On Models for Interference Calculations between Radio Communication Systems

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On Models for Interference Calculations

between Radio Communication Systems

FREDRIK VIHLBORG

Master’s Degree Project

Stockholm, Sweden December 2011

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Abstract

When installing a new radio system, it is of great importance to know that it will not interfere with the already existing systems, and that they can coexist side by side. The problems that will follow if interference occurs, can be of huge magnitude, e.g. radars not working, trains stopping etc. The idea of this thesis is to find an analysing method that can take several parameters into account when evaluating the scenario and its possible conflicts, and since many of the radio systems today are digital, give the bit error rate as a result.

The problem is to find a way to model both the victim signal and the interfering signal(s), that also takes as many variables as possible into account when doing so. The model should be as general as possible, making it applicable on many different scenarios. Since many of the older radio systems are narrowband systems (e.g. GSM), and many of the newly deployed radio systems are wideband systems (e.g. UMTS, LTE), it is also necessary be able to represent such systems in the same environment. Also, is it possible to replace the modulated interferer with some random process?

When a good model to describe the signal and interference was found, simulations were made in Matlab to test it. Variables such as modulation, power, frequencies, losses and filters were all included in the implementation.

The results of the simulations show bit error rates, i.e. how much the interfering system affects the victim system, as a function of the geographical distance between them, and also their difference in frequency. In the case with a GSM-R system with a cell radius of 8 km being interfered by a LTE system, the minimum distance from the LTE transmitter to the GSM-R receiver to keep a BER ≤ 10−3 _{was found to be 1.5 km. If a frequency guard band were}

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Sammanfattning

Vid installation av ett nytt radiosystem, är det av stor vikt att veta att det inte kommer att störa de redan befintliga systemen, och att de kan samexistera sida vid sida. Problem som kan uppst˚a vid s˚adana störningar kan vara av stor omfattning, t ex att radar inte fungerar, t˚ag stannar etc. Idén bakom detta examensarbete är att hitta en analysmetod som kan ta flera parametrar i beaktande när ett möjligt störscenario och dess eventuella konflikter ska simuleras. Eftersom m˚anga radiosystem idag är digitala, presenteras resultaten genom bitfelskurvor.

Problemet är att hitta en metod att modellera b˚ade den störda signalen samt den eller de signaler som stör, samtidigt som s˚a m˚anga parametrar som möjligt tas i beaktning. Modellen ska vara s˚a generell som möjligt, vilket gör den applicerbar i m˚anga olika scenarion. Eftersom m˚anga äldre system är smalbandiga (t ex GSM), och m˚anga nya system är bredbandiga (t ex UMTS, LTE), m˚aste modellen ocks˚a klara av att hantera b˚ade smal- och bredbandiga system. Det ska ocks˚a utvärderas om det är möjligt att istället använda en statistisk fördelning som ersättare för störsignalen.

Modellen implementerades i Matlab. Variabler s˚asom modula-tion, utsänd effekt, frekvenser, förluster och filter är inkluderade i implementeringen.

Resultaten visas i bitfelskurvor, vilka p˚avisar hur mycket sys-temet blir p˚averkat av störsignalen. B˚ade olika geografiska avst˚and samt avst˚and i frekvens har simulerats. I fallet med ett GSM-system med en cellradie p˚a 8 km som störs av ett LTE-system, visar resultaten att ett säkerhetsavst˚and p˚a omkring 1.5 km krävs. Detta för att h˚alla bitfelshalten lägre än 10−3_{. N¨}_{ar ett}

frekvenssky-ddsband inf¨ordes minskade det avst˚andet till 800 m. Att ers¨atta LTE-systemet med en sekvens genererad fr˚an en Middleton Class A-process, kunde inte liknande resultat uppn˚as.

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List of Tables

3.1 Excerpt from the Specifications for the RF-5800H-MP . . . 14

3.2 Parameters used in the RAx 6 taps model . . . 27

3.3 Parameters used in the EVA model . . . 28

4.1 List of variables that can be set in the implementation . . . 35

5.1 Parameters used when simulating the first scenario . . . 37

5.2 Parameters used when simulating the second scenario . . . 43

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List of Figures

1.1 A generic model of two interfering radio systems . . . 5

2.1 A generic model of a radio system . . . 7

2.2 Simulation transmitter model . . . 8

2.3 Simulation receiver model . . . 9

2.4 900 MHz frequency band allocation of interest. . . 10

2.5 A sketch of the GSM-R vs LTE scenario . . . 10

3.1 Model of the radio channel . . . 12

3.2 Time sequences of a Middleton Class A noise model . . . 14

3.3 Path loss for different outdoor models . . . 16

3.4 Path loss for indoor models . . . 18

3.5 Power spectrum estimate using Welch’s method . . . 21

3.6 QPSK signal constellation . . . 22

3.7 Real part of a QPSK signal . . . 22

3.8 PSD of a QPSK signal . . . 23

3.9 Real part of a GMSK signal . . . 24

3.10 PSD of a GMSK signal. . . 25

3.11 Real part of an OFDM signal . . . 25

3.12 PSD of an OFDM signal . . . 26

4.1 Flow Chart over the General Implementation . . . 32

5.1 Scenario 1 - Power Spectrum estimation . . . 38

5.2 Scenario 1 - Filtered Power Spectrum estimation . . . 39

5.3 Scenario 1 - BER vs CIR and ∆fk . . . 39

5.6 Scenario 2 - Received power . . . 42

5.7 Scenario 2 - BER surface, filtered . . . 44

5.8 Scenario 2 - BER curves, filtered . . . 44

5.9 Scenario 2 - Power Spectrum estimation, half 1st channel blocked 45 5.10 Scenario 2 - Power Spectrum estimation, half 1st channel blocked 46 5.11 Scenario 2 - BER surface, filtered, half 1st channel blocked . . . 47

5.12 Scenario 2 - BER curves, filtered, half 1st channel blocked . . . . 47

5.13 Scenario 2 - BER, Middleton interference, A = 10, Γ = 0.0001 . . 48

5.14 Scenario 2 - BER, Middleton interference, A = 0.01, Γ = 0.0001 . 49

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List of Abbreviations

3GPP 3rd Generation Partnership Project AWGN Additive White Gaussian Noise BER Bit Error Rate

BPSK Binary Phase Shift Keying CDF Cumulative distribution function CIR Carrier-to-Interference Ratio

ECC Electronic Communications Committee EMC Electromagnetic Compatibility

E-UTRA Evolved Universal Terrestrial Radio Access GMSK Gaussian Minimum Shift Keying

GSM Global System for Mobile Communications GSM-R GSM-Railway

ICF Impulsiveness Correction Factor LTE Long Term Evolution

GMSK Minimum Shift Keying NBI Narrowband Interference

OFDM Orthogonal Frequency-Division Multiplexing PAM Pulse Amplitude Modulation

PBI Partial Band Interference pdf Probability density function PSD Power Spectral Density

QPSK Quadrature Phase Shift Keying SINAD Signal-to-Noise-and-Distortion Ratio SIR Signal-to-Interference Ratio

SNR Signal-to-Noise Ratio

SNIR Signal-to-Noise-and-Interference Ratio SOI Signal of Interest

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Chapter 1

Introduction

1.1 General Background

Guglielmo Marconi is often referred to as the father of radio communications. In December 1901, he managed to establish a wireless communication between St. Johns, Newfoundland, Canada and Poldhu, Cornwall, England. This gave him, in 1909, together with Karl Ferdinand Braun the Nobel Prize in Physics, as a ”recognition of their contributions to the development of wireless telegra-phy”. On the other hand, in 1893 during a presentation before Franklin Insti-tute, Philadelphia, and also later before the National Electric Light Association, Nikola Tesla had already demonstrated wireless communications [1].

Disputes on whom of them was the real inventor of radio communication did emerge. After some patent conflicts, Tesla came out as the winner (U.S. Patent 645576). This could be considered the first time a telecommunication conflict was dealt with. Conflicts of that kind will, however, not be covered in this thesis (since it had had nothing to do with actual radio communications, but was merely a conflict of academic interest and lust for fame).

When this futuristic way of distant communication did catch on, and the use of radio communication grew, so did the need of regulations. Lists of radio station frequencies in Europe have existed since at least the 1920’s.

With a steady increasing number of active users ever since, the radio spec-trum has gotten more and more crowded. That makes telecommunication con-flicts of today an always present dilemma. The issues arise when unwanted radio signals reach the antenna at the receiving node. It becomes a problem if their frequency components and enough power are in the very same frequency band as the wanted signal. Normally this is prevented by careful frequency planning, but as time goes on, and new systems are being invented and installed, the need for more space in the frequency spectrum grows, and old frequency bands that acted as guard bands might now be used for communication and traffic. Therefore the ability to make an adequate analysis of the possible conflicts and interferences is as significant as ever.

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2 CHAPTER 1. INTRODUCTION

1.2 Motivation

It is of great importance to be able to foresee any problems and conflicts that may occur when using a radio system. Depending on what kind of radio system it is, various assessments need to be done, and different interferences may or may not be acceptable. An example of a system that cannot under any circumstances be disturbed and thus not functioning as intended, is the defence radar on a military ship. This was however exactly what happened during the Falklands War, when the British ship HMS Sheffield got attacked by Argentine air planes. Later investigations have shown that the reason the attacking planes were not detected in time, was because the satellite communication system on the ship blocked the radar that was supposed to detect enemy planes. This probably would have been avoided if a telecommunication conflict analysis had been made before the ship went into the water.

Another, more recent case where it is significant to have a working radio sys-tem is in the railway. Today trains and railway regulation control centres uses GSM-R for communication. In Europe GSM-R uses the frequency bands 876-880 MHz (uplink) and 921-925 MHz (downlink). With the recent deployment of Long Term Evolution(LTE) in the frequency band just above 925 MHz, GSM-R could experience signal blocking with the consequences of trains stopping due to them having no contact with the control stations. This was tested by the German rail road (Deutsche Bundesbahn), using regular base stations for GSM mobile phones in the frequency band above 925 MHz [2]. Around 200 experi-mental tours were made, and several stoppages occurred. The communication was lost, and the trains stopped without permission to go on.

Although thorough frequency planning has been done and the specified fre-quency masks are being followed, some conflicts are inevitable and will most likely occur, both due to worst case situations that might happen, e.g. being very far away from the transmitting base station of the system, and close to the interfering base station, but also due to imperfections in the electronic com-ponents that are used in the systems. These comcom-ponents differ from the ideal models that are often used in calculations and constructions. The electronic components will generate intermodulation products, that might land in other frequency bands and interfere with the ongoing communication in these bands. Some systems are better at handling this than others, and depending on which one is used, different results will be obtained.

As the two examples above show, it is very important to know about these possible conflicts, and what can be done to prevent them. This thesis will propose a method to estimate if telecommunication conflicts will occur. The method and its models will be implemented in Matlab, making it possible for a user to specify known parameters of the involved systems and as an output get an analysis of the scenario, showing possible error rates, which might lead to system failure.

1.3 Previous Work

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1.3. PREVIOUS WORK 3

become of topmost importance. If a new system is to be installed and used in the same area where there are already other systems operating, it is a vital part of the process to get to know if the new system will interfere with, or be interfered by, the existing ones.

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AF has been working with the studies of telecommunication conflicts and interference protection functionality for many decades. Up until the 1980’s, the task was to deal with a few, narrowband, analogue radio systems with a limited geographic spread. The wireless networks of today are instead built up of wideband, digital radio systems. To complicate the matter even further, the amount of mobile radio systems have increased rapidly during the last years.

Since the work of ˚AF, which is mainly implemented in the software TEXAS [5], was initially made for analogue narrowband systems, and not done with wideband signals in mind, a straight application of yesterdays models on the radio systems of today might give a skew result. One of the potentially major drawbacks with TEXAS, is the assumption that the whole frequency channel of interest is being exposed to interference as soon as there is just a small overlap from the interfering signal (e.g. 1% overlap being treated as 100% overlap, in the frequency domain). Instead it should be treated as a partial-band interference (PBI) which has been discussed in [6], which also in [7] shows different results depending on the frequency offset, and on how much of the interfered frequency band that is actually being affected.

Other previous work in this field includes several methods to approach the problem, e.g. to model the interference from a narrowband signal, so called narrowband interference (NBI), as a sinusoid [8], or as a narrowband auto re-gression [9, 10]. However, these methods do not take into account that it is an actual signals that are interfering, with its corresponding waveform and fre-quency spectrum, making them insufficient for this study.

In the 70’s, David Middleton proposed to describe the statistics of the noise and interference as Class A or Class B Noise Models [11,12]. The noise that is being modelled by a Class A model has a bandwidth which is comparable to, or less than, the bandwidth of the receiving system. Class B noise is the noise with a bandwidth that is larger than the bandwidth of the receiving system. Examples of the two models are; radiated narrowband signals and different kinds of unintentionally man-made noise for Class A, and atmospheric noise and also various kinds of man-made noise for Class B.

These models are often used to model different kinds of interferers, and later it has been looked at the possibility to introduce an Impulsiveness Correction Factor (ICF) [13, 14], to be able to model the interference as pure Additive White Gaussian Noise (AWGN), to give a better estimate of the Bit Error Rate (BER).

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1.4 Problem Statement

The problem investigated in this Master’s thesis project is the telecommunica-tion conflict that may arise between two or more radio systems. Here, telecom-munication conflict refers to accidental interference, i.e. not intentional interfer-ence, so called jamming, of one user by another. One of the issues is often that at least one of the conflicting radio systems was designed a long time ago (i.e. a simpler technique compared to the modern systems, possibly more sensitive to disturbance), without knowledge of what properties the newer radio systems have, thus it might not co-operate as well as two newer systems do. One thing that could cause problems for the older system, is if the newer system will op-erate in a frequency band that was acting as a guard band for the older system (i.e. a frequency band that was unused). This is a potential problem when installing new radio systems and equipment.

The radio systems looked at in this report that are under influence of conflict, may or may not be co-located. Though, the conflicts are probably more prone to occur when the radio equipment are co-located, or at least close to each other, as the power of the interfering signals will still be at a high enough level to cause problems when they reach the victim receiver.

A sketch of two interfering systems is shown in Figure 1.1. The two radio systems, System A and System B, communicates within themselves, and unin-tentionally the signal from the transmitter in System B reaches and interferes with the receiver in System A.

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1.5. SCOPE OF WORK 5 Transmitter System A System A Receiver Receiver Transmitter System B System B System A communication System B communication Unwanted interference

Figure 1.1: A generic model of a radio system (System A) being unintention-ally interfered by an adjacent radio system (System B). The arrow representing the interference can go in any direction between any of the boxes, depending on the frequencies in use.

1.5 Scope of Work

This thesis is an analysis of the interference that may occur between two or more radio systems, not the interference within a single radio system. The work includes identifying the concept of radio systems as well as identify and classify modern radio technologies. The focus will be on combining existing tools and methods with newer models to enable more accurate assessments of the conflict scenario described in Section1.4.

The following tasks will be performed during this thesis work:

• Gain knowledge of how different modulation techniques work, and when and where they are used;

• Investigate how the new wideband radio systems operate side by side with old, narrowband systems;

• Propose methods and models to analyse telecommunication conflicts be-tween radio systems;

• Simulate some interesting radio communication scenarios, and possible conflicts.

The outcome of this thesis will be used by ˚AF to:

• Implement the models into ˚AF’s existing software for telecommunication conflict analysis;

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The influence of electromagnetic compatibility (EMC) will not be studied. Nei-ther will the near-field case be studied, i.e. only distances greater than 10λ will be considered.

1.6 Outline

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Chapter 2

System Model

In this chapter a brief overview on how the radio system that is being looked at in this thesis is presented. An introduction to the scenarios that will be investigated is also given.

2.1 System Architecture

A generic radio system can be modelled by a transmitter (Tx), a receiver (Rx) and a channel over which the radio wave propagates, as in Figure 2.1. Every radio receiver will be affected by noise (e.g. thermal noise), and in the presence of other transmitting units, also interference occurs at the receiver. This inter-ference is dependent on many different things; distance between the receiving unit and the interferer, on which frequency the signal is being sent, the power of which the interferer transmits, what kind of modulation techniques are used by the two systems, etc. All of these parameters are essential to know if a good analysis of the conflict is to be made.

Transmitter Receiver

Antenna Antenna

Wave propagation

Noise

Interference

Figure 2.1: A generic model of a radio system.

The received signal r(t) at the receiver can in general be described by a sum of the useful signal s(t), the interfering signal i(t) and some noise n(t). The definition of these three components depends on how the systems are designed

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8 CHAPTER 2. SYSTEM MODEL

and what assumptions that are made about the radio channel over which the signals propagate. This is further discussed in Chapter3.

2.2 General System Model

This section briefly describes a radio system, and how it is modelled in this thesis. A more detailed description is given in Chapter4.

2.2.1 The Transmitter

In this thesis each transmitting unit is modelled as in Figure2.2.

Modulator

Data source Pulse shaping Upconversion

Figure 2.2: Each transmitter used in the simulations in this thesis is roughly composed according to this layout. The individual transmitting power and antenna gain is also taken into account.

The different boxes perform the following:

• The data source generates a random sequence of 0’s and 1’s.

• Next the modulator modulates the bit sequence by some modulation tech-nique, e.g. QPSK etc.

• The modulated signal is then being upsampled and pulse shaped by filter-ing through a filter of choice.

• The last step in the transmitter is to upconvert (basically a shift in the frequency domain) the signal to its carrier frequency, and then transmit the signal over the channel. Note that this step is actually only performed on the interfering signals, because at the transmitter of the victim the frequency upconversion step is skipped, which means that the signal is kept at the baseband.

2.2.2 The Radio Channel

In the radio channel, over which the signal propagates from the transmitter to the receiver, interference will be added to the signal. The interference is coming from a neighbouring radio system, from which the victim system receives an unwanted signal. Assume that the wanted signal is s(t), and the interfering signal is ik(t). The signal that ends up at the receiver is then the sum of these

two, plus some noise at the receiver, i.e. r(t) = s(t) + ik(t) + n(t).

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2.3. SCENARIOS 9

2.2.3 The Receiver

Following the same procedure as for the transmitter above, the receiver is mod-elled as in Figure2.3. Since the signal of interest (SOI) is kept at the baseband throughout the simulations, there will not be any frequency downconversion in the receiver. Thermal noise from the receiver gets added to the received signal, which now contains both the SOI and the interfering signal.

Filter Demodulator

Figure 2.3: The receiver used in the simulations in this thesis is roughly composed like this. The antenna gain, if any, is also taken into account.

In the receiver the following steps are performed:

• The received baseband signal is filtered with a given filter.

• The signal is then demodulated, and in this thesis also compared with the original bit sequence to estimate the amount of errors.

All the above steps in both the transmitter and the receiver, as well as the channel, are further described in Chapters3 and4.

2.3 Scenarios

In this section the scenarios that will be simulated in this thesis are presented.

2.3.1 A General Scenario

The first scenario is a general scenario, made up to test and confirm the model, and to see that the implementation of it works. Also, it gives the possibility to verify that it produces reasonable results when simulating a known system. It consists of the SOI being transmitted from A to B, one interfering system, and noise. Both the SOI and the interferer will be modulated using QPSK, having a bit rate of 200 kbps, a symbol rate of 100 kbaud, thus making the bandwidth approximately 100 kHz.

The SNR will be kept at 10 dB throughout the simulation, and the CIR will vary from 0–15 dB in steps of 1 dB and the distance in carrier frequency between the two systems will vary from 0–150 kHz in steps of 10 kHz, i.e. from a complete overlap to zero significant overlap.

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10 CHAPTER 2. SYSTEM MODEL

2.3.2 GSM-R vs LTE

In scenario two, the GSM-R case mentioned in Section1.2will be looked at. A train using a GSM-R mobile station will travel within its GSM-R cell, crossing a LTE base station cell, which is also operating at the 900 MHz band (see Figure 2.4). It will be investigated if the GSM-R system is affected by any interference. f 876 880 915 921 925 960 LTE UL GSM-R DL LTE DL GSM-R UL [MHz]

Figure 2.4: 900 MHz frequency band allocation of interest.

GSM-R

LTE

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Chapter 3

Methods and Models

In this chapter the theory behind models that are used in this thesis are pre-sented. The theory that is presented here are well known from the literature, and can be found in books on communication theory, wireless communication, and digital signal processing such as [16,17,18].

The layout of this chapter is as follows. First of all, a way to describe the received signal is presented. This is based on the concept given in the previously mentioned article [15], which taking into account the signal power, the waveform, the propagation etc. The received signal includes the useful signal, interference and noise.

Further on in this chapter, models to describe the propagation of the signal is presented, alongside with how a signal can be digitally modulated and how to estimate the frequency spectrum of a signal.

Finally some ways to measure the performance of a system is presented.

3.1 The Received Signal

Considering the model in Figure3.1, which basically describes the radio channel from Section2.1, the received signal r(t) can be written in a complex baseband representation as r(t) = s(t) + K X k=1 ik(t) + n(t) (3.1)

where s(t) is the transmitted useful signal (including channel effects, see Eq. (3.2)), which is assumed to be band limited, n(t) is the AWGN with zero mean and a two-sided power spectral density (PSD) N0

2 . In this model, ik(t) represents the

kth interference signal. s(t) is given by

s(t) = Ssm(t)ejφ0 (3.2)

where sm(t) is the modulated signal, φ0is the phase of the desired signal, which

from here on is assumed to be 0, thus keeping the signal at the baseband. This model is limited to describe narrowband communication (or frequency flat channels). If the useful signal is wideband, the channel will be frequency selective, and can be modelled by a convolution with a multi-tap filter, or e The

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12 CHAPTER 3. METHODS AND MODELS

term S in Eq. (3.2) represents the power of the signal s(t) at the receiver, and can be described by a product of different deterministic quantities and random variables, i.e.

S =Y

l

Sl (3.3)

where Sl can be, for example, the used transmit power, the path loss, fading

etc. Both the path loss and the fading are described later on in this chapter.

s_(t) n_(t) K P k=1 ik(t) r_(t) Tx Rx

Figure 3.1: A model of the radio channel, with additive noise and interference.

3.2 The Interference

When looking at the interference of a signal, both the interference power and the frequency spectrum are of interest. Factors that influence the interference power at the receiver are described in Section 3.4. The interpretation of interference in the frequency domain is described in Section3.5.

3.2.1 General Interference Model

The interference component ik(t) in Eq. (3.1) can be described as

ik(t) = Ikηk(t)ej2π∆fkt+φk (3.4)

where ∆fkis the carrier frequency of the interfering signal (relative to the carrier

frequency of the desired signal), φk is the phase and ηk(t) represents a zero

mean complex random process, modulated with a known technique, with a corresponding Power Spectrum Density (PSD). For more details of the PSD, see Section 3.5.

Ikis the received power of the kth interferer. Ikcan, similar to S in Eq. (3.1),

be modelled as a multiplication of deterministic quantities and random vari-ables representing different properties, i.e. the transmitter power, antenna gain, channel attenuation, path loss, fading and other factors. This is mathematically described by

Ik =

Y

l

Ik,l (3.5)

where Ik,l is a deterministic or random variable that represents the above

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3.3. SIGNAL-TO-NOISE RATIO 13

3.2.2 Statistical Interference Model - Middleton Class A

As mentioned in Section 1.3, the Middleton Class A is a statistical model to describe the interference power in time, of a process with a bandwidth smaller than, or equal to, the system of interest. In this model the received interference is assumed to be a process consisting of two components,

X(t) = XP(t) + XG(t) (3.6)

where XP(t) and XG(t) are independent processes. They represent the

non-Gaussian (impulsive, Poisson distributed) and non-Gaussian components, respec-tively. The probability density function (pdf) of the model is given by [11]

fx(x) = e−A ∞ X m=0 Am m!p2πσ2 m e− x2 2σ2m with σ2 m= m A + Γ 1 + Γ (3.7) where A = vtTs is the Impulsive index, vtthe average impulse rate and Ts the

mean duration of a typical interfering signal. The impulsive index (or overlap index) is a measurement of the amount of temporal overlap among the wave-forms of the interfering signals. A large value of A (about 10 or greater) means a large overlap, which makes the model approach a Gaussian interference (due to the central limit theorem), while a small A describes very impulsive inter-ference. Γ is called the Gaussian factor, and it is the ratio of the power in the Gaussian portion of the interference to the power of the non-Gaussian portion, i.e. Γ = X 2 G X2 P . (3.8)

Examples of random sequences with different values of A is shown in Figure3.2. In this thesis it will be investigated if the interference ik(t) described by Eq. (3.4)

and the effect it has on the interfered system can be approximated by a Middle-ton Class A process. If that is possible, it might give an easier implementation and simulation of the scenario.

3.3 Signal-to-Noise Ratio

Before proceeding any further, it is necessary to define a way to measure the quality of a communication link, the so called signal-to-noise ratio (SNR) of the link. The SNR is in general defined as

SNR = S N =

Psignal

Pnoise

(3.9)

which in a logarithmic decibel scale becomes

SNRdB= 10 log10

Psignal

Pnoise

= Psignal,dB− Pnoise,dB (3.10)

where Psignal = S is the received signal power, and Pnoise = N is the power of

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14 CHAPTER 3. METHODS AND MODELS Time [s] A m p li tu d e 0 20 40 60 80 100 120 140 160 180 200 -20 -15 -10 -5 0 5 10 15 20 (a) Time [s] A m p li tu d e 0 20 40 60 80 100 120 140 160 180 200 -20 -15 -10 -5 0 5 10 15 20 (b)

Figure 3.2: Time sequences of a Middleton Class A noise model, with different parameter values. The sequence in (a) was generated with the parameters set to A = 0.01 and Γ = 0.0001, the sequence in (b) with A = 10 and Γ = 0.0001. As expected, with a lower value of A, the sequence is more impulsive, and with the larger A, the sequence behaves as a Gaussian process.

In the presence of interfering radio systems with interfering power I, the term Signal-to-Noise-and-Interference Ratio(SNIR) if often used. SNIR is defined as

SNIR = 10 log _S

N + I

= SdB− NdB− IdB. (3.11)

Another way to measure the quality of a signal is the Signal-to-Noise and Dis-tortion Ratio (SINAD). It is defined as

SINAD = 10 log Psignal+ Pnoise+ Pdistortion Pnoise+ Pdistortion

(3.12)

where P is the average power. SINAD is often given in specifications and data sheets, when stating the sensitivity of the radio receiver. An example of how this can look in a data sheet is given in Table3.1, quoted from the specifications of the RF-5800H-MP tactical radio system by Harris [20]. The lower the input voltage needed to achieve the given level of SINAD, the better the receiver performance.

Table 3.1: Excerpt from the Specifications for the RF-5800H-MP

Receiver

Sensitivity: SSB: -113 dBm (0.5 µV) for 10 dB SINAD

3.4 Propagation, Path Loss and Fading

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3.4. PROPAGATION, PATH LOSS AND FADING 15

transmitted power, the antenna gain of both the transmitter and the receiver, the loss due to propagation, the bandwidth and the temperature of the receiver. Most of the above mentioned factors are straightforward insertion of num-bers, but the calculation of the loss due to propagation is often more compli-cated. To be able to calculate this loss, a model to describe the propagation is needed. This model is normally denoted Lp, and describes the path loss of the

link. There are several path loss models in the literature, some more compli-cated than others. The ones presented below are widely used, and has shown to be a good fit to reality. A comparison between the models can be seen in Figure3.3and Figure3.4. Sometimes the term path gain (denoted Gp) is used,

with the relationship Gp= −Lp.

3.4.1 Free Space

This is the simplest way to model the path loss. All obstacles that might affect the propagation are neglected. The path loss is given by

LFS=

(4πr)2

λ2 (3.13)

and in dB

LFS,dB= 32.45 + 20 log (r) + 20 log (f ) (3.14)

where r is the distance in kilometers, f the frequency in MHz.

3.4.2 Okumura-Hata

The Okumura-Hata Model is a widely used model to predict the path loss in both open land and in built up areas. It is an empirical model based on data collected in Tokyo, Japan. The model is valid for frequencies between 150– 1500 MHz, base station antenna heights, hb, between 30–200 m, mobile antenna

heights, hm, between 1–10 m and distances between 1–20 km. The general

expression is given by [17]

LOH= 69.55 + 26.16 log (f ) − 13.82 log (hb) + A log (r) − a(hm) + B (3.15)

where

A = 44.9 − 6.55 log (hb) .

The parameters a(hm) and B are both area dependent. For open areas

(some-times referred to as rural areas) they are given by

a(hm) = (1.1 log (f ) − 0.7) hm− (1.56 log (f) − 0.8) (3.16)

B = −4.78 (log (f))2+ 18.33 log (f ) − 40.94 (3.17) where f is the carrier frequency given in MHz, and r is the distance between the transmitter and the receiver, given in km. In a suburban area, a(hm) is as

in Eq. (3.16), and B is given by

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For medium cities, B = 0 and a(hm) as before. In a large city B = 0 and a(hm)

becomes frequency dependent

a(hm) = ( 8.29 (log (1.54hm))2− 1.1 f ≤ 400 MHz 3.2 (log (11.75hm))2− 4.97 f ≥ 400 MHz. (3.19) Distance [km] P a th lo ss [d B ] 0 2 4 6 8 10 12 14 16 18 20 90 100 110 120 130 140 150 160 170 180 190 Free space O-H, medium city O-H, open area C231-H, medium city

Figure 3.3: Path loss for different models, at 1500 MHz frequency. O-H and C231-H refers to the Okumura-Hata model and COST 231-Hata model, respectively. As can be seen, the free space model gives a more optimistic result, i.e. less attenuation, than the empirical models.

3.4.3 COST 231-Hata

The Okumura-Hata Model has been extended by the European Co-operative for Science and Technical research (COST) to extend the frequency range to 1.5–2 GHz (the other parameter restrictions are the same as for the Okumura-Hata model). This model is given by [17]

L_C231−H= 46.3 + 33.9 log (f ) − 13.82 log (hb) + A log (r) − a(hm) + C (3.20)

where a(hm) is taken from the Okumura-Hata Model, and

C = (

0 dB medium sized cities and suburbs,

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3.4.4 Keenan-Motley

The Keenan-Motley model describes indoor propagation. It takes into account the number of walls and floors that the wave propagates through. The model is given by [21] LKM= L1+ 20 log (r) + kfaf+ kwaw (3.22) where L1= 20log10 4πf c

is a reference value given by the loss at 1 m, r is the distance between the transmitter and the receiver (in meters), kf and kw are

the number of floors and walls that intersects the propagation, af and aw are

the attenuation factors per floor and per wall, respectively. Rough estimates of af and aw are [21];

• 1.5 dB for plaster board walls in office buildings etc.,

• 6 dB for reinforced concrete walls (<10 cm), e.g. in stairwells and car parks,

• 17 dB for thicker concrete walls (>10 cm), • 23 dB for floors.

The above estimates are valid in the frequency ranges 1–2 GHz. For higher frequencies, the attenuation will increase, and equivalent for lower frequencies, the attenuation will decrease.

If the number of walls and floors are unknown, or when just considering indoor propagation in general, an approximation of Eq. (3.22) can be made:

LKM= L1+ 20 log (r) + max{0, α (r − rbp)} (3.23)

where α is the mean attenuation, rbpis the breakpoint, i.e. the distance to the

first wall, up to which only the free space path loss is considered. The modified version is the one that will be used in this thesis. See Figure 3.4 on the next page for a comparison between the Keenan-Motley model and the free space model.

3.4.5 Fading Models

A wireless channel has a variety of properties. The characteristics of the channel determine the attenuation of the signals. In this thesis the total power loss due to propagation is modelled by three parts

L = Lp+ Ls+ Lm [dB] (3.24)

where the path loss Lp is one of the described models from the previous

subsec-tions. Lsand Lmare the losses caused by shadow fading and multipath fading,

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18 CHAPTER 3. METHODS AND MODELS Distance [m] P a th lo ss [d B ] 0 5 10 15 20 25 30 35 40 45 50 30 40 50 60 70 80 90 Free space Keenan-Motley K-M, modified

Figure 3.4: Path loss for indoor models, at 1500 MHz frequency. K-M refers to the Keenan-Motley model. Simulating inside an office building, penetrating 4 plaster board walls with 10 m distance between them, making α = 0.15 and rbp= 10.

Multipath Fading

The radio waves that reach the receiver have both travelled different paths and been scattered. The received signal is thus a sum of many signal components with different phases due to the reflections, which can lead to interference of the signal components. This is called multipath fading.

Under the above assumption of a scattering channel and a limited delay spread (the time from the first significant signal component to the last), and if there is no dominant component, this process will have a zero mean and a uniform distributed phase, and the pdf of the amplitude a(t)

pA(a) =

a σ2e

−_2σ2a2 _, _{a ≥ 0} _(3.25)

which is the Rayleigh distribution.

If one of the received signal components is stronger than the other, typically when there is a line-of-sight (LOS) path, the amplitude will instead be Rician distributed, with the corresponding amplitude pdf

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where I0(·) is a zero-order modified Bessel function of the first kind. When

a0= 0, i.e. no line-of-sight component, they Rician pdf becomes the Rayleigh

pdf. Two implementations of this multipath fading is presented later on, in Section3.7.

Shadow Fading

A receiver in almost any environment will be under the effect of shadowing by different objects, such as buildings or hills, which might partially block the signal from the transmitter. This is called shadow fading. If the receiver is a mobile unit, either walking or being inside a vehicle, it will take some time to get out of the shadowed area, the fluctuations of the fading is slowly varying (shadow fading is sometimes referred to as slow fading). These average signal level variations are often modelled as a log-normal distribution [17]

Ls∼ log N (µ, σ)

where the mean µ is often set to 0, and the standard deviation σ is typically in the range 4–10 dB. In this thesis, if in the simulated scenario the victim receiver can be affected by shadow fading, this variable will be implemented as in Eq. (3.5).

In Section3.7, two channel models that both implement the fadings above are briefly described.

3.4.6 Other Factors Affecting the Performance

Other factors that affects the amount of received power than the ones mentioned above, are presented and explained in this section.

Antenna Gain

The gain of an antenna describes how much the power is increased before sending it out in the air. Normally the gain is given in dBi (dB isotropic), which is relative to the hypothetical isotropic antenna, which uniformly distributes its energy in all directions.

The antenna gain is reciprocal, which means that the gain has the same effect regardless of the antenna is sending or receiving. Though it should be stated, having a larger gain on the antenna will not increase the receiving performance in that sense that both the interference as well as the signal of interest will be increased just as much. However, a large gain on the antenna when transmitting, will increase the system performance, due to the fact that the signal of interest will be sent with a higher power, ultimately increasing the Signal-to-Interference ratio (SIR).

Antennas can also be directional, i.e. have more gain in a specified direction (so called radiation pattern). This gives a stronger signal sent (or received) in that direction, and this property can be used to avoid interference coming from other directions. Radiation patterns will not be covered in the simulations in this thesis, since the gain will be assumed omni directional.

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Noise Figure and Temperature

This describes the thermal noise introduced in a radio receiver. The general formula is given by

N = kBBT (3.27)

where kB is the Boltzmann constant (1.3806488 × 10−23), B is the bandwidth

and T is the system temperature in Kelvin.

Sensitivity

The sensitivity of a radio receiver is defined as the lowest signal level (often expressed as the antenna- or input voltage) that is needed to obtain a certain SNR [17].

3.5 Power Spectrum Estimation

To be able to get a frequency representation of the random processes used as signals in this thesis, which is good because it gives a quick idea of how the different radio systems will affect each other, Welch’s method of averaging modified periodograms is used. In this thesis, it is used mainly for presenting the results in the frequency domain, and does not affect the actual performance of the system.

This method reduces the variance of the periodogram by dividing the process into sequences xi(n) of length L, that might or might not overlap, then applying

a data window w(n) of choice to each of the sequences. There exists several different windows, each with different properties of resolution and side lobe suppression. In this thesis, a Hamming window with an overlap of 50% is used, if not stated otherwise. Welch’s method was chosen because of it’s implementation simplicity. For further details on this method see a textbook on statistical digital signal processing, such as [18].

By averaging over more windows of shorter length L, the variance of the periodogram is reduced, with the trade-off of reduced resolution in frequency. To illustrate an example of this variance against resolution trade-off, the spectrum estimate of a 600 Hz sinusoid in white noise is shown in Figure3.5.

3.6 Modulation

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3.6. MODULATION 21 Frequency [kHz] P o w e r/ fr e q u e n c y [d B / H z ] 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 -36 -34 -32 -30 -28 -26 -24 -22 -20 -18 (a) Frequency [kHz] P o w e r/ fr e q u e n c y [d B / H z ] 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 -45 -40 -35 -30 -25 -20 -15 -10 -5 (b)

Figure 3.5: Power spectrum estimate using Welch’s method with a Hamming window. The total length of the sequence is N = 4096. In (a) a window size of L = 64 was used, and in (b) the window size was L = 1024. As expected, with the larger window size, the resolution is much better, but with the cost of a higher variance. As expected, with the higher resolution the signal power is concentrated closer to the carrier frequency, and approaching 0 dB.

3.6.1 BPSK and QPSK

A common way to modulate the signal is by altering the phase component, so called Phase Shift Keying (PSK). The total phase of the signal is divided equally between the M different symbols that can be transmitted. The general signal si(t) in this modulation scheme is given by

si(t) =pEsej(φ0+i

2π M)g

t(t), i = 0, 1, ..., M − 1 (3.28)

where φ0 is some constant phase, Esis the average symbol energy, and gt(t) is

again some chosen pulse shape. The simplest way to implement PSK is Binary Phase Shift Keying (BPSK), which represents the bit stream (binary digits 1 and 0) by the analog levels +√Eb and −

√

Eb respectively, i.e. M = 2, where

Eb is the energy per bit. Another common implementation of this method is

Quadrature Phase Shift Keying (QPSK). In QPSK, M = 4 and thus QPSK has 4 different symbols in its constellation, e.g. {(1, i) , (−1, i) , (−1, −i) , (1, −i)} or some phase shifted version of it. This QPSK signal constellation is shown in Figure3.6. A time signal created by using QPSK modulation, and pulse shaped by a Square Root Raised Cosine-filter, is shown in Figure3.7. The PSD of that time signal is shown in Figure3.8.

3.6.2 GMSK

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22 CHAPTER 3. METHODS AND MODELS ℜ ℑ s1 s2 s4 s3

Figure 3.6: An example of a QPSK signal constellation. Each dot represents a symbol, given by Eq. (3.28), with M = 4.

Time [ms] A m p li tu d e 0 1 2 3 4 5 6 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2

Figure 3.7: Real part of a QPSK signal. The delay in the beginning of the sequence is because of the filter that was used when pulse shaping the signal.

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3.6. MODULATION 23 Frequency [kHz] P o w e r/ fr e q u e n c y [d B / H z ] -400 -300 -200 -100 0 100 200 300 400 -110 -100 -90 -80 -70 -60 -50 -40 Figure 3.8: PSD of a QPSK signal. h(t) = k√1B πe k2 1B2t2 _(3.29) where k1 = √π

2ln2 and B is the half power bandwidth. For a more detailed

explanation of GMSK, please refer to a textbook or paper on the subject. A paper that describes the technique in a good way is [22].

3.6.3 OFDM

Orthogonal Frequency Division Multiplexing (OFDM) is the main modulation technique used in LTE. It is a wideband technique that is very spectrum efficient. Creating an OFDM can be quite complex, thus in this thesis it is kept at a simple level, just to get the basic properties of the signal. However, the general idea is to:

• Modulate a bit stream, in this thesis by using Binary Phase Shift Keyeing (BPSK), which is a simpler version of QPSK;

• Split up the now modulated stream into multiple (parallel) symbols, each with a length of the number of sub carriers used in the standard that is being followed (300 in this thesis);

• Perform Inverse Fourier Transform on the parallel symbols;

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24 CHAPTER 3. METHODS AND MODELS Time [µs] A m p li tu d e 0 20 40 60 80 100 120 140 160 180 -1 -0.5 0 0.5 1

Figure 3.9: Real part of a GMSK signal.

The signal is then ready to be upconverted (if needed) to its carrier frequency, and sent out through the antenna.

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3.6. MODULATION 25 Frequency [MHz] P o w e r/ fr e q u e n c y [d B / H z ] -3 -2 -1 0 1 2 3 -120 -110 -100 -90 -80 -70 -60 -50 Figure 3.10: PSD of a GMSK signal. Time [µs] A m p li tu d e 0 10 20 30 40 50 60 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2

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26 CHAPTER 3. METHODS AND MODELS Frequency [MHz] P o w e r/ fr e q u e n c y [d B / H z ] -3 -2 -1 0 1 2 3 -120 -110 -100 -90 -80 -70 -60 -50

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3.7. CHANNEL MODELS 27

3.7 Channel Models

To perform a realistic simulation, that can also be compared with other sim-ulations, standardized models are needed. In this section, two different stan-dardized Channel models that could be used when simulating Scenario 2 from Section2.3.2are presented. They will however not be implemented during the simulations in this thesis, but is left as a reference for future work. When im-plementing them, a channel equalization would also have been needed, which is outside the scope of this thesis.

3.7.1 GSM Channel Model

The 3rd Generation Partnership Project (3GPP) has specified several standard-ized channels for simulations. One of them, that would be a good fit for the GSM-R vs LTE scenario in this thesis, is the channel model called the typical case for rural area(RAx) 6 taps [23]. It models the multipath fading mentioned in Section 3.4.5, in this case a Rician fading model, i.e. there is a LOS com-ponent which is stronger than the other received comcom-ponents. The delay and average relative power of the different paths in this model is given in Table3.2.

Table 3.2: Parameters used in the RAx 6 taps model.

Excess tap delay [µs] Average relative power [dB]

0.0 0.0 0.1 -4.0 0.2 -8.0 0.3 -12.0 0.4 -16.0 0.5 -20.0

3.7.2 E-UTRA Channel Model

For the Evolved Universal Terrestrial Radio Access (E-UTRA), also known as LTE, 3GPP has also standardized channel models to use when simulating LTE communication. One of the models that could be a good fit when simulating GSM-R vs LTE is the Extended Vehicular A model (EVA) [24]. Also this model, just as the one described above, is a multipath fading model. The path delays and relative power of this model is given in Table3.3on page28.

3.8 Performance Measurements

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Table 3.3: Parameters used in the EVA model.

Excess tap delay [ns] Relative power [dB]

0 0.0 30 -1.5 150 -1.4 310 -3.6 370 -0.6 710 -9.1 1090 -7.0 1730 -12.0 2510 -16.9

3.8.1 Bit Error Rate

The intuitive way to measure the performance of a digital transmission system, i.e. where bits are being transmitted, is to measure the bit error rate (BER). BER is a unitless performance measure, and it is the number of bit errors divided by the total number of transferred bits. A common way to present the BER is to plot it on a logarithmic y-axis versus different values of SNRdB(SNIR, CIR

or CNIR depending on the current system) on the x-axis.

3.8.2 Time Availability

A simpler way of presenting the results is by expressing them in terms of time availability. Time availability is directly connected to the SNR of the system, mentioned in Section3.3. Every radio receiver has a minimum threshold, here denoted by γt, which is the lowest possible SNR level at which the receiver is

able to distinguish the signal intended for it, from the noise and interference. Assume that the SNR has the cumulative distribution function (CDF)

PΓ(γ) = Pr [Γ < γ] . (3.30)

The amount of time that the received signal power is above the threshold, γt,

is called the time availability at γt, denoted A (γt), and given by

A (γt) = Pr [Γ > γt] = 1 − Pr [Γ < γt] . (3.31)

In the same way, the time that the received signal power is below the threshold is called the outage probability, which can be written as

Po= 1 − A (γt) . (3.32)

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3.9. FREQUENCY INTERMODULATION 29

3.9 Frequency Intermodulation

All transmitters are supposed to send out their signals at a given set of fre-quencies. However, harmonics of these frequencies will also originate, with decreasing power for each harmonic. Another malicious creature in the land of frequency origination, are the intermodulation products [25] [26]. Intermodula-tion products are caused by the non-linearity of the electronic components and the signal processing being used in the transmitters and receivers.

When there are two or more transmitting units close to each other and the signal from one of the transmitters enters through the other transmitter’s an-tenna, these frequency products arise. These non-linearities can be modelled by using Taylor series, or Bessel functions. Although the calculation of intermod-ulation products is not implemented in this thesis, their possible impact on the performance can be implemented using the idea of frequency offset (refer to ∆fk

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Chapter 4

Implementation

In this chapter it is described how the theory mentioned up until now has been implemented to be able to simulate the scenarios that were presented in Section2.3. All simulations are implemented in Matlab. Figure4.1is included as a reference, to provide a quick survey of the simulation environment.

Another common way to evaluate telecommunication conflicts is to disregard some of the system parameters, e.g. the modulation techniques used, and how they have been implemented. With that simpler model, the performance is usually estimated by comparing the received power from the victim system to the power from the interfering system. ˚AF already has a software that does this, so to bring something new to the table, a model which is taking more details into account was sought.

The reason that the simulation method which is used in this thesis was chosen, is that it is a bit more advanced than just comparing power levels, and it uses more details of the involved systems to simulate. Also, one of the goals with this thesis work was to gain knowledge of how different modulation techniques work, preferably newer ones like OFDM, and also to have a model that can handle both wideband and narrowband systems. Other than that, the model should be able to handle intermodulation products, and the partial frequency overlap that they might create. That can be done with the model presented in this thesis, giving performance results that can not be obtained by only comparing power levels, in this case presented as BER-curves (which are good to have when comparing different systems to each other).

With this method it is also possible to get an idea of how the frequency spectrum will look, which greatly helps understanding the problem at hand.

4.1 Implementation in General

When implementing the units described below, a combination of both own made, as well as built-in functions in Matlab were used.

The first thing that had to be taken care of during the implementation was the fact that the simulation is carried out in a sampled world. Since the systems simulated in this thesis all operate with a different bandwidth, it was necessary to find a way to be able to represent signals from the different systems summed up to one single signal, as described in Section3.1. This means in general that

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32 CHAPTER 4. IMPLEMENTATION

Modulator Upsample and_{Pulse Shape} Data Source

Demodulator Filter

The Radio Channel The Transmitter

The Receiver

Interferers

Channel Receiver Noise

Figure 4.1: Flow chart over the general implementation of the simulation method described in this thesis.

the signal with the smaller bandwidth has to be upsampled by some large enough factor, so that its sampling frequency (Fs) also suffices as sampling frequency for

the signal with the larger bandwidth. The expression for the sampling frequency is Fs= rSym × sps =symbols sec × samples symbol =samples sec = Fs. (4.1)

and it is this Fs that should be large enough, i.e. 2 times the bandwidth of

the widest signal (remember the Nyquist–Shannon sampling theorem). When the Fsis chosen, the factor of which the smaller bandwidth-signal needs to be

upsampled is then given by the signals symbol rate.

4.1.1 The Transmitter

All transmitters in the simulations are implemented as described in this section. The differences between them are which modulation technique that has been used, and the filters at the output.

Bit generator

The information bits {0, 1} that acts the data in both the victim signal as well as in the interfering signal are generated with equal probability, to form a bit sequence bi(n) where n = 0, 1, 2, . . . , N − 1. This sequence of bits will be

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4.1. IMPLEMENTATION IN GENERAL 33

Modulator

In this part, the bit sequence gets modulated according to a given modulation technique, e.g. QPSK, GMSK or OFDM described in Section3.6.

The QPSK modulation is implemented as described in Section 3.6.1, i.e. mapping each pair of bits to a symbol in the complex plane, then upsample and filter.

The GMSK modulation is performed using a built-in function in the Com-munications System Toolbox in Matlab, called comm.GMSKModulator, due to its convenience when it comes to demodulating the signal later on.

The implementation of OFDM also follows its description in Section 3.6.3, i.e. first generating the data, modulate this data using BPSK, then splitting up this modulated sequence into parallel sequences of a specified length (in this case a length of 300, as specified in the LTE standards). These parallel symbols are then Inverse Fourier Transformed, using a number of FFT-points, N F F T . The derivation of this number is described in the next chapter, in Eq. (5.2). These symbols are then reshaped into one sequence.

Pulse Shaping and Filtering

The now modulated sequence gets upsampled (if needed) and filtered (pulse shaped) through some predefined filter, to produce a signal that can be sent out through the antenna over the radio channel.

4.1.2 The Radio Channel

Here the interferers are being added to the transmitted signal. Each interferer is created in the same way as the system being interfered, which includes bit stream generation, modulation, upsampling and filtering, as described above.

Channel

The Channel in this implementation refers to the attenuation of the signals (i.e. the path loss). Depending on their placement, frequencies used, height of antennas and other parameters, the different signals will be affected accord-ingly. If fading was also taken into account in the scenario, it would have been implemented here.

4.1.3 The Receiver

Now all the signals have been added together, and been adjusted in power accordingly, and is being received at the victim receiver. This section describes what happens with the received signal, and how.

Receiver Noise

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34 CHAPTER 4. IMPLEMENTATION

Filter

A receiver filter is used to filter the received signal around the baseband, to remove as much of the received interference as possible. In this thesis, in the second scenario, a 10-taps Butterworth filter with a width of 500 kHz has been used, because it is easily implemented using the function butter in Matlab, and is a reasonable approximation of what could be used inside a GSM-R re-ceiver.

Demodulator

In the demodulator, the received symbols are mapped back to the corresponding bits, to form the estimate ˆx(n) of the originally transmitted signal x(n). The number of errors when comparing ˆx(n) to x(n) is calculated to get the BER, which is presented as a result of the simulation.

When demodulating the GMSK-signal in Scenario 2, the built-in Matlab function comm.GMSKDemodulator was used. This function uses a hard decision Viterbi decoder, which means that it looks for the most probable symbol of the possible ones being sent, by comparing to a Trellis diagram. More information about Viterbi and Trellis diagrams can be found in a textbook on communication theory, e.g. [16].

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4.2. ADJUSTABLE VARIABLES 35

4.2 Adjustable Variables

When simulating a scenario using the implementation mentioned in the above section, there are several variables than can be set. They are listed in Table4.1.

Table 4.1: List of variables that can be set in the implementation.

Variable Description

Data Rate At which rate the transmitter transmits its data.

Distance The distance between the transmitters and re-ceivers involved in the simulated scenario. Filter If there are any filters at either the transmitter

or the receiver, to shape the pulses or to block out of band transmissions, they can be defined in the model.

Frequency The carrier frequency for the systems that are being simulated.

Gain and Losses If any particular gain or loss are given for the system, it can be adjusted here. Applies to both the receiver and the transmitter. Height Placement of the antennas, both transmitting

and receiving.

Modulation This determines what kind of modulation technique the systems use to transmit their data.

Path Loss Model Use the path loss model that suits the scenario the best.

Receiver Noise The thermal noise level at the receiver. Transmit Power Power level used at the transmitter, adjustable

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Chapter 5

Results

In this chapter, the results from simulations of the scenarios described in Chap-ter 2 are presented, together with a small discussion around each figure. For more discussion, regarding the results and work as a whole, read the next chap-ter.

5.1 A General Scenario

When simulating the scenario described in Section2.3.1, the following results were obtained. The parameters and settings when performing the simulations are found in Table5.1. The first thing that is interesting to know, is if the fre-quency spectrum looks as expected, with both the original signal, the interferer and the AWGN. A sample of the PSD estimation is shown in Figure5.1. It can be seen that the SNR is indeed 10 dB, and in this particular snapshot the CIR was at 5 dB and the difference in carrier frequencies, here ∆f1, was at 50 kHz,

which also can be seen in the figure.

Table 5.1: Parameters used when simulating the first scenario.

Parameter Value

Symbol Rate 100000 Symbols/sec Samples per Symbol 8

Number of bits 216

Filter Square Root Raised Cosine

β 0.35

Step size, ∆fk 10 kHz

Step size, CIR 1 dB

After the filtering process with a matched filter (matched to the Square Root Raised Cosine filter that was used at the output of the transmitter, when pulse shaping the signal), the PSD looks as in Figure5.2. Another, and perhaps the most, interesting result in Scenario One is how the system performs concerning the BER. This is presented as a surface plot in Figure 5.3. The reason that

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38 CHAPTER 5. RESULTS Frequency [kHz] P o w e r/ fr e q u e n c y [d B / H z ] -400 -300 -200 -100 0 100 200 300 400 -130 -120 -110 -100 -90 -80 -70 -60 Transmitted signal Interfering signal Signal at receiver

Figure 5.1: A sample of the Power Spectrum estimation in Scenario One, taken when the CIR and ∆f1 was 5 dB and 50 kHz respectively.

the BER never drops below 10−3 _{is because the SNR-level was kept at 10 dB}

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5.1. A GENERAL SCENARIO 39 Frequency [kHz] P o w e r/ fr e q u e n c y [d B / H z ] -400 -300 -200 -100 0 100 200 300 400 -130 -120 -110 -100 -90 -80 -70 -60

Signal at filter input Signal at filter output

Figure 5.2: A sample of the filtered Power Spectrum estimation in Scenario One. A small ripple can be seen at the lower right side of the signal bandwidth (the main lobe), as a rest from the interfering signal that could not be completely filtered out. CIR [dB] _∆f_k_[kHz] B E R 0 5 10 15 ₀ 50 100 150 10−3 10−2 10−1 100

Figure 5.3: The BER performance in Scenario One, here versus both the CIR and the ∆fk. The SNR level is kept constant at 10 dB, which explains why the

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40 CHAPTER 5. RESULTS

5.2 GSM-R vs LTE

In this scenario, a simulation of a GSM-R system being disturbed by a LTE system were made. When running the simulations that gave the results pre-sented in this section, the size of the useful bit stream was 20000 bits, and for every different simulation point (be it SNR-value, distance relationship etc.), the mean was taken over 10 frames, each with a length of 20000 bits. To be able to represent both the GMSK and the OFDM signals in the same signal, a high enough sampling frequency is required. Because the OFDM signal has a bandwidth of approximately 5 MHz, a sampling frequency of at least twice that is required to be able to represent the signal without aliasing. Since the OFDM signal can have a frequency offset compared to the GMSK signal, the wanted sampling frequency was increased to at least thrice the bandwidth of the OFDM signal, i.e. at least 15 MHz.

To find a more exact value of a functioning sampling frequency, the value of the samples per symbol (denoted sps) for the GMSK signal needs to be set. To do that, the GMSK symbol rate was looked at. From the GSM-R specifications, the symbol rate (denoted rSym) is given as 270.84 ksymbols per second, which gives a symbol duration ofe3.69 µs. These values is then inserted into Eq. (4.1),

which is presented again below for simplification

Fs= rSym × sps =symbols sec × samples symbol =samples sec = Fs. (5.1)

It can be seen that for Fs≥ 15 MHz, and with rSym given as 270.84

ksym-bols/sec, the value of sps needs to be at least 56. It was decided to be set to 64, or 26_{, because of the binary beauty of it. This yields a sampling frequency}

of about 17.3 MHz. If a higher sampling frequency is wanted, it should be kept in mind that it will also increase the computational time used.

Now the number of IFFT points (NFFT ) in the OFDM modulation needs to be determined. From the LTE specifications, and also found in Table 5.2, it is read that the LTE carrier frequency spacing is 15 KHz. The number of IFFT points needed to accomplish the correct sampling frequency of 17.3 MHz, NFFT is calculated as

N F F T = Fs

carrier frequency spacing = rSym × sps

carrier frequency spacing =270840 × 64

15000 ≈ 1156.

(5.2)

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5.2. GSM-R VS LTE 41 Frequency [MHz] P o w e r/ fr e q u e n c y [d B / H z ] -8 -6 -4 -2 0 2 4 6 8 -220 -210 -200 -190 -180 -170 -160 -150 -140 -130 Received GSM-R signal Received LTE signal Total signal Thermal noise

Figure 5.4: A sample of the Power Spectrum estimation in GSM-R vs LTE, taken at maximum distance (8000 m) between the GSM-R base station and receiver, and at a distance of 1500 m between the LTE base station and GSM-R receiver.

The parameters used in this scenario are listed in Table 5.2. Most of the parameters were taken from the standards. The BS and MS specific parameters were taken from an ECC-report [27]. The frequencies of the signals were chosen so that it would correspond to the worst case scenario, i.e. the GSM-R sending at the highest available band, and the LTE at the lowest available.

As listed in Table5.2, the GSM-R cell range is assumed to be 8 km. The cell range of the LTE system is set to be 3 km. When simulating, the GSM-R cell radius was changed in steps of 250 m, and the LTE cell radius was changed in steps of 100 m. As mentioned before, every cell radii combination was averaged over 10 frames, to get a more accurate result.

The path loss model used, Okumura-Hata for open areas, was chosen due to the fact that the frequencies and antenna heights are all well within the valid range of the model, and also because of the assumption that the trains with GSM-R runs in open areas, where LTE might be launched on the 900 MHz band.

In Figure 5.6the received power from the two systems as a function of the distance from the transmitting base station to the receiving GSM-R mobile station is plotted. The small difference in the power level is because of the different operation frequencies.

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42 CHAPTER 5. RESULTS Frequency [MHz] P o w e r/ fr e q u e n c y [d B / H z ] -8 -6 -4 -2 0 2 4 6 8 -220 -210 -200 -190 -180 -170 -160 -150 -140 -130 Received GSM-R signal Received LTE signal Total signal, filtered Thermal noise

Figure 5.5: A sample of the Power Spectrum estimation in GSM-R vs LTE, taken at maximum distance (8000 m) between the GSM-R base station and receiver, and at a distance of 1500 m between the LTE base station and GSM-R receiver. The total signal has been filtered, using the filter specified in Table5.2.

Distance from base stations to GSM-R receiver [m]

P o w e r [d B ] 0 1000 2000 3000 4000 5000 6000 7000 8000 −50 −40 −30 −20 −10 0 10 20 GSM-R signal power LTE signal power

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5.2. GSM-R VS LTE 43

Table 5.2: Parameters used when simulating the second scenario. GSM-R MS refers to a train mounted mobile station.

Parameter Value

GSM-R Carrier Frequency 924.9 MHz

GSM-R Symbol Rate 270.84 ksymbols/sec GSM-R Samples per Symbol 64

GSM-R BT product 0.3

GSM-R BS Tx Power (max) 30 W (14.8 dBW, 44.8 dBm) GSM-R BS Antenna Height 45 m

GSM-R BS Antenna Gain 18 dBi GSM-R BS Feeder Loss 3 dB GSM-R MS Antenna Height 4.5 m GSM-R MS Antenna Gain 2 dBi GSM-R MS Noise Figure 7 dB GSM-R MS Feeder Loss 3 dB GSM-R Cell range 8 km

Filter Low Pass Butterworth, 10-taps, 500 kHz bandwidth

LTE Center Frequency 927.7 MHz LTE Carrier Frequency Spacing 15 kHz Number of LTE carriers 300

FFT Size 1156

LTE Tx Power (max) 43 dBm LTE BS Antenna Gain 18 dBi LTE BS Antenna Height 45 m LTE BS Feeder Loss 3 dBi LTE Cell range 3 km

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44 CHAPTER 5. RESULTS LTEBS–GSMRMSdistance [m] GSMRBS–GSMRMS distance [m] B E R 0 500 1000 1500 2000 2500 3000 0 2000 4000 6000 8000 10−6 10−5 10−4 10−3 10−2 10−1 100

Figure 5.7: BER surface of the GSM-R system being interfered by a LTE system. A low pass Butterworth filter was used at the GSM-R receiver, with a bandwidth of 500 kHz. LTEBS- GSMRMSdistance [m] B E R 0 500 1000 1500 2000 2500 3000 10−6 10−5 10−4 10−3 10−2 10−1 100 8000 m 7000 m 6000 m 5000 m 4000 m 3000 m 2000 m 1000 m

On Models for Interference Calculations between Radio Communication Systems