Capacity and optimal resource allocation for fading broadcast channels-Part II: Outage capacity

In this two-part paper, we study three capacity regions for fading broadcast channels and obtain their corresponding optimal resource allocation strategies: the ergodic (Shannon) capacity region, the zero-outage capacity region, and the capacity region with outage. In Part I, we obtained the ergodic capacity region of the fading broadcast channel under different spectrum-sharing techniques. In this paper, we derive the outage capacity regions of fading broadcast channels, assuming that both the transmitter and the receivers have perfect channel side information. These capacity regions and the associate optimal resource allocation policies are obtained for code division (CD) with and without successive decoding, for time division (TD), and for frequency division (FD). We show that in an M-user broadcast system, the outage capacity region is implicitly obtained by deriving the outage probability region for a given rate vector. Given the required rate of each user, we find a strategy which bounds the outage probability region for different spectrum-sharing techniques. The corresponding optimal power allocation scheme is a multiuser generalization of the threshold-decision rule for a single-user fading channel. Also discussed is a simpler minimum common outage probability problem under the assumption that the broadcast channel is either not used at all when fading is severe or used simultaneously for all users. Numerical results for the different outage capacity regions are obtained for the Nakagami-m fading model.