Abstract: Under Alpha stable distribution noise background, the existing fading-signal modulation recognition methods based on traditional cyclic statistics were always invalid. To solve this problem, a new modulation recognition method is proposed, by introducing normalized compression function to generate a series of novel generalized cyclic statistics. Firstly, the generalized cyclostationary feature of the signals are extracted as decision criterion; and then the tree classifier is used to achieve modulation recognition of signals such as FSK, PSK and MSK in fading channels under Alpha stable distribution noise background. Finally, simulation results show that the proposed method has good performance in different channels with single or multiple propagation paths under Alpha stable distribution noise background. Moreover, it exhibits higher flexibility, better performance but lower complexity than other methods based on generalized cyclic statistics using non-linear transform.