On the application of subspace migration from scattering matrix with constant-valued diagonal elements in microwave imaging

We apply subspace migration (SM) for fast identification of a small object in microwave imaging. Most research in this area is performed under the assumption that the diagonal elements of the scattering matrix can be easily measured if the transmitter and the receiver are in the same location. Unfortunately, it is very difficult to measure such elements in most real-world microwave imaging. To address this issue, several studies have been conducted with the unknown diagonal elements set to zero. In this paper, we generalize the imaging problem by using SM to set the diagonal elements of the scattering matrix to a constant. To demonstrate the applicability of SM and its dependence on the constant, we show that the imaging function of SM can be represented by an infinite series of Bessel functions of integer order, antenna number and arrangement, and the applied constant. This result allows us to discover additional properties, such as the unique determination of the object. We also demonstrated simulation results using synthetic data to back up the theoretical result.