Localization of a Time-Harmonic Electromagnetic Point Source in a Cavity With Magnitude-Only Measurements and Backpropagation

This article presents a method for the localization of a time-harmonic source in a cavity with magnitude-only measurements using the principle of backpropagation in electromagnetic time reversal (EMTR). A time-harmonic point source that radiates an electromagnetic field at a specific frequency is considered. The source is assumed to be at an unknown position within the cavity. Scatterers of known geometry and dielectric constants, present in the cavity, alter the source field. The magnitude of the electric field is measured at certain locations within the cavity. Using these magnitude measurements, the position of the source has to be determined. Linear constraints based on backpropagation are derived. These constraints depend only on the magnitude of the electric fields. A convex optimization problem minimizing the $\mathcal {L}_{1}$ norm of the vector of source amplitudes subject to the derived linear constraints is formulated. The matching pursuit (MP) algorithm is used to solve the optimization problem. The solution to this optimization problem reveals the source location. The proposed method is validated by numerical experiments in both 2-D and 3-D cavities. Numerical results suggest that it is possible to localize a time-harmonic point source with three magnitude-only measurements in the ideal noise-free case. In case of noisy measurements, having ten or more measurements provides a good localization.