Duality and Rate Optimization for Multiple Access and Broadcast Channels With Amplify-and-Forward Relays
Syed A. Jafar, Krishna Srikanth Gomadam, Chia-Chi Huang · IEEE Transactions on Information Theory · 2007
In this paper, we consider multihop multiple access (MAC) and broadcast channels (BC) where communication takes place with the assistance of relays that amplify and forward (AF) their received signals. For a two-hop parallel AF relay MAC, assuming a sum power constraint across all relays we characterize optimal relay amplification factors and the resulting optimal rate regions. We find the maximum sum rate and the maximum rate for each user in closed form and express the optimal rate pair (R1, R2) that maximizes mu1R1+mu2R2as the solution of a pair of simultaneous equations. We find that the parallel AF relay MAC with total transmit power of the two users P1+P2=P and total relay power PRis the dual of the parallel AF relay BC where the MAC source nodes become the BC destination nodes, the MAC destination node becomes the BC source node, the dual BC source transmit power is PRand the total transmit power of the AF relays is P. The duality means that the rate region of the AF relay MAC with a sum power constraint P on the transmitters is the same as that of the dual BC. The duality relationship is found to be useful in characterizing the rate region of the AF relay BC as the union of MAC rate regions. The duality is established for distributed multiple antenna AF relay nodes and multiple (more than 2) hops as well.