Stochastic analysis of an error power ratio scheme applied to the affine combination of two LMS adaptive filters

The affine combination of two adaptive filters that simultaneously adapt on the same inputs has been actively investigated. In these structures, the filter outputs are linearly combined to yield a performance that is better than that of either filter. Various decision rules can be used to determine the time-varying parameter for combining the filter outputs. A recently proposed scheme based on the ratio of error powers of the two filters has been shown by simulation to achieve nearly optimum performance. The purpose of this paper is to present a first analysis of the statistical behavior of this error power scheme for white Gaussian inputs. Expressions are derived for the mean behavior of the combination parameter and for the adaptive weight mean-square deviation. Monte Carlo simulations show good to excellent agreement with the theoretical predictions. ► We study the behavior of an error power ratio scheme applied to the affine combination of LMS adaptive filters. ► We analyze the statistical behavior of the scheme for Gaussian input signals. ► We derive expressions for the mean behavior of the combinations parameter. ► We derive expressions for the adaptive weight mean-square deviation.