On MAC-BC Duality of Multihop MIMO Relay Channel with Imperfect Channel Knowledge

Abstract

In this paper, we establish the signal-to-interference-noise ratio (SINR) duality between multipleaccess (MAC) and broadcast (BC) multihop amplify-and-forward (AF) multiple-input multiple-output(MIMO) relay systems under an imperfect channel state model, which is a generalization of severalpreviously established MAC-BC duality results. We show that identical SINRs in the MAC and BCsystems can be achieved by two approaches. The first one is to use the Hermitian transposed MACrelay amplifying matrices at the relay nodes in the BC system, under the same total network transmission power constraint. The second one is to use the scaled and Hermitian transposed MAC relay amplifying matrices in the BC system, under the transmission power constraint at each node of the system, where the scaling factors are obtained by swapping the power constraints of the nodes in the MAC system. Moreover, we derive the MAC-BC mean-squared error (MSE) and capacity duality properties based on the SINR duality. Numerical results show the utility of the duality results established.