220 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 58, NO. 1, JANUARY 2009
angular spread at the base station (as for outdoor environments
[24]), adaptation of user subset and precoders is able to provide
significant throughput gains compared to the fixed strategy. On
the other hand, simulation results prove that the benefits of
adaptation vanish for large angular spreads.
The paper is organized as follows: After the definition of
the system and the channel model in Sections II and III, the
GoB spatial multiplexing solution is recalled in Section IV.
Section V deals with the proposed structure for the BS and
MS processing according to the AGoB solution. A perfor-
mance analysis is carried out in Section VI for both the AGoB
and the GoB methods for varying spatial channel conditions.
The performance of opportunistic random beamforming [13]
is introduced as a reference. The impact of the considered
scheduling solutions on the cell coverage is also investigated.
II. S
YSTEM MODEL
We consider the downlink channel of a multiuser MIMO-
OFDMA wireless system, where L active MSs share the same
cell. The BS is equipped with a uniform antenna array with
N
T
Δ
T
-spaced elements, whereas each MS has N
R
Δ
R
-spaced
receiving antennas (N
R
≤ N
T
). FDD is used to separate uplink
and downlink communications.
In the system under study, multiple access is handled by
a combination of time, frequency, and space division. As
shown in Fig. 2, the OFDM channel is indeed organized in
time–frequency resource units, each consisting of a frame of
W subsequent slots (or bursts) of D OFDM symbols and a
frequency bin (or subchannel) of B adjacent Δf-spaced subcar-
riers. The same time–frequency unit is allocated to a subset S
of M ≤ N
T
users separated by means of spatial multiplexing.
The setting under consideration can be equivalently adapted to
fit the radio interface requirements for the IEEE 802.16-2005
standard [9], [10], where the AMC mode assigns a modulation
and coding scheme per time–frequency unit, and it can also be
used in conjunction with multiple antennas at the transmitter
and the receiver (AAS option).
We assume that channel estimation (or prediction [35], [36])
can be performed by each user from pilot subcarriers (or
preambles) included in each slot, as indicated in Fig. 2. Notice
that this feature is available for the AMC mode (with AAS
option) of the IEEE 802.16-2005 standard [9], [10].
As shown in Fig. 1, a scheduler at the BS chooses the best
subset S of M users and assigns to them M spatially separated
channels by means of M precoding vectors {w
m
}
M
m=1
.User
selection is performed in each time–frequency unit based on
some channel measurements drawn by the MS during a previ-
ous training phase and transmitted to the BS through a feedback
channel.
In any given time–frequency unit, the N
R
× 1 signal received
by the kth user (k =1,...,M) on a single subcarrier and
within a single OFDM symbol can be modeled as
y
k
=
P
k
H
k
w
k
h
kk
c
k
+
M
m=1,m=k
P
m
H
k
w
m
h
km
c
m
+ n
k
(1)
where for the kth user, H
k
denotes the N
R
× N
T
channel
matrix, w
k
is the N
T
× 1 precoding vector, P
k
is the trans-
Fig. 1. Downlink multiuser MIMO system.
TABLE I
IEEE 802.16-2005 T
RANSMISSION MODES AND REQUIRED SNR RANGES
(OVER ADDITIVE WHITE GAUSSIAN NOISE CHANNELS)
mitted power, and c
k
∈C
(n)
is the transmitted symbol with
E[|c
k
|
2
]=1. Adaptive transmission is used, and it is adjusted
to attain a fixed BER target (BER =10
−6
from Table I). The
complex symbol c
k
can belong to any of the N available
modulation sets {C
(n)
}
N
n=1
(e.g., according to the IEEE 802.16-
2005 standard [9], [10]). Furthermore, the additive noise n
k
is assumed to be zero-mean white complex Gaussian with
E[n
k
n
H
k
]=σ
2
I
N
R
. In (1), we defined as h
km
= H
k
w
m
the
N
R
× 1 equivalent single-input–multiple-output (SIMO) chan-
nel between the BS and the kth MS when the transmitted signal
is precoded by w
m
. The channel response is herein considered
as frequency flat within the frequency bin; thus, the bin size
(the number B of adjacent subcarriers; see Fig. 2) needs to
be adequately designed according to the specific propagation
environment [31].
As shown in Fig. 1, MVDR spatial filtering y
k
= a
H
k
y
k
is
performed at the receiver side on the signal (1) to maximize the
SINR [29], i.e.,
a
k
=
1
√
P
k
×
Q
−1
M
h
kk
h
H
kk
Q
−1
M
h
kk
. (2)
Here, Q
M
=
M
m=1,m=k
P
m
h
km
h
H
km
+ σ
2
I
N
R
denotes the
noise-plus-interference spatial covariance at the kth MS. This
beamforming technique is known to minimize interference
under the constraint of a distortionless response to the desired
channel (i.e., a
H
k
h
kk
=1). CSI is required not only at the MS
for the evaluation of the MVDR filter but at the BS as well
(in the form of partial or quantized information) for scheduling
purposes. For all the considered schemes, specific training
phases are carried out to estimate the required parameters.
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