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 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.
Highlights
Sensor arrays are used in a wide range of application areas including Direction Of Arrival (DOA) estimation and beamforming [1], vehicle health maintenance [2] and many others
When considering fixed beamformer design, it is well known that an adjacent antenna separation of less than half a wavelength is required if using Uniform Linear Arrays (ULAs) in order to avoid the introduction of grating lobes [1]
To ensure the desired sparsity is achieved, we propose two Compressive Sensing (CS)-based methods of solving this problem: (i) the optimisation can be formulated as a modified l1 norm minimisation; (ii) the sparsity can be further improved by converting the problem into a series of iteratively solved reweighted minimisations
Summary
Sensor arrays are used in a wide range of application areas including Direction Of Arrival (DOA) estimation and beamforming [1], vehicle health maintenance [2] and many others. We could consider minimising the Peak Sidelobe Level (PSL) or matching the response to an acceptable reference response Stochastic optimisation methods such as Genetic Algorithms (GAs) [4,5,6,7] and Simulated Annealing (SA) [8,9] have been shown to be able to solve such a problem. Such vector sensors have been used in various configurations for DOA and polarisation estimation [36,37,38,39,40,41,42,43] In these works, fixed sensor locations are considered rather than addressing the location optimisation problem associated with sparse array design. Unlike for isotropic array elements (consisting of array elements of a single antenna), we have three complex valued weight coefficients (one for each co-located dipole) that have to be simultaneously minimised for each potential tripole location.
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