Infinite series computation of probability of error in BPSK/QPSK OFDM systems with post-FFT phase error

In OFDM systems both time synchronization error and channel estimation error contribute to a post-FFT phase error in the received symbols. The combined effect of this phase error and the channel noise results in bit errors. A numerical technique for evaluating the probability of error due to the post-FFT phase error and channel noise in the context of OFDM (where small constellations such as BPSK and QPSK are used) has not been reported in the literature so far. In this paper, a Fourier series based numerical technique of evaluating the probability of error in OFDM systems is presented. Formulae are derived for probability of error in terms of the phase error variance and channel noise variance for an OFDM system incorporating BPSK and QPSK constellations. A comparison between the numerical results for the proposed technique and the average symbol/bit error rate (SER/BER) estimates obtained through simulation demonstrates the accuracy of the technique.