On the Distribution of Peak-to-Average Power Ratio for Non-Circularly Modulated OFDM Signals

In this paper we investigate the distribution of the peak-to-average power ratio for noncircularly modulated OFDM system. In contrast to circularly modulated OFDM systems, we find the following characteristics for non-circularly modulated OFDM symbols: i) They do not converge to complex Gaussian sequence asymptotically. ii) The correlation among OFDM symbol powers does not diminish as the number of subcarriers goes to infinity. We further derive, based on the above two observations, an expression for the distribution of peak-to-average power ratio for non-circular constellation. While not in closed form, the obtained expression allows easy numerical evaluation. For the special case of BPSK, the expression can be simplified to a form that admits closed-form approximation. We show that the analytical prediction matches well with empirical result obtained through simulation.