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

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 ¿D¿ is employed in the broadcast channel (BC), and vice versa, where re 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 cases.

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