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In addition to the filter coefficients, the location of the microphone array is a crucial factor in improving the overall performance of a beamformer. The optimal microphone array placement can considerably enhance speech quality. However, the optimization problem with microphone configuration variables is non-convex and highly non-linear. Heuristic algorithms that are frequently employed take a long time and have a chance of missing the optimal microphone array placement design. We extend the Bayesian optimization method to solve the microphone array configuration design problem. The proposed Bayesian optimization method does not depend on gradient and Hessian approximations and makes use of all the information available from prior evaluations. Furthermore, Gaussian process regression and acquisition functions make up the Bayesian optimization method. The objective function is given a prior probabilistic model through Gaussian process regression, which exploits this model while integrating out uncertainty. The acquisition function is adopted to decide the next placement point based upon the incumbent optimum with the posterior distribution. Numerical experiments have demonstrated that the Bayesian optimization method could find a similar or better microphone array placement compared with the hybrid descent method and computational time is significantly reduced. Our proposed method is at least four times faster than the hybrid descent method to find the optimal microphone array configuration from the numerical results.

In designing acoustic broadband beamformers, the complexity can grow significantly when the number of microphones and the filter length increase. It is advantageous if many of the filter coefficients are zeroes so that the implementation can be executed with less computation. Moreover, the size of the array can also be pruned to reduce complexity. These problems are addressed in this paper. A suitable optimization model is proposed. Both array pruning and filter thinning can be solved together as a two-stage optimization problem to yield the final sparse designs. Numerical results show that the complexity of the designed beamformers can be reduced significantly with minimal effect on performance.

Near-optimal transmit beamformers are designed for multiuser multiple-input single-output interference channels with slowly time-varying block fading. The main contribution of this article is to provide a method for deriving closed-form solutions to effective beamforming in both low and high signal-to-noise ratio regimes. The proposed method basically leverages side information obtained from the channel correlation between adjacent coding blocks. More specifically, our methodology is based on a linear algebraic approach, which is more efficient than the optimal scheme based on the Gaussian input in the sense of reducing the average number of search space dimensions for designing the near-optimal transmit beamformers. The proposed method is shown to exhibit near-optimal performance via computer simulations in terms of the average sum-rate.