On the convergence of fixed-step power control algorithms with binary feedback for mobile communication systems

The mobile transmitter power control algorithms that need to exchange the tract information on link gains, interference levels, or signal-to-interference ratio (SIR) between transmitters and receivers have been proved to converge to a unique fixed power allocation. However, such exact exchange requires an excessive bandwidth for signalling traffic. In practical systems, only 1 bit is sent back to each transmitter. The 0-1 binary feedback is used by the transmitter either to increase or to decrease the power level by a predetermined amount. In this study, we prove a convergence property of the binary feedback power control algorithm. Since the power level of each transmitter is changed by a fixed amount at every iteration, we cannot claim that the power converges to a fixed point. Instead, we show that the received SIR of each user falls within a certain specific range that is determined by an SIR target and a power control step-size.