LTE Channel Modelling for SystLTE Channel Modelling for System Levelem Level

8/13/2019 LTE Channel Modelling for SystLTE Channel Modelling for System Levelem Level

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Supervised by:

M.Sc. B.Sc. Yasir Zaki

Prof. Dr. rer. nat. habil. C. Grg

Master Mini-Project

LTE Channel Modelling for System LevelSimulations

of

Safdar Nawaz Khan Marwat

Bremen, September 27, 2011

Communication Networks

University of Bremen

Prof. Dr. rer. nat. habil. C. Grg


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Ich versichere, da die vorliegende Arbeit bis auf die offizielle Betreuung durch denLehrstuhlohne Fremde Hilfe von mir durchgefhrt wurde. Die verwendete Literaturist im Literaturverzeichnis vollstndig angegeben.

I certify that I have conducted this work on my own and no other supporting materialhas been used other than those which are listed as references.

Bremen, den 27. September 2011

(Safdar Nawaz Khan Marwat)


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ACKNOWLEDGEMENT

I thank the Almighty for all his blessings. I am thankful to my parents whose prayers areall-important for me. I would like to thank my project supervisor, Yasir Zaki who hashelped and inspired whenever I have turned to him. I would also like to thank LiangZhao of the Department of Communication Networks, Mark Petermann, RonaldBhnke and Yidong Lang of the Department of Communications Engineering for theirvaluable suggestions and clarification of various topics. In the end, special thank toProf. Dr. Carmelita Grg.

Safdar Nawaz Khan Marwat

Bremen 2011


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ABSTRACT

Advancements in mobile communication techniques have helped in introducing variousnew wireless applications. This has caused an increase in the demand of capacity and

performance. Long Term Evolution (LTE) addresses such demands. It exploitsOrthogonal Frequency Division Multiplexing (OFDM) for downlink as a digitalmodulation technique based on dividing the transmission bandwidth into smallersubcarriers. Channel modelling is a fundamental task during the modelling of mobilecommunication systems. Various channel models have been proposed in the past to beused for simulating the mobile communication systems. With advent of LTE, the needto modify the existing channel models also has surfaced, especially as new frequency

bands have been allocated to LTE and new transmission techniques are used. Thisreport analyses various channel models for LTE. Path loss, slow fading and fast fadingmodels are investigated separately within this thesis. The frequency dependence of pathloss, the distance correlation of the slow fading, and the frequency/time selectivity ofthe fast fading are of special interest in the channel modelling. The pros and cons ofeach model are discussed and the appropriate models are selected for the developmentof the system level LTE simulator. The overall fading effect of the channel isdetermined by accumulating the results of the individual path loss, slow fading and fastfading models at a particular time, frequency and location.


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KURZFASSUNG

Fortschritte in mobilen Kommunikationstechniken haben die Einfhrung verschiedenerneuer Wireless-Anwendungen begnstigt. Dies hatte eine Erhhung der Nachfrage nachKapazitt und Leistung zur Folge. Long Term Evolution (LTE) bedient diese

Nachfrage. Es nutzt Orthogonal Frequency Division Multiplexing (OFDM) fr denDownlink als digitales Modulationsverfahren und Teilt dadurch diebertragungsbandbreite die auf kleinere Untertrger auf. Kanal-Modellierung ist eineder fundamentalen Aufgaben bei der Modellierung von mobilenKommunikationssystemen. Verschiedene Kanalmodelle wurden in der Vergangenheitzur Simulation von mobilen Kommunikationssystemen vorgeschlagen. Mit

dem Aufkommen von LTE, wurde es notwendig, die vorhandenen KanalModelle zu modifizieren, zumal LTE auch neue Frequenzbnder zugeteilt wurden, undneue bertragungstechniken verwendet werden. Diese Arbeit analysiert verschiedeneKanalmodelle fr LTE. Path loss, slow und fast fading models werden im Rahmendieser Arbeit separat untersucht. Die Frequenzabhngigkeit des path loss, dieAbstandskorrelation des slow fading, und die Frequenz / Zeit-Selektivitt des fastfading sind bei der Kanal-Modellierung von besonderem Interesse. Die Vor-und

Nachteile der einzelnen Modelle werden diskutiert und die sinnvollen Modelle fr dieEntwicklung des LTE Simulators auf System-Ebene ausgewhlt. Der gesamte Fading-Effekt des Kanals wird durch die Akkumulierung der Ergebnisse von path loss, slowfading und fast fading-Modellen bestimmt, die zeitlich, rumlich und in ihrer Hufigkeit

definiert sind.


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TABLE OF CONTENTS

1. Introduction ............................................................................................................. 111.1 Long Term Evolution ....................................................................................... 111.2 Orthogonal Frequency Division Multiple Access ............................................ 13

2. Radio Channel ......................................................................................................... 152.1 Channel Model ................................................................................................. 172.2 Types of Fading ................................................................................................ 17

3. Path Loss ................................................................................................................. 193.1 Free Space Path Loss Model ............................................................................ 203.2 Maxwell Equations ........................................................................................... 213.3

Ray Tracing Models ......................................................................................... 21

3.4 Empirical Models ............................................................................................. 22

3.4.1 Okumura Model ........................................................................................ 223.4.2 Hata Model ................................................................................................ 233.4.3 COST 231 Hata Model .............................................................................. 23

3.5 Simplified Model .............................................................................................. 243.6 Other Simplified Models .................................................................................. 25

3.6.1 Indoor Office Test Environment ............................................................... 253.6.2 Outdoor to Indoor and Pedestrian Test Environment ............................... 253.6.3 Vehicular Test Environment ..................................................................... 27

3.7 Path Loss Models Used in LTE Simulations .................................................... 284. Slow Fading ............................................................................................................ 294.1 Shadowing ........................................................................................................ 29

4.2 Shadowing Parameters of ETSI ........................................................................ 294.3 Shadowing Correlation over Distance .............................................................. 304.4 Shadowing Correlation over Area .................................................................... 30

4.4.1 Conventional Approach using Cholesky Factor ....................................... 314.4.2 Summing Sinusoids Based Approach ....................................................... 314.4.3 Holger Claussen Proposed Method using Cholesky Factor ...................... 31

4.5 Shadowing Correlation over Frequency ........................................................... 354.6 Shadow Fading Models Used in LTE Simulations .......................................... 35

5. Fast Fading .............................................................................................................. 375.1 Frequency Selectivity ....................................................................................... 375.2 Time Selectivity ................................................................................................ 385.3 Terminology ..................................................................................................... 395.4 Fast Fading Models .......................................................................................... 42

5.4.1 Clarkes Model .......................................................................................... 425.4.2 Jakes Model ............................................................................................... 425.4.3 Dent Model ................................................................................................ 445.4.4 Jakes-like Method of Complex Gain Generation ...................................... 455.4.5 Other Improvements for Jakes Model ....................................................... 465.4.6 IDFT Methods ........................................................................................... 47

6. Simulation Result and Analysis .............................................................................. 49


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1 Introduction10

6.1 Link Level and System Level Simulations ....................................................... 496.2 Path Loss Simulations ...................................................................................... 506.3 Slow Fading Simulations .................................................................................. 506.4 Fast Fading Simulations ................................................................................... 516.5 WINNER Spatial Channel Models ................................................................... 56

7. Conclusion and Outlook .......................................................................................... 597.1 Path Loss .......................................................................................................... 597.2 Slow Fading ...................................................................................................... 607.3 Fast Fading ....................................................................................................... 61


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1 Introduction12

lower cost per bit increase services economically adaptable use of prevailing and new frequency bands uncomplicated architecture with open interface fair power consumption at terminal

In December 2004, a feasibility study was commenced by 3GPP for Long TermEvolution (LTE) system. The motivation for this study was to establish a plan of actionfor the evolution of a packet only system with higher data rates, high quality of service(QoS) and simple infrastructure. The details of the performance requirements can besummarized as follows (taken from [2]):

Peak Data Rate: Downlink: 100 Mb/s within a 20 MHz downlink spectrum

allocation (5 bps/Hz); Uplink: 50 Mb/s (2.5 bps/Hz) within a 20 MHz uplinkspectrum allocation Control Plane Latency: Transition time below 100 ms from a camped state1to

an active state; transition time below 50 ms between a dormant state2 and anactive state

Control Plane Capacity: Support for minimum 200 users in a cell in the activestate for up to 5 MHz bandwidth allotment

User Plane Latency: Below 5 ms in unload condition for small IP packet User Throughput: Downlink: average user throughput per MHz, 3 to 4 times

Release 6 HSDPA; Uplink: average user throughput per MHz, 2 to 3 timesRelease 6 Enhanced Uplink

Spectrum Efficiency: Downlink: spectrum efficiency (bits/sec/Hz/site) 3 to 4times Release 6 HSDPA in loaded condition; Uplink: spectrum efficiency(bits/sec/Hz/site) 2 to 3 times Release 6 Enhanced Uplink in loaded condition

Mobility: Network optimized for mobile speed of 0 to 15 km/h; Highperformance support for mobile speed between 15 and 120 km/h;Communication in network to be sustained at speeds of 120 km/h to 350 km/h(or even till 500 km/h in certain frequency bands)

Coverage: Requirements regarding throughput, spectrum efficiency andmobility to be met for 5 km cells; with minor deterioration for 30 km cells; evencell range up to 100 km to be acceptable

Multimedia Broadcast Multicast Service (MBMS): Reduced terminalcomplexity in terms of modulation, coding and UE bandwidth along withMBMS service

Spectrum Flexibility: Ability of radio network to operate in various sizes ofspectrum allocations ranging from 1.25 MHz to 20 MHz in both the uplink anddownlink along with ability to operate in paired and unpaired spectrum

1 In camped state, the terminal location (cell) is not known to the radio access network and no radioresources are assigned to it. The terminal may be in sleep mode (i.e. listening to the network at particularintervals of time).2In dormant state, the terminal location (cell) is known to the radio access network but it has no radio

resources assigned to it. The terminal may be in sleep mode.


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1.2 Orthogonal Frequency Division Multiple Access 13

Co-existence and Inter-working with 3GPP Radio Access Technology(RAT): Ability of LTE radio network to operate simultaneously with GSM andUMTS radio networks in a particular location with interruption time less than

300 ms in case of inter-system handover Architecture: Packet based architecture to be designed supporting the end-to-

end QoS (e.g. to guarantee customers that end-to-end latency remains under aspecific level)

Complexity: Reduce the number of alternatives and eradicate repetitiousmandatory features.

The accomplishment of the wide-ranging requirements summarized above demands theemployment of advanced technology [3]. The recent progress in mobile radiotechnology has made the task of realizing these requirements achievable. The radiotechnology proposed for LTE features: multicarrier technology, multiple-antennatechnology, and the utilization ofpacket-switchingfor radio interface.

1.2 Orthogonal Frequency Division Multiple Access

In December 2005, after the approval of using the multicarrier approach as the multipleaccess technique in LTE, the Orthogonal Frequency Division Multiple Access(OFDMA) was chosen for downlink and Single-Carrier Frequency Division MultipleAccess (SC-FDMA) for uplink. OFDMA is the multiuser extension of OFDM. OFDMsplits the spectrum into smaller subcarriers closely spaced and orthogonal to each otherfor the transmission of a single date stream using prevailing modulation schemes. As

compared to a single-carrier system where a deep fade in power level or an interferercan be sufficient to terminate the link between transmitter and receiver, in OFDMsystems, only few of the subcarriers are disturbed which allows transmission throughthe subcarriers that are least affected. OFDMA utilizes the spectrum division of OFDM

by allocating subsets of subcarriers to individual users. This allows a flexible use ofbandwidth with the conventional equipment.

Figure 1.1: OFDMA downlink frequency domain view


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CHAPTER 2

Failing to plan is planning to fail. - Alan Lakein

2. Radio Channel

adio channel is the medium which carries information from a transmitter to a

receiver in the form of electromagnetic waves. Information is carried bymodulating a carrier wave at the transmitter. . The carrier wave propagates through theair and is demodulated at the receiver to retrieve the transmitted data.

A radio signal encounters several hindrances not only due to noise and interference, butalso due to the arrival of additional copies of the same signal and the motion oftransmitter and/or receiver. The signal can propagate as simple as passing through aLine Of Sight (LOS) path between stationary transmitter and receiver or as complex as

being obstructed and scattered by buildings, trees and mountains with arrival of multiplesignal copies delayed in time with transmitter and/or receiver in motion. Thesehindrances change with time and also due to the speed of the transmitter and/or receiverwhich make the assessment of signal propagation more complex. As mentioned above,a radio channel faces several obstacles in signal propagation. High speed datatransmission with reliability is a major challenge for wireless communication. Therandomness of wireless propagation makes the task of analysing the radio channel quitedifficult.

Three basic phenomena influence the propagation of signal, namely reflection,diffractionandscattering. Reflections are caused by the incidence of propagating waveon surface having dimensions quite larger than its wavelength. Diffraction takes placeas a result of an obstruction between the transmitter and receiver antennas, generating

secondary waves behind the obstruction. Scattering takes place due to the incidence ofpropagating wave on surface having dimensions comparative to or smaller than that ofwavelength, resulting in the signal being redirected to several paths. The result of theinfluence of these phenomena is termed as multipath propagation. As a consequence ofmultipath transmission; the attenuated, delayed, and phase-shifted copies of thetransmitted signal accumulate at the receiver. The superposition of signal copies iseither constructive or destructive.

The motion of transmitter and/or receiver also affects the power of the signal duringpropagation. The phenomenon resulting because of this motion is known as Dopplershift. It causes shift in the frequency domain of the transmitted signal and results in the

expansion of the spectral width. It is directly proportional to the speed of the mobile. At

R


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2 Radio Channel16

a carrier frequency, a signal received at an angle by a mobile moving at a velocity has a Doppler shift given as

(2.1)Where is the maximum Doppler shift at . The spectrum of the received signallies between which is having U-shape around and illustrated in Figure 5.3.The power outside this range is ideally zero.

The geographical environment of the propagation of signal between a transmitter and areceiver is known as propagation environment. The physical parameters of the mediumsuch as street axes, buildings, vegetation and land use etc. characterize the propagationenvironment [4]. The geographical area covered by a base station and the type ofantenna used determine the type of cell. Four types of cell can be defined: macrocell,small cell, microcell and picocell. The categorization of a cell is established by thelocation, power, height etc. of the base station.

Macrocell:Macrocell covers a huge geographical area, in the order of tens of thousandsof kilometres as radius. It is generally employed in rural or mountainous areas with basestation positioned at a high altitude. Typically, there are very few mobile users in amacrocell.

Small Cell:For a relatively larger number of users in a given area, such as in urbanareas, the size of the cell has to be reduced to enable frequency reuse within shorterdistances. The radius of the area covered by a small cell is in the order of a fewkilometres. Base station is usually positioned at the roof top.

Microcells:In densely populated urban areas, the size of the cell is further reduced. Theradius of area covered by microcell is a few hundreds of meters, enabling frequencyreuse within much shorter distances. Antennas are positioned below roof levels,whereas the streets act as wave guides.

Picocells: The radius of area covered by picocell is a few tens of meters. The basestation antenna is position inside the building where communication occurs.

The position of antenna corresponds to the type of cell. Antennas perform the functionof transmission or reception of radio signal. A transmit antenna is connected to anelectric power generator which supplies the power at certain frequency, facilitating theantenna to radiate the radio wave. The radio wave is generated by emitting variablecurrent in the transmit antenna. On the other hand, a receive antenna determines theeffects of the radio waves transmitted by a transmit antenna and facilitate the receiverwith these effects. The effect of radio waves at the receive antenna is the generation ofvariable current at the receive antenna, which is conveyed to the receiver. Severaldifferent types of antennas are in use, having different shapes, dimensions and operablefrequency ranges. Some commonly used forms of antennas are linear, helical, reflector,

loop, horn and patch antennas. In antennas; the radiation pattern, power gain,


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2.1 Channel Model 17

directivity, beamwidth, aperture, polarisation, current distribution, effective height, andimpedance are some of the distinguishing characteristics of antennas.

2.1 Channel Model

Channel model is a mathematical representation of the relationship between powertransmitted and received during a wireless transmission. Channel model describes theeffect of channel on the transmitted signal. Fading in a channel is the variation of thestrength of transmitted signal during propagation over time and over frequency. Itshows the alteration of signal amplitude and phase caused by the transmission medium.Fading occurs due to several reasons including distance attenuation, obstacles, motionof transmitter and/or receiver and the arrival of multiple signals.

The purpose of channel modelling is to figure out how well a communication systemperforms. Channel modelling is the fundamental phase of designing mobilecommunication systems. Wired transmission of signal is stationary and results areforeseeable, however, in wireless case, the severe randomness of the channel leads tothe development of statistical channel models. Multipath effect, motion of transmitterand/or receiver and shadowing make that propagation of signal in radio channel a verycomplex phenomenon. Depiction of this phenomenon using simple mathematicalrepresentations may not emulate the propagation effects appropriately [5]. On the otherhand, a complex model may not be useful for analytical purposes. Significant effortshave been made to achieve statistical models illustrating precise depiction of the

propagation effect for various scenarios without being complicated.

Figure 2.1: Channel model block diagram

2.2 Types of Fading

Fading encountered by a wireless signal is in general, an aggregate of three primarytypes of fading. These fading constituents are:

Path loss Slow fading Fast fading

Transmit SignalChannel

Receive Signal


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2 Radio Channel18

Path loss and slow fading fall in the category of large scale fading. Large scale fadingoccurs if the mobile travels a distance which is comparable to the diameter of the cell.Path loss depends upon the distance between the transmitter and the receiver, while

slow fading occurs typically due to shadowing effect when the signal is obstructed bylarge objects. Fast fading is categorized as small scale fading and occurs due tomultipath propagation and motion of the mobile a distance comparable to the carrierwavelength. Over the subsequent chapters, these three different fading constituents arediscussed with their respective mathematical models.

In general, a signal transmitted from the transmitter reaches the receiver with fluctuatedamplitude. Each of the above mentioned type of fading contributes to this variation ofthe signal strength. The ratio of the receive power to transmit power in overlog of distance

can be seen as in Figure 2.2.

Figure 2.2: Path loss, slow fading and fast fading versus distance


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CHAPTER 3

The number of books will grow continually, and one can predict that a time will

come when it will be almost as difficult to learn anything from books as from the

direct study of the whole universe. It will be almost as convenient to search for some

bit of truth concealed in nature as it will be to find it hidden away in an immense

multitude of bound volumes. Denis Diderot

3. Path Loss

ath loss is the power attenuation of the transmit signal in the propagationenvironment as the signal travels from the transmitter to the receiver. Path loss

modelling plays a vital role in development of mobile communication systems. Thesemodels are useful in determining the number of cell sites required to cover a network[6]. These models also facilitate in determining the location of cell sites for optimalnetwork performance. Inaccuracy of model can lead to inappropriate positioning of cellsite locations. Other advantages of path loss models can be optimization of parameterssuch as handoff schemes, antenna positioning, power levels etc. A single model may not

be able to capture the effects of all practical variations, but using a combination ofmodels may give accurate path loss results. To design an efficient communicationsystem, the strengths and weaknesses of various models have to be understood.

Mathematically, path loss is formulated as the ratio of transmit power to receivepower of a signal. In its simplest form

(3.1)Path loss in can be expressed by variable as (3.2)Path loss between a transmitter and receiver is always assumed to be the same at a givendistance if slow and fast fading are not taken into account. Path loss is a prime source ofsignal fading. It has to be considered when a fading channel model is developed. Pathloss occurs because of the propagation losses of the radio wavefront in free space due toits expansion in spherical manner. Also during propagation, signal passes through

P


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3 Path Loss20

various kinds of media. Signal can come across a medium which absorbs the signalpower.

Extensive effort has been made to develop mathematical models for depiction of pathloss in various environments. Path loss models are classified [7] into three differentcategories; statistical (or empirical), deterministic and semi-deterministic models.Statistical models express distance dependent average value of path loss obtained fromseveral measurements performed in various fading environments such as rural, urban,suburban etc. The data obtained from these measurements can be given either in agraphical form or as formulas that best fit the measurements obtained for average pathloss against distance in a particular environment. Extensive information specific to the

propagation environment is not a vital issue in the statistical models. Okumura and Hatamodels are good examples of such statistical models. In contrast, deterministic modelsrequire comprehensive information about the propagating environment for assessment

of resulting signal strength after taking into account the multipath effect. Terrain andbuilding database information is essential for deterministic models. Such models arehelpful only for depiction of simple environments like a small microcell; otherwise themodels can be severely complicated without useful practical application in complexenvironments. Free space and ray tracing models are examples of deterministic models.Semi-deterministic models combine the statistical data from measurements of path losswith the deterministic method of acquiring site related information for assessment of theeffect on signal strength. COST 231 is an example of semi-deterministic models.

3.1 Free Space Path Loss Model

The simplest model for path loss of a propagating wave is the case of a wavepropagating in free space [6]. Free space path loss model considers the transmission tobe only LOS in space between transmitter and receiver. Such a transmission assumesthat the signal propagates without any obstruction, the transmitter and the receiver areseparated by a region having no object able to reflect or absorb the signal, and the earthis at an infinite distance away from the signal. Free space strictly represents vacuum,however this model can also be efficiently used to depict short-range space-wave paths

between antennas which are elevated. In this model, the radiation is emitted by anisotropic antenna. Such kind of antenna radiates in all directions uniformly and istermed as omnidirectional. An isotropic antenna practically does not exists, therefore it

is only a concept assumed theoretically for various purposes but without physicalexistence. Free space path loss model can be given mathematically as in [8] as follows

(3.3)where and are the gain factors of transmit and receive antenna respectively, is the carrier frequency and is the speed of light in vacuum. In

d

(3.4)


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3.2 Maxwell Equations 21

3.2 Maxwell Equations

Researchers have long been of the view that electricity and magnetism are two distinct

phenomena without any mutual dependence. However, by the nineteenth centuries,laboratory experiments revealed that magnetic field can be generated by an electriccurrent. Similarly, electric field can be generated by a varying magnetic field. Thesediscoveries helped Maxwell to develop a set of equations by incorporating the work ofearlier scientists [9]. These equations form a relationship between electric charge,electric current, electric field strength, magnetic field strength, electric flux density andmagnetic flux density. Maxwell equations can be applied to model multipath wirelesschannels by investigating boundary conditions and dielectric properties of the scatterers,reflectors and deflectors [10].

The propagation of electromagnetic waves is influenced by scattering, reflection anddiffraction with buildings, trees and uneven landscape. The dielectric properties of theseobjects affecting the signal wave should be determined before using Maxwell equationsto deduce propagation details. Such calculations are usually marked by complexitiesdue to the calculation of Radar Cross Sections (RCSs) of huge and complex structures[11]. The radar cross section of an object indicates the amount of electromagneticenergy obstructed and reradiated by an object at a certain wavelength. RCS dependsupon size, shape, material edges, wavelength and polarization of the object. RCScalculation is an advanced topic and covered in various text books and research papers.

3.3 Ray Tracing Models

Ray tracing models are deterministic models. These models assume the scatterers to besimply reflectors or refractors and considered finite in number [11]. In addition, thelocation and dielectric properties of scatterers are also known. The wave fronts areconsidered as particles so that simple geometric equations can be employed instead ofthe complicated Maxwell equations. A ray can be described as the path of an ideal bullettravelling in a straight line and is being reflected or deflected by surfaces coming itsway. Accuracy can be achieved in ray tracing model if the receiver is at distance greaterthan several wavelengths from the nearest scatterers; the scatterers are also required to

be smooth and larger than wavelength.

Ray tracing is analogous to an imaginary world, filled all over with mirrors which arepartially silvered. Due to this partial silvering, an incident ray of light striking a mirrorwould generate two rays; a transmitted ray going straight through the mirror, and areflected ray. The orientation of the mirror would determine the direction of reflectedray, whereas the transmitted ray would continue to travel in the direction of incident ray.The incident ray itself would culminate after the impact. Many efficient algorithms have

been proposed for ray tracing models and are available in literature.


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3 Path Loss22

3.4 Empirical Models

In complex propagation environment, such as urban built-up, empirical models are

better alternative for channel modelling. In empirical models, path loss is measured at agiven distance for a particular frequency range and certain location. However, suchmodel can be applied to other locations as well. The average path loss at a distance istermed as Local Mean Attenuator (LMA) at . The path loss measured at a specific

point at a distance from the transmitter in a certain environment shall contain theimpact of the multipath arrivals. To eliminate fluctuations due to multipath, LMA istaken so that the multipath effects are averaged out. LMA measurements are dependenton the location of the antennas in the environment (e.g. city) where the calculations are

performed. The generalization of LMA requires extensive measurements all over theenvironment. Also, the measurements are to be taken in several environments withcomparable features. In the following subsections, three of the most important and wellknown empirical models are discussed in details.

3.4.1 Okumura Model

Okumura model is a quite popular empirical model. Its applicability ranges from 1 to100 km of distance and 150 to 1500 MHz of frequency. In 1960, Okumura performed

plenteous trials all over Tokyo to evaluate path loss at various distances from a basestation. His model provides only graphical path loss measured data depending upon thetype of environment.

The applicability of the Okumura model covers three categories of environment namelyurban area, suburban area and open area [12]. The model of urban area characterizes acity or large settlement with high buildings having two or more storeys, or big villageshaving buildings close to each other and huge trees. The suburban area model depicts asmall village or highway surrounded by houses and trees, but not jam-packed. The openarea model illustrates open plain without having any buildings or huge trees for 300400 m ahead. Okumura used the urban area as a standard model and introducedcorrection factors for application of the model to other categories. He also identified anumber of terrain types. Quasi-smooth terrain, a terrain having smooth undulations withmaximum peak-to-peak amplitude of 20m around a flat surface, was used as thestandard terrain and correction factors apply for other types of terrain. The empirical

path loss formula devised by Okumura expressed in terms of at carrier frequency and distance is given as (3.5)where is the free space path loss, is the median of path loss additional to freespace path loss in urban area with quasi-smooth terrain for base station antenna height of 200m and mobile antenna height of 3m, and and are the base stationantenna and mobile antenna height gain factors respectively. The empirical formulas for

and

are derived by Okumura as given below:


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3.4 Empirical Models 23

m (3.6)

m (3.7)3.4.2 Hata ModelThe Hata model is also termed as OkumuraHata model. This model empiricallyformulates Okumura Model by utilizing the graphical information retrieved byOkumura. Like Okumura model, the applicable frequency range for Hata model is also150 to 1500MHz. Hata model provide three separate formulas for each type ofenvironment, namely urban areas, suburban areas and open areas.

For urban area, Hata formulated the path loss as follows:

(3.8)where is the correction factor for mobile antenna height. This factor dependsupon the coverage area. If the city is small to medium sized, this factor in can begiven as

(3.9)whereas for large cities at

> 300MHz, the factor is given as

(3.10)For suburban area, Hata model gives path loss as:

(3.11)For open area, the formulation is as follows:

(3.12)

Okumura model is generally used by the utilization of Hata model. The formulasdeveloped by Hata make Okumura model much simpler to use and convenient. Hatamodel does not require correction factors for various types of environments. In case of1G mobile systems, can be greater than 1000m. For, greater than 1000m, Hatamodel provides very nice approximation for path loss.

3.4.3 COST 231 Hata Model

The COST 231 Hata model is an extension of the Hata model developed by EuropeanCooperation in Science and Technology (EURO-COST). This model extends the range


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3 Path Loss24

of Hata model, as the validity of this model ranges from 1500 and 2000MHz. Theconstraints for this model can be summarized as:

This model is limited to cases where the base station antenna is placed higher than thesurrounding building roofs. The median path loss determined by this model can beexpressed as:

(3.13)

Where is for medium and small sized cities and for metropolitan areas.3.5 Simplified Model

The signal propagation is a quite complex phenomenon. Development of a model thatcan befittingly illustrate path loss for every type of propagation environment is verychallenging. Nevertheless, if a model is desired for an evaluation of a system to analyzetrade-off between several system designs, a simple model can be utilized. Such a modelis able to differentiate between various propagation environments without being

complicated. Such model provides only rough resemblance of real channel path losscalculations.

It has long been established from both theoretical propagation models and measureddata for path loss that the average of received signal power decreases with distancelogarithmically, no matter which type of propagation environment (outdoor or indoorradio channels) is under study. Simplified models have been widely used. A simplified

path loss model which is used frequently is given in [10] as:

(3.14)

In terms of : d d (3.15)where is a constant without any unit and depends upon , and, while is areference distance of antennas far field and determined either empirically oranalytically, and is the path loss exponent. The value of is presumed 1-10 mindoors and 10-100 m outdoors [10]. The value of

is determined by assigning it the


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3.6 Other Simplified Models 25

value of the free space path gain (reciprocal of free space path loss) at distance whileconsidering transmit and receive antennas to be Omnidirectional (i.e. ).

(3.16)Value of varies with the type of environment. Some typical values of are given inTable 3.1 (taken from [13]).

Table 3.1: Path loss exponents for various environments

Propagation Environment Path Loss Exponent

Free space 2

Urban area cellular radio 2.7 to 3.5

Shadowed urban cellular radio 3 to 5

In building line-of-sight 1.6 to 1.8

Obstructed in building 4 to 6

Obstructed in factories 2 to 3

3.6 Other Simplified Models

The European Telecommunications Standards Institute (ETSI) has proposed severalpath loss models, depending upon various environments for LTE system [14]. Thesemodels assist in simulations based on channel models for wireless system evaluation.The various environments models specified by ETSI are discussed below:

3.6.1 Indoor Office Test Environment

The indoor office test environment consists of small cells with antennas transmitting atlow power. The transmitters and receivers are placed indoor and their motion is alsorestricted indoor. The variation in path loss is caused by scattering and attenuation bywalls, floors, and metallic structures; for instance partitions, file cabinets and frames of

the building. For such an environment, 3GPP formulates path loss using a simplifiedmodel as follows:

(3.17)where is the number of floors between the transmitter and receiver. should always

be greater than the free space path loss.

3.6.2 Outdoor to Indoor and Pedestrian Test Environment

The outdoor to indoor and pedestrian test environment also consists of small cells with

antennas transmitting at low power. The base stations are equipped with low height


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3 Path Loss26

antennas and are normally placed outdoors. The mobile users can move without anyrestrictions indoor and outdoor. Such an environment corresponds to various scenarios.The path loss being proportional to

nicely approximates this environment.

However, for accurate modelling, variations in this environment should be taken intoaccount. The path loss might be proportional to in case of a LOS transmission,proportional to for non-LOS case and proportional to if obstructions like treesare also added to non-LOS case. Normally, the non-LOS case can be expressed as:

(3.18)A model encompassing both LOS and non-LOS propagation is also proposed in [14].This model considers the densely built-up urban propagation. It recursively determines

path loss by discovering the shortest path along the streets between the transmitter andthe receiver through the urban built-up. In this case, the path loss is given as in(3.19).

(3.19)where is termed as the illusory distance [15] and is the number of streetsegments along the shortest path (see Figure 3.1). is the sum of street segmentsand acquired by a recursive utilization of the expressions

(3.20)where determines how much path loss depends upon the angle. Therefore, incase the angle of the street crossing is zero. Similarly, with a 90 degree street canrange between . Thus increases with increasing the angle of streetcrossing. Also, is the length in meters of the segment of the street. The expression(3.20) is initialized with and . The last value of obtained is the illusorydistance.

This model can be modified to encompass the dual-slope characteristics of propagationin microcells. The dual-slope behaviour of path loss has been revealed in measurementsdone in [16]. The measurements illustrate that a path loss model with a single path loss

exponent is not accurate. Alternatively, dual-slope model depicts two distinct path lossexponents along the propagation path with a breakpoint distance of a few hundredmeters between the transmitter and the receiver. Here, the path loss can be expressed bymodifying the equation(3.19) to

(3.21)

(3.22)


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3.6 Other Simplified Models 27

where is the break point which is set to 300 meters.

Figure 3.1: Calculation of illusory distance for n= imax= 3

The effects of the propagation above roof tops are also depicted here. In many cases,diffraction is the major propagation phenomenon. Therefore, path loss related to theshortest distance is to be calculated. COST 231 Walfish-Ikegami model is utilized withthe assumption that the antennas are placed below roof tops. The model is expressed as

below:

(3.23)

where is the shortest geographical distance between transmitter and receiver. Theminimum value of path loss from propagation through streets(3.21) and path loss basedon shortest distance(3.23) is chosen as the end value of path loss.

3.6.3 Vehicular Test Environment

The vehicular test environment consists of large cells with antennas transmitting at highpower. In this environment, a path loss proportional to is presumed. The path lossfor the vehicular environment can be formulated as:


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3 Path Loss28

(3.24)

where is the height of the base station antenna in meters from the average roof toplevel, and . If and , the pass loss model shrinks to (3.25)should always be greater than the free space path loss. This model can be utilized onlyfor non-LOS case of transmission.

3.7 Path Loss Models Used in LTE Simulations

An evaluation of the hard handover performance for LTE system is described in [17]. Inthis paper, the vehicular environment path loss model in (3.25) is chosen to beemployed in the simulation. The operating frequency of LTE coincides with thefrequency range of the model.

Reference [18] provides a few methods for evaluating the 3G LTE system from systemlevel. The performance of LTE system is evaluated through a system level simulation.To avoid co-channel interference (CCI), fractional frequency reuse (FFR) scheme is

proposed. It is shown with simulation results that FFR scheme brings higher channelcapacity and lower CCI. Also, the simulations show that the cell edge data rateimproves. In this paper also, the vehicular environment path loss model(3.25) is chosen

for employment in simulation.


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CHAPTER 4

4. Slow Fading

low fading is a long-term amplitude fluctuation of the transmitted signal. Slow fadingis primarily caused by shadowing and, therefore, frequently termed as shadow fading.

4.1 Shadowing

Shadowing is the obstruction that a signal encounters due to objects blocking its path. A

signal originating at the transmitter is obstructed by several objects like trees and buildingsduring propagation. These obstructions lead to random variation in the amplitude of thesignal. These variations are not taken into account by the simplified path loss models andtherefore should be modelled separately. Normally, the characteristics of the blockingobjects like size, location, dielectric properties etc. are unknown; hence shadowing effectsare modelled statistically. Experimentally, it has been established that the fluctuation in theratio of transmit and receive power can be depicted by a log-normal shadowing.

Let the ratio of the power transmitted and the power received after being shadowed berandom variables

in linear scale and

in

scale such that

. In linear

scale, the probability distribution of

, which is log-normally distributed, is given in [10]

as

d d d (4.1)where is the mean of in and is the standard deviation of in . isnormally distributed. The probability distribution of in shall be Gaussian and can beexpressed as

d d

d (4.2)

To generate such a probability distribution, and should be known. If path loss andshadowing are modelled as a single model, then is equal to path loss because theaverage attenuation from shadowing is already included in the results. However, ifshadowing is modelled separately, then would be . In this case, addition ofshadowing to path loss would inflict fluctuations in path loss curve as depicted inFigure2.2.

4.2 Shadowing Parameters of ETSI

The ETSI has proposed mean and standard deviations of log-normal shadow fading forvarious environments for LTE system [14]. The purpose of these models is to facilitatesimulations based on channel models for wireless system evaluation. Mean value of the

S


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4 Slow Fading30

log-normal shadowing is generally accepted as , however, the standard deviationvaries with the type of the environment. In indoor office test environment, a log-normalshadow fading standard deviation of

is probable. In outdoor to indoor and

pedestrian test environment, probable standard deviation of shadow fading for outdoor isand for indoors is . In vehicular test environment, probable standard deviationof shadow fading in urban and suburban areas is .4.3 Shadowing Correlation over Distance

Shadowing measurements at two points within a cell that are at a certain distance apartfrom each other are presumed to have correlation among them. When modelling shadowfading, this correlation over distance is also modelled. Gudmundson [19] suggested amodel which depicts correlation between two points separated by a distance

. This model

can be represented mathematically as

d (4.3)where is the covariance of shadowing between two point at distance apart and isthe decorrelation distance, i.e. the distance at which the covariance between the two pointis (where is the maximum value that can have). The decorrelationdistance has been determined in various research papers for various types of propagationenvironments. In [20], the variability of shadowing has been studied through field tests in aheavily built-up urban environment at carrier frequency of 900MHz. Distancedecorrelation was measured between 44 and 112m. In [21], various correlation properties

of shadow fading have been investigated for the analysis of interference, handoff gain, andother parameters at carrier frequency of 1800MHz. The range of the decorrelation distancehas been shown to be between 25 to 100m. In the simulations performed in [17], thedecorrelation distance has been assumed to be 50m. However, in [14], ETSI has describedthat the decorrelation distance depends upon the environment; therefore, it is 20m for theurban environment and 5m for the indoor environment.

This shadowing correlation over distance model has to be integrated into the log-normalshadowing model. This has been demonstrated in [22] and [23]. For such an integratedmodel, consider a moving mobile user to be positioned at an initial point where theshadow fading value is to be randomly generated using the log-normal distribution in(4.2).

Let the value of the shadowing at distance from point be equal to . Todetermine the shadowing at points which are at distance , , ... away from ,according to [22], we use (4.4)

where are independent identically distributed (i.i.d.) normal random variables with mean and variance in .4.4 Shadowing Correlation over Area

Shadowing correlation model in (1-D) may not correctly model the effects of fadingbecause the shadowing effects occur over a large geographical area [24]. 1-D approach can


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4.4 Shadowing Correlation over Area 31

be utilized if the mobile is moving along a straight line. However, if the user is movingalong a closed route, 1-D approach may not be a good evaluation tool for shadowing [25].Therefore, for appropriate illustration of the shadowing in a large area to emulate realistic

effects, a two-dimensional (2-D) approach is required such that the shadowing in the areaunder study (or cell) is spatially correlated and log-normally distributed. For system levelsimulations, development of a 2-D map can be helpful in emulating the spatial correlation

properties of shadowing [26]. The 2-D approach is also useful for handover performanceassessment. Various methods have been proposed for development of a 2-D map depictingshadowing, some of these methods are discussed over the next subsections.

4.4.1 Conventional Approach using Cholesky Factor

Generally, the correlated shadowing values can be generated by multiplying a set ofrandomly generated independent random values with the Cholesky factor of the

corresponding correlation matrix. Correlation matrix is a square matrix that illustrates thecorrelation values between each two elements in the map. The randomly generateduncorrelated values are placed in a vector. The Cholesky factor of correlation matrix has to be multiplied withto obtain the correlated shadowing matrix

(4.5)Such that . This method requires a large number of correlated shadowingvalues, which implies that greater correlation matrices are required even for small mapsizes. If the map is

sized, a correlation matrix of size

is required. The

Cholesky factorization requires

multiplications and subtractions.

Additionally, square roots have to be taken. The memory requirements and thework load of this algorithm make it unaffordable and difficult to use for system levelsimulations.4.4.2 Summing Sinusoids Based Approach

In [25] other methods have been proposed for map generation in 2-D shadowingcorrelation modelling. These methods are based on summing of sinusoids and used formapping shadowing and fast fading values over a geographical area. However, thesemethods are not discussed here due to their complexity and because a less complex method

proposed by Holger Claussen is described in the next subsection which works quite

efficiently [26].

4.4.3 Holger Claussen Proposed Method using Cholesky Factor

The elements in shadowing matrix are generated by calculations depending only uponneighbouring elements (Figure 4.1). This decreases the memory requirements and workload. If a vector with two values and has to be generated, (4.6) and (4.7) (given

below) have to be used. Equation(4.6) can be obtained by dividing(4.3)by (4.6)

where is the correlation between two points separated by a distance in meters andis set to 20m. Equation(4.7) shows the correlation matrix and its Cholesky factor .


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4 Slow Fading32

Figure 4.1: Generation of correlated shadowing values

and

(4.7)

The shadowing values can be generated as follows:

(4.8) (4.9)

where and are randomly generated using Gaussian distribution. Similarly, for thegeneration of ,(4.9) can be modified to:

(4.10)where is generated randomly as normally distributed. All values are generated in such away that the neighbouring values are correlated as in(4.6).Correlation between and can be given as . This helps in deduction of avaluable rule in the model:

(4.11)

Figure 4.2: Generate 2-D correlated shadowing map using four neighbours

s1 s2 s3

s4 s5

s1 s2 s3

r() r()

r(2)


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4.4 Shadowing Correlation over Area 33

The shadowing value of depends only upon the correlation with its neighbour , butstill, this method provides true correlation between and as well. Similarly, correctcorrelation can be generated between any two points as shown in(4.11).

This model can be applied for the generation of a 2-D map with spatially correlatedshadowing values. Four neighbouring points in the map are used to generate the fifth pointas shown inFigure 4.2. Consider as the known points and with to be generated. The corresponding correlation matrices and can be deducedusing (4.6) such that the correlation between any two point is according to the distance

between them. For illustration, matrix of size 55 is given here

(4.12)

The Cholesky factors and corresponds to correlation matrices and respectively.Also and . Since which implies that , therefore, the following equation can be written:

(4.13)where is generated randomly through normal distribution. The required correlatedshadowing value is expressed as

(4.14)where is the last row of . In general, this formula can be extended to point. Thegeneral form shall be

(4.15)


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4 Slow Fading34

Figure 4.3: Shadowing 2-D map with 150 x 150 elements using 4 neighbours

This method efficiently generates shadowing values in 2-D map. During initialization or atthe edges of the map, instead of using four neighbours, the available number of (alreadydetermined) neighbouring elements can be utilized. In this method, the correlation withneighbouring elements is correct; however, the analysis shows that small correlation errorsare still possible in the overall map. To reduce these errors, the number of elements used togenerate a new value can be increased from four to eight as in Figure 4.4.Results showsignificant improvement against correlation error in the map.

Figure 4.4: Generate 2-D correlated shadowing map using eight neighbours

Compared to the conventional approach given above, this method has lower memoryrequirements and less work load. If a map of elements has to be generated, the sizeof correlation matrix required is

instead of

where w is the number of

neighbours used for generation of new value. The Cholesky factorization requires

instead of multiplications and subtractions, additionally, square roots have to be taken instead of .

s1 s2 s3

s4

s5 s6

s8s7

s9


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4.5 Shadowing Correlation over Frequency 35

4.5 Shadowing Correlation over Frequency

Shadow fading occurs in a spatially correlated manner as discussed so far. Correlation of

shadow fading values across subcarriers has also to be investigated. If the subcarriers areshadowed equally, i.e. strongly correlated to each other, a separate correlation model forfrequency is not essential. However, if shadow fading occurs with frequency selectivity,the effect has to be modelled.

According to [27], shadow-fading is highly correlated for the two carrier frequencies, 955MHz and 1845 MHz, because the same shadowing effects occur for each carrier frequency.This has been illustrated in an example where the power received along a street

perpendicular to the base station is calculated. The effect of path loss is subtracted from thetotal received power to make shadowing values available for analysis. The results showedthat shadowing is highly correlated even between frequency bands quite far apart fromeach other. The correlation coefficient of shadow fading between the two frequencies,955MHz and 1845MHz for different urban areas (in Denmark) were measured and areillustrated in the table below.

Table 4.1: Correlation coefficient of shadow fading between 955 MHz and 1845 MHz

Site Salling Badehusvej Dannebrogsgade Urbansgage Copenhagen

Corr.

Coeff.0.90 0.91 0.85 0.94 0.91

4.6 Shadow Fading Models Used in LTE Simulations

In reference [17], the log-normal distribution in(4.2) is chosen to be used in the simulatoras the shadow fading model. Shadowing correlation is modelled over distance with themobile stations moving in straight line in one direction. The decorrelation distance is set to50m. In reference [18], the log-normal distribution in(4.2) is also chosen to be used in thesimulator as the shadow fading model. Shadowing correlation in distance, area orfrequency is not modelled at all.


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CHAPTER 5

5. Fast Fading

ast fading is a short-term amplitude fluctuation of the transmitted signal. Fast fadingcauses the signal amplitude to fluctuate for a shorter period of time. The scale of

fading effect is smaller as compared to path loss and slow fading, and is superimposedupon the two to obtain the overall signal fading gain.

5.1 Frequency Selectivity

Multipath propagation characterizes the reception of a radio signal at the receiver frommore than one path. During propagation, a signal can be reflected, scattered ordiffracted by mountains, buildings and other objects. This causes the reception ofadditional copies of the signal at the receiver with different attenuations and delays.

Figure 5.1: Channel impulse response and frequency response

The impulse response is usually a chain of pulses. Consider a time invariant channel i.e.transmitter, scatterers and receiver are stationary. The signal arrives from propagatingpaths at the receiver. Path has attenuation and delay . The channel impulseresponse can be given as

(5.1)where is the Dirac impulse function and is the centre frequency of thesubcarrier. This arrival of additional copies produces the effect of filtering at the

receiver such that certain frequencies are attenuated more than the others. This is known

F

FourierTransform

Time Frequency

Impulse Response Frequency Response


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5 Fast Fading38

as frequency-selective fading. If the transmission band is wider than the coherencebandwidth, then the channel would have much more frequency selectivity compared tonarrowband transmission. Coherence bandwidth is the range of frequency bandwidth

where subcarriers fade in correlated manner and is discussed later.

5.2 Time Selectivity

In practice, channels are time variant with transmitter, scatterers and receiver in motion.In this case, the impulse response would be time dependent because and are timedependent.

(5.2)

Figure 5.2: Time varying channel impulse response

Time selectivity is encountered by channel gain because of two reasons. Firstly, thechannel changes with time and the amplitude of additional arriving paths fluctuates.Secondly, the transmitter and/or receiver are moving and causing Doppler shift.

In the first case, the sum of all paths at the receiver can be estimated by the centrallimits theorem as a complex Gaussian process with independent in-phase andquadrature Gaussian components. The magnitude of this process should be Rician

h ,t

t


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5.3 Terminology 39

distribution with non-zero mean if there is a LOS transmission, and a Rayleighdistribution with zero mean in case of non-LOS transmission.

Secondly, the Doppler shift also has an effect on fading. Doppler shift occurs due to themotion of transmitter and/or receiver. It shifts and broadens the signal in frequencydomain. The Doppler shift encountered by a ray at carrier frequency , arriving atthe receiver moving at velocity with arrival angle to the direction of motion isgiven as

(5.3)(similarly ). Here, is the maximum Doppler shift(similarly

). This spectral broadening corresponds to a U-shaped Doppler

power spectral density. For example, if the maximum Doppler shift

is 25 Hz, then

the power spectral density shall be as in Figure 5.3.In case of time invariant channel,the spectrum shall be impulse shaped corresponding to zero Doppler spread.

Figure 5.3: Doppler spectrum

In summary, frequency selectivity occurs due to multipath propagation of the signal and

time selectivity occurs due to the motion of transmitter, scatterers and receiver.Frequency selectivity is practically unavoidable; however time selectivity can benegligible if the transmitter and the receiver are stationary.

5.3 Terminology

In channel modelling, the understanding of the below mentioned terms is vital.

Total Delay Spread: The total delay spread , is the time difference between the firstand the last pulse of the signal copies received.


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5.3 Terminology 41

(5.7)

Root Mean Square Delay: Root mean square (RMS) delay is the standarddeviation of the time delay of pulses weighted by power.

(5.8)

If the power delay profile,

is given, the RMS delay can be given as

(5.9)So, the power delay profile can be given as a one-sided exponential distribution as in[30].

(5.10)In such a case, where power delay profile is exponentially distributed, it can be shownthat .Coherence Bandwidth:Coherence bandwidth of a signal is the width of the frequencyspectrum where fading is highly correlated. Auto correlation of the signal amplitudesfor the upper and lower frequency limit of coherence bandwidth should be 0.5 at least.

If coherence bandwidth is greater than the transmission bandwidth, it would beconsidered narrowband transmission and the fading would be frequency flat. In case,transmission bandwidth exceeds the coherence bandwidth, wideband transmission takes

place resulting in frequency selective fading.

Coherence bandwidth depends upon the total delay spread of the channel.Conventionally, coherence bandwidth and total delay are considered to be inversely

proportional to each other. According to [31], the following equation can be used toapproximately determine, the coherence bandwidth of a channel.

(5.11)Coherence Time: Coherence time of a signal is the time span where the fading ishighly correlated. For the first and the last instance of this time span, auto correlation of


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5 Fast Fading42

the signal amplitudes should be 0.5 at least. If two instances are having a timeseparation more than the coherence time, the fading of amplitudes at these two instancesshould be uncorrelated.

Coherence time depends upon Doppler spread of the channel. Conventionally,coherence time and Doppler spread are considered inversely proportional to each other.According to [31], the following relation holds to get (an approximation of) coherencetime of a channel.

(5.12)5.4 Fast Fading Models

Several models have been proposed for fast fading depiction. However, for system levelsimulation purposes, the widely used models are discussed here.

5.4.1 Clarkes Model

Clarke's model [31] is quite popular as a flat fading and time selective model. Clarkeassumed that the receiver is moving at speed , and the transmitter is stationary. Thescatterers are assumed to be stationary. The receiver receives equal power scatteredrays with arrival angles being distributed uniformly, in such a way thatray

encounters a Doppler shift of

where

is the

maximum Doppler shift which can be encountered at receiver speed of

, carrier

frequencyand speed of light . is assumed to be very large. If a path arrives at theangle with time delay of and gain (time invariant gain), then the impulseresponse can be given by

(5.13)As a frequency flat model, the delay spread of the signal is not taken into account. In theabsence of the delay spread, all the subcarriers encounter correlated fading. A general

assumption in Clarke's model which has been incorporated here is the uniform powerdistribution among all paths and the antennas being isotropic. Based on theseassumptions, if is the total amplitude of all paths (and power ), then theamplitude of ray is given as .5.4.2 Jakes Model

Jakes Model is a simplified simulation model for Clarkes Model and has been widelyused. Jakes model is deterministic model for modelling of Rayleigh fading. In Jakesmodel, time correlated fading waveforms are generated by adding up sinusoids [32].This is known as sum-of-sinusoid (SOS) method. Jakes model considers a moving

receiver which receives rays, each having equal signal strength and arriving at angles


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5.4 Fast Fading Models 43

, which are uniformly distributed in such a way that ray encounters aDoppler shift of where is the maximum Doppler shiftwhich can be encountered at receiver speed of

, carrier frequency

and speed of light

.The magnitude of Doppler shift has a quadrantal symmetry for all excluding 0 and. Therefore, it is possible to simulate the resulting waveform using complexoscillators, such that . The waveform can be given as a function oftime as

(5.14)

Figure 5.5: Jakes model with N = 10

where is a normalization constant, , and are the model parameters. Theparameters and are set to certain values so that zero cross correlation among realand imaginary parts of may be achieved. Therefore, by setting and , the desired statistical property is achieved. is set to zero when onlysingle waveform is to be generated for frequency flat channel. Equation (5.14) is afrequency flat, time selective and narrowband channel model. In order to generatemultiple uncorrelated waveforms for frequency selective multipath channel, Jakes

proposed that for

paths, the

value of

should be


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5 Fast Fading44

(5.15)where

to

and is the index for the respective waveform. The model looks like

(5.16)

5.4.3 Dent Model

Dent suggested some modifications to Jakes Model by setting and . The magnitude of the Doppler shift now has a quadrantal symmetry for all . Therefore, it is possible to simulate the resulting waveform using complexoscillators. The normalization constant was suggested to be . Setting results in the real and imaginary parts being uncorrelated. This new arrangementis free of parameter and gives us the model as

(5.17)The parameter can be randomized to get randomly generated waveforms. This modelis narrowband and time selective. In order to get multiple uncorrelated waveforms forfrequency selective channel, Dent proposed using orthogonal vectors called Walsh-Hadamard (WH) codewords. For this purpose, should be a power of two. The waveforms can be given as

(5.18)

where denotes the WH code sequence among sequences. The correlationbetween waveform pairs is not effected by random number seed for . Results showedthat the resulting waveforms are highly uncorrelated.


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Figure 5.6: Dent Model with N = 12

5.4.4 Jakes-like Method of Complex Gain Generation

This model assesses the gain of the channel by taking into account the Doppler spreadfor time selectivity and the delay spread for frequency selectivity. Change of phase ofthe received signal occurs due to Doppler spread and delay spread. The time selectivity,which is caused by Doppler spread, is modelled according to Clarke's model and the

frequency selectivity which occurs due to delay spread, is modelled as in [33]. Since thefrequency selectivity depends upon the carrier frequency, therefore, the channel gain ismodelled as a function of both time and carrier frequency. The end result of thesimulation is a 3-dimensional plot with it axes representing time, frequency and channelgain as inFigure 5.7.

In this model, scatterers are assumed to be around the receiver moving at velocity with arrival angle of the scattered ray being uniformly distributed. All the rays havethe same amplitude but the phase varies. The number of subcarriers is assumed to be .At subcarrier , for each ray , the phase change due to delay spread , and due toDoppler spread

is determined.

can be determined as

(5.19)where is the centre frequency of the subcarrier , is time delay of ray and isgenerated as an exponentially distributed random number with mean . can becalculated as

(5.20)


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5 Fast Fading46

The resulting phase for subcarrier is the sum of phase shift caused by all raysaccumulatively. Hence, the generated complex gain is a function of time acquired bysumming up the amplitude of the phase of all the rays at subcarrier

.

(5.21)

Figure 5.7: Channel gain versus time and frequency

This gain is a function of time because varies with time. At time , gain isdetermined for all subcarriers. The process is repeated for .... for all subcarriers. This results in a figure similar to Figure 5.7.The random numbers and are generated once for each subcarrier and each ray. The values can be maintainedfor a time span equal to coherence time or even less, after which, the values have to beregenerated using the respective distributions.

5.4.5 Other Improvements for Jakes Model

Jakes model provides a simple ways of simulating Rayleigh fading by using SOSmethod. However, statistical inconsistencies of Jakes model have led to several

proposals for improvement.

In 1998, the statistical properties of Jakes model were analysed in [34]. The two majordrawbacks of this model were indicated. Firstly, it was observed that correlation exists

between the inphase and quadrature components. Secondly, the inphase and quadraturecomponents are not Gaussian distributed in satisfactory manner. It was argued thatincreasing can compensate for the performance loss; particularly, if greater than10, reasonable results can be achieved. Based on these analyses, Jakes model wastermed as useful for Rayleigh fading channel models.


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In [35], the reformulation of the classical Jakes model has been proposed. Differentarrival ray angles

and

for Doppler shift components, and different phase shift

to

each oscillator have been introduced. This facilitates the generation of multipleuncorrelated fading waveforms. The autocorrelation and cross-correlationcharacteristics of the resulting waveform are claimed to be similar to theory.

In [36], an improved method for simulating sum-of-sinusoids statistical models isproposed for the Rayleigh fading. In this method, the Doppler frequency and the initialphase of the sinusoids are randomized to get nondeterministic simulators with desiredstatistical properties. The autocorrelations and cross-correlations properties of the newsimulators are shown to match the theory even if the number of sinusoids used is only asingle-digit integer.

In [37]and [38], an improved deterministic method for generating multiple independentRayleigh fading waveforms has been proposed, which overcomes these statisticalinconsistencies. Asymmetrical arrival angle arrangement has been used and incidentwave phases are chosen appropriately. This gives independent and almost identical in-

phase and quadrature. The independence between the multiple waveforms has also beenguaranteed. Also, efforts have been made to reduce the computational complexities.

In other research papers, the statistical properties of the above mentioned improvedJakes model have been analyzed and compared with the classical Jakes model, as in[39] and [40]. It has been shown that the model results in the generation of multipleRayleigh faders which are independent of each other. Results also revealed that thismethod nicely depicts the essential properties of the real world.

There are many more proposals for improving the Jakes model, but almost all of themhave certain correlation issues. However, this model is still very popular and in useworldwide because of its simplicity.

5.4.6 IDFT Methods

The purpose of the fast fading models is to generate Rayleigh fading process havingpower spectral density of zero beyond the maximum Doppler frequency. So far, thesimulation methods based on sum-of-sinusoids (SOS) approach are discussed.Algorithms based on the inverse discrete Fourier transform (IDFT) approach are alsovery popular. Researchers have found some considerable problems with SOSapproaches; for instance, their stochastic properties have certain irregularities. TheIDFT approaches are highly efficient; however, they have huge storage requirements.

In 1975, Smith published an algorithm [41] where independent Gaussian randomsamples are provided as input and correlated Rayleigh signals are generated as anoutput. The IDFT is used to generate the two independent vectors of correlatedGaussian samples. The vectors are combined in quadrature producing a correlatedvector of Rayleigh samples.


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5 Fast Fading48

Modifications and improvements to the Smith algorithm were proposed in [42]. Smithalgorithm required large number of IDFT operations and computer memory. The newmethod reduced the number of IDFT operations to half. The computer memory

requirements were reduced to about two-thirds of the original Smiths methodrequirement.


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CHAPTER 6

6. Simulation Result and Analysis

imulation models for mobile radio channels are widely used for the simulation ofthe fading channels. Simulation makes system testing and evaluation very easy.

Simulation approach is economical and more reproducible as compared to field trials[43]. Modern the computer networks are complex systems. Therefore, the task ofnetwork analysis has become quite tough. Due to the complexity and speed of networks,simulation has become a vital analysis tool. Nowadays, network simulation is not only

restricted to system analysis [44]. Its uses can be summarized as

System analysis Research and development Protocol understanding and verification Evaluation of future networks Substituting software networks Scenario analysis

To facilitate the simulations of LTE systems, channel models are vital; they play afundamental role in evaluation and testing of the system design before theimplementation of the system. This project was aimed to propose such a channel modelencompassing the effects of path loss, slow fading and fast fading. Before discussing theresults and analysis of the simulations using various channel models, a brief note isgiven to understand the difference between link level and system level simulations.

6.1 Link Level and System Level Simulations

The focus of link level simulations is determining the performance of a radio linkbetween the transmitter and the receiver. However, several mobiles can be involved in alink level simulation as in case of multiuser detection (demodulation of mutually

interfering signals) in Code Division Multiple Access (CDMA). Similarly, several basestations can be involved in a link level simulation, e.g. handover is to be modelled [45].Link level simulations deal with physical layer functionalities such as comparison ofchannel coding and decoding algorithms, modulation and demodulation algorithms, bit-error-rate (BER), frame-error-rate (FER) etc.

The performance evaluation of a single link cannot be used to interpret system levelperformance. System level simulations involve several base stations communicatingwith several mobile stations. System level simulations are used for evaluation of the airinterface capacity. These results generated in link level simulations are used as theinputs for system level simulations. System level simulations are the focus of this

project.

S


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6 Simulation Result and Analysis50

6.2 Path Loss Simulations

Various path loss models are discussed in this report. Among these models, the

simplified path loss model and the path loss model of ETSI for vehicular testenvironment for carrier frequency of 2GHz in(3.25) are of our interest. The simplified

path loss model is simulated for three types of environments; free space, shadowedurban cellular radio, and obstructed in building. The carrier frequency of 2 GHz is used.The vehicular test environment model has parameters similar to that of LTE system.

Figure 6.1: Path loss simulation results

6.3 Slow Fading Simulations

As discussed, shadowing is correlated for all the carrier frequencies and thus, it is notrequired to perform separate modelling for frequency domain shadowing. In timedomain, shadowing can be modelled over a distance, or it can be modelled over an area.Shadowing model over distance works perfectly if mobile station moves in a straightline; but if the motion is closed path, then the shadowing model over area should beutilised. In case the mobile station moves in a closed path and the shadowing modelover distance is applied, the correlation results would be very inaccurate. Anotherdrawback is the case when the paths of two mobile stations intersect each other, becausethe shadowing values at the point of intersection might differ. Therefore, the shadowingvalues obtained in distance model would give inappropriate values. On the other hand,


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6.4 Fast Fading Simulations 51

shadowing 2-D map has the disadvantage that it has to be generated quite regularly tomodel the changing shadowing situation in the cell. The shadowing matrix obtainedfrom area model is depicted inFigure 4.3.

6.4 Fast Fading Simulations

The fast fading models discussed here, such as Jakes model and its improvements aredifferent methods of simulating Clarkes model. Since Clarkes model is frequency flatdepending upon Doppler spread, frequency selectivity has to be modelled as well alongwith Clarkes model. Since frequency selectivity depends upon the delay spread of themultipath signal; therefore, the resulting magnitude and phase of channel expressed intime and frequency is the combined effect of Doppler spread and delay spread.

In simulations of fast fading, nine different scenarios are considered. These scenariosare based on how much the channel is time and frequency selective. In time selectivity,three types of scenarios are considered.

1. Zero Doppler spread (e.g. stationary mobile)2. Small Doppler spread (e.g. pedestrian mobile)3. Large Doppler spread (e.g. vehicular mobile)

Similarly, in frequency selectivity, three types of scenarios are considered.

1. Zero delay spread (e.g. free space)2. Small delay spread (e.g. typical urban)3. Large delay spread (e.g. bad urban)

This gives nine different combinations of scenarios to be examined in simulations. Thegraphs below are generated using Jakes like method of complex gain generation incombination with Clarkes model.


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Figure 6.2: Zero Doppler Spread and zero delay spread

Figure 6.2 depicts a perfect channel for wireless communication having no fast fading.This channel is free of delay spread and Doppler spread. Therefore, there is no time orfrequency selectivity. Attaining such a channel gain is possible only in free space withthe transmitter and receiver being stationary. Practically, such a channel may not exist.

Figure 6.3: Zero Doppler Spread and small delay spread

Figure 6.3 depict a fast fading channel gain where the transmitter and the receiver arestationary, so there is no Doppler spread and no time selectivity. Small delay spreadcauses low frequency selectivity.


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Figure 6.4: Zero Doppler spread and large delay spread

Figure 6.4 illustrates a channel gain where the transmitter and the receiver arestationary, so there is no Doppler spread and no time selectivity. Large delay spreadcauses high frequency selectivity.

Figure 6.5: Small Doppler spread and zero delay spread

Figure 6.5 depicts channel gain where the transmitter and/or the receiver move with lowspeed as in case of pedestrian user, so there is small Doppler spread and low timeselectivity. Zero delay spread means there is no frequency selectivity.


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Figure 6.6: Small Doppler spread and small delay spread

Figure 6.6 depicts channel gain where the transmitter and/or the receiver move with lowspeed, so there is small Doppler spread and low time selectivity. Small delay spreadcauses low frequency selectivity.

Figure 6.7: Small Doppler spread and large delay spread

Figure 6.7 depicts channel gain where the transmitter and/or the receiver move with lowspeed, so there is small Doppler spread and low time selectivity. Large delay spreadcauses high frequency selectivity.


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Figure 6.8: Large Doppler spread and zero delay spread

Figure 6.8 depicts channel gain where the transmitter and/or the receiver move withhigh speed as in case of user moving in a vehicle, so there is large Doppler spread andhigh time selectivity. Zero delay spread means there is no frequency selectivity.

Figure 6.9: Large Doppler spread and small delay spread

Figure 6.9 depicts channel gain where the transmitter and/or the receiver move withhigh speed, so there is large Doppler spread and high time selectivity. Small delayspread causes low frequency selectivity.


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6 Simulation Re

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