Power Control in Networks With Heterogeneous Users: A Quasi-Variational Inequality Approach

• Published in: IEEE transactions on signal processing Vol. 63; no. 21; pp. 5691 - 5705
• Main Authors: Stupia, Ivan, Sanguinetti, Luca, Bacci, Giacomo, Vandendorpe, Luc
• Format: Journal Article
• Language: English
• Published: New York IEEE 01-11-2015; The Institute of Electrical and Electronics Engineers, Inc. (IEEE); Institute of Electrical and Electronics Engineers
• Subjects: Algorithms; Centralized power control; distributed power control; Economic models; energy efficiency maximization; Engineering Sciences; Game theory; Games; heterogeneous users; Inequalities; Interference; Mathematical analysis; Mathematical models; Mathematics; Nash equilibria; Networks; Power control; quasi-variational inequality; Radio transmitters; Receivers; Resource management; spectral efficiency maximization; Statistics; Wireless communication; Index Terms—Nash equilibria; centralized power control; spectral efficiency maximization; quasi-variational inequality; energy efficiency maximization; dis-tributed power control; heterogeneous users
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2015.2452231

This paper deals with the power allocation problem in a multipoint-to-multipoint network, which is heterogenous in the sense that each transmit and receiver pair can arbitrarily choose whether to selfishly maximize its own rate or energy efficiency. This is achieved by modeling the transmit and receiver pairs as rational players that engage in a noncooperative game in which the utility function changes according to each player's nature. The underlying game is reformulated as a quasi variational inequality (QVI) problem using convex fractional program theory. The equivalence between the QVI and the noncooperative game provides us with all the mathematical tools to study the uniqueness of its Nash equilibrium points and to derive novel algorithms that allow the network to converge to these points in an iterative manner, both with and without the need for a centralized processing. Numerical results are used to validate the proposed solutions in different operating conditions.