Mean-square performance of a convex combination of two adaptive filters

Combination approaches provide an interesting way to improve adaptive filter performance. In this paper, we study the mean-square performance of a convex combination of two transversal filters. The individual filters are independently adapted using their own error signals, while the combination is adapted by means of a stochastic gradient algorithm in order to minimize the error of the overall structure. General expressions are derived that show that the method is universal with respect to the component filters, i.e., in steady-state, it performs at least as well as the best component filter. Furthermore, when the correlation between the a priori errors of the components is low enough, their combination is able to outperform both of them. Using energy conservation relations, we specialize the results to a combination of least mean-square filters operating both in stationary and in nonstationary scenarios. We also show how the universality of the scheme can be exploited to design filters with improved tracking performance

Steady-State Performance of Convex Combinations of Adaptive Filters

Combination approaches can improve the performance of adaptive schemes. In this paper, we study the steady-state performance of an adaptive convex combination of transversal filters and show its universality in the sense that the combination performs, in steady-state, at least as well as its best component. We specialize the results to a convex combination of LMS filters using energy conservation arguments