Stochastic power control for cellular radio systems

For wireless communication systems, iterative power control algorithms have been proposed to minimize the transmitter power while maintaining reliable communication between mobiles and base stations. To derive deterministic convergence results, these algorithms require perfect measurements of one or more of the following parameters: (1) the mobile's signal-to-interference ratio (SIR) at the receiver; (2) the interference experienced by the mobile; and (3) the bit-error rate. However, these quantities are often difficult to measure and deterministic convergence results neglect the effect of stochastic measurements. We develop distributed iterative power control algorithms that use readily available measurements. Two classes of power control algorithms are proposed. Since the measurements are random, the proposed algorithms evolve stochastically and we define the convergence in terms of the mean-squared error (MSE) of the power vector from the optimal power vector that is the solution of a feasible deterministic power control problem. For the first class of power control algorithms using fixed step size sequences, we obtain finite lower and upper bounds for the MSE by appropriate selection of the step size. We also show that these bounds go to zero, implying convergence in the MSE sense, as the step size goes to zero. For the second class of power control algorithms, which are based on the stochastic approximations method and use time-varying step size sequences, we prove that the MSE goes to zero. Both classes of algorithms are distributed in the sense that each user needs only to know its own channel gain to its assigned base station and its own matched filter output at its assigned base station to update its power.