This work discusses full-dimension multiple-inputmultiple- output (FD-MIMO) technology, which is currently an active area of research and standardization in wireless communications for evolution towards Fifth Generation (5G) cellular systems. FD-MIMO utilizes an active antenna system (AAS) with a two-dimensional (2D) planar array structure, that not only allows a large number of antenna elements to be packed within feasible base station form factors but also provides the ability of adaptive electronic beamforming in the threedimensional (3D) space. However, the compact structure of largescale planar arrays drastically increases the spatial correlation in FD-MIMO systems. In order to account for its effects, the generalized spatial correlation functions for channels constituted by individual elements and overall antenna ports in the AAS are derived. Exploiting the quasi-static channel covariance matrices of users, the problem of determining the optimal downtilt weight vector for antenna ports, which maximizes the minimum signalto- interference ratio of a multi-user multiple-input-single-output system, is formulated as a fractional optimization problem. A quasi-optimal solution is obtained through the application of semi-definite relaxation and Dinkelbach’s method. Finally, the user-group specific elevation beamforming scenario is devised, which offers significant performance gains as confirmed through simulations. These results have direct application in the analysis of 5G FD-MIMO systems.