5336 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 58, NO. 9, NOVEMBER 2009
On Multiuser MIMO Multistream Transmission
Haixia Zhang, Member, IEEE, Michel T. Ivrla
˘
c,
Josef A. Nossek, Fellow, IEEE,and
Dongfeng Yuan, Senior Member, IEEE
Abstract—We present a system for multiuser multiple-input–multiple-
output (MIMO) multistream downlink transmission, which employs
covariance-based linear precoders at the transmitter and a minimum-
mean-square-error (MMSE) equalizer at each receiver. Antennas of user
equipment are arranged to receive different streams bound to this user.
Furthermore, these antennas receiving different streams are allowed to
cooperate with each other through a joint equalizer, leading to a multiuser
MIMO multistream transmission link. The precoders are designed per
stream based on the covariance channel state information (CSI). Numeri-
cal analysis shows the feasibility and usefulness of the presented system.
With the proposed approach, the covariance-based precoding concept
for multiuser multiple-input–single-output (MISO) single-stream trans-
mission can effectively be extended to a multiuser MIMO multistream
transmission link.
Index Terms—Code-division multiple access (CDMA), covariance-based
precoding, minimum mean square error (MMSE), multiuser multiple-
input–multiple-output (MIMO).
I. INTRODUCTION
The transceiver design of a multiple-input–multiple-output (MIMO)
system has attracted tremendous attention in the field of wireless
communication [1]–[7]. In [1] and [2], transmit processing based on
channel decomposition is proposed and analyzed. Iterative beamform-
ing is proposed in [3]. Dirty-paper coding is also widely explored [4].
In a multiuser system, the transceiver cannot jointly be optimized
because there is no closed-form solution for joint design of the
transceivers in such systems. Accordingly, some researchers have
proposed to decouple the multiuser MIMO downlink channel into
parallel independent single-user MIMO channels through which the
optimized transceiver design approaches for the single-user case can
separately be applied to each user [1], [2]. To do this, the number
of transmit antennas s hould be large enough, compared with the total
number of receive antennas of all the users, such that the multiuser
MIMO channel matrix has a null space of sufficient dimensionality.
This will greatly limit the number of users, as well as the number of
receive antennas of each user. To overcome this, based on our former
work, we propose a system for multiuser MIMO multistream system
transmission with power constraint.
To design precoders, we need to know the instantaneous chan-
nel state information (CSI) at the transmitter, which is always a
demanding task. This is particularly true for systems operating in
frequency-division duplex (FDD). Therefore, precoder design ap-
proaches with only partial CSI or covariance channel knowledge
available at the transmitter are of more interest [5], [6]. In our for-
mer work, covariance-channel-knowledge-based precoders have been
proposed for multiuser multiple-input–single-output (MISO) systems
Manuscript received September 2, 2008; revised May 20, 2009. First pub-
lished June 16, 2009; current version published November 11, 2009. This work
was supported in part by the National Science Foundation of China under Grant
60672036. The review of this paper was coordinated by Prof. H. H. Nguyen.
H. Zhang and D. Yuan are with Shandong University, 250100 Shandong,
China (e-mail: haixia.zhang@sdu.edu.cn; dfyuan@sdu.edu.cn).
M. T. Ivrla
˘
c and J. A. Nossek are with the Institute for Circuit Theory
and Signal Processing, Technische Universität München, 80333 München,
Germany (e-mail: Ivrlac@nws.ei.tum.de; Nossek@nws.ei.tum.de).
Digital Object Identifier 10.1109/TVT.2009.2025282
in [6], [8], and [9]. In this paper, we extend the covariance-based
precoder design approach to multiuser multistream MIMO scenarios.
To achieve this, we first allow cooperation between users who are
closely located. Then, integrating the one-antenna users to a single user
leads to a user with multiple antennas. We assume that, in the proposed
MIMO system, there is no cooperation between users, and the streams
bound to the same user cooperate through a joint equalizer, aiming
to minimize the mean square error (MSE) of the received streams.
The numerical analysis and the simulation results show that, with
the proposed approach, the covariance-based precoding concept can
successfully be extended to MIMO systems. Thus, a multiuser multi-
stream MIMO transmission system with a covariance-based precoder
is formulated.
The notation used in this paper is described as follows. Matrices
and vectors are denoted by bold uppercase and lowercase letters,
respectively. (•)
∗
, (•)
T
, (•)
H
, ⊗,andE[•] denote, respectively,
complex conjugation, transposition, complex conjugate transposi-
tion, Kronecker product, and expectation. Operator vec(•) is de-
fined as producing a vector by stacking the columns of a matrix
one by one. 0
M
, 0
M×N
,andI
M
represent the M-dimensional
zero vector, the M × N zero matrix, and the identity matrix with
dimension M.
II. S
IGNAL MODEL
The system layout for the downlink is shown in Fig. 1. The trans-
mitter is equipped with N
Tx
antennas. Without loss of generality, users
are assumed to have the same number of antennas, which is denoted
by N
Rx
. We assume that the number of streams belonging to a user
equals the number of its antennas and that only the covariance knowl-
edge of CSI based on the restricted reciprocity between the uplink
and the downlink of an FDD system is available to the transmitter.
The receivers have the instantaneous CSI, based on which the joint
equalizers are designed.
Let k ∈ 1,...,K denote the index of transmit signal streams, and
K
is referred to as the number of users. The kth transmitted signal
is denoted by d
k
[m]. Signal s
k
[n] is the upsampled version of d
k
[m].
The spreading code denoted by c
k
[0],c
k
[1],...,c
k
[χ − 1] is of length
χ, and we assume the normalization
χ−1
j=0
|c
k
[j]|
2
= χ. As our focus
is not on designing spreading codes, the classic Walsh codes are
employed. The vector p
k
[n] ∈ C
N
Tx
denotes the covariance-based
precoder with (L +1)taps for the kth data stream. As described in
[6], it can be designed based on the covariance channel knowledge to
minimize the MSE, maximize the SNR, or annihilate the interference
at the total power constraint. In this paper, we choose the precoder
to minimize the MSE. The spreading codes are embedded in the
precoders; therefore, the length of the precoder should be larger than
or equal to the length of spreading codes, i.e., L ≥ χ − 1. Then, the
precoder p
k
[n] can be written as
p
k
[n]=
L
l=0
p
k,l
c
k
[l]δ[n − l] ∈ C
N
Tx
.
All the signals after precoding are added up to form the transmitted
signal
x[n]=
K
k=1
L
l=0
p
k,l
s
k
[n − l] ∈ C
N
Tx
.
The obtained signals are then sent over the MIMO multipath channel,
whichisassumedtobeof(Q +1) temporal taps. Let us define
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