United Kingdom

Testing of ITU-R P.1812 diffraction models with respect to mobile
measurement data

# Introduction

A recent campaign of mobile measurements was undertaken on behalf of the
UK regulator, Ofcom, at frequencies of 2.4 GHz, 3.4 GHz and 5.7 GHz.
While only one of these frequencies falls within the range formally
covered by P.1812, the opportunity has been taken to test the
performance of the new recommendation against this data.

# Mobile measurement data

The mobile measurements were made in three areas:

-   A predominantly rural area around the Rutherford Appleton laboratory
    in Oxfordshire

-   Winchester, a small cathedral city

-   Croydon, a densely urbanised part of South London

In all cases, the transmit terminal for the measurements used
directional antennas on a 16m vehicle-mounted mast, while the receive
terminal employed nominally omni-directional antennas mounted on a small
saloon car.

A total of 35 measurement routes are included in the database, the
majority of which were measured at all three frequencies. The majority
of the data relates to path lengths of between 1-8 km.

# Testing of P.1812 against data

Two versions of P.1812 were tested against the data; the version as
published, using the Deygout 3-edge (D3E) diffraction model, and an
alternative implementing the Bullington model, as described in
\[CGD-12\]. In the latter case, the ninth-order polynomial 'correction
for long paths' described in \[CGD-14\] was implemented, though the
paths contained in the measurement data are much shorter than those the
correction is intended to address.

![](media/image1.wmf){width="4.196527777777778in"
height="3.348611111111111in"}

**Figure 1: 9-th order polynomial correction proposed in CGD-14**

It is likely that this correction is not intended for application to
paths of less than 1km, and measurements containing such paths were
therefore excluded from the tests described below.

The correction was implemented in two forms; as an addition
('*Bullington+correction'*) to the algorithm described in CGd-12, and as
a substitution ('*Bullington sub correction'*) for the *10+0.02d* term
in that algorithm.

For all models tested, a UK, 50m resolution clutter data base was used,
which assigns one of 16 land-use categories to each pixel. As described
in P.1812 the representative clutter height was added to each profile
point, and used in the terminal correction of Eq.55a (Fresnel
diffraction loss).

## Overall results

The performance of the two models for the entire set of measurement data
is summarised in the table and figures below.

Table 1: Overall model performance

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

  **D3E**                                2.36            10.22

  **Bullington**                         -1.96           8.43

  **Bullington+correction**              3.21            8.94

  **Bullington sub correction**          -4.64           7.90
  -------------------------------------- --------------- ----------------

It can be seen that the Bullington method gives the best results in
terms of both mean error and standard deviation.

![](media/image2.wmf){width="6.586805555555555in"
height="3.0680555555555555in"}

**Figure 2: Mean error of models versus pathlength**

![](media/image3.wmf){width="6.593055555555556in"
height="2.9868055555555557in"}

**Figure 3: Standard deviation of error versus pathlength**

## Sensitivity to assumed clutter heights

The results shown in table 1 were derived using a mapping from clutter
category to clutter height that had previously been optimised for use in
a separate, but similar model. In this mapping, it had been found
necessary to assign non-zero clutter heights to nominally open areas
(fields, roads)to account for the clutter that is statistically present
(hedges, walls, vehicles) and to avoid the identification of spurious
line-of-sight paths. In addition, lower-than-physical clutter heights
were used in dense urban areas to account for the existence of
diffraction paths around the sides of buildings, rather than over
rooftops.

The performance of the Bullington and Deygout models was compared for
this '*tuned*' mapping, where 'open' = 4m and 'dense urban' = 7m, and
for the '*original*' mapping where the same categories are 0m and 15m
respectively.

Table 2: Impact of clutter category-height mapping

  -------------------------- -------------- ----------- -------------- -----------
  **model**                  **Mean**                   **SD**         

                             **original**   **tuned**   **original**   **tuned**

  **D3E**                    -1.39          2.36        10.54          10.22

  **Bullington**             -5.36          -1.96       8.90           8.43
  -------------------------- -------------- ----------- -------------- -----------

It can be seen that the performance of both models improves when the
'tuned' data set is used, and the Bullington model gives a lower SD in
both cases. The degradation of the Bullington mean error when the
'original' mapping is used should be noted, and emphasises the need for
careful testing of model sensitivity to such assumptions, and the
difficulty of making meaningful comparisons between models using
different data sets.

## Individual routes

The good performance of the Bullington model on this data had not been
anticipated, and it was initially assumed that it might reflect the fact
that this construction has fewer degrees of freedom.

The Deygout construction, as specified in P.1812 suffers from the
tendency to identify spurious adjacent profile points as separate knife
edges. Small changes in the profile (e.g. as the mobile route evolves)
can lead to large changes in estimated diffraction loss that have no
physical basis. This noisy behaviour can cause the performance of this,
and similar models, to be inferior to much simpler methods, such as
those assuming an empirical distance exponent for path loss. As the
Bullington model has fewer parameters, it might be expected to give a
lower standard deviation, while failing to follow the detailed structure
of measured path loss along a route.

To give a better understanding of the behaviour of the two models,
comparisons between the model and prediction are plotted below for a
number of arbitrarily-chosen measurement routes.

### Rural route at 2.4 GHz

This route lies across gently rolling countryside between the Rutherford
Appleton Laboratory and the town of Abingdon. The transmitter was
located on high ground some 5km from the start of the route, and the
route is away from the transmitter.

Figure 4 compares the performance of the two models for this route, and
it can be seen that, not only is the Bullington method not
overestimating diffraction loss at points such as 3.3km, but that it
does not appear to be missing any significant detail of the route,
either.

![](media/image4.png){width="6.061805555555556in"
height="5.738888888888889in"}

**Figure 4: Comparison of model performance for rural route**

### Urban route, 5.7 GHz 

The route shown in Figure 5 was in the north of Winchester. The
transmitter was located some 3km away, on rising ground on the other
side of the city centre. The route passed through a succession of
streets of terraced housing.

It can be seen from the figure that neither model follows the evolution
of path loss particularly well. In particular, the impact of local
clutter is being greatly underestimated between 0-500 and 1200-1500m.
The additional 'detail' on the Deygout prediction at 700-1100m is
clearly spurious.

![](media/image5.png){width="6.061805555555556in"
height="5.738888888888889in"}

**Figure 5: Comparison of model performance for urban route**

### Rural route at 5.7 GHz

The measurements shown in Figure 6 were made along a main road (the A30)
near Winchester. The route started at the transmitter, moved away from
it along the undulating road, before turning at around 2km and
returning.

Both models follow the variations in path loss as the road rises and
falls, but the Deygout model tends to overestimate the path loss in the
dips, while the Bullington model gives an impressively accurate estimate
without sacrificing detail.

![](media/image6.png){width="6.145138888888889in"
height="5.853472222222222in"}

**Figure 6: Comparison of model performance for rural route**

## Impact of profile point spacing

A test was made of the sensitivity of the model to the choice of profile
point spacing. In all cases, the estimated path loss increases as
profile point spacing is reduced. This reflects the importance of the
penultimate profile point (i.e. adjacent to the receiver) in determining
overall path loss to vehicle or portable (low height) terminals.

For the Bullington construction, standard deviation shows some signs of
approaching an asymptote as resolution is increased. For the Deygout
3-edge model the reverse trend is seen, suggesting that closer point
spacing increases the noise due to spuriously-identified adjacent edges.

![](media/image7.wmf){width="6.588888888888889in"
height="3.157638888888889in"}

**Figure 7: Mean error versus profile point spacing**

![](media/image8.wmf){width="6.588888888888889in"
height="3.157638888888889in"}

**Figure 8: SD of error versus profile point spacing**

# Conclusions and comments

This brief note has examined the performance of the Bullington and
Deygout 3-edge models over short paths to low-height terminals at
frequencies largely outside the range of P.1812. In these circumstances,
the Bullington model appears to give the better performance, largely
because it does not identify spurious edges. This increase in
performance is achieved with no sacrifice of accuracy over moderately
undulating terrain.

It is important to bear in mind that the Deygout 3-edge model was
originally chosen for use in P.452 and P.1812 for reasons completely
unrelated to accuracy of prediction over such short paths as those
considered here. In particular, P.452 was developed primarily for
application to much longer paths, where the D3E model could be expected
to identify much larger topological features correctly, and provided a
simple approximation to spherical surface losses over sea paths. If the
Bullington model were to be adopted for use in P.1812, some means will
need to be found to correct the underestimate of loss on long paths.
Before making any change to the algorithms in P.1812, it would be
worthwhile to undertake a wider review of alternative models.

The Deygout model is often cited as providing a good compromise between
complexity and accuracy. It has been shown \[1\] that the errors
produced are systematic, and a number of corrections, such as that of
\[2\] have been formulated. It may be that the use of such corrections,
while improving standard deviation on short paths, will also reduce the
estimate of loss on smooth earth (sea) paths that is a necessary feature
of the current D3E algorithm; further work is planned to investigate
this.

# References

\[1\] Millington, G, Hewitt, R and Immirzi, F.. \"Double knife-edge
diffraction in field strength prediction\", Proc. IEE 109C, 419-29, 1961

\[2\] Causebrook, J.H. and Davies, B. "Trospheric radio wave propagation
over irregular terrain: the computation of field strength for UHF
broadcasting", BBC Research Department Report 1971/43, 1971

*RFR / 7 Mar 08*

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