Convexity of some feasible QoS regions and asymptotic behavior of the minimum total power in CDMA systems

Link scheduling and power control are efficient mechanisms to provide quality-of-service (QoS) to individual users in wireless networks. When developing optimal access-control strategies, a good understanding of the geometry of the feasible QoS region is essential. In particular, if the feasible QoS region is a convex set, the effect on scheduling is to prefer simultaneous transmission of users. Moreover, the convexity property plays a key role in the development of optimal power-control strategies. This paper provides sufficient conditions for the convexity of the feasible QoS region in systems with and without power constraints. Furthermore, we prove necessary conditions for the feasibility of QoS requirements to better understand the optimal QoS tradeoff. Finally, the paper provides insight into the interrelationship between QoS requirements and the minimum transmission power necessary to meet them. Although the results are obtained in the context of a power-controlled code-division multiple-access system, they also apply to some other communications systems. A key assumption is that there is a one-to-one relationship between a QoS parameter of interest (data rate, service delay, and etc.) and the signal-to-interference ratio at the output of a linear receiver.