Performance analysis of the augmented complex-valued least mean kurtosis algorithm

The augmented complex-valued least mean kurtosis (ACLMK) algorithm was proposed to enhance the performance of adaptive filters by utilizing the negated kurtosis of the error signal. This paper provides a comprehensive physical insight into its stochastic behaviors and a more thorough performance analysis. By using Isserlis’ theorem, the evolutions of both the covariance and complementary covariance matrices of the weight error vector are established, based on which the expressions for transient mean-square deviation (MSD) and excess mean-square error (EMSE) are derived. Moreover, the higher-order moments of the measurement noise are also taken into account. Different from the existing framework which treats the ACLMK as a variable step-size augmented complex-valued least mean square (ACLMS) algorithm, the steady-state mean-square performance of the ACLMK is analyzed through the approximate uncorrelating transform (AUT) to yield the theoretical steady-state MSD and EMSE. The proposed framework of performance analysis is shown to provide more accurate models for the theoretical MSD and MSE. Simulation results are provided to validate the theoretical findings for second-order noncircular input signals in second-order circular and noncircular noisy environments.