Quaternion Recursive Maximum Correntropy and Versoria Criterion Algorithm for Channel Estimation Under Impulsive Noise

Quaternion-based machine learning algorithms have emerged as a promising candidate for four dimensional (4D) signal processing, which utilize 4D signal dimensions’ correlations for estimation purposes. The existing quaternion least mean square (QLMS) and quaternion maximum correntropy criterion (QMCC) algorithms are based on stochastic gradient descent and gradient ascent methods, respectively. Due to their reliance on instantaneous gradient approximations, these approaches exhibit slower convergence characteristics. To circumvent this limitation, quaternion recursive least square (QRLS) algorithm is proposed in the literature, which exhibits fast convergence and achieves lower MSE. However, the QRLS algorithm is based on minimum MSE (MMSE) criterion which optimizes error-energy, and is thus not a sufficient statistic for impulsive noise. In this paper, we propose novel non-MMSE criterion based recursive algorithms, namely quaternion recursive maximum correntropy criterion (QRMCC) and quaternion recursive maximum Versoria criterion (QRMVC). The proposed QRMCC and QRMVC algorithms exhibit robustness against impulsive/non-Gaussian distortions due to the inclusion of higher order error statistics. Simulations are presented for quaternion-valued channel estimation, which indicate that the proposed QRMCC and QRMVC algorithms deliver improved convergence compared to existing approaches. Lastly, the convergence of the proposed algorithms is analyzed with performance-validation using relevant computer simulations.