Methods of Signal Processing

On estimating the time shift of a random periodic OFDM signal

G. K. Golubev, V. G. Potapov

Kharkevich Institute for Information Transmission Problems of the Russian Academy of Sciences, Moscow

Abstract: We consider the problem of estimating the time shift of an unknown, random, wideband OFDM signal with $N$ subcarriers and periodic synchronization insertions. The signal is assumed to be observed against a background of white Gaussian noise, and a small amount of received data is used to construct the estimate. Such problems arise in geolocation using low-orbit satellite constellations. To estimate the maximum posterior probability (MPP) of the time shift, we find its limiting distribution as $N\to\infty$ and investigate its large deviations using the method of fractional derivatives.

Keywords: OFDM, geolocation, white Gaussian noise, Wiener process, maximum posterior probability estimation, Bayesian estimator, fractional derivative.

UDC: 621.391 : 519.218.5

Received: 23.05.2025
Revised: 29.07.2025
Accepted: 20.08.2025

DOI: 10.31857/S0555292325020033