Performance analysis of the conventional complex LMS and augmented complex LMS algorithms

• Published in: 2010 IEEE International Conference on Acoustics, Speech and Signal Processing pp. 3794 - 3797
• Main Authors: Douglas, Scott C, Mandic, Danilo P
• Format: Conference Proceeding
• Language: English
• Published: IEEE 01.03.2010
• Subjects: Adaptive arrays; adaptive filters; adaptive signal processing; adaptive systems; Algorithm design and analysis; Array signal processing; Convergence; Covariance matrix; Independent component analysis; least mean square methods; Least squares approximation; Performance analysis; Signal analysis; Signal processing algorithms
• ISBN: 9781424442959; 1424442958
• ISSN: 1520-6149
• DOI: 10.1109/ICASSP.2010.5495851

Recently, the augmented complex LMS (ACLMS) algorithm has been proposed for modeling complex-valued signal relationships in which a widely-linear model can be more appropriate. It is not clear, however, how the behavior of ACLMS differs from that of the conventional complex LMS (CCLMS) algorithm. In this paper, we leverage a recently-developed analysis for the complex LMS algorithm to illuminate the performance relationships between the ACLMS and CCLMS algorithms. Our analysis shows that the ACLMS algorithm can potentially achieve a lower steady-state mean-squared error as compared to that of CCLMS, but the convergence speed of ACLMS is slowed in the presence of highly non-circular complex-valued input signals. An adaptive beamforming example indicates the utility of the results.