Quaternion Maximum Versoria Criterion Algorithm for Channel Estimation Under Non-Gaussian Noise

Abstract

Quaternion adaptive filtering algorithms have emerged as promising candidate for addressing system identification and channel estimation problem for 4D signals. The existing methods such as quaternion least mean square (QLMS) algorithm relies on minimum mean square error (MMSE) based learning, which delivers suboptimal performance under non-Gaussian/impulsive noise due to the consideration of only second-order error statistics. To overcome these shortcomings, quaternion maximum correntropy criterion (QMCC) algorithm have been introduced, which is found to be robust against impulsive/non-Gaussian distortions. Despite its robustness, QMCC algorithm suffers from high steady-state error and heavy computational loads from exponential error calculations. To circumvent this limitation, we propose a novel quaternion adaptive filtering algorithm based on maximum versoria criterion (MVC) called QMVC, which alleviates the requirement of exponentiation and enhances the estimation accuracy and robustness against non-Gaussian distortions. To further improve the estimation accuracy over sparse channel, a novel sparsity-aware QMVC (SA-QMVC) algorithm is proposed by invoking a novel approximation of L0 -norm. Simulations performed for a quaternion channel estimation problem indicate that the proposed QMVC and SA-QMVC algorithms outperform the existing state-of-art approaches. Lastly, convergence analysis of the proposed algorithm is also performed and validated by simulations. © 2013 IEEE.