Virtual matrix pencil method for 2-D DOA estimation with a two-nested-shape-array

new two-nested-shape array geometry with three different inter-sensor spacings is designed to achieve enhanced degrees of freedom and doubled aperture length. The virtual matrix pencil method (VMPM) is proposed for this new array to estimate the two-dimensional direction-of-arrival (2-D DOA) of the signal sources, where the three different inter-sensor spacings are used to construct a virtual sparse two-parallel-shape array with much larger number sensors and achieve more accurate DOA estimations. Compared with the improved propagator method, the VMPM has better angle estimation accuracy, and is capable of resolving O(P^2/32) sources with P sensors. The statistical analysis of these two methods are studied, and the asymptotic variance expressions of their estimation errors are derived. Moreover, these asymptotic variance expressions are simplified for the case of one signal, and the quantitative comparisons are performed to demonstrate the performance advantage of the VMPM. The simulation results verify the validity of the VMPM.