Solving binary and continuous knapsack problems for radio resource allocation over High Altitude Platforms

In this paper, radio resource allocation for multicasting in OFDMA based High Altitude Platforms is considered. An optimization problem for the model described in the paper is formulated which turns out to be a Mixed Integer Non-Linear Program. Due to its high complexity, we use Lagrangian relaxation to dualize some constraint sets. The Lagrangian relaxed problem is then decomposed into two Lagrangian subproblems, one is a binary knapsack Lagrangian subproblem (BKLSP) and the other is continuous knapsack Lagrangian subproblem (CKLSP). The BKLSP is responsible for the assignment of the OFDMA subchannels and time slots to multicast sessions as well as user assignment to the multicast groups in a particular frame. The CKLSP is responsible for HAP power allocation to multicast sessions in the HAP service area. The two subproblems can be solved iteratively in search for a better solution, if there is any, for the Lagrangian problem. For the BKLSP we use two different solution algorithms, one based on dynamic programming and the other is a greedy algorithm. A greedy algorithm is also used for the CKLSP. The entire approach can be used to obtain bounds in a branch and bound algorithm for each of its nodes.