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We study the problem of channel uncertainty on wireless transmissions from different users with mutual interference. Specifically, the channel gains from the transmitters to the receivers are available only through their mean and covariance rather than complete distributions. Our goal is to maximize the energy efficiency among all transmitter-receiver pairs while guaranteeing their capacity requirements. For this problem, we employ chance-constrained programming (CCP), which allows occasional violation of target capacity threshold as long as the probability of such violation is below a small tolerable constant (risk level). We propose a solution based on a novel reformulation technique that converts the original CCP into a deterministic optimization problem without relaxation errors. Then the deterministic optimization problem is approximated into a Geometric Program (GP) based on tight polynomial approximations …