K user fading broadcast channels with CSI at the receivers

For an arbitrary number of users, we examine the capacity region of fading broadcast channels with channel state known at the receivers but unknown at the transmitter. Generalizing prior work for two-user broadcast channels, we find the capacity region of the layered erasure broadcast channel. We show that weighted sum rate maximization assigns each signal level to the user that derives maximum weighted expected rate from that level. The outer bound is based on a channel enhancement that creates a sequence of degraded component channels in the order of decreasing user weights. This same approach is then used to find an outer bound to the capacity region of the fading Gaussian broadcast channels.