On the Dependence Between User Detection and Timing Advancement in LTE Ranging Channels

Uplink ranging in long-term evolution (LTE) includes the detection of the user preamble index and estimating the timing advancement value of the detected user. In this letter, analytical expressions are derived for the probability distribution of user preamble index detection and timing advancement for ranging in LTE. The expressions are derived for multipath channel with known power delay profile. Detection of the preamble index uses the Neymann-Pearson criteria, and timing advancement is estimated by conventional peak detection. It is also theoretically shown that below a threshold signal-to-noise ratio (SNR), the probability distribution of the preamble index detection and the probability distribution of the timing advancement error are not statistically independent. However, above the threshold SNR (which our results indicate to be about -12 dB for the PedestrianB channel model), these two distributions become statistically independent. These results are also verified by simulations.