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

Abstract

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.