Linear Relaying for the Gaussian multiple-access and broadcast channels

Linear relaying (LR) is the extension of amplify-and-forward to full-duplex operation, and consists of relay nodes transmitting (on every channel use) a linear combination of previously received signals. From a practical standpoint, it is one of the most profitable and easily deployed forwarding techniques, as only requires buffering and amplifying capabilities. In this paper, we propose to use it at multiple relays in order to enlarge the capacity region of single-antenna multiple-access (MAC) and broadcast channels (BC). Relays are assumed to be fixed, and without own data to transmit. The first part of our contribution is devoted to the MAC. Assuming channel awareness at the users and destination, the achievable rate region with LR is derived, and iterative algorithms are devised to compute the maximum sum-rate (SR) and weighted sum-rate (WSR). From both maximizations, the sources´ temporal correlation to attain the boundary points of the region is obtained. In the second part, the BC with LR is studied. Its rate region, achievable through dirty paper coding, is shown to be equal to that of the MAC with a sum-power constraint. As a result, we demonstrate that MACBC duality holds. Making use of duality, iterative algorithms to compute the SR and WSR of the BC are presented.