Compound Gaussian multiple access channels with noisy feedback

In this paper, we study the role of noisy feedback in compound Gaussian multiple access channels, where both the set of active users and their respective channels are unknown a priori. The system is modeled as a special form of two-way network, where transmitters and receivers can interact with each other to improve the overall communication efficiency, but the information flow is not bi-directional. We first characterize the compound channel capacity when there is no feedback in the system, which turns out to be simply an intersection of several capacity regions. Next, we analyze a polling, channel estimation and feedback protocol, which achieves a rate region to within log(K) bits/use of a K-user system with perfect feedback.