Massive Full-Dimensional multiple-input multiple-output (FD-MIMO) base stations (BSs) have the potential to bring multiplexing and coverage gains by means of three-dimensional (3D) beamforming. Key technical challenges for their deployment include the presence of limited-resolution front ends and the acquisition of channel state information (CSI) at the BSs. This paper investigates the use of FD-MIMO BSs to provide simultaneously highrate data communication and mobile 3D positioning in the downlink. The analysis concentrates on the problem of beamforming design by accounting for imperfect CSI acquisition via Time Division Duplex (TDD)-based training and for the finite resolution of analog-to-digital converter (ADC) and digital-to-analog converter (DAC) at the BSs.Both unstructured beamforming and a low-complexity Kronecker beamforming solution are considered, where for the latter the beamforming vectors are decomposed into separate azimuth and elevation components. The proposed algorithmic solutions are based on Bussgang theorem, rank-relaxation and successive convex approximation (SCA) methods. Comprehensive numerical results demonstrate that the proposed schemes can effectively cater to both data communication and positioning services, providing only minor performance degradations as compared to the more The work of O. 2 conventional cases in which either function is implemented. Moreover, the proposed low-complexity Kronecker beamforming solutions are seen to guarantee a limited performance loss in the presence of a large number of BS antennas. Index Terms 3D beamforming, localization, full-dimensional MIMO (FD-MIMO), digital-to-analog converter (DAC), analogto-digital converter (ADC), Bussgang theorem, successive convex approximation (SCA). I. INTRODUCTION Mobile broadband communication in the New Radio (NR) physical layer of 5G systems is not only expected to increase data rate and reliability, but also to cater to new services, including proactive radio resource management, intelligent traffic systems, autonomous vehicles, Internet of Things (IoT), and device-to-device communication for disaster response and emergency relief. Services such as these can benefit from location awareness at the mobile users [1], [2]. According to [3], 5G is envisioned to attain positioning accuracy of one meter or less, outperforming existing positioning techniques such as GPS and wireless local area network (WLAN) fingerprinting-based systems. The support for positioning in Long-Term Evolution (LTE) systems has been standardized in the form of downlink observed time difference of arrival (OTDOA) in Release 9 and unlink TDOA (UTDOA) in Release 11, with additional work on dedicated signals, procedures, and requirements for vertical localization accuracy to be carried out for in Release 14, which marks the start of 5G [4]. Among the key technologies introduced to boost the spectral efficiency of 5G, the use of very large antenna arrays, or massive multiple-input multiple-output (MIMO) systems, [5]-[12] at the base stations (BSs) ...