Thesis Mu Mimo

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Master Thesis

Electrical Engineering Emphasis on Telecommunications

Thesis no: MEE10:78

September 2010.

User Scheduling Algorithm for

MU-MIMO System with limited feedback

Sudhir Kumar Burra (861019-4717)

Reddy Prasad Reddy Yendrapalli (860808-1553)

Under the esteemed guidance of

Prof. Abbas Mohammed

Blekinge Institute of Technology

September 2010

Department of Electrical Engineering

School of Engineering

Blekinge Institute of Technology

SE-37179 Karlskrona

Sweden.



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ACKNOWLEDGEMENTS

We express our sincere gratitude to our guide P r o f . A B B A S M O H A M M E D for his

guidance and constant encouragement throughout the project work. We are very grateful to him

for providing us his valuable time through various sessions to discuss the issues related to our

thesis work which enabled us to take this thesis to fruitful completion.

Special thanks to Mr. MICHAEL ASMAN, Program Manager for DDP in SWEDEN, for

his valuable suggestions and guidance during the entire course work.

We would like to thank Mr. GURUDUTT KUMAR VELPULA, International Coordinator

for DDP, for providing us the opportunity to study in BTH, SWEDEN and also we would like to

thank Dr. MADHAVI LATHA, Coordinator for DDP, JNTU.

We would like to convey our heartful thanks to all the Professors of BTH and JNTU for

their immense help and moral support in completing our course work successfully.

We express our sincere thanks to all my friends at BTH, who supported us during our stay

in SWEDEN and made it really enjoyable and memorable.

We are very grateful to our parents and our sisters for their support and constant

encouragement.

Sudhir Kumar Burra

Reddy Prasad Reddy Yendrapalli.



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ABSTRACT

In conventional cellular systems, each base station (BS) transmits signals intended for a single

user in a particular resource allocation. As bandwidth is a scarce resource, effective utilization of

the available bandwidth in the system is essential in modern wireless systems especially for

applications such as video streaming and voice over internet protocol (VoIP) which demands

high data rate. Fortunately since the users feedback the channel state information to the network,

there is an opportunity for the BS to schedule more than one users data in a single resource

allocation by designing precoders which beamform the data to the intended user. This technique

which is called multi-user multiple-input and multiple-output (MU-MIMO) is adopted in the

evolving radio interface technologies. For properly utilizing the feedback information,

scheduling algorithms are designed which selects pairs of users which would maximize system

capacity. In this thesis we describe MU-MIMO technique with codebook based precoding that

has been proposed for the IEEE 802.16m mobile broadband standard. A multi-user proportional

fair (PF) scheduling algorithm is designed to improve both sum capacity and fairness among

users.

Key words: MU-MIMO, Bandwidth, Limited feedback, Data rate, Precoder.



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GLOSSARY

AWGN Additive White Gaussian Noise

BS Base Station

CCI Co-Channel Interference

CQI Channel Quality Indicator

CL Closed Loop

DR DataRegion

FDD Frequency Division Duplex

LOS Line Of Sight

LTE Long Term Evolution

LTE-A Long Term Evolution Advanced

MIMO Multiple Input Multiple Output

MMSE Minimum Mean Square Error

MRC Maximum Ratio Combining

MS Mobile Station

MU-MIMO Multi User MIMO

MUI Multilingual User Interface

OFDM Orthogonal Frequency Division Multiplexing

OL Open Loop

PF Proportional Fair

PMI Precoder Matrix Information

QoS Quality of Service



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RF Radio Frequency

SFBC Space Frequency Block Coding

SINR Signal to Interference plus Noise Ratio

SISO Single Input Single Output

SNR Signal to Noise Ratio

STBC Space Time Block Coding

UE User Environment

UT User Terminal

VoIP Voice over Internet Protocol

ZF Zero Forcing



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CONTENTS

Ack nowledgements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

Abstract. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1 Intr oduction 9

1.1 Motivation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10

1.2 Objectives. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

1.3 Back ground . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . 11

1.4 Outline. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2 Theory of MIMO System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .13

2.1 MIMO. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .13

2.2 MIMO System. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.3 MIMO Precoding 15

2.3.1 Optimal Unitary or SVD precoding. . . . . . . . . . . . . . .16

2.3.2 Codebook Based Precoding. . . . . . . . . . . . 16

2.3.3 Zero Forcing Precoding 16

2.3.4 Dirty Paper Precoding . . . . . . . . . . . . . . . . . . . . . . . . .16

3 Literature Survey 17

3.1 Multi User MIMO . . . . . . . . . . . . . . . . . . 17

3.1.1 Spatial Diversity Gain . . . . . . . . . . . . . . 17

3.1.2 Spatial Multiplexing Gain. . . . . . . . . . . . 17



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3.1.3 Multi User Diversity Gain. . . . . . 18

3.2 Challenges of MU-MIMO. . . . . . . . . . . . . . . . . . 19

3.2.1 Interference . . . . . . . . . . . . . . . 19

3.2.2 Post-processing. . . . . . . . . . . . 19

3.2.3 Pre-processing/Precoding. . . . . . . . . . . . . . . . . . . . . . .20

3.2.4 CQI Modelling . . . . . . . . . . . . . . 20

3.2.5 Scheduling. . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3.3 Precoding Techniques of MU-MIMO . . . . . . . . . . . . 21

3.3.1 Zero Forcing Beamforming and Unitary Precoding . . . .21

3.3.2 Channel Inversion Method and Diagnolization Method.21

3.4 System Model. . . . . . . . . . . . . 22

3.4.1 Uncorrelated Channel Model . . . . . . . . . . . 23

3.4.2 Correlated Channel Model. . . . . . . . . . . . 24

3.5 Proportional Fair Scheduler . . . . . . . . . . . . . . . 24

4 Mathematical Procedure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..25

4.1 MU-MIMO Capacity Formulation. . . . . . . . . . . . . . 25

4.1.1 MMSE Receiver . . . . . . . . . . . . . . . . . . . . 26

4.1.2 CQI Calculation. . . . . . . . . . . . . . . . . . . . . . . 27

4.2 Procedure 29

5 Results and Discussion…………………………………………… 31

6 Conclusions and Future work.. ……………………………………. 36

7 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .37



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List of Figures

2.1 MIMO system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.2 MIMO pre and post processing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .15

3.1 MU-MIMO system setup. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

4.1 Procedure for MU-MIMO. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

5.1 Sum capacity of MU-MIMO for 4×2 with uncorrelated channel. . . . . . . . . . 33

5.2 Sum capacity of MU-MIMO for 4×1with uncorrelated channel. . . . . . . . . . .33

5.3 Sum capacity of MU-MIMO for 4×2 with correlated channel. . . . . . . . . . . . 34

5.4 Sum capacity of MU-MIMO for 4×1 with correlated channel. . . . . . . . . . .. 34



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CHAPTER 1

1. INTRODUCTION

As the demand for high data rate applications like video and audio streaming, VoIP, video

conferencing are increasing, future wireless systems should be able to provide high speed broad

band services for mobile users with sufficient quality of service (QoS) support. As the bandwidth

and power are scarce or limited resources, techniques which lead to efficient utilization of these

resources are quite necessary in the next generation wireless systems. At the same time the

wireless channel creates a challenging environment because of variety of channel impairments.

Thus, future wireless systems are to be designed taking all these factors into consideration.

For scenarios with a large number of users to be served in one cell, high capacity

gains can be achieved by transmitting independent data streams to different users sharing the

same time-frequency resources. This technique is referred to as multi-user multiple-input

multiple-output (MU-MIMO) [1]. It is one of the techniques which can be used in cellular

systems to increase spectral efficiency.

In MU-MIMO operation two or more user environment’s (UE) share the same time-

frequency resources. Several parallel data streams are transmitted simultaneously, one for

each UE. It is assumed that the UE feeds back a quantized version of the observed channel, so

that base station (BS) can schedule in MU-MIMO mode terminals with good channel

separation.

Long term evolution (LTE) and its successor LTE-Advanced (LTE-A) are some of next

generation wireless systems, which use advanced features like MIMO, link adaptation,

orthogonal frequency division multiplexing (OFDM) and many other techniques to help in

achieving high spectral efficiencies.



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1.1 MOTIVATION

MIMO systems which employ multiple antennas at transmitter and receiver is a very

useful technique in wireless environments to combat the effects of fading and to use the radio

channel efficiently by transmitting multiple streams to a user in the same resource allocation,

thus achieving diversity gain and multiplexing gain, which is the first step in achieving high

spectral efficiencies. Transmit diversity (space frequency block coding) is one such scheme

which sends multiple copies of the same data to a user which makes use of multiple replicas of

transmitted data to combat fading. This is a very useful scheme in fast fading environments. Also

the fact that each user experiences different channel conditions and quantized channel state

information is available at the BS, which can be utilized to achieve additional gain by jointly

precoding users which makes them orthogonal to each other. Thus allowing the BS to schedule

more than one user in a resource allocation. This leads to a situation where efficient user

scheduling and pairing algorithms are required, which uses the feedback information

intelligently at BS to maximize the capacity achievable in the system.



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1.2 OBJECTIVE

The main goal is to study and evaluate the performance of MU-MIMO

systems using feedback sent by the users.

Create a cellular environment with single or multiple BSs with multiple users with

multiple antennas spread randomly positioned inside the cells.

First the BS will transmit reference symbols which are known to the users.

Calculate signal to interference plus noise ratio (SINR) and sum capacity.

Plot the graph of sum capacity vs signal-to-noise ratio (SNR).

1.3 Background

MU-MIMO has generated considerable interest recently. The main idea emerging from

this research is that multiple users can be simultaneously multiplexed to take simultaneous

advantage of multi-user and spatial diversity. The optimal BS interference cancellation strategy

is the so called dirty paper coding (DPC) [6], but it is not directly practical. More realistic linear

multi-user precoding techniques have been developed. BS does not have knowledge of the

channel unless it is feedback by the mobile station (MS) such as in the case of Frequency Division

Duplex (FDD) systems. It is huge amount for MS to feedback the complete channel, hence

quest for f inite feedback systems arises. One of the solutions to this problem is codebook based

precoding technique which is a linear precoding technique. Here, a codebook which contains a

set of precoding matrices known to the BS and MS is used.

This thesis describes MU-MIMO technique with codebook based precoding that has

been proposed for the IEEE 802.16m mobile broadband standard. A multi-user PF schedulingalgorithm is designed to improve both sum capacity and fairness among users.



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1.4 Outline

Chapter 2

This chapter will give a detailed description of MIMO systems.

Chapter 3

This chapter will give a detailed description of MU-MIMO systems.

Chapter 4

This chapter will discuss the actual formulation used to calculate channel quality indicator (CQI)

and capacity of users.

Chapter 5

This chapter includes the MATLAB results and discussion.

Chapter 6

This chapter presents the conclusions.



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CHAPTER 2

2. Theory of MIMO System

2.1 MIMO

The use of multiple antennas allows independent channels to be created in space and it is

possible to achieve spatial diversity, which can be created without any additional bandwidth

and transmit power . In addition to providing spatial diversity, antenna arrays can be used to

focus energy (beamforming) or create multiple parallel channels for carrying unique data

streams (spatial multiplexing). When multiple antennas are used at both the transmitter and the

receiver, it is commonly referred as MIMO system. These systems can be used to:

Increase the system reliability (decrease the bit or packet error rate).

Increase the achievable data rate and hence system capacity.

Increase the coverage area.

Decrease the required transmits power.

However, these four desirable attributes usually compete with one another. For example, an

increase in data rate will often require an increase in either the error rate or transmit power.



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2.2 MIMO System

Figure 2.1 shows MIMO system where there are M (>1) antennas at the BS and N (>1)

antennas at the MS.

1 1

2 2

BS . H . MS

M N

Figure 2.1: MIMO System

The wireless channel matrix H can be expressed as

11 12 1

21 22 2

1 2

H

M

M

N N NM NXM

h h h

h h h

h h h

(2.1)

where hij is the channel gain from ith receive antenna to the j th transmit antenna. In case of

MIMO systems along with diversity, spatial multiplexing can also be exploited which refers

to breaking the incoming high rate data stream into M independent data streams. Assuming that

the streams can be successfully decoded, the nominal spectral efficiency is thus increased by a

factor of M. This is certainly exciting which implies that adding antenna elements can greatly

increase the viability of the high data rates desired for wireless broadband access. The MS has to

estimate M×1 transmit vector from N×1 receive vector. In order to adjust the number of

streams, some sort of pre-processing also called precoding is done before actual transmission,

which can be thought as a kind of beamforming. More insights about MIMO can be found in

reference [2]. MIMO systems can be classified as:



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Single-user or Multi-user

When a single-user is scheduled in a dataregion it is referred as single-user MIMO (SU-

MIMO). If more than one user is scheduled in a dataregion then it becomes MU-MIMO.

These two are differ in terms of precoding and scheduling. The number of streams allocated to

each user is configurable.

Open loop or Closed loop

When the precoders are fixed to subbands and chosen from a codebook which is known to

BS and MS is referred as Open loop MIMO (OL-MIMO). If the precoders are formed by the

scheduler based on the preferred matrix index (PMI) feedback from each of the MSs, then it iscalled Closed loop MIMO (CL-MIMO).

From the above classification, there are four possible MIMO configurations:

(1) OL-SU-MIMO (2) OL-MU-MIMO (3) CL-SU-MIMO (4) CL-MU-MIMO.

2.3 MIMO precoding

Precoding is done mainly to map K transmitted symbols to M transmitting antennas. In case of

SU-MIMO these K symbols belong to single-user, whereas in MU-MIMO they are intended

for K different users (assuming single stream per user). There are various ways of precoding,

some of them are discussed here in brief.

1 x 1 1

1 x

2 x Pre 2 2 Post2

x

. Processing . . processing .. . . .

K x M N

k x

Figure 2.2: MIMO pre and post processing.



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2.3.1 Optimal Unitary or SVD precoding

In case of SU-MIMO, when the channel is known at the transmitter, the best precoder to use is

the matrix formed by the right singular vectors of the channel, which has proven to achieve the

channel capacity of MIMO systems, at the cost of feeding back signaling of the channel state

information from MS to the BS.

2.3.2 Codebook based precoding

Here a codebook which contains a set of precoders is known at the transmitter and receiver.

In case of OL-MU-MIMO, precoders are fixed to all the subbands and the user needs to

feedback which precoding vector in the precoder is to be used to precode the data. Detail

description on how code books are designed is found in references [7] and [8].

2.3.3 Zero Forcing (ZF) precoding

For SU-MIMO the precoder is just the pseudo inverse of the channel, which can completely

cancel out the inter stream interference and reproduce the data vector transmitted with additive

noise. In case of MU-MIMO the precoder has to cancel out multi-user interference, so a block

diagonalization method is proposed in reference [9] which is used to find the precoder under

some constraints.

2.3.4 Dirty Paper Coding (DPC)

All the techniques discussed previously were linear techniques, but DPC is a non-linear coding

technique that pre-cancels known interference without power penalty. Once the transmitter is

assumed to know the interference signal regardless of channel state information knowledge at

the receiver. This category includes Costa Precoding, Tomlinson-Harashima Precoding and the

Vector Perturbation Technique as discussed in references [4] and [5].



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CHAPTER 3

3. Literature Survey of MU-MIMO

3.1 MU-MIMO

In MU-MIMO more than one user can be served in the same bandwidth using appropriate

precoders at BS. This technique is just like SU-MIMO where one or more streams transmitted

at a time using multiple antennas belonging to the same user. In MU-MIMO each stream could

belong to a different user i.e., instead of stream multiplexing, MU-MIMO does user

multiplexing. For scenarios where large number of users is to be served in one cell or to serve a

limited number of users with increased throughput, MU-MIMO can be used.

The three gains that are useful in increasing the performance of MU-MIMO systems are

defined as follows [11].

3.1.1 Spatial diversity gain

This is the technique for improving communication quality by transmitting and receiving

with multiple antennas. Each pair of transmit and receive antennas provides a signal path by

sending signals that carry the same information through different paths. Hence multiple

independently faded replicas of the data symbol can be obtained and more reliable reception is

achieved.

3.1.2 Spatial multiplexing gain

This is the performance improvement derived from using multiple antennas to transmit

multiple signal flows through space in parallel. For a MIMO system with Nt transmitting

antennas and Nr receiving antennas, the maximum achievable spatial multiplexing gain is

minimum of Nt and Nr .



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3.1.3 Multi-user diversity gain

The improvement in system throughput derived from using a scheduler which exploits the

disparities fading and interference characteristics between users.

The first two (spatial diversity gain, spatial multiplexing gain) can be typically achieved

using precoders at the transmitter side by using the feedback information sent by UE and using

multiple antennas. But the latter can be achieved by using proper scheduling techniques.

MU-MIMO offers additional degrees of freedom when compared to SU-MIMO since

multiple users are multiplexed in the same physical channel. This can be achieved by pairing

users whose precoders are orthogonal to each other in a dataregion and then precoding them

appropriately so that each user sees only its own information. As UE feedback quantized

channel information, the users will not be perfectly orthogonal to each other so some remnant

inter user interference will be seen by each of the users who are paired. This can be minimized

by using a minimum mean square error (MMSE) receiver at UE to minimize the effect of

multilingual user interference (MUI) on capacity [17].

The main advantages that lead to MIMO paradigm shift to MU-MIMO from SU-MIMO

communications are

1. MU-MIMO schemes allow for direct gain in multiple-access capacity (proportional to

number of transmit antennas) because of multiplexing of data of several users in the same radio

channel.

2. MU-MIMO schemes are more immune to loss of channel rank because of line of sight

(LOS) conditions or antenna correlation, which is a major problem that causes performance

degradation in SU-MIMO communications.



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3.2 Challenges of MU-MIMO

MU-MIMO has tremendous benefits which are achieved by overcoming some challenges.

Multiple users using the same resources at the same time would lead to several issues that need

to be considered, some of them are mentioned here.

3.2.1 Interference

When multiple users are using the same resources at the same time, there would be

severe interference between their signals. Each user should be capable of decoding his

respective stream by reducing the interference due to other stream. This can be achieved by

careful pre-processing at the transmitter and post-processing at the receiver.

3.2.2 Post-processing

In single-user transmission, MIMO could be used for spatial multiplexing, where

multiple symbols are transmitted to the same user. For example, c onsi der a 2×2 single-user

system, in which the received vector can be represented as

y = Hx + n (3.1)

where the transmitted 2×1 vector x represents 2 symbols that are transmitted simultaneously

to a particular user, thus doubling the user throughput. In order to decode the 2 symbols from

the received 2×1 vector y, a simple approach would be to build a linear receiver that

diagonalises the system, i.e., multiply the received vector y by H−1. This decouples the system

and we get back the two transmitted symbols.

In the MU-MIMO case, the effective received vector y, is a concatenation of the

symbols received by geographically separated users, and post processing must be done in such

a way to reduce the interference from the other user. Several receiver configurations such as

MMSE, maximum ratio combining (MRC) and ZF are possible but MMSE receiver is shown to

reduce the interference effectively.



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3.2.3 Pre-processing/precoding

Because of this limitation on the interference cancellation that can be done at the MS,

good precoders need to be designed, such that we beamform efficiently towards the two users.

However this would require good knowledge of the channels to both users at the BS, which

requires heavy amounts of feedback. So we would need to come up with the best possible

precoders to use at the BS, with a limitation on the feedback rate.

3.2.4 Channel Quality Indicator (CQI) modeling

CQI is a feedback by the user in frame (n), for the allocation of modulation and coding

schemes in frame (n+1). CQI modeling is to be done so that the user experiences a good

throughput. In the single input single output (SISO) case, CQI is a function of the channel to a

particular user, which (for low Doppler ’s shift) does not fluctuate much between adjacent

frames. But in case of MU-MIMO, in addition to being a function of the channel to the user,

CQI is also a function of the precoder used at the BS. Hence, better the precoding is lesser is the

interference and higher CQI will be.

3.2.5 Scheduling

When we have a number of users contending for same resource, throughputs can be

increased by scheduling those users who experience a good channel. This increase in system

performance merely because of scheduling the best-set of users at any point of time is known as

multi-user diversity. However, maximizing system throughput must not come as a result of

cell-edge users (who face poor channel conditions) never being scheduled. System performance

must be maximized and at the same time a certain amount of fairness must be ensured among

the users in the system. A multi-user scheduler that meets these demands needs to be

implemented.



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3.3 Precoding techniques of MU-MIMO

3.3.1 Zero Forcing Beamforming (ZFBF) and Unitary precoding

ZFBF and unitary precoding are two useful precoding techniques for MU-MIMO in

limited feedback environments. ZF precoding is a potential precoder design for MU-MIMO.

The main benefit of ZF scheme is that the interference is pre-cancelled at the transmitter side. It

implies that eNodeB has most of the computational complexity in designing the precoder and each

terminal needs only information regarding its own data streams for reception. However the

quantized channel information has to be precise, so that the multi-user interference becomes

sufficiently low in order to get gains from this scheme. The ZF precoder can be designed using

the moore-penrose psuedo inverse as given below (assuming “u” users are paired together)

( )eq eq eqT W

(3.2)

where eq is the equivalent channel feedback andT

W is the precoder used.

3.3.2 Channel Inversion Method and Diagnolization method (BD)

Channel inversion method is one of the linear precoding MU-MIMO techniques

which is simple and has capacity limit. When spatial correlation is increased, the multi-user

channel capacity decreases rapidly. BD can perfectly cancel co-channel interference (CCI), but

has antenna constraint at the BS and MS. The computation burden for system is very heavy

when the number of users is very large. Both channel inversion method and BD are based on the

feedback of the MIMO channel matrix, so the feedback is very large. More information about

these techniques can be found in [13][14][15].



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3.4 System Model

Let us consider a MIMO system with M transmitting antennas at the BS and N

receiving antennas at each MS as shown in figure 3.1. There is a codebook known a prior to

both the BS and all MSs. If U users are waiting to be scheduled at the BS, the scheduler will

determine K (<U) users according to scheduling algorithm and the feedback sent by the MSs. At

the same time, the scheduler will select a precoding matrix W from the codebook to precode for

the scheduled K users before transmission [3].

1 x

User 1

User 1 data1

x 1

User 2 data2

x 2 2

x

. . . User 2

User U datak

x M

. .

. .

k x

User K

Feedback: CQI, Precoder Vector index.

Figure 3.1: MU-MIMO System setup.

The OFDM technique has become one of the most promising techniques for next generation

wireless communication systems. Since OFDM technique can deal frequency selective fading as

flat fading, so in this thesis, we model the MIMO channel as the flat fading MIMO channel [3].

SCHEDULER PRECODER



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l

3.4.1 Uncorrelated Channel Model

The received signal vector at the k th MS is given by

k k k y =H Wx+n k = 1,2,.....,U (3.3)

where

11 12 11

2 21 22 2

1 21

x and

k k k

M

k k k

M

k

k k k k N N NM KX NXM

h h h x

x h h h H

x h h h

• xk is the complex symbol transmitted for k th user.

• Hk ∈ C N ×M is the N×M wireless channel matrix from the k th MS to BS and hij ∼CN (0,

1) which represents the channel impulse response coupling the j th antenna at the BS to the ith

antenna at the MS and its amplitude obeys independent and identical Rayleigh-distribution.

• 1 2 k M K W= v v . . . v

W∈C is a precoder chosen from the codebook C which contains set of

unitary precoders and vk represents precoding vector used to precode k

th

user data, where k iscalled stream indicator or precoding vector index.

• nk ∼ CN (0, NoI N ) is noise vector at the k th MS.

3.4.2 Correlated Channel model

The antennas at the BS are magnitude correlated i.e., each antenna at the BS sees same

channel gain to all receiver antennas of k th user. Now the channel in the previous subsection can

be modified as

2 3 4

1

2 3 4

2

( )

( )

k k k k

k k k k

j j j j

k j j j j

h e e e e H

h e e e e

(3.4)



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Here θk ∼u [−π/ 3, +π/ 3] for k th user, hi is Rayleigh distributed random variable representing

the channel gain between ith receive antenna and any of the antennas at BS.

3.5 Proportional Fair (PF) Scheduler

The PF scheduler is designed to take advantage of multi-user diversity while

maintaining comparable long-term throughput for all users. Let R k (t) denote the instantaneous

data rate that user k can achieve at time t, and let Tk (t) be the average throughput for user k

up to time slot t. The PF scheduler selects the user denoted as k ∗ with the highest R k (t)/ Tk

(t) for transmission. In the long term, this is equivalent to selecting the user with the highest

instantaneous rate relative to its average throughput.

The average throughput Tk (t) for all users is then updated according to

*

*

1 1( 1) (1 ) ( ) ( ) k=k

1= (1 ) ( ) k k

( )PF Metric =

( )

k k k

c c

k

c

k

k

T t T t R t t t

T t t

R t

T t

(3.5)

Thus consistently underserved users receive scheduling priority, which promotes fairness.

The parameter tc controls the latency of the system. If tc is large, the latency increases, with the

benefit of higher sum throughput. If tc is small, the latency decreases, since the average

throughput values change more quickly, at the expense of some throughput.

There are other schedulers like Round Robin scheduler (RR scheduler) which schedules

users one after another without any priority and greedy scheduler, which schedule the users

based on their instantaneous rates by ignoring the average throughput and sacrificing the

fairness.



25 | P a g e

CHAPTER 4

4. Mathematical Procedure

In this chapter we introduce formulation used to calculate CQI and capacity of users.

4.1 MU-MIMO Capacity Formulation

Referring to the system model in figure 3.1 the received signal vector for 1st user can be

expressed as

1 1 1x y H W n (4.1)

Now the transmitted symbol for the 1st user xi is to be estimated from this received vector.

For traditional MIMO detection a linear receiver is used to detect the transmit data. ZF,

MMSE and MRC detection criterions are commonly employed. In order to obtain good

performance, we consider a linear MMSE receiver equation discussed earlier and can be re-

written as

1

2

1 1 1 2 1k

k

x

x y H v v v n

x

1 1 1 1 1 1

1, 1

K

i i

i i

y H v x H v x n

(4.2)

The first term represents the desired signal, the second term is inter stream interference

caused by scheduling more than one user and the third term is complex Additive White Gaussian

Noise (AWGN) at the receiver. Let the effective channel after precoding be expressed as

H̃ 1= H1W, where H̃

1 is N × K precoded channel matrix.



26 | P a g e

4.1.1 MMSE Receiver

MMSE receiver will try to reduce the MSE between the desired and estimated symbols. The

linear 1× N MMSE receiver b1 to decode 1st user data can be expressed as

12 2 *

1 1 1 1 1min { } min { }R

b bb x x x y p

| | | | (4.3)

where

• R is N × N auto-correlation matrix of received vector y1.

• p is N × 1 cross-correlation vector between the desired symbol x1 and received

vector y1 .

Assuming noise and data are i.i.d and uncorrelated random vectors. The total power constraint P

is divided equally among K users, expressions for R and p is calculated as follows

*

1 1{ } R y y

* * *1 1 1 1

{ } { } XX n n

*

1 1 0 N P N I K

=

(4.4)

*

1 1{ } p y x

*

1 1 1 1{ }v x x

1 1

P v

K

=

1 P h K

=

(4.5)



27 | P a g e

where h̃ 1 = H1 v1 = [H̃

1 ]1 = [H1W]1 and “ ∗ ” indicates conjugate transpose operation. The

final expression for MMSE filter is written as

1

* * 01 1 1 1 N

KN b h I

P

(4.6)

From the matrix inversion term, it is evident that MMSE receiver will try to reduce inter stream

interference but cannot remove it completely. Here the criterion is not to make the inter stream

interference zero but to minimize the MSE.

4.1.2 CQI Calculation

Let us calculate the C QI of the 1st user. The estimated symbol at the k th MS can be written as

1 1 1 1 1 1 1 1 1 1 1

1, 1

K

i i

i i

x b y b H v x b H v x b n

(4.7)

where bl is MMSE receiver vector. Assuming the total power P is divided equally among K

users, expressions for signal (S), interference (I), and noise powers (N) of 1st user is calculated as

follows

*

1 1 1 1 1 1 1 1{( )( ) }S b H v x b H v x

2 *

1 1 1 1 1{ }b H v E x x=| |

2

1 1 1

P b H v

K

= | |

(4.8)

*

1 1 1 1

1, 1

{( )( ) } K

i i i i

i i

I b H v x b H v x

* 2

1 1 1 1

1, 1

2

1 1

1, 1

{ } K

i

i i

K

i

i i

E x x b H v

P b H v

K

= | |

= | |

(4.9)



28 | P a g e

*

1 1 1 1 N {( )( ) } E b n b n=

* *

1 1 1 1

2

1 0

{ } E b n b

b N

= b

(4.10)

1

S

I + NCQI

2

1 1 1

2 2

1 1 1 0

1, 1

K

i

i i

P b H v

K

P b H v b N

K

| |

| |

(4.11)

Here“

. ”indicates norm of the vector. Since noise is assumed to be Gaussian distributed,

Capacity of 1st user C1 can be calculated from Shannon’s channel capacity theorem as

C1 = log2 (1 + C QI1)

(4.12)

After calculating all individual capacities, the sum capacity can be calculated by adding

individual capacities.

.

1

K

sum i

i

C C

(4.13)



29 | P a g e

4.2 Procedure

This section explains how abstraction is performed at the BS and MS.

1. In case of MU-MIMO each user has to feedback the following information to the BS.

(a) CQI for all the subbands.

(b) Stream Indicator or Precoding vector index for all the subbands.

The above information can be calculated based on the desired and interfering channels to

each user. Note that the feedback sent by the MS during frame number (n) is used to schedule

users in frame number (n+1). Hence the feedback path is indicated as frame (n+1).

2. Now it is the job of PF Scheduler to select which set of K users need to be scheduled out of U

users in a particular subband based on the above feedback.

(a) First the PF Scheduler will calculate the PF metrics for all users.

(b) It will try to find set of K users who prefer different stream indicators.

(c) If there are more than one set of users then it will select those set of users who has

maximum sum PF metric.

(d) If there is no such set of users then scheduler will randomly force the users to use

different stream indicator so that pairing can be done.

3. After scheduling a dataregion the average throughput of all the users are updated. Then the

scheduler will schedule the users for next dataregion. This way scheduler will schedule users

to all dataregions one by one. When there are large numbers of users contending for service then

pairing is not a problem, since there is very high probability that at least K users will choose

different stream indicators.

4. After scheduling, the SINR is calculated at the MS.

5. The SINR calculated in the previous step is used to calculate performance metrics like sum

capacity and throughput.



30 | P a g e

BS MS

frame (n) frame (n)

frame (n+1) frame(n)

frame (n+1)

frame (n)

Figure 4.1 Procedure for MU-MIMO.

CQI and precodingvector calculation

Scheduler

Desired and

interfering channelinformation

Feedback from

MS:

1) CQI

2) PVI

SINR

calculation

Performance

Metrics:

1) sum capacity

2) Throughput



31 | P a g e

CHAPTER 5

5. Results and Discussion

5.1 Matlab Simulation Results

In this section we will discuss how the capacity will effect when multiple users are

paired in a dataregion. Here in total we have 12 subbands and 20 users competing for

resources.

System Parameters

Parameters Values

No. of antennas at BS station

No. of antennas at MS station

Frames transmitted

Channel

Subbands

Iterations

SNR (dB)

Users contending for resource

Users served

Channel repetition across

subbands

2/4

2/4

100

uncorrelated/correlated

12

100

0:1:50

20

[ 2 3 4 ]

1



32 | P a g e

Figure 5.1 represents the sum capacity of MU-MIMO for 4×2 wi th uncorrelated

channel. In this figure we clearly observe that the sum capacity of 2 users is higher when

compared to 3 users and 4 users. It is well understood that as the number of users increases, the

inter stream interference will increase hence the CQI of each user will decrease and also thecapacity per user decreases. Since the number of antennas at the mobile station are only two, the

receiver can suppress only one interferer effectively resulting in higher sum capacity in case of 2

users when compare to sum capacity of 3 users and 4.

Figure 5.2 represents the sum capacity of MU-MIMO for 4×1 with uncorrelated

channel. In this figure, we can clearly notice that the sum capacity of 2 users is higher when

compared to that of 3 and 4 users. The main difference between the two graphs is that, in figure5.1 the sum capacity for 2 users increases linearly, where as in case of figure 5.2 the sum

capacity increases exponentially.

Figure 5.3 and figure 5.4 represents the sum capacity of MU-MIMO for 4×2 and 4×1

with correlated channel. Here also, as the number of users increases the sum capacity decreases.

In the case of single receiving antenna (i.e. M=1) the sum capacity of users is smaller when

compared to that of two receiving antenna at the MS. For both correlated and uncorrelated cases,

as the number of users increases, the sum capacity decreases.



33 | P a g e

Figure 5.1Sum capacity of MU-MIMO for 4×2 with uncorrelated channel

Figure 5.2 Sum capacity of MU-MIMO for 4×1 with uncorrelated channel

0 5 10 15 20 25 30 35 40 45 500

5

10

15

20

25

30

35

SNR in dB

S U M C

A P A C I T Y

p e r s u b b a n d i n

s y m b o l s / s e c / H z

SUM CAPACITY of MU-MIMO for 4Tx X 2Rx,UnCorrelated channel

2-Users

3-Users

4-Users

0 5 10 15 20 25 30 35 40 45 502

4

6

8

10

12

SNR in dB

S U M C

A P A C I T Y

p e r s u b b a n d i

n s y m b o l s / s e c / H z SUM CAPACITY of MU-MIMO for 4Tx X 1Rx,UnCorrelated Channel

2-Users

3-Users

4-Users



34 | P a g e

Figure 5.3 Sum capacity of MU-MIMO for 4×2 with correlated channel

Figure 5.4 Sum capacity of MU-MIMO for 4×2 with correlated channel

0 5 10 15 20 25 30 35 40 45 500

5

10

15

20

25

30

35

SNR in dB

S U M C

A P A C I T Y

p e r s u b b a n d i n s y m b o l s / s e c / H z SUM CAPACITY of MU-MIMO for 4Tx X 2Rx,Correlated channel

2-Users

3-Users

4-Users

0 5 10 15 20 25 30 35 40 45 502

4

6

8

10

12

SNR in dB

S U M C

A P A C I T Y

p e r s u b b a n d i n s y m b o l s / s e c / H z SUM CAPACITY of MU-MIMO for 4Tx X 1Rx,Correlated channel

2-Users

3-Users

4-Users



35 | P a g e

From figures 5.1 to 5.4, we can clearly observe that

As the number of users increases the sum capacity decreases.

The optimum number of users that can be scheduled in a dataregion to achieve

maximum throughput is equal to minimum of the number of antennas at the BS and MS. The sum capacity increases linearly with S NR (dB) when number of users paired is

not greater than minimum of the number of antennas at the BS and MS i.e., when

K min {M, N} then sum capacity increases linearly, otherwise it saturates at some

point.



36 | P a g e

CHAPTER 6

CONCLUSIONS

MU-MIMO is a promising technique which allows more than one user that can be served

in each subband. An efficient multi-user proportional fair (PF) scheduler algorithm is designed

and implemented in MU-MIMO technique with code book based precoding that has been

proposed for the IEEE 802.16m mobile broadband standard. Optimum number of users can be

scheduled in a dataregion to achieve maximum sum capacity, which is equal to minimum

number of antennas at the base station and the mobile station. The sum capacity increases

linearly with SNR (db) when the number of users paired is not greater than the minimum of the

number of antennas at the BS and MS i.e. when K min {M, N} then sum capacity increases

linearly, otherwise it saturates at some other point. From the results discussed in the previous

chapter, multiple users can be paired in a dataregion resulting in higher sum capacity. In

addition, we observe that as the number of user’s increases, the sum capacity decreases.



37 | P a g e

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http://www.eurecom.fr/~gesbert/papers/TutorialMUMIMOv3.pdf



http://users.ece.utexas.edu/~rheath/papers/2006/SP_mag/paper.pdf





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