MSE duality for multi-user MIMO relay system

This paper shows how uplink (UL)-downlink (DL) mean square error (MSE) duality holds in a single relay aided multi-user multiple-input multiple-output (MU-MIMO) system. Specifically, it is shown that the MSE duality holds for three levels of MSE which are sum-MSE (SMSE), per user MSE, and per stream MSE. For each case of duality level, we consider both total power constraint and separate power constraint. We also provide a conversion method which transforms a given transceiver and scale factor in DL to equivalent ones in UL for each case of duality level and each case of power constraint.