Stochastic power control for wireless systems: classical and viscosity solutions

This paper considers power control for log-normal fading channels. A rate based power set point control model and an associated performance measure are introduced. Within this framework, a stochastic optimal power control law exists and the associated value function satisfies a degenerate HJB equation in a viscosity solution sense. The HJB equation is approximated by a uniformly parabolic second order equation which has a classical solution and a suboptimal control is derived. The suboptimal control is more realistic for practical implementation