A Closed-Form Phase Difference Estimation Method for BLE Direction Finding using the Best Linear Unbiased Estimator

Since Bluetooth version 5.1, Angle of Arrival (AoA) and Angle of Departure (AoD) techniques have been integrated to improve the accuracy of localization. The utilization of radio frequency switches between Bluetooth Low Energy (BLE) transceivers and antennas can save the cost and power consumption of BLE direction finding systems. As a result, the direction of an input signal can be determined by the measured phase difference between signals sampled from different slots. Nevertheless, due to the limitation of only one active antenna at a given time, the precision of the estimated phase difference is considerably influenced by the frequency offset of incident signals. To address this issue, our study introduces a novel method for estimating phase differences by employing the Best Linear Unbiased Estimator (BLUE). The proposed method allows for direct phase difference calculation without the requirement to estimate the frequency of the incident signals in the reference period. Consequently, our method not only eliminates phase errors caused by carrier frequency offset (CFO) but also reduces phase errors caused by carrier frequency drift (CFD). Numerical analysis demonstrates that when the signal-to-noise ratio (SNR) exceeds 7 dB, the mean square error (MSE) of our proposed method closely approximates the Cramér-Ran Lower Bound (CRLB), while maintaining a computational complexity of O(N).