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On the Convexity of Feasible QoS Regions

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2 Author(s)
Sawomir Stanczak ; Fraunhofer German-Sino Lab for Mobile Commun., Berlin ; Holger Boche

The feasible quality-of-service (QoS) region is the set of all QoS vectors that can be provided to the users by means of power control, with interference treated as noise. In an interference-limited scenario, this set is determined by the Perron root of some QoS-dependent nonnegative matrix. In a previous work, we showed that if the signal-to-interference ratio (SIR) is a log-convex function of the QoS, then the Perron root is a log-convex function. This implies convexity of the feasible QoS region. In this correspondence, we prove that the log-convexity property is also necessary for the Perron root to be convex for any choice of the (path) gain matrix. Interestingly, a significantly less restrictive property is sufficient when the gain matrix is confined to be symmetric positive semidefinite

Published in:

IEEE Transactions on Information Theory  (Volume:53 ,  Issue: 2 )