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Most localization methods for mixed far-field (FF) and near-field (NF)sources are based on uniform linear array (ULA) rather than sparse linear array(SLA). In this paper, we propose a localization method for mixed FF and NFsources based on the generalized symmetric linear arrays, which include ULAs,Cantor array, Fractal array and many other SLAs. Our method consists of twosteps. In the first step, the high-order statistics of the array output isexploited to increase the degree of freedom. Then the direction-of-arrivals(DOAs) of the FF and NF sources are jointly estimated by using the recentlyproposed atomic norm minimization (ANM), which belongs to the gridlesssuper-resolution method since the discretization of the parameter space is notrequired. In the second step, the ranges are given by MUSIC-likeone-dimensional searching. Simulations results are provided to demonstrate theadvantages of our method.

Atomic Norm Based Localization of Far-Field and Near-Field Signals with Generalized Symmetric Arrays