Abstract
Based on crossed-dipole antenna arrays, quaternion-valued data models have been developed for both direction of arrival estimation and beamforming in the past. However, for almost all the models, and especially for adaptive beamforming, the desired signal is still complex-valued as in the quaternion-valued Capon beamformer. Since the complex-valued desired signal only has two components, while there are four components in a quaternion, only two components of the quaternion-valued beamformer output are used and the remaining two are simply discarded, leading to significant redundancy in its implementation. In this work, we consider a quaternion-valued desired signal and develop a fully quaternion-valued Capon beamformer which has a better performance and a much lower complexity. Furthermore, based on this full quaternion model, the robust beamforming problem is also studied in the presence of steering vector errors and a worst-case-based robust beamformer is developed. The performance of the proposed methods is verified by computer simulations.
Highlights
Electromagnetic (EM) vector sensor arrays can track the direction of arrival (DOA) of impinging signals as well as their polarization
Since there are four components for each vector sensor output in a crossed-dipole array, a quaternion model instead of long vectors has been adopted in the past for both adaptive beamforming and direction of arrival estimation [5,6,7,8,9,10,11,12]
signal-to-interference-plus-noise ratio (SINR) performance part, the full quaternion-valued Capon (Q-Capon) beamformer, full quaternion worst-case constraint beamformer (FQWCCB), and the Q-Capon beamformer are compared in two scenarios: one without steering vector mismatch, and one with steering vector mismatch
Summary
Electromagnetic (EM) vector sensor arrays can track the direction of arrival (DOA) of impinging signals as well as their polarization. A crossed-dipole sensor array—firstly introduced in [1] for adaptive beamforming—works by processing the received signals with a long polarization vector Based on such a model, the beamforming problem was studied in detail in terms of output signal-to-interference-plus-noise ratio (SINR) [2]. With the development of quaternion-valued communications [14,15,16], it is very likely that in the future we will have quaternion-valued signals as the SOI, where two traditional complex-valued signals with different polarisations arrive at the antenna array with the same DOA In such a case, a full quaternion-valued array model is needed to compactly represent the four-component desired signal and make sure the four components of the quaternion-valued output of the beamformer are fully utilised. In [11], the worst-case-based method is extended to the quaternion-valued case for crossed-dipole arrays; it is not a full quaternion model, since the desired signal is still complex-valued.
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