Robust high-order superdirectivity of circular sensor arrays

Abstract

This paper presents a detailed study of the high-order superdirectivity of circular sensor arrays, which is aimed at completing the authors' recently proposed analytical superdirectivity model. From the limit expression of the maximum directivity factor, it is shown that the circular arrays possess good potential for directivity improvement. It is found that the sensitivity function used as a robustness measurement can also be accurately decomposed into a series of closed-form sensitivity functions of eigenbeams, similar to the optimal beampattern and its corresponding directivity factor. Moreover, the performance of eigenbeams can be regarded as an indicator of error sensitivity, and the robustness constraint parameters can be estimated easily. Two specific approaches are proposed for obtaining robust superdirectivity on the basis of robustness analyses, and their performance is demonstrated experimentally.

A general superdirectivity model for arbitrary sensor arrays

“…The DFs and levels of robustness of all mode-beams can then be readily calculated with the use of Eqs. (23) and (22). However, an additional process is needed to clearly show the regularity of the GSMDS model for circular arrays.…”

“…Circular arrays are desired in many circumstances because they have simple configurations, do not have left-right ambiguities, and can provide uniform beams along with 360°azimuthal directions [4,21,22,37]. A six-sensor uniform circular array with radius a is Fig.…”

“…Actually, the inverse of matrix R nn can also be calculated using the eigen-decomposition, as was the case for circular arrays in [21,22], but the eigenvalues and eigenvectors in relation to other array geometries cannot be expressed in closed-form and computed analytically. Therefore, the GS-based decomposition is more advantageous than the eigen-decomposition for computing the inverse of the normalized noise covariance matrix.…”

“…Answers were provided in [21,22] for the abovementioned problem in which an eigen-beam decomposition and synthesis (EBDS) model was formulated. However, the array shapes were restricted to a circular form.…”

Robust Adaptive Beamforming with Sensor Position Errors Using Weighted Subspace Fitting-Based Covariance Matrix Reconstruction

“…To extract and enhance the desired signal from a certain direction, beamforming is being widely applied in various fields, including wireless communication, radar, sonar, and audio processing [1,2,3]. As a data-dependent algorithm, adaptive beamforming can adjust the weight vector according to the observation data.…”