Concavity of the Feasible Signal-to-Noise Ratio Region in Power Control Problems

Signal-to-noise (SNR) ratio is commonly regarded as a reliable performance measure for wireless communication systems. Knowledge of fundamental properties of the feasible SNR region can facilitate the performance optimization of multi-user wireless systems. This paper examines the concavity of the feasible SNR region. In particular, it is shown that for systems with only three users, the feasible SNR region is always concave. As concavity for 2-D systems is well known and concavity for 4-D systems does not hold in general, this result fills in a gap on this issue. A concavity result for systems with a general number of users is also established under certain technical conditions.