Non-Coherent Direction of Arrival Estimation from Magnitude-Only Measurements

Abstract

We consider the classical Direction of arrival (DOA) estimation problem in the presence of random sensor phase errors are present at each sensor. To eliminate the effect of these phase errors, we propose a DOA recovery technique that relies only on magnitude measurements. This approach is inspired by phase retrieval for applications in other fields. Ambiguities typically associated with phase retrieval methods are resolved by introducing reference targets with known DOA. The DOA estimation problem is formulated as a nonlinear optimization in a sparse framework, and is solved by the recently proposed GESPAR algorithm modified to accommodate multiple snapshots. Numerical results demonstrate good DOA estimation performance. For example, the probability of error in locating a single target within 2 degrees is less than 0.1 for ${\rm SNR} \geq 15~\hbox{dB}$ and one snapshot, and negligible for ${\rm SNR} \geq 10~\hbox{dB}$ and five snapshots.