Multi-user MIMO systems: The future in the makingkk/dtsp/tutoriaalit/Kurve.pdf · Dirty paper...
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NOVEMBER/DECEMBER 2009 370278-6648/09/$26.00 © 2009 IEEE
V ery few technologies have had
as much impact on the trajectory
of evolution of wireless commu-
nication systems as multiple input mul-
tiple output (MIMO) systems. MIMO sys-
tems have already been employed in the
existing 802.11n and 802.16e standards
resulting in a huge leap in their achiev-
able rates. A relatively recent idea of ex-
tending the benefits of MIMO systems to
multi-user scenarios seems promising in
the context of achieving high data rates
envisioned for future cellular standards
after 3G. Although substantial research
has been done on the theoretical front,
recent focus is on making multi-user
MIMO (MU-MIMO) practically realiz-
able. It offers an enormous scope for
further research in the coming years. As
in the case of any evolving technology
in communication systems, the literature
concerning MU-MIMO systems involves
complex mathematical analysis, making
it difficult for an ordinary reader to com-
prehend. This article aims at giving an
insight into MU-MIMO systems—its con-
cept, fundamentals, and trends includ-
ing an overview of important research
results. It is intended at giving a good
start to amateurs interested in being part
of the community that shapes the future
of wireless systems.
Spatial diversity and multiplexingMultiple antennas at the transmitter
and receiver side have been traditionally
used to realize diversity in order to im-
prove reliability of the channel. Spatial
diversity is achieved by transmitting the
data signal over multiple channel links
created due to the use of multiple trans-
mit and receive antennas. Diverse mul-
tipath fading at the receiver antennas
offers multiple “views” of the transmit-
ted data at the receiver thus increasing
its robustness. Figure 1 explains spatial
diversity using a common scenario. The
two cameras viewing the object from
different locations offer the observer
additional information about the object
as compared to a single camera. In a
multipath scenario where each antenna
would experience a different interfer-
ence environment, there is high prob-
ability that, if one antenna is suffering
a deep fade, another antenna has a suf-
ficient signal level. Spatial diversity im-
proves channel reliability without using
any additional spectrum or transmission
time but at the expense of increase in
the transmitted power.
In 1996, A.J. Paulraj and T. Kailath
showed that multiple transmit and re-
ceive antennas can improve the chan-
nel capacity by transmitting independent
data streams over multiple channel
links created by multiple transmit and
receive antennas. The gain in channel
capacity is proportional to the available
number of antennas at the transmitter
or receiver side, whichever is less. The
antenna arrays at the transmitter and
the receiver side create a multilink Digital Object Identifier 10.1109/MPOT.2009.934896
TUNNEL: WING, ROUTER: PLANET
ADITYA KURVE
Multi-user MIMO systems: The future in the making
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38 IEEE POTENTIALS
channel that can be expressed in the
form of a channel matrix HNR3NT (shown
in Fig. 2) where NR and NT are the
number of transmit and receive anten-
nas. If x is a vector containing transmit-
ted symbols, then a simplistic way to
express the symbol at the receiver
can be
y5Hx1w (1)
where w is additive white Gaussian noise.
The number of independent data streams
that can be transmitted is less than or
equal to min 1NT, NR 2 . It was found out
that decoding at the receiver (i.e., separat-
ing data streams from the received sym-
bols at each receiver antenna) is possible
if the receiver knows the channel matrix.
The equalization of a MIMO channel
is done at the receiver using zero forcing
(linear transformation of the received
symbol for removing interchannel inter-
ference by multiplying it with the inverse
of channel matrix) or by maximum likeli-
hood detection (mapping the received
data vector to its closest match), both of
which require the receiver to have
channel matrix information that can be
derived from suitable training. The format
of typical 802.11n packet is shown in
Fig. 3. A training field is a fixed symbol
specified in the standard and is known
both at the transmitter and receiver. The
training fields help the receiver in fre-
quency and phase correction, detecting
symbol boundaries, and tone equaliza-
tion. The high throughput long training
field (HT-LTF) is used for estimating the
channel. The number of HT-LTFs is equal
to the number of data streams multi-
plexed by the transmitter. The receiver is
expected to extract the channel matrix
HNR3NT from these training fields.
A look a MU-MIMOThe use of MIMO systems was tradi-
tionally intended for point to point
communication. The natural extension
of this thought would be to consider
MIMO systems in a multi-user scenario.
The vision for next generation cellular
networks includes data rates approach-
ing 100 Mb/s for highly mobile users
and up to 1 Gb/s for low mobile or sta-
tionary users. This calls for efficient use
of the existing spectrum. MU-MIMO
technology is expected to play a key
role in this context.
There are two challenges in a multi-
user MIMO scenario: uplink (where mul-
tiple users transmit simultaneously to
single base station) and downlink (where
the base station transmits to multiple in-
dependent users). The uplink challenge
is addressed using array processing and
multi-user detection techniques by the
base station in order to separate the sig-
nals transmitted by the users. The down-
link challenge is somewhat different.
MU-MIMO downlink channel is similar
to that of single-user MIMO (SU-MI-
MO) except that the receiver antennas
are distributed among different indepen-
dent users as shown in Fig. 4. This cre-
ates a challenge in decoding the received
symbols since joint decoding requires
each user to have the symbol received
from all the receiver antennas of all the
users. It is practically impossible to
achieve this level of coordination be-
tween all users.
Almost all of the proposed techniques
ideated for addressing the MU-MIMO
downlink challenge employ processing
of data symbols at the transmitter itself
known as precoding. Although precod-
ing is not a new concept and has been
used in SU-MIMO systems as well, it was
optional and used only to improve signal
to noise ration (SNR) at the receiver.
However, in MU-MIMO systems precod-
ing is essential to eliminate or minimize
inter-user interference. Precoding is per-
formed with the help of downlink chan-
nel state information or channel state
information (CSI). This requires the
transmitter to know the downlink CSI of
each user in order to model the precod-
ing transformation variables for each
user. A number of different techniques
to address the issue of MIMO downlink
transmission and reception have been
Multipath
Fading
Spatial Diversity
Two Different
Views of
the Same
Signal
Fig. 1 Spatial diversity.
h11h21
h22
h23
h24
h14
h32h31h13
h33
h34
h12
H =
h11 h21 h31
h12 h22 h32
h13 h23 h33
h14 h24 h34
Fig. 2 Multilink channel created due to multiple transmitter and receiver antennas.
HT-STF HT-LTF1 HT-LTF HT-LTF HT-LTF DATAHT-SIG
802.11n Greenfield Frame Format
Number of HT-LTFs is equal to
number of space multiplexed data
streams
HT-STF : Short Training Field - Helps to correct frequence and phase offsets
HT-LTF1: Long Training Field - Helps to detect symbol boundary timing
HT-SIG : Signal Field - Frame Header
HT-LTFs : Long Training Fields - Help to estimate channel matrix needed for
channel equalization
Fig. 3 An 802.11n Greenfield frame.
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NOVEMBER/DECEMBER 2009 39
proposed. A few of them have been
described in the sections below.
Dirty paper codingDirty paper coding is an information
theoretic concept proposed by M. Costa
in 1983. It states that if the transmitter
knows the interference that will affect
the signal during its propagation, then
the capacity of such a channel is same as
that of a channel without interference.
This means that preemptive interference
cancellation at the transmitter is possible
without an increase in signal power.
Although Costa’s approach is theoretical
and practically difficult to implement, it
serves as a yardstick for practical MU-
MIMO techniques to characterize the
sum capacity of multi-antenna, multi-user
channels as each proposed technique
aims to reach close to this theoretical
limit. The sum capacity in a multi-user
MIMO broadcast channel is defined as
the maximum aggregation of all users’
data rates. In spite of its complexity,
dirty paper coding has inspired a few
nonlinear precoding techniques that are
described later in this article.
Quality of service paradigmOne issue inherent to MU-MIMO sys-
tems is choosing the measure of quality
of service (QoS). The dirty paper coding-
based approach uses sum capacity as a
measure of QoS. This approach aims at
maximizing sum capacity with a con-
straint on transmitted power. The prob-
lem with this approach is that it may
result in an uneven QoS to individual
users by creating “strong users” who take
a dominant share of the available power
leaving the “weak users” with little or
no throughput. The second approach
is each user-centric. It aims at minimizing
the transmitted power subject to achiev-
ing a desired arbitrary rate or threshold
for signal-to-interference noise ratio
(SINR) for each user. For single user sys-
tems with the absence of SINR and as-
suming Gaussian noise, these two
approaches are equivalent.
Downlink precoding techniquesA typical configuration of a MU-
MIMO downlink system is shown in Fig. 4.
In this section, some approaches to solv-
ing MU-MIMO downlink challenge are
described in brief.
Decomposition of MU-MIMO channel to SU-MIMO channel
This approach is aimed at perfect can-
cellation of inter user interference at each
user at the transmitter itself. Figure 5
shows the linear precoding applied to
symbols to achieve this cancellation.
Assume that the base station has M trans-
mit antennas and there are k users, each
with one receiver antenna. Let b 1k 2 be the
symbol meant for kth user. Each user is
assigned a precoding matrix M 1k 2 that
will transform the symbol for kth user
before it is mixed with symbols from other
users at the transmit antennas. This is a
simplistic model assuming flat fading
channel. The symbol seen by the kth user
is expressed as
r 1k 2 5H 1k 2a i51 to KM 1 i 2b 1 i 2 1 n 1k 2 .
(2)
Here, H 1k 2 is the downlink channel
for kth user and n 1k 2 represents the
additive white Gaussian noise (AWGN).
Note that the received symbol consists
of interference from other users. This
component of interuser interference is
given by
H 1k 2ai2k
i51 to K M 1 i 2b 1 i 2 . (3)
In order to cancel interuser interfer-
ence, the task is to design the precod-
ing matrix M 1 i 2 for each user such that
H 1k 2ai2k
i51 to K M 1 i 2b 1 i 2 5 0. It implies
that the precoding matrix M 1k 2 should
lie in the subspace, which is the inter-
section of the kernels of the channel ma-
trices H 1 i 2of all the users except that of
kth user. M 1k 2 can be expressed as
M 1k 25V 1k 2A 1k 2 where V 1k 2 represents
the orthonormal basis of the above sub-
space, which achieves diagonalization
Effective Channel Matrix
HsMs
Ms
b (1)
b (2)
b (k)M (k)
M (2)
M (1)
++
+
Hs
Downlink
Channel
Linear Precoding
User 1
User 2
H(K )Σ M(k)b(k)
H(2)Σ M(k)b(k)
H(1)Σ M(k)b(k)
User K
Fig. 5 Linear precoding for a MU-MIMO downlink channel.
H(1) = [ h11 h21 h31]
H(2) = [ h12 h22 h32]
h11h21
h31
H(3) = [ h13 h23 h33]
H(4) = [ h14 h24 h34]
User 1
User 2
User 3
User 4
h12h22
h13h23h33
h14h24h34
h32
Fig. 4 A MU-MIMO downlink channel.
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40 IEEE POTENTIALS
of the effective channel matrix after
considering the precoding as a part of
the transformation. A 1k 2 is a nonzero
matrix that can be designed alone by
some criteria or jointly de signed with
the structure of the receiver or based
on the QoS targeted. The precoding
vector in this case decomposes the
effective channel matrix into parallel
single user MIMO channels as seen
by the receiver so that the receiver
can use SU-MIMO detection techniques
without being bothered with inter-
user interference.
This technique can be extended for
use in scenarios where each user is
equipped with more than one receive
antenna and is capable of receiving more
than one space multiplexed symbols. In
this scenario we need not achieve diago-
nalization of effective channel matrix for
each user antenna since joint decoding
is possible for antennas of the same
user. If the network channel matrix is
expressed as Hs5 3H T1 H T
2 c
HTK 4 and
precoding matr ix for al l users as
Ms5 3M1 M2 c
MK 4 then the optimal
transmit precoding vectors Ms are found
such that the resulting product Hs Ms is
block diagonal. Note that the single
antenna per user case described previ-
ously is a subset of this method when
the product Hs Ms will be completely
diagonalized.
Signal to leakage ratio maximization algorithm
The above method of perfect cancel-
lation of interuser interference puts forth
a constraint that the number of transmit
antennas at the base station should be
greater than the sum of all the receive
antennas of all the users. An alternative
to this approach is the maximization of
signal to leakage ratio for each user
given a constraint on total transmitted
power. As seen from (1), each user sees
some amount of interference from other
users’ signal (i.e., there is some power
leakage from the effective channel of
one user to that of others). It can be
proved that the signal to leakage ratio
for kth user is given by
SLR 1k 2 5 7H 1k 2M 1k 2 72/ 7H rs M rs 7 2 (4)
where H rs is Hs without H 1k 2 and M rs is Ms without M 1k 2 . This approach can
support as many subchannels as the
user’s antennas, which is not achiev-
able in perfect interference cancellation
schemes. This algorithm further em -
ploys an iterative process called suc-
cessive optimization to calculate the
precoding vectors for each user. After
determining the precoding vector for
the first user, it calculates the leakage
from the first user to all the other users
in order to calculate SLR and the pre-
coding vector for next successive users
and so on.
Vector perturbation, lattice precoders, and regularized precoding
The channel inversion technique de -
scribed above is an attractive solution due
to its simplicity. However, the data trans-
mitted after precoding using channel
inversion has a large norm, which means
that there is increase in the transmitted
signal power. Due to this, the sum rate for
channel inversion in its plain form is poor.
The sum rate does not grow linearly with
minimum of transmit or user antennas as
expected due to the large spread in the
singular values of the channel matrix.
Nonlinear precoding techniques, although
more complex than zero forcing tech-
niques, perform closer to sum capacity.
Vector perturbation technique modi-
fies the data to be transmitted b to b
before multiplying it with inverse of chan-
nel matrix by perturbing it with an inte-
ger offset so that the data vector after
zero forcing has a smaller norm and re-
duced power compared to the plain chan-
nel inversion method
b r 1k 2 5 b 1k 2 1tl (5)
where t is a positive real number and l is a complex vector a1 ib with dimen-
sions equal to the number of user anten-
nas where a and b are integers. The
receiver uses modulo operation to re-
cover the signal (see Fig. 6). It has been
proved that choosing the optimum value
of l makes the power of the transmitted
signal independent of the number of
transmitter or receiver antennas, which-
ever is less and also achieves its lower
bound. It does so by placing the largest
signal components along the smallest
singular values of the inverse channel
and the smallest signal components
along the largest singular values of the
inverse channel.
Finding the optimum value of l is a
K-dimensional integer-lattice least squares
problem where K is the number of user
antennas. Recent efforts are aimed at dis-
covering a solution to this problem of
finding optimum integers from a lattice.
One solution could be the use of a
sphere decoder developed by Fincke
and Pohst. It avoids an exhaustive search
over all possible integers in a lattice by
limiting the search space to a sphere of
some given radius centered on a starting
point. The scalar t is chosen to provide
symmetric decoding region around
every signal constellation point. A
large t increases the decoding region at
the upper and lower extremes of the
constellation but reduces the effect of
b (1) Precoder for
User 1
Precoder for
User K
Precoder for User K
b ′(k)
User 1 Receiver
Detector
Nonlinear Precoding
Mod τ
User k Receiver
User k Receiver
Downlink
Channel
HsHk Noise
b (k )
b (k )
–1τk
+ + +× ×
Fig. 6 Nonlinear precoding for a MU-MIMO downlink channel.
The channel inversion technique
described above is an attractive
solution. However, the data
transmitted after precoding
using channel inversion has
a large norm.
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NOVEMBER/DECEMBER 2009 41
vector perturbation by increasing the
norm of the transmitted data matrix. The
plain channel inversion technique de-
composes the effective channel matrix
using singular value decomposition. In
order to cancel multi-user interference, it
assumes that each receiver has the knowl-
edge of the left singular matrix of the SVD.
This requires global channel state infor-
mation (CSI) at the receivers or additional
training. It has been shown that lattice-
based techniques used in conjunction
with zero forcing techniques eliminate
this requirement. In this case, the receiver
requires a simple decoding filter.
Another method to improve the per-
formance of channel inversion tech-
nique in low SNRs and high values of
K is regularization of the channel in -
verse by adding a multiple of identity
matrix before inverting, i.e., using s5
H * 1HH *1aIK 221b 1k 2 instead of plain
inversion s5H * 1HH * 221b 1k 2 . Using
channel inverse regularization along
with vector perturbation has been
shown to achieve near-capacity perfor-
mance at all SNRs.
Multi-user diversity and scheduling
A practical situation that has not been
considered in the discussion until now is
multi-user diversity. Multi-user diversity is
a form of selection diversity among users;
the base station can schedule its transmis-
sion to those users with favorable channel
fading conditions to improve the system
throughput. In MU-MIMO schemes, this
feature is particularly important due to
the possibility for the base station to
group users for spatial multiplexing that
improve the sum rate. It has been proved
that the suboptimal zero forcing tech-
niques approach optimal performance by
scheduling due to the large available
sample space when the number of users
is large. An optimum scheduling algo-
rithm performs an exhaustive search over
all possible combination of all active users
so as to find a group that will help achieve
the maximum sum rate. A user is consid-
ered to be active if there is incoming data
for intended for it at the access point.
However, such a technique is computa-
tionally onerous. Moreover, it neglects
the fairness criterion, which expects time
constrained service delay for each user
irrespective of its downlink channel qual-
ity. A “greedy” scheduling scheme reduces
computational complexity by choosing
the user with the highest channel capac-
ity and then choosing successive users of
the group who will maximize the sum
capacity. To address the fairness criteria
the greedy scheduling scheme can be
combined with round-robin scheduling.
It means that after the first group of users
is scheduled for transmission, a second
group of users is selected from the
remaining users in the same “greedy”
fashion. This procedure is iterated until
each active user is accommodated in
some group.
Converging toward a realizable solution
The recent focus of research work in
MU-MIMO systems has been toward ad-
dressing practical challenges in imple-
menting MU-MIMO systems as a tangible
technology for future cellular standards.
Imperfect CSI, quantization of CSI feed-
back by the users to the transmitter,
feedback overhead, receiver training,
and application to frequency selective
fading channels are some of the practi-
cal difficulties.
The necessity of CSI at the transmit-
ter will introduce substantial overhead
on the system throughput. A number of
limited feedback schemes have been
proposed to minimize this overhead.
One scheme proposes to feedback only
the shape of the channel (i.e., normal-
ized channel vector). This is because
the shape vector mainly captures the
directional knowledge of paths, which
usually varies much more slowly than
the amplitude of the channel. In other
schemes it has been proposed to quan-
tize the precoder for a MIMO channel
and not simply the channel coefficients.
The challenge of extending this work to
the multi-user channel is that the trans-
mit precoder depends on the channels
of the other users in the system.
A codebook based quantized feedback
is another promising scheme that incurs
the least feedback overhead. The base sta-
tion and the users have access to a CSI
codebook, which is designed offline. Each
user sends the binary index of the best
code vector from the codebook through a
zero-error, zero-delay feedback channel to
the base station. It has also been shown
that the channel shape alone does not
achieve the full multiplexing and multi-
user diversity gain simultaneously. To
achieve both gains, channel quality infor-
mation (CQI) feedback is necessary, and
that CQI should be the SINR rather than
just the channel magnitude, since SINR
captures both the channel magnitude and
the quantization error.
The optimal gain due to multi-user
diversity is achieved when there is a
large number of users. However, as the
users increase, the CSI feedback over-
head also increases. One scheme to
address this issue proposes the use of
Downlink Framing
Uplink Framing
Contention
Channel 1
Contention
Channel Mt
Broadcast
MessageListen
Uplink
TransmissionCC1 CC Mt Feedback Uplink Transmission
Random
Access
Minislots
Example of framing structure for use with MIMO opportunistc feedback
Courtesy: Tang, Heath, Cho and Yun, “Opportunistic Feedback for Multi-User MIMO
Systems with Linear Receivers”
PollingDownlink Transmission
of Mt Data Streams
. . .
. . .
Fig. 7 Framing structure for opportunistic feedback.
A “greedy” scheduling scheme
reduces computational complexity
by choosing the user with the
highest channel capacity and
then choosing successive users
of the group who will maximize
the sum capacity.
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42 IEEE POTENTIALS
threshold-based feedback before sched-
uling the users (i.e., the users only send
the information that whether the SINR at
their end is greater than a required thresh-
old value). This allows the base station to
schedule users for transmission. Only then
are the scheduled users requested for a
full CSI feedback.
Grassmannian line packing has also
been proposed to compute precoding
vectors that generate nearly orthogonal
beams. This method allows the base sta-
tion to generate number of beams larger
than the number of available base station
antennas, which have minimum correla-
tion. The number of beams generated
depends on the minimum rate-per-user
requirement. In the training phase each
user sequentially calculates the SINR for
each beam and feeds back the index of
the beam with minimum SINR along with
the SINR value.
Figure 7 shows a media access con-
trol layer framing structure proposed in
“Opportunistic Feedback for Multi-User
MIMO Systems with Linear Receivers” by
Tang, et al. The broadcast message is fol-
lowed by Mt contention channel fields
each with K mini slots for feedback from
the users. Each user with its channel
quality above certain level vies for one
of the channel slots selected randomly
for transmitting its id and channel quality
information to the base station. A user
can successfully send its information to
the base station only if there is no con-
tention for that mini slot. The number of
feedback slots K is chosen in order to
minimize contention at the same time
controlling feedback overhead. It was
shown that this strategy requires lower
feedback overhead and at the same time
exploits multi-user diversity.
Conclusion The consummation of all the research
work in MU-MIMO systems will be in the
form of a standard. It will require collating
all the research findings into a deployable
standard with well defined transmit and
receive processing, scheduling options,
receiver training fields, CSI feedback rates,
and other specifications essential for com-
patibility. MU-MIMO technology offers
aspiring researchers an exciting challenge
and an opportunity to work on a solution
that vies for a spot that will make it key
technology in future cellular systems.
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About the authorAditya Kurve ([email protected]) is
a member of the IEEE and a graduate stu-
dent in the electrical engineering depart-
ment at The Pennsylvania State University
in University Park. He received his bache-
lor of engineering degree in electronics
engineering from the University of Pune,
India, in 2006. He has worked on the digi-
tal part of the 802.11n baseband PHY pro-
cessor at Conexant Systems, Pune.
MU-MIMO technology offers
aspiring researchers an
exciting challenge and an
opportunity to work on a
solution that vies for a spot
that will make it key technology
in future cellular systems.
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From the Beginning
07-PUBS-0258c Proc 6th PG.indd 1 12/5/07 11:58:00 AM
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