TY - GEN
T1 - Strict log-convexity of the minimum power vector
AU - Stańczak, Sławomir
AU - Boche, Holger
AU - Wiczanowski, Marcin
PY - 2006
Y1 - 2006
N2 - In a previous work, it was shown that the l1-norm of the minimum power vector is log-convex if the signal-tointerference ratio (SIR) is establish log-convex function of the quality-of-service (QoS) value of interest. Assuming irreducibility of the gain matrix, the ll-norm was further shown to be strictly log-convex in two special cases of SIR-QoS functions. In this paper, we extend this result in two directions: First, we drop the requirement on irreducibility of the gain matrix and, secondly, we consider any log-convex SIR-QoS relationship. Finally, we point out a connection of these results to strong convexity of a utility-based power control problem.
AB - In a previous work, it was shown that the l1-norm of the minimum power vector is log-convex if the signal-tointerference ratio (SIR) is establish log-convex function of the quality-of-service (QoS) value of interest. Assuming irreducibility of the gain matrix, the ll-norm was further shown to be strictly log-convex in two special cases of SIR-QoS functions. In this paper, we extend this result in two directions: First, we drop the requirement on irreducibility of the gain matrix and, secondly, we consider any log-convex SIR-QoS relationship. Finally, we point out a connection of these results to strong convexity of a utility-based power control problem.
UR - http://www.scopus.com/inward/record.url?scp=39049158325&partnerID=8YFLogxK
U2 - 10.1109/ISIT.2006.262054
DO - 10.1109/ISIT.2006.262054
M3 - Conference contribution
AN - SCOPUS:39049158325
SN - 1424405041
SN - 9781424405046
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 2471
EP - 2475
BT - Proceedings - 2006 IEEE International Symposium on Information Theory, ISIT 2006
T2 - 2006 IEEE International Symposium on Information Theory, ISIT 2006
Y2 - 9 July 2006 through 14 July 2006
ER -