Adaptive Equalization Algorithm Based on Quaternion in Pulsed Noise Environment

This paper explores the equalization of orthogonal polarized channels through the use of quaternion adaptive filtering algorithms. Specifically, we examine the limitations of the quaternion constant-mode blind equalization (QCMA) algorithm in pulse noise environments. To address this issue, we model pulse noise using the alpha-stable distribution and propose the Quaternion Maximum Correlation Entropy Criterion (QMCC) as a replacement for the Quaternion Minimum Mean Square Error Criterion. Based on this criterion, we introduce the QMCC-CMA algorithm. To improve the steady-state performance of the QCMA algorithm, we propose the QMCC-RLS-CMA algorithm. This algorithm combines the QCMA algorithm with the Quaternion Recursive Least Squares (QRLS) algorithm under the Quaternion Maximum Correlation Entropy Criterion. Theoretical derivation and MATLAB simulations demonstrate that the proposed algorithm achieves better equilibrium results under impulse noise while maintaining algorithm stability.