Cramer-Rao Lower Bounds for the Task of Joint Estimation of Signal Initial Phase and AoA in Multi-Element Antenna Arrays

In this paper, we thoroughly investigate the task of joint estimation of signal initial phase and angle-of-arrive (AoA) in multi-element antenna arrays (AA). The accurate estimation of the initial phase of the signal with simultaneous estimation of the AoA is very important and highly relevant for solving mobile objects precise positioning in 5G systems. Analytical expressions for Cramer-Rao lower bounds for the estimated signal parameters under various a priori assumptions are found and effective estimation algorithm is proposed. It is shown that the accuracy of the initial phase estimate, if it is unknown, strongly depends on the choice of the antenna element in which it is estimated, and vice versa, when the initial phase of the signal is known a priori, the choice of the base element of the AA has a significant impact on the accuracy of estimating the signal AoA. The simulation results have shown that the mean square errors of the obtained estimates achieve the Cramer-Rao bounds when SNR exceeding defined threshold values.