A Duality Study for Fading Multiple Access / Broadcast Channels without Channel State Information at the Transmitter

In this paper, we study duality relations for the fading broadcast channel (BC) under additive white Gaussian noise and a strict ordering of the fading distributions without channel state information at the transmitter and the natural corresponding dual fading multiple-access channel (MAC). We show that if the fading distribution for the weaker user is non-deterministic, the achievable rate region using superposition coding and successive decoding and Gaussian signaling, which is conjectured to be the capacity region, is different from the dual MAC region. Duality holds only in the case of one-sided fading, where the fading distribution for the weaker user is deterministic. Despite this lack of duality, we propose to use the dual MAC in order to approximatively solve a non-convex problem for the BC. Specifically, we consider the problem of weighted sum-rate optimization for the BC and give, under some assumptions, upper bounds on the error incurred using this procedure.