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In this paper, we investigate the achievable coverage and the information rate of an aerial base station. The air-to-ground link is analysed by considering random fading and shadowing effects impairing the wireless transmission, together with a homogeneous spatial distribution of the terrestrial users. The distribution of the buildings in the underlying coverage region is modeled using the International Telecommunication Union-Recommendation statistical city model. For a given urban environment/region, we analytically quantify the achievable coverage probability and the information rate of users on the ground at a particular base station altitude. Furthermore, we analytically find the optimal altitude of the aerial base station to maximise the terrestrial coverage given a certain service region. Simulations are conducted to verify our analysis, and a close match between the analytical and simulation results is observed. [ABSTRACT FROM AUTHOR]