In this work, the performances of Shift Register based Frequency Hopping Orthogonal Frequency Multiplexing (SR-FH-OFDM) signals over a Doppler spread flat Rayleigh channel is investigated. Besides, the frequency hopping system is compared with the conventional OFDM system in terms of Bit Error Rate (BER). In the flat Rayleigh fading channel, a Doppler effect is modeled by Jakes Channel model. Considered baseband modulation techniques are 16 level Quadrature Amplitude Modulation (QAM) and 16 level Phase Shift Keying (PSK). Numerical results show that conventional and the frequency hopping schemes have similar BER results over the considered channel.