An approach to direction-of-arrival (DOA) estimation for multiple broadband farfield signals is proposed. The approach uses a beamspace preprocessing structure based on frequency domain frequency-invariant beamforming. The frequency-invariant beamformers are designed using the optimal array pattern synthesis technique based on second-order cone programming (SOCP). The proposed method only ensure that the beam patterns are constant within the main beam region while control the sidelobes, which leads to smaller focusing error. Numerical results show that the proposed method provides lower resolution threshold and lower root-mean-square error (RMSE) of estimate compared with the existing method.

An approach to time-domain broadband beamforming with sidelobe control is proposed. The array response is expressed as a linear function of the finite impulse response filters tap weights. The filters are designed by minimizing beamformer output power while maintaining the distortionless response in the direction of the desired signal and guaranteeing the sidelobes to be below some given threshold values. Norm constraint on tap weights is also imposed to improve the robustness of the beamformer. Computationally efficient convex formulation for the beamformer design problem is derived using second-order cone programming. Simulation results demonstrate the satisfactory performance of the proposed approach.

Broadband beamformers with constant mainlobe response over the frequency of interest are desirable in many applications including underwater acoustics, ultrasonics, acoustic imaging and communications, and so on. Solutions to this problem have been presented for specific array geometry often requiring a larger number of sensors. And the array pattern synthesis error minimization is employed for the whole field of view, which leads to suboptimal designs. In this paper, a broadband array pattern synthesis approach to designing time-domain constant mainlobe response beamformer is proposed. By imposing constraints both on the mainlobe spatial response variation over frequency and on the sidelobes of the beamformer, several optimization criteria are presented and the corresponding convex second-order cone programming implementations are given. In this approach, no preliminary desired beampattern is required and the beam responses variation minimization is employed only in the mainlobe region and not in the sidelobe regions, which improves the beamformer mainlobe synthesis accuracy. Equally, one can obtain lower sidelobes at the same mainlobe synthesis accuracy. This approach is applicable to arrays with arbitrary geometry. Simulation and experimental results are presented to illustrate the effectiveness of this approach. Performance comparisons of the proposed beamformers and the existing beamformer are also provided.

The directivity pattern of an array is known to degrade in the presence of errors in the array manifolds, with respect to the desired nominal array pattern. This paper describes a new robust pattern synthesis approach to arrays with manifold vectors perturbation. This synthesis technique optimizes the worst case performance by minimizing the worst case sidelobe level while maintaining a distortionless respect to the worst case signal steering vector. The possible values of the manifold are covered by an ellipsoid that describes the uncertainty in terms of errors in element gains and phase angles. The pattern synthesis parameters can be optimally chosen based on known levels of uncertainty in the manifold vectors. Two optimization criteria, l 2 regularization and l 1 regularization, of a robust beamformer are proposed. Both criteria of the robust beamformer problem can be reformulated in a convex form of second-order cone programming, which is computationally tractable. A simple lower bound on the difference between the worse case sidelobe level of the robust beamformer and the sidelobe level of the nominal optimal beamformer with no array manifold uncertainty is derived. This robust approach is applicable to arrays with arbitrary geometry. Its effectiveness is illustrated through its application to a circular hydrophone array. An experiment is performed to measure the manifold vectors uncertainty set of hydrophone arrays. Results of applying the algorithms to both simulated and experimental data are presented and they show good performance of the proposed robust pattern synthesis approach.

An approach to optimal array pattern synthesis based on spherical harmonics is presented. The array processing problem in the spherical harmonics domain is expressed with a matrix formulation. The beamformer weight vector design problem is written as a multiply constrained problem, so that the resulting beamformer can provide a suitable trade-off among multiple conflicting performance measures such as directivity index, robustness, array gain, sidelobe level, mainlobe width, and so on. The multiply constrained problem is formulated as a convex form of second-order cone programming which is computationally tractable. We show that the pure phase-mode spherical microphone array can be viewed as a minimum variance distortionless response (MVDR) beamformer in the spherical harmonics domain for the case of spherically isotropic noise. It is shown that our approach includes the delay-and-sum beamformer and a pure phase-mode beamformer as special cases, which leads to very flexible designs. Results of simulations and experimental data processing show good performance of the proposed array pattern synthesis approach. To simplify the analysis, the assumption of equidistant spatial sampling of the wavefield by microphones on a spherical surface is used and the aliasing effects due to noncontinuous spatial sampling are neglected.