In this paper, an unmanned aerial vehicles (UAV)-based heterogeneous network is studied to solve the problem of transferring massive traffic of distributed small cells to the core network. First, a detailed three-dimensional (3D) model of the downlink channel is characterized by taking into account the real antenna pattern, UAVs' vibrations, random distribution of small cell base stations (SBSs), and the position of UAVs in 3D space. Then, a rigorous analysis of interference is performed for two types pf interference: intra-cell interference and inter-cell interference. The interference analysis results are then used to derive an upper bound of outage probability on the considered system. Using numerical results show that the analytical and simulation results match one another. The results show that, in the presence of UAV's fluctuations, optimizing radiation pattern shape requires balancing an inherent tradeoff between increasing pattern gain to reduce the interference as well as to compensate large path loss at mmWave frequencies and decreasing it to alleviate the adverse effect of a UAV's vibrations. The analytical derivations enable the derivation of the optimal antenna pattern for any condition in a short time instead of using time-consuming extensive simulations.