Robust Broadband Beamformer Design Research Articles

A Chance-Constrained Programming Approach to the Design of Robust Broadband Beamformers With Microphone Mismatches

This paper addresses the design of robust broadband beamformers by taking into account the prior knowledge of uncertain means and variances of microphone mismatches. A chance-constrained programming CCP based design approach is proposed, which is a generic extension of the existing worst case mean performance optimization WMPO based counterpart by using a chance-constrained stopband level constraint instead of a hard one. The original CCP-based design problem, however, is NP-hard to solve. To deal with the problem, a relaxed convex optimization formulation is developed by exploiting the distribution property of array response distortion due to microphone mismatches. The relation between the proposed CCP- and WMPO-based design approaches is analyzed theoretically. It shows that there always exists a chance constraint probability under which the CCP-based design is comparable to the WMPO-based one, which provides an insight into the overconservatism problem in the WMPO-based design from the perspective of the CCP-based framework. Moreover, a criterion on the setting of the chance constraint probability is also derived for the proposed design approach in order to remedy the overconservatism problem. Simulation and real experimental results are presented to show the superior performance of the proposed design approach compared with its state-of-the-art counterparts.

Design of Robust Broadband Beamformers With Discrete Coefficients and Least Squared Criterion

This brief investigates the performance of robust and nonrobust broadband beamformers with least squares and discrete coefficients to achieve low complexity and efficient hardware implementation. The broadband beamformer coefficients are expressed as the sum of power-of-two terms with a restriction on the total number of power-of-two terms for the beamformer coefficients. An iterative algorithm is employed to reduce the number of nonzero coefficients and, thereby, multipliers in both the robust and nonrobust beamformers. A quantization scheme in combination with a random search is then applied to efficiently distribute the power-of-two terms for the beamformer coefficients. Design examples show that the number of nonzero coefficients for the beamformers can be significantly reduced without a significant degradation in the integral squared error. In addition, robust beamformers are shown to be less sensitive to nonzero coefficient reduction and quantization than nonrobust beamformers.

A Computationally Efficient Procedure for the Design of Robust Broadband Beamformers

Broadband beamformers using superdirective arrays are sensitive to errors in the sensor characteristics. Recently, a method that considers the probability distributions of errors to synthesize a robust optimal beamformer has been proposed. Unfortunately, the entire synthesis process may become unacceptably long due to the computational burden of the cost function. Here, we present an alternative procedure for computing the same cost function, drastically reducing such a problem.

Design of Robust Broadband Beamformers With Passband Shaping Characteristics Using Tikhonov Regularization

Broadband beamformers are known to be highly sensitive to the errors in microphone array characteristics, especially for small-sized microphone arrays. This paper proposes an algorithm for the design of robust broadband beamformers with passband shaping characteristics using Tikhonov regularization method by taking into account the statistics of the microphone characteristics. To facilitate the derivation, a weighted least squares based broadband beamforming algorithm with passband shaping characteristics is also proposed, while keeping a minimal stopband level. Unlike the existing criteria for broadband beamforming for microphone arrays, the proposed approaches fully exploit the degrees of freedom in weighting functions of the criteria used to design broadband beamformers. By doing so, efficient and flexible broadband beamforming can be achieved with the desired passband shaping characteristics. In addition, this paper also shows that the robust broadband beamforming using the statistics of the microphone characteristics recently proposed (Doclo and Moonen, 2003 and 2007) belongs to the class of white noise gain constraint-based techniques, which gives an insight into the nature of the state-of-the-art approach. The performance of the proposed beamforming algorithms is illustrated by the design examples and is compared with the existing approaches for microphone arrays.