As is well known, in through-the wall imaging one needs to estimate the wall electromagnetic parameters in order to get properly focused images. Even under the simplest case in which the wall can be assimilated as a single homogeneous slab, this problem puts some difficulties since the wall dielectric permittivity and thickness are nonlinearly linked to the reflected field data. The usual way to go on that problem is through some optimization iterative procedure which can be time consuming and can suffer from false solutions. In this contribution we propose a method that avoids the previously mentioned drawbacks by leveraging on a MIMO configuration. The main idea is to estimate the wall transmission coefficient rather than its electromagnetic properties. This way, one estimates the kernel of the relevant (for imaging) scattering operator instead of constructing it after wall parameters have been estimated. More in detail, it is shown that the characterization stage is cast as a linear inverse problem which is solved by a Truncated-Singular Value Decomposition method. The proposed method avoids optimization but in principle can be applied only for lossless walls. However, multi layered walls can be dealt with as well. In this contribution we focus only on the wall transmission coefficient estimation; once it has been obtained imaging can be achieved by standard back-propagation algorithms. In particular, the study is developed for a single wall and 3D vector case and some numerical examples are reported to check the theory.