High-Resolution Time of Arrival Estimation with Small Samples Considering Time-Varying Channel Fading Coefficient Correlation in OFDM

Abstract

This paper proposes a new method using orthogonal frequency division multiplexing (OFDM) signals for time-of-arrival (TOA) estimation in complex environments, such as electromagnetic interference and short burst received signals. Under that circumstance, sometimes only a short period of signals that were seriously interfered [i.e., low signal-to-noise ratio (SNR) and small samples] can be received for estimation. However, the traditional algorithm would be faced with a decrease in estimation accuracy under that conditions. Due to the fact that the sparse reconstruction method can recover the original signal from a small number of observations with high probability, this paper proposes an OFDM TOA estimation algorithm based on it. The algorithm not only considers the correlation of the channel complex fading coefficients in the samples at adjacent moments but also considers the off-grid effect. Under the Bayesian learning framework, this correlation and off-grid parameter are introduced into the estimation process, which effectively improves the estimation accuracy under small samples and low SNR conditions. The proposed algorithm first constructs a sparse representation model based on the channel frequency response estimated by the OFDM signal physical layer protocol data unit and then introduce the correlation characterization matrix and the off-grid parameter and make probability assumptions for the noise vector, the off-grid parameter, and the sparse coefficient vector in the model. Finally, according to Bayesian inference, the expectation-maximization algorithm is used to solve the hyperparameters to achieve high-resolution estimation of TOA. The simulation results show that the proposed algorithm has a better estimation performance than the traditional algorithms and existing sparse reconstruction algorithms. In addition, its performance curve is closer to the Cramer-Rao bound at low SNR. At the same time, based on the universal software radio peripheral, the effectiveness of the proposed algorithm is verified by the actual OFDM signal.