data reusing methods

The coloring of input sequences can significantly reduce the effective convergence rate of normalized least mean squares (LMS) adaptive filtering algorithms. Recently, there has been significant interest in affine projection adaptive filtering algorithms. These algorithms offer improved performance over traditional normalized LMS algorithms. They can achieve the performance of recursive least squares techniques at a lower computational cost. Unfortunately, these algorithms can greatly amplify measurement noise leading to higher overall misadjustment and poor tracking abilities. In this paper, the new forms of data reusing developed by the authors will be shown to be able to approximate the convergence performance of the affine projection methods without the large misadjustment. In addition, a comprehensive analysis of the steady-state statistical convergence properties of a broad class of data-reusing algorithms will be presented.