Performance Analysis of Time of Arrival Estimation on OFDM Signals

This letter characterizes the error performance of realistically modelled orthogonal frequency division multiplexing (OFDM) signals, when their time of arrival has to be estimated in an additive white Gaussian noise channel. In particular, different power distributions on the available sub-carriers of the OFDM signal are considered, and bounds on the corresponding root mean square estimation error (RMSEE) are evaluated. The tools used for such purpose are the widely adopted Cramér-Rao bound and the Ziv-Zakai bound, which is tight in a wide range of signal-to-noise ratio (SNR) values. The presented analysis reveals that, for a given signal bandwidth, a proper power distribution on the OFDM sub-carriers is crucial for achieving a good performance in the low to medium SNR region, where the RMSEE curve exhibits the typical threshold behavior. Moreover, a trade-off between asymptotic and threshold performance is identified, thanks to the adoption of a novel performance figure, which directly describes the threshold RMSEE behavior.