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.
TAO Jianwu, CHANG Wenxiu
. Quaternion MMSE Algorithm and Its Application in Beamforming[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2011
, 32(4)
: 729
-738
.
DOI: CNKI:11-1929/V.20110212.1357.002
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