Capacity Region and Capacity-Achieving Signaling Schemes for 1-bit ADC Multiple Access Channels in Rayleigh Fading

This paper investigates the capacity region and detailed characterizations of capacity-achieving signaling schemes of a multiple access channel (MAC) with two users communicating to a base station (BS) equipped with 1-bit quantizers. We consider Rayleigh fading channels where channel state information (CSI) is known only at BS. Towards this end, we first study the weighted sum-rate maximization problem over the set of input distributions of one user for a fixed input signal at another user. By examining a necessary and sufficient Kuhn-Tucker condition (KTC) for an input to be optimal, it is first shown that the power constraint is active, i.e., the equality in the power constraint is achieved. By further exploiting novel bounds on the output distribution functions, the optimal distribution is shown to have a bounded amplitude. In the next step, we prove that if a fixed input with bounded amplitude is used at one user, the other user also needs to use a bounded amplitude signal to maximize the weighted sum-rate. To effectively analyze the KTC, our approach is to divide the domain of fading into two disjoint regions and examine the region with non-zero measure. It is then concluded that any boundary point in the capacity region is achieved by using bounded amplitude signals, and they are \pi /2 circularly symmetric. Building upon these results, we turn our focus to the sum-capacity segment, and demonstrate that any \pi /2 circularly symmetric input distribution having a constant amplitude is sum-capacity achieving. The sum-capacity can then be established.