Rate Regions and Optimal Power Allocation for TD Fading Broadcast Channels without CSIT

We study the achievable rate region and optimal power allocation for broadcast channels (BC) under orthogonal access schemes. The channel follows a block fading model with channel side information (CSI) perfectly known at the receiver but not at the transmitter. The region boundary is determined by finding the optimal power allocation associated with all boundary points. For the two-user case, the optimal strategy balances power between the users via a Tangent Match algorithm. In a Rayleigh fading BC with more than two users, the optimal power allocation is obtained by applying the tangent match algorithm to the pair of users with the largest and smallest average channel gain, respectively.