Is Compressive Sensing really useful for radar?

Compressive Sensing (CS) was originally developed to directly acquire a compressed description of a sparse scene. This can be possible provided that the sampling scheme meet certain criteria. In Radar applications, the main advantage highlighted in the literature is the reduction of the data-flow between the R.F. front-end and processing that would be intractable in number of cases. However thanks to the technological progresses in fast Analog to Digital Conversion (ADC) and subsequent digital processing, the real problem is not at this level except in some special cases. The real issue is that it is not always possible to sample the radar signal ideally for practical and uncontrollable reasons. So far, most of the work in the literature has focused on the mathematical aspect of the underlying L1 inverse problem. This paper shows some examples where the use of sparse or incomplete sampling is really justified. We also show that the inverse problem resolution based on the minimization of the L1 norm, even if it is elegant way to solve the problem, is not the only means to address the problem.