In this paper, we derive exact and asymptotic bit error rate (BER) formulas of differential binary phase shift keying (DBPSK) and non-coherent frequency shift keying (NCFSK) modulations for orthogonal frequency division multiplexing (OFDM) system employing maximal ratio combining (MRC) receive diversity technique, especially over correlated Nakagami-m fading channels. In particular, exploiting the derived asymptotic BER formulas, asymptotic modulation gain and diversity order can be subsequently achieved, which enable us to easily predict the performance limit of the considered system and channel environments. Based on our asymptotic analysis, we can also analytically demonstrate the asymptotic SNR performance gap between DBPSK and NCFSK.