Roles of equalization in radar imaging: modeling for superesolution in 3D reconstruction

Abstract

In radar imaging, resolution is generally dictated by its corresponding system point spread function, the response to a point source as a result of an external excitation. This notion of resolution turns out to be rather questionable, as the interpretation of echoes received from a range of continuous targets according to a linear model allows one to cast the imaging problem as a communication system that maps the target reflectivity function onto measurements, which in turn suggests that by virtue of sampling and equalization, one can achieve unlimited spatial resolution. This article reviews the fundamental problem inherent to pulse compression in a multistatic multi-input-multi-output (MIMO) scenario, from a communications viewpoint, in both focused and un-focused scenarios. We generalize the notion of 1D range compression and replace it by a more general 4D pulse compression. The process of focusing and scanning over a 3D object can be interpreted as a MIMO 4D convolution between a reflectivity tensor and a space-varying system, which naturally induces a 4D MIMO channel convolution model. This implies that several well-established block and linear equalization methods can be easily extended to a 3D scenario with the purpose of achieving exact reconstruction of a given reflectivity volume. That is, 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. Exact reconstruction under a zero-forcing or least-squares criterion depends solely on the amount of diversity induced by sampling in both space (via scanning rate) and time (via sampling rate), which further allows for a tradeoff between range and cross-range resolution. For instance, the fastest scanning rate is achieved by steering non overlapping beams, in which case portions of the object can be reconstructed independently from each other.