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RAIN MODELS FOR THE PREDICTION OF FADE DURATION

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					RAIN MODELS FOR THE PREDICTION OF FADE DURATION
         AT MILLIMETER WAVELENGTHS




            MOHD AFZAN BIN OTHMAN




        UNIVERSITI TEKNOLOGI MALAYSIA
                                                                                                       2


                     UNIVERSITI TEKNOLOGI MALAYSIA


              BORANG PENGESAHAN STATUS TESIS♦
         JUDUL : RAIN MODELS FOR PREDICTION OF FADE DURATION AT
                           MILLIMETER WAVELENGTHS

                          SESI PENGAJIAN:              2006/2007

 SAYA                              MOHD AFZAN BIN OTHMAN
                                         (HURUF BESAR)

  mengaku membenarkan tesis (PSM/Sarjana/Doktor Falsafah)* ini disimpan di Perpustakaan
  Universiti Teknologi Malaysia dengan syarat-syarat kegunaan seperti berikut:

   1.    Tesis adalah hak milik Universiti Teknologi Malaysia.
   2.    Perpustakaan Universiti Teknologi Malaysia dibenarkan membuat salinan untuk tujuan
         pengajian sahaja.
   3.    Perpustakaan dibenarkan membuat salinan tesis ini sebagai bahan pertukaran antara institusi
         pengajian tinggi.
   4.    **Sila tandakan ( √ )


                 SULIT             (Mengandungi maklumat yang berdarjah keselamatan atau
                                   kepentingan Malaysia seperti yang termaktub di dalam AKTA
                                   RAHSIA RASMI 1972)

                 TERHAD            (Mengandungi maklumat TERHAD yang telah ditentukan oleh
                                   organisasi/badan di mana penyelidikkan dijalankan)

                 TIDAK TERHAD
                                                                   Disahkan oleh



___________________________________                ___________________________________
     (TANDATANGAN PENULIS)                              (TANDATANGAN PENYELIA)

Alamat Tetap:
   NO 270 TAMAN PERTAMA,                                ASSOC PROF DR JAFRI DIN                   .
   272000 KUALA LIPIS,                                        (Nama Penyelia)
   PAHANG DARUL MAKMUR.

Tarikh    :    23 NOVEMBER 2006                    Tarikh    :   23 NOVEMBER 2006
                 “I hereby declare that I have read this thesis and in
              my opinion this thesis is sufficient in terms of scope and
quality for the award of the degree of Master of Engineering (Electrical-Electronics &
                                Telecommunication)”




             Signature              :…………………………..
             Name of Supervisor : Assoc. Prof. Dr Jafri Din
             Date                   : 23rd November 2006
RAIN MODELS FOR THE PREDICTION OF FADE DURATION
              AT MILLIMETER WAVELENGTHS




                 MOHD AFZAN BIN OTHMAN




       A project report submitted in partial fulfilment of the
            requirements for the award of the degree of
Master of Engineering (Electrical-Electronics & Telecommunication)




                 Faculty of Electrical Engineering
                  Universiti Teknologi Malaysia




                        NOVEMBER 2006
                                                                                     ii




I declare that this thesis entitled “Rain Models for the Prediction of Fade Duration at
Millimeter Wavelength” is the result of my own research except cited in the references.
The thesis has not been accepted for any degree and is not concurrently submitted in
candidature of any other degree.




              Signature      :………………………………….
              Name           : MOHD AFZAN BIN OTHMAN
              Date           : 23rd November 2006
                                                     iii




“To my beloved mother, father, fiancé and family…”
                   Thank you.
                                                                                           iv




                               ACKNOWLEDGEMENTS




        Alhamdulillah. First of all, I would like to express my gratitude to Allah S.W.T
because of his blessing; I have managed to complete my master project successfully
within the given time without any difficulties.

        Here, I wish to take this opportunity to express my appreciation and gratitude of
myself to my helpful and knowledgeable supervisor, Assoc. Prof. Dr Jafri Din from
Wireless Communication Center, UTM, whom I deeply indebted, in the process of
finishing this project. Without his brilliant suggestions and encouragement, I would
never be able to write this thesis completely as I am right now. Thank you so much for
your commitment and your very active participation in helping me doing this project,
and again, I am very proud to have you as a supervisor. Thank you so much.

        Also, a million thanks to all of the lecturers in Faculty of electrical Engineering
who involves direct or indirectly in this project. I am really appreciate of your great
assistances and would like to truly thank you for your magnificent teaching, and also for
the wonderful and worthwhile experience I had during my course of study in UTM.

        Last but not the least, I would like to say thank you to all of my friends for their
helps, support, and valuable hints.

        Finally, my heartfelt thanks and appreciation goes to my beloved family,
especially my Mum and Dad; and most important of all, to my fiancée. I am really
grateful to have them in my life. Thanks for all of your helps and supports when I am
trapped in a difficult time. Thanks for everything you have done for me.

To all, I wish you success in your future endeavors.
Thank you
                                                                                            v




                                       ABSTRACT




       The planning of radio communications system requires an estimate of the
average annual outage due to fading, which at millimeter wavelengths, is generally
dominated by the effects of rain attenuation. Current ITU-R recommendations provide
algorithm for estimating the exceedance static of rain-induced attenuation on terrestrial
links. Another factor of interest, not currently covered by ITU-R recommendations is
the distribution of the durations of rain fades. Hence this project involved an extensive
review on the available models describing annual rain fade distributions on line-of-sight
links. Also, analysis on the rain attenuation data conducted on an experimental 350m,
and 38GHz in frequency in UTM campus for 1 year will be used to obtain information
on the rain fade statistic. Previous researches pointed out that the distribution of the
durations of rain events at different intensities is more fundamental than distributions of
link fades. Thus, this project aim is to establish an expression for the average number of
events per year of rain intensity greater than a given threshold. This could be achieved
from the detail analysis of the 38GHz link signal level profile database. Thus, the rain
fade statistic describing annual rain fade distributions on line-of-sight could be
developed. To predict rain attenuation on complex multi hop or route diverse links, it is
necessary to have a statistical representative of rainfall in time and space, which is
accurate over wide ranges of spatial and temporal scales. Various available statistical
models will be used to demonstrate the influence of the developed rain fade statistic
when applied for more complex microwave links.
                                                                                      vi




                                      ABSTRAK




       Pada masa kini, perkembangan dalam bidang telekomunikasi adalah amat
memberangsangkan. Untuk menghasilkan system telekomunikasi radio, perkara penting
yang amat dititikberatkan ialah kesan isyarat radio terhadap hujan. Di mana seperti yang
kita sedia maklum, bagi isyarat yang lebih daripada 10 GHz, kesan hujan terhadap
isyarat ini adalah sangat tinggi. Dengan itu ITU-R telah memperkenalkan algorithm
bagi menganggarkan kesan hujan ini. Tetapi ada satu lagi faktor yang tidak kelaskan
oleh ITU-R, iaitu masa semasa isyarat ini menjadi lemah disebabkan oleh kesan hujan.
Oleh itu, projek ini akan merangkumi analisis terhadap data yang diamabil di UTM
kampus bagi tempoh 1 tahun iaitu pada 1999, 350m, 38GHz serta mengenal pasti model
kesan hujan terhadap isyarat yang telah dicadangkan oleh beberapa penyelidik. Model
hujan yang sesuai dengan data yang sedia ada akan diambil sebagai rujukan dan
pemalarnya akan diubah mengikut kesesuaian data hujan di Malaysia. Tujuan projek ini
dilaksanakan adalah untuk mencari nilai purata ‘event’ ini berlaku bagi tempoh setahun.
Ini membolehkan kita membuat ramalan berapa lama isyarat akan menjadi lemah
bergantung kepada jumlah hujan yang turun. Maka dengan itu sebuah model yang baru
akan dihasilkan untuk meramalkan kesan hujan terhadap isyarat radio ini.
                                                      vii




                    TABLE OF CONTENTS




CHAPTER     TITLE                             PAGE
            DECLARATION                        ii
            DEDICATION                         iii
            ACKNOWLEDGEMENTS                   iv
            ABSTRACT                           v
            ABSTRAK                            vi
            TABLE OF CONTENTS                  vii
            LIST OF TABLES                     x
            LIST OF FIGURES                    xi
            LIST OF ABBREVIATIONS              xiii
            LIST OF SYMBOLS                    xiv
            LIST OF APPENDICES                 xv




CHAPTER I   INTRODUCTIONS                      1
            1.1   Project Background           1
            1.2   Problem Statement            3
            1.3   Objective                    4
            1.4   Scopes of Project            4
            1.5   Importance of the Project    5
                                                                         viii

CHAPTER II    LITERATURE REVIEW                                     7
              2.1   Rain Attenuation on Satellite Communication     7
              2.2   Fade Mitigation Techniques                      9
                    2.2.1   Power Control                           10
                    2.2.2 Signal Processing                         11
                    2.2.3 Diversity                                 11
              2.3   Available Prediction Models                     12
                    2.3.1 ITU-R Model                               12
                    2.3.2   Chris J. Gibbins/ Kevin S. Paulson      17
                    2.3.3   Kormayos/ Lena Pedersen/ Cyril Sagot/   19
                            Janos Bito
              2.4   Summary                                         21




CHAPTER III   METHODOLOGY                                           22
              3.1   Methodologies                                   22
              3.2   Data Collection                                 24
              3.3   Data Extractions                                26
              3.4   Existing Rain Models Programming                29
                    3.4.1   ITU-R Model Programming                 30
                    3.4.2   Chris J. Gibbins/ Kevin S. Paulson      32
                            Programming
                    4.4.3   Kormayos/ Lena Pedersen/ Cyril Sagot/   33
                            Janos Bito Programming
              3.5   Comparison                                      33




CHAPTER IV    RESULTS                                               35
              4.1   Introduction                                    35
              4.2   Measured Data Interpretations                   35
                    4.2.1   Power Received                          35
                                                             ix

                  4.2.2   Measured Data Analysis        37
            4.3   Result and Analysis                   41
                  4.3.1   Obtain Rain Fade Statistics   41
                  4.3.2   Comparison                    45




CHAPTER V   CONCLUSIONS                                 49
            5.1   Conclusions                           49
            5.2   Future Works                          50




            REFERENCES                                  51
                                                                     x




                       LIST OF TABLES




TABLE NO   TITLE                                              PAGE




    4.1    Convert AGC (V) to decibel (dBm)                    38
    4.2    Analysis on fade duration                           40
    4.3    Number of events which duration exceeds abscissa    42
           at 1, 3, 6, 9, 12, 15, 18 and 21 dB levels
    4.4    Number of events for each month over one year       44
    4.5    Fade duration statistics information                46
                                                                         xi




                        LIST OF FIGURES




FIGURE NO   TITLE                                                 PAGE




    1.1     Features characterizing the dynamic of fade             2
            Events[1]
    3.1     Research methodology flow chart                         23
    3.2     Path profile for Ericson Microwave Link at              25
            38GHz in WCC, UTM
    3.3     Rain rate contour map in Peninsular Malaysia            26
    3.4     Read data form text file                                27
    3.5     Converts AGC (volts) values to dBm                      27
    3.6     Compile fade duration statistic for attenuation         28
            exceeding threshold
    3.7     Save fade duration statistics data to corresponding     29
            files
    3.8     Set parameters with correct values                      30
    3.9     Matlab programming for corresponding equations          31
    3.10    Matlab programming for total numbers of fade            31
            durations
    3.11    Matlab programming for number of fades NA               32
    3.12    Matlab programming for probability numbers of fades     33
            durations
                                                                xii

3.13   Matlab programming for comparison among measure     34
       data and studied rain fade models
4.1    Received power level time series on clear weather   36
4.2    Received power level time series on rainy weather   37
4.3    Power received signal attenuation                   39
4.4    Analysis on fade duration                           40
4.5    Fade duration grouping by attenuation levels        43
4.6    Fade duration grouping by months                    45
4.7    Comparison among existed rain models with           47
       measured data
                                                                      xiii




                   LIST OF ABBREVIATIONS




DTH      -   Direct To Home
FMT      -   Fade Mitigation Technique
MEASAT   -   Malaysia East Asia Satellite
WCC      -   Wireless Communication Centre
AGC      -   Automatic Gain Control
UTM      -   Universiti Teknologi Malaysia
CD       -   Cumulative Distribution
ITU-R    -   International Telecommunications Union - Radiocommunications
sec      -   seconds
                                                        xiv




                        LIST OF SYMBOLS




f       -   frequency
φ       -   elevation angle
A       -   attenuation
σ       -   standard deviation
γ       -   power law distribution
Dt      -   boundary time
k       -   fraction time
Q       -   standard cumulative distribution function
N       -   number of fade events
R       -   rain rate
r       -   path reduction factor
L       -   path length
V       -   AGC value (volt)
R0.01   -   rain intensity at 0.01% of time
dBm     -   decibel meter
                                               xv




                   LIST OF APPENDICES




APPENDIX   TITLE                        PAGE




    A      FLOW CHART                     53
    B      PROGRAMMING CODES              57
                                      CHAPTER I




                                  INTRODUCTIONS




1.1    Project Background




       The planning of radio annual outage due to fading at millimeter wavelengths is
generally dominated by the effects of rain attenuation. This is usually determined from
long-term statistic of annual rainfall rates, applying the procedures in ITU-R
Recommendation P.530 for terrestrial links.




       In the design of a variety of telecommunication systems, the dynamic
characteristics of fading due to atmospheric propagation are of concern to optimize
system capacity and meet quality and reliability criteria. Examples are fixed networks
that include a space segment and systems that apply fade mitigation or resource sharing
techniques.
                                                                                             2

       Several temporal scales can be defined, and it is useful to have information on
fade slope, fade duration and interfade duration statistics for a given attenuation level
(Figure 1.1).




            Figure 1.1: Features characterizing the dynamic of fade events [1]




       Fade duration is defined as the time interval between two crossings above the
same attenuation threshold whereas interfade duration is defined as the time interval
between two crossings below the same attenuation threshold. Fade slope is defined as
the rate of change of attenuation with time. Of particular interest in the context of
availability criteria is the distinction between fades of shorter and longer duration than
10 s. Knowledge of the distribution of fade duration as a function of fade depth is also a
prerequisite for the application of risk concepts in the provision of telecommunication
services.




       In addition, information about the expected fade slope is essential to assess the
required minimum tracking rate of a fade mitigation system.
                                                                                             3


1.2    Problem Statement




       Nowadays, the advancement in microwave communication technologies
especially in telecommunication and broadcasting has resulted in congestion for
frequencies below 10GHz. This has forced microwave designers to look for higher
frequencies. Unfortunately for the frequencies that greater than 10GHz, rain become the
main factor of attenuation especially for tropical and equatorial countries that
experience high rainfall rate throughout the year such as in Malaysia. Where is for the
frequencies above 10GHz, it will lead to outages that compromise the availability and
quality of service, making this one of the most critical factors in satellite link design.
Thus, in some cases the use of suitable compensation techniques to counter excessive
attenuation will be needed to maintain reliable system operation. The proper design of
fade mitigation techniques on satellite links requires not only knowledge of long-term
statistics, but also of second-order statistics describing the dynamic behavior of
attenuation, such as duration of fades, duration between fades and fade rate. So due to
this circumstance it is important to have a predication of fade duration.




       Usually, fade duration statistics are presented as conditional distributions of the
number of fades exceeding certain durations, given that specified fade threshold has
been exceeded. This representation provides information on the number of outages and
system availability due to propagation on a link, given a fade margin and an availability
specification.
                                                                                          4


1.3       Objective




          The main objective of this project is to estimate of the average number of events
per year of rain attenuation greater than a given threshold. As we know, the cumulative
probability distribution of the system (take Astro as an example) will down for one year
is about 0.01%. This downtime is equal to 52mins/year that the signal will drop due to
the attenuation of rain. In this case we don’t know the exact number of events occur per
year, how much the signal drop and also the duration for one event occurs. Hence, this
project is expected to answer all of the questions stated previously.




1.4       Scope Of Project




          This project will involve an extensive review on the available models describing
annual rain fade distribution on line-of-sight links. There are many fade duration
models that was published in order to predict the rain fade duration. The examples of
the published prediction models of fade duration are;


      •   ITU-R Model [1]
      •   Chris J Gibbins and Kevin S Paulson [2]
      •   Zsolt Kormanyos/ Lena Pedersen/ Cyril Sagot/ Janos Bito [3]
      •   Mopfouma [4]
      •   A two component rain model [5]


Details on ITU-R Model [1], Chris J Gibbins and Kevin S Paulson [2] and Zsolt
Kormanyos/ Lena Pedersen/ Cyril Sagot/ Janos Bito [3] will be discussed in the next
chapter.
                                                                                                5

          Secondly, do analysis on the available rain attenuation data in UTM. This data
was conducted on an experimental 350m, 38GHz by Wireless Communication Center
(WCC) [6]. At first, the purpose of these rain attenuation data is to produce cumulative
distribution (CD) of rain attenuation data. And for the purpose of this project, these data
will be used to obtain information on the rain fade statistics.




          This rain fade statistics will be developed by using Matlab software. The result
from this rain fade statistics will be used to compare with the available empirical
models. The best empirical models that suit to the obtained rain fade statistic will be
adopted as rain fade model in Malaysia.




1.5       Importance Of The Project




Fade duration is an important parameter to be taken into account in system design for
several reasons;




      •   System outage and unavailability: fade duration statistics provide information on
          number and duration of outages and system unavailability due to propagation on
          a given link and service;


      •   Sharing of the system resource: it is important from the operator’s point-of-view
          to have an insight into the statistical duration of an event in order to assign the
          resource for other users. For example, nowadays most of the telecommunication
          systems are based on bandwidth on demand. In this case, when signal is dropped
          then we must assign small bandwidth to users in order to make sure that C/N
                                                                                       6

    (Carrier to Noise ratio) is high. If not, user will no longer receive any signal
    during that event;


•   FMT (Fade Mitigation Technique): fade duration is of concern to define
    statistical duration for the system to stay in a compensation configuration before
    coming back to its nominal mode. This FMT will be discussed in more detail
    later;


•   System coding and modulation: fade duration is a key element in the process of
    choosing forward error correction codes and best modulation schemes; for
    satellite communication systems, the propagation channel does not produce
    independent errors but blocks of errors. Fade duration impacts directly on the
    choice of the coding scheme (size of the coding word in block codes,
    interleaving in concatenated codes, etc.).
                                     CHAPTER II




                               LITERATURE REVIEW




2.1    Rain Attenuation on Satellite Communication




       Satellite transmissions are carried on one of two frequencies: C-band or Ku-
band. When operating at the higher frequency Ku-band, the strength of the satellite
signal may be temporarily reduced under severe rain conditions. To compensate for
these potential effects, earth stations located in heavy rain areas are designed with more
transmit power. C-band transmissions are virtually immune to adverse weather
conditions.




       Signal attenuation due to rain is a characteristic of both microwave and satellite
transmissions. It is the interference caused by raindrops on electromagnetic signals
traveling through the atmosphere. When this phenomenon occurs, the transmission is
weakened by absorption and scattering of the signal by raindrops.
                                                                                           8

       The level of attenuation is the product of a number of variables, and to minimize
its effect, a rain fade margin should be included when designing satellite services and
equipment. The rain fade margin is the amount of extra power of satellite adds to the
signal strength to compensate for the possibility of rain attenuation. In most cases the
reduction in signal strength due to rain does not surpass the rain fade margin and does
not have any noticeable effect on transmission.




       Generally, rain attenuation increases as the signal frequency increases.
Therefore, transmissions at 6/4 GHz will experience insignificant attenuation, while
transmissions at 14/12 GHz will experience greater attenuation. For 6/4 GHz signals to
be affected would require rain storms approaching hurricane conditions. Signals at
higher frequencies can be affected by less severe storms.




       This is due to the wavelength of each frequency and the size of the raindrop
through which the signal has to pass. Transmissions at 6/4 GHz have a longer
wavelength than transmissions at 14/12 GHz, and are less susceptible to rain
attenuation. For example, a 6/4 GHz frequency has a wave-length of approximately 7
cm, and a 14/12 GHz frequency has a wavelength of approximately 2 cm. Any raindrop
in the path of either signal which approached half the wavelength in diameter will cause
attenuation.




       How long a transmission will be affected by rain attenuation and how deep the
attenuation will be is determined by the amount of rainfall. Generally, signal strength
can be affected for two to three minutes during an average rainfall, and up to 15 minutes
for extremely heavy rain periods. However, attenuation periods of up to 15 minutes are
extremely rare, and although signal strength may be affected, there will be no noticeable
effect on transmission as long as the attenuation does not exceed the allocated rain fade
margin.
                                                                                            9

        To offset the effects of external forces on satellite transmissions, satellite
provider must builds a link margin into its calculations when designing satellite
services. This margin is the amount of extra transmission power of signal strength
satellite provides so the service is not affected by rain attenuation during normal
rainfalls.




        The rain fade margin is a component of the link margin, and is a calculation of
expected rain attenuation over one year. It is based on rainfall data, elevation angle, and
weather patterns. This margin gives each customer more power than is needed at any
given time, so that when rain attenuation occurs, it rarely affects the service.




        Based on the link margin and the built-in rain attenuation margin, each customer
should typically meet or exceed space segment performance specifications 99.9 per cent
of the time over one year for 14/12 GHz service, and 99.95 per cent of the time over one
year for 6/4 GHz service. This reduces the possibility of rain attenuation affecting your
service, and confines the effects to very heavy and very infrequent rain periods.




2.2     Fade Mitigation Techniques




        Many research groups have investigated the use of fade countermeasures. It is
important for the system to stay in compensation configuration during the fade duration.
This means, users still can get the signal even though at that time the rain attenuation
happens. As a result the fade mitigation techniques (FMT) have been proposed. This
FMT can be divided into three main classes;
                                                                                         10


   •    Power control
   •    Signal Processing
   •    Diversity




2.2.1   Power Control




        The transmitter power is adjusted to compensate for change in signal attenuation.
For example; if the signal dropped about 10dB so the system must transmit at 10dB also
in order to compensate the change.




        The uplink is the critical portion of the connection; the connection is enhanced if
the uplink operates with an increased EIRP in rain (ULPC). There are two type of
ULPC;




   •    Closed loop ULPC – signal power is detected at the satellite and a control signal
        is sent back to earth station to adjust the power.


   •    Opened loop ULPC - The fade on the downlink signal is used to predict the
        likely fade level occurring on the uplink.




        Closed loop operation is always more accurate but is more expensive to
implement. It is due to the operations must always looping until the signal back to it
normal mode. Hence, most ULPC systems are, at present is open loop.
                                                                                         11


2.2.2   Signal Processing




        For this type of fade mitigation, an on board processing (OBP) have been
introduced. Where the OBP is used to translates the digital carriers arriving at the
satellite to base band for processing and onward transmission back to earth. For
example, when the rain attenuation occurs, the OBP will adjust the bandwidth so that all
users get the same bandwidth. It is doesn’t matter if the bandwidth is too small as long
as users still can use the service during that time.




        The use of OBP separates the uplink from the downlink and each part of the link
can be treated separately in developing a link budget.




2.2.3   Diversity




There are three types of diversity available. They are;


   •    Time diversity – it is only used when OBP are being used on the satellite.
        Additional slots in the TDMA frame can be assigned to the rain affected link so
        that the same signal can be sent at a slower rate; essentially lowering the
        bandwidth and raising the C/N.


   •    Frequency diversity – switch from high frequency to the lower frequency. For
        example; a rain affected Ku-band link could be switched to C band, which is not
        attenuated significantly by rain. This technique only can be done if the satellite
        operates in a number of frequency bands.
                                                                                              12



      •   Site diversity - A technique whereby two or more earth stations are located
          sufficiently far apart. Where or this technique, the signal will be divert to the
          earth station where it is uncorrelated with the rain effect. The paths through the
          rain that are uncorrelated and so the technique is more accurately described as
          Path diversity




2.3       Available Prediction Model




          There are a lots of fade duration models that was published by the researchers in
the recent years. These models are used to predict the fade duration of rain attenuation.
So as the purpose of this project, the comparison and analyze of the available models
will be made with the available rain data. Then the best model that suit with the
measured data will be adopted for used in Malaysia.




2.3.1     ITU-R Model




          ITU-R Model [1] is the newest prediction model that proposed by ITU-R. A few
reasons have been considered in order to develop this model [1]. Below are three main
reasons that have been considered for developing this model [1].
                                                                                            13


     •   For a variety of radio communication services, they required the information on
         the dynamic of outage events


     •   For the evaluation of parameters associated with the risk of failure to provide a
         certain quality and reliability of services, the probability of occurrences of fades
         of a certain duration must be known


     •   There is a need to provide engineering information for the calculation of fade
         duration




         According to [1], the model are consists of a log-normal distribution function for
long fades and a power-law function for short fades. The boundary between short and
long fades is given by the threshold duration Dt calculated in the model [1]. The power-
law model is valid for fade durations longer than 1 s. Fades of shorter duration do not
contribute significantly to total outage time.




         The following provides estimates of the parameters required for the model [1]
and finally defines for distribution functions, i.e. the occurrence probability P and the
exceedance probability (or fraction of time) F.




The model [1] is expected to be valid for duration longer than 1 s.
The following parameters are required as input to the model [1];




f:       frequency (GHz): 10-50 GHz
ϕ:       elevation angle (degrees): 5-60°
A:       attenuation threshold (dB)
                                                                                           14

The step by step calculation of the fade duration distribution is as follows;


Step 1: Calculate the mean duration D0 of the log-normal distribution of the fraction of
fading time due to fades of long duration, given that the attenuation is greater than A, as:


                               D0 = 80ϕ −0.4 f 1.4 A −0.39                           (1)


Step 2: Calculate the standard deviation ⌠ of the lognormal distribution of the fraction
of fading time due to fades of long duration as:


                               σ = 1.85 f −0.05 A −0.027                             (2)


Step 3: Calculate the exponent γ of the power-law distribution of the fraction of fading
time due to fades of short duration as:


                               γ = 0.055 f 0.65 A−0.003                              (3)


Step 4: Calculate the boundary between short and long fade durations, Dt, as:


                                              2
                               Dt = D0e p1σ       + p 2σ − 0.39
                                                                                     (4)


where;


                               p1 = 0.885γ − 0.814                                   (5)

                               p2 = −1.05γ 2 + 2.23γ − 1.61                          (6)


Step 5: Calculate the mean duration D2 of the log-normal distribution of the probability
of occurrence of fading events of long duration as:
                                                                                             15

                                              2
                                D2 = D0e −σ                                            (7)


Step 6: Calculate the fraction of time k due to fades of duration less than Dt as:


                                                                                −1
                             ⎡                      ⎛ ln( Dt ) − ln( D0 ) ⎞ ⎤
                             ⎢      D0 D2 (1 − γ )Q⎜                      ⎟⎥
                                                    ⎝          σ          ⎠⎥
                         k = ⎢1 +                                                      (8)
                             ⎢               ⎛ ln( Dt ) − ln( D 2) ⎞        ⎥
                                       Dt γQ⎜                      ⎟
                             ⎢
                             ⎣               ⎝          σ          ⎠        ⎥
                                                                            ⎦


where;


         Q:    standard cumulative distribution function for a normally distributed
               variable.


                                                         ∞   1
                                                    1     − x2

                                                    2π ∫
                                         Q( z ) =        e 2 dx                        (9)
                                                       z




Step 7: Calculate the probability of occurrence of fade events of duration d longer than
D given that attenuation a is greater than A as:

                                                                                     (10)
         For 1≤ D ≤ Dt         P(d > D|a > A) = D–γ


                                                         ⎛ ln( D) − ln( D2 ) ⎞
                                                        Q⎜                    ⎟
                                                     −γ  ⎝          σ         ⎠
         For D > Dt             P(d > D | a > A) = Dt ⋅                              (11)
                                                         ⎛ ln( Dt ) − ln( D2 ) ⎞
                                                        Q⎜                     ⎟
                                                         ⎝          σ          ⎠
Step 8: Calculate the cumulative probability of exceedance, i.e. the total fraction of fade
time due to fades of duration d longer than D:


                                                               1− γ
                                                    ⎡      ⎛D⎞ ⎤
         For 1≤ D ≤ Dt          F (d > D | a > A) = ⎢1 − k ⎜ ⎟ ⎥
                                                           ⎜D ⎟                        (12)
                                                    ⎢
                                                    ⎣      ⎝ t⎠ ⎥   ⎦
                                                                                           16


                                                              ⎛ ln( D) − ln( D0 ) ⎞
                                                             Q⎜                    ⎟
                                                                         σ         ⎠
       For D > Dt              F (d > D | a > A) = (1 − k ) ⋅ ⎝                         (13)
                                                              ⎛ ln( Dt ) − ln( D0 ) ⎞
                                                             Q⎜                     ⎟
                                                              ⎝          σ          ⎠


Step 9: If required, the total number of fades of duration d longer than D for a given
threshold A can be calculated from:


                       N(D, A) = P(d > D|a > A) x Ntot(A)                               (14)




Where D is the mean duration time of fade duration
The total fading time due to fades of duration d longer than D for the threshold A is:


                       T(d > D|a > A) = F(d > D|a > A) x Ttot(A)                        (15)


Where Ttot(A) is the total time the threshold A is exceeded and Ntot(A) is the total
number of fades exceeding the minimum duration of 1s. These parameters can be
obtained in the following way: Ttot(A) should be obtained from local data. If this long-
term statistic is not available, an estimate can be calculated from Recommendation ITU-
R P.618 [7]. In this case the procedure consists in calculating the CDF of total
attenuation, deriving the percentage of time the considered attenuation threshold A is
exceeded and then the associated total exceedance time Ttot(A) for the reference period
considered.




Once Ttot(A) has been obtained, Ntot(A) can be calculated as:

                                                          k 1− γ
                               N tot ( A) = Ttot ( A) ⋅       ⋅                         (16)
                                                          γ Dt1 − γ
                                                                                             17

        The above method [1] was tested against the Radio communication Study Group
3 fade duration data bank for frequencies between 11 and 50 GHz and for elevation
angles between 6° and 60°. The arithmetic mean of the logarithmic error (ratio of the
predicted to the measured fade duration at the same probability level) was found to be
30% for fade durations shorter than 10 s and between –25% and –80% for fade
durations longer than 10 s. As far as the standard deviation is concerned, it was found to
range between 80% and 150%, demonstrating the high natural variability of this
parameter.




2.3.2   Chris J. Gibbins / Kevin S. Paulson




        The model [2] is proposed to predict the system outages due the rain attenuation.
Where is, it presents two algorithms for estimating the distribution of the durations of
rain fade. According to [2], the distribution of the durations of rain events at different
intensities is more fundamental than distributions of link fade. An expression for the
average number of events per year of rain intensity greater than a give threshold has
been developed from rain duration data gathered in the South East UK over three years.




        As mentioned earlier, in this model [2], two mathematical models have been
considered. These models are the lognormal model and power law mode. The
lognormal model was chosen due to it fit to each of the distributions of durations with
given rain rates. The lognormal model as shown below;


                                         −1.76           (ln t d − 2) 2
                        N = 1.70 x10 R
                                     4
                                                 exp(−                  )             (17)
                                                       3.86 − 0.0409 R
                                                                                           18

where R is the rain rate, N represent of number of rain events per year and td is the
duration of rain rate.




        In order to develop this model [2], the lognormal model above had been
extended to provide an estimate number of rain fading events, using an analysis of fade
duration at 38 GHz over a 9 km path. The model [2] is based on the rainfall rate R
(mm/h) which gives rise to a given path attenuation, A, from the expression: A = k
Rα.d.r(dB); where k and a are constants obtained from ITU-R Rec.P.838 [8] and d is
the path length in km. The path length reduction factor r takes account of the fact that
rain is not uniformly distributed along the path. In developing the model, two
expressions for the path length reduction factor were considered, that in ITU-R
Rec.P.530 [9] and the RAL model for the path reduction factor developed from radar
data [10], in which r is given by the minimum of the following two expressions.


                         r = 1.35 + s(d) log R             and         r=1              (18)


        Where R is the rainfall rate and s(d) = 2d-0.053 – 2.25. For a given fade depth A,
in dB, the appropriate point rainfall RA can then be determined. In analogy with the path
length reduction factor, a similar time dilation factor is necessary to convert between the
durations experienced by a point rain rate measurement device, such as rain gauge, and
the duration of rain fade experienced by a link. Fade durations are longer than
equivalent point rain duration as the rain can interact with the link anywhere along its
length. A proportion of rain events will travel along the length of the link with the
prevailing wind and cause fade much longer duration than the rain duration measured at
a point. This duration effect was found to fit the following expression, (19);


                         t d = 273R −0.89 + (0.166 + 0.0194 R )t ' d                    (19)


where t’d is the fade duration experienced by the link.Using this procedure, the model
for rain rate durations was fitted to the 38 GHz fade data, with the best fit being
                                                                                                 19

provided by the RAL path reduction factor, to yield the following expression for the
number of fades NA exceeding a depth of A dB and duration of td seconds;


                                         [ln(273R A.39 + (0.166 + 0.0194 R A )t ' d −2] 2
                                                  0
        N A = 1.70 x10 4 R −1.76 exp(−                                                    )   (20)
                                                       3.86 − 0.0409 R A


        From this model [2], the average number of fading events per year can be
estimated; taking account of the fact that rain is generally not uniformly distributed
along a path, so using the path length reduction factor as a solution. It should be in mind,
however, that the above expression, (20) was derived from point rainfall rate
measurements. For practical link lengths, it may underestimate the number of fade
events exceeding a given duration and attenuation for the following reason. Rain cells
typically have diameters of the order of 2km. if such rain cell passes transversely across
a radio link, fade duration of certain period will occur. If however, the same rain cell
travels along the link, the durations of events with the same level of attenuation would
be somewhat longer than in the transverse case, depending on the length of the link and
the speed which the rain cell travels.




2.3.3   Kormanyos/ Lena Pedersen/ Cyril Sagot/ Janos Bito




        According to [3], for mobile operators it is very important to plan highly reliable
millimeter wave links. Where, there are several proposed methods for predicting rain
attenuation statistic. For example the International Telecommunication Union (ITU) has
issued a recommendation for rain attenuation prediction [9]. The method is clearly of
high quality, but it is still of interest to check the method and investigated a new
attenuation prediction method [3].
                                                                                           20

       The new method [3] is based on Moupfouma’s semiempirical rain intensity
distribution prediction [4]. The method given in [9] is valid for temperate zones, it
calculates attenuation distribution for 38 GHz in frequency and it also applies the
measured R0.01 value;


                                                                    b
                                      1 α
                                   ⎛ A0./01 + (k ⋅ L. ⋅ r )1 / α   ⎞
                                   ⎜ 1/ α
                        P ( Ai ) = ⎜                               ⎟ ⋅ 10 − 4⋅a         (21)
                                                           1/ α    ⎟
                                   ⎝ Ai + (k ⋅ L. ⋅ r )            ⎠


                                       1/ α
                          ⎛ A ⎞                    ⎡ ⎛ A ⎞1 / α ⎤
                        b=⎜ i ⎟
                          ⎜A ⎟                ⋅ ln ⎢1 + ⎜ i ⎟ ⎥                         (22)
                          ⎝ 0.01 ⎠                 ⎢ ⎜ A0.01 ⎟ ⎥
                                                   ⎣ ⎝       ⎠ ⎦



                                       1 − ( Ai / A0.01 )
                                                          1/ α

                        a = 1−                                                          (23)
                                 1 + 4.56 ⋅ ( Ai / A0.01 )
                                                             1.03 / α




                                                                      1 α
Where k, A, and r are taken from ITU recommendation [9]. A0.01 = k ⋅ R0./01 ⋅ L ⋅ r ,where
L and r are the path length and the path reduction factor. This prediction model [3] is
based on rain intensity prediction.




           Beside the rain attenuation distribution, fade duration and other dynamic
statistics are also important for mobile operators. They [3] have presented rain
attenuation rate of change statistic. In this contribution to evaluate the dynamics of rain
attenuation, the number of events and fade duration statistics have been determined for
links in Hungary, for the long link in Norway and for a short link in Ireland. Fade
duration statistics have been compiled for attenuation exceeding 4, 8, 12, 16 and 20 dB
levels and plotted graph shown the number of events for which duration exceeds
abscissa at the level given. As it was expected the number of events on longer links is
higher than on the shorter ones, and also the duration of fade events is longer. From the
analysis that being made, they found out that at 4dB level the number of events with
short duration (10-100 sec) is remarkably smaller in Hungary. At higher levels these
                                                                                         21

differences in number of fades disappear for long links. On the links events with long
duration (greater than 1000 sec) are presumably caused by melting snow on antennas.




2.4 Summary




       This proposed model will be based on the available prediction models that have
been stated as above. Where for the purpose of this project, to obtain the annual rain
fade distributions on line-of-sight from the 38GHz link profile and determine the
appropriate rain fade model to be adopted in Malaysia.
                                     CHAPTER III




                                  METHODOLOGY




3.1    Methodologies




       The methodologies of this project as shown in the flow chart in figure 3.1 below.
In the beginning, there are two tasks that need two do simultaneously. First task is to do
some literature reviews on the concept of the rain fade duration as well as to find out the
available of existing models that proposed by other researchers. This literature reviews
will help to understand in more details what fade durations and rain attenuations are.
Beside it can help to identify the comparison of the previous prediction methods that
have been proposed. So it can give some ideas to develop the empirical models
efficiently. The second task to do is study and mastering the Matlab software. In this
part, the main agenda here is how to make the programming. Since this project doesn’t
need the simulation, so it will based on programming only. For simplicity of the
analysis of the data, necessary graphs are recommended to be plotted.
                                                                                            23


                                               Start



                        Literature Reviews                 Mastering in Matlab
                                                             programming




                                   Analyisis of the rain data in
                                              UTM



                                  Identifying existing models [1]



                                   Obtain rain fade statistics [2]



                                  Result analysis and comparison
                                       between [1] and [2]



                                                End


                         Figure 3.1: Research methodology flow chart




       Then do analysis on available rain attenuation data in UTM campus. This
analyzing will help to know deeply about the rain attenuation. Hence from the analyzing,
the best value to determine the threshold can be identified. This threshold is used to
determine how many dB the signal attenuate. This is the most critical part of this
research, because once the threshold set wrongly then the incorrect result will get.




       After the threshold has been set, then proceed with programming in Matlab in
order to obtain rain fade statistic. At this stage, measured data will be extracted into
particular signal drops (for attenuation exceeding 1, 3, 6, 9, 12, 15, 18, 21 dB levels).
Once the data completed extracted, the number of events and fade duration statistics can
                                                                                            24

be determined by plotting graphs. These graphs then will be compared with the existing
models in the next stage.




       From the literature reviews and analysis have been made, we can identify the
best existing model that can be adopted in Malaysia. The model that has to choose must
perform well and has wide validity range with the locally measured data.




       Finally do result analysis and comparison. In this stage, tasks that have to do are
do analysis on the result and compare the result with available statistical models. And
finally determine the appropriate rain fade model to be adopted in Malaysia.




3.2    Data Collection




       The rain attenuation data collection can be divided into terrestrial and satellite
rain attenuation data. The terrestrial rain attenuation data was measured from an
experimental point-to-point microwave link operating at 38GHz. While the satellite rain
attenuation data was collected from Malaysia-East Asia Satellite (MEASAT).
MEASAT is a broadcasting satellite catering Direct-To-Home (DTH) broadcasting
services to the South East Asia region operating at Ku band (14/12GHz). But for this
project only data measured from terrestrial rain attenuation is concerned. The
availability of terrestrial rain attenuation data is for 1 year period from January 1, 1999
to December 31, 1999. The set-up of the terrestrial receiver is shown on Figure 3.
                                                                                        25




       Figure 3.2: Path profile for Ericson Microwave Link at 38GHz in Wireless
            Communication Centre (WCC) University Teknlologi Malaysia




       The experimental setup of the link consists of a transmitter and a receiver 350m
apart. The diameter of both antennas is 0.6m. The operating frequency is 38 GHz. The
link is applying horizontal polarization. The Automatic Gain Control (AGC) level (in
Volts) of the receiver is connected to a data acquisition system continuously. The signal
level is collected in one-second integration time. The signal level is then converted into
dBm for analysis. The 350m path length suggests that rain can be assumed homogenous
along the signal path. Thus no correction factor both horizontal and vertical is needed.
The experimental link setup located in Wireless Communication Center (WCC), UTM
Skudai. The data used is the signal level collected by the data acquisition system
throughout the year 1999. These rain attenuation data collected were analyzed to
produce cumulative distribution (CD) of rain attenuation data.




       In addition to the rain attenuation data collected, one-minute integration time of
rainfall data was also measured downloaded from TRMM satellite system. A total of
one year data were collected from January 2000 to February 2002 where the TRMM
data is centred at Skudai, Malaysia (1.473°, 03.745°).
                                                                                          26

Figure 3.3 below show the rain contour map in Peninsular Malaysia;




Figure 3.3: Rain Rate Contour Map (exceeding depicted rain intensity at 0.01 % of time,
                              R0.01) in Peninsular Malaysia




3.3    Data Extractions




       As mentioned previously, collected data will be extracted in order to obtain
number of events per year and also fade duration statistics. Matlab software is used to
extract and manipulate these data. Below are some Matlab programming on how the
data are manipulated.
                                                                                              27

         First step to do is import data from text file (*.txt) into Matlab. This importing
data can be done by using textread function. The programming code to read text file as
below;




                %read data from text file
                [voltan] = textread('nov.txt','%*s %*s %*s %f');

                         Figure 3.4: read data from text file




         Second step is converting read data from AGC values (volt) to dBm values. This
can be performed by using this formula;


                                   A = (40 × V ) − 120                                 (24)


where is;
         A = Attenuation (dBm)
         V = AGC value (volt)


And by using Matlab programming, the syntax as below can be writing;



                  %converts AGC values to dBm
                  voltage = 40*voltan-120;

                   Figure 3.5: Converts AGC (volts) values to dBm




         Third step is set the threshold value into the programming. For this project, the
value of threshold chooses is -25.5dB. Where is, the threshold value can be determined
                                                                                            28

from (25). After threshold is set, then compiled fade duration statistics for attenuation
exceeding the 1, 3, 6, 9, 12, 15, 18, 21 dB levels and plotted.


                                                1 α
                                       A = k ⋅ R0./01                                (25)


where k and α are taken from ITU recommendation [9]




     %set threshold value = -25.5dB
     threshold = -25.5;

     while x<bil
       k=k+1;
       if voltage(k) < threshold
       if voltage(k) <= voltage(k-1)
          c=c+1;
          if (voltage(k)-threshold)< v0          %attenuation exceeding 1db
             c0=c0+1;
          else
          end
          if (voltage(k)-threshold)< v1          %attenuation exceeding 3db
             c1=c1+1;
          else
          end
             .
             .
             .
             .
       end
       end
     end

             Figure 3.6: Compile fade duration statistic for attenuation
                               exceeding threshold
                                                                                            29

          Finally save the compiled fade duration statistics into particular file in order to
be plotted and manipulated later. This save file can be writing by using save function.




      %save file
      y0=[volt0',masa0'];
      save('1db.txt','y0','-ascii','-append') %save file for attenuation exceeding 1dB
      save('1209.txt','y0','-ascii','-append') %save file through month of events
      save('overall.txt','y0','-ascii','-append') %save all fade duration statistics here
      y1=[volt1',masa1'];
      save('3db.txt','y1','-ascii','-append') %save file for attenuation exceeding 3dB
      save('1209.txt','y1','-ascii','-append') %save file through month of events
      save('overall.txt','y1','-ascii','-append') %save all fade duration statistics here
                       .
                       .
                       .

            Figure 3.7: Save fade duration statistics data to corresponding
                                         files




3.4       Existing Rain Models Programming




          In this topic, it will discuss how to develop the programming for the existing
rain models that mentioned earlier. This programming must be done in order to make
comparison between measured data with the published rain models. After the
comparison has been made, the best prediction model can be determined and will be
adopted for the prediction of fade duration in Malaysia.


          As mentioned in previous chapter only three models are considered for this
project. Those models are;
                                                                                         30


     •   ITU-R Model [1]
     •   Chris J Gibbins and Kevin S Paulson [2]
     •   Zsolt Kormanyos/ Lena Pedersen/ Cyril Sagot/ Janos Bito [3]




3.4.1    ITU-R Model Programming




         As discussed previously, this model [1] is consisting of a log-normal distribution
function for long fades and power-law function for short fades. The boundary between
short and long fades is given by the threshold duration Dt.




There are three parameters are required as input for the model [1];


f:       frequency (GHz): 10-50 GHz
ϕ:       elevation angle (degrees): 5-60°
A:       attenuation threshold (dB)


         For the purpose of this project, the frequency used is 38GHz, elevation angle
used is 38.98° (this value got from MEASAT) and attenuation threshold is -25.5dB.
First step to do is set all these three values into the Matlab programming. Followed by
develop all the equations involved in model [1] into Matlab. Then simulate the model
and plotting graph.




                  f=38;            %frequency GHz
                  e=0.6803;        %elevation angle degress
                  a=26;            %attenuation threshold (dB)          .

                      Figure 3.8: Set parameters with correct values
                                                                               31



d0 = 80 * 38.98^(-0.4) * 38^1.4 * 26^(-0.39);       %equation (1)
sigma = 1.85 * 38^(-0.05) * 26^(-0.027);            %equation (2)
y = 0.055 * 38^0.65 * 26^(-0.003);                  %equation (3)
p1 = 0.885*y - 0.814;                               %equation (5)
p2 = (-1.05)*y^2 + 2.23*y -1.61;                    %equation (6)

dt = d0 * exp(p1*(sigma^2) + p2*sigma - 0.39);      %equation (4)
d2 = d0*exp(-(sigma^2));                            %equation (7)

q1 = (log(dt) - log(d0)) / sigma;
q2 = (log(dt) - log(d2)) / sigma;

denom1 = (0.661*q1) + (0.339*sqrt((q1^2)+5.51)); %equation (9) Q functions
denom1 = denom1*sqrt(2*pi);
denom2 = (0.661*q2) + (0.339*sqrt((q2^2)+5.51));
denom2 = denom2*sqrt(2*pi);
Q1 = (1/denom1)* exp(-(q1^2) / 2);               %equation (9) Q functions
Q2 = (1/denom2)* exp(-(q2^2) / 2);

k = (1 + ((sqrt(d0*d2) * (1-y) * Q1) / (dt * y * Q2)))^(-1); %equation (8)

            Figure 3.9: Matlab programming for corresponding equations




if masa3(n)<dt                                      %for 1<D<Dt
P(n)= masa3(n)^(-(y));                              %equation (10)
else
q3 = (log(masa3(n)) - log(d2)) / sigma;             %for D>Dt
denom3 = (0.661*q3) + (0.339*sqrt((q3^2)+5.51));
denom3 = denom3*sqrt(2*pi);
Q3 = (1/denom3)* exp(-(q3^2) / 2);                  %Q functions
P(n)= (dt^(-(y)))*(Q3/Q2);                          %equation (11)
end

N(n)=P(n)*event3(n);                                %total number of fade
                                                    %duration; equation (14)

      Figure 3.10: Matlab programming for total number of fade durations
                                                                                           32

3.4.2   Chris J Gibbins and Kevin S Paulson Model Programming




        This model [2] has considered two mathematical models – the log-normal model
and power-law model. The log-normal was chosen due to it fit to each of the
distributions of durations with given rain rates. The model [2] is based on the rainfall
rate R (mm/h) which gives rise to a given path attenuation, A from the expression: A =
k Rα.d.r(dB); where k and a are constants obtained from ITU-R Rec.P.838 [8] and d is
the path length in km. Take notes, for this project path length reduction factor, r is
neglected due to the length from transmitter and receiver is short only 350m.


        As usual first step to do is develop Matlab programming for all equations
involved to this model [2]. After that, simulate the model and plotting graph.




   %the number of fade exceeding threshold,A; equation (9)
   event(1)=1.7*(10^4)*(R^(-1.76))* exp(-(log(td1)-2)^2/(3.86-(0.0409*R)));

             Figure 3.11: Matlab programming for number of fades NA
                                                                                           33

3.4.3   Zsolt Kormanyos/ Lena Pedersen/ Cyril Sagot/ Janos Bito Model
        Programming




        The model [3] is based on Mopfouma’s semiemprical rain intensity prediction
[4]. Where is, the model [3] is based on rain intensity prediction and it also valid for
temperate zones. The Matlab programming codes as stated below.




 b=(((Ai/A)^(1/alfa))-1)*log((1+((Ai/A)^(1/alfa))));                    %equation (22)
 a=1-((1-((Ai/A)*(1/alfa)))/(1+(4.56*((Ai/A)^(1.03/alfa)))));           %equation (21)

 %probability numbers of fades duration; equation (20)
 P=((((A^(1/alfa))+((k*L*r)^(1/alfa)))/((Ai^(1/alfa))+((k*L*r)^(1/alfa))))^b)*(10^(-
 4*a))

           Figure 3.12: Matlab programming for probability numbers of fades
                                      duration




3.5     Comparison




        Finally do comparison with measured data and these three models. This
comparison can be done by plotting the graph for each models and measured data. From
this graph, the appropriate rain fade model can be determined where is the graph is
closely to the measure data graph. Below is some Matlab programming codes on how to
do this comparison.
                                                                                      34


%read fade duration statistic data (measured data)
[masa, db] = textread('overall-time.txt','%f %f');
itutrydt                                      %call Itu-R model [1]
empirical                                     %call gibbins model [2]
bito                                          %call bito model [3]
figure(2);
loglog(masa,db,time2,N2,time,N,masa1,event)                         %plot log graph
legend('measured data','Bito model','Itu-r model','Paulson model') %legends
xlabel('Duration [sec]')                                            %x-axis label
ylabel('No of events exceeding abscissa')                           %y-axis label
title('Anuual Fade duration in UTM 99 (38GHz)')                     %graph title

      Figure 3.13: Matlab programming for comparison among measure data
                           and studied rain fade models
                                      CHAPTER IV




                                        RESULTS




4.1     Introduction




        This chapter will discuss the results that obtained from the project that has been
studied. Where is, it consist of two section. First section is how to interpret the
measured data into fade duration statistic. Second section is the comparison that being
made among fade duration statistic (measured data) with studied models.




4.2     Measured Data Interpretation




4.2.1   Power Received
                                                                                        36

       Figure 4.1 and 4.2 below shows the differences between signal attenuation on
clear weather and signal attenuation on rainy weather. On the clear day, the signal
received at receiver is above the attenuation threshold, -25.5 dB. So on this weather the
satellite and telecommunication systems are free from any outage due to rain
attenuation. But on the rainy weather the signal received at receiver are below the
attenuation threshold, -25.5 dB. This happens due to interference cause by raindrops
and electromagnetic signal traveling through the atmosphere. When this phenomenon
occurs, the transmission is weakened by absorption and scattering of the signal by
raindrops. As a result any telecommunication and satellite systems that operate during
this duration will experience outage due to rain attenuation. The more signal attenuated
below threshold, the more system will experience the outage. Thus, the use of suitable
compensation techniques such as FMT will be needed to maintain reliable system
operation. In order to use the suitable compensation techniques, one must know the
information of fade duration statistics. This fade duration statistics can be obtained from
studying the number and duration the signal received at receiver below the attenuation
threshold.




              Figure 4.1; Received power level time series on clear weather
                                                                                     37




              Figure 4.2: Received power level time series on rainy weather




4.2.2   Data Analyzed




        Measure data will be converted first from AGC (V) value to decibels (dBm)
values before analysis can be preceded. As mentioned previously, power received
(dBm) can be obtained from equation below;


               Power received (dBm) = 40 * V -120                                 (26)


        Table 4.1 shows the sample of measured data that been converted from AGC
(V) values to decibel (dBm) values.
                                                                                     38



                      Table 4.1: Convert AGC (V) to decibel (dBm)




       After converting have been done, the next step plotting signal attenuation graph
in order to ease in analyzing the measured data.
                                                                                           39




                         Figure 4.3: Power received signal attenuation




       Figure 4.4 shows how the fade durations have been analyzed. For example, the
fade duration statistic have been compiled for attenuation exceeding the 1 and 2dB
levels (take notes; for the purpose of this project the exceeding levels are divided for
attenuation exceeding the 1, 3, 6, 9, 12, 15, 18, 21 dB levels. Attenuation exceeding 1
and 2dB levels only shows for example only. But the process is still the same.)
                                                                                                                                  40


                           -25


                          -25.5


                           -26
   Power Received [dBm]

                                                                             3 sec                    9 sec

                          -26.5


                           -27
                                                                                                    2 sec
                          -27.5


                           -28


                          -28.5
                                  13 49 58




                                             13 50 03




                                                                  13 50 08




                                                                                         13 50 13




                                                                                                            13 50 18




                                                                                                                       13 50 23
                                                                             Time [Hr:min:sec]


                                                         Figure 4.4: Analysis on fade duration




                                                        Table 4.2: Analysis on fade duration




                           Table 4.2 and Figure 4.4 show how the fade duration statistics have been
analyzed. First let’s look at attenuation exceeding 1dB level. There are two events
where the power received signal drops exceeding 1dB level. First event occurred at
about 13:50:08 hours and ended about 13:50:11 hours, fade duration taken
approximately 3 sec. While the second event for exceeding 1dB level is about started at
13:50:12 and ended at about 13:50:21 where is, the fade duration taken approximately 9
sec.
                                                                                            41

        There is only one event for attenuation exceeding 2dB level. This event occurred
about at 13:50:15 and fade duration taken approximately 2 seconds. From this
information, the number of events longer than abscissa can be obtained. This is shown
in Table 4.2. Where is for attenuation exceeding 1dB level, there are two events number
of fades longer than 1 sec and only one event number of fade longer that 5 sec. While
no event occur for fade duration longer than 10 sec. For attenuation exceeding 2dB
level, only one event occurs at fade duration longer than 1sec. This analysis processes
will be carried on to other data with different durations and dB levels.




4.3     Result and Analysis




4.3.1   Obtain Rain Fade Statistics




        After all measured data have been processed; the next task is do analysis and
comparison for each data processed. This task can be done by plotting graphs. Where
from this graph, information on fade duration statistics can be obtained more precisely
and details. Table 4.3 shows the number of events for which duration exceeds abscissa
at 1, 3, 6, 9, 12, 15, 18 and 21 dB levels. From this table known that when the
attenuation is increased the time duration will decrease. This is due that the heavy rains
which cause higher attenuation level only happen in short duration. It is because the
higher attenuation depending on rain drops size and also the rain intensity. Then all
information represents in this table will be plotted to graph in order to get the details
scenario of the fade duration statistics.
                                                                                             42

Table 4.3: Number of events for which duration exceeds abscissa at 1, 3, 6, 9, 12, 15, 18
                                     and 21 dB levels




       Figure 4.5 shows the number of events grouped by exceeding levels versus
duration (sec). As it was expected the number of events of attenuation exceeding 1dB
level is higher than other levels, and also the duration of fade events is longer. This is
due for attenuation exceeding 21dB level; it needs bigger rain intensity and longer
raining time compare to attenuation exceeding 1dB level.
                                                                                     43




                 Figure 4.5: Fade duration grouping by attenuation levels




       Figure 4.6 shows the number of fade events grouped by months. As expected,
August, September, October and November are months that have higher number of fade
events compare to other months. This is due to monsoon season during these 4 months
in Malaysia. Where is, in monsoon season the intensities of rain are bigger than normal
season and the rain drop size also bigger. So no wonder during this season, the number
of fade events is higher and the fade durations are longer too.
Table 4.4: Number of events for each month for one year
                                                                                       45




                    Figure 4.6: Fade duration grouping by months




4.3.2 Comparison




       Finally comparison among measured data and available rain models have been
made in order to determine the best model that suit with locally measured data to be
adopted as prediction model in Malaysia.
                                                                                        46

                     Table 4.5: Fade duration statistics information




       Table 4.5 above shows the fade duration statistics information. This table
represented the number of fade events which exceeds abscissa per year. The information
of this fade duration statistics will be transferred to graph in order to make comparison
with studied models. Figure 4.7 below shows the comparison among the available rain
models with fade duration statistics that we obtained previously.
                                                                                        47




                 Figure 4.7: Comparison among existed rain models with
                                     measured data




       From Figure 4.7 above, ITU-R rain model [1] obviously have wide validity
range and performed very well with the locally measured data compare to Paulson
model [2] and Bito model [3]. It is because; ITU-R model has used wide range of rain
database in order to develop the model. So as a result it suit to any climate around of the
world. Besides, ITU-R model also depends on local data parameters such as elevation
angle, frequency being used and also the local rain rate.




       The second best model perform well with locally measured data is Bito model.
This is because Bito model only used to predict the rain fade duration for temperate
climate only, but the studied area is in extreme climate where is Malaysia received rain
throughout the year. This model can still be used in Malaysia but needed some
                                                                                       48

modification of the coefficients of this model. Paulson model not perform very well
because this model is developed by using UK rain database only. Most of the
coefficients from this model cannot be used in Malaysia. Besides, this model depends
on the length of the link and the speed with which the rain cell travels.




       So as a result, the ITU-R model is the appropriate rain fade model to be adopted
in Malaysia as a rain fade prediction model.
                                      CHAPTER V




                                    CONCLUSSION




5.1    Conclusions




       The conclusion that can be made from this project is the rain fade duration
statistics can be obtained from measured data. Where is, from locally measure data,
these data have been interpreted into number of groups of attenuation exceeding given
threshold. After the data have been interpreted, then do analysis on that data and obtain
the rain fade duration statistics for one year duration. Finally, the number of events per
year can be estimated from these measured data.




       Secondly, ITU-R prediction model [1] is the best model that can be adopted for
Malaysia climate. This can be proved from observation and comparison that being made
previously. Besides, the ITU-R model is updated regularly for every two years by using
more rain database. So no wonder ITU-R model becomes a global model that suit to any
climates around the world. It is because ITU-R model is dependently on local
parameters such as rain rate, frequency used and elevation angle.
                                                                                          50

          This prediction model is important in system design especially to have flexible
and broadband feeder network. As we know, nowadays all telecommunication systems
are based on bandwidth demand. So this prediction model will help the service provider
to provide best service during raining day.




5.2       Future Work




          From this project, there are three suggestions that I can suggest in order to
enhance this prediction models. They are;




      •   Proposed for rain fade satellite measurement. It is because this project is based
          on line-of-sight measurement.
      •   Analysis with different frequency. Instead of using 38GHz as frequency, why
          not use other frequencies especially Ku and Ka band that usually being used in
          satellite and telecommunication systems.
      •   Obtain new Fade Mitigation Techniques (FMT)
                                REFERENCES




[1] ITU-R P.1623-1, “Prediction method of fade dynamics on Earth-space paths”,
   ITU, Geneva, 2005


[2] Paulson, K.S.; Gibbins, C.J.; “Rain models for the prediction of fade duration at
   milimetre wavelengths”, IEEE Journal, Volume 147, Issue 6, Dec. 2000
   Page(s):431 – 436


[3] Zsolt Kormayos, Lena Pedersen, Cyril Sagot, Janos Bito; “Rain attenuation and
   fade duration statistic at 38 GHz derived from long term radio link measurement
   in Hungary, Norway and Ireland”, AP2000, Davos, 13 April 2000


[4] F. Moupfouma and L. Martin, “Point rainfall rate cumulative distribution
   function valid at various locations,” Electronic Letters, vol. 29, no. 17, pp. 1503-
   1505, 1993


[5] M.M.J.L. van de Kamp; “Short-term prediction of rain attenuation using two
   samples”, Electronic Letters, vol. 38, no. 23, pp. 1476-1477, 7th November 2002


[6] R. Singliar, J. Din, L. Csurgai, A.R. Tharek, P. Horvath and J. Bito,
   “Comparison of 38 GHz rain fade dynamics between Malaysia and Hungary”,
   15th IST Mobile & Wireless Communication Summit Myconos 4-8 June 2006
                                                                                52

[7] ITU-R P.618-6, “Propagation data and prediction methods required for the
   design of earth-space telecommunication systems”, ITU, 1999


[8] ITU-R P.838-6, “Specific attenuation model for rain for use in prediction
   methods”, ITU, 1999


[9] ITU-R P.530-8, “Propagation data and prediction method required for the design
   of terrestrial line of sight systems”, ITU, 1999


[10] J.W.F. Goddard and M. Thurai, “Radar derived path reduction factors for
   terrestrial systems,” Proc. Tenth International Conference on Antenna and
   Propagation, ICAP’ 97, 14-17 April 1997, Edinburg UK, pp. 2.218-2.221
APPENDIX A




FLOW CHART
                                                                                54




                           APPENDIX A




    FLOW CHART FADE DURATION STATISTICS PROGRAMMING




                        Start


                    Set threshold



               Read measured data from
                      text file


               Convert AGC (V) to dBm
                        value




                        A<
                     threshold




                        A=               Yes
                       1dB?


                                                Count fades duration time
                      No                       Save data into particular file




D                          B
                                                   55



D    B



     A=     Yes
    3dB?


    No             Count fades duration time
                  Save data into particular file




     A=     Yes
    6dB?


    No             Count fades duration time
                  Save data into particular file




     A=     Yes
    9dB?


    No             Count fades duration time
                  Save data into particular file




     A=     Yes
    12dB?


    No             Count fades duration time
                  Save data into particular file




D    C
                                                   56



D    C



     A=     Yes
    15dB?


    No             Count fades duration time
                  Save data into particular file




     A=     Yes
    18dB?


    No             Count fades duration time
                  Save data into particular file




     A=     Yes
    21dB?


    No             Count fades duration time
                  Save data into particular file
    APPENDIX B




PROGRAMMING CODES
                                                                                  58




                                  APPENDIX B




Fade Duration Statistic (Measured Data)



[voltan] = textread('dec.txt','%*s %*s %*s %f');  %read data from text file
voltage = 40*voltan-120;                          %convert AGC values to dBm
bil = length(voltage);
bil=bil-1;
threshold = -25.5;                                %set threshold
x=0;
k=1;
c=0;c0=0;c1=0;c2=0;c3=0;c4=0;c5=0;c6=0;c7=0;
v0=-1;v1=-3;v2=-6;v3=-9;v4=-12;v5=-15;v6=-18;v7=-21;
n0=1;n1=1;n2=1;n3=1;n4=1;n5=1;n6=1;n7=1;
b0=1;b1=1;b2=1;b3=1;b4=1;b5=1;b6=1;b7=1;
while x<bil
   k=k+1;
   if voltage(k) < threshold                %Attenuation < threshold
   if voltage(k) <= voltage(k-1)            %Attenuation(k) <= Attenuation(k-1)
      c=c+1;
      if (voltage(k)-threshold)< v0          %Attenuation exceeding 1dB
         c0=c0+1;
      else
      end
      if (voltage(k)-threshold)< v1         %Attenuation exceeding 3dB
         c1=c1+1;
      else
      end
      if (voltage(k)-threshold)< v2         %Attenuation exceeding 6dB
         c2=c2+1;
      else
      end
      if (voltage(k)-threshold)< v3         %Attenuation exceeding 9dB
         c3=c3+1;
      else
      end
      if (voltage(k)-threshold)< v4         %Attenuation exceeding 12dB
         c4=c4+1;
                                                                 59

  else
  end
  if (voltage(k)-threshold)< v5    %Attenuation exceeding 15dB
     c5=c5+1;
  else
  end
  if (voltage(k)-threshold)< v6    %Attenuation exceeding 18dB
     c6=c6+1;
  else
  end
  if (voltage(k)-threshold)< v7    %Attenuation exceeding 21dB
     c7=c7+1;
  else
  end

else

  if (voltage(k)-threshold)<= v0   %Attenuation exceeding 1dB
     c0=c0+1;
     if k > bil
        masa0(n0) = c0;
        volt0(b0)= -1;
        c1=0;
        n0=n0+1;
        b0=b0+1;
     end
  else
     if c0 == 0
     else
     masa0(n0) = c0;
     volt0(b0)= -1;
     c0=0;
     n0=n0+1;
     b0=b0+1;
     end
  end

  if (voltage(k)-threshold)<= v1   %Attenuation exceeding 3dB
     c1=c1+1;
     if k > bil
        masa1(n1) = c1;
        volt1(b1)= -3;
        c2=0;
        n1=n1+1;
        b1=b1+1;
     end
                                                              60

else
   if c1 == 0
   else
   masa1(n1) = c1;
   volt1(b1)= -3;
   c1=0;
   n1=n1+1;
   b1=b1+1;
   end
end

if (voltage(k)-threshold)<= v2   %Attenuation exceeding 6dB
   c2=c2+1;
   if k > bil
      masa2(n2) = c2;
      volt2(b2)= -6;
      c3=0;
      n2=n2+1;
      b2=b2+1;
   end
else
   if c2 == 0
   else
   masa2(n2) = c2;
   volt2(b2)= -6;
   c2=0;
   n2=n2+1;
   b2=b2+1;
   end
end

if (voltage(k)-threshold)<= v3   %Attenuation exceeding 9dB
   c3=c3+1;
   if k > bil
      masa3(n3) = c3;
      volt3(b3)= -9;
      c4=0;
      n3=n3+1;
      b3=b3+1;
   end
else
   if c3 == 0
   else
   masa3(n3) = c3;
   volt3(b3)= -9;
   c3=0;
                                                               61

  n3=n3+1;
  b3=b3+1;
  end
end

if (voltage(k)-threshold)<= v4   %Attenuation exceeding 12dB
   c4=c4+1;
   if k > bil
      masa4(n4) = c4;
      volt4(b4)= -12;
      c5=0;
      n4=n4+1;
      b4=b4+1;
   end
else
   if c4 == 0
   else
   masa4(n4) = c4;
   volt4(b4)= -12;
   c4=0;
   n4=n4+1;
   b4=b4+1;
   end
end

if (voltage(k)-threshold)<= v5   %Attenuation exceeding 15dB
   c5=c5+1;
   if k > bil
      masa5(n5) = c5;
      volt5(b5)= -15;
      c6=0;
      n5=n5+1;
      b5=b5+1;
   end
else
   if c5 == 0
   else
   masa5(n5) = c5;
   volt5(b5)= -15;
   c5=0;
   n5=n5+1;
   b5=b5+1;
   end
end

if (voltage(k)-threshold)<= v6   %Attenuation exceeding 18dB
                                                                 62

     c6=c6+1;
     if k > bil
        masa6(n6) = c6;
        volt6(b6)= -18;
        c7=0;
        n6=n6+1;
        b6=b6+1;
     end
  else
     if c6 == 0
     else
     masa6(b6) = c6;
     volt6(b6)= -18;
     c6=0;
     n6=n6+1;
     b6=b6+1;
     end
  end

  if (voltage(k)-threshold)<= v7   %Attenuation exceeding 21dB
     c7=c7+1;
     if k > bil
        masa7(n7) = c7;
        volt7(b7)= -21;
        c8=0;
        n7=n7+1;
        b7=b7+1;
     end
  else
     if c7 == 0
     else
     masa7(n7) = c7;
     volt7(b7)= -21;
     c7=0;
     n7=n7+1;
     b7=b7+1;
     end
  end

end
else                               %Attenuation > threshold

  if c0==0                         %Attenuation exceeding 1dB
  else
  masa0(n0) = c0;
  volt0(b0)= -1;
                                                63

c0=0;
n0=n0+1;
b0=b0+1;
end
if c1==0          %Attenuation exceeding 3dB
else
masa1(n1) = c1;
volt1(b1)= -3;
c1=0;
n1=n1+1;
b1=b1+1;
end
if c2 == 0
else              %Attenuation exceeding 6dB
masa2(n2) = c2;
volt2(b2)= -6;
c2=0;
n2=n2+1;
b2=b2+1;
end
if c3 == 0
else              %Attenuation exceeding 9dB
masa3(n3) = c3;
volt3(b3)= -9;
c3=0;
n3=n3+1;
b3=b3+1;
end
if c4 == 0
else              %Attenuation exceeding 12dB
masa4(n4) = c4;
volt4(b4)= -12;
c4=0;
n4=n4+1;
b4=b4+1;
end
if c5 == 0
else              %Attenuation exceeding 15dB
masa5(n5) = c5;
volt5(b5)= -15;
c5=0;
n5=n5+1;
b5=b5+1;
end
if c6 == 0
else              %Attenuation exceeding 18dB
                                                                                     64

    masa6(n6) = c6;
    volt6(b6)= -18;
    c6=0;
    n6=n6+1;
    b6=b6+1;
    end
    if c7 == 0
    else                                      %Attenuation exceeding 21dB
    masa7(n7) = c7;
    volt7(b7)= -21;
    c7=0;
    n7=n7+1;
    b7=b7+1;
    end
  end

  x=x+1;
end

%save file
y0=[volt0',masa0'];
save('1db.txt','y0','-ascii','-append')       %save file for attenuation exceeding 1dB
save('1209.txt','y0','-ascii','-append')      %save file through month of events
save('overall.txt','y0','-ascii','-append')   %save all fade duration statistics here
y1=[volt1',masa1'];
save('3db.txt','y1','-ascii','-append')       %save file for attenuation exceeding 3dB
save('1209.txt','y1','-ascii','-append')      %save file through month of events
save('overall.txt','y1','-ascii','-append')   %save all fade duration statistics here
y2=[volt2',masa2'];
save('6db.txt','y2','-ascii','-append')       %save file for attenuation exceeding 6dB
save('1209.txt','y2','-ascii','-append')      %save file through month of events
save('overall.txt','y2','-ascii','-append')   %save all fade duration statistics here
y3=[volt3',masa3'];
save('9db.txt','y3','-ascii','-append')       %save file for attenuation exceeding 9dB
save('1209.txt','y3','-ascii','-append')      %save file through month of events
save('overall.txt','y3','-ascii','-append')   %save all fade duration statistics here
y4=[volt4',masa4'];
save('12db.txt','y4','-ascii','-append')      %save file for attenuation exceeding 12dB
save('1209.txt','y4','-ascii','-append')      %save file through month of events
save('overall.txt','y4','-ascii','-append')   %save all fade duration statistics here
y5=[volt5',masa5'];
save('15db.txt','y5','-ascii','-append')      %save file for attenuation exceeding 15dB
save('1209.txt','y5','-ascii','-append')      %save file through month of events
save('overall.txt','y5','-ascii','-append')   %save all fade duration statistics here
y6=[volt6',masa6'];
save('18db.txt','y6','-ascii','-append')      %save file for attenuation exceeding 18dB
                                                                                        65

save('1209.txt','y6','-ascii','-append')      %save file through month of events
save('overall.txt','y6','-ascii','-append')   %save all fade duration statistics here
y7=[volt7',masa7'];
save('21db.txt','y7','-ascii','-append')      %save file for attenuation exceeding 21dB
save('1209.txt','y7','-ascii','-append')      %save file through month of events
save('overall.txt','y7','-ascii','-append')   %save all fade duration statistics here




Calculate k and α value


kh=0.263;kv=0.233;
ah=0.979;av=0.963;
elevation=38.98;
t=45;
R=120;
L=0.30132;
r=1;
k=(kh+kv+((kh-kv)*(cos (elevation))^2*(cos(2*t))))/2;
alfa=((kh*ah)+(kv*av)+(((kh*ah)-(kv*av))*(cos(elevation))^2*(cos(2*t))))/(2*k);
Attenuation=k*(R^alfa)*L*r




ITU-R Rain Model


f=38;                                         %frequency GHz
e=0.6803;                                     %elevation angle degress
a=26;                                         %attenuation threshold (dB)

d0 = 80 * 38.98^(-0.4) * 38^1.4 * 26^(-0.39);        %equation (1)
sigma = 1.85 * 38^(-0.05) * 26^(-0.027);             %equation (2)
y = 0.055 * 38^0.65 * 26^(-0.003);                   %equation (3)
p1 = 0.885*y - 0.814;                                %equation (5)
p2 = (-1.05)*y^2 + 2.23*y -1.61;                     %equation (6)

dt = d0 * exp(p1*(sigma^2) + p2*sigma - 0.39);       %equation (4)
d2 = d0*exp(-(sigma^2));                             %equation (7)

q1 = (log(dt) - log(d0)) / sigma;
q2 = (log(dt) - log(d2)) / sigma;
                                                                                  66

denom1 = (0.661*q1) + (0.339*sqrt((q1^2)+5.51)); %equation (9) Q functions
denom1 = denom1*sqrt(2*pi);
denom2 = (0.661*q2) + (0.339*sqrt((q2^2)+5.51));
denom2 = denom2*sqrt(2*pi);
Q1 = (1/denom1)* exp(-(q1^2) / 2);               %equation (9) Q functions
Q2 = (1/denom2)* exp(-(q2^2) / 2);

k = (1 + ((sqrt(d0*d2) * (1-y) * Q1) / (dt * y * Q2)))^(-1); %equation (8)

[masa3,event3] = textread('overall-time.txt','%f %f');      %read measured data
total = length(masa3);
bil=total;
x=0;
n=1;
while x<bil
if masa3(n)<dt                                        %for 1<D<Dt
P(n)= masa3(n)^(-(y));                                %equation (10)
else
q3 = (log(masa3(n)) - log(d2)) / sigma;               %for D>Dt
denom3 = (0.661*q3) + (0.339*sqrt((q3^2)+5.51));
denom3 = denom3*sqrt(2*pi);
Q3 = (1/denom3)* exp(-(q3^2) / 2);                    %Q functions
P(n)= (dt^(-(y)))*(Q3/Q2);                            %equation (11)
end
F(n)=(1 - (k * ((masa3(n)/dt)^(1-y))));

N(n)=P(n)*event3(n);                                %total number of fade
time(n)=masa3(n);                                   %duration; equation (14)
n=n+1;
x=x+1;
end
y1=[time',N'];
loglog(time,N)                                      %plot ITU-R rain model




Chris J Gibbins and Kevin S Paulson Rain Model


R=1.2;
td=10;
x=0;
n=2;
td1=10;
                                                                                      67

%the number of fade exceeding threshold,A; equation (9)
event(1)=1.7*(10^4)*(R^(-1.76))* exp(-(log(td1)-2)^2/(3.86-(0.0409*R)));
masa1(1)=1;

while x<400
event(n)=1.7*(10^4)*(R^(-1.76))* exp(-(log(td)-2)^2/(3.86-(0.0409*R)));
masa1(n)=td;
x=x+1;
td=td+(10);
n=n+1;
end

loglog(masa1,event)                                  %plot Gibbins rain model




Zsolt Kormanyos/ Lena Pedersen/ Cyril Sagot/ Janos Bito Rain Model


atten1                               %call k and α functions
Ai=1;                                %Attenuation exceeding threshold in dB
A=Attenuation;
b=(((Ai/A)^(1/alfa))-1)*log((1+((Ai/A)^(1/alfa))));
a=1-((1-((Ai/A)*(1/alfa)))/(1+(4.56*((Ai/A)^(1.03/alfa)))));

P=((((A^(1/alfa))+((k*L*r)^(1/alfa)))/((Ai^(1/alfa))+((k*L*r)^(1/alfa))))^b)*(10^(-
4*a))
Pnew = P*100;

[masa2,event2] = textread('overall-time.txt','%f %f');
total2 = length(masa2);
bil2=total2;
x=0;
n=1;

while x<bil2
N2(n)=Pnew*event2(n);                 %number of fade durations
time2(n)=masa2(n);                    %total time durations
n=n+1;
x=x+1;
end

loglog(time2,N2)                      %plot bito rain model
                                                                                      68

Comparison and Analysis


%read fade duration statistic data (measured data)
[masa, db] = textread('overall-time.txt','%f %f');
itutrydt                                      %call Itu-R model [1]
empirical                                     %call gibbins model [2]
bito                                          %call bito model [3]
figure(2);
loglog(masa,db,time2,N2,time,N,masa1,event)                         %plot log graph
legend('measured data','Bito model','Itu-r model','Paulson model') %legends
xlabel('Duration [sec]')                                            %x-axis label
ylabel('No of events exceeding abscissa')                           %y-axis label
title('Anuual Fade duration in UTM 99 (38GHz)')                     %graph title

				
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