Power minimization in the multiple stream MIMO Broadcast Channel with imperfect CSI

We address the design of linear precoders and receivers in a MIMO Broadcast Channel (BC) with perfect Channel State Information (CSI) at reception but partial CSI at the transmitter. Our aim is to minimize the transmit power subject to per-user rate constraints when multiple streams of data are sent to each user. We develop a gradient-projection algorithm to convert the per-user constraints into per-stream constraints. The MIMO BC linear precoders and receivers that minimize the transmit power are then obtained with an alternating optimization algorithm.