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

Beamforming and Direction of Arrival Estimation Based on Vector Sensor Arrays

Array signal processing is a technique linked closely to radar and sonar systems. In communication, the antenna array in these systems is applied to cancel the interference, suppress the background noise and track the target sources based on signals'parameters. Most of existing work ignores the polarisation status of the impinging signals and is mainly focused on their direction parameters. To have a better performance in array processing, polarized signals can be considered in array signal processing and their property can be exploited by employing various electromagnetic vector sensor arrays. In this thesis, firstly, a full quaternion-valued model for polarized array processing is proposed based on the Capon beamformer. This new beamformer uses crossed-dipole array and considers the desired signal as quaternion-valued. Two scenarios are dealt with, where the beamformer works at a normal environment without data model errors or with model errors under the worst-case constraint. After that, an algorithm to solve the joint DOA and polarisation estimation problem is proposed. The algorithm applies the rank reduction method to use two 2-D searches instead of a 4-D search to estimate the joint parameters. Moreover, an analysis is given to introduce the difference using crossed-dipole sensor array and tripole sensor array, which indicates that linear crossed-dipole sensor array has an ambiguity problem in the estimation work and the linear tripole sensor array avoid this problem effectively. At last, we study the problem of DOA estimation for a mixture of single signal transmission (SST) signals and duel signal transmission (DST) signals. Two solutions are proposed: the first is a two-step method to estimate the parameters of SST and DST signals separately; the second one is a unified one-step method to estimate SST and DST signals together, without treating them separately in the estimation process

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

Design of Fixed Beamformers Based on Vector-Sensor Arrays

Vector-sensor arrays such as those composed of crossed dipole pairs are used as they can account for a signal’s polarisation in addition to the usual direction of arrival information, hence allowing expanded capacity of the system. The problem of designing fixed beamformers based on such an array, with a quaternionic signal model, is considered in this paper. Firstly, we consider the problem of designing the weight coefficients for a fixed set of vector-sensor locations. This can be achieved by minimising the sidelobe levels while keeping a unitary response for the main lobe. The second problem is then how to find a sparse set of sensor locations which can be efficiently used to implement a fixed beamformer. We propose solving this problem by converting the traditional norm minimisation associated with compressive sensing into a modified norm minimisation which simultaneously minimises all four parts of the quaternionic weight coefficients. Further improvements can be made in terms of sparsity by converting the problem into a series of iteratively solved reweighted minimisations, as well as being able to enforce a minimum spacing between active sensor locations. Design examples are provided to verify the effectiveness of the proposed design methods

Twenty-five years of sensor array and multichannel signal processing: a review of progress to date and potential research directions

In this article, a general introduction to the area of sensor array and multichannel signal processing is provided, including associated activities of the IEEE Signal Processing Society (SPS) Sensor Array and Multichannel (SAM) Technical Committee (TC). The main technological advances in five SAM subareas made in the past 25 years are then presented in detail, including beamforming, direction-of-arrival (DOA) estimation, sensor location optimization, target/source localization based on sensor arrays, and multiple-input multiple-output (MIMO) arrays. Six recent developments are also provided at the end to indicate possible promising directions for future SAM research, which are graph signal processing (GSP) for sensor networks; tensor-based array signal processing, quaternion-valued array signal processing, 1-bit and noncoherent sensor array signal processing, machine learning and artificial intelligence (AI) for sensor arrays; and array signal processing for next-generation communication systems

Adaptive Beamforming for Vector-Sensor Arrays Based on Reweighted Zero-Attracting Quaternion-Valued LMS Algorithm

In this work, reference signal based adaptive beamforming for vector sensor arrays consisting of crossed dipoles is studied. In particular, we focus on how to reduce the number of sensors involved in the adaptation so that reduced system complexity and energy consumption can be achieved while an acceptable performance can still be maintained, which is especially useful for large array systems. As a solution, a reweighted zero attracting quaternion-valued least mean square algorithm is proposed. Simulation results show that the algorithm can work effectively for beamforming while enforcing a sparse solution for the weight vector where the corresponding sensors with zerovalued coefficients can be removed from the system

Filtering and Tracking with Trinion-Valued Adaptive Algorithms

A new model for three-dimensional processes based on the trinion algebra is introduced for the first time. Compared with the pure quaternion model, the trinion model is more compact and computationally more efficient, while having similar or comparable performance in terms of adaptive linear filtering. Moreover, the trinion model can effectively represent the general relationship of state evolution in Kalman filtering, where the pure quaternion model fails. Simulations on real-world wind recordings and synthetic data sets are provided to demonstrate the potentials of this new modeling method