Wide-sense linear mean square estimation and prediction

Optimum mean square estimation of a random variable y in terms of an observation vector x is realized by the conditional expectation value. When x and y are real and jointly normal this expectation is linear in x. This is no longer the case when x and y are complex and jointly normal and the expectation is linear in x and in its complex conjugate x*, which introduces a widely linear procedure. The purpose of the paper is to study the properties of widely linear systems for estimation and prediction. The structure of such systems is calculated and the gain in performance is analyzed. The results are applied to autoregressive signals, which introduces widely linear prediction