**Comparison of Swiss results presented in 3K/171 and document
"CompareBul_DNR"**

The Bullington model proposed by the Swiss delegation has been compared
with the 3K1 DNR in two Swiss documents: Doc 3K/171 (input to the last
SG3 meeting) and document "CompareBul_DNR" provided by Markus Liniger on
the 3K1 Website.

These two set of testing results are compared in the tables below,
broken down by the source data. Note that:

(1) Values of mean and standard deviation are given directly in
    "CompareBul_DNR". There are also plots of model error against
    distance but these are not considered here. In 3K/171 values of mean
    and standard deviation are not given explicitly. They are presented
    in graphical form, and here have been read from the graphs in that
    document (the "All" values, which includes all the data, rather than
    the data split down by number of obstacles). These values have been
    read from the graphs to an accuracy of \~0.2dB.

(2) The labels describing the datasets were not always identical. I
    think I am comparing like with like, but I could be wrong. The US
    Phase 1 and 2 data and the EBU data are fairly unambiguous. In the
    case of the Swiss data, 3K/171 splits it into two sets: rural and
    urban but doesn't give a combined result. In "CompareBul_DNR" there
    is only one set of results. Here I compare both sets (in the case of
    3K/171) with the single set (from "CompareBul_DNR").

The comparisons raise some issues:

\(1\) In 3K/171, results from the cascaded knife-edge model from *both*
ITU-R P.526-9 *and* the PDNR are given. But the diffraction model in the
PDNR is intended to be the same as the P.526-9 model. However the 3K/171
results show very large differences between the two implementations.
Actually one addition to P.526-9 was introduced into the PDNR at the
Boulder workshop: the addition requested by the Swiss to deal with
"sloping" knife-edges. However this certainly should not give rise to
the magnitude of the differences seen in the tables below. So we need to
address the reason for the large differences in 3K/171. Are there typos
in the PDNR? A careful examination of the two implementations used in
3K/171 should reveal the reason for the differences.

\(2\) There are a number of major differences between the 3K/171 and
"CompareBul_DNR" means and standard deviations for the same models and
datasets (in two cases by \> 20dB). This suggests that the
implementations of the Bullington and PDNR models have changed between
the two documents. In most cases, the changes have resulted in improved
results in the case of Bullington, and poorer results in the case of the
PDNR (although the standard deviation of the PDNR model against the US
data have improved significantly). Clarification of these changes would
be welcome.

**US Phase 1 data**

  ---------------------- ------------ ------------ ---------------- ------------
  Model                  3K/171                    CompareBul_DNR   

                         Mean         SD           Mean             SD

  Bullington             27.5         11.2         24.3             11.3

  Casc. Knife edge PDNR  10.3         22.6         31.1             13.8

  Casc. Knife edge       19.3         13.7                          
  P.526-9                                                           
  ---------------------- ------------ ------------ ---------------- ------------

**US Phase 2 data**

+---------------------+-----------+-----------+-----------+-----------+
| Model               | 3K/171    |           | Compa     |           |
|                     |           |           | reBul_DNR |           |
|                     | used set  |           |           |           |
|                     | described |           |           |           |
|                     | as        |           |           |           |
|                     | "single   |           |           |           |
|                     | mea       |           |           |           |
|                     | surments" |           |           |           |
+---------------------+-----------+-----------+-----------+-----------+
|                     | Mean      | SD        | Mean      | SD        |
+---------------------+-----------+-----------+-----------+-----------+
| Bullington          | 8.2       | 13.8      | 7.8       | 12.6      |
+---------------------+-----------+-----------+-----------+-----------+
| Casc. Knife edge    | -5.9      | 18.1      | 16        | 13.1      |
| PDNR                |           |           |           |           |
+---------------------+-----------+-----------+-----------+-----------+
| Casc. Knife edge    | -3.8      | 19.7      |           |           |
| P.526-9             |           |           |           |           |
+---------------------+-----------+-----------+-----------+-----------+

**EBU data**

  ---------------------- ------------ ------------ ---------------- ------------
  Model                  3K/171                    CompareBul_DNR   

                         Mean         SD           Mean             SD

  Bullington             11.5         9.2          3.3              9.3

  Casc. Knife edge PDNR  7.2          11.4         8.2              13.1

  Casc. Knife edge       -1.0         14.9                          
  P.526-9                                                           
  ---------------------- ------------ ------------ ---------------- ------------

**Swiss data**

  ---------------------- ------------ ------------ ---------------- ------------
  Model                  3K/171                    CompareBul_DNR   
                         (Swiss                                     
                         rural)                                     

                         Mean         SD           Mean             SD

  Bullington             9.4          7.2          -0.0             7.2

  Casc. Knife edge PDNR  -7.2         14.4         -3.9             15.1

  Casc. Knife edge       -12.9        17.5                          
  P.526-9                                                           
  ---------------------- ------------ ------------ ---------------- ------------

**Swiss data**

  ---------------------- ------------ ------------ ---------------- ------------
  Model                  3K/171                    CompareBul_DNR   
                         (Swiss                                     
                         urban)                                     

                         Mean         SD           Mean             SD

  Bullington             20.3         8.9          -0.0             7.2

  Casc. Knife edge PDNR  7.8          12.4         -3.9             15.1

  Casc. Knife edge       2.4          15.0                          
  P.526-9                                                           
  ---------------------- ------------ ------------ ---------------- ------------

K H Craig

8 May 2007