Content uploaded by M. Arif Khan
Author content
All content in this area was uploaded by M. Arif Khan on Jan 15, 2015
Content may be subject to copyright.
User and Transmit Antenna Selection for MIMO
Broadcast Wireless Channels with Linear Receivers
M. Arif Khan, Rein Vesilo, Linda M. Davis∗, Iain B. Collings∗∗
Department of Electronic Engineering, ICS Division, Macquarie University, Sydney, NSW 2109 Australia
Email: (mkhan,rein)@ics.mq.edu.au
∗Institute for Telecommunications Research, University of South Australia
Email: (linda.davis@unisa.edu.au)
∗∗CSIRO Marsfield ICT Centre, Sydney Australia
Email: (iain.collings@csiro.au)
Abstract— This paper considers a signalling scheme for a
multi-user wireless broadcast system where the base station
has multiple transmit antennas and users can have multiple
receive antennas. Independent data streams are transmitted in
this system by allocating different transmit antennas to different
selected users where multiple transmit antennas may be allocated
to each selected user. The signalling scheme is used to select the
particular users to receive data in a transmission block and to
allocate transmit antennas to those users. We examine two partial
feedback schemes for selecting users: one that we call norm-
based and the other that we call SINR-based. We also present a
novel transmit-antenna selection scheme for allocating multiple
transmit antennas to selected users based on the Gram-Schmidt
orthogonalisation algorithm. The signalling scheme presented in
this paper reduces the amount of channel information required by
the base station. We study the performance of the user selection
and transmit-antenna selection schemes when linear receivers are
used at the receiver side for decoding the transmitted signal. In
particular, we consider zero-forcing (ZF) and minimum mean
square-error (MMSE) receivers. We examine the sum capacity
performance of the system compared to schemes with no feedback
and using random antenna selection. We show that the best
performance is achieved with norm-based user selection, Gram-
Schmidt antenna selection and MMSE receivers.
I. INTRODUCTION
Multiple-input multiple-output (MIMO) wireless communi-
cation has received a lot of attention in recent years. In a point-
to-point link, MIMO can be used to provide both multiplexing
gain and diversity gain, and these can be traded off against
each other. With pure multiplexing gain the capacity increases
linearly with the minimum of the number of transmit and
receive antennas [1]. Diversity gain improves signal-to-noise
ratio (SNR) performance and can be used to reduce bit error
rates.
In a broadcast (BC) system multiple transmit antennas can
be used to send independent data streams simultaneously to
multiple users. In this arrangement, there is a base station
(BS) with an array of antennas and, in the MIMO setting,
each user can have multiple receive antennas. In some BC
systems all transmit antennas are used to carry the data of all
users selected to receive data. This is achieved by precoding
the data at the BS before transmission; however this requires
full knowledge of the channel at the transmitter. We consider
a different system where such full knowledge is not required.
Instead, we partition the transmit antennas so that a particular
subset of transmit antennas is used to transmit to a particular
user. Multi-user transmission is achieved by using multiple
subsets of transmit antennas, with each subset disjoint from
the other subsets. The operation of this system requires that
the receiver has knowledge of the channel from the subset of
transmit antennas used to transmit to the user. This is a more
reasonable assumption than assuming the transmitter has full
channel knowledge. The transmitter in such an environment
can operate with no information (no feedback) about the
channel or it can receive partial feedback (not the full channel
matrix) such as signal-to-interference plus noise ratio (SINR)
at the receiver.
In a practical wireless system, there are normally more
users than the number of transmit antennas at the base station
(BS). Therefore, the BS has to select a subset of users for
transmission in such a way that the system is both efficient
and capable of meeting quality-of-service requirements. This
task is achieved by using an efficient scheduling scheme at
the BS. The communication of user information between the
BS and users to make scheduling decisions and to notify
which users have been selected is implemented by a signalling
scheme. The user-selection algorithm should be as close to the
optimal algorithm as possible while keeping its complexity
to a reasonable level. The optimal user-selection scheme is,
of course, a complete exhaustive search, but its complexity
increases tremendously even for a moderate number of users.
Therefore, many sub-optimal scheduling algorithms with less
complexity are proposed in the literature with their perfor-
mance near to the optimal algorithm. Most of the scheduling
algorithms in multi-user MIMO literature are based on a sum-
capacity maximization criterion e.g. [2], [3].
The work by [4], considered such a broadcast MIMO system
with partitioning of transmit antennas between selected users
where users could have multiple receive antennas, but only
one transmit antenna was used to transmit data to a selected
user. The model used in [4] considered linear receivers. In
particular, the receiver was either a zero-forcing (ZF) receiver,
a minimum mean squared error (MMSE) receiver or a maximal
978-1-4244-2603-4/08/$25.00 © 2008 IEEE ATNAC 2008276
ratio combining (MRC) receiver. The system considered in [4]
either had no feedback, in which case users were selected on
a Round Robin (RR) basis, or the SINR at the receiver was
sent to the BS which chooses the users with the best SINR
values in an opportunistic scheduling scheme.
The main aim of this paper is to develop techniques
that allow multiple transmit antennas to be incorporated into
the user- selection and transmit antenna selection signalling
scheme. Allowing multiple transmit-antennas to be allocated
to a user complicates the allocation of antennas at the BS, and
one of the main contributions of this paper is the proposal
of a transmit antenna selection algorithm based on the Gram-
Schmidt orthogonalisation algorithm. One scenario where mul-
tiple transmit antennas per user may be desirable is when it is
important to reduce bit error rates to users.
The overall signalling scheme per transmission time block
consists of two phases. The first phase involves selecting which
set of users to transmit to and the second phase consists of
allocating transmit antennas to selected users.
User selection in phase one is done at the base station. The
paper discusses three different user selection schemes: (i) a
Round Robin scheme that uses no feedback from users, (ii) a
user ordering scheme using what we call norm-based feedback
from users, and (iii) a user ordering scheme using what we
call SINR-based feedback from users. In the Round Robin
scheme the BS picks a subset of users in a Round Robin
fashion. After a large number of time slots each user will
have received an approximately equal share of transmission
time. The sum-capacity of the system in this case is equal to
that using random user selection.
In the second user-selection scheme, each user calculates
the squared Frobenius norm (a scalar value) of its channel
matrix and sends this back to the BS. The BS then orders
the users based on this feedback and picks a subset of users
with maximum channel norm. In the third scheme, each user
calculates the best SINR from each transmit antenna (i.e. a
vector of SINR values) and sends this back to the BS which
then selects a subset of users with the maximum SINR values.
In the second phase, transmit antennas are allocated to each
selected user. In the scheme we are proposing, transmit anten-
nas are allocated to the selected users in the order they were
chosen in phase one and the Gram-Schmidt orthogonalisation
algorithm is used to find the subset of transmit antennas that
have the best channels to the selected user. As antennas are
allocated the pool of available antennas is reduced until all
antennas have been allocated. To assess the performance of this
antenna-selection scheme, we compare it against one where
antennas are selected at random.
We simulate the performance of the different user-selection
schemes and the proposed and random-allocation antenna-
selection schemes for MMSE and ZF receivers. It is shown
that the proposed antenna-selection scheme performs better
for both MMSE and ZF receivers as compared to the random-
antenna-selection scheme. We show that the best user-selection
scheme is the norm-based scheme. The paper also compares
the performance of linear MMSE and ZF receivers for our
signalling scheme and, as expected, the MMSE receiver per-
forms better. However, for high SNR values the performance
gap diminishes between ZF and MMSE receivers.
The rest of the paper is organized as follows. Section II
examines related work on user scheduling, antenna selection,
and linear receivers. Section III describes the system model,
notation and assumptions made in the paper. Section IV
presents the user subset selection and transmit-antenna selec-
tion schemes. Section V discusses the linear receiver structures
used in the paper and associated SINR calculations. Section
VI presents the numerical results of the proposed scheme and,
finally, Section VII presents the conclusion.
II. RELATED WORK
The sum-capacity analysis of a MIMO broadcast channel
with Round Robin scheduling and opportunistic scheduling
is discussed in [4] for the case of one transmit antenna being
allocated to each selected user and involves analytic techniques
and approximations. It is shown that MMSE receivers perform
better in both Round Robin and opportunistic scheduling.
Algorithms for user selection in MIMO BC systems with full
channel knowledge at the receiver, where ZF precoding or
dirty-paper coding is employed, are discussed in [5] [3] [6] [2]
and [7]. Detailed discussion of linear receivers can be found
in [8], [9] and [10]. Zero-forcing receivers are based on the
concept of channel inversion and are simple to implement. But
complete channel inversion enhances the noise at the receiver.
Furthermore ZF linear processing also requires that the number
of receive antennas of each user should be equal or greater
than the number of transmit antennas at the base station [11].
In order to overcome this problem and to get a better trade
off between channel inversion and noise enhancement, MMSE
receivers are used.
III. SYSTEM MODEL
We consider a multi-user MIMO downlink system model
with an array of Nttransmit antennas at the base station (BS)
and a set of Nuusers in the system, with each user equipped
with Nrk receive antennas. We assume that each selected user
has a fixed number, Ntk, of transmit antennas allocated to
it. The total number of selected users is K. The number of
selected users is Ns=Nt/Ntk . For simplicity we assume
that Ntis an integer multiple of Ntk and we also assume that
the pool of potential users is larger than Ns, i.e. Ns≤K.
The channel is assumed to be block stationary, where the
channel matrix varies randomly from block to block but during
each block it remains constant. Each block consists of a fixed
number of time slots (with index t). Blocks are assumed long
enough to ensure that theoretical capacity limits are reached.
Channel matrices in blocks are assumed to be independent
and identically distributed. It is also assumed that transmission
occurs in a frequency-flat-fading propagation environment.
Total transmit power is equally distributed among all transmit
antennas at the base station.
During each block, a subset, S, of the pool of potential
Kusers is selected using one of the user-selection schemes
277
discussed in Section IV, to send data to users, where the
identity of the users selected may vary from block to block,
depending on the user scheduling scheme and the channel
conditions.
The received signal vector of the kth user at time slot tin
a block can be written as
yk(t)=Hkx(t)+nk(t),(1)
where yk(t)∈CNrk×1is the received signal vector, Hk∈
CNrk×Ntcharacterizes the channel gain matrix between trans-
mit and receive antennas, x(t)∈CNt×1is the transmitted
signal vector and nk(t)∈CNrk×1is the additive noise at
the kth receiver. It is assumed that the components of the
block channel matrices Hkand the noise vectors nk(t)are
circularly symmetric complex Gaussian random variables with
zero mean and normalized to have unit variance.
Define a subset, πk, of indices of the transmit antennas
selected for user k. The cardinality of πkis Ntk. This paper
considers two antenna-selection schemes which are discussed
in section IV. Antenna selection is done at the receiver side
and the information of πkis sent back to the BS through a
feedback channel. Further assume that the BS communicates
this information among all users so that each selected user
selects a different subset of the transmit antennas. The channel
matrix for user kfrom the πjtransmit antennas allocated to
user jis defined as Hkj, which has dimensions Nrk ×Ntk.
There are Ntk independent data streams transmitted from the
BS to the user k. Based on these assumptions the signal and
interference model for user kcan be written as (suppressing
the argument t)
yk=Hkkxk+
Nt
j=1,j=k
Hkjxj+nk.(2)
IV. MULTIUSER SCHEDULING AND ANTENNA SELECTION
In this section, we present the user-subset selection (phase
one) and transmit-antenna selection (phase two) algorithms.
A. User Selection
In general, a wireless system has more users than can be
supported by the number of transmit antennas at the BS. The
purpose of the user-selection algorithm is to select a suitable
subset of users to transmit to. We denote this subset of users
by Sand denote the maximum number of users that can be
served in a block by Ns. An important factor in the selection
of the best possible user subset under a certain criterion is
the information that is sent back to the BS from each user. In
the following, we present three user subset selection schemes
based on the feedback available at the BS from users.
1) Round Robin Selection: In this scheme, for each block,
the BS picks a subset of Nsusers to transmit to in a Round
Robin fashion, where at the end of a large number of blocks
all users will have received an approximately equal share of
transmission time. This scheme requires no feedback informa-
tion from users to the BS. The average sum-capacity of the
Round Robin scheme is the same for randomly selected users
since we have assumed that the channel state distributions are
identically distributed for all users.
2) Norm-based Selection: In this scheme, let the channel
matrix of the kth user be Hk, which has dimensions Nrk ×
Nt, where Nrk is the number of receive antennas of user k.
Each user calculates the squared Frobenius norm of its channel
matrix, Hk, and sends back this scalar value to the base station.
This squared Frobenius norm can be considered as the total
power gain of the channel of the user (see [8]) and is defined
as follows
||Hk||2
F=trace(HkHH
k).(3)
At the beginning of each block, the BS receives Nunorm
values, one from each user. The BS orders these values and
selects the Nsusers in order, starting from the largest norm
value.
3) SINR-Based Selection: In this scheme, each user calcu-
lates a separate SINR value from each transmit antenna and
then sends back the vector of NtSINR values to the BS. In
particular, if γkjl is the SINR for receive antenna lof user k
for a signal transmitted from transmit antenna jand γkj is the
average SINR for user kfor a signal transmitted from transmit
antenna j, define for each user
γ∗
k=max
j∈{1,··· ,Nt}γkj .(4)
The BS orders the values γ∗
kand selects the Nsusers in order,
starting from the largest value.
B. Antenna Selection
Once the subset Sof Nsusers is selected, the next step is
to select a subset of transmit antennas πkwhere k∈S.
1) GS Based Selection: In the Gram-Schmidt (GS) antenna-
selection scheme, users are considered in the order determined
through the user-selection process discussed in Section IV-
A. Antenna selection is done at the receivers. Initially all
transmit antennas are available. At each stage of the transmit
antenna-selection algorithm, a particular user is considered,
say user k. We think of the receive antennas for user kas
transmit antennas (with Nrk antennas present) and the transmit
antennas not yet allocated at the BS as a pool of users (each
with one antenna). We assume that the channel is reciprocal
and use the GS algorithm to choose the antennas at the BS to
give the strongest set of Ntk orthogonal channels from the user
to the BS. This is used to select a subset of transmit antennas
πk. This selection is done by user kand it sends the indices
of the selected antennas to BS which then updates the pool of
available antennas by culling πkfrom the available antennas.
The BS then sends the set of available transmit antennas to the
next user in order. This user then picks its subset of transmit
antennas and then sends back this information to BS. In this
way, all selected users select their subset of transmit antennas,
sending their selected set of transmit antennas back to the BS.
To describe the Gram-Schmidt algorithm for a particular
user, let Hk=[h1,··· ,hNt]denote the channel column
vectors of the user kchannel Hk.Let(h)Tand (h)Hdenote
278
the non-conjugate and complex-conjugate transpose of (h)
respectively. Then the Gram-Schmidt algorithm implemented
at the receiver side is as follows:
Step 1: Let i=1and πk=∅
Step 2: Calculate ||hj||2
Fwhere j=1,··· ,N
t
Find σi=argmax
j||hj||2
F
Then update πkto πk∪{σi}
Step 3: Update hjfor all j=1,··· ,N
tto
hj=hj−(hj)T((hσi)T)H
||hσi||2
F
hσi
Step 4: If i=Ntk , terminate the algorithm
Else, i=i+1 and go to step 2.
2) Random Selection: In the case of random selection, the
BS randomly selects a subset of transmit antennas πkfor each
user. The BS then transmits the data for user kthrough this
selected set of antennas for this user. There is no information
sharing required between the BS and users for random transmit
antenna selection.
V. L INEAR RECEIVER STRUCTURES AND SINR
CALCULATION
The received vector ykis multiplied by a linear filter in
order to extract the original transmitted signal. In this section,
we discuss the two linear receive filters used in this paper. In a
multi-user MIMO BC each user receives its own signal along
with the signals transmitted for other users. The interfering
signals cause a reduction in SINR which reduces the capacity
for a particular user. We give in this section the associated
linear-filter SINR calculations for a selected user.
A. ZF Receive Decoder
The basic idea of a ZF receiver is to invert the channel
at the receiver in order to completely eliminate the interfer-
ence between different transmitted data streams. In a MIMO
configuration, the ZF receiver decomposes all data streams
transmitted into parallel SISO channels at the receiver. The
ZF receive filter for the jth stream of user kcan be given as
vZF
kj =gkj ,(5)
where gkj is the jth column of Hk[HH
kHk]−1. However, by
completely inverting the channel, there is an enhancement in
noise at the receiver. A better trade-off between interference
nulling and noise enhancement can be achieved by using the
MMSE filter discussed in the following section.
B. MMSE Receive Decoder
The basic idea of a MMSE receiver is to build a better
receive filter by minimizing the mean square error between
the actual signal and the received signal. This produces a
better balance between interference cancellation and noise
enhancement. A standard MMSE filter for MIMO systems can
be derived using the Wiener filter theory. The MMSE filter for
the jth stream of user kis given as follows
vMMSE
kj =
Hk
HH
k+ρ
Nt
INrk −1
Hkk ,(6)
where
Hkis a Nrk ×(Nt−1) matrix with the same elements as
Hkbut with the πkjth column removed. A detailed discussion
of MMSE receivers can be found in [10] and [8].
C. SINR Calculation
We consider a BC system where multiple streams are
transmitted to each user. Let Hkbe the Nrk ×Ntchannel
matrix of user kand we have Ktotal users selected for
transmission, i.e. k=1,··· ,K. Each user receives Ntk
independent data streams of its own signal plus the signals
from all other transmit antennas. Let γkj ,ukj and vkj be
the SINR, transmit and receive beamforming vectors for the
jth substream of user krespectively. Then the SINR of each
substream j=1,··· ,L
kwhere Lk≤Ntk for the user kis
given as [12]
γkj =vH
kjSkj vkj
vH
kjTkj vkj
,(7)
where
Skj =HkukjuH
kjHH
k,(8)
Tkj =
Lk
l=1,l=j
HkukluH
klHH
k
intra-user interference
+
K
i=1,i=k
Li
m=1
HkuimuH
imHH
k
inter-user interference
+σ2INrk
noise
,(9)
where Lkis the number of data streams for user k. Then the
capacity of each substream of user kcan be calculated as
ckj =log
2det(1 + γkj)and the sum-capacity of user kcan
be written as ck=Lk
j=1 ckj bits/sec/Hz. The SINR values
for the ZF and MMSE filters are obtained by substituting in
the corresponding filter matrices given by equations (5) and
(6), respectively.
VI. SIMULATION RESULTS AND DISCUSSION
In this section, we examine the performance of the proposed
user-selection and transmit-antenna-selection schemes, using
simulation techniques because the algorithm is too complex
to evaluate using analytical techniques. A MIMO system with
a(Ntk ×Nrk)=(2×4) configuration with the parameters
Nu=4,N
t=4,N
tk =2,N
rk =4,N
s=2is considered
except in the single-input multiple-output (SIMO) case, where
Ntk =1. For all ZF receiver simulations, it is required to
keep Nrk ≥Nt. The sum-capacity was obtained by averaging
the sum-capacities over independent channel realizations in all
simulations.
Figure 1 compares the performance of an MMSE receiver
with Round Robin and GS-based antenna selection with the
three different user-selection schemes. The figure plots the
average sum-capacity for random, SINR and norm-based user-
selection schemes with random and GS antenna selection.
The proposed GS antenna-selection scheme shows better sum-
capacity performance for all three user-selection schemes
279
0 5 10 15 20 25
0
5
10
15
20
25
SNR (dB)
Sum−Capcity (bits/sec/Hz)
Round Robin User Selection/RR Ant Selection
SINR User Selection/RR Ant Selection
Norm Based User Selection/RR Ant Selection
Round Robin User Selection/GS Ant Selection
SINR User Selection/GS Ant Selection
Norm Based User Selection/GS Ant Selection
Fig. 1. Comparison of different user-selection schemes with Round Robin
and GS antenna-selection algorithm for MMSE Receiver.
0 5 10 15 20 25
0
5
10
15
20
25
SNR (dB)
Sum−Capcity (bits/sec/Hz)
Round Robin User Selection/RR Ant Selection
SINR User Selection/RR Ant Selection
Norm Based User Selection/RR Ant Selection
Round Robin User Selection/GS Ant Selection
SINR User Selection/GS Ant Selection
Norm Based User Selection/GS Ant Selection
Fig. 2. Comparison of different user-selection schemes with Round Robin
and GS antenna-selection algorithm for ZF Receiver.
compared to random antenna selection. The norm-based user-
selection scheme performs best compared to Round Robin and
SINR user selection schemes for both random and GS antenna
selections.
Figure 2 shows the performance of the different user-
selection and antenna-selection schemes with a ZF receiver.
The proposed GS antenna-selection scheme shows better sum-
capacity performance for all three user-selection schemes
compared to random antenna selection. Both the norm-based
and SINR user-selection schemes perform significantly better
than Round Robin user-selection scheme. We conjecture that
the norm-based user selection performs better than SINR
selection because the Frobenius norm is better able to capture
the benefits of orthogonal channels.
Figure 3 compares the performance of an MMSE and a
ZF receiver with GS antenna selection for the Round Robin,
SINR and norm-based user-selection schemes. MMSE clearly
performs better than ZF in all three cases, as is to be expected.
However, at high SNR values the performance of the ZF
receiver is close to that of the MMSE receiver. In both
the MMSE and ZF receivers, the norm-based user-selection
scheme with GS antenna-selection performs best.
Figure 4 examines the sum-capacity of a SIMO system and
0 5 10 15 20 25
0
5
10
15
20
25
SNR (dB)
Sum−Capcity (bits/sec/Hz)
MMSE / GS Ant. Selection / Random User Selection
MMSE / GS Ant. Selection / SINR User Selection
MMSE / GS Ant. Selection / Norm User Selection
ZF / GS Ant. Selection / Random User Selection
ZF / GS Ant. Selection / SINR User Selection
ZF / GS Ant. Selection / Norm User Selection
Fig. 3. Comparison of MMSE and ZF Receivers for different user-selection
schemes with GS antenna-selection.
0 5 10 15 20 25
0
5
10
15
20
25
SNR (dB)
Sum−Capcity (bits/sec/Hz)
MMSE: SIMO System
MMSE: MIMO System
NTx = 2 , Ns = 2
NTx = 1 , Ns = 4
Fig. 4. Comparison of MMSE SIMO and MIMO systems with different
number of users served.
a MIMO system with an MMSE receiver using SINR user
selection and the GS antenna-selection scheme. In the SIMO
case, the number of users served is 4while in the MIMO
case the number of users served is 2. The total number of
transmit antennas and the total transmit powers are the same
in both systems. The figure shows that the sum-capacity is
higher in the 4-user case. To show what benefits there are
to compensate for this reduction in sum capacity we present
Figure 5 which shows that the 2-user system gives a higher
average SINR at the receiver. This is true for both MMSE
and ZF receivers. Higher SINRs translate into lower bit error
rates and this is helpful in increasing effective data rates in
systems where retransmission of the data is required, e.g. in
systems using the Transmission Control Protocol (TCP) for
the communication.
VII. CONCLUSION
We have presented a novel MIMO broadcast signalling
scheme with different user-selection methods and proposed
a transmit-antenna-selection algorithm based on the Gram-
Schmidt orthogonalisation algorithm. For comparison, we in-
cluded random antenna selection. We considered user-selection
schemes with feedback (norm-based and SINR) and without
280
0 5 10 15 20 25 30
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
SNR (dB)
Average SINR
MMSE: SIMO System (NTx = 1, NRx = 4, Ns = 4)
MMSE: MIMO System (NTx = 2, NRx = 4, Ns = 2)
ZF: SIMO System (NTx = 1, NRx = 4, Ns = 4)
ZF: MIMO System (NTx = 2, NRx = 4, Ns = 2)
Fig. 5. Comparison, for MMSE SIMO and MIMO systems, of average SINR
with different number of users served.
feedback (Round Robin) capabilities. We have compared the
performance of this scheme with two linear receivers: MMSE
and ZF. The simulation results show that the best performance
is achieved with norm-based user selection, Gram-Schmidt
antenna selection and MMSE receivers. Future work will
involve the performance analysis of the proposed scheme with
optimal power allocation in the MIMO downlink.
REFERENCES
[1] E. Telatar, “Capacity of multi antenna Gaussian channels,” European
Trans. on Telecommunications, vol. 10, pp. 585 – 598, Nov 1999.
[2] G. Dimic and N. Sidiropoulos, “On downlink beamforming with greedy
user selection: performance analysis and a simple new algorithm,” Signal
Processing, IEEE Transactions on [see also Acoustics, Speech, and
Signal Processing, IEEE Transactions on], vol. 53, no. 10, pp. 3857–
3868, Oct. 2005.
[3] R. Zhenyu Tu; Blum, “Multiuser diversity for a dirty paper approach,”
Communications Letters, IEEE, vol. 7, no. 8, pp. 370–372, Aug. 2003.
[4] R. Louie, M. McKay, and I. B. Collings, “Sum capacity of opportunistic
and round robin scheduling for multiuser MIMO systems with linear
receivers,” Pre-print 2008.
[5] Q. Spencer, A. Swindlehurst, and M. Haardt, “Zero-forcing methods
for downlink spatial multiplexing in multiuser MIMO channels,” Signal
Processing, IEEE Transactions on [see also Acoustics, Speech, and
Signal Processing, IEEE Transactions on], vol. 52, no. 2, pp. 461–471,
Feb. 2004.
[6] J. Jing, R. Buehrer, and W. Tranter, “Greedy scheduling performance
for a zero-forcing dirty-paper coded system,” Communications, IEEE
Transactions on, vol. 54, no. 5, pp. 789–793, May 2006.
[7] A. Khan, R. Vesilo, and I. B. Collings, “Efficient user selection
algorithms for wireless broadcast channels,” Wireless Broadband and
Ultra Wideband Communications, 2007. AusWireless 2007. The 2nd
International Conference on, 27-30 Aug. 2007.
[8] A. Paulraj, R. Nabar, and D. Gore, Introduction to space-time wireless
communications. Cambridge University Press, 2003.
[9] D. Tse and P. Vishwanath, Fundamentals of Wireless Communication.
Cambridge University Press, 2005.
[10] A. Goldsmith, Wireless Communications. Cambridge University Press,
2005.
[11] R. W. Heath Jr., M. Airy, and A. J. Paulraj, “Multiuser diversity
for MIMO wireless systems with linear receivers,” Signals, Systems
and Computers, 2001. Conference Record of the Thirty-Fifth Asilomar
Conference on, vol. 2, pp. 1194–1199 vol.2, 2001.
[12] A. Khachan, A. Tenenbaum, and R. Adve, “Linear processing for the
downlink in multiuser MIMO systems with multiple data streams,”
Communications, 2006. ICC ’06. IEEE International Conference on,
vol. 9, pp. 4113–4118, June 2006.
281
