*Proc. IEEE International Symposium on Information Theory*,
July 9-14, 2006, pp. 886-890, Seattle, Washington USA.
# Sum Capacity of Multiuser MIMO Broadcast Channels
with Block Diagonalization

*Zukang Shen*,
*Runhua Chen*,
*Jeffrey G. Andrews*,
*Robert W. Heath, Jr.*,
and
*Brian L. Evans*
Wireless Networking and
Communications Group,
The University of Texas at Austin,
Austin, TX 78712 USA

shen@ece.utexas.edu -
rhchen@ece.utexas.edu -
jandrews@ece.utexas.edu -
rheath@ece.utexas.edu -
bevans@ece.utexas.edu

Paper Draft

## Abstract

The sum capacity of a Gaussian broadcast MIMO channel can be achieved
with Dirty Paper Coding (DPC).
Deploying DPC in real-time systems is, however, impractical.
Block Diagonalization (BD) is an alternative precoding technique for
downlink multiuser MIMO systems, which can eliminate interuser
interference at each receiver, at the expense of suboptimal sum
capacity vs. DPC.
In this paper, we study the sum capacity loss of BD for a fixed channel.
We show that
- if the user channels are orthogonal to each other, then
BD achieves the complete sum capacity; and
- if the user channels lie in a common row vector space, then
the gain of DPC over BD can be bounded by the minimum
of the number of transmit and receive antennas and the number
of users.

We also compare the ergodic sum capacity of DPC with that of BD
in a Rayleigh fading channel.
Simulations show that BD can achieve a significant part of the total
throughput of DPC.
An upper bound on the ergodic sum capacity gain of DPC over BD is
derived, which can be evaluated with a few numerical integrations.
With this bound, we can easily estimate how far away BD is from
being optimal in terms of ergodic sum capacity, which is useful in
directing practical system designs.

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Last Updated 02/25/07.