On the Lambert-W function for CDIT-based power allocation in cooperative relay networks

In some fading environments, there may not be a feedback link sufficiently fast to convey the full channel state information (CSI) to the transmitter. This paper considers a power allocation problem for cooperative relay networks, where the transmitter node knows only the channel distribution information (CDI). The goal is to maximize the ergodic capacity. The application of the Lambert-W function to obtain a closed-form solution for the underlying power allocation problem constitutes the principal contribution of this paper. By using the Lambert-W function, power allocation can not only be expressed in closed-form but it can also quickly be determined without resorting to complex algorithms since a number of popular mathematical softwares, including Matlab, contain the Lambert-W function as an optimization component.