导向矢量失配条件下多约束鲁棒波束形成算法

Multiple Constraints Robust Beamforming Algorithm Under Steering Vector Mismatch Conditions

自适应波束形成随着数字信号处理技术的不断发展,已广泛应用于雷达、语音、医疗等领域。然而,当阵列发生扰动时,将会导致干扰偏离零陷位置,甚至会导致算法完全失效。为了解决现有波束形成算法在发生导向矢量失配和干扰位置扰动时波束形成器性能急剧下降的问题,本文提出了一种导向矢量失配条件下多约束鲁棒波束形成算法。本文参照实际情况引入更多约束,增加了双边范数扰动约束以及二次相似性约束,允许了误差产生的范围。此外,本文确保感兴趣信号(Signal Of Interest,SOI)的到达方向(Direction Of Arrival,DOA)远离干扰导向矢量的所有线性组合的DOA区域,保证了最优导向矢量的DOA位于SOI的角扇形区域。首先,以波束形成器输出最大功率为目标,并结合实际环境下的约束条件,建立了最优导向矢量的数学模型。其次,利用定义的干扰范围重构协方差矩阵,以此来展宽零陷,提高系统的抗干扰性能。最后,先用内点法求得替代变量的解,以此求解针对导向矢量的二次不等式约束问题;随后在约束模型中代入替代变量,用交替方向乘子法迭代求解导向矢量,在每一次的迭代中都会得到显示解。同时,本文还对算法的时间复杂度和收敛性进行了分析。实验结果显示,相较于传统的波束形成算法,所提方法加宽了干扰处零陷,使得波束形成器的抗干扰性能得到了一定的提高,且能够很好地校正失配导向矢量。

With the development of digital signal processing technology,adaptive beamforming has been widely employed in many applications including radar,microphone array speech/audio processing,and medical imaging.However,when the array is disturbed,it causes the disturbance to deviate from the null position,and even causes the algorithm to fail completely.To solve the disturbance and steering vector mismatch occurring at the interference position,we proposed a multiple constraints robust beamforming algorithm based on the alternating direction multiplier method(ADMM).More constraints were introduced according to the actual situation,including the bilateral norm perturbation constraint,and the quadratic similarity constraint,which were added to allow the range of error generation.In addition,we ensured that the direction of arrival(DOA)of the signal of interest(SOI)was far away from the DOA region of all linear combinations of interfering steering vectors,which ensured that the DOA of the optimal steering vector lay in the angular sector region of the SOI.First,based on the maximum output power criterion and practical constraints,an optimization model of the steering vector was designed.Next,the covariance matrix was reconstructed using the defined interference range to widen the null and enhance the ability of resisting motion interference.Finally,the interior point method was used to obtain the solution of the substitute variable,to solve the quadratic inequality constraint problem for the guiding vector.Substitute variables were then inserted into the constraint model,and the directional vector was iteratively solved using the alternating direction multiplier method.The explicit solution was obtained in each iteration.Meanwhile,we also analyzed the time complexity and convergence of the algorithm.The experimental results showed that,compared to traditional beamforming algorithms,the proposed method widens the nulls at the interference point,improves the robustness of the algorithm against system errors,and effectively corrects the mismatched steering vector.