TY - JOUR

T1 - Near-Field Superdirectivity

T2 - An Analytical Perspective

AU - Levin, Dovid Y.

AU - Markovich-Golan, Shmulik

AU - Gannot, Sharon

N1 - Publisher Copyright:
© 2014 IEEE.

PY - 2021

Y1 - 2021

N2 - The gain achieved by a superdirective beamformer operating in a diffuse noise-field is significantly higher than the gain attainable with conventional delay-and-sum weights. A classical result states that for a compact linear array consisting of $N$ sensors which receives a plane-wave signal from the end-fire direction, the optimal superdirective gain approaches $N^2$. It has been noted that in the near-field regime higher gains can be attained. The gain can increase, in theory, without bound for increasing wavelength or decreasing source-receiver distance. We aim to address the phenomenon of near-field superdirectivity in a comprehensive manner. We derive the optimal performance for the limiting case of an infinitesimal-aperture array receiving a spherical-wave signal. This is done with the aid of a sequence of linear transformations. The resulting gain expression is a polynomial, which depends on the number of sensors employed, the wavelength, and the source-receiver distance. The resulting gain curves are optimal and outperform weights corresponding to other superdirectivity methods. The practical case of a finite-aperture array is discussed. We present conditions for which the gain of such an array would approach that predicted by the theory of the infinitesimal case. The white noise gain (WNG) metric of robustness is shown to increase in the near-field regime.

AB - The gain achieved by a superdirective beamformer operating in a diffuse noise-field is significantly higher than the gain attainable with conventional delay-and-sum weights. A classical result states that for a compact linear array consisting of $N$ sensors which receives a plane-wave signal from the end-fire direction, the optimal superdirective gain approaches $N^2$. It has been noted that in the near-field regime higher gains can be attained. The gain can increase, in theory, without bound for increasing wavelength or decreasing source-receiver distance. We aim to address the phenomenon of near-field superdirectivity in a comprehensive manner. We derive the optimal performance for the limiting case of an infinitesimal-aperture array receiving a spherical-wave signal. This is done with the aid of a sequence of linear transformations. The resulting gain expression is a polynomial, which depends on the number of sensors employed, the wavelength, and the source-receiver distance. The resulting gain curves are optimal and outperform weights corresponding to other superdirectivity methods. The practical case of a finite-aperture array is discussed. We present conditions for which the gain of such an array would approach that predicted by the theory of the infinitesimal case. The white noise gain (WNG) metric of robustness is shown to increase in the near-field regime.

KW - Superdirectivity

KW - array processing

KW - beamforming

KW - near-field

KW - white noise gain

UR - http://www.scopus.com/inward/record.url?scp=85103885725&partnerID=8YFLogxK

U2 - 10.1109/taslp.2021.3070686

DO - 10.1109/taslp.2021.3070686

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AN - SCOPUS:85103885725

SN - 2329-9290

VL - 29

SP - 1661

EP - 1674

JO - IEEE/ACM Transactions on Audio Speech and Language Processing

JF - IEEE/ACM Transactions on Audio Speech and Language Processing

M1 - 9395250

ER -