中文摘要：

目前,作为多维信号处理的一个重要工具,四元数代数理论已在各种领域有所应用,并取得了良好的效果。基于四元数的复数形式,本文提出了四元数复数形式的最小均方（LMS-QC）自适应滤波算法。首先推导了LMS-QC自适应滤波算法,并且对其性能进行了分析,给出了步长的选择范围。进一步针对某一机载简化矢量传感器阵列,给出了归一化LMS-QC波束形成算法。此算法克服了四元数实数形式的最小均方（QLMS）自适应滤波算法的局限性,更适合复信号的多维处理,并且加权矢量每次迭代的计算量仅为QLMS算法的一半。计算机仿真结果表明LMS-QC算法是收敛的。稳态时估计均方误差达到了最小值,权矢量的模值和输出信干噪比也接近最优值。在主要区间内,LMS-QC算法的性能优于QLMS算法。

英文摘要：

Nowadays,the quaternion algebra,as an important tool in the multi-dimensional signal processing,has been applied to some fields and the better effects are obtained.In the paper,a least mean square algorithm based on C-expansion of quaternion （LMS-QC） is proposed for adaptive filtering.First,a LMS-QC algorithm for adaptive filtering is derived.The performance of LMS-QC algorithm is analyzed and the select range of stepsize is given.Further,a normalized LMS-QC beamformer is provided.The LMS-QC algorithm overcomes the limit of the least mean square algorithm based on R-expansion of quaternion（QLMS） and is conveniently applied to the multi-dimensional complex-signal processing.Comparing the LMS-QC algorithm with the QLMS algorithm,the computation of weight vector is only half in one iteration.The simulation results show that the LMS-QC algorithm is convergent.In stable state,the mean square error of estimation reaches to the minimum value,and the norm of weight vector and output SINR are close to the optical values.The LMS-QC algorithm performs better than the QLMS algorithm in main measuring range.