  We consider linear precoding and decoding in the downlink of a multiuser
multiple-input, multiple-output (MIMO) system, wherein each user may receive
more than one data stream. We propose several mean squared error (MSE) based
criteria for joint transmit-receive optimization and establish a series of
relationships linking these criteria to the signal-to-interference-plus-noise
ratios of individual data streams and the information theoretic channel
capacity under linear minimum MSE decoding. In particular, we show that
achieving the maximum sum throughput is equivalent to minimizing the product of
MSE matrix determinants (PDetMSE). Since the PDetMSE minimization problem does
not admit a computationally efficient solution, a simplified scalar version of
the problem is considered that minimizes the product of mean squared errors
(PMSE). An iterative algorithm is proposed to solve the PMSE problem, and is
shown to provide near-optimal performance with greatly reduced computational
complexity. Our simulations compare the achievable sum rates under linear
precoding strategies to the sum capacity for the broadcast channel.
