Direction finding using non-coherent measurements in large antenna arrays

Direction finding based on array elements capable of acquiring only non-coherent or phaseless measurements is considered. Fundamental limits on the angle estimation error for a finite number of planar wavefronts impinging on the array as a function of the number of antennas are derived through a characterization of the Fisher information matrix. The performance of sparsity-based computationally efficient algorithms for direction finding from recent advances in the phase retrieval literature are also presented. Estimation error under both coherent and noncoherent measurements is shown to decrease as the cube of the number of antennas when this number is large, with a small gap in performance for the non-coherent case.