Super Supplementary Nested Array: A Sparse Array With Enhanced Degrees of Freedom and Reduced Mutual Coupling

For sparse array design, degrees of freedom (DOFs) and mutual coupling (MC) are two essential metrics to be taken into account, and high DOFs and low MC are favorable to generating better direction of arrival (DOA) estimation performance. In light of this, this paper proposes a sparse array design scheme named super supplementary nested array (SSNA) whose virtual difference co-array (DCA) is hole-free. Specifically, the scheme first shifts the subarrays of the second layer of the two-dimensional representation of the super nested array down two layers for enlarging the physical array aperture. Then, the subarrays located in the first layer are fixed, and the remaining physical sensors are shifted to the left by one unit. Finally, a supplementary sensor is selected from these physical sensors to move to a suitable location to fill the holes in the DCA of the current structure, thereby enhancing the DOFs. Theoretical analyses and results of comparison with competing sparse arrays can conclude that the SSNA structure presents a good compromise in relation to uniform DOFs (uDOFs) and the MC effect. In particular, the advantages of the SSNA structure with regard to uDOFs and the MC effect are more prominent for a small number of sensors. In addition, the findings from numerical simulations confirm that, with or without considering the MC effect, the SSNA structure is superior and effective in comparison with the competing sparse arrays.