Design of Novel Nested Arrays Based on the Concept of Sum-Difference Coarray

Abstract

Nested arrays have recently attracted considerable attention in the field of direction of arrival (DOA) estimation owing to the hole-free property of their virtual arrays. However, such virtual arrays are confined to difference coarrays as only spatial information of the received signals is exploited. By exploiting the spatial and temporal information jointly, four kinds of novel nested arrays based on the sum-difference coarray (SDCA) concept are proposed. To increase the degrees of freedom (DOFs) of SDCA, a modified translational nested array (MTNA) is introduced first. Then, by analyzing the relationship among sensors in MTNA, we give the specific positions of redundant sensors and remove them later. Finally, we derive the closed-form expressions for the proposed arrays as well as their SDCAs. Meanwhile, different index sets corresponding to the proposed arrays are also designed for their use in obtaining the desirable SDCAs. Moreover, the properties regarding DOFs of SDCAs and physical apertures for the proposed arrays are analyzed, which prove that both the DOFs and physical apertures are improved. Simulation results are provided to verify the superiority of the proposed arrays.

Fast Underdetermined DOA Estimation Based on Generalized MRA via Original Covariance Vector Sparse Reconstruction

“…Although minimum redundancy array (MRA) [5] is able to deal with more sources than sensors, there is usually no corresponding MRA structure under some aperture, so it is difficult to realize the array design by using MRA. Lately, several new sparse array structures with closed form expression were proposed, such as the nested array (NA) [6] [7], coprime array (CPA) [8]- [10], generalized coprime array (GCPA) [11], super nested array (SNA) [12], generalized nested array (GNA) [13] and their combinations [14]. However, these sparse arrays all have less consecutive virtual sensors in the difference co-array [15]- [18] than the MRA under the same number of physical sensors while the number of consecutive virtual sensors is the main factor of underdetermined DOA estimation performance.…”