Optimal Linear Precoding Strategies for Wideband Non-Cooperative Systems based on Game Theory-Part I: Nash Equilibria
In this paper, we study the joint rate and multi-channel power allocations in spectrum sharing networks (SSNs) with balanced QoS provisioning and power saving. We formulate this cross layer problem as a non-cooperative game <i>G</i><sub><i>JRPA</i></sub> in which each user aims to achieve its target data rate as exactly as possible and minimize its power consumption at the same time. We investigate the properties of Nash equilibrium (N.E.) for <i>G</i><sub><i>JRPA</i></sub>, including its existence, and properties of QoS provisioning as well as power saving. With the decomposition technique, we propose a distributed algorithm to find the N.E. for <i>G</i><sub><i>JRPA</i></sub> from any feasible initialization and provide a sufficient condition for its convergence. Simulation results are presented to show the validity of our proposed algorithm. Performance tradeoff between QoS provisioning and power saving are investigated via tuning the weighting factors. Besides, advantages of our <i>G</i><sub><i>JRPA</i></sub> over conventional iterative water filling (IWF) are also analyzed.