Positioning of Devices in LTE networks. Part 3. Analysis of Correlation Functions for Reference Signals

Purpose: In modern LTE networks, especially in urban and indoor conditions, the accuracy of device positioning often decreases due to the limitations of existing methods, such as A-GNSS and Cell-ID. This is due to the lack of direct visibility of satellites and low accuracy of cell identification. This study is devoted to the analysis of the correlation functions of synchronization signals and reference signals in LTE networks to optimize the process of time delay estimation. The objective of the work is to study the autocorrelation function (ACF) of synchronization signals and reference signals to improve the accuracy of device positioning. The work includes the development of a mathematical model for ACF estimation, analysis of the influence of pilot subcarrier distribution, the number of resource blocks and other system parameters on the ACF characteristics, and assessment of their impact on the accuracy of time delay determination. Methods: The study applied the methods of OFDM signal modeling, LTE signal structure analysis at the physical layer and mathematical calculations of the time delay based on the autocorrelation function of reference signals using the maximum likelihood (ML) method. Novelty: The novelty of the work lies in the mathematical formalization of the ACF estimate of the reference signals, depending on the frequency bandwidth with a scientific justification of the potential accuracy of the primary measurements of the signal arrival time in the additive white Gaussian noise (AWGN) channel. Results: the study shows that an increase in the number of resource blocks leads to a narrowing of the main lobe of the ACF, which improves the accuracy of the primary measurements of the signal arrival time. Uniform distribution of pilot subcarriers in the reference signals causes the appearance of periodic correlation peaks, which also contributes to a more accurate estimate of the signal parameters. Theoretical / Practical significance: The theoretical significance of the work lies in the development of a mathematical model for calculating the ACF for LTE reference signals, which serves as a basis for assessing the accuracy of primary measurements of the signal arrival time, including subsequent comparison with the Cramer-Rao lower bound (CRLB). The practical significance lies in the scientific substantiation of the required LTE signal frequency bands to achieve a given accuracy of primary measurements of the signal arrival time in LTE networks, as well as for the development of similar models in 5G networks with OFDM signals.