Quaternion MMSE Algorithm and Its Application in Beamforming
Wen-xiu Chang · Acta Aeronautica Et Astronautica Sinica · 2011
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.