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We present a d-dimensional exponential analysis algorithm that offers a range of advantages compared to other methods. The technique does not suffer the curse of dimensionality and only needs O((d + 1)n) samples for the analysis of an n-sparse expression. It does not require a prior estimate of the sparsity n of the d-variate exponential sum. The method can work with sub-Nyquist sampled data and offers a validation step, which is very useful in low SNR conditions. A favourable computation cost results from the fact that d independent smaller systems are solved instead of one large system incorporating all measurements simultaneously. So the method also lends itself easily to a parallel execution. Our motivation to develop the technique comes from 2D and 3D radar imaging and is therefore illustrated on such examples.

Traditionally regularly spaced antenna arrays follow the spatial Nyquist criterion to guarantee an unambiguous analysis. We present a novel technique that makes use of two sparse non-Nyquist regularly spaced antenna arrays, where one of the arrays is just a shifted version of the other. The method offers several advantages over the use of traditional dense Nyquistspaced arrays, while maintaining a comparable algorithmic complexity for the analysis. Among the advantages we mention: an improved resolution for the same number of receivers and reduced mutual coupling effects between the receivers, both due to the increased separation between the antennas. Because of a shared structured linear system of equations between the two arrays, as a consequence of the shift between the two, the analysis of both is automatically paired, thereby avoiding a computationally expensive matching step as is required in the use of so-called co-prime arrays. In addition, an easy validation step allows to automatically detect the precise number of incoming signals, which is usually considered a difficult issue. At the same time, the validation step improves the accuracy of the retrieved results and eliminates unreliable results in the case of noisy data. The performance of the proposed method is illustrated with respect to the influence of noise as well to the effect of mutual coupling. Index Terms-Array Antennas, Direction of Arrival Estimation, Sparse Arrays. I. INTRODUCTION D IRECTION of arrival (DOA) estimation, using array antenna systems, is a topic of increasing interest in a variety of applications including radar, remote sensing, radio frequency interference mitigation, and smart wireless networks [1]-[3]. One of the most well-known limitations in regularly spaced antenna array systems is, arguably, the requirement that the elements should have spacing closer than a half-wavelength (the spatial Nyquist criterion) in order to avoid aliasing resulting in ambiguous arrival angle estimates. Unique results can be obtained for larger spacings if a limited range of near-broadside receiving angles are considered, or if the antenna element patterns exhibit zeros in the end-fire directions, but in general this still limits the allowable spacing to distances close to the Nyquist limit.

Accurate placement of elements in large antenna arrays is a difficult and costly process. We explore the use of the validated exponential analysis (VEXPA) technique that was previously formulated to solve a direction-of-arrival (DOA) estimation problem, to find the antenna element positions in an array after the installation phase, so that cost-savings can be realised during placement of the antenna elements. Measurements are taken from harmonically related input signals transmitted from an Unmanned Aerial Vehicle (UAV) for which the position in the sky is known. It is shown how the UAV's zenith angle can be manipulated to generate parameters required for VEXPA's de-aliasing step. A simple simulation illustrates the functioning of the proposed method.

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