Abstract
The design of sparse spatially stretched tripole arrays is an important but also challenging task and this paper proposes for the very first time efficient solutions to this problem. Unlike for the design of traditional sparse antenna arrays, the developed approaches optimise both the dipole locations and orientations. The novelty of the paper consists in formulating these optimisation problems into a form that can be solved by the proposed compressive sensing and Bayesian compressive sensing based approaches. The performance of the developed approaches is validated and it is shown that accurate approximation of a reference response can be achieved with a 67% reduction in the number of dipoles required as compared to an equivalent uniform spatially stretched tripole array, leading to a significant reduction in the cost associated with the resulting arrays.
Highlights
In this work the problem of designing sparse SSSTA has been addressed for the first time
Novel compressive sensing (CS) and BCS based approaches have been proposed to solve the problem of simultaneously optimising dipole locations and orientations, with a minimum spacing being used to avoid co-located dipoles
Design examples have been provided and show that an accurate approximation of a reference pattern can be achieved using fewer dipoles than a comparable uniform spatially stretched tripoles (SST) array (48%-67% reduction in the number of dipoles)
Summary
For uniform linear arrays (ULAs), an adjacent antenna separation of no larger than half of the operating wavelength is used to avoid the introduction of grating lobes [1], [2]. The sidelobe behaviour of sparse arrays is unpredictable This means that optimisation of the antenna locations is required in order to achieve a desired beam response. Further work has shown that it is possible to improve the sparseness of a solution by considering a reweighted l1 norm minimisation problem [17], [20]–[22] The aim of these methods is to bring the minimisation of the l1 norm of the weight coefficients closer to that of the minimisation of the l0 norm. When tripoles are used it is possible to measure the full electromagnetic (EM) field at a given point [35] These arrays have been applied in the area of direction and polarisation estimation [34]. An SST is a tripole where the three orthogonal dipoles are spread over a given geometry, leading to reduced mutual coupling effects
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