Spectrum sensing and awareness are challenging requirements in cognitive radio (CR). To adequately adapt to the changing radio environment, it is necessary for the CR to detect the presence and classify the on-the-air signals. The wireless industry has shown great interest in orthogonal frequency division multiplexing (OFDM) technology. Hence, classification of OFDM signals has been intensively researched recently. Generic signals have been mainly considered, and there is a need to investigate OFDM standard signals, and their specific discriminating features for classification. In this paper, realistic and comprehensive mathematical models of the OFDM-based mobile Worldwide Interoperability for Microwave Access (WiMAX) and third-Generation Partnership Project Long Term Evolution (3GPP LTE) signals are developed, and their second-order cyclostationarity is studied. Closed-from expressions for the cyclic autocorrelation function (CAF) and cycle frequencies (CFs) of both signal types are derived, based on which an algorithm is proposed for their classification. The proposed algorithm does not require carrier, waveform, and symbol timing recovery, and is immune to phase, frequency, and timing offsets. The classification performance of the algorithm is investigated versus signal-to-noise ratio (SNR), for diverse observation intervals and channel conditions. In addition, the computational complexity is explored versus the signal type. Simulation results show the efficiency of the algorithm is terms of classification performance, and the complexity study proves the real time applicability of the algorithm.