Optimality conditions for throughput maximization on the reverse link of a CDMA network

We consider the information-theoretic sum capacity of the reverse link of a CDMA wireless network. In particular we consider the problem of maximizing the throughput of this channel. The decision variables are the transmission powers that are allocated to the mobiles in the network. The major contribution of this paper is the derivation of thresholds that determine when it is: (a) optimal to serve only a single user; and (b) optimal to simultaneously serve multiple users. We also derive the optimal power allocations for the case where users are provided guaranteed minimum rates. Finally we provide a numerical example where we compare the gains of scheduling subsets of users at a time instead of all users simultaneously while maintaining some degree of fairness.