On the Stability of Distributed Power Control Algorithms Under Imperfect Estimation of Channel and Interference

The distributed power control algorithms available in this paper assume perfect estimation of interference power at the receivers and often, the availability of perfect local channel state information (CSI). However, perfect estimation of interference power or acquisition of channel information is impractical. In this paper, we consider a generic class of distributed power control algorithms and analyze the resulting performance loss when faced with errors in CSI and/or interference level estimation. We approximate such power control algorithms with linearized state space dynamics wherein the errors in the estimation of received interference or the CSI, can be modeled as additive observation noise. Based on the proposed model, we derive lower bounds on the norm of the errors in the transmit power vector and receive signal-to-interference-plus-noise ratio (SINR) vector. Our analysis suggests that when the target SINR vector approaches the Pareto-optimal bound, the errors in the transmit vectors could grow without bound. As a consequence, to maintain a performance loss within an acceptable range, either much longer estimation times or lower target SINRs are required. Our numerical results confirm the validity of our analysis and the validity of the proposed bounds.