In this paper, we study the problem of resource allocation for a multiuser orthogonal frequency-division multiple access (OFDMA) downlink with eavesdropping. The considered setup consists of a base station, several users, and a single eavesdropper that intends to wiretap the transmitted message within each OFDMA subchannel. By taking into consideration the existence of the eavesdropper, the base station aims to assign subchannels and allocate the available power in order to optimize the max-min fairness criterion over the users’ secrecy rate. The considered problem is a mixed integer nonlinear program. For a fixed subchannel assignment, the optimal power allocation is obtained by developing an algorithm of polynomial computational complexity. In the general case, the problem is investigated from two different perspectives due to its combinatorial nature. In the first, the number of users is equal or higher than the number of subchannels, whereas in the second, the number of users is less than the number of subchannels.
In the first case, we provide the optimal solution in polynomial time by transforming the original problem into an assignment one for which there are polynomial time algorithms. In the second case, the secrecy rate formula is linearly approximated and the problem is transformed to a mixed integer linear program, which is solved by a branch-and-bound algorithm. Moreover, optimality is discussed for two particular cases where the available power tends to infinity and zero, respectively. Based on the resulting insights, three heuristic schemes of polynomial complexity are proposed, offering a better balance between performance and complexity. Simulation results demonstrate that each one of these schemes achieves its highest performance at a different power regime of the system.