Fair Resource Allocation in Multiuser OFDMA Downlink with Passive Eavesdropping

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 indents 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 investigated problem is hard to be solved because of its combinatorial and nonlinear nature. Thus, optimality is discussed for two particular cases where the available power tends to infinity and zero, respectively. The optimal solution is obtained by formulating a mixed integer linear problem in the first case and a series of linear sum assignment problems in the second. In addition, two low-complexity solutions are presented which are based on decoupling the subchannel and the power allocation subproblems. Numerical results are provided to illustrate the performance of the presented solutions.