四元数最小均方误差算法及其在波束形成中的应用

 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。

Quaternion MMSE Algorithm and Its Application in Beamforming

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.