回响环境下的最优波束形成器设计

Optimal beamformer design in the reverberant environment

目前大多数波束形成器(beamformer)的设计方法在模型建立时都是为了得到期望的波束形成响应(beamformer response),如最小方差无失真响应(minimum variance distortionless response,MVDR)方法和线性约束最小方差(linearly constrained minimum variance,LCMV)方法.为了构造人们期望的波束形成响应,最简单的方法就是采用从目标声源点到波束形成器输出点的脉冲响应(impulse response),加上一个波束形成器群延迟(group delay).然而对于波束形成器群延迟的估计却是未知的,经验地,人们将其选择为波束形成器长度的一半.可是在回响环境下,这样的波束形成响应选择往往不是最优的.为了设计最优波束形成器,本文考虑波束形成响应与波束形成器的联合设计问题.首先,引入一个新的变量来表示波束形成响应,并且将波束形成响应与波束形成器联合设计问题建模成一个结构型约束凸优化(structured constrained convex optimization,SCCO)问题.其次,利用SCCO问题的结构可分性,引入交替方向法(alternating direction method of multipliers,ADMM)来加以求解.为了文章的完整性,本文还给出ADMM算法收敛性结果的一个简单证明框架.最后,数值实验结果表明,提出的波束形成器设计方法在回响环境下是有效的,并且比LCMV方法效果更好.

Most existing methods on beamformer design, such as the minimum variance distortionless response（MVDR） method and the linearly constrained minimum variance（LCMV） method, assume that the group delay is known and often heuristically preselected to be half of the filter length. However, the optimal group delay is problem-dependent in practice, and the beamformer design performance based on the optimal beamformer response can be significantly better than the one based on the preselected beamformer response in the reverberant environment. In this paper, we consider the optimal beamformer design problem, i.e., the joint beamformer response and beamformer design problem. We introduce a new variable to represent the beamformer response and formulate the joint beamformer response design and beamformer design problem as a structured constrainedconvex optimization（SCCO） problem. Moreover, we exploit the separable structures of the SCCO problem and propose to use the alternating direction method of multipliers（ADMM） to solve it, and give a simple proof for the analysis of convergence. Numerical simulation results show the effectiveness of the proposed method in the reverberant environment by comparing it with the LCMV method.