On the stability of the Foschini-Miljanic algorithm with time-delays

Many of the distributed power control algorithms for wireless networks in the literature ignore the fact that while the algorithms necessitate communication among users, propagation delays exist in the network. This problem is of vital importance, since propagation delays are omnipresent in wireless networks. The Foschini-Miljanic algorithm is provably stable if there are no time-delays in the execution of the algorithm. However, since the interference measurements are fed back to the transmitter by its corresponding receiver, time-delays are inevitably introduced into the system. This work presents a more realistic version of the well known Foschini-Miljanic algorithm for distributed power control since it considers the time-delays introduced to the system due to propagation delays. In both the continuous and discrete time cases we prove global stability of the system in the presence of propagation delays.