An affine combination of two augmented CLMS adaptive filters for processing noncircular Gaussian signals.

• We propose affine combining of two ACLMS filters and present its optimal mixing parameter, based on which an explicit expression describing the steady state mean behavior of the optimal mixing parameter is quantified for doubly white noncircular Gaussian input data. The so established physical insight shows that in steady state, the optimal mixing parameter is, statistically, negative and monotonically increases against the input SO noncircularity coefficient. • Upon applying the optimal mixing parameter, we perform the MSE analysis of the proposed affine-combined ACLMS filters. The so derived explicit MSE expression not only theoretically presents the universality of the combination scheme, that is, smaller or equal steady state MSE than either of the individual ACLMS subfilters, but also demonstrates that the overall MSE in steady state is approximately a monotonic increasing function of the input SO noncircularity coefficient. • Considering that the optimal affine combiner is unacquirable in practical applications, we provide an error power based scheme to iterate the affine combiner. Numerical examples verify that the proposed iterative combiner converges to the optimal one. The overall MSE curves respectively obtained via the iterative and optimal combiners are shown to be in close agreement. This paper investigates the statistical behavior of an affine combination of two augmented complex least mean-square (ACLMS) adaptive filters for processing noncircular Gaussian signals. First, the optimal affine combiner is studied and its steady state mean behavior is explicitly quantified. This makes it possible to reveal the impact of the input second-order noncircularity coefficient on the combiner. Next, the mean square error analysis of the proposed affine-combined ACLMS filters is provided, proving that the combined scheme performs no less than the best of the individual ACLMS subfilters. Besides, to facilitate physically realization of the combination strategy, an error power based algorithm that can iterate the affine combiner to the optimal one is also proposed. Finally, illustrative numerical simulations are provided to support the theoretical results. [ABSTRACT FROM AUTHOR]