Joint power allocation for OFDM system with cooperation at the transmitters

It is known that traditional water-filling (WF) provides a closed form solution for capacity maximization in orthogonal frequency division multiplex (OFDM) system. The solution is derived from a maximum mutual information argument with a single transmitter. Motivated by the novel technology of cooperative communication, we consider a new power allocation problem for OFDM systems with two cooperative transmitters, where each transmitter has an individual power constraint and can obtain their own perfect channel state information (CSI). The transmitters first cooperate by sharing the CSI, and then jointly optimize power allocation in the metric of sum throughput, which can be modeled as a non-convex constrained optimization problem. Through an application of Karush-Kuhn-Tucker conditions, the problem is reformulated as a convex one. Then, the closed form solution is derived with the nature of traditional WF as well as cooperative properties. Based on the derived solution, an iteration algorithm for joint water level is given for the first time, which can be explained as a cooperative WF relative to the traditional WF. Motivated by the deriving process, we extend parts of the conclusion to N-transmitter case. Numerical results are presented to evaluate the optimal power allocation scheme in OFDM cellular system. For comparison, we also evaluate the traditional non-cooperative WF and equal power allocation scheme.