*IEEE Transactions on Wireless Communications*,
vol. 6, no. 6, June 2007, pp. 2040-2045.
# 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

Draft of Paper

## Abstract

The sum capacity of a Gaussian broadcast MIMO channel can be
achieved with dirty paper coding (DPC).
However, algorithms that approach the DPC sum capacity do not appear
viable in the forseeable future, which motivates lower complexity
interference suppression techniques.
Block diagonalization (BD) is a linear precoding technique
for downlink multiuser MIMO systems.
With perfect channel knowledge at the transmitter, BD can eliminate
other users' interference at each receiver.
In this paper, we study the sum capacity of BD with and without
receive antenna selection.
We analytically compare BD without receive antenna selection to DPC
for a set of given channels.
It is shown that
- if the user channels are orthogonal to each other, then
BD achieves the same sum capacity as DPC;
- if the user channels lie in the same subspace, then the gain of DPC
over BD can be upper bounded by the minimum of the number of transmit and
receive antennas.

These observations also hold for BD with receive antenna selection.
Further, we study the ergodic sum capacity of BD with and without receive
antenna selection 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 proposed
for easy estimation of the gap between the sum capacity of
DPC and BD without receive antenna selection.

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