Phaseless Transmitter Synchronization for Multi-Static Synthetic Aperture Imaging

A multi-static configuration enables phaseless synthetic aperture formation by generating a spatially incoherent incident field from the superposition of stochastically generated waveforms. The key requirement to this approach is the synchronization of spatially distributed transmitters to correctly form the incident field model at the inversion stage. In this paper, we consider a time-synchronization method feasible for a large scale multi-static synthetic aperture imaging configuration, using the intensity only measurements of the superposed direct path signals. The proposed approach utilizes the collection of distributed receivers for estimating the clock errors of among multiple transmitters, using exact phase retrieval theory. In particular, we use noise radar signals to facilitate the exact recovery of the transmitter clock errors, which yields a measurement model analogous to coded-diffraction models commonly leveraged in the phase retrieval literature. Numerical simulations demonstrate the capability of our approach under the narrow-band assumption by leveraging both the frequency diversity and the spatial diversity of the system.