Maximizing the Minimum Achievable Secrecy Rate for a Two-User Gaussian Weak Interference Channel

This paper is a study of the Gaussian weak interference channel in which two single-antenna sources aim to send their messages to legitimate destinations such that all messages are kept confidential from non-intended receivers. Under the Gaussian codebook assumption, the problem of secrecy rate balancing with the objective of exploring the optimal power allocation policy at the sources in an attempt to maximize the minimum achievable secrecy rate is investigated, assuming each source is subject to a transmit power constraint. It is shown that at the optimal point, the two secrecy rates are equal; hence, the problem is abstracted to maximize the secrecy rate associated with one destination, while the other is restricted to having the same secrecy rate. The optimum secrecy rate associated with the investigated max-min problem is analytically derived, leading to the solution of the secrecy rate balancing problem. An additional scenario is considered in which sources can transmit artificial noise in addition to their signals. In this case, the max-min problem is solved and a suboptimal solution is provided. Numerical results show that the proposed solution is near-optimal and can be used as a suitable alternative.