Shefeng Yan

Optimal Modal Beamforming for Spherical Microphone Arrays

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.

Optimal array pattern synthesis for broadband arrays

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.

Robust Minimum Sidelobe Beamforming for Spherical Microphone Arrays

A robust minimum sidelobe beamforming approach based on the spherical harmonics framework for spherical microphone arrays is proposed. It minimizes the peaks of sidelobes while keeping the distortionless response in the look direction and maintaining the mainlobe width. A white noise gain constraint is also derived and employed to improve the robustness against array errors. The resulting beamformer can provide optimal tradeoff between the sidelobe level, the beamwidth and robustness, so it could be more practical than the existing spherical array Dolph-Chebyshev modal beamformer in the presence of array errors. The optimal modal beamforming problem is formulated as a tractable convex second-order cone programming program, which is more efficient than conventional element-space based approaches, since the dimension of array weight vectors can be significantly decreased by using the properties of spherical harmonics and Legendre polynomials. For the purpose of performance comparison, we also formulate current robust modal beamformers as equivalent optimization problems based on the proposed array model. Numerical results show the high flexibility and efficiency of the proposed beamforming approach.

Persymmetric adaptive detection of distributed targets in partially-homogeneous environment

In this paper we deal with the problem of detecting distributed targets in the presence of Gaussian noise with unknown but persymmetric structured covariance matrix. In particular, we consider the so-called partially-homogeneous environment, where the cells under test (primary data) and the training samples (secondary data), which are free of signal components, share the same structure of the interference covariance matrix but different power levels. Under the above assumptions, we derive the generalized likelihood ratio test (GLRT) and the so-called two-step GLRT. Remarkably, the new receivers ensure the constant false alarm rate property with respect to both the structure of the covariance matrix as well as the power level. The performance assessment, conducted by resorting to both simulated data and real recorded dataset, highlights that the proposed detectors can significantly outperform their unstructured counterparts, especially in a severely heterogeneous scenario where a very small number of secondary data is available.

Convex optimization based time-domain broadband beamforming with sidelobe control

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.

Array Pattern Synthesis With Robustness Against Manifold Vectors Uncertainty

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 Autocalibration Algorithm for Uniform Circular Array With Unknown Mutual Coupling

A new subspace-based autocalibration algorithm for a uniform circular array with unknown mutual coupling is presented in this letter. In allusion to the existing ambiguity problems and the limitation of nonzero coupling coefficients in earlier work by Lin and Yang, a more generalized iterative method is proposed to jointly estimate the direction-of-arrival (DOA) and unknown mutual coupling. It suffers from no ambiguity problems and does not require the prior knowledge of the number of nonzero elements in the coupling vector. Simulation results show the robustness, effectiveness, and higher estimated accuracy of the proposed algorithm.

Optimal Higher Order Ambisonics Encoding With Predefined Constraints

In this paper, we propose a design method for 3-D higher order ambisonics (3-D HOA) encoding matrices which offers the possibility to impose spatial stop-bands in the directivity patterns of all the spherical-harmonic audio channels while keeping the transformed audio channels still compatible with the 3-D HOA reproduction sound format. This might be useful as an encoding technique which suppresses interfering signals from specific directions in a 3-D HOA recording, or in other situations where certain spatial areas should be suppressed. The design method is adapted from recent work on the optimization of spherical microphone array beamforming. Using the proposed optimization method and the spherical harmonics mathematics framework, the relationship between several design factors, e.g., distortions in the desired response, the dynamic range of matrix coefficients, can be analyzed and illustrated as function of frequency. Based on the proposed optimization formulation, additional constraints can also be easily included and solved. In some of the formulations, the processing can be applied as a matrix multiplication to recorded spherical harmonics coefficients, that is, already encoded 3-D HOA format signals. The modified signals can be of the same or a lower spherical harmonics order. For a full optimization that gives a globally optimal solution, on the other hand, the processing must be applied to the microphone signals themselves. Numerical and experimental results validate the proposed method.

2-D Unitary ESPRIT-Like Direction-of-Arrival (DOA) Estimation for Coherent Signals with a Uniform Rectangular Array

A unitary transformation-based algorithm is proposed for two-dimensional (2-D) direction-of-arrival (DOA) estimation of coherent signals. The problem is solved by reorganizing the covariance matrix into a block Hankel one for decorrelation first and then reconstructing a new matrix to facilitate the unitary transformation. By multiplying unitary matrices, eigenvalue decomposition and singular value decomposition are both transformed into real-valued, so that the computational complexity can be reduced significantly. In addition, a fast and computationally attractive realization of the 2-D unitary transformation is given by making a Kronecker product of the 1-D matrices. Compared with the existing 2-D algorithms, our scheme is more efficient in computation and less restrictive on the array geometry. The processing of the received data matrix before unitary transformation combines the estimation of signal parameters via rotational invariance techniques (ESPRIT)-Like method and the forward-backward averaging, which can decorrelate the impinging signals more thoroughly. Simulation results and computational order analysis are presented to verify the validity and effectiveness of the proposed algorithm.

ADAPTIVE DETECTION OF MULTIPLE POINT-LIKE TARGETS UNDER CONIC CONSTRAINTS

This paper addresses the problem of detecting multiple point-like targets in the presence of steering vector mismatches and Gaussian disturbance with unknown covariance matrix. To this end, we flrst model the actual useful signal as a vector belonging to a proper cone whose axis coincides with the whitened direction of the nominal array response. Then we develop two robust adaptive detectors resort- ing to the two-step GLRT-based design procedure without assignment of a distinct set of secondary data. The performance assessment has been conducted by Monte Carlo simulation, also in comparison to pre- viously proposed detectors, and conflrms the efiectiveness of the newly proposed ones. In the last part of the work, in order to restore the detection performance of the newly proposed detectors in the presence of a large number of range cells contaminated by useful signals, we consider two adaptive detectors which resort to the structure informa- tion of the disturbance covariance matrix, and show that the a-priori information on the covariance structure can lead to a noticeable per- formance improvement.