Radio Frequency fingerprints (RFF) authentication is one of the methods for the physical-layer information security, which uses the hardware characteristics of the transmitter to identify its real identity. In order to improve the performance of RFF based on preamble with fixed duration, a nonlinear RFF authentication method based on payload symbols is proposed for the wireless OFDM devices with the bit mapping scheme of QPSK. The communication system is modeled as a Hammerstein system containing the nonlinear transmitter and wireless multipath fading channel. A parameter separation technique based on orthogonal polynomial is presented for the estimation of the parameters of the Hammerstein system. The Hammerstein system parameter separation technique is firstly used to estimate the linear parameter with the training signal, which is used to compensate the adverse effect of the linear channel for the demodulation of the successive payload symbols. The demodulated payload symbols are further used to estimate the nonlinear coefficients of the transmitter with the Hammerstein system parameter separation technique again, which is used as the novel RFF for the authentication of the QPSK-OFDM devices. Numerical experiments demonstrate that the proposed method is feasible. The novel method can also be extended to the OFDM signals with other bit mapping schemes.