基于四元数的直接判决并行恒模均衡算法

Concurrent Decision Directed and Constant Modulus Equalization Algorithm Based on Quaternion

近年来4元数理论成为各界学者研究的热点并被应用到许多领域。该文基于4元数自适应滤波算法对正交极化信道均衡问题进行研究。为了解决4元数恒模(QCMA)算法的相位模糊问题,该文将QCMA算法与4元数最小均方算法(QLMS)相结合提出一种4元数直接判决并行恒模(QCMA+DD-QLMS)算法。基于广义哈密顿实演算(GHR)的梯度运算规则对新的算法做了理论推导并进行MATLAB实验仿真,仿真结果表明该文所提算法不但能够解决QCMA算法相位模糊问题,还具有更小的稳态均方误差(MSE)。

In recent years,quaternion theory has become a research hotspot for scholars and has been applied to many fields.In this paper,the quadrature polarization channel equalization problem is studied based on quaternion adaptive filtering algorithm.In order to solve the phase ambiguity problem of Quaternion Constant Modulus Algorithm(QCMA),a concurrent quaternion Direct Decision constant modulus algorithm(QCMA+DD-QLMS)is proposed by combining QCMA algorithm with Quaternion Least Mean Square(QLMS)algorithm.Based on the gradient operation rules of Generalized Hamilton-Real(GHR),the new algorithm is theoretically deduced and simulated by MATLAB.The simulation results show that the algorithm proposed in this paper can not only solve the phase ambiguity problem of the QCMA,but also has smaller steady-state Mean Square Error(MSE).