In order to implement unmanned aerial vehicle (UAV)-based wireless communications, a better understanding of wireless channels and the corresponding channel characterizations are critical. In this paper, air-to-ground (AG) channel measurements are carried out at some candidate frequencies, i.e., 1 GHz, 4 GHz, 12 GHz, and 24 GHz. With measurement data, the crucial channel parameters are comprehensively analyzed. Firstly, based on the channel model in the 3rd Generation Partnership Project (3GPP), the essential coefficients for modeling path loss, including path loss exponents (PLEs) and heightdependent factors, are obtained for AG channels. Then, a novel autocorrelation model for shadow fading is proposed. Besides, the small-scale fading is statistically analyzed, where the log-logistic distribution is found as the best fit among popular distributions. Moreover, the second-order statistical characteristics, including the level crossing rate (LCR) and average fade duration (AFD), are extracted to describe indepth the fading behavior. Overall, the results and findings in this paper are essential for realizing reliable communications in AG wireless systems. INDEX TERMS Air-to-ground (AG) channel, characterizations, fading behavior, measurements, UAV.