Maximum likelihood binary detection in improper complex Gaussian noise

In a wide range of communication systems, including DS-CDMA and OFDM systems, the signal-of-interest might be corrupted by an improper [1] (also called non circularly symmetric [2] interfering signal. This paper studies the maximum likelihood (ML) detection of binary signals in the presence of additive improper complex Gaussian noise. Proposing a new measure for noncircularity of complex random variables, we will derive the ML decision rule and its performance based on this measure. It will be shown that the ML detector performs pseudo correlation [1] as well as conventional correlation of the observation to the signals-of-interest. As an alternative solution, we will propose a filter for converting improper signals to proper ones, called circularization filter, and will utilize it together with a conventional matched-filter (MF) to construct an ML detector.