基于波束空间的四阶累积量LCMV波束形成算法

Fourth Order Cumulant LCMV Beamforming Algorithm Based on Beamspace

针对基于高阶累积量的线性约束最小方差(LCMV)自适应波束形成技术存在计算量大、实际应用中适用性不好的问题,提出基于波束空间的四阶累积量LCMV波束形成算法。将优化扩展后的原位替换求逆算法引入自适应阵列处理中,将阵列接收信号从阵元域变换到波束域,在波束域中构造四阶累积量相关矩阵。引入约化系数矩阵,在原位替换算法的基础上,通过主元交换与对角线修正完成求逆运算,求解最优权矢量。仿真结果与计算量分析表明,与传统LCMV算法相比,该算法波束主瓣更窄,旁瓣更低,抗干扰性能更好;与阵元域四阶累积量的LCMV相比,计算复杂度由Ο(M^(2)×M^(2))变为Ο(r^(2)×r^(2)),且矩阵求逆的实际应用性更好。该算法的波束域处理与求逆运算对高阶累积量在自适应阵列处理领域的应用具有很大意义。

In order to solve the problem that the linear constrained minimum variance(LCMV)adaptive beamforming technology based on high-order cumulant has a large amount of computation and poor applicability in practical applications,the fourth-order cumulant LCMV beamforming algorithm based on beamspace is proposed.The optimized and extended in-situ replacement inverse algorithm is introduced into adaptive array processing.The received signal is transformed from the array domain to the beam domain,and the fourth-order cumulant correlation matrix is constructed in the beam domain.The reduced coefficient matrix is introduced,and the inverse operation is completed by principal element exchange and diagonal correction based on the principle of in-situ replacement algorithm to solve the optimal weight vector.Simulation results and computational analysis show that,compared with the traditional LCMV algorithm,the proposed algorithm has narrower beam main lobe,lower side lobe and better anti-interference performance.Compared with the LCMV of the fourth-order cumulant in the matrix domain,the computational complexity is changed from O(M^(2)×M^(2))to O(r^(2)×r^(2)),and the practical application of matrix inverse is better.The application of beam-domain processing and inverse algorithm is of great significance to the application of high-order cumulants in adaptive array processing.