TWI for an Unknown Symmetric Lossless Wall

A through-wall-imaging problem where the scatterers are located beyond a 1-D nonhomogeneous unknown wall is considered. As is well known, as part of the propagation takes place within the wall, the knowledge of its electromagnetic properties is mandatory in order to obtain properly focused images. Accordingly, this paper's focus is on the wall estimation problem. To this end, a simple procedure to estimate the wall transmission coefficient is introduced and validated by synthetic data. The proposed estimation procedure works for a symmetric lossless wall and does not rely on optimization schemes but requires a multistatic configuration. As a proof of the principle, we address the problem for a 2-D scalar configuration. Moreover, the role of obscured scatterers on the estimation procedure is discussed, and a procedure for mitigating their effect is proposed as well. Finally, the procedure is also checked against a wall with losses.