基于压缩感知的频率不变波束旁瓣水平优化方法

A frequency invariant beam sidelobe level optimization method based on compressed sensing

摘要:

频率不变波束形成技术属于恒定束宽波束形成，能解决宽带信号中不同频率分量对应的波束响应不一致的问题。针对现有的一类将恒定主瓣宽度作为约束条件的频率不变波束形成方法，当阵元个数确定以后，形成的波束旁瓣水平往往达不到实际需求的问题，借助压缩感知理论，提出了一种改善波束旁瓣水平的新方法。提出的方法引入压缩感知理论（Compressed Sensing，CS）进行信号的预处理，并利用二阶锥规划（Second Order Cone Programming,SOCP）进行频率不变波束形成。由于压缩感知的恢复算法可以对压缩采样矩阵采集的信号进行精确重构，从而达到以更少的阵元获得相同的波束形成器性能。换言之，在相同的阵元个数条件下，通过阵列虚拟扩展增大了阵列的孔径，提出的方法比基于SOCP的频率不变波束形成方法有更低的旁瓣水平，仿真结果也表明了该方法的有效性，在相关的工程实践中具有一定的参考价值。

Abstract:

The frequency invariant beamforming belongs to constant beamwidth beamforming which can solve the problem of inconsistent beam response corresponding to different frequency components in a wideband signal. At present, most frequency invariant beamforming methods often have an invariant main lobe width as a constraint. When the number of array elements is determined, the formed beam sidelobe level often fails to meet the actual demand. Aiming at this problem, a new method to improve the beam sidelobe level is proposed by means of compressed sensing(CS). The method introduces the CS to preprocess the signal and uses second order cone programming (SOCP) for frequency invariant beamforming. Since CS recovery algorithm can accurately reconstruct the signals acquired by the compressed sampling matrix, the same beamforming performance can be obtained with fewer array elements. In other words, the method has a lower sidelobe level than the method based on SOCP in case of the same number of elements. The simulation results also show the effectiveness of the proposed method which has certain reference value in related engineering practice.