GLRT for testing separability of a complex-valued mixture based on the Strong Uncorrelating Transform

• Published in: 2012 IEEE International Workshop on Machine Learning for Signal Processing pp. 1 - 6
• Main Authors: Ramirez, D., Schreier, P. J., Via, J., Santamaria, I.
• Format: Conference Proceeding
• Language: English
• Published: IEEE 01.09.2012
• Subjects: circularity coefficients; Coherence; Complex independent component analysis (ICA); Covariance matrix; Electronic mail; generalized likelihood ratio test (GLRT); hypothesis test; maximum likelihood (ML) estimation; Maximum likelihood detection; Maximum likelihood estimation; Testing; Transforms
• ISBN: 1467310247; 9781467310246
• ISSN: 1551-2541
• DOI: 10.1109/MLSP.2012.6349785

The Strong Uncorrelating Transform (SUT) allows blind separation of a mixture of complex independent sources if and only if all sources have distinct circularity coefficients. In practice, the circularity coefficients need to be estimated from observed data. We propose a generalized likelihood ratio test (GLRT) for separability of a complex mixture using the SUT, based on estimated circularity coefficients. For distinct circularity coefficients (separable case), the maximum likelihood (ML) estimates, required for the GLRT, are straightforward. However, for circularity coefficients with multiplicity larger than one (non-separable case), the ML estimates are much more difficult to find. Numerical simulations show the good performance of the proposed detector.