Multi-frequency Symmetric Sparse Nested Array with Scalable Aperture for Mixed Near-Field and Far-Field Source Localization

To improve the performance of direction of arrival and range estimation for mixed far-field and near-field sources, we propose a localization scheme tailored for space-constrained platforms, which incorporates a symmetric sparse nested array (SSNA) with scalable aperture and multiple coprime rational frequencies. The physical aperture of the SSNA, formulated as a function of antenna number of subarrays, can scale with uniform step, significantly improving flexibility to maximize the utilization of the available geometric space on platforms. Benefiting from its extended unit inter-antenna spacing, the SSNA cooperated with multi-frequency can give enhanced aperture and degrees of freedom (DOF) in space-frequency domain, both of which outperform those provided by the existing arrays, thereby enabling unambiguous and high-precision parameter estimation. The closed-form expressions of coarray DOFs with the scaled apertures, are derived for both space- and space-frequency-based difference coarrays. A closed-form solution for the optimal array configuration which maximizes DOF is presented, and the maximum DOFs for the array with two and multiple frequencies are analyzed. The simulation results validate the superior performance of the proposed scheme over the existing techniques.