  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 NF
sources based on the generalized symmetric linear arrays, which include ULAs,
Cantor array, Fractal array and many other SLAs. Our method consists of two
steps. In the first step, the high-order statistics of the array output is
exploited to increase the degree of freedom. Then the direction-of-arrivals
(DOAs) of the FF and NF sources are jointly estimated by using the recently
proposed atomic norm minimization (ANM), which belongs to the gridless
super-resolution method since the discretization of the parameter space is not
required. In the second step, the ranges are given by MUSIC-like
one-dimensional searching. Simulations results are provided to demonstrate the
advantages of our method.
