Capacity of fading broadcast channels with transmitter ordering CSI

We derive the ergodic capacity region for a fading broadcast channel when the transmitter knows only the channel ordering information of the users and the receiver knows its transmitter-receiver channel gain and the ordering information at any time instant. We show that superposition coding based on the ordering information achieves the ergodic capacity region. Moreover, we prove that as the number of users goes to infinity, the capacity region with just transmitter ordering information is the same as the capacity region with perfect channel knowledge at the transmitter. Numerical results are provided for a Rayleigh fading channel.