Computationally tractable stochastic power control laws in wireless communications

This note considers uplink power control for lognormal fading channels by a stochastic control approach. We seek approximate solutions to the Hamilton-Jacobi-Bellman (HJB) equation in terms of a local polynomial approximation, and solve a two user system for illustration. An important issue for practical systems is to reduce implementational complexity when operating in large population conditions; we show that a single user based control design may be applied to such systems for partially decentralized optimization.