CDMA uplink power control as a noncooperative game

IEEE/ACM Transactions on Networking, 2005

We propose a new algorithm for distributed power control in cellular communication systems. We define a cost for each mobile that consists of a weighted sum of power and signal-tointerference ratio (SIR) error and obtain the static Nash equilibrium for the resulting costs. The algorithm requires only interference power measurements and/or SIR measurements from the base station, and converges even in cases where limits on available power render the target SIR's unattainable. Simulations of a CDMA wireless network demonstrate that in demanding environments, the Nash equilibrium power provides substantial power savings over the power balancing solution, while reducing achieved SIR only slightly. Additional simulations show that the benefit of the equilibrium power control over the power balancing solution increases as receiver noise power or number of users in the cell increases. The algorithm has the advantage that it can be implemented distributively. An additional benefit of the algorithm is that, based on their chosen cost function, mobiles may choose to "opt out", i.e. stop transmitting, if they determine that the power required to achieve their SIR objective is exceeds its cost of not transmitting.

IEEE Vehicular Technology Conference, 2006

This paper presents a new pricing function for noncooperative power control game in a single cell CDMA data network. Considering a utility function for each terminal, the purpose of power control in wireless data networks is to maximize network utility. In the proposed game, the pricing function is a linear function of the terminal's Signal to Interference plus Noise Ratio (SINR). We first prove that the new game is a supermodular game and then we show the strategy space of the new game is such that it is possible to reach better equilibrium point compared to pricing function based on terminal's power. Simulation results show that the game with the proposed pricing function can improve the utility and power consumption of the terminals at equilibrium.

2008 IEEE/ACS International Conference on Computer Systems and Applications, 2008

Our goal in this paper is to study the performance of the game-theoretic power control algorithms for wireless data introduced by Saraydar et al in two realistic channels: (a1) Fast flat fading channel and (a2) Slow flat fading channel. The fading coefficients under both (a1) and (a2) are studied under an appropriate small scale channel model that is used in the CDMA cellular systems, namely Nakagami channel model. To do so, we derive a closedform expression of the average utility function which represents the number of bits received correctly at the receiver per one Joule expended. Then, using this expression we study the existence, uniqueness of Nash equilibrium (NE), and the social desirability of NE in the Pareto sense.

Proceedings of SPIE, 2003

In wireless communication systems, each user's signal contributes to the interference seen by the other users. Given limited available battery power, this creates a need for effective and efficient power control strategies. These strategies may be designed to achieve quality of service (QoS) or system capacity objectives, or both. We show how the power control problem is naturally suited to formulation as a noncooperative game in which users choose to trade off between signal-to-interference ratio (SIR) error and power usage. Koskie (2003) studied the static Nash game formulation of this problem. The solution obtained led to a system of nonlinear algebraic equations. In this paper we present a novel distributed power control strategy based on the Newton iteration used to solve the corresponding algebraic equations. That method accelerates the convergence of the Nash game algorithm owing to the quadratic convergence of the Newton iterations. A numerical example demonstrates the efficiency of the new algorithm.

IEEE Transactions on Wireless Communications, 2000

We present a game-theoretic treatment of distributed power control in CDMA wireless systems using outage probabilities. We first prove that the noncooperative power control game considered admits a unique Nash equilibrium (NE) for uniformly strictly convex pricing functions and under some technical assumptions on the SIR threshold levels. We then analyze global convergence of continuous-time as well as discrete-time synchronous and asynchronous iterative power update algorithms to the unique NE of the game. Furthermore, we show that a stochastic version of the discrete-time update scheme, which models the uncertainty due to quantization and estimation errors, converges almost surely to the unique NE point. We finally investigate and demonstrate the convergence and robustness properties of these update schemes through simulation studies.

2007 IEEE International Conference on Signal Processing and Communications, 2007

In this paper, We formulate the SINR-constrained power allocation problem in the wideband Multiantenna CDMA cellular system as a game. Using the cooperative theory and Nash bargaining model, we compared it to the noncooperative game scheme proposed in (S. Koskie, Z. Gajic, IEEE trans. on Networking, 2005). We define a utility function which considers both power usage and QoS. We show that the resulting operating point using Nash bargaining model is fair and Pareto optimal, however, the Nash equilibrium operating point obtained in the noncooperative game scheme is not in general Pareto optimal. Also, we proposed a centralized power control algorithm based on conjugate gradient algorithm for multiantenna CDMA cellular systems, when the transmitted power and SINR which each user experience is constrained. In addition, we can extend the result to a fair rate optimization in a multiuser multiple antenna regime through a power control problem subject to SINR constraints.

IEEE International Symposium on Personal, Indoor and Mobile Radio Communications, 2007

In this paper, we formulate the SINR-constrained power control problem in the wideband CDMA cellular system as a game. Using the cooperative theory and Nash bargaining model, we compared it to the non-cooperative game scheme proposed in (S. Koskie and Z. Gajic, 2005). We show that the resulting operating point using Nash bargaining model is fair and Pareto optimal, however, the Nash equilibrium operating point obtained in the non-cooperative game scheme is not in general Pareto optimal.

Performance and Control of Next-Generation Communications Networks, 2003

In wireless communication systems, each user's signal contributes to the interference seen by the other users. Given limited available battery power, this creates a need for effective and efficient power control strategies. These strategies may be designed to achieve quality of service (QoS) or system capacity objectives, or both. We show how the power control problem is naturally suited to formulation as a noncooperative game in which users choose to trade off between signal-to-interference ratio (SIR) error and power usage. Koskie (2003) studied the static Nash game formulation of this problem. The solution obtained led to a system of nonlinear algebraic equations. In this paper we present a novel distributed power control strategy based on the Newton iteration used to solve the corresponding algebraic equations. That method accelerates the convergence of the Nash game algorithm owing to the quadratic convergence of the Newton iterations. A numerical example demonstrates the efficiency of the new algorithm.

61st IEEE Vehicular Technology Conference, Vol. 1, Stockholm, Sweden, pp. 314 - 318, 30 May-1 June 2005, 2005

In this paper we present an analysis of power control algorithms established over the past decade for cellular telephone systems, in conjunction with utility functions introduced recently to specify quality of service in wireless systems providing data services. These algorithms are compared with power control algorithms based on game theory established relatively recently. The analysis shows that the Nash equilibrium points to which the game theory based algorithms for power control converge are not efficient, and that better solutions are possible.

IEEE Antennas and Propagation Magazine, 2000

In wireless cellular communication, it is essential to find effective means for power control of signals received from randomly dispersed users within one cell. Effective power control will heavily impact the system capacity. Distributed power control (DPC) is a natural choice for such purposes, because, unlike centralized power control, DPC does not require extensive computational power. Distributed power control should be able to adjust the power levels of each transmitted signal using only local measurements, so that, in a reasonable time, all users will maintain the desired signal-to-interference ratio. In this paper, we review different approaches for power control, focusing on CDMA systems. We also introduce state-space methods and linear quadratic power control (LQPC) to solve the power-control problem. A simulation environment was developed to compare LQPC with earlier approaches. The results show that LQPC is more effective, and is capable of computing the desired transmission power of each mobile station in fewer iterations, as well as being able to accommodate more users in the system.