MIMO BC/MAC MSE duality with imperfect transmitter and perfect receiver CSI

A mean square error (MSE) duality between the multiple-input multiple-output (MIMO) broadcast channel (BC) and the MIMO multiple access channel (MAC) is proposed,where the transmitter has partial or even only statistical knowledge of the channels and the receivers have complete channel state information (CSI). The dual MIMO MAC has transmitters with full CSI, whereas the receiver has partial CSI or only statistical channel knowledge. The duality connects the average user MSEs of the two channels conditioned on the CSI of the transmitter in the BC and can be used to solve MIMO BC average MSE problems, as is demonstrated for the special case of a MIMO BC average sum MSE minimization with a transmitter having only partial CSI.