联合协方差矩阵重构和ADMM的鲁棒波束形成

Robust beamforming by joint covariance matrix reconstruction and ADMM

为解决传统波束形成器在干扰位置发生扰动和导向矢量失配时,造成自适应权重的不匹配,从而导致算法性能急剧下降,甚至期望信号相消的问题,提出一种联合协方差矩阵重构和交替方向乘子法(Alternating direction method of multipliers,ADMM)的鲁棒波束形成方法。对此,首先基于波束形成器最大输出功率准则,设计了求解最优导向矢量的优化模型。接着,根据Capon算法空间功率谱函数,利用定义的干扰范围对协方差矩阵进行重构,以展宽零陷并增强系统抗运动干扰能力。最后,关于导向矢量的二次不等式约束问题,本质为估计导向矢量和期望导向矢量间的差异,该方法利用ADMM对该二次规划问题进行迭代求解,并在每次迭代中获得导向矢量的具体解。另外,也分析了算法的复杂度。实验结果表明:对比现有的波束形成算法,在干扰处加宽了零陷,提高了波束的抗干扰性;结合复杂度也证明了其计算速度优于现有的算法,并且能够很好地校正失配导向矢量。本方法也为求解二次不等式约束问题和提高波束形成算法性能提供了一种思路和途径。

In view of the problem of adaptive weight mismatch caused by disturbance and steering vector mismatch in traditional beamformers,which leads to sharp decline of algorithm performance and even cancellation of expected signal,a robust beamforming method combining covariance matrix reconstruction and alternating direction method of multipliers(ADMM)was proposed.Firstly,on the basis of the maximum output power criterion of beamformer,an optimization model was designed to solve the optimal steering vector.Then,according to the spatial power spectrum function of the Capon algorithm,the covariance matrix was reconstructed with the defined interference range to widen the null and enhance the anti-motion interference ability of the system.Finally,for the quadratic inequality constraint problem of the steering vector,the essence was to estimate the difference between the steering vector and the expected steering vector.In this method,ADMM was adopted to solve the quadratic programming problem iteratively,and the specific solution of the steering vector in each iteration was obtained.In addition,the complexity of the algorithm was analyzed.Experimental results showed that compared with the existing beamforming algorithms,the proposed method widened the null at the interference point and improved the anti-jamming performance of the beam.Combined with complexity,it was proved that the algorithm was faster than the existing algorithm and could correct the mismatched steering vector well.This paper also provides a way to solve the quadratic inequality constraint problem and improve the performance of beamforming algorithm.