航空学报 > 2011, Vol. 32 Issue (4): 729-738   doi: CNKI:11-1929/V.20110212.1357.002

四元数最小均方误差算法及其在波束形成中的应用

陶建武1, 常文秀2   

  1. 1. 空军航空大学 航空控制工程系, 吉林 长春 130022;
    2. 吉林大学 通信工程学院, 吉林 长春 130025
  • 收稿日期:2010-07-07 修回日期:2010-10-27 出版日期:2011-04-25 发布日期:2011-04-25
  • 通讯作者: Tel.: 0431-86959065 E-mail: jianwu.tao@gmail.com E-mail:jianwu.tao@gmail.com
  • 作者简介:陶建武(1959- ) 男,博士,教授,硕士生导师。主要研究方向:阵列信号处理。 Tel: 0431-86959065 E-mail: jianwu.tao@gmail.com 常文秀(1957- ) 女,教授。主要研究方向:阵列信号处理。 Tel: 0431-86105617 E-mail: wenxiu.chang@gmail.com
  • 基金资助:

    国家自然科学基金(60872088)

Quaternion MMSE Algorithm and Its Application in Beamforming

TAO Jianwu1, CHANG Wenxiu2   

  1. 1. Department of Air Control Engineering, Air Force Aviation University, Changchun 130022, China;
    2. Communication Academy, Jilin University, Changchun 130025, China
  • Received:2010-07-07 Revised:2010-10-27 Online:2011-04-25 Published:2011-04-25

摘要: 作为多维信号处理的一个重要工具,四元数代数已在各个领域有所应用。对四元数最小均方误差(QMMSE)算法进行了研究,首先推导了四元数实数形式的最小均方误差(QRMMSE)算法,进一步推导了四元数复数形式的最小均方误差(QCMMSE)算法,并且分析了两种算法的区别和计算量。最后将QMMSE算法应用到机载简化矢量传感器阵列的波束形成中,与复数长矢量最小均方误差(LVMMSE)算法相比较,QCMMSE算法的性能有所提高,计算量有所减少。计算机仿真结果验证了所提算法的有效性。

关键词: 信号处理, 信号滤波, 四元数最小均方误差算法, 电磁矢量传感器阵列, 四元数代数, 波束形成

Abstract: As an important tool in multi-dimension signal processing, quaternion algebra is applied to many domains. A quaternion minimum-mean-square-error (QMMSE) algorithm is proposed in this paper. First, a QMMSE algorithm based on the real-expansion of a quaternion (QRMMSE) is derived. Then, another form of the QMMSE algorithm based on the complex-expansion of the quaternion (QCMMSE) is derived. The difference of the two algorithms and the computational complexity are analyzed. Finally, the QMMSE algorithm is applied to the beamforming of an airborne trimmed vector-sensor array. Comparing with a complex long-vector MMSE (LVMMSE) algorithm, the QCMMSE algorithm has a better performance and lower computational load. Simulation results are given to validate the performance of the proposed algorithms.

Key words: signal processing, signal filtering, QMMSE algorithm, electromagnetic vector-sensor array, quaternion algebra, beamforming

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