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.

[1]  H. Mooers,et al.  Power Control , 2020, Encyclopedia of Wireless Networks.

[2]  Emeric Deutsch,et al.  Derivatives of the Perron root at an essentially nonnegative matrix and the group inverse of an M-matrix☆ , 1984 .

[3]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

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

[5]  Dimitri P. Bertsekas,et al.  Data Networks , 1986 .

[6]  Eytan Modiano,et al.  Dynamic power allocation and routing for time varying wireless networks , 2003, IEEE INFOCOM 2003. Twenty-second Annual Joint Conference of the IEEE Computer and Communications Societies (IEEE Cat. No.03CH37428).

[7]  H. Boche,et al.  Iterative algorithm for finding optimal resource allocations in symbol-asynchronous CDMA channels with different SIR requirements , 2002, Conference Record of the Thirty-Sixth Asilomar Conference on Signals, Systems and Computers, 2002..

[8]  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).

[9]  Lijun Qian,et al.  Uplink Scheduling in CDMA Packet-Data Systems , 2006, Wirel. Networks.

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

[11]  H. Boche,et al.  Characterization of optimal resource allocation in cellular networks , 2004, IEEE 5th Workshop on Signal Processing Advances in Wireless Communications, 2004..

[12]  Slawomir Stanczak,et al.  Log-convexity of minimal feasible total power in CDMA channels , 2003, 14th IEEE Proceedings on Personal, Indoor and Mobile Radio Communications, 2003. PIMRC 2003..

[13]  Valerie Isham,et al.  Non‐Negative Matrices and Markov Chains , 1983 .

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