Bargaining Over the Fair Trade-Off Between Secrecy and Throughput in OFDM Communications

The problem of ensuring the secrecy of a communication while simultaneously maintaining sufficient throughput is a fundamental challenge facing secret communication. One of the challenges for such problems is that the optimal solution for one of objective might be not optimal for the other (e.g., an increase in secrecy might yield a decrease in throughput). Thus, there is a need for finding a trade-off solution for these objectives. In this paper, we consider a two-step approach to solve such problems and illustrate it for orthogonal frequency-division multiplexing-style communications. In the first step, we use the α-fairness criteria for formulating the tradeoff between objectives. A generalized water-filling equation for this tradeoff problem is solved. This equation includes, as a limit case, the classical case for secret communication with secrecy capacity as payoff. In the second step, we aim to find the best α-fair strategy, and show that Jain's fairness can potentially lead to an unbalanced tradeoff between the two objectives. We arrive at a more balanced tradeoff by means of bargaining over the continuum of α-fair solutions. Both the Nash and Kalai-Smorodinsky bargaining solutions for fulfillment of both objectives are found, and the algorithms for finding the bargaining solutions are derived.