An Efficient Block Diagonalization Method for
Multiuser MIMO Downlink
Jie An, Yuan-an Liu, Fang Liu
School of Electronics Engineering, Beijing University of Post and Telecommunication, Beijing, China
E-mail: an-jie@bupt.edu.cn
Abstract—Block diagonalization (BD) based on singular value
decomposition (SVD) is a well-known precoding method that
eliminates interuser interference in multiuser multi-input multi-
output (MIMO) broadcast channels, but it is computationally
inefficient. In this paper, we propose an alternative method
replacing SVD to obtain the precoding matrix in the BD scheme.
Analysis and simulation results show that our proposal has lower
complexity than the conventional BD method, while there is no
any degradation in sum throughput.
Keywords-MIMO; multiuser; broadcast channels; precoding
I. INTRODUCTION
Multiple-input multiple-ouput (MIMO) systems have
gained a lot of attention in the past years due to their
promising improvement in terms of performance and
bandwidth efficiency in wireless communication systems [1].
In the downlink multiuser environment, because of individual
users’ receivers cannot cooperate with each other, the co-
channel interference (CCI) should be suppressed at transmitter
by the space precoding [2].
In [3][4], it was shown that the maximum sum rate in the
multiuser MIMO broadcast channels (BC) can be achieved by
dirty paper coding (DPC). However, the DPC is difficult to
implement in practical systems due to its high computational
complexity. As a suboptimal strategy of the DPC [5], the
Tomlinson-Harashima precoding, is still impractical due to its
complexity, since this algorithm is based on nonlinear modulo
operations.
In linear processing systems, several practical precoding
techniques have been proposed, typically as the channel
inversion method [6], the block diagonalization (BD) method
[7]. A zero-forcing channel inversion (ZF) scheme [6] can
suppress CCI completely for the case where all users employ a
single antenna. However its performance is rather poor due to a
transmit power boost issue. Although a minimum mean-squared
error channel inversion (MMSE) method [6] overcomes the
drawback of the ZF, this is still confined to a single receive
antenna case. For the case where the users in the network have
multiple antennas, the block diagonalization (BD) is well-
known precoding algorithm [7]. As a generalization of the ZF
scheme, the BD can eliminate the multiuser interference (MUI)
completely. Owing to the singular value decomposition (SVD)
in the algorithm, the BD is not computationally efficient.
In this paper, we propose a new scheme using LQ
decomposition and eigenvalue decomposition (LQ-EVD) for
the case where each user has multiple antennas. As a new
approach of the conventional BD scheme, LQ-EVD shows a
significant advantage in computational complexity by avoiding
SVD operation in the processing of computing the user’s
precoding matrix. In addition, we prove that the proposed LQ-
EVD algorithm has the same sum rate as the conventional BD
scheme.
II.
SYSTEM MODEL
W
e
consider a single-cell multiuser MIMO downlink
system with independent users and a base station. Each user
i
s equipped with ( ) receiver antennas and the base
station is equipped with transmit antennas. The downlink
channel between the base station and user is described by the
matrix . We assume that and the
total channel matrix
HH is known
perfectly at the base station.
K
^
k
N
kT
NN
1
k
N t
T
N
k
t
k
u
H
1
K
T
k
N
¦
T
T
K
ªº
¬¼
HH
k
N
n
k
12
TT
In the MIMO BC, the signal received at user
k
can be
written as
1,
yx x
K
kkkk kjj
jjk
z
¦
HW HW
(1)
where represents information data of user
k ,is an x
k k
W
1
T
N u precoding vector associated with user k and denotes
the complex-valued additive white Gaussian noise at user
k
,
which has a variance of
n
k
2
V
. Note that the precoding vectors
are normalized to be unity, i.e.,
2
1
k
W for
1, ,kK
.
Furthermore, the power allocated to user k is given by
x
H
Ex
k
P
and a sum power constraint is applied at the BS,
corresponding to
1
K
k
P
k
P d
¦
. In (1), the second term on the
right hand side represents the co-channel interference (CCI),
which is desirable to be eliminated by designing appropriate
precoding algorithms.
III. BLOCK DIAGONALIZATION METHOD
In this section, we represent a novel block diagonalization
method for multiuser MIMO systems. First, we review the
conventional BD algorithm presented in [5]. Then, we
introduce an alternative way to obtain the precoding matrix.
This work is supported by The Fundamental Research Funds for the Central
Universities (G470427 and 2009RC0308) and NFSC (60802033, 60973111
and 61170275).
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