Fourth order cumulants in distinguishing single carrier from OFDM signals

In this paper, we propose to use the fourth order cumulants to distinguish OFDM from single carrier signals. We show analytically the value of C40(N) and C42(N) as a function of the number of subcarriers of the OFDM signal and its SNR. By taking these values as an estimate of these cumulants, we compare it to the estimate of different single carrier modulation signals including SC-BC as it was given in the literature or by experiments we performed as for others. From these values we create thresholds detectors use either one cumulant or both depending on the assumed environments which include timing offset, phase rotation, frequency offset of the received signals, and pulse shaping. Last, we use Monte Carlo simulations under different scenarios to examine the probability of detecting OFDM from different single carrier signals.