基于二阶锥规划的任意传感器阵列时域恒定束宽波束形成

Broadband constant beamwidth beamforming for arbitrary sensor arrays in time domain via second-order cone programming

提出了基于FIR滤波器的适用于任意几何形状和阵元方向性的传感器阵列的时域恒定束宽波束形成方法。首先将设计频带分成若干窄带,采用优化方法,通过对各窄带波束施加约束,设计出具有设定主瓣形状要求的各窄带波束。然后针对每个传感器,根据其各频率波束形成加权向量,采用约束优化方法,设计出具有要求幅度和相位响应的FIR滤波器。各滤波器输出相加即得到时域恒定束宽波束输出时间序列。波束图主瓣形状设计与期望频率响应FIR滤波器的设计问题都可以转化为二阶锥规划(Second-Order Cone programming)的形式,然后利用已有的内点方法(Interior-Point,Methods)求出其数值解。计算机仿真结果显示,设计出的各子带波束主瓣宽度比较接近,FIR滤波器设计精度高。湖上实验数据处理结果表明,该方法可以适用于实际水声系统,时域宽带波束能够满足恒定束宽要求。

A method of broadband constant beamwidth beamforming (BCBB) based on finite impulse response (FIR) filters is presented. Firstly, the working frequency band is decomposed into a number of narrow-band frequency bins, and the beamforming weights for each frequency bin are deduced by array pattern synthesis methods. Then, the BCBB is implemented by a set of FIR filters corresponding to the input channels, which provides the frequency response derived from BCBB weights for each sensor. Finally, the outputs of the digital filters are summed up to yield the time domain broadband beam output. BCBB weights can be designed via array pattern synthesis at each frequency bin in bands of interest by imposing mainlobe pattern constraints. The FIR filters are designed to provide required magnitude and phase response by a constrained optimization method. Both the design of beamformers and that of FIR filters can be converted to a convex optimization form as the so-called Second-Order Cone Programming (SOCP) and solved efficiently via the well-established interior point method. Results of computer simulation and lake-experiments for a twelve-element arc array confirmed the satisfactory performance of the approaches developed in this paper.