Steady-State Behavior of General Complex-Valued Diffusion LMS Strategies

• Published in: IEEE signal processing letters Vol. 23; no. 5; pp. 722 - 726
• Main Authors: Kanna, Sithan, Mandic, Danilo P.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.05.2016; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Adaptive systems; Analytical models; augmented statistics; Covariance matrices; diffusion adaptation; distributed optimisation; LMS; Nickel; Optimized production technology; Signal processing algorithms; Steady-state; widely linear; widely linear; distributed optimization; Augmented statistics; least mean square (LMS); diffusion adaptation
• ISSN: 1070-9908; 1558-2361
• DOI: 10.1109/LSP.2016.2547219

A novel methodology to bound the steady-state mean square performance of the diffusion complex least mean square (D-CLMS) and the diffusion widely linear (augmented) CLMS (D-ACLMS) algorithm is proposed. This is achieved by exploiting the almost identical nature of the steady-state filter weights at all nodes. The proposed approach allows for the consideration of the second-order terms in the recursion for the weight error covariance matrix, without compromising the mathematical tractability of the problem. The closed form expressions for the mean square deviation (MSD) and excess mean square error (EMSE) for both the D-CLMS and D-ACLMS allow for the performance of the algorithms to be quantified as a function of the noncircularity of the input data.