A self-orthogonalizing efficient block adaptive filter

This paper deals with the development of a unique self-orthogonalizing block adaptive filter (SOBAF) algorithm that yields efficient finite impulse response (FIR) adaptive filter structures. Computationally, the SOBAF is shown to be superior to the least mean squares (LMS) algorithm. The consistent convergence performance which it provides lies between that of the LMS and the recursive least squares (RLS) algorithm, but, unlike the LMS, is virtually independent of input statistics. The block nature of the SOBAF exploits the use of efficient circular convolution algorithms such as the FFT, the rectangular transform (RT), the Fermat number transform (FNT), and the fast polynomial transform (FPT). In performance, the SOBAF achieves the mean squared error (MSE) convergence of a self-orthogonalizing structure, that is, the adaptive filter converges under any input conditions, at the same rate as an LMS algorithm would under white input conditions. Furthermore, the selection of the step size for the SOBAF is straightforward as the range and the optimum value of the step size are independent of the input statistics.