四元数复数形式的最小均方算法  

LMS Algorithm Based on C-expansion of Quaternion

作　　者：常文秀[1] 陶建武[2] 

机构地区：[1]吉林大学通信工程学院,吉林长春130025 [2]空军航空大学控制工程系,吉林长春130022

出　　处：《信号处理》2011年第10期1515-1519,共5页Journal of Signal Processing

基　　金：国家自然科学基金资助项目(60872088)

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。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.

关 键 词：四元数最小均方自适应算法 四元数输出模型 波束形成 

分 类 号：TN911.7[电子电信—通信与信息系统]