Multi-User Uplink Power Control under Imperfect-CSI and Probabilistic Constraints

The problem of multi-cell multi-user uplink sum-power minimization with required quality of service (QoS) under imperfect Channel State Information (CSI) and Probabilistic Contraints (PrCons) is solved. This paper is an extension of our previous work on statistical-CSI and PrCons. Deterministic constraints at times are infeasible or too expensive to implement, further, the CSI could be imperfect due to limited feedback or improper channel estimation. In such cases, PrCons with low outage probability are a good substitute. To handle the PrCons, a conservative approximation of PrCons resulting in a deterministic formulation is required. In this paper, Extreme Value Theory (EVT) is combined with an Interior Point Method (IPM) to obtain the solution. EVT approach is compared with an existing method based on Bernstein-type inequality (BI). Numerical results show that EVT approach outperforms BI approach.