On the duality of MIMO transmission techniques for multi-user communications

Since the downlink has a difficult algebraic structure, it is more convenient to switch to the dual uplink problem which has better algebraic properties. We consider the uplink/downlink duality with respect to the mean square error (MSE), where our system model is as general as possible, i.e., we allow not only for correlations of the symbols and noise, but also model the precoders, the channels, and the equalizers as compact linear operators. We show that a duality with respect to the MSE per user is preferable to the state-of-the-art stream-wise MSE duality, since the uplink/downlink transformation of the user-wise MSE duality has a considerably lower complexity than the one of the stream-wise MSE duality. Interestingly, the uplink/downlink transformation for the total MSE duality is trivial, i.e., a simple weighting with a scalar common for all filters has to be computed. We apply the uplink/downlink duality to derive the operator form of the well-known transmit Wiener filter (TxWF).