Design of Fixed Beamformers Based on Vector-Sensor Arrays

Abstract

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 traditionall1norm minimisation associated with compressive sensing into a modifiedl1norm 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.

Low-Complexity Direction-of-Arrival Estimation Based on Wideband Co-Prime Arrays

“…Construct a column vector consisting of elements, each representing a potential source signal at the corresponding incident angle. Denote (12) The last element in can also be considered as a variable because the noise power is unknown. All the elements in are powers, and therefore positive real numbers.…”

“…In the past, sparse arrays have been proposed as a solution [6]- [12], where their non-uniform configuration can avoid grating lobes, while allowing adjacent physical sensor spacings to be greater than . Recently, a new class of sparse arrays, referred to as co-prime arrays, was proposed [13], [14].…”

Channel equalization and beamforming for quaternion-valued wireless communication systems

“…Recently, quaternion-valued signal processing has been introduced and studied in details to solve problems related to three or four-dimensional signals [3], such as vector-sensor array signal processing [4,5,6,7,8,9], and wind profile prediction [10]. With most recent developments in this area, especially the derivation of quaternion-valued gradient operators and the quaternion-valued least mean square (QLMS) algorithm [10,11,12], we are now ready to effectively solve the 4-D equalisation and interference suppression/beamforming problem associated with the proposed 4-D modulation scheme.…”

Filtering and tracking with trinion-valued adaptive algorithms

“…Multidimensional (m-D) signal processing has a variety of applications and the modeling of multiple variables is carried out traditionally within the real-valued matrix algebra, while in recent years we have observed the successful exploitation of hypercomplex numbers in areas including colour image processing (Pei and Cheng, 1999;Pei et al, 2004;Sangwine and Ell, 2000;Parfieniuk and Petrovsky, 2010;Ell et al, 2014;Liu et al, 2014), vector-sensor array processing (Le Bihan and Mars, 2004;Miron et al, 2006;Le Bihan et al, 2007;Tao, 2013;Tao and Chang, 2014;Zhang et al, 2014;Hawes and Liu, 2015;Jiang et al, 2016a,b), and quaternion-valued wireless communications (Zetterberg and Brandstrom, 1977;Isaeva and Sarytchev, 1995;Liu, 2014). The most widely used hypercomplex numbers are quaternions, with rigorous physical interpretation for 3-D and 4-D rotational problems (Kantor et al, 1989;Ward, 1997).…”