Power Control By Geometric Programming

• Published in: IEEE transactions on wireless communications Vol. 6; no. 7; pp. 2640 - 2651
• Main Authors: Chiang, M., Chee Wei Tan, Palomar, D.P., O'Neill, D., Julian, D.
• Format: Journal Article
• Language: English
• Published: Piscataway, NJ IEEE 01.07.2007; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Access methods and protocols, osi model; Ad hoc networks; Admission control; Algorithms; Applied sciences; CDMA power control; Cellular; Cellular networks; Constraint optimization; Convex optimization; Distributed algorithms; Exact sciences and technology; Interference constraints; Mathematical models; Nonlinearity; Operation, maintenance, reliability; Optimization; Power control; Programming; Quality of service; Robustness; Studies; Systems, networks and services of telecommunications; Telecommunications; Telecommunications and information theory; Teleprocessing networks. Isdn; Throughput; Transmission and modulation (techniques and equipments); Wireless communication; Wireless networks; Access control; Non convex programming; CDMA power control; Wireless telecommunication; Information rate; Convex programming; Successive approximation; Convex optimization; Pricing; Delay time; Ad hoc network; Distributed algorithms; Outage; Nonlinear problems; Signal to interference ratio; Information transmission; Constrained optimization; Algorithm performance; Power control; Optimal solution; Code division multiple access; Distributed algorithm; Heuristic method; Numerical simulation; Service quality
• ISSN: 1536-1276; 1558-2248
• DOI: 10.1109/TWC.2007.05960

In wireless cellular or ad hoc networks where Quality of Service (QoS) is interference-limited, a variety of power control problems can be formulated as nonlinear optimization with a system-wide objective, e.g., maximizing the total system throughput or the worst user throughput, subject to QoS constraints from individual users, e.g., on data rate, delay, and outage probability. We show that in the high Signal-to- interference Ratios (SIR) regime, these nonlinear and apparently difficult, nonconvex optimization problems can be transformed into convex optimization problems in the form of geometric programming; hence they can be very efficiently solved for global optimality even with a large number of users. In the medium to low SIR regime, some of these constrained nonlinear optimization of power control cannot be turned into tractable convex formulations, but a heuristic can be used to compute in most cases the optimal solution by solving a series of geometric programs through the approach of successive convex approximation. While efficient and robust algorithms have been extensively studied for centralized solutions of geometric programs, distributed algorithms have not been explored before. We present a systematic method of distributed algorithms for power control that is geometric-programming-based. These techniques for power control, together with their implications to admission control and pricing in wireless networks, are illustrated through several numerical examples.