Modeling and equalization in radar imaging for 3-D reconstruction

We revisit the fundamental problem of 1-D pulse compression in a multistatic MIMO focused scenario, from a communications viewpoint, and extend it to a more general 4-D pulse compression. The process of focusing and scanning over a 3-D object is interpreted as a MIMO 4-dimensional convolution between a reflectivity tensor and a space-varying system. This implies that several well established equalization methods employed in communications can be easily extended to a 3-D scenario with the purpose of achieving exact reconstruction of a given reflectivity volume. Assuming that no multiple scattering occurs, resolution is only limited in range by the sampling device in the unfocused case, while unlimited in case of focusing at multiple depths. Reconstruction under zero-forcing or least-squares criterion depends solely on the amount of diversity induced by sampling in both space and time, which further allows for a tradeoff between range and cross-range resolution.