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 (adikurve@gmail.com) 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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