**Post: #1**

An Affine Combination of two LMS adaptive filters transient mean square analysis

Abstract:

The design of many adaptive filters requires a tradeoff between convergence speed and steady-state mean-square error (MSE). A faster (slower) convergence speed yields a larger (smaller) steady-state mean-square deviation (MSD) and MSE. This property is usually independent of the type of adaptive algorithm, i.e., least mean-square (LMS), normalized least

Mean-square (NLMS), recursive least squares (RLS), or affine projection (AP).

This design tradeoff is usually controlled by some design parameter of the weight update, such as the step size in LMS or AP, the step size or the regularization parameter in NLMS or the forgetting factor in RLS. Variable step-size modifications of the basic adaptive algorithms offer a possible solution to this design problem.

METHODOLOGY:

This project studies the statistical behavior of an affine combination of the outputs of two LMS adaptive filters that simultaneously adapt using the same white Gaussian inputs. The purpose of the combination is to obtain an LMS adaptive filter with fast convergence and small steady-state mean-square deviation (MSD). The linear combination studied is a generalization of the convex combination, in which the combination factor lambda (n) is restricted to the interval (0, 1). The viewpoint is taken that each of the two filters produces dependent estimates of the unknown channel.

Thus, there exists a sequence of optimal affine combining coefficients which minimizes the MSE. First, the optimal unrealizable affine combiner is studied and provides the best possible performance for this class. Then two new schemes are proposed for practical applications.

The mean-square performances are analyzed and validated by Monte Carlo simulations. With proper design, the two practical schemes yield an overall MSD that is usually less than the MSD's of either filter.

Tool used: MATLAB

REFERANCE:

An Affine Combination of two LMS adaptive filters transient mean square analysis-IEEE 2008