Dilated Nested Arrays With More Degrees of Freedom (DOFs) and Less Mutual Coupling-Part I: The Fundamental Geometry

The recent criteria of a preferable linear sparse array for a robust direction of arrival (DOA) estimation are: the closed-form expression for its sensor locations; the large central uniform linear array (ULA) segment in its resulting co-array; and the fewer sensor pairs with small separations in its arrangement. These features, in turn, will lead to a straightforward array design process, more sources being resolved and strong helpful performance for the array within a real-world mutual coupling environment. This paper introduces a new array called the dilated nested array (DNA), which takes into account all these considerations. The sensors of the DNA are arranged in a way that yields an effective difference co-array with a central virtual ULA part larger than that of the co-prime array and equal to that of the nested array, and in an equivalent importance, a physical arrangement with smaller numbers of sensor pairs with small separations than those of the super nested array, so that the array can notably reduce the mutual coupling effects in comparison. A displaced arrangement obtained from the DNA geometry is also introduced to further increase the co-array total number of DOFs and at the same time to decrease the numbers of sensor pairs with small separations. Extensive numerical simulations are included to demonstrate the effectiveness of the proposed DNAs over other sparse arrays.