Fully Quaternion-Valued Adaptive Beamforming Based on Crossed-Dipole Arrays

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

Quaternion-valued robust adaptive beamformer for electromagnetic vector-sensor arrays with worst-case constraint

A robust adaptive beamforming scheme based on two-component electromagnetic (EM) vector-sensor arrays is proposed by extending the well-known worst-case constraint into the quaternion domain. After defining the uncertainty set of the desired signal׳s quaternionic steering vector, two quaternion-valued constrained minimization problems are derived. We then reformulate them into two real-valued convex quadratic problems, which can be easily solved via the so-called second-order cone (SOC) programming method. It is also demonstrated that the proposed algorithms can be classified as a specific type of the diagonal loading scheme, in which the optimal loading factor is a function of the known level of uncertainty of the desired steering vector. Numerical simulations show that our new method can cope with the steering vector mismatch problem well, and alleviate the finite sample size effect to some extent. Besides, the proposed beamformer significantly outperforms the sample matrix inversion minimum variance distortionless response (SMI-MVDR) and the quaternion Capon (Q-Capon) beamformers in all the scenarios studied, and achieves a better performance than the traditional diagonal loading scheme, in the case of smaller sample sizes and higher SNRs

Study of four-dimensional DOA and polarisation estimation with crossed-dipole and tripole arrays

Electromagnetic (EM) vector sensor arrays can track both the polarisation and direction of arrival (DOA) of the impinging signals. For linear crossed-dipole arrays, as shown by our analysis, due to inherent limitation of the structure, it can only track one DOA parameter and two polarisation parameters. For full four-dimensional (4-D, 2 DOA and 2 polarization parameters) estimation, we could extend the linear crossed-dipole array to the planar case. In this paper, instead of extending the array geometry, we replace the crossed-dipoles by tripoles and construct a linear tripole array. It is proved that such a structure can estimate the 2-D DOA and 2-D polarisation information effectively in general and a dimension-reduction based MUSIC algorithm is developed so that the 4-D estimation problem can be simplified into two separate 2-D estimation problems, significantly reducing the computational complexity of the solution. The Cramr-Rao Bound (CRB) is also derived as a reference for algorithm performance. A brief comparison between the planar crossed-dipole array and the linear tripole array is performed at last, showing that although the planar structure has a better performance, it is achieved at the cost of increased physical size

Quaternion-Valued Adaptive Signal Processing and Its Applications to Adaptive Beamforming and Wind Profile Prediction

Quaternion-valued signal processing has received more and more attentions in the past ten years due to the increasing need to process three or four-dimensional signals, such as colour images, vector-sensor arrays, three-phase power systems, dual-polarisation based wireless communica- tion systems, and wind profile prediction. One key operation involved in the derivation of all kinds of adaptive signal processing algorithms is the gradient operator. Although there are some derivations of this operator in literature with different level of details in the quaternion domain, it is still not fully clear how this operator can be derived in the most general case and how it can be applied to various signal processing problems. In this study, we will give a detailed derivation of the quaternion-valued gradient operator with associated properties and then apply it to different areas. In particular, it will be employed to derive the quaternion-valued LMS (QLMS) algorithm and its sparse versions for adaptive beamforming for vector sensor arrays, and another one is its application to wind profile prediction in combination with the classic computational fluid dynamics (CFD) approach. For the adaptive beamforming problem for vector sensor arrays, we consider the crossed- dipole array and the problem of how to reduce the number of sensors involved in the adap- tive beamforming process, so that reduced system complexity and energy consumption can be achieved, whereas an acceptable performance can still be maintained, which is particularly use- ful for large array systems. The quaternion-valued steering vector model for crossed-dipole arrays will be employed, and a reweighted zero attracting (RZA) QLMS algorithm is then pro- posed by introducing a RZA term to the cost function of the original QLMS algorithm. The RZA term aims to have a closer approximation to the l0 norm so that the number of non-zero valued coefficients can be reduced more effectively in the adaptive beamforming process. For wind profile prediction, it can be considered as a signal processing problem and we can solve it using traditional linear and non-linear prediction techniques, such as the proposed QLMS algorithm and its enhanced frequency-domain multi-channel version. On the other hand,it using traditional linear and non-linear prediction techniques, such as the proposed QLMS algorithm and its enhanced frequency-domain multi-channel version. On the other hand,wind flow analysis is also a classical problem in the CFD field, which employs various simulation methods and models to calculate the speed of wind flow at different time. It is accurate but time-consuming with high computational cost. To tackle the problem, a combined approach based on synergies between the statistical signal processing approach and the CFD approach is proposed. There are different ways of combining the signal processing approach and the CFD approach to obtain a more effective and efficient method for wind profile prediction. In the combined method, the signal processing part employs the QLMS algorithm, while for the CFD part, large eddy simulation (LES) based on the Smagorinsky subgrid-scale (SGS) model will be employed so that more efficient wind profile prediction can be achieved