Asymptotically optimal power control in CDMA with random spreading and MMSE multiuser detector

We derive two types of optimal uplink transmission power control in synchronous and asynchronous CDMA time varying fading channel with multiple user classes, random spreading sequences and MMSE multiuser detector. One optimal policy minimizes the outage probability subject to maximum average power budget and maximum transmission power constraints. The other minimizes the average power budget subject to maximum outage probability and maximum transmission power constraints. We show that for a system with a large number of users and a proportionally large processing gain, both optimal policies are threshold cut-off policies. We express the policies explicitly and show how to compute their outage probabilities.