Weighted ergodic sum-rate maximisation in uplink orthogonal frequency division multiple access and its achievable rate region

The weighted ergodic sum-rate maximisation problem subject to per-user power and rate constraints in the orthogonal frequency division multiple access uplink is formulated and solved. The solution is found via dual optimisation techniques, and the duality gap between the primal and dual solutions is analysed. Ergodicity allows taking advantage of the temporal dimension in addition to the frequency and multiuser dimensions. The per-user rate constraints allow an improved fairness level in the system. The achievable rate region of the weighted ergodic sum-rate maximisation problem is determined, and the effect of the per-user rate constraints on this region is studied. Offline and online iterative techniques to obtain the Lagrangian parameters are presented, and the results show that online iterations converge to the offline solution within a limited time.