基于多维傅里叶变换的阵列空时信号处理与应用

Array Space Time Signal Processing and Application Based on Multidimensional Fourier Transform

目前常用的阵列空时信号处理方法需要计算全部阵元接收信号的采样矩阵,并通过对矩阵的各种运算来提取信息,但是大中型阵列的阵元数量众多导致矩阵维数较大,高维矩阵的巨大运算量使其难以在具有实时性要求的工程中应用。针对这一问题,将傅里叶变换从时域推广至空域,指出了空域与角度域之间存在的傅里叶变换关系。在此基础上,借鉴多维傅里叶变换方法阐释了线阵与面阵各自空时联合处理的二维与三维傅里叶变换表达及其物理意义。通过示例性仿真验证了前述理论建模与特性分析的正确性与有效性,从而为大中型阵列的空时信号实时处理工程应用提供了新的技术手段。

At present,the conventional array space time signal processing methods need to calculate the sampling matrix of signals received by all array elements,and extract information through various operations on the matrix.However,more array elements in large-and-medium-sized arrays lead to large dimension number of the matrix,and the large amount of computation on high-dimensional matrix makes it difficult to applied to the engineering with real-time requirements.In order to resolve this problem,the Fourier transform is extended from the time domain to space domain,and the Fourier transform relationship between the space domain and angle domain is pointed out.On this basis,the two-dimensional and three-dimensional Fourier transform expression and its physical significance of the space time joint processing for linear array and plane array are explained by referring to the multi-dimensional Fourier transform method.The correctness and effectiveness of the above theoretical modeling and characteristic analysis are verified by an example simulation,which provides a new technical approach for the engineering applications of space time signal real-time processing of large-and-medium-sized arrays.