Asymptotically optimal transmission power and rate control for CDMA channels with multiple user classes

An asymptotically combined optimal transmission power and rate control policy is derived for a DS-CDMA time varying fading channel with multiple user classes, random spreading codes and a linear MMSE multiuser detector. The rigorous optimization problem is presented as a non-convex constrained program explicitly solved in a closed-form given by a function of a single Lagrangian multiplier. The optimal multiplier is derived by a low number of independent bisection searches for a zero, where each search is done in a single-valued function. The optimal control policy is demonstrated by an application, where the transmission power is adapted to the channel fade variations, and the transmission rates are adapted to the tier in which the mobile is located. The effect of the number of tiers on the optimal transmission rate is presented in an environment with lognormal and Rayleigh fading.