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This paper characterizes the SER for a non-ideal OFDM system with either M-PSK or M-QAM constellations operating over a frequency-selective, time-varying, Rayleigh fading channel. The imperfections that we consider are inter-carrier interference (ICI) and/or inter-symbol interference (ISI), imperfect time and frequency synchronization, and noisy channel estimates. We consider an MRC receiver with L diversity branches. We present SER characterizations with and without ISI, and show that the effect of ISI, especially for higher order modulation schemes, e.g., 8PSK and above, can be very severe, irrespective of the number of diversity branches.