Duality of MIMO multiple access channel and broadcast channel with amplify-and-forward relays

Authors:
Krishna S. Gomadam;Syed A. Jafar
Affiliations:
Electrical Engineering and Computer Science, University of California, Irvine, CA;Electrical Engineering and Computer Science, University of California, Irvine, CA
Venue:
IEEE Transactions on Communications
Year:
2010

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Abstract

In this work, we consider a two-hop multiuser amplify-and-forward relay network with multi-antenna nodes. The results are three-fold. First, for any relay amplification matrix D in the multiple-access channel (MAC), we show that duality holds when κD† is employed in the broadcast channel (BC), and vice versa, where κ is obtained from switching the total source and relay power constraints. Second, under a total network power constraint, we show that MAC-BC duality holds when D and D† are the relaying matrices in the MAC and BC respectively. Third, for any D in the MAC and cD† in the BC where c is any positive real scalar, MAC-BC duality under total network power constraint holds only for the above two cses.