In this paper, we present an initial development of simple approximations for the the performance of real-aperture radar ATR systems. In particular. we develop estimates of target separability using channel-capacity-like approximations, based on sensor constraints. and combinatoric-driven approximations, based on constraints imposed by the target. We then use these approximations to form estimates of the classification error probability for the ATR system. Finally, these estimates are compared with classification results for a small data set containing both synthetic and measured down-range responses from aircraft objects.