Abstract
In this paper, a biquaternion beamspace, constructed by projecting the original data of an electromagnetic vector-sensor array into a subspace of a lower dimension via a quaternion transformation matrix, is first proposed.To estimate the direction and polarization angles of sources, biquaternion beamspace multiple signal classification (BB-MUSIC) estimators are then formulated. The analytical results show that the biquaternion beamspaces offer us some additional degrees of freedom to simultaneously achieve three goals. One is to save the memory spaces for storing the data covariance matrix and reduce the computation efforts of the eigen-decomposition. Another is to decouple the estimations of the sources’ polarization parameters from those of their direction angles. The other is to blindly whiten the coherent noise of the six constituent antennas in each vector-sensor. It is also shown that the existing biquaternion multiple signal classification (BQ-MUSIC) estimator is a specific case of our BB-MUSIC ones.The simulation results verify the correctness and effectiveness of the analytical ones.
Highlights
An electromagnetic (EM) vector-sensor, which consists of six spatially collocated antennas, measures the complete electric and magnetic fields induced by EM signals [1]
Once the biquaternion beamspace matrix Tp is got, the direction of arrival (DOA) parameters and polarization estimations can be obtained by using the same method as DOA-PBB-multiple signal classification (MUSIC) algorithm
Refer to (3.4) in [4], the Cramer-Rao bound (CRB) of the DOA-PB-BB-MUSIC algorithm in the presence of the coherent corrupting noise is given as σ2
Summary
An electromagnetic (EM) vector-sensor, which consists of six spatially collocated antennas, measures the complete electric and magnetic fields induced by EM signals [1]. Two types of the quaternion transformation matrices are analytically chosen to conduct two enhanced versions of the BB-MUSIC estimator Such two estimators are capable of decoupling the estimations of polarization parameters from those of the direction angles. To construct a biquaternion beamspace, which can be used to blindly whiten all of the noise coherence of the electric and magnetic components of each vector-sensor in an array, an optimal problem with a solution is given. Based on such a constructed biquaternion beamspace, an enhanced DOA-PBB-MUSIC estimator, nominated as DOA-PB-BB-MUSIC estimator, is proposed for the direction findings and polarization estimations.
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