| The direction of arrival(DOA)estimation is a main branch in the field of array signal processing,which is widely used in radar,sonar,medical imaging and wireless communication and other fields.When traditional uniform linear arrays(ULA)are used for DOA estimation,the maximum number of detectable signals cannot exceed the number of array elements.In order to break through the limitation of physical array elements on the number of signals that can be estimated by DOA,scholars have proposed some classic sparse arrays in recent years.Compared with ULA,sparse array has higher degrees of freedom and more dispersed arrangement of array elements,so it has higher DOA estimation accuracy and lower mutual coupling effect.The traditional sparse array is usually designed based on difference co-array,and its virtual array is generated by the relative position difference between array elements,so its degree of freedom is limited within the physical array aperture.In this paper,the sparse array is designed based on the sum-difference co-array,which solves the problem that the degree of freedom of the traditional sparse array is limited by the array aperture,and effectively improves the degree of freedom.Based on this,we reduce the redundancy and holes of the sparse array,and design sparse arrays based on nested array and coprime array to further improve the degree of freedom and reduce the mutual coupling.The main work and innovations are as follows:First,in order to maximize the degree of freedom of the array,a novel transfromed nested array is proposed based on the sum-difference co-array.Firstly,a subarray reconstruction strategy based on transfromed nested arrays is proposed by analyzing the element redundancy and hole properties of transfromed nested arrays.According to this strategy,a novel transfromed nested array is proposed by shifting part of the elements of the transfromed nested array dense sub-array to the right to reduce the redundancy of the sum-difference co-array and to fill holes to improve the degree of freedom.Finally,the mathematical expression of the degrees of freedom of the proposed array is provided,and both theoretical and simulation results prove that the novel transfromed nested array has a higher degrees of freedom.Second,in order to fully suppress the coupling effect of the array,two improved coprime arrays are proposed based on the sum-difference co-array.First of all,an extended coprime array is obtained by shifting the short subarray of the conventional coprime array to the right,which effectively expands the array element spacing and reduces the array element redundancy,so it reduces the array mutual coupling while improving the degree of freedom.Then,an improved extended coprime array is obtained by folding some of the array elements of the extended coprime array along the reference array element position,which further enlarges the array aperture and reduces the mutual coupling between array elements.The two proposed arrays have the characteristics of the same continuous degrees of freedom and different physical apertures under the same number of array elements,and different physical configurations can be selected according to the actual carrier size,which has strong applicability.Finally,the lowcoupling and high-degree-of-freedom characteristics of the proposed two arrays are verified by simulation experiments. |
