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We conduct an in  depth study on the performance of deep learning based radio signal classification for radio communications signals. We consider a rigorous baseline method using higher order moments and strong boosted gradient tree classification, and compare performance between the two approaches across a range of configurations and channel impairments. We consider the effects of carrier frequency offset, symbol rate, and multipath fading in simulation, and conduct over-the-air measurement of radio classification performance in the lab using software radios, and we compare performance and training strategies for both. Finally, we conclude with a discussion of remaining problems, and design considerations for using such techniques.