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This paper presents the details of a simulation based study performed to investigate the BER performance degradation (sensitivity) of OFDM systems due to time synchronization error at the demodulator. It is shown that an OFDM system incorporating a cyclic prefix (CP) has an asymmetric effect on the received constellation with synchronization error away from CP introducing intersymbol interference (ISI), while that towards the CP introducing only a phase error. We approximate the time synchronization error by a Gaussian distributed random variable, in order to evaluate the BER sensitivity of OFDM systems to timing error. The BER performance was evaluated for an AWGN channel and a multipath fading channel in terms of the synchronization error variance. The results of this investigation will be useful in developing time synchronization algorithms in OFDM systems to achieve a particular BER performance target for a given channel condition.