Robustness of CDMA Power Control Against Disturbances and Time-Delays

This paper studies the robustness of a gradient-type CDMA power control algorithm with respect to disturbances and time-delays. This problem is of practical importance because unmodeled secondary interference effects from neighboring cells play the role of disturbances, and propagation delays are ubiquitous in wireless data networks. We first show L/sub p/-stability, for p/spl isin/[1, /spl infin/], with respect to additive disturbances. Then, using the L/sub /spl infin// property and a loop transformation, we prove that global asymptotic stability is preserved for sufficiently small time-delays in forward and return channels. For larger delays, we achieve global asymptotic stability by scaling down the step-size in the gradient algorithm.