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In this paper, we investigate the downlink transmission for full-dimension multiple-input multiple-output (FD-MIMO) systems over correlated Rician fading channels. With only statistical channel state information at the BS, the beamforming vectors of each user are decoupled from each other through the maximization of average signal-to-leakage-plus-noise ratio (SLNR) lower bound, and the optimal beamforming vector which involves the line-of-sight component and correlation matrix of both directions is derived. To reduce the time of acquiring the beamforming vector for each user, a deep learning (DL)-based algorithm is proposed. A sub-optimal analytical beamforming algorithm is also proposed for comparison. Based on the proposed beamforming method, the ergodic rate of each user is analyzed and simple closed-form approximations are derived, which are very useful in evaluating the system performance and …