An Active Set Approximation Method For The Design Of Broadband Beamformer

Broadband beamformer have been studied extensively due to their wide applications.How to choose the appropriate filter design criteria according to the specific filter type,and design the filter coefficients,to optimize a given performance index,is the main research di?rection.In this thesis,we consider the optimal design of broadband beamformer.By analyzing the performance limit of the problem,we apply two effective algorithms,the discretization method and the active set approximation method,to solve the optimization problem.The optimal solution,optimal error and running times of these two algorithms are compared and analyzed.The main contents of this thesis are as follows.In the first part,we study the optimal error value limit of broadband beamforming design.First,we establish the optimization problem model in far-field and near-field environments,respectively,according to the signal processing principle.In order to judge the rationality of the desired response function setting in advance,we discuss the limit of optimal error value for all possible filter lengths,and formulate a series of optimization sub-problems to compute this limit.Numerical examples are illustrated to verify the method for the limit.In the second part,we study the algorithm for the design of broadband beamforming prob-lem.First,we introduce the discretization method to solve the optimal value of the broadband beamforming problem.Next,we propose the active set approximation method to solve the optimal value of the problem.Finally,these two methods are applied to solve the problem in far field and near field,respectively,and the optimal solution,optimal error and running time are compared.Finally,we summarize the work above and make a prospect for future research.