Power Control and Multiuser Diversity for the Distributed Cognitive Uplink

This paper studies optimum power control and sum-rate scaling laws for the distributed cognitive uplink. It is first shown that the optimum distributed power control policy is in the form of a threshold based water-filling power control. Each secondary user executes the derived power control policy in a distributed fashion by using local knowledge of its direct and interference channel gains such that the resulting aggregate (average) interference does not disrupt primary's communication. Then, the tight sum-rate scaling laws are derived as a function of the number of secondary users $N$ under the optimum distributed power control policy. The fading models considered to derive sum-rate scaling laws are general enough to include Rayleigh, Rician and Nakagami fading models as special cases. When transmissions of secondary users are limited by both transmission and interference power constraints, it is shown that the secondary network sum-rate scales according to $\frac{1}{\e{}nh}\log\logp{N}$, where $nh$ is a parameter obtained from the distribution of direct channel power gains. For the case of transmissions limited only by interference constraints, on the other hand, the secondary network sum-rate scales according to $\frac{1}{\e{}\gammag}\logp{N}$, where $\gammag$ is a parameter obtained from the distribution of interference channel power gains. These results indicate that the distributed cognitive uplink is able to achieve throughput scaling behavior similar to that of the centralized cognitive uplink up to a pre-log multiplier $\frac{1}{\e{}}$, whilst primary's quality-of-service requirements are met. The factor $\frac{1}{\e{}}$ can be interpreted as the cost of distributed implementation of the cognitive uplink.