We consider the problem of equalizing data blocks of signals, which have been transmitted over an aeronautical channel using two different modulation schemes. The equalization is performed using the block-processing constant modulus algorithm (CMA), and in order to achieve real-time processing a Fast Fourier Transform (FFT) is used to compute the gradient of this cost function during equalization. The equalizer length is chosen to be five times of the channel length. For the first experiment, we present the result of equalizing a set of measured data, which was modulated and transmitted using the iNET packet structure with SOQPSK modulation. In this case, the CMA equalizer is first initialized using MMSE and the equalizer coefficients are then updated once, using each entire block (iNET packet). In the second experiment, we apply the FFT-based block processing equalizer to received data blocks of QPSK signals, which have been randomly generated and transmitted over an aeronautical channel. A modified constant modulus algorithm and alphabet matched algorithm (CMA + AMA) equalizer is used to recover these data blocks. For this case of QPSK signals, the equalizer performance is evaluated over 500 Monte Carlo runs, using the average symbol error rate (SER).