An Analysis of the Performance of ML Blind OFDM Symbol Timing Estimation

Abstract

Symbol timing offset (STO) estimation constitutes an important part in orthogonal frequency-division multiplexing (OFDM) signal synchronization, and many blind methods based on the maximum likelihood (ML) principle have been proposed. A theoretical analysis of the estimation performance, however, is very difficult, due in part to the discrete nature of the STO. As a result, most studies on OFDM STO estimation have relied only on computer simulation for performance evaluation. This paper presents a theoretical performance analysis for ML-based blind OFDM STO estimation. We start with a review of the formulation of ML blind STO estimation problem and its solution. We then conduct the said performance analysis. The analysis turns out to involve a study of the eigenvalues of some matrix functions of the autocorrelation of the received signal. As the general case leads to highly complicated mathematics, we treat the case of full-band OFDM in additive white Gaussian noise in more detail. In this case, we are able to obtain mathematically tractable bounds and approximation to the estimation error probability and the corresponding mean-square error. In high signal-to-noise ratio (SNR), these bounds and approximation show inverse power-law dependence on the SNR. We also compare the bounds with simulation results and with an existing approximation in the literature.