In direction finding (DF) and localization applications, coherency among the signals is an important source of error for parameter estimation. In this paper, a method is proposed to solve the DF problem where there are coherently mixed arbitrary number of far- and near-field sources. In order to estimate the direction-of-arrival (DOA) and the range parameters, compressed sensing (CS) approach is presented where a dictionary matrix is constructed with far- and near-field steering vectors. A sparse vector including the supports of the source signals is estimated in spatial domain. The supports of coherent signals are recovered by using convex minimization techniques. It is shown that the proposed approach recovers the signal components of the array output as well as determining the source locations.
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