Closed-Form Expressions for the BER/SER of OFDM Systems With an Integer Time Offset

This paper provides a detailed mathematical analysis of the impact of integer time offsets on the performance of OFDM systems. Although a number of approximate expressions for the probability of error in OFDM systems with integer time offset can be found in the literature, to the best of our knowledge, this work is the first that provides exact expressions. In particular, we derive exact closed-form expressions for the bit error rate (BER) and the symbol error rate (SER) of BPSK, QPSK, and 16-QAM modulation for transmission over both AWGN and Rayleigh fading channels. The effect of the fractional carrier frequency offset (CFO) is taken into consideration in the derivations. This makes the derived expressions more useful in evaluating the probability of error for OFDM systems with CFO only, especially in cases like 16-QAM modulation for transmission over Rayleigh fading channels where exact closed-form expressions are not available. For OFDM systems with a large number of subcarriers, an approximate method for evaluating the BER/SER is given. Finally, numerical results are included to demonstrate the exactness of the derived expressions and the accuracy of the approximate method.