Distributed Discrete Power Control in Wireless Data Networks Using Stochastic Learning

Distributed power control is an important issue in wireless networks. Recently, noncooperative game theory has been applied to investigate interesting solutions to this problem. Majority of these studies assume that the transmitter power level can take values in a continuous domain. However, recent trends such as the GSM standard and QUALCOMM’s proposal to the IS-95 standard use a finite number of discretized power levels. This motivates the need to investigate solutions for distributed discrete power control which is the primary objective of this paper. We first note that, by simply discretizing the previously proposed continuous power adaptation techniques will not suffice. This is because, a simple discretization does not guarantee convergence and uniqueness. Therefore, we propose a probabilistic power adaptation algorithm and analyze its theoretical properties along with the numerical behavior. The distributed, discrete power control problem is formulated as a N-person, non-zero sum game. In this game each user evaluates a power strategy by computing a utility value. This evaluation is performed using a stochastic iterative procedure. We approximate the discrete power control iterations by an equivalent ordinary differential equation to prove that the proposed stochastic learning power control algorithm converges to a stable Nash equilibrium. Conditions when more than one stable Nash equilibrium may exist are also studied. Experimental results are presented for several cases and compared with the continuous power level adaptation solutions.