We present a unified system model and framework for the analytical performance study of two heterogeneous and physically-distinct, but coexisting, networks that work harmoniously at the same time, space, and frequency domains. The two-tier network model considered in this paper is an overlaying of femtocells on a macrocell. Overlaying femtocells improves the performance by offloading traffic from macrocells and providing spatial diversity. The mmWave channel model employed considers the number of clusters and rays within each cluster to vary due to the end-user mobility. This is a new and different model compared to the widely used channel models for mmWave two-tier networks. Optimal power control is formulated as a sum-rate maximization problem for downlink and uplink transmissions at two-tier networks and a power allocation scheme is proposed by following Shannon-Hartley theorem. A comprehensive and interesting performance investigation is provided, where it is shown that the upper bound on the number of admitted secondary users has a linear relationship with the outage probability threshold, logarithmic relationship with SINR and exponential relationship with channel gain factors. Simulation results show that the proposed scheme with algorithm 2 is very effective at managing the cross-tier interference and can outperform a competitive scheme from literature that is based on cognitive radio technology. The computational complexity analysis of proposed algorithms are also given, since the complexity of algorithm 2 can be a performance-complexity trade-off issue for systems with limited computation power and time requirements.
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