Compressive Sensing Based Design of Sparse Tripole Arrays

TL;DR

This paper introduces a novel compressive sensing approach for designing sparse tripole antenna arrays, enabling effective array pattern approximation with fewer elements by optimizing complex weight coefficients.

Contribution

It formulates the sparse tripole array design as an optimization problem and proposes a reweighted minimization method to ensure truly sparse solutions, which was not previously addressed.

Findings

Achieves good pattern approximation with fewer tripoles than a uniform linear array

Proposes a modified l1 norm and reweighted minimization for true sparsity

Demonstrates effectiveness through design examples

Abstract

This paper considers the problem of designing sparse linear tripole arrays. In such arrays at each antenna location there are three orthogonal dipoles, allowing full measurement of both the horizontal and vertical components of the received waveform. We formulate this problem from the viewpoint of Compressive Sensing (CS). However, unlike for isotropic array elements (single antenna), we now have three complex valued weight coefficients associated with each potential location (due to the three dipoles), which have to be simultaneously minimised. If this is not done, we may only set the weight coefficients of individual dipoles to be zero valued, rather than complete tripoles, meaning some dipoles may remain at each location. Therefore, the contributions of this paper are to formulate the design of sparse tripole arrays as an optimisation problem, and then we obtain a solution based on the minimisation of a modified l1 norm or a series of iteratively solved reweighted minimisations, which ensure a truly sparse solution. Design examples are provided to verify the effectiveness of the proposed methods and show that a good approximation of a reference pattern can be achieved using fewer tripoles than a Uniform Linear Array (ULA) of equivalent length.