Mathematical Model for Delay Locked Loop Discriminator for 5G Demodulation Reference Signal

The vulnerable nature of satellite-based positioning systems under certain conditions such as urban canyons and indoors has given rise to the need for alternative positioning system. Cellular signal based positioning is gaining popularity and development of an accurate cellular signal-based positioning receiver is in progress. Among the cellular signals, 5G is the most preferable due to its high carrier frequency, high bandwidth, high power, ease of access and low infrastructure cost. A review of the literature suggests that 5G based positioning receiver uses a Delay Locked Loop (DLL) to track the phase of the demodulation reference signal (DMRS) of the received 5G signal. An essential part of the DLL is the discriminator, which is used to estimate the phase difference between the received DMRS and the replica of transmitted DMRS. In order to understand the working involved in the discriminator, it is ideal to study its mathematical model. The discriminator’s mathematical model includes the mathematical representation of early, prompt and late DMRS symbols, the correlations between received DMRS symbols and early, prompt and late DMRS symbols, and the S-curve. These mathematical representations, available in the literature, are analyzed in this work using the MATLAB plots. It is observed that the plots do not accurately depict the theory. Therefore, the need for an improved mathematical model arises. This work is an effort to obtain improved mathematical model for the DLL discriminator processing which is also analyzed using MATLAB plots. The plots show that the improved mathematical model accords with the theory involved in the discriminator.