The infeasible SIR region is not a convex set

This paper deals with the geometry of a feasible SIR region, which is defined as a set of all signal-to-interference ratios that can be supported in a power-controlled wireless network when no link scheduling is involved. It was conjectured that the complement of the feasible SIR region, a so-called infeasible SIR region, is in general a convex set under a total power constraint. The conjecture was supported by some partial results and the fact that the infeasible SIR region is a convex set in the 2 dimensional case. This paper disproves this conjecture, thereby showing that the geometry of the infeasible SIR region is more complicated than it was supposed to be. The paper discusses some possible implications of these results on optimal link scheduling policies

[1]  Bernard Fino,et al.  Multiuser detection: , 1999, Ann. des Télécommunications.

[2]  Gregory J. Pottie,et al.  Channel access algorithms with active link protection for wireless communication networks with power control , 2000, TNET.

[3]  Sergio Verdu,et al.  Multiuser Detection , 1998 .

[4]  Chi Wan Sung.  Log-convexity property of the feasible SIR region in power-controlled cellular systems , 2002, IEEE Commun. Lett..

[5]  Roy D. Yates,et al.  A Framework for Uplink Power Control in Cellular Radio Systems , 1995, IEEE J. Sel. Areas Commun..

[6]  David Tse,et al.  Power control and capacity of spread spectrum wireless networks , 1999, Autom..

[7]  Slawomir Stanczak,et al.  Information theoretic approach to the Perron root of nonnegative irreducible matrices , 2004, Information Theory Workshop.

[8]  Slawomir Stanczak,et al.  Towards better understanding of medium access control for multiuser beamforming systems , 2005, IEEE Wireless Communications and Networking Conference, 2005.

[9]  Jens Zander,et al.  Distributed cochannel interference control in cellular radio systems , 1992 .

[10]  Slawomir Stanczak,et al.  Convexity of some feasible QoS regions and asymptotic behavior of the minimum total power in CDMA systems , 2004, IEEE Transactions on Communications.

[11]  Rudolf Mathar,et al.  Power control, capacity, and duality of uplink and downlink in cellular CDMA systems , 2004, IEEE Transactions on Communications.

[12]  Rene L. Cruz,et al.  Optimal routing, link scheduling and power control in multihop wireless networks , 2003, IEEE INFOCOM 2003. Twenty-second Annual Joint Conference of the IEEE Computer and Communications Societies (IEEE Cat. No.03CH37428).

[13]  Gerard J. Foschini,et al.  A simple distributed autonomous power control algorithm and its convergence , 1993 .

[14]  Slawomir Stanczak,et al.  Log-convexity of the minimum total power in CDMA systems with certain quality-of-service guaranteed , 2005, IEEE Transactions on Information Theory.