Date Added: Apr 2011
This paper combines Convex analysis and Game theory to investigate the problem of maximizing the sum rate of transceivers operating in the same frequency band. In the authors' earlier work, they proved that for transceivers operating under a total power constraint, the power distribution that maximizes the sum rate lies on the boundary of the feasible set formed by the power constraint. In this paper, they first prove that for two users, the sum rate is convex on the boundary formed by the line segment representing the power constraint, and the maximum sum rate is achieved when all the power is allocated to one of the users. Obviously, such a power allocation is unfair to the other user.