Generalized Nested Array Configuration Family for Direction-of-Arrival Estimation

Sparse arrays have obvious superiority in array element layout and the number of degrees of freedom (DOF) for resolving more sources than the number of physical sensors with high estimation accuracy. Nevertheless, any of the existing array configurations with fixed number of sensors corresponds to a certain array element arrangement, the virtual coarray and the uniform DOF may be affected significantly when the positions of one or several sensors changed. In this paper, a generalized nested array (GNA) configuration family is proposed by incorporating the concept of family into array design. The arrays in GNA family generally consist of three subarrays, and the inherent geometric characteristic is analyzed from the perspective of two-dimensional (2D) representation. For the array configurations of GNA family, one can be transformed into another by setting order factor, thus they can provide more flexible element arrangements as compared to a specific array configuration. Moreover, each array of the GNA family has hole-free difference coarray. Based on the GNA family, compressive sensing (CS) approach is employed for direction-of-arrival (DOA) estimation by solving an
l
₁
norm minimization problem. The theoretical propositions are proved and numerical simulations are performed to demonstrate the superior performance of the proposed GNA family and the DOA estimation.