The problem of maximizing the sum of the transmit rates while limiting the outage probability below an appropriate threshold is investigated for networks where the nodes have limited processing capabilities. We focus on CDMA wireless network whose rates are characterized under mixed Rayleigh- lognormal fading. The outage probability is given implicitly by a complex function so that solving the optimization problem requires substantial computing. In this paper, we propose a novel explicit approximation of this function that allows solving the problem in an affordable manner. We propose two solutions of the maximization problem with the simplified outage probability constraint: one solves the problem using mixed integer-real programming. The other relaxes the constraints that rates be integers yielding a standard convex programming optimization that can be solved much faster. Numerical results show that our approaches perform well for average values of the outage requirements.