  In this research, a novel adaptive filtering algorithm is proposed for
complex domain signal processing. The proposed algorithm is based on Wirtinger
calculus and is called as q-Complex Least Mean Square (q-CLMS) algorithm. The
proposed algorithm could be considered as an extension of the q-LMS algorithm
for the complex domain. Transient and steady-state analyses of the proposed
q-CLMS algorithm are performed and exact analytical expressions for mean
analysis, mean square error (MSE), excess mean square error (EMSE), mean square
deviation (MSD) and misadjustment are presented. Extensive experiments have
been conducted and a good match between the simulation results and theoretical
findings is reported. The proposed q-CLMS algorithm is also explored for
whitening applications with satisfactory performance. A modification of the
proposed q-CLMS algorithm called Enhanced $q$-CLMS (Eq-CLMS) is also proposed.
The Eq-CLMS algorithm eliminates the need for a pre-coded value of the
q-parameter thereby automatically adapting to the best value. Extensive
experiments are performed on system identification and channel equalization
tasks and the proposed algorithm is shown to outperform several benchmark and
state-of-the-art approaches namely Complex Least Mean Square (CLMS), Normalized
Complex Least Mean Square (NCLMS), Variable Step Size Complex Least Mean Square
(VSS-CLMS), Complex FLMS (CFLMS) and Fractional-ordered-CLMS (FoCLMS)
algorithms.
