Broadband pattern synthesis for circular sensor arrays

EURASIP J. Adv. Signal Process.

Yang

et al. 2015

Self Cite

This paper proposes a general model of superdirectivity to provide analytical and closed-form solutions for arbitrary sensor arrays. Based on the equivalence between the maximum directivity factor and the maximum array gain in the isotropic noise field, Gram-Schmidt orthogonalization is introduced and recursively transformed into a matrix form to conduct pre-whitening and matching operations that result in superdirectivity solutions. A Gram-Schmidt mode-beam decomposition and synthesis method is then presented to formally implement these solutions. Illustrative examples for different arrays are provided to demonstrate the feasibility of this method, and a reduced rank technique is used to deal with the practical array design for robust beamforming and acceptable high-order superdirectivity. Experimental results that are provided for a linear array consisting of nine hydrophones show the good performance of the technique. A superdirective beampattern with a beamwidth of 48.05°in the endfire direction is typically achieved when the inter-sensor spacing is only 0.09λ (λ is the wavelength), and the directivity index is up to 12 dB, which outperforms that of the conventional delay-and-sum counterpart by 6 dB.

Section: Circular Arraysmentioning

confidence: 99%

A general superdirectivity model for arbitrary sensor arrays

EURASIP J. Adv. Signal Process.

Yang

et al. 2015

Self Cite

“…The optimal weight of a space-time broadband beamformer can be found by the following linear constrained minimum variance problem min w H R xx w s.t. C H w = F (5) where matrix C and vector F are the KL×J dimensional constraint matrix and the J -dimensional response vector, respectively. Each column in constraint matrix C imposes a constraint on the weight vector w, which is termed stacked constraint vector.…”

Section: Problem Background a Space-time Broadband Beamformingmentioning

confidence: 99%

“…Broadband beamforming has been an important research topic over the past few decades, and its applications cover many different fields, such as sonar, radar, wireless communications, microphone arrays, and medical imaging [1], [2], [3], [4], [5].…”

Section: Introductionmentioning

confidence: 99%

Optimal Array Phase Center Study for Frequency-Domain Constrained Space-Time Broadband Beamforming

et al. 2023

IEEE Access

The frequency-domain constrained broadband space-time beamformer has been widely used in many fields because of its excellent performance and no need for pre-steering delay. However, the beam response of the frequency-domain constrained space-time broadband beamformer depends heavily on the phase center location of the array. The wrong phase center location of the array will lead to undesirable wide main lobe and high side lobe. To choose the location of the phase center of the array correctly, this paper makes an in-depth theoretical discussion on this dependency based on the uniform linear array. First, the dependence of the quiescent beam response of the frequency-domain constrained space-time broadband beamformer on the phase center location of the array is theoretically derived, and it is proved that there is an optimal phase center location of the array which can make the beamformer obtain the best quiescent beam response. Then, a selection criterion of the optimal array phase center location is proposed, and based on this criterion, the closed-form solution of the optimal array phase center location is theoretically derived when the constraint matrix contains two pre-selected points. Finally, based on the closed-form solution, through correct extrapolation, the suboptimal solution for the optimal array phase center location is obtained when the constraint matrix contains any preselected points. Numerical simulations verify the correctness and effectiveness of the proposed methods.INDEX TERMS Quiescent beam response, array phase center, space-time broadband beamformer, frequency-domain constraints.

“…3,6,18,[26][27][28] Consequently, their superdirectivity has also received much attention. The aforementioned DL and WNG constraint methods have also been applied to circular arrays.…”

Section: Introductionmentioning

confidence: 99%

Robust high-order superdirectivity of circular sensor arrays

The Journal of the Acoustical Society of America

Yang

et al. 2014

Self Cite

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.