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In this paper, an aerial heterogeneous wireless network consists of a high altitude platform (HAP) and low altitude platforms (LAPs) as aerial base stations (ABSs) in a downlink orthogonal division multiple access (OFDMA) transmission is investigated. Two types of spectrum sharing, including spectrum underlay access (SUA) and spectrum overlay access (SOA) are employed to evaluate the inter-tier interference. Distributed problem formulation and solving method are used to reduce the computational complexity, communication overhead and system latency. Subcarrier assignment and power allocation in spectral efficiency (SE), energy efficiency (EE) and transmission power optimization problems are accomplished by the proposed two-layer algorithm. In the proposed algorithm, first, subcarrier assignment based on constraints of the optimization problems is carried out to cover both SUA and SOA with low computational complexity. Second, the proposed algorithm performs power allocation. The simulation results show the relation between spectrum reuse and inter-tier interference, such that system SE, EE and the number of served users are maximized when both spectrum reuse and inter-tier interference management are performed together.