Instead of the point-target based sensing matrix described in Eq. (7), where each antenna accumulates the contributions of all the pixels, we use an alternate sensing matrix, proposed in 68, to relate the scene vector, , and the observation vector, . This matrix underlines the specular reflections produced by the walls. Due to wall specular reflections, and since the array is assumed parallel to the front wall and, thus, parallel to interior walls, the rays collected at the ’th antenna will be produced by portions of the walls that are only in front of this antenna [see Fig. 4(a)]. The alternate matrix, therefore, only considers the contributions of the pixels that are located in front of each antenna. In so doing, the returns of the walls located parallel to the array axis are emphasized. As such, it is most suited to the specific building structure imaging problem, wherein the signal returns are mainly caused by EM reflections of exterior and interior walls. The alternate linear model can be expressed as Display Formula
(22)where Display Formula
(23)with defined as Display Formula
(24)In Eq. (24), is the two-way signal propagation time associated with the downrange of the ’th pixel, and the function works as an indicator function in the following way: Display Formula
(25)That is, if and represent the cross-range coordinates of the ’th pixel and the ’th antenna location, respectively, and is the cross-range sampling step, then provided that [see Fig. 4(b)].