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MULTIPATH FADING IN LINE-OF-SIGHT MICROWAVE LINKS VARIATION WITH

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					 MULTIPATH FADING IN LINE-OF-SIGHT MICROWAVE LINKS: VARIATION WITH

                           LOCAL TIME AND FADE DURATION STATISTICS

                             A. Zygielszyper(1), E. Costa(2), L. Silva Mello(3), R. S. L. Souza(4)

             (1)
                   CETUC-PUC/Rio; Rua Marquês de São Vicente 225; 22543-900 Rio de Janeiro RJ Brasil;
                                         E-mail: epoc@cetuc.puc-rio.br
                                                          (2)
                                                                As (1) above
                                    (3)
                                          As (1) above, but E-mail: smello@cetuc.puc-rio.br
                                   (4)
                                         As (1) above, but E-mail: rodolfo@cetuc.puc-rio.br

ABSTRACT

The records from line-of-sight paths have been processed to display variations of the occurrence of selected fade depths
with local time. The results show that even the occurrence of shallow fading can vary with local time. However, the
variations can be more impressive for deep fading. Data from one space-diversity path have also been processed to
show the distributions of the number of events and the exceedance time as functions of the fade depth and the duration.
The results indicate that space diversity has only effectively decreased the number and the duration of deep fade events.

INTRODUCTION

Multipath fading measurements were performed in several Brazilian links operated by Empresa Brasileira de
Telecomunicações (EMBRATEL) to obtain information on propagation parameters relevant to the design of future line-
of-sight microwave links. The specific objectives of the project were to extract the geo-climatic factor from worst-
month cumulative distribution functions of single-frequency fading and to investigate the accuracy of available
prediction models for the improvement factor of space diversity [1]. The list of selected paths, information on data
analysis and the main results from this project are available elsewhere [2].

More recently, the available records from 18 line-of-sight paths have been processed to display variations of the
occurrence of selected fade depths with local time. This phenomenon is frequently cited but more rarely quantified in
the open literature. The well-accepted model for the prediction of the the percentage of time pw that fade depth A (dB) is
exceeded in the average worst month [1] does not consider possible variations of the occurrence of fade depths with
local time.

The same data set has also been processed to display the distributions of the number and the duration of fade events for
selected fade depths. This is another aspect of multipath fading inadequately discussed in the open literature, to which
no consolidated prediction models are available. The effects of space diversity on these parameters will also be
discussed.

It should be observed that the next sections will mainly present the results from data processing. Features that perhaps
should be considered in any prediction models will only be indicated. However, results from modeling efforts will be
the object of future contributions.

RESULTS

The main features of the analog paths that provided the result to be presented and discussed in this paper are shown in
Table 1. Measurements on these paths have been performed for one year only. Due to this limitation on data
availability, the full one-year data from each site have been used in the current analysis, instead of only the records
contributing to the characterization of the worst month.
                                                                                                Table1. Main features of selected paths

                                                            Path                                         Latitude                                Longitude    d (km)                           f (MHz)                    εp (mrad)
                                  Itinga – Entroncamento                                                     04S30’                                47W30’       56.4                              6123                         0.18
                                     Bela Vista – Guará                                                      09S00’                                48W30’       46.1                              6123                         1.20
                                      Tiririca – Guará                                                       09S00’                                48W30’       50.4                              6123                         0.70
                    Aliança do Tocantins – Gurupi                                                            11S25’                                49W02’       49.1                              6123                         0.75
                                             Toniel – Itiquira                                               17S13’                                54W45’       46.5                              6256                         2.28
                                                 Buriti – Itiquira                                           17S13’                                54W45’       51.1                              6256                       0.98
                                                                                                                                                                                                                           0.59 (P)
                                        Bonsucesso – Jataí                                                   17S46’                                51W40’       44.2                              4730
                                                                                                                                                                                                                           0.81 (D)

The results from the first four paths in Table 1 are displayed in Figure 1.

                                                     Percentagem de Ocorrência vs. Hora do Dia                                                                                                   Percentagem de Ocorrência vs. Hora do Dia



                                                                                                                                             1                                                                                                                                    1



                                                                                                                                             0.1                                                                                                                                  0.1



                                                                                                                                             0.01                                                                                                                                 0.01



                                                                                                                                             0.001      %                                                                                                                         0.001      %



                                                                                                                                             0.0001                                                                                                                               0.0001



                                                                                                                                             0.00001                                                                                                                              0.00001



                                                                                                                                             0.000001                                                                                                                             0.000001
                                                                                                                                     1   0                                                                                                                                1   0
                                                                                                                             3   2                                                                                                                                3   2
                                                                                                                     5   4                                                                                                                                5   4
                                                                                            7                    6                                                                                                                                7   6
                                                                                       9 8                                                                                                                                                   9 8
                                                                                 11 10                                                                                                                                                 11 10
                                                                           13 12       Hora                                                                                                                                      13 12       Hora
                                                                     15 14                                                                                                                                                 15 14
                    5
                        10                                  18 17 16                                                                                                      5
                                                                                                                                                                              10                                  18 17 16
                             15                                                                                                                                                    15
      Desv. (dB)                20                    20 19                                                                                                  Desv. (dB)               20                    20 19
                                   25
                                      30        22 21                                                                                                                                    25
                                                                                                                                                                                            30        22 21
                                          24 23
                                         35                                                                                                                                                     24 23
                                                                                                                                                                                               35




                                                                                      (a)                                                                                                                                     (c)
                                                     Percentagem de Ocorrência vs. Hora do Dia                                                                                                   Percentagem de Ocorrência vs. Hora do Dia



                                                                                                                                             1                                                                                                                                     1



                                                                                                                                             0.1
                                                                                                                                                                                                                                                                                  0.1


                                                                                                                                             0.01

                                                                                                                                                                                                                                                                                  0.01

                                                                                                                                             0.001      %                                                                                                                                    %

                                                                                                                                                                                                                                                                                  0.001
                                                                                                                                             0.0001


                                                                                                                                                                                                                                                                                  0.0001
                                                                                                                                             0.00001



                                                                                                                                             0.000001                                                                                                                             0.00001
                                                                                                                                     1   0                                                                                                                                    0
                                                                                                                             3   2                                                                                                                                    2   1
                                                                                                                     5   4                                                                                                                                    4   3
                                                                                                             7   6                                                                                                                                    6   5
                                                                                                     9   8                                                                                                                                        7
                                                                                                10                                                                                                                                           9 8
                                                                                          12 11                                                                                                                                        11 10
                                                                                    14 13            Hora                                                                                                                        13 12       Hora
                    5                                                         16 15                                                                                                                                        15 14
                        10
                             15                                         18 17                                                                                             5
                                                                                                                                                                              10                                     17 16
                                  20                              20 19                                                                                                            15                             18
       Desv. (dB)                      25                 22 21                                                                                              Desv. (dB)               20                    20 19
                                            30
                                                  24 23
                                                 35
                                                                                                                                                                                         25
                                                                                                                                                                                            30        22 21
                                                                                                                                                                                                24 23
                                                                                                                                                                                               35



                                                                                      (b)                                                                                                                                     (d)

 Fig 1. Percent occurrence of fade depths as a function of local time on the following paths: (a) Aliança do Tocantins –
   Gurupi; (b) Itinga – Entroncamento; (c) Bela Vista – Guará; and (d) Tiririca – Guará. Front scale: local time in 1h
  intervals from 0 h (right) to 24 h (left). Depth scale: fade depth in 5 dB intervals from 5dB (back) to 35 dB (front).
               Vertical logarithmic scale: percentage in powers of 10 from 1.0 (top) to 0.000001 (bottom).
These results show that even the occurrence of the more frequent shallow fading (5 dB to 10 dB) can vary with local
time (decrease of one order of magnitude or more around noon as compared with the occurrence during late night
hours). The variations of the occurrence of deep fading (25 dB or more) with local time are more dramatic (decrease of
several orders of magnitude around noon as compared with the occurrence during late night hours). It is also interesting
to observe the features of two distinct periods. The first period, characterized by high occurrence of multipath fading,
begins around sunset and lasts from 14 hours to 18 hours. Consequently, the second period, characterized by low
occurrence of multipath fading, is relatively shorter. It also seems that two transitions between these periods could be
asymmetric. Indeed, the results corresponding to shallow fading and those corresponding to the path Tiririca–Guará in
Fig.1(d) shows the transition around sunrise is sharper than the one around sunset. In addition to the main behavior
describer above, one should observe the possibility of short-term fluctuations in the dependence of the occurrence of
deep fading (25 dB or more) with local time, such as those in the post-midnight hours in Fig. 1(c) (Bela Vista–Guará
path).

It is also important to note that the features indicated in the previous paragraphs are not present in the data from all the
paths. For example, the results from the paths Toniel–Itiquira and Buriti–Itiquira in Fig. 2 show a relatively flat
variation of the percentage of occurrence of fade depths (less than or equal to 25 dB) with local time. The features
indicated in Fig.1 are only present for deeper fades, but in a less evident way. Therefore, it necessary to identify the
causes for the different behaviors displayed in Figs. 1 and 2 before a successful model can be developed.
                                       Percentagem de ocorrência vs. Hora do Dia                                                                                             Percentagem de Ocorrência vs. Hora do Dia



                                                                                                                        1                                                                                                                                       1


                                                                                                                        0.1                                                                                                                                     0.1


                                                                                                                        0.01                                                                                                                                    0.01


                                                                                                                        0.001                                                                                                                                   0.001
                                                                                                                                    %                                                                                                                                       %
                                                                                                                        0.0001                                                                                                                                  0.0001


                                                                                                                        0.00001                                                                                                                                 0.00001


                                                                                                                        0.000001
                                                                                                                                                                                                                                                                0.000001


                                                                                                                        0.0000001
                                                                                                                                                                                                                                                                0.0000001
                                                                                                                1   0
                                                                                                        3   2                                                                                                                                           1   0
                                                                                                    4                                                                                                                                           3   2
                                                                                            6   5                                                                                                                                           4
                                                                                        7                                                                                                                                           6   5
                                                                                   9 8                                                                                                                                    8     7
                                                                             11 10                                                                                                                                       9
                                                                       13 12       Hora                                                                                                                            11 10
                 5                                               15 14                                                                                                                                       13 12       Hora
                   10
                      15                                18 17
                                                              16
                                                                                                                                                 5 10                                                  15 14
      Desv.   (dB)       20
                            25                    20 19                                                                                                 15                                       17 16
                               30           22 21                                                                                       Desv. (dB)           20
                                                                                                                                                                  25                    20 19 18
                                  35
                                      24 23
                                     40                                                                                                                              30
                                                                                                                                                                        35        22 21
                                                                                                                                                                            24 23
                                                                                                                                                                           40



                                                                        (a)                                                                                                                                 (b)


  Fig 2. Percent occurrence of fade depths as a function of local time on the following paths: (a) Toniel–Itiquira; (b)
                   Buriti–Itiquira. Same scales as in Fig. 1, with the additional fade depth of 40 dB.

Fig. 3 shows the distributions of the number of events and the exceedance time (s) as functions of the fade depth (dB)
and the duration (s) [3] on the path Bonsucesso-Jataí indicated in the last line of Table 1, which operates with space
diversity. The decrease of the number of events and the exceedance time with both the fade depth and the duration is
evident, particularly for fade depths greater than or equal to 10 dB. A comparison between Figs. 3(a) and 3(c), as well
as between Figs. 3(b) and 3(d), respectively, indicates that, in this particular example, space diversity has only
effectively decreased the number and the duration (consequently, also the exceedance time) of fade events deeper than
20 dB. This is an indication that shallower fades simultaneously affected the principal and the diversity paths.

CONCLUSION

The records from line-of-sight paths have been processed to display variations of the occurrence of selected fade depths
with local time. The results have show that even the occurrence of shallow fading can vary with local time, but that the
observed variations can be more impressive for deep fading. It is important to note that these variations are not present
in the data from all the paths. Therefore, successful models for this phenomenon should be able to predict the results
displayed in both Figs. 1 and 2 from the path parameters, as well as from terrain and climatic information. Data from
one space-diversity path have also been processed to investigate how fast do the number of events and the exceedance
time decrease as functions of the fade depth and the duration. The results have also indicated that space diversity has
only effectively decreased the number and the duration of deep fade events.
It may be important to have results such as these incorporated into prediction models of multipath fading. These models
could be useful in the design of new microwave line-of-sight paths and in interference calculations. It should be noted
that these paths would be more robust to interference during hours when they do not experience fading. Therefore,
models that are able to predict the features described in this paper would have a potential to facilitate sharing between
systems in the fixed service and new systems in other services with busy hours coinciding with the unfaded hours line-
of-sight paths. One such new system is the short-message satellite communication system between vehicles and central
stations operating in the C band.



                                                                                                                                                                                   10000
                                                                                                                                                                                                                                                                                                                  40 dB
             10000
                                                                                                                                                             40 dB                                                                                                                                                30 dB
                                                                                                                                                             30 dB                     1000                                                                                                                       25 dB
              1000
                                                                                                                                                             25 dB                                                                                                                                                20 dB
                                                                                                                                                                       Number of
 Number of                                                                                                                                                   20 dB                      100                                                                                                                       15 dB
               100                                                                                                                                                      Events
  Events                                                                                                                                                     15 dB                                                                                                                                                10 dB
                                                                                                                                                             10 dB                       10
                                                                                                                                                                                                                                                                                                                   5 dB
                 10
                                                                                                                                                              5 dB                                                                                                                                    5 dB
                                                                                                                                                   5 dB                                       1                                                                                                 15 dB
                     1                                                                                                                       15 dB                                                10                                                                                          25 dB            Fade
                                                                                                                                                            Fade                                           30    60 120
                         10

                                  30




                                                                                                                                           25 dB                                                                        180 300
                                                                                                                                                                                                                                                                                                             Depth (dB)
                                        60

                                              120




                                                                                                                                                                                                                                600 900                                                  40 dB
                                                      180

                                                              300




                                                                                                                                                                                                                                        1200 1500
                                                                                                                                                          Depth (dB)
                                                                          600

                                                                                      900




                                                                                                                                         40 dB                                                                                                                    1800 2400
                                                                                              1200

                                                                                                        1500




                                                                                                                                                                                                                 Duration (s)                                                   3600
                                                                                                                 1800

                                                                                                                          2400

                                                                                                                                  3600




                                       Duration (s)



                                                                                            (a)
                                                                                                                                                                                                                                                   (c)



               100000                                                                                                                                        40 dB
                                                                                                                                                                                        10 0000                                                                                                                     40 dB
                                                                                                                                                             30 dB
                10000                                                                                                                                                                                                                                                                                               30 dB
                                                                                                                                                             25 dB                       10 000
                                                                                                                                                                                                                                                                                                                    25 dB
                     1000                                                                                                                                    20 dB                                                                                                                                                  20 dB
 Exceedance                                                                                                                                                            E xceed an ce
                                                                                                                                                                                              10 00
                                                                                                                                                             15 dB                                                                                                                                                  15 dB
   Time (s)           100                                                                                                                                                 T im e (s)
                                                                                                                                                             10 dB                                10 0
                                                                                                                                                                                                                                                                                                                    10 dB
                         10                                                                                                                                   5 dB                                 10                                                                                                                 5 dB
                                                                                                                                                5 dB                                                                                                                                                     5 dB
                              1                                                                                                              15 dB                                                                                                                                                    15 dB
                                                                                                                                                            Fade                                       1
                                                                                                                                                                                                                                                                                                                   F ad e
                                  10




                                                                                                                                           25 dB
                                        30




                                                                                                                                                                                                         10
                                             60




                                                                                                                                                                                                                30




                                                                                                                                                                                                                                                                                                 25 dB
                                                    120




                                                                                                                                                                                                                      60
                                                            180




                                                                                                                                                                                                                           120

                                                                                                                                                                                                                                 180
                                                                    300




                                                                                                                                                          Depth (dB)
                                                                                600




                                                                                                                                                                                                                                       300




                                                                                                                                         40 dB                                                                                                                                                                  D ep th (dB )
                                                                                                                                                                                                                                             600
                                                                                        900




                                                                                                                                                                                                                                                                                              40 dB
                                                                                                                                                                                                                                                    900
                                                                                                 1200




                                                                                                                                                                                                                                                          1200
                                                                                                          1500




                                                                                                                                                                                                                                                                 1500
                                                                                                                   1800




                                                                                                                                                                                                                                                                        1800
                                                                                                                           2400




                                                                                                                                                                                                                                                                               2400
                                                                                                                                  3600




                                        Duration (s)                                                                                                                                                                 D u ratio n (s)                                                   3600




                               (b)                                                                  (d)
 Fig 3. Number of events and exceedance time as functions of fade depth (dB) and duration (s) on the path Bonsucesso-
 Jataí: (a) number of events in the principal channel; (b) exceedance time in the principal channel; (c) number of events
  resulting from space diversity; and (d) exceedance time resulting from space diversity. Front scale: duration of 10 s,
  30 s, 60 s, 120 s, 180 s, 300 s, 600 s, 1200 s, 1500 s, 1800, 2400 s, and 3600 s (left to right). Depth scale: fade depths
(dB) also shown in the legends. Vertical logarithmic scales: number of events in powers of 10 from 1 (bottom) to 10000
                      (top) and exceedance time in powers of 10 from 1 s (bottom) to 100000 s (top)

REFERENCES

[1]     Recommendation ITU-R P.530-9, “Propagation data and prediction methods required for the design of terrestrial
line-of-sight systems”, Geneva, ITU, 2001.
[2]     L. Silva Mello, E. Costa, R. S. Souza, M. S. Pontes, N. R. Dhein, Multipath fading and fading correlation in
multi-hop links: results of measurements in tropical regions in Brazil, Proceedings of URSI Commission F Meeting on
Climatic Parameters in Radiowave Propagation Prediction, Budapest, Hungary, pp. 79-82, May, 2001.
[3]     E. Matricciani, M. Mauri, A. Paraboni, Dynamic characteristics of rain attenuation: duration and rate of change,
Alta Frequenza, vol. LVI, pp. 33-45, January-April, 1987.

				
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