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A network of n communication links operating over a shared wireless channel is considered. Power management is crucial to such interference-limited networks to improve the aggregate throughput. We consider sum-rate maximization of the network by optimum power allocation when conventional linear receivers (without interference cancellation) are utilized. It is shown that in the case of n=2 links, the optimum power allocation strategy is such that either both links use their maximum power or one of them uses its maximum power and the other keeps silent. An asymptotic analysis for large n is carried out to show that in a Rayleigh fading channel the average sum-rate scales at least as log(n). This is obtained by deriving an on-off power allocation strategy. The same scaling law is obtained in the work of Gowaikar et al., where the number of links, their end-points (source-destination pairs), and the relay nodes are optimally chosen all by a central controller. However, our proposed strategy can be implemented in a decentralized fashion for any number of links, arbitrary transmitter-receiver pairs, and without any relay nodes. It is shown that the proposed power allocation scheme is optimum among all on-off power allocation strategies in the sense that no other strategies can achieve an average sum-rate of higher order.