Efficient power control over fading channels

This paper introduces a novel concept of efficient power control in nonergodic fading channels. We use the risk-reward approach to quantitatively describe the performance of power control schemes. A power control scheme is said to be efficient if it minimizes the risk for a given level of reward. The reward and risk are measured, respectively, as the expected value of the link spectral efficiency in excess of some predefined target value and the below-target semideviation of the link spectral efficiency distribution. Furthermore, we introduce a novel fundamental limit on the performance of adaptive power control schemes. The new fundamental limit, which we call the efficient frontier, is the set of all efficient power control schemes. We analytically derive the adaptive power control rule that achieves the fundamental limit. We show that no power control scheme can be constructed with the performance above the efficient frontier. The numerical results suggest that various state-of-the-art power control schemes are suboptimal, i.e., their risk-reward performance is below the efficient frontier.