Optimizing radio resources for multicasting on high-altitude platforms

High-altitude platforms (HAPs) are quasi-stationary aerial wireless communications platforms meant to be located in the stratosphere, to provide wireless communications and broadband services. They have the ability to fly on demand to temporarily or permanently serve regions with unavailable infrastructure. In this paper, we consider the development of an efficient method for resource allocation and controlling user admissions to multicast groups in a HAP system. Power, frequency, space and time domains are considered in the problem. The combination of these many aspects of the problem in multicasting over an OFDMA HAP system were not, to the best of our knowledge, addressed before. Due to the strong dependence of the total number of users that could join different multicast groups on the possible ways we may allocate resources to the different multicast groups, it is important to consider a joint user to multicast group assignments and radio resource management across the groups. From the service provider's point of view, it would be in its best interest to be able to admit as many users as possible, while satisfying their quality of service requirements. The problem turns out to be a mixed integer non-convex non-linear program for which branch and bound solution framework is guaranteed to solve the problem. Branch and bound (BnB) can be also used to obtain sub-optimal solutions with desired quality. Even though branch and bound is guaranteed to find the optimal solution, the computational cost could be extremely high, which is why we considered different types of enhancements to BnB. Mainly, we consider reformulations by linearizing a specific set of quadratic constraints in the derived formulation, as well as the application of different branching techniques to find the one that performs the best. Based on the conducted numerical experiments, it was concluded that linearization, applied for at least 100 presolving rounds, and cloud branching achieve the best performance.