Power allocation under noise floor uncertainty

It is well known that, when the channel state information and noise power is perfectly known, the optimal power allocation policy is given by waterfilling procedure. In this paper, we derive the necessary and sufficient conditions for optimal power allocation policy under noise power uncertainty, and express it in terms of Hilbert transformation. A two step algorithm is developed to allocate power in such a case. We then examine the consequences of such a policy in multi user power allocation problem using non-cooperative game theory and show the existence of a unique, pure, and stable Nash equilibrium. For multi user case, an iterative approach is used to allocate power to each user in a distributive manner.