  This letter investigates the non-coherent Direction of Arrival (DOA)
estimation problem dealing with the DOA estimation from magnitude only
measurements of the array output. The magnitude squared of the array output is
expanded as a superposition of some harmonics. Hence, a frequency estimation
approach is used to find some nonlinear relations between DOAs, which results
in inherent ambiguities. To solve the nonlinear equations and resolve the
ambiguities, we assume a high amplitude reference target at low angles to
estimate the true DOA's with no ambiguities. However, the proposed algorithm
requires a large number of antenna array elements to accurately estimate the
DOA's. To overcome this drawback, and to enhance the estimation accuracy, we
suggest two variants of the algorithm. One is to add virtual elements in the
array and the second is to integrate multiple snapshots. Simulation results
show that the proposed frequency estimation-based algorithm outperforms the
non-coherent GESPAR algorithm in the low signal to noise ratio (SNR) regime and
it is two orders of magnitude faster than the non-coherent GESPAR algorithm.
