Evaluation on the stability of discrete power control algorithms

In mobile radio communication systems, the power control algorithm adjusts the power of mobile users in order to make the signal to interference ratio (SIR) higher than a predefined threshold. Distributed algorithms are devised to solve the power control problem, using locally available quantities such as measured SIR. This paper studies the effect and impact of power quantization on the stability of these algorithms. In the IS-95 1-bit power control algorithm, the power trajectory goes up and down and will never stabilize on a power level. The usual notion of convergence in continuous power control algorithm may not apply in the discrete case. We address, the problem of whether the power of each mobile user fluctuates around the desired value. A new criterion is defined to measure the stability. This criterion is applied to three discrete power control algorithms and their stabilities are compared.