The Sparse Array Synthesis Method Based On Compressed Sensing Theory

Compared with the uniform antenna array,the sparse antenna array due to its advantages of low cost and lightweight is widely used in communication,sonar and direction finding,and other fields.In this paper,to synthesize the maximally sparse antenna arrays by the compressed sensing method that using to estimate the direction of arrival,the synthesis of the sparse antenna array is equivalent to the direction of arrival(DOA)problem.The main work and innovation are as follows.(1)Introducing the compressed sensing method into the synthesis of sparse linear arrays,a sparse linear array synthesis method based on compressed sensing is proposed.given the array aperture of the linear array and its generated reference pattern,the sampling data of the reference pattern is equivalent to the known information in the DOA estimation,and the dense discretization step of the array aperture is equivalent to the discretization of the incident direction angle in the DOA estimation,the sparse linear array synthesis problem is equivalent to the single-shot DOA estimation problem of linear arrays,then the positions and excitations of sparse antenna elements can be estimated through the convex optimization algorithm.Experimental results show that this method can reconstruct the reference pattern with fewer antenna elements,and effectively reduce the number of antenna elements used.(2)Aiming at the problem that the sparse array synthesis algorithm based on compression sensing has low computational efficiency and cannot be directly applied to large sparse linear arrays,improved the original iterative weighting method,a weighting method of protecting the maximum excitation is proposed,which enables the compressive sensing sparse linear array method to obtain a part of the position of the sparse array and its excitation,and a part of the antenna element group that hides the antenna element of the sparse array.To find out the precise position and excitation of antenna array elements hidden in the group’s interval,a method of merging antenna array element groups is proposed.The experimental results show that the discretization interval of the array aperture is extended to 0.05 the wavelength,which reduces the amount of calculation and does not increase the error with the original pattern,and this method has no restrictions on the reference pattern.(3)Introducing the compressed sensing method into the synthesis of sparse concentric ring arrays,a sparse concentric ring arrays synthesis method based on compressed sensing is proposed.Under the conditions of giving the ring diameter and the three-dimensional pattern,the Bessel function of the three-dimensional pattern is used,combined with the theory of compressive sensing,establishes compressed sensing to find the maximum sparse continuous current ring array’s position and its excitation.Then,according to the obtained excitation and the requirement of the error of the original three-dimensional pattern,the total number of discrete antenna array elements is obtained by using the density reduction technique,a sparse concentric ring array is obtained by combining the density reduction technique,achieved the purpose of generating the three-dimensional pattern with fewer array elements.(4)To reduce the amount of calculation,introduced the compressive sensing method into the large sparse concentric circular arrays synthesis,the off-grid method used in DOA estimation is applied to search the position and excitation of the sparse continuous current ring.at the same time,in fixing the disadvantage that the error of the off-grid method increases with the increase of the discretization interval,a movable off-grid method is proposed.This method sets the first-order Taylor expansion point of each circle ring to be movable and changes continuously with iterations.Experiments show that when searching for position and excitation of the maximally sparse continuous current loop,this method increases the allowable maximum sampling interval range of the array aperture,which can increase the maximum value to 0.3 times the wavelength,which reduces the amount of calculation in this step.