DOA Estimation Using Virtual ESPRIT with Successive Baselines and Coprime Baselines
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DOA Estimation Using Virtual ESPRIT with Successive Baselines and Coprime Baselines Xiaolin Li1 · Wenjun Zhang1 Received: 14 August 2020 / Revised: 22 September 2020 / Accepted: 25 September 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract In this paper, we exploit the idea of virtual ESPRIT (VESPA) to develop a multibaseline VESPA (MB-VESPA) approach for direction finding. Specially, we define several cumulant matrices to provide ambiguous direction estimates under different baselines. Fine and unambiguous estimation is then obtained by a simple refinement step. Two refine approaches, termed as successive baseline approach and coprime baseline approach, are subsequently introduced. MB-VESPA shares all the advantages of the VESPA. It is simple, closed-form, search-free, and is applicable to irregularly linear array. In addition, it is free of the impact on the sensor gain uncertainties. Keywords Array signal processing · Direction finding · Virtual ESPRIT · Cumulant
1 Introduction Direction finding of multiple source signals is an important problem in sensor array processing. It is of practical applications in radar, sonar, and wireless communications [18,24,25]. The most popular solution to solve this problem is the so-called subspace-based techniques [10], such as the Estimation of Signal Parameters via Rotational Invariance Techniques (ESPRIT) algorithm [16]. The ESPRIT algorithm, along with a large number of its variants [2,9,12,23], requires the array is of some specific structures such as vandermonde structure and/or shift-invariant structure. In addition, the “rotational distance” between two ESPRIT’s subarrays has to be within a halfwavelength to prevent direction aliasing, which obeys Shannon’s sampling theorem of spatial version.
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Xiaolin Li [email protected]; [email protected] Wenjun Zhang [email protected]
1
School of Communication and Information Engineering, Shanghai University, Shanghai 200072, China
Circuits, Systems, and Signal Processing
Since the estimation accuracy of the ESPRIT algorithm is in proportion to the distance of the two subarrays, a larger spacing between the subarrays would give a more accurate estimation. However, no unique solution is available when this distance exceeds a half-wavelength, so that additional refine processing is required to extract the true estimates. To handle this problem, many ESPRIT-based algorithms that assume the arrays contain two or more spatial invariances have been proposed [4,7,11,20]. In these algorithms, each spatial invariance provides a set of direction estimates under a corresponding baseline. The short baseline (less than a half-wavelength) is used to avoid ambiguity, while the long baseline (greater than a half-wavelength) is used to guarantee the estimation accuracy. These algorithms are also known as the extended aperture ESPRIT algorithms. The extended aperture ESPRIT algorithms, like their original versions, are also restricted to utilize the regular array configurations. By exploiting the
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