Combining Linear Estimation with Scalar Widely Linear Estimation

Abstract

We study the capabilities of a filter configuration where a linear filter is applied to an improper vector, and the output is processed by scalar widely linear filters afterwards. Assuming that this filter configuration is used to estimate a vector of interest from a noisy observation, we aim at finding the optimal filter coefficients in the sense of minimizing the mean square error. To this end, we propose a filter design algorithm based on alternating optimization. The resulting filter turns out to achieve an intermediate performance between the optimal widely linear filter and the optimal linear filter. As an application example, we discuss how the considered filter structure fits to the concept of linear transceivers in communication systems.