This paper considers the optimum single cell power-control maximizing the aggregate (uplink) communication rate of the cell when there are peak power constraints at mobile users, and a low-complexity data decoder (without successive decoding) at the base station. It is shown, via the theory of majorization, that the optimum power allocation is binary, which means links are either "on" or "off". By exploiting further structure of the optimum binary power allocation, a simple polynomial-time algorithm for finding the optimum transmission power allocation is proposed. Sufficient conditions under which channel-state aware time-division-multiple-access (TDMA) maximizes the aggregate communication rate are established. Finally, a simulation study is performed and it is observed that two dominant modes of communication arise, wideband or TDMA. The heuristic algorithm that chooses the best of these two modes is observed to be extremely close to optimal.