Fundamental Limit of OFDM Range Estimation in a Separable Multipath Environment

In this paper, orthogonal frequency division multiplexing (OFDM) for time-based range estimation (TBRE) in a separable multipath channel is investigated and analyzed with respect to its accuracy. First, the Cramer–Rao lower bound (CRLB) in a separable multipath channel is theoretically derived, and indicates a similar expression to that for a single path channel. The CRLB for non-data-bearing (NDB) OFDM transmission is compared to that for pseudo-noise (PN) transmission, demonstrating a large performance gap in favor of the NDB OFDM. Furthermore, the maximum likelihood estimator (MLE) for TBRE in a separable multipath channel is theoretically derived, also demonstrating a similar expression to that in a single path channel, except that several peaks instead of one peak are expected in a separable multipath channel corresponding to all arrival paths. The MLE for TBRE is then compared to the commonly used MLE for channel estimation, showing an equal performance in terms of mean square error when using an NDB OFDM transmission. Simulation results demonstrate a good agreement with our proposed theory.