A Practical Analysis of the E�ects of

Opportunistic Nulling in LTE-based

Systems

VANESSA BELEC

Master's Degree Project

Stockholm, Sweden

XR�EE�SB 2012:009

A Practical Analysis of the Effects ofOpportunistic Nulling in LTE-based

Systems

VANESSA BÉLEC

Master’s Thesis at Signal,Sensors and SystemsRoyal Institute of Technology (KTH)

Stockholm, SwedenSupervisor and Examiner: Mats Bengtsson

iii

Abstract

Due to the Internet expansion over the last decades, the pressure for the telecom-munications companies to deliver a high performance broadband communication,especially wireless is imminent. Future wireless networks will need to support highdata rates in order to meet the requirements of multimedia services. Furthermore,the user density will be much higher for every year and it will be an increase ofamount of data communication between mobile devices. Consequently, a new gen-eration network has been introduced, i.e. LTE also called 4G, promising betterperformance and speed. Nevertheless, it is not only the network that plays animportant role in achieving speed and performance, but also the communicationsystem including number of antennas used, antenna deployment, power, number ofbase station, and so on. Most research papers agree on one point and this is the factthat the performance and reliability may be improved when using multiple inputsand/or multiple outputs, i.e. MIMO.

This Master Thesis concerns the performance acquired by studying on one handthe capacity achieved by using multiple antennas in the receiver (1 x 4 MIMO) andon the other hand studying different methods used by the base stations for schedul-ing the transmission to users according to their channel quality. Furthermore, theevaluation has been done numerically using measured radio channels, obtained byEricsson.

One of the methods used in this paper is opportunistic scheduling, which in-volves the tracking of each of the fading users’ channel fluctuation and schedulingtransmission to these users when their instantaneous channel quality is close to theirmaximum. In order to improve the communication of those users with low channelquality, a well-known algorithm was added to the Opportunistic scheduling. Thismethod considers previous capacity rates and it is called Proportional Fair schedul-ing.

Another effect of using the Opportunistic scheduling is the suppression of theinter-cell interference (ICI) generated by close-by base stations, called Opportunisticnulling. In this paper, Opportunistic nulling is analysed in order to find out whethera practical suppression is achieved by this scheduling and whether factors suchas delayed channel information may affect the scheduling and prevent a reliablecommunication with minimum interference.

iv

Sammanfattning

Med anledning av Internets utbredning under de senaste decennier, är trycketpå att få telekombolagen att leverera en hög standard bredbandskommunikation,särskilt trådlös, som allra starkast. De framtida trådlösa nätverken kommer nogatt behöva stöda höga datahastigheter för att uppfylla de kraven som multimediatjänsterna ställer på dem. Dessutom blir tätheten bland användarna högre för varjeår så att mängden datakommunikation som överförs mellan mobila enheter ökar.Därför har en ny generation av mobila nätverk introducerats, m.a.o LTE eller ävens. k. 4G, som lovar bättre prestanda och hastighet. Det är dock inte bara nätet somspelar en stor roll för att uppnå höga hastigheter och prestanda, utan också kom-munikationssystemet är viktigt, inklusive antalet använda antenner, antennernasutplacering, effekt, antalet basstationer, etc.

De flesta forskningsuppsatser är överens om en sak och det är faktumet att pre-standa och tillförlitlighet kan förbättras då multipla ingångar och utgångar införs,m.a.o MIMO. Denna uppsats avser å ena sidan den prestandan som man får avatt studera kapaciteten som erhållits genom multipla antenner i mottagaren (1 x4 Single Input Multiple Output, SIMO) och å andra sidan av att studera de olikametoder som används av basstationer för att skedulera överföringen till användarnaenligt deras kanalegenskap. Dessutom har utvärderingen gjorts numeriskt genomatt använda uppmätta radiokanaler från Ericsson.

En av de metoderna som används i denna uppsats är opportunisitsk skedule-ring, vilket innebär att kanalsvängningar spåras för de fädande kanalerna till varjeanvändare och att överföringen skeduleras till de användare vars momentana kanale-genskap är nära sitt maximum. För att förbättra kommunikationen till de användaremed sämre kanalkvalitet, har man stoppat in en välkänd algoritm i den Opportu-nistiska skeduleringen. Metoden kallas för Proportional Fair och den tar hänsyn tilltidigare värden på datahastigheter i sin algoritm.

En annan effekt av att använda Opportunistisk skedulering är den undertryck-ningen som skapas på den störning som genereras av närliggande basstationer(ICI),den s.k. Opportunistisk störningsundertryckning (Opportunistic Nulling). I dennauppsats analyseras den opportunistiska störningsundertryckningen för att ta redapå ifall en praktisk undertryckning är uppnådd och ifall faktorer såsom försenadkanalinformation kan drabba skeduleringen och ev förhindra en tillförlitlig kommu-nikation med minsta interferens.

Contents

Contents v

Definitions ix

1 Background 11.1 OFDMA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 LTE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.3 MIMO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.4 Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2 System Description 72.1 Channel Measurements . . . . . . . . . . . . . . . . . . . . . . 72.2 Emulated System Scenario . . . . . . . . . . . . . . . . . . . . 8

3 Channel factors and scheduling methods 113.1 Channel Data Rate . . . . . . . . . . . . . . . . . . . . . . . . 113.2 Thermal noise variance . . . . . . . . . . . . . . . . . . . . . . 153.3 Opportunistic scheduling . . . . . . . . . . . . . . . . . . . . . 153.4 Max Throughput Scheduling . . . . . . . . . . . . . . . . . . . 163.5 Proportional Fair Scheduling . . . . . . . . . . . . . . . . . . . 163.6 Interference . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183.7 Delay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

4 Results and Analysis 214.1 Data Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214.2 Max Throughput Scheduling . . . . . . . . . . . . . . . . . . . 234.3 Proportional Fair . . . . . . . . . . . . . . . . . . . . . . . . . 274.4 Delayed Scheduling . . . . . . . . . . . . . . . . . . . . . . . . 314.5 Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374.6 Comparison between different schedulers . . . . . . . . . . . . 40

5 Conclusions and Future Research 41

v

vi CONTENTS

Appendices 42

Bibliography 43

List of Figures 45

Acknowledgement

I would like to express my gratitude to Mats Bengtsson, my supervisor andexaminer at KTH, for giving me the opportunity to complete this thesis,spending time with me when I needed it the most and for supporting andhelping me to achieve my goal.I would also like to thank with all my heart my husband Martin for his patienceand full support during this study time.Finally, I would like to dedicate this work to my boys, Christoffer and Nicklas,with all my love.

vii

Definitions

AbbreviationsLTE Long Term EvolutionOFDMA Orthogonal frequency division multiplexing AccessTDMA Time division multiplexing AccessMIMO Multiple Input Multiple OutputSIMO Single Input Multiple OutputSNR Signal to Noise ratioSINR Signal to Interference plus Noise ratio3GPP Third Generation Partnership ProjectICI Inter-Celll InterferenceCDM Code DomainTDM Time DomainFDM Frequency DomainPF Proportional Fair

Symbolsσ2 Variance of noisen(t) Gaussian noisex(t) Transmitting signaly(t) Receiving signalH(t) Channel Responseλ Memory FactorP Power

ix

Chapter 1

Background

During the last decade, high speed wireless broadband is being preferred overwired communication due to its mobility, relatively low maintenance, and highpracticality. The use of laptops, smart phones and Ipads has never been sopopular. However, the speed and performance in wireless systems has notalways been as expected and there is still plenty of work to do to meet theseexpectations.

In order to fulfil the need of the market, the Third Generation PartnershipProject (3GPP), which is a collaboration that brings together several telecom-munications standard bodies in USA, Europe, Japan, South Korea and China,has released a considerable amount of specifications that provide great speedand capacity. One of these releases is the Long-term evolution (LTE), whichintroduces OFDMA technology in the downlink and DFTS-OFDMA for theuplink.

1.1 OFDMAOrthogonal frequency division multiplexing Access (OFDMA) has as well asOFDM scheme multiple subcarriers in one channel. The subcarriers are di-vided into groups of sub-channels allocated to multiple users allowing simul-taneously data transmission in a time-frequency selective resource. In thedownlink, each sub-channel may be intended for a different receiver. In theuplink, a transmitter may be assigned one or more sub-channels. Furthermore,in case of frequency multiplexing of OFDM signals from multiple users, it iscritical that the transmission of each user arrives at the base station with timealignment of less that the length of the cyclic prefix to preserve orthogonality

1

2 CHAPTER 1. BACKGROUND

Figure 1.1: The LTE Physical layer

between subcarriers in order to avoid inter-channel interference.[11] The cyclicprefix may vary between normal or extended status depending on how it isconfigured. In a downlink slot with normal cyclic prefix there are six OFDMsignals, whilst for an extended one there are instead seven OFDM signals.The advantage of an extended cyclic prefix is to be able to cover large cellsizes with higher delay spread of the radio channel.

The structure of the OFDMA symbol consists of three types of subcarriers[6],[1]:

• data subcarriers for data transmission

• pilot subcarriers for estimation and synchronization purposes

• null subcarriers, where no signal is transmitted, used for guard bandsand DC carriers.

OFDMA is normally used in the multiplexing scheme of LTE.

1.2 LTELong-Term Evolution, LTE (also called 4G) is the new generation mobile net-work offering higher data rates, lower latency and higher capacity.

1.2. LTE 3

LTE has a physical layer (LTE PHY) which is a highly efficient for con-veying both data and control information between an enhanced base station(eNodeB) and mobile user equipment (UE). The LTE PHY employs someadvanced technologies that are new to cellular applications. These includeOrthogonal Frequency Division Multiplexing (OFDMA) and Multiple InputMultiple Output (MIMO) data transmission.

The LTE physical layer supports different bandwidths from 1.4 MHz to 20MHz. The smallest amount of resource that can be allocated in the uplink ordownlink is called a resource block (RB). One RB is divided in 12 subcarriersof ∆f = 15kHz each, which makes a total of 180 kHz wide. In addition, eachRB lasts for one time slot which is 0.5ms (see FIG. 1.1). In both cases, thesubcarrier spacing is constant regardless of the channel bandwidth. [8]

Moreover, LTE supports more than 300Mbps in the downlink and 80Mbpsin the uplink. Thanks to its introduction to OFDMA technology, LTE pro-vides orthogonality between users within a cell contributing to an intra-cellinterference free zone.[7]

One of the basic principles for LTE is the use of channel-dependent schedul-ing. Although the scheduling is not specified by 3GPP, the overall goal ofscheduling is to take advantage of the channel variations between users andpreferably schedule transmission to a user when the channel conditions areadvantageous. The scheduling can be realised in both the downlink and up-link transmission.

The main difference between the uplink and the downlink scheduling ishow the power resource is distributed. In the uplink scheduling, the powerresource is generated among the users, whilst in the downlink scheduling, theresource is centralised within the base station. Though the power resource inthe downlink scheduling is centralised in the base station, it may also need tobe shared among multiple users within a cell depending on in which domain thedownlink signal is transmitted. If the signal is divided in frequency (FDMA)or in code (CDMA), then the power resource needs to be shared within thecell. On the other hand if TDMA is used, no instantaneous sharing is neededbecause per definition, there is only one transmission at a time. Often, thedownlink scheduling uses only the time domain so no cell sharing is neededand in combination with the centralised power resource, the link capacity isefficiently utilised.[3]

Another difference between the uplink and the downlink scheduling is thatthe transmission power of a mobile device for the uplink is significantly lower

4 CHAPTER 1. BACKGROUND

than the output power for the downlink from a base station to multiple users.For this reason, the uplink scheduling uses not only the time domain but alsothe frequency and code domain to obtain better reliability.

For simplicity, we use in this thesis the time domain downlink schedulingfor each frequency sub-channel because the transmission that sends from thebase stations to the users varies in time.

1.3 MIMO

As previously discussed, the future communication requires an increase of datarates so higher data rates can be provided to multiple mobile users. However,the power and bandwidth allocation are limiting factors together with the in-terference which make this task even more complicated to fulfill.

A solution that may increase the performance without affecting the lim-iting factors is the use of Multiple-input, multiple-output (MIMO) wirelesssystem.[4] In a MIMO system there are several transmitting and receiving an-tennas. This system which is multifading can actually achieve among othershigh capacity levels compare to those with only a single antenna. One of thereasons for that is that MIMO provides spatial diversity with multiple parallelspatial channels working independently. [9]:

1.4 Objective

The main goal of this project is to analyse the effects of opportunistic nulling.For this task, channel data measured by Ericsson corresponding to LTE (OFDM )has been evaluated. This data is used to emulate a model where three base sta-tions are used as transmitters and each has a cell of four users/receivers. Eachtransmitter/base station has one antenna and each receiver has four antennas.

One of the objectives of this project is to evaluate the opportunistic schedul-ing by calculating the maximal throughput for each user in a cell. In order toobtain more accurate results, the delay between the moment the scheduler re-ceives the information and the moment when time slots are actually allocatedamong the users, is also considered when calculated the maximal throughput.

1.4. OBJECTIVE 5

Accordingly, the capacity is newly calculated considering this delay and isthen compared to the originally scheduled max throughput without delay.

Another objective of this project is to investigate the proportional fair al-gorithm by calculating the throughput of the system and by evaluating theresults.

The third objective of this project is to evaluate the maximal throughputscheduling without considering any interference from adjacent base stations.

The last objective of this project is to define a factor/parameter in thechannel data that may affect the throughput of each user in relation to inter-ference.

The channel is affected by a AWGN noise with variance σ2 and E[n] = 0.The results from each cell are averaged over both time and frequency for bet-ter accuracy.

Chapter 2

System Description

2.1 Channel MeasurementsHere follows the specification for the data received from Ericsson. The datacomprises 89 files and each file includes the channel data or frequency responseH, which is a four dimension complex matrix which varies with time, frequency,base station and receive antenna. As seen in Table 2.1, H is divided in 432frequencies and 2000 time slots. In this thesis, the results have been averagedover both time and frequency for better accuracy.

Table 2.1: LTE Drive Test Data Details

7

8 CHAPTER 2. SYSTEM DESCRIPTION

2.2 Emulated System ScenarioThe system model is extracted from a test drive where the driving car wasequipped with four receiving antennas mounted on the roof of the car. Thereceived information came from three different base stations placed at a rea-sonable distance from each other and equipped with only one antenna each.The channel frequency response was measured along the whole test drive soit varies with the distance and coverage from the base stations. The measure-ment was then stored in 89 files with a time interval of 10.66 seconds each,normalised for each combination of antennas and channel sample to be readyfor analysis.

Figure 2.1: Three base stations linked with four users each.

In this thesis, 12 files were selected among the 89 Ericsson files to repre-sent the twelve users in the system model. Each file contains the 4D complexchannel data divided in 432 sub frequencies (also subcarriers), each having abandwidth of 45MHz and 2000 time slots equivalent to 10,66s, i.e. 5,33 msfor each time slot.

In order to obtain a strong signal from the base station, the users wereselected to be those files which were closest to a specific base station.

2.2. EMULATED SYSTEM SCENARIO 9

As shown in Figure 2.1, there are a total of 12 users receiving the signalsfrom different base stations and each of the three base stations is associatedwith four users. The number written below each user is the number of the fileselected among the 98 Ericsson files.

A picture of where the drive test took place and the location of each basestation is depicted in Fig 2.2. The drive test is indicated as a blue lightedroute and each base station is depicted as a green triangle. The stars indicatethe location of the users and the colour of each star represents which basestation the user belongs to. In addition, the number in each star representsthe number of the user.

Figure 2.2: The location of the users in Kista

Chapter 3

Channel factors and schedulingmethods

This chapter describes factors that affect the channel in different ways andscheduling methods that are used in this thesis.

3.1 Channel Data RateIn order to analyse the complex data channel, the first step involves calculatingthe data rate R of each selected file/ user. It is assumed that the received signalis an additive white Gaussian Noise (AWGN ) with zero mean and a varianceof σ2.Let’s begin with a channel model of a single link in the system.

Figure 3.1: A model of AWGN channel

11

12 CHAPTER 3. CHANNEL FACTORS AND SCHEDULING METHODS

In figure 3.1, x(t) is the transmitting signal, H(t) is the channel response,n(t) is the white noise and y(t) is the received signal with four antennas. Thisis a model where the narrow band subchannel or subcarrier is constant overtime slots of length T samples and it is also assumed that the bandwidth ofeach sub-channel is narrow enough so the channel response is flat across theband of the sub-channel.

According to Fig.3.1, the receiving signal y(t) results in:

y1(t) = x(t)H1(t) + n(t)y2(t) = x(t)H2(t) + n(t)y3(t) = x(t)H3(t) + n(t)y4(t) = x(t)H4(t) + n(t)

(3.1)

where it shows that the transmitting signal x(t) is multiplexed by thematrix H(t) resulting in four receiving signals r1(t), r2(t), r3(t), r4(t) aimed atfour receiving antennas (NR = 4). In this model, only one transmitting unitis being considered (NT = 1).

Now we need to calculate the power. In this thesis, we assume that thetransmit power P is constant at all times, i.e. E[|x(t)|2] = PT , where T is thelength of each time slot.

During a T interval we have[13] :

E[|x1(t)|2] = PE[|x2(t)|2] = PE[|x3(t)|2] = P

(3.2)

where xi(t) is the transmitting signal from each base station i.

According to the general Shannon capacity theory [15], the rate is:

R = log2 det{

(INR+ P

σ2 HHH)}

bits/s/Hz (3.3)

where I is an identity matrix, NR is number of receiving antennas, P is thepower of the input signal, σ2 is the variance of Gaussian noise and H ∈ CNR×NT

and is the normalised channel matrix. In the special case, where NT = 1, theformula is then:

R = log2

(1 + P

σ2

NR∑i=1|hi|2)

bits/s/Hz (3.4)

3.1. CHANNEL DATA RATE 13

where i is the number of receiving antennas and NR = 4 .

In general, the Signal to Noise Ratio (SNR) is formulated as :

SNR = 10 log10

(PsignalPnoise

)(3.5)

If considering Eq.3.5 and Eq.3.4, the SNR here results in P |hi|2σ2 .

As previously explained, the interference from close-by base stations shouldnot be neglected and should therefore be considered into the calculations forthe capacity. Accordingly, since we are not only dealing with white Gaussiannoise but also with ICI, we need to replace the value of SNR with the SINR(Signal to Interference and Noise Ratio) value.

The SINR for base station 1 is :

SINR1 = Ph1HR−1

w1h1 (3.6)

where R−1w1

is the inverted autocorrelation of the interference plus noise.The same applies for SINR2 and SINR3.

Accordingly, the next step is to calculate the autocorrelation Rw1 [15]which is a NR ×NR matrix, where NR is the number of receiving antennas inthe system. In this thesis, NR = 4 which means that the autocorrelation ofthe interference Rw is a 4× 4 matrix.

Rw1(t) = E[W1(t)W1(t)H ] == E[(h2(t)x2(t) + h3(t)x3(t) + n(t))(h2(t)x2(t) + h3(t)x3(t) + n(t))] == h2(t)h2(t)HE[x2(t)x2(t)] + h3(t)h3(t)HE[x3(t)x3(t)] + E[n(t)2] =={P = E[x2(t)x2(t)] and P = E[x3(t)x3(t)]

}=

= Ph2(t)h2(t)H + Ph3(t)h3(t)H + σ2I.(3.7)

The same procedure applies for Rw2 and Rw3 .

In equation 3.7, we assumed that W(t) is the ICI plus noise as following:

14 CHAPTER 3. CHANNEL FACTORS AND SCHEDULING METHODS

W1(t) = h2(t)x2(t)+ h3(t)x3(t) + n(t)W2(t) = h1(t)x1(t)+ h3(t)x3(t) + n(t)W3(t) = h1(t)x1(t)+ h2(t)x2(t) + n(t)

(3.8)

In equation 3.8, the ICI plus noise Wi(t), the input signal xi(t) and thechannel response hi(t) are represented for each base station i, where i=1,2,3.

Figure 3.2: The ICI generated by BS2 affecting a user with four receivingantennas served by BS1.

For a better understanding, the figure 3.2 shows how the ICI (h21, h22, h23, h24),generated by base station 2, affects the receiving signal of a user with four re-ceiving antennas (h11, h12, h13, h14) served by base station 1.

The last step when calculating the data rate for our model is to inserteq.3.6 into eq. 3.4 and we obtain the following:

R1,k(t) = log2(1 + Ph1(t)R−1w1

(t)h1(t)H)R2,k(t) = log2(1 + Ph2(t)R−1

w2(t)h2(t)H)

R3,k(t) = log2(1 + Ph3(t)R−1w3

(t)h3(t)H) (3.9)

The data rate is calculated for each base station i and user k at each timeinstant t, where Ri,k(t) is a scalar value, i=1...3 and k=1...4.

3.2. THERMAL NOISE VARIANCE 15

3.2 Thermal noise variance

The white noise added to the system may be considered as a thermal noisewhich is a noise generated by the random thermal motion of charge carriersinside an electrical conductor which happens regardless of any applied voltage.The formula for the power of the thermal noise is:σ2 = kBTNS∆f , where kB is the Boltzmann’s constant, T is the room’s tem-perature, NS is the Noise Figure, which is the noise sensibility factor for thereceiver unit in particular and ∆f is the bandwidth for each subcarrier.

In this thesis the Noise Figure NS is the noise value for a mobile device indB which in this case is assumed to be 7. The temperature is 273+20 K andthe bandwidth is 45kHz.

3.3 Opportunistic scheduling

In a MIMO system where the channel conditions are time-varying due to fad-ing from multiple spatial signals, different wireless users experience differentchannel conditions at a given time. In other words, the conditions within aradio cell vary independently for each user in that cell, and at each point intime there is a high probability that a user is having its channel quality nearits peak [2]. In order to increase the total throughput of this system, onlythose users having a high channel quality are assigned time slots for trans-mission/reception. This method of enhancing the total system throughput iscalled opportunistic scheduling [12]. It is opportunistic because this methodtakes advantage of favourable channel conditions in sharing the radio chan-nel. However, opportunistic scheduling requires a flexible and tolerant user interms of delay in transmission/reception, especially when the radio conditionsare not ideal. Therefore, the Opportunistic Scheduling may not be as usefulfor voice signals. [5]. Consequently, this method is widely used in data signalswhich allow a balance between efficiency and delay.

Another effect of the Opportunistic scheduling is the suppression of theinter-cell interference (ICI) produced by other close-by base stations, calledOpportunistic nulling. In this thesis, Opportunistic nulling is analysed in orderto find out whether a practical suppression is achieved by this scheduling andwhich factors may be of importance to be considered for obtaining a reliablecommunication with minimum interference in the near future.

16 CHAPTER 3. CHANNEL FACTORS AND SCHEDULING METHODS

3.4 Max Throughput SchedulingMaximum Throughput scheduling is an opportunistic scheduling which cal-culates the maximum throughput among all users within a cell at a given time.

The opportunistic scheduling works as following:

• Each receiver tracks its own channel through a downlink single pilot sig-nal and feeds back the instantaneous channel quality to the base station.

• The base station schedules transmission among the users by selectingthe user that have the maximum capacity at a given time instant toassign any transmission/reception slots.

Mathematically, the Max Throughput or Rate Scheduler can be expressedas a selected user k* given by:

k∗ = arg maxk

Rk (3.10)

where Rk is the instantaneous data rate for user k.

However, this opportunistic scheduling may be far from fair. In real con-ditions, users are spread over a radio cell and some of those may have thebase stations far from their locations. This type of scheduling will only favourthose with high throughput e.g. closer to the base station and the rest of theusers will have to struggle to be assigned any time slots.

In order to improve the communication of those users with temporarilylow channel quality, another version of opportunistic scheduling may be used.This version uses previous values of capacity rates and it is called ProportionalFair scheduling.

3.5 Proportional Fair SchedulingProportional Fair scheduling tries to satisfy different rate requirements of eachuser without missing out too much of the efficiency of multiuser diversity. Inother words, the system can accommodate more users that are near theirpeak rates. The downside of such a scheduling is that many users may notreach their target/maximum rates and for those users the communication sys-tem will feel slower. For instance, if there are k users in a cell and Rk is anachievable rate for user k∗ at the transmission interval t, which depends onthe user’s current channel conditions, the scheduler keeps then track of the

3.5. PROPORTIONAL FAIR SCHEDULING 17

running average rate for every user.

According to [12], this general version of the proportional fair algorithmworks as following:

Given a time slot t, a user k, the algorithm keeps track on:

• Users’ average throughputs T1(t), T2(t), ...Tk(t).

• Current requested data rates R1(t), R2(t), ...Rk(t) [14] transmit to theuser k with the largest Rk(t), Tk(t).

Specifically, at each time slot t, the decision of the PF scheduler is toschedule the user k∗ with the largest rate Rk(t)/Tk(t) among all active usersin the system. In other words, user k∗ is selected for transmission accordingto:

k∗ = arg maxk

Rk

Tk(3.11)

where Rk is the rate (bit/s) achieved by the user and Tk(t) is the aver-age rate calculated over a time window as a moving average. The averagethroughputs Tk(t) can be updated using a memory factor λ as following:

Tk(t+ 1) ={

(1− λ)Tk(t)+ λRk(t), k = k∗

(1− λ)Tk(t), k 6= k∗(3.12)

In this equation, the time window is defined by the memory factor λ whichvaries between 0 and 1. This memory factor is chosen to balance between theneeds of estimating throughput which requires a small value of λ and theability to track changes in the channel characteristics requiring a larger valueof λ.

Hence, the algorithm allows the user with the statistically strongest chan-nel to be chosen for transmission. The running average rates will howeverlower the total throughput over the maximum possible and instead will pro-vide more acceptable levels to users with poorer SNRs. In this case, the usersdo not compete for the resources based on their requested rates but only afternormalization by their respective average throughputs.

18 CHAPTER 3. CHANNEL FACTORS AND SCHEDULING METHODS

Wide Band ChannelsThe communication system LTE provides a wide band channel divided innarrow band subchannels due to its OFDM signals. In such a wide bandchannel, it is important to consider not only the time selective fading but alsothe frequency selective fading. A simple model of such a system is used in thisthesis which involves a set of l parallel narrow band subchannels or subcarriers,each of these channels has a invariant frequency level that fluctuates withtime. The model is then consisting of 432 frequency divided subchannels, eachwith a bandwidth of 45 kHz making a total of 19.4 MHz, and transmittinga total transmitting power of 1W. Accordingly, the transmit power for eachsubchannel is very small (2.3mW) but it does not need to be higher sincethe noise level of each subchannel is even a smaller value. This issue will bediscussed in a later chapter complemented with simulations regarding capacityvalues vs SNR values.In order to be able to schedule the transmission to users within a cell, theusers need to measure the SNR on each of the subchannels and feed backthe requested rates or SNRs to the base station. The scheduler receives theinformation and allocates at each time a single user to transmit to for eachof the narrow-band subchannels. If the proportional fair scheduler is used,the scheduler needs to keep track of the average throughputs Tk(t) across allnarrow-band subchannels in a past window of length 1/λ for each user k. [12]The algorithm is then modified from being used for the aforementioned puretime-selective channel to the following:

For each sub-channel l, the scheduler transmits to the user k∗(l), where

k∗(l) = arg maxk

Rkl(t)Tk(t)

(3.13)

where Rkl(t) is the requested rate of user k in channel l at time slot t. Itis important to realise that Tk(t) is averaged over all the narrow-band sub-channels and not just the subchannel l. This is because the fairness criterionbelongs to the total throughput of the users across the entire wide band chan-nel.

3.6 InterferenceInterference emerges as the key performance limiting factor, because it deter-mines how many users per area can be served at a certain data rate. If thenumber of users is high then each user will get just a small fraction of the

3.7. DELAY 19

overall resource. [10]

In order to avoid this to happen, the 4G/LTE network provides orthogo-nality between users within a cell contributing to no inter-channel interferencebetween multiple users from a signal sent by the same base station. However,inter-cell interference (ICI ) can be generated if more adjacent base stationsare sending to their users at the same time.

As explained above, MIMO offers another degree of freedom to avoid andmitigate interference. In such a multiuser network, the users within a cellcompete for the available resources. This results in that the performance ofsome users can be increased at the cost of decreasing the performance of otherusers. The selected strategy is often a compromise between fairness and effi-ciency. Therefore, dynamic interference management and resources allocationare key factors to achieve a full exploitation of the available system capacity.In other words, the available resource needs to be designed in a flexible wayconsidering the current interference situation.[17]

In this thesis, the focus lies on whether different types of downlink schedul-ing such a Opportunisitc Nulling may mitigate the inter-cell interference pro-duced by three base stations in a LTE system with (1 x 4) MIMO.

3.7 DelayIn this report, delay refers to the delay caused by the latency between themoment the scheduler receives the information, as well as adapting users’ datarates to the instantaneous channel quality and the time when the time slotsare actually allocated among the users. There is no doubt that this time delayaffects the performance of the radio resources in a real time system. However,the question is how much such a delay may affect the users in such a system. Asdiscussed earlier, one of the important issues when developing new systemsis to give a better Quality of Service (QoS). If a user does not obtain theexpected performance because the scheduler allocated time slots erroneouslydue to the above discussed delay, the delay is then affecting seriously the QoS.When exploiting higher capacity in an opportunistic way, it is necessary toconsider the trade-off problem between wireless resource efficiency and levelsof satisfaction among users.

Chapter 4

Results and Analysis

In this chapter, the results from the simulations of the scenarios described inChapter 3 are presented below. Moreover, an analysis of each figure is givenwhen appropriate.

All simulations were performed by generating data following the systemmodel introduced in chapter 2 and were implemented in MATLAB.

In short, the system model has three base stations linked with four userseach. In addition, the channel has an additive white Gaussian noise and thereis an inter-cell interference (ICI ) between the base stations.

In order to be able to analyse the performance of the opportunistic schedul-ing, the rate of each user from all three base stations has been calculated. Forsimplicity, the power used for each subcarrier has been chosen to be 2.3mW,which makes a total of 1W for the whole frequency band. Since the frequencyband has 432 subcarriers, we have either randomly chosen the subcarrier inthe position 200 or calculating the average of the results from all subcarriers,depending on what it was more appropriate at that time.

4.1 Data Rate

As explained in section 3.1, the data rate for each user at a time t is calculatedaccording to the formula 3.9, where the ICI and white noise are considered inthe calculations.

21

22 CHAPTER 4. RESULTS AND ANALYSIS

Figure 4.1: (a) Rate of four users vs Time for BS1 using four receiving An-tennas. (b) Rate of four users vs Time for BS2 using four receiving Antennas.

Figure 4.2: (a) Rate of four users vs Time for BS3 using four receiving Anten-nas. (b) Estimated Round Robin scheduling for total system vs Time usingfour receiving Antennas.

4.2. MAX THROUGHPUT SCHEDULING 23

In Fig. 4.1 and 4.2, the rate has been calculated for each user served bybase station 1 (BS1), base station 2 (BS2) and base station 3 (BS3) .The timeperiod selected here is set to 30 frames (0.16s) of a maximum of 2000 frames.In these figures, four receiving antennas have been taken into account.It can be seen from these figures that the rate varies severely among the usersand base stations. Since each user has a different position in the map shownin Fig 2.2, it reveals that those users that are further away from their basestation have a lower signal than other users that are closer to theirs. However,it is also clear from these results that the signal coming from BS3 is weakerthan the other base stations. In BS3, the range in rates varies between 2 - 9b/s/Hz, whilst in BS1 and BS2, the ranges vary between 8 -14 b/s/Hz and 5-14 b/s/Hz respectively.

The second graph in Fig. 4.2 is depicting the estimated total throughputin the system considering an average user per time instant, i.e. ’Round RobinScheduling’. This means that the time is shared equally by all four usersand no consideration is taken to the instantaneous channel information whenscheduling. [8]

4.2 Max Throughput SchedulingAs mentioned in Chapter 3, Opportunistic Scheduling involves assigning timeslots for transmission/reception to those users with the highest channel qual-ity, and Maximum Throughput scheduling assigns time slots to the user thathas the maximum throughput among all the users within a cell at a given time.

In Figure 4.3, the Max Throughput scheduling is marked as a continuousred line with crosses in all graphs. For a clearer view, the time period iszoomed in to 0.2s for the three capacity/users graph.

As seen in the last graph in Fig. 4.4, the the total throughput is shown forthe full 10.66 s (2000 time frames). Further, the Max Throughput schedulinghas a higher total throughput in the system than the Round Robin sheduling.This is comprehensible because the Max Throughput scheduling selects theusers with the highest rate values within a cell instead of sharing the timeequally without considering the instantaneous channel conditions, so the to-tal throughput in the system per time instant is increased. In this case theincrease varies between 5-7 b/s/Hz. However, the advantage of using RoundRobin scheduling is that it gives more equal service quality in time betweendifferent users.

24 CHAPTER 4. RESULTS AND ANALYSIS

Figure 4.3: Max throughput scheduling/Rate vs Time for BS1 and BS2 usingfour receiving Antennas.

Figure 4.4: (a) Max Throughput scheduling/Rate vs Time for BS3 usingfour receiving Antennas. (b) Mean Max Troughput scheduling/Round RobinScheduling vs Time using four receiving Antennas.

4.2. MAX THROUGHPUT SCHEDULING 25

Max Throughput scheduling without InterferenceAs explained in previous chapters, the rate has been calculated consideringthe presence of interference signals from adjacent base stations. In this case,this Max Throughput scheduling was computed to be free from inter-cell in-terference (ICI) so the performance of this scheduling could be analysed.

Figure 4.5: Max throughput scheduling with and without Interference vs Timefor the total system using 1 or 4 receiving Antennas.

In Fig 4.5, each graph represents the Max Throughput with and withoutinterference depending on a different number of receiving antennas. The MaxThroughput was calculated over the whole system, which means adding therate of the three base stations and obtaining an average over the 432 subcar-riers in the frequency band.As observed in these graphs in Fig. 4.5, the throughput is much higher whenthere is no ICI around and the difference in rate between the Max Throughputwith and without interference decreases with the addition of antennas to thereceiver.

Other figures that show the performance of the Max Throughput schedul-ing are Fig 4.6 and Fig 4.7.

26 CHAPTER 4. RESULTS AND ANALYSIS

Figure 4.6: Max throughput scheduling for a selected Bestuser with or withoutinterference vs Time using 1 or 2 receiving Antennas.

Figure 4.7: Max throughput scheduling for a selected Bestuser with or withoutinterference vs Time using 3 or 4 receiving Antennas.

4.3. PROPORTIONAL FAIR 27

In particular, these figures show how the Max Throughput scheduling (alsocalled here Cmax) sometimes do not assign any transmission to the ’right’ bestuser in a ICI free environment (also called here ’bestuser without ICI’), i.e thehighest rate user that would have been selected if no intercell interference wasin the system.As seen in the figures 4.6 and 4.7, the continuous blue line represents the MaxThroughput scheduling with ICI, whilst the green line represents the Maxthroughput with ICI vs the best user without ICI.Every time the best user with present interference selected by the Max Through-put scheduling does not coincide with the best user selected in a ICI free en-vironment, it means that this Max Throughput schedules the transmission toanother user in that base station at that time instant. Consequently, the bestuser without ICI is not assigned any transmission at that time instant. Fromthe figures, this can be seen as sharp variations in rate (the rate for that bestuser turns to zero bringing a lower average for the whole system) from oneinstant to another.For instance, Fig. 4.6 shows a green curve with drastic variations in someplaces when using one receiving antenna. With the addition of receivingantennas, the variations get less sharp but the number of variations is notnecessarily reduced with the exception of the last graph in Fig. 4.7 using fourreceiving antennas. Accordingly, it seems like the reliability for a user is im-proved not only in achieving better performance or higher levels of throughputbut also in accessibility, i.e being assigned time slots if the channel quality isbetter than for other users in that cell , when multiple receiving antennas areused.

4.3 Proportional Fair

Memory factor λIn section 3.3.1, the Proportional Fair algorithm is discussed. In this algo-rithm, the average rates are updated using a memory factor λ. In general,λ should be chosen small enough so that it provides an acceptable mea-sure of the throughput. In order to see how the memory factor influencesthe outcome of the algorithm, three different values have been then selected:λ = 1/10, 1/50, 1/100, which means that the average rate is computed overthe previous 10, 50 and 100 time slots.

28 CHAPTER 4. RESULTS AND ANALYSIS

Table 4.1: Total throughput in the system for PF; λ=1/10, 1/50, 1/100 forone selected subcarrier F1 and for Fmean.

In Table 4.1, the total throughput of the system when using the propor-tional fair algorithm mentioned in eq. 3.12 is evaluated. F1 in the tablerepresents the subcarrier located in the position 200 of the frequency bandand as well as all subcarriers it has a narrowband of 45kHz. The values shownin the second part of the table are first obtained for each subcarrier to beconsequently averaged over all the subcarriers.

As seen in Fig 4.8, the staple graph represents the results from the secondvalues of the Table 4.1, where the rate increases with the number of antennas.However, there is no major improvement in throughput when increasing thevalue of λ. This figure also compares the throughput of the Proportional Fairscheduling with the Max Throughput scheduling, which shows that the latterachieves a higher throughput.

FairnessAs already discussed, the idea behind the Proportional Fair algorithm is tocreate fairness in the system. This means that users that have a relativelyconstant rate, but not higher than other users in the same cell, will be able tobe assigned a time slot.

In Fig 4.9, the rate of four different users is shown and how the Max-and PF throughput methods schedule these users in base station 3. Fig 4.10is depicting the total estimated rate that is requested from each user in allthree base stations and the rate that is scheduled when using either the MaxThroughput or PF Throughput scheduling. In both figures, the first graphis using only one receiving antenna whilst the second graph is using four re-ceiving antennas. Again, the frequency values were averaged over the wholefrequency band equivalent to 432 subcarriers.

4.3. PROPORTIONAL FAIR 29

Figure 4.8: Staple graph showing the total Max throughput and PF through-put for different values of λ and number of receiving antennas N.

As seen in the first graph in Fig 4.9 for a single receiving antenna, the MaxThroughput scheduling prioritises the user #4 during this short period of time.On the contrary, PF Throughput scheduling assigns more the transmission toother users than to user #4. Accordingly, it seems like the latter mentionedscheduling is fairer than Max Throughput as expected. The same is validwhen using four receiving antennas shown in the second graph.

The estimated capacity for all three base stations is shown in Fig 4.10 forboth a single receiving antenna and four receiving antennas. It is apparentthat the PF Max Throughput and Max Throughput are at least fourfolded incapacity when using four antennas instead of a single one. Furthermore, thePF Throughput is lower than the Max throughput in the total system, whichis a direct consequence of a fairer system.

30 CHAPTER 4. RESULTS AND ANALYSIS

Figure 4.9: PF Throughput with λ = 1/100/Max Throughput/Capacity vsTime for BS3 with 1 or 4 receiving Antennas.

Figure 4.10: Estimated PF Throughput with λ = 1/100 / Max Throughputscheduling/ Capacity vs Time for the total system using 1 or 4 receivingAntennas.

4.4. DELAYED SCHEDULING 31

4.4 Delayed Scheduling

Figure 4.11: Delayed Max Throughput/Max Throughput scheduling vs Timeusing 4 receiving Antennas

In this thesis the delay described in section 3.6 was set to be one timeframe or 5.33ms which is the smallest amount of time measured by Ericsson.In general, this sort of delay is considered to be less than 5ms and often nomore than 1ms. [16]

In Fig 4.11, it is possible to see how the delay affects Max throughput inBS1 when four receiving antennas are used. During this short lapse of time,user #2 is here prioritised by the Max Throughput. However, when there is adelay in the scheduling, user#2 is missing out at certain points. For instanceat t=1.13s, user #2 is not receiving any transmission slot when delay occurseven if this is a best user at this time instant.

This is better shown by Fig 4.12 and Fig 4.13. These figures represent howthe Delayed Max Throughput differs from the Max Throughput in terms ofchoice of best user. When the best user chosen by the Max throughput doesnot coincide with the best user from the Delayed Max Throughput, it meansthat not all the users with the maximum rate were allocated transmisson slotsand consequently less total throughput is achieved in the system as depictedby the figures.

32 CHAPTER 4. RESULTS AND ANALYSIS

Figure 4.12: Delayed Max Throughput/Max Throughput scheduling with ICIvs Time using 1 or 2 receiving Antennas.

Figure 4.13: Delayed Max Throughput/Max Throughput scheduling with ICIvs Time using 3 or 4 receiving Antennas.

4.4. DELAYED SCHEDULING 33

This decrease in capacity for the delayed scheduling is more evident whenusing more than one antenna.

Figure 4.14: Estimated Max Throughput/ Delayed Max Throughput schedul-ing with and without ICI for a selected Bestuser without ICI vs Time using 1or 2 receiving Antennas

Other figures 4.14 and 4.15, show the difference in rate between the MaxThroughput /Delayed Max Throughput with and without interference vs theselected best user that should be selected when no ICI is around (bestuserwithout ICI). It is clear from the figures that when no interference is present,the rate level is high. Furthermore, it is also clear that even a delay of 1 timeframe(5.33ms) may contribute to a rate loss of up to 29 bps/Hz at a giventime (at approx. 0.8 sec) if one receiving antenna is used and up to 10 bps/Hz(at approx.7 sec) when four receiving antennas are used and no ICI is around.Even when the interference or ICI is considered in the calculations, the ratemay decrease with up to 1-2 bps/Hz for such a small delay.Another interesting matter is that the Max Throughput scheduling with ICIis rapidily approaching the curve for Max Throughput without ICI for everyadded receiving antenna. The same is valid for the delayed Max Throughputcurve.

Another way of seeing how much throughput is lost because of a delay ofone time frame is to calculate both the Max Throughput and the Delayed Max

34 CHAPTER 4. RESULTS AND ANALYSIS

Figure 4.15: Estimated Max Throughput/ Delayed Max Throughput schedul-ing with and without ICI for a selected Bestuser without ICI vs Time using 3and 4 receiving Antennas.

Figure 4.16: Delayed Max Throughput/ MaxThroughput scheduling vs Timefor a selected Bestuser without Interference in comparison with Max/ De-layed Throughput scheduling for a Bestuser with Interference and using 1 or2 receiving Antennas.

4.4. DELAYED SCHEDULING 35

Figure 4.17: Delayed Max Throughput/ MaxThroughput scheduling vs Timefor a selected Bestuser without Interference in comparison with Max/ De-layed Throughput scheduling for a Bestuser with Interference and using 3 or4 receiving Antennas.

Throughput in relation to best users when the system is free from interference.Those best users that were not assigned the transmission/reception accordingto the scheduling will give a null throughput making it easier to differentiatethe performance between the two scheduling. Fig 4.16 and Fig 4.17 showhow the Delayed Max Throughput has a lower total capacity for all numberof antennas. Especially, it can be noted that the Delayed Max Throughputscheduling with ICI does not allocate as much time slots to the ’true’ best users(Bestuser without ICI) than the Max Throughput with ICI without delay.In other words, the delayed Max Throughput provides less performance thanwithout delay. This is specially notourious when using four receiving antennas.

Another interesting matter in the above figures is that the rate for MaxThroughput scheduling without delay is increasing faster than when havingdelay for more than two receiving antennas. This is due to the mitigationof ICI achieved by the combination of Max Throughput scheduling with theincreasing number of receiving antennas (SIMO). A staple graph in Fig. 4.18shows the rate for all four scheduling vs number of antennas where the timeand frequency has been averaged for simplicity.

In order to obtain some conclusions about how the delay decreases the

36 CHAPTER 4. RESULTS AND ANALYSIS

Figure 4.18: Staple graph showing a Delayed Max Throughput/ MaxThrough-put scheduling vs number of Antennas for a selected Bestuser without Interfer-ence in comparison with Max/Delayed Throughput scheduling for a Bestuserwith Interference.

Figure 4.19: Delayed Max Throughput vs Delay using 1 or 4 receiving Anten-nas.

4.5. POWER 37

Figure 4.20: Delayed Max Throughput vs Delay using 1 to 4 receiving Anten-nas.

total throughput of the system, we have calculated the rate for each user withdifferent values of delay, i.e. 1-10 time frames (approx. 5-53ms). The Maxthroughput has been taken on the delayed rates for each time instant to befinally averaged over time. In this case, only one subcarrier is chosen forsimplicity. See Fig 4.19 for 1 and 2 receiving antennas and Fig 4.20 for 3 and4 receiving antennas.

The abovementioned figures show that the total throughput has decreasedfive times more when using one receivng antenna than when using four receiv-ing antennas. In other words, the more receiving antennas we have, the morerate is decreased in the system. However, from 4.20, it can be noted thatthe loss in rate is almost negligible when all different numbers of receivingantennas are illustrated in the same graph due to the difference in rate level.

4.5 PowerIn earlier chapters, we have explained that the transmit power (Pt) used inmost of the calculations in this thesis is Pt=2.3 mW per subcarrier, which isa very small value. However, it does not need to be higher since the noise

38 CHAPTER 4. RESULTS AND ANALYSIS

level of each subcarrier is 9.12e-16 W. In this case, whe are having a channelresponse for example of |Hi| of around 3.0e-5 for each base station and user.In addition, if we apply eq. 3.5, this would correspond to a SNR of about32dB. (see Fig. 4.21 and eq.4.1). It is also important to see how the MaxThroughput varies with the Signal to Noise Ratio (SNR), which is propor-tional to power.

SNR = 10 log10(Psignal

Pnoise)

If signal y(t) = x(t)H(t) then:

Psignal = E[|x(t)H(t)|2] = |H(t)|2E[|x(t)|2];

Since E[|x(t)|2] = Pt then Psignal = Pt|H(t)|2;

We know also that Pnoise = σ2 which in this case:

Pnoise = 9.12 e-16 W;

Accordingly if for example|H(t)| = 3.0e-5 and Pt = 2.3e-3 W then:

SNR = 10 log10( (3.0e−5)2∗2.3e−39.12e−16 ) ' 32dB.

(4.1)In Fig 4.21, we can see the expected rate for different methods and number

of antennas vs SNR. The highest rate when using one antenna is achieved ataround 32dB (P=2.3mW) by Max Throughput scheduling without any delayor using a proportional fair algorithm. Furthermore, when using four antennasat the same time, the expected rate is increased nearly seven times comparedwith the use of only one antenna for the same amount of power. In addition,the rate does not saturate as it is the case when using one antenna. Instead,the rate increases with power during this specified SNR range. It is remarkablehow the proportional fair method does not achieve more rate than 4 b/s/Hzwhen using one antenna and can be as high as 55 b/s/Hz when using fourantennas. Another interesting finding is that the rate of the Max Throughputscheduling with a delay of 5.3ms is as high as the Max Throughput schedulingwithout delay when using at least four receiving antennas.

In Fig 4.22, we have the same graph as before but we have added the MaxThroughput without interference. As seen here, the rate without interferencecan only be higher with the increase of the SNR. This is quite obvious becausethere is no limiting factor more than the (small-value) white noise to slow down

4.5. POWER 39

Figure 4.21: Expected Max Throughput/Delayed Max Throughput/ PF MaxThroughput vs SNR for different numbers of receiving Antennas.

Figure 4.22: Expected Max Throughput/Delayed Max Throughput/ PF MaxThroughput with and without Interference vs SNR for different numbers ofreceiving Antennas.

40 CHAPTER 4. RESULTS AND ANALYSIS

the power. For simplicity reasons, we only show the Max throughput whenusing one antenna or four antennas in this figure. Hereby, it can be seen thatthe Max throughput is only slightly affected by interference when a pluralityof antennas is used.

4.6 Comparison between different schedulers

Figure 4.23: Cummulative Distribution Function vs different types of schedul-ing using one or four Antennas.

Figure 4.23 show that for all base stations the highest performance withrespect to highest data rate is achieved by the Max Throughput scheduli-ing when using four receiving antennas. it can also be noted that the MaxThroughput with 5 delayed time frames is slightly less reliable than with justone delayed time frame for all base stations. Regarding the Proportional FairMax throughput scheduling, as for the others variations of scheduling, it in-creases in data rate with the addition of antennas and it gets closer in rateto the Max Throughput without ICI . This can be explained as how the fairsystem works, where even weak users have the opportunity to be assignedtime slots though the quality of the channel is not at their maximum.

Chapter 5

Conclusions and FutureResearch

In this thesis, the main purpose has been to analyse how inter-cell interference(ICI ), latency from delayed scheduling and the level of fairness may affect auser in a LTE-based system.According to the results from the simulations shown in previous chapters, it isclear that the inter-cell interference is mitigated during opportunistic schedul-ing, especially when using the Max Throughput Scheduling. As explainedearlier, the Round Robin scheduling does offer an equal time sharing amongthe users but the performance in terms of throughput is much lower than wheninstantaneous channel information is considered.It is also clear from all figures that an increase in receiving antennas doescontribute to obtain a higher throughput in the system. In this case, we onlyhave four receiving antennas but it would be interesting to see how much theinterference can be mitigated by increasing the number of antennas. Obvi-ously, it would be of great interest to increase also the number of transmittingantennas, obtaining a MIMO system.

Regarding the latency from a delayed opportunistic scheduling, severaldelays have been considered in the simulations. As expected, the more thescheduled signal is delayed, lower throughput is achieved in the system. How-ever, for each antenna added to the receiver, the throughput increases.

In the terms of fairness, the analyses show that the opportunistic schedul-ing may benefit some users more than others due to its lack of considerationfor users situated far from base stations and for users surrounded with sev-eral obstacles that are fading the signals. The simulations show that someusers may have as much as sixty five percent of the transmission signal inaverage, whilst other less favourable users will only receive six percent of thetransmission as an average during a period of time of 10 seconds. However,

41

42 CHAPTER 5. CONCLUSIONS AND FUTURE RESEARCH

the level of fairness is often increased by a few percent with every additionalantenna. In order to test the fairness of one of the general proportional fairalgorithms, simulations have been performed with different memory factors,λ.It is evident from the figures that the higher the memory factor is, the higherthroughput is in the system. However, this is a borderline because the ac-tual difference is almost negligible. This is probably because this algorithmfocuses on the fairness of sending transmission to any user and not only tothose users who have the maximum rate in the system at any time instant. Inother words, the simulations show that the algorithm works well by achiev-ing a fairer system for the users. When considering higher memory factors,the level of fairness was not increased as expected. In summary, this thesishas shown that the Opportunistic Nulling is a fact, i.e. the Opportunisticscheduling in combination with a SIMO system does mitigate the ICI.

Bibliography

[1] Physical channels and modulation (36.211) for LTE Overview. Technicalreport, 3GPP,E-UTRA, 2011.

[2] W. Ajib and D. Haccoun. An Overview of Scheduling Algorithms inMIMO-Based Fourth-Generation Wireless Systems. IEEE Network, p.43-48, 2005.

[3] Furuskar A Jading Y Lindström M Astely D, Dahlman E and ParkvallS. LTE: the evolution of mobile broadband. Communications Magazine,IEEE, 47(4):44–51, April 2009.

[4] Helmut Bölcskei. Space-time wireless systems: from array processing toMIMO communications. Cambridge Press, 2006.

[5] Thomas Bonald and Lucas Muscariello. Opportunistic scheduling of voiceand data traffic in wireless networks. In EuroFGI Workshop on IP QoSand Traffic Control, Portugal, 6-7 December 2007.

[6] C.Gessner. UMTS Long Term Evolution(LTE) Technology Introduction.Technical report, Rohde & Schwarz, September 2008. Application notes1MA111.

[7] K. Hassan and H. Haas. User Scheduling for Cellular Multi User AccessOFDM System Using Opportunistic Beamforming. pages 26–30, Ham-burg, Germany, 2005.

[8] S. Parkvall J. Sköld, E. Dahlman and P. Beming. 3G Evolution: HSPAand LTE for Mobile Broadband. Academic Press, 2nd edition edition,2008.

[9] Niklas Jaldén. Analysis and Modelling of Joint Channel Propertiesfrom Multi-site, Multi-Antenna Radio Measurements. PhD thesis, KTH,School of Electrical Engineeering, March 2010.

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[10] J. Zander L. Ahlin and Slimane. Principles of Wireless Communications.Studentlitteratur AB, 2008.

[11] L.J Cimini P. Svedman, S.K. Wilson and Björn Ottersten. OpportunisticBeamforming and Scheduling for OFDMA systems. IEEE Transctionson Communications, 55(5), 2007.

[12] D.N. C. Tse P. Viswanath and R. Laroia. Opportunistic Beamformingusing Dumb Antennas. IEEE Trans. on information theory, 48(6), 2002.

[13] John G. Proakis. Digital Communications. McGRAW-HILL, London,4th. edition edition, 2001.

[14] Bilal Sadiq and Seung Jun Baek. Delay-optimal opportunistic schedul-ing and approximations: The log rule. In IEEE/ACM Trans. Network,number 19(2), pages 405–408, 2011.

[15] M. Sellathurai and S. Haykin. Space-Time Layered Information Process-ing for Wireless Communications. John Wiley & Sons Inc, 2009.

[16] Rohit Kapoor Siddharth Mohan and Bibhu Mohanty. Latency in HSPAData Networks. Technical report, Qualcomm, 2011.

[17] Hui Zhang Xiaodong Xu and Qiang Wang. Inter-cell Interference Mit-igation for Mobile Communication System, Advances in Vehicular Net-working Technologies. Dr Miguel Almeida, 2011.

List of Figures

1.1 The LTE Physical layer . . . . . . . . . . . . . . . . . . . . . . . 2

2.1 Three base stations linked with four users each. . . . . . . . . . . 82.2 The location of the users in Kista . . . . . . . . . . . . . . . . . . 9

3.1 A model of AWGN channel . . . . . . . . . . . . . . . . . . . . . 113.2 The ICI generated by BS2 affecting a user with four receiving an-

tennas served by BS1. . . . . . . . . . . . . . . . . . . . . . . . . 14

4.1 (a) Rate of four users vs Time for BS1 using four receiving Anten-nas. (b) Rate of four users vs Time for BS2 using four receivingAntennas. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

4.2 (a) Rate of four users vs Time for BS3 using four receiving Anten-nas. (b) Estimated Round Robin scheduling for total system vsTime using four receiving Antennas. . . . . . . . . . . . . . . . . 22

4.3 Max throughput scheduling/Rate vs Time for BS1 and BS2 usingfour receiving Antennas. . . . . . . . . . . . . . . . . . . . . . . 24

4.4 (a) Max Throughput scheduling/Rate vs Time for BS3 using fourreceiving Antennas. (b) Mean Max Troughput scheduling/RoundRobin Scheduling vs Time using four receiving Antennas. . . . . . 24

4.5 Max throughput scheduling with and without Interference vs Timefor the total system using 1 or 4 receiving Antennas. . . . . . . . 25

4.6 Max throughput scheduling for a selected Bestuser with or withoutinterference vs Time using 1 or 2 receiving Antennas. . . . . . . 26

4.7 Max throughput scheduling for a selected Bestuser with or withoutinterference vs Time using 3 or 4 receiving Antennas. . . . . . . 26

4.8 Staple graph showing the total Max throughput and PF through-put for different values of λ and number of receiving antennas N. 29

4.9 PF Throughput with λ = 1/100/Max Throughput/Capacity vsTime for BS3 with 1 or 4 receiving Antennas. . . . . . . . . . . . 30

45

46 List of Figures

4.10 Estimated PF Throughput with λ = 1/100 / Max Throughputscheduling/ Capacity vs Time for the total system using 1 or 4receiving Antennas. . . . . . . . . . . . . . . . . . . . . . . . . . 30

4.11 Delayed Max Throughput/Max Throughput scheduling vs Timeusing 4 receiving Antennas . . . . . . . . . . . . . . . . . . . . . . 31

4.12 Delayed Max Throughput/Max Throughput scheduling with ICIvs Time using 1 or 2 receiving Antennas. . . . . . . . . . . . . . . 32

4.13 Delayed Max Throughput/Max Throughput scheduling with ICIvs Time using 3 or 4 receiving Antennas. . . . . . . . . . . . . . . 32

4.14 Estimated Max Throughput/ Delayed Max Throughput schedulingwith and without ICI for a selected Bestuser without ICI vs Timeusing 1 or 2 receiving Antennas . . . . . . . . . . . . . . . . . . . 33

4.15 Estimated Max Throughput/ Delayed Max Throughput schedulingwith and without ICI for a selected Bestuser without ICI vs Timeusing 3 and 4 receiving Antennas. . . . . . . . . . . . . . . . . . 34

4.16 Delayed Max Throughput/ MaxThroughput scheduling vs Timefor a selected Bestuser without Interference in comparison withMax/ Delayed Throughput scheduling for a Bestuser with Inter-ference and using 1 or 2 receiving Antennas. . . . . . . . . . . . . 34

4.17 Delayed Max Throughput/ MaxThroughput scheduling vs Timefor a selected Bestuser without Interference in comparison withMax/ Delayed Throughput scheduling for a Bestuser with Inter-ference and using 3 or 4 receiving Antennas. . . . . . . . . . . . . 35

4.18 Staple graph showing a Delayed Max Throughput/ MaxThrough-put scheduling vs number of Antennas for a selected Bestuserwithout Interference in comparison with Max/Delayed Through-put scheduling for a Bestuser with Interference. . . . . . . . . . . 36

4.19 Delayed Max Throughput vs Delay using 1 or 4 receiving Antennas. 364.20 Delayed Max Throughput vs Delay using 1 to 4 receiving Antennas. 374.21 Expected Max Throughput/Delayed Max Throughput/ PF Max

Throughput vs SNR for different numbers of receiving Antennas. 394.22 Expected Max Throughput/Delayed Max Throughput/ PF Max

Throughput with and without Interference vs SNR for differentnumbers of receiving Antennas. . . . . . . . . . . . . . . . . . . . 39

4.23 Cummulative Distribution Function vs different types of schedulingusing one or four Antennas. . . . . . . . . . . . . . . . . . . . . . 40