Power Allocation Over Time-Varying Multi-User Multi-Relay Amplify-and-Forward Networks

In this paper, power allocation over time-varying multi-user multi-relay amplify-and-forward networks is studied. Specifically, stochastic network sum-rate, max-min rate power allocation and total power minimization problems are formulated. However, solving such stochastic problems relies on perfect global instantaneous channel state information (CSI), and thus entails complex computations and excessive communication overheads. To circumvent these issues, second-order statistics of the CSI (i.e. partial CSI) are utilized to transform the stochastic formulations into deterministic optimization problems in terms of ergodic capacity while satisfying quality-of-service constraints via target outage probability. The obtained optimal deterministic problems are non-convex and thus are computationally prohibitive. However, at high enough signal-to-noise ratio, such problems can be transformed into asymptotically convex ones, and thus solved efficiently. Simulation results illustrate that the proposed approximate deterministic power allocation reformulations closely agree with their optimal exact deterministic and dynamic counterparts.