United Kingdom

Further Testing of ITU-R P.1812 with respect to long-term measurement
data

# Introduction

The recently-adopted point-area propagation model, ITU-R P.1812, has
been developed to a large extent, from algorithms already embodied in
ITU-R P.542. The earlier Recommendation has been extensively tested
against empirical data, and has gained wide acceptance as a reliable
model.

The new Recommendation, however, is intended to cover a frequency range
with a lower limit of 30 MHz, compared with a lower limit of \~700 MHz
in P.452. A previous 3K contribution \[1\] examined the frequency
dependence of the algorithms in P.452 and concluded that they should,
generally, be applicable over the wider frequency range, with the caveat
that the model be limited to use at greater than 1%-time below 700 MHz.
Furthermore, it was noted that the troposcatter and ducting/layer
reflection models might require further optimisation.

Workers in the UK have now produced six independent implementation of
P.1812 that provide results agreeing to better than 0.001dB for a set of
agreed test paths. These results give confidence that the algorithms
have been correctly implemented, but offer no indication of the
performance of the Recommendation.

It is likely that, to inform the current discussions within the CG
regarding the choice of diffraction model, the bulk of the initial
testing will focus on relatively short paths, for which diffraction is
the dominant mechanism.

This contribution, however, concerns the testing of the overall
Recommendation against empirical data gathered from long-term
measurements on paths of, typically, 100km-400km. This note is intended
only to give an initial insight into the performance of the overall
Recommendation, and further contributions will present more detailed
analysis of the behaviour of individual elements of the model.

# Long-term measurement data

A substantial body of empirical data has been gathered over some 60
years, relating to the variability of transmission loss over long paths.
Unfortunately, the bulk of this data relates to North West Europe and
North America, with little coverage of other latitudes.

An attempt is currently being made to assemble a reliable database of
such measurement results, for the purpose of testing P.1812 and other
ITU-R models. The main source for this work is the set of data collated
by R.S.Sandell (RSS) of the UK some 15 years ago, and currently archived
on the SG3 website at
<http://www.itu.int/ITU-R/study-groups/software/dbsg5/index.html> under
the heading "*Databanks of VHF/UHF measurements relating to terrestrial
broadcasting*". Part of this data follows a format similar to, but not
identical with, that given in Table VI-I of P.311 for signal variation
with time, and includes some 3,300 records.

The amount of directly usable data is, however, considerably less than
this figure might suggest. Almost half of the 3,300 records relate to
the statistics for monthly subsets of longer measurements. In a further
300 records, information is missing on terminal position or aerial
height. Finally, 1300 records are for durations significantly shorter
than a year. Excluding these records leaves a database of 328 records,
spanning frequencies between 45 MHz and 3 GHz, as indicated in Figure 1.

![](media/image1.wmf){width="6.700694444444444in"
height="3.470138888888889in"}

***Figure 1: Long-term measurement database statistics***[^1]

The vast majority of the paths represented in the original and filtered
database are in North West Europe, with others in North America, Japan
and the Gulf. The geographical extent of these links is indicated in
Figure 2, with details (where colour indicates frequency band) in
Figures 3 and 4.

![](media/image2.png){width="6.584722222222222in" height="3.29375in"}

***Figure 2: Geographical extent of filtered data***

![](media/image3.png){width="3.1902777777777778in"
height="2.814583333333333in"}
![](media/image4.png){width="2.9993055555555554in"
height="2.8208333333333333in"}

***Figure 3: American links Figure 4: European links***

In addition to the RSS data, some long-term measurements are also
included in the data already converted to 3K1 format by Dr Fryderyk
Lewicki; the set 'IRTs' describes 11 paths at Band II in Southern
Germany, while 'YLEs' relates to paths in Finland that are also included
in the filtered data set. The data set 'ABU' makes a very useful
geographical extension to the existing data, but currently requires some
further validation.

The 'sanitising' of the available measurement database is still
continuing, and it is hoped to add further data as missing path
information becomes available from original documentation. Conversely,
some existing data will need to be excluded as measurement errors are
traced (examples already detected include paths with undocumented local
clutter and measurements at the receiver noise floor).

Some of the records in the original database include details of the path
profile. In all cases, the new, filtered, database includes terrain data
taken from the best source, which is of 50m horizontal resolution around
the UK, from SRTM data at latitudes below 60, and from GLOBE data
elsewhere. Regardless of underlying terrain resolution, these profiles
have been generated with a point-spacing of 1km (the impact of
point-spacing is considered in 3.2 below)

A collated and filtered long-term database has now been made available
to the group via the Rutherford Appleton Laboratory website at:

# Testing of P.1812 using long-term data

One of the UK implementations of P.1812 has been exercised using the
filtered database described above. No corrections[^2] for clutter were
made as it is believed that all terminal locations in the database
described above were intended to be free of local clutter.

The initial aim of this exercise was to provide an understanding of the
performance of the new Recommendation for long paths, typical of those
relevant to the international co-ordination of broadcast stations.

The opportunity has also been taken, however, to investigate the
comparative performance of the existing P.1812 diffraction model, based
on the Deygout construction (limited to three edges) with a number of
proposed alternatives based on the Bullington construction.

The 'baseline' Bullington results implement the algorithm set out in CG
document CGD-12. It is clear that this algorithm significantly
underestimates diffraction loss for long paths, particularly those
involving smooth-earth or sea paths.

A proposal has been made (in CGD-14) for an empirical[^3] correction
based on a 9^th^ order polynomial with *log(d)* as the parameter. The
author of the present document initially interpreted this as a
correction to be applied *in addition* to the *10+0.02d* term in the
CGD-12 definition of Bullington, but colleagues have suggested that the
intention may have been to use the polynomial correction as a
*substitute* for the *10+0.02d* term. Both interpretations have been
implemented and tested.

In the band-by band comparisons below, the current Recommendation P.1812
is referred to as '*D3E*' and the Bullington construction as formulated
in CGD-12 as '*Bullington*'. The application of the ninth-order
polynomial distance correction as an [addition]{.underline} to the
CGD-12 description is labelled '*Bullington + correction'*.and as a
substitute for the 10+0.02d term is labelled '*Bullington sub
correction'.*

Clearly, a change in the diffraction model will generally be masked at
smaller percentage-times by ducting effects. The relationship of
prediction error on pathlength, and the overall statistical performance
of the models are therefore detailed for 50% time.

## Band I

These measurements span the range 41.5-68 MHz.

![](media/image5.wmf){width="6.596527777777778in"
height="2.7493055555555554in"}

***Figure 5a: Band 1 results (D3E)***

![](media/image6.wmf){width="6.596527777777778in"
height="2.738888888888889in"}

***Figure 5b: Band 1 results (Bullington)***

Examination of the detailed model output shows that at the smallest
%-times, the ducting model is underestimating the loss, while at 50%
both the troposcatter and diffraction models also show tendency to
underestimate the loss. The underestimate is significantly larger for
the Bullington model.

In common with results for other bands, the ducting model shows lower
mean errors for longer paths, while the performance at 50% is largely
independent of path length.

Figure 6 below, and the corresponding plots for other frequency bands,
is a set of scatter plots of predicted versus measured path loss, with
the propagation mechanism dominant in the model indicated by colour.
Points where ducting is dominant are blue, diffraction is indicated in
yellow and troposcatter in red.

![](media/image7.wmf){width="3.279166666666667in"
height="2.473611111111111in"}![](media/image8.wmf){width="3.3055555555555554in"
height="2.4784722222222224in"}

![](media/image9.wmf){width="3.28125in"
height="2.45625in"}![](media/image10.wmf){width="3.2645833333333334in"
height="2.45in"}

***Figure 6a-d: Prediction-measurement (Band 1)***

Figure 6a shows a tendency of the D3E model to under-predict path loss
for the points on the left of the plot where the ducting model
dominates.

The most striking feature of the Bullington model is that the
diffraction model underestimates loss compared with the D3E case,
ensuring that diffraction is always a more significant mechanism than
troposcatter. In 6c (bottom-left), the 'Bullington+correction' model has
successfully made the results more 'Deygout-like', a result reflected in
the statistics of Table 1, below. The 'Bullington sub correction'
diffraction model makes little overall difference to the model
performance.

The performance of the different diffraction models is further examined
in Figures 7a and b, below, where the difference[^4] between the
predicted diffraction loss and the measured loss is plotted with respect
to distance, for all %-times. These plots need careful interpretation,
as it must be borne in mind that, for most of the points plotted,
diffraction will not be the dominant mechanism.

In Figure 7a, it can be seen that the D3E prediction is close to
measurement for paths up to around 250km. Beyond that point, diffraction
losses increase, and other mechanisms dominate. For the Bullington
model, however, the trend is reversed, with predicted diffraction loss
falling below the total measured loss value as pathlength increases.
This gives the masking of tropscatter[^5] seen in Figure 6b.

The impact of the two corrections is seen in Figure 7b, where it can be
seen that the additive correction gives a trend that is similar to D3E,
while the substitute correction reduces the spread of the predictions,
but without ensuring that diffraction becomes a secondary mechanism.

![](media/image11.wmf){width="6.261805555555555in"
height="2.770138888888889in"}

***Figure7a: Diffraction model performance (Band 1)***

![](media/image12.wmf){width="6.596527777777778in"
height="2.7493055555555554in"}

***Figure7b: Bullington correction performance (Band 1)***

The overall performance of the model is summarised in Table 1, from
which it can be seen that the use of the Bullington diffraction model
gives the lowest overall standard deviation. This result appears to be
an artefact of re-assigning ducting paths (for which the P.1812 model
has an inherently large SD, as seen in Figure 6) to the diffraction
model. The mean results show an underestimate of path loss, very
significantly so in the case of Bullington.

Table 1: Overall model comparison (Band 1)

  ----------------------- ----------------------- -----------------------
  **Model**               **Mean**                **SD**

  Deygout 3E              -9.57                   8.47

  Bullington              -15.40                  7.32

  Bullington + DE         -9.44                   8.69

  Bullington substitute   -15.49                  7.50
  DE                                              
  ----------------------- ----------------------- -----------------------

The models were also compared for the measurements made at 50%-time,
where only diffraction and troposcatter are relevant mechanisms, and in
this case the D3E model performs significantly better.

**Table 2: Model comparison at 50% time** (Band 1)

  ----------------------- ----------------------- -----------------------
  **Model**               **Mean @ 50%**          **SD @ 50%**

  Deygout 3E              -7.66                   4.62

  Bullington              -18.57                  5.61

  Bullington + DE         -8.31                   5.40

  Bullington substitute   -19.43                  5.91
  DE                                              
  ----------------------- ----------------------- -----------------------

## Band II

Band II nominally covers the frequency range 87.5-108 MHz.

![](media/image13.wmf){width="6.596527777777778in"
height="2.7493055555555554in"}

***Figure 8a: Band 1I results (D3E)***

![](media/image14.wmf){width="6.596527777777778in"
height="2.707638888888889in"}

***Figure 8b: Band 1I results (Bullington)***

Much the same trends are evident at Band II as for the Band I results.
The outlier at 50% time represents an 860km path (200126) for which it
is suspected that the signal was below the noise floor of the receiver;
this point has been excluded from the statistics.

![](media/image15.wmf){width="3.245833333333333in"
height="2.4604166666666667in"}![](media/image16.wmf){width="3.2354166666666666in"
height="2.4256944444444444in"}

![](media/image17.wmf){width="3.225in"
height="2.452777777777778in"}![](media/image18.wmf){width="3.311111111111111in"
height="2.502083333333333in"}

***Figure 9a-d: Prediction-measurement (Band 1I)***

As for Band 1, the difference between the predicted diffraction loss and
the measured loss is plotted below, with similar trends, though the D3E
model is now exhibiting a greater spread of errors for paths where
diffraction dominates.

![](media/image19.wmf){width="6.115972222222222in"
height="2.7597222222222224in"}

***Figure10a: Diffraction model performance (Band 1)***

![](media/image20.wmf){width="6.596527777777778in"
height="2.7805555555555554in"}

***Figure10b: Bullington correction performance (Band 1)***

The increased spread in the prediction error is clear in the summary
tables below, for which Bullington still gives the lowest standard
deviation overall

**Table 3: Overall model comparison (Band I**1)

  ----------------------- ----------------------- -----------------------
  **Model**               **Mean**                **SD**

  Deygout 3E              -10.89                  12.73

  Bullington              -16.28                  10.45

  Bullington + DE         -11.02                  12.70

  Bullington substitute   -16.67                  10.52
  DE                                              
  ----------------------- ----------------------- -----------------------

**Table 4: Model comparison at 50% time (Band I**1)

  ----------------------- ----------------------- -----------------------
  **Model**               **Mean @ 50%**          **SD @ 50%**

  Deygout 3E              -4.46                   6.16

  Bullington              -16.43                  6.28

  Bullington + DE         -5.70                   6.17

  Bullington substitute   -17.71                  6.57
  DE                                              
  ----------------------- ----------------------- -----------------------

## Band III

Band III covers the spectrum between \~170 to 230 MHz.

![](media/image21.wmf){width="6.596527777777778in"
height="2.707638888888889in"}

***Figure 11a: Band 1II results (D3E)***

![](media/image22.wmf){width="6.596527777777778in"
height="2.707638888888889in"}

***Figure 11b: Band 1II results (Bullington)***

Note that the Y-axis in Figure 11 has been extended to accommodate the
outliers. These points relate to a single path of 930km in the Gulf on
which path losses approached the free space value for a significant
portion of the time, and remained within 40dB of free-space at 50% time.
The statistics given in the tables below exclude this path.

![](media/image23.wmf){width="3.2597222222222224in"
height="2.4451388888888888in"}![](media/image24.wmf){width="3.2784722222222222in"
height="2.4604166666666667in"}

![](media/image25.wmf){width="3.26875in"
height="2.459722222222222in"}![](media/image26.wmf){width="3.2958333333333334in"
height="2.48125in"}

***Figure 12a-d: Prediction-measurement (Band 1II)***

The relationship between diffraction model performance and pathlength is
illustrated in Figure 7 below, with Bullington systematically giving
lower losses than either D3E or the overall measured value..

![](media/image27.wmf){width="6.588888888888889in"
height="3.157638888888889in"}

***Figure13a: Diffraction model performance (Band 1)***

![](media/image28.wmf){width="6.588888888888889in"
height="3.157638888888889in"}

***Figure 13b: Bullington correction performance (Band 1)***

As before, the Bullington model gives the best overall standard
deviation, as a result of re-assigning points from 'ducted' to
'diffracted', while for median time, D3E gives the best performance.

**Table 5: Overall model comparison (Band II**1)

  ----------------------- ----------------------- -----------------------
  **Model**               **Mean**                **SD**

  Deygout 3E              -7.18                   10.07

  Bullington              -12.15                  8.79

  Bullington + DE         -6.71                   10.22

  Bullington substitute   -11.94                  9.13
  DE                                              
  ----------------------- ----------------------- -----------------------

**Table 6: Model comparison at 50% time (Band II**1)

  ----------------------- ----------------------- -----------------------
  **Model**               **Mean @ 50%**          **SD @ 50%**

  Deygout 3E              -3.58                   7.13

  Bullington              -14.17                  8.03

  Bullington + DE         -3.95                   7.50

  Bullington substitute   -14.33                  8.93
  DE                                              
  ----------------------- ----------------------- -----------------------

## Band IV

Band IV refers to the lower part of the UHF broadcast band, at 470-610
MHz.

![](media/image29.wmf){width="6.596527777777778in"
height="2.7493055555555554in"}

***Figure 14a: Band 1V results (D3E)***

![](media/image30.wmf){width="6.596527777777778in"
height="2.6659722222222224in"}

***Figure 14b: Band 1V results (Bullington)***

At Band IV frequencies (400-610 MHz) there is some evidence that the
ducting model is starting to perform somewhat better, as might be
expected from its origin in P.452.

![](media/image31.wmf){width="3.2784722222222222in"
height="2.4784722222222224in"}![](media/image32.wmf){width="3.26875in"
height="2.466666666666667in"}

![](media/image33.wmf){width="3.2881944444444446in"
height="2.49375in"}![](media/image34.wmf){width="3.2777777777777777in"
height="2.4868055555555557in"}

***Figure 15a-d: Prediction-measurement (Band IV)***

The relationship between diffraction model performance and pathlength is
illustrated in Figure 16, below. It can be seen that the spread of
results is significant, but it should be remembered that this does not
necessarily represent a large spread of errors, as other mechanisms may
be dominant. However, the overall SD achieved by all the models is high
(tables 7 & 8)..

![](media/image35.wmf){width="6.588888888888889in"
height="3.157638888888889in"}

***Figure16a: Diffraction model performance (Band 1)***

![](media/image36.wmf){width="6.588888888888889in"
height="3.157638888888889in"}

***Figure 16b: Bullington correction performance (Band 1)***

**Table 7: Overall model comparison (Band IV**)

  ----------------------- ----------------------- -----------------------
  **Model**               **Mean**                **SD**

  Deygout 3E              -5.69                   12.53

  Bullington              -8.89                   13.01

  Bullington + DE         -5.48                   12.58

  Bullington substitute   -9.15                   13.23
  DE                                              
  ----------------------- ----------------------- -----------------------

**Table 8: Model comparison at 50% time (Band IV**)

  ----------------------- ----------------------- -----------------------
  **Model**               **Mean @ 50%**          **SD @ 50%**

  Deygout 3E              -3.90                   12.96

  Bullington              -15.12                  12.72

  Bullington + DE         -4.68                   12.68

  Bullington substitute   -16.36                  12.63
  DE                                              
  ----------------------- ----------------------- -----------------------

## Band V

Band V refers to the upper part of the UHF broadcast band, at 610-860
MHz.

![](media/image37.wmf){width="6.596527777777778in"
height="2.8333333333333335in"}

***Figure 17a: Band V results (D3E)***

![](media/image38.wmf){width="6.596527777777778in"
height="2.707638888888889in"}

***Figure 17b: Band V results (Bullington)***

The pairs of outliers between 1% and 50% relate to two paths in the Gulf
(500421 & 500434) . The statistics given in the tables below exclude
these paths.

![](media/image39.wmf){width="3.2784722222222222in"
height="2.475in"}![](media/image40.wmf){width="3.290277777777778in"
height="2.4791666666666665in"}

![](media/image41.wmf){width="3.3020833333333335in"
height="2.5006944444444446in"}![](media/image42.wmf){width="3.2777777777777777in"
height="2.466666666666667in"}z

***Figure 18a-d: Prediction-measurement (Band V)***

The relationship between model error and pathlength, at 50% time, is
illustrated in Figures 19a-19d, below for the different models. The D3E
model results show a smaller spread than for Band IV.

![](media/image43.wmf){width="6.588888888888889in"
height="3.157638888888889in"}

***Figure19a: Diffraction model performance (Band V)***

![](media/image44.wmf){width="6.588888888888889in"
height="3.157638888888889in"}

***Figure 19b: Bullington correction performance (Band V)***

The summary tables below show that the D3E construction gives the best
performance both overall, and for median time.

**Table 9: Overall model comparison (Band V**)

  ----------------------- ----------------------- -----------------------
  **Model**               **Mean**                **SD**

  Deygout 3E              -7.19                   8.88

  Bullington              -11.15                  11.56

  Bullington + DE         -7.5                    9.25

  Bullington substitute   -11.96                  11.68
  DE                                              
  ----------------------- ----------------------- -----------------------

**Table 10: Model comparison at 50% time (Band V**)

  ----------------------- ----------------------- -----------------------
  **Model**               **Mean @ 50%**          **SD @ 50%**

  Deygout 3E              -4.02                   6.84

  Bullington              -17.10                  10.42

  Bullington + DE         -5.4                    8.35

  Bullington substitute   -18.74                  10.83
  DE                                              
  ----------------------- ----------------------- -----------------------

## Band VI

For the purposes of this report, spectrum between 1-3 GHz is referred to
as Band VI.

![](media/image45.wmf){width="6.596527777777778in"
height="2.8020833333333335in"}

***Figure 20a: Band VI results (D3E)***

![](media/image46.wmf){width="6.596527777777778in"
height="2.6972222222222224in"}

***Figure 20b: Band VI results (Bullington)***

The results for frequencies between 1 and 3 GHz appear quite good, but
the small number of measurements in the database allows little
confidence.

The positive outliers at 10% and 50% relate to a path in Germany, the
negative outlier at 10% to a path in Florida. No explanation is apparent
in either case.

![](media/image47.wmf){width="3.2604166666666665in"
height="2.475in"}![](media/image48.wmf){width="3.3020833333333335in"
height="2.502083333333333in"}

![](media/image49.wmf){width="3.2993055555555557in"
height="2.5006944444444446in"}![](media/image50.wmf){width="3.2916666666666665in"
height="2.4895833333333335in"}

***Figure 21a-d: Prediction-measurement (Band VI)***

From Fig.21 it can be seen that diffraction is the dominant mechanism on
only a few paths; nevertheless, the behaviour of the diffraction models
with pathlength is plotted below, for completeness..

![](media/image51.wmf){width="6.195833333333334in"
height="2.8020833333333335in"}

***Figure22a: Diffraction model performance (Band 1)***

![](media/image52.wmf){width="6.596527777777778in"
height="2.7916666666666665in"}

***Figure 22b: Bullington correction performance (Band 1)***

**Table 11: Overall model comparison (Band VI**)

  ----------------------- ----------------------- -----------------------
  **Model**               **Mean**                **SD**

  Deygout 3E              -5.11                   10.31

  Bullington              -8.75                   10.00

  Bullington + DE         -5.39                   9.64

  Bullington substitute   -9.70                   10.33
  DE                                              
  ----------------------- ----------------------- -----------------------

**Table 12: Model comparison at 50% time (Band VI**)

  ----------------------- ----------------------- -----------------------
  **Model**               **Mean @ 50%**          **SD @ 50%**

  Deygout 3E              -4.67                   14.30

  Bullington              -15.28                  12.58

  Bullington + DE         -5.98                   12.47

  Bullington substitute   -17.43                  12.61
  DE                                              
  ----------------------- ----------------------- -----------------------

#  Summary results

The performance of the existing P.1812 model, across the entire database
is as follows:

***Table 13***: Overall performance of P.1812

  ----------------------- ----------------------- -----------------------
                          **0.01% -- 50%**        **1%-50%**

  **Mean error**          -7.51                   -6.16

  **SD of error**         11.86                   10.89
  ----------------------- ----------------------- -----------------------

## Impact of profile point spacing

A brief check was made of the sensitivity of the existing P.1812 model
to the choice of profile point spacing. This issue will be of greater
relevance for shorter paths, and it was expected that differences would
be slight for the database tested here, and confined to the higher
time-percentages.

Table 15: Average errors versus point-spacing

  ----------------- ----------------- ----------------- -----------------
  **%-time**        **0.5 km**        **1 km**          **2 km**

  **0.01**          -7.9              -8.1              -8.2

  **0.1**           -8.9              -9.2              -9.4

  **0.3**           -7.9              -8.2              -8.4

  **0.5**           -8.5              -8.3              -8.9

  **1.0**           -11.4             -11.2             -11.6

  **3.0**           -7.1              -7.2              -7.3

  **5.0**           -4.5              -4.6              -4.7

  **10**            -7.8              -8.0              -8.5

  **50**            -5.6              -6.0              -6.6
  ----------------- ----------------- ----------------- -----------------

Table 16: Standard deviation of errors versus point-spacing

  ----------------- ----------------- ----------------- -----------------
  **%-time**        **0.5 km**        **1 km**          **2 km**

  **0.01**          11.5              11.5              11.7

  **0.1**           10.2              10.4              10.5

  **0.3**           9.8               9.9               10.1

  **0.5**           10.0              10.2              10.2

  **1.0**           10.2              10.1              10.2

  **3.0**           9.2               9.2               9.1

  **5.0**           8.5               8.5               8.4

  **10**            10.6              10.5              10.6

  **50**            9.6               9.4               9.5
  ----------------- ----------------- ----------------- -----------------

As shown in tables 15 and 16, these expectations were met, with only the
statistics for average error at 10% and 50% showing a significant
improvement as the profile resolution is increased. No reduction in the
standard deviation of error is evident. The overall impact of profile
point spacing for the D3E and Bullington models is indicated in Figures
23 and 24, below:

![](media/image53.wmf){width="6.588888888888889in"
height="3.157638888888889in"}

**Figure 23: Impact of profile spacing on mean error (Band III)**

![](media/image54.wmf){width="6.591666666666667in"
height="3.1638888888888888in"}

**Figure 24: Impact of profile spacing on standard deviation of error
(Band III)**

# Conclusions

It appears that the model given in the new Recommendation, P.1812
performs reasonably well for long paths, at times down to 1% and
frequencies down to 40 MHz, giving a mean error of -6.2dB with a
standard deviation of 10.9dB.

There is a general tendency to underestimate both diffraction and
troposcatter loss by 4-6dB, and there are some indications that the
ducting model works better at frequencies above 500 MHz.

The model fails to reproduce the (few available) measured statistics of
path loss experienced in the extreme radio-climactic conditions found in
the Gulf.

The substitution of the existing diffraction algorithm with the
Bullington method causes the predicted diffraction loss to decrease to
such an extent that troposcatter seldom becomes significant. The use of
this construction, however, can have the effect of reducing the SD of
overall error, though this appears to be fortuitous rather than
reflecting underlying physical processes.

Applying the 9^th^ order polynomial correction of CGD-14 as an addition
to the Bullington model gives a fair approximation to the behaviour of
the D3E model. The alternative approach of implementing the correction
as a *substitute* for the 10 + 0.02d term in the original Bullington
algorithm invariably gives a worse overall performance. The implication
is that the additive correction is intended, in which case the overall
model makes use of empirical terms in both distance and log(distance).

It is clear from the results shown here that it is necessary to consider
the behaviour of candidate diffraction models in the context of all the
mechanisms modelled within P.1812.

# References

\[1\] 3K/132 Information document on using Rec. ITU-R P.452 in the
frequency range 30 MHz to 3000 MHz: a candidate for a deterministic
Point-To-Area model, UK

*RFR / 7 Mar 08*

\_\_\_\_\_\_\_\_\_\_\_\_\_\_

[^1]: Band I: 41-72 MHz, Band II: 88-108 MHz, Band III: 160-216 MHz,
    Band IV: 400-600 MHz, Band V: 600-950 MHz, Band VI:1297-3000 MHz.

[^2]: either by additions to along-path terrain heights or in the form
    of terminal corrections

[^3]: Strictly, the correction is with respect to the Deygot
    construction, rather than to measured data

[^4]: The Y-axis on the graphs is labelled 'error' which is not strictly
    accurate, as the comparison is between modelled diffraction loss and
    measured loss due to all mechanisms

[^5]: it must, of course, be borne in mind that there is no direct
    evidence that troposcatter rather than diffraction is the dominant
    mechanism for these paths