In the United States, the Federal Communications Commission has adopted rules permitting commercial wireless networks to share spectrum with federal incumbents in the 3.5 GHz Citizens Broadband Radio Service band (3550-3700 MHz). These rules require commercial wireless systems to vacate the band when coastal sensor networks detect radars operated by the U.S. military; a key example being the SPN-43 air traffic control radar. For such coastal sensor networks to meet their operating requirements, they require highly-accurate detection algorithms. In addition to their use in sensor networks, detection algorithms can assist in the generation of descriptive statistics for libraries of spectrum recordings. In this paper, using a library of over 14,000 3.5 GHz band spectrograms collected by a recent measurement campaign, we investigate the performance of three different methods for SPN-43 radar detection. Namely, we compare classical energy detection to two deep learning algorithms: a convolutional neural network and a long short-term memory recurrent neural network. Performing a thorough evaluation, we demonstrate that deep learning algorithms appreciably outperform energy detection. Finally, we apply the best-performing classifier to generate descriptive statistics for the 3.5 GHz spectrogram library. Overall, our findings highlight potential weaknesses of energy detection as well as the strengths of modern deep learning algorithms for radar detection in the 3.5 GHz band.