# Presentation: 085524

## A correction to adjust the mean of the Bullington diffraction model

- David Bacon

- A correction to adjust the mean of the Bullington diffraction model

## Motivation

- It also has advantages in being less sensitive to profile spacing, and less susceptible to point-hopping when effective earth radius is changed.

## Motivation - continued

## Motivation - continued

- Comparison with P.1546 VHF and UHV, which are close to the earlier Rec.370 curves based on measurements;
- Agreement with the cylinder model originally used for P.452 based on the COST 210 measurement program, including higher frequencies than Rec.370.

## Motivation - concluded

- So the correction must take no account of hills, etc, but can be a function of any general parameters, such as distance, frequency, etc, as needed.

## The two models:

- Bullington:

- with correction: Ld = Le + (1 - exp(-Le/6)(10 + 0.02d)

-  as in P.1812

## Delta  ''

- The objective is to derive a correction which, when added to the Bullington method, brings the mean of  close to zero.

- Delta  ''

## Deltas for random paths

- The map shows 1 000 of these paths

## Deltas for random paths

- As expected,  rises with increasing distance.
- For NLOS paths the 'line' tends to be central in the scatter.

## Correction fitted to highest density of  points

- Correction fitted to highest density of  points

- Point 1 is the 0.6 Fresnel clearance distance.Empirical fits were obtained to the positions of points 2 and 3.The correction consists of straight segments between points plus an auxiliary correction to smooth the change of slope at point 2.

## Full correction: Ht = 10m, Hr = 10m, 1 GHz

- "3K-1_March08_BullLongPathCorrection.doc"

## Antenna heights both 10m.

- Correction must adapt as a function of distance and frequency.

## Antenna heights both 100m.

- Correction must also adapt as a function of antenna heights.

## ' = 3-edge loss - corrected Bull loss.

- Antenna heights both 100m.

- ' = 3-edge loss - corrected Bull loss.

## P.1812 compared to measurements with:3-edgeBull + taperBull + taper + corr

- P.1812 compared to measurements with:3-edgeBull + taperBull + taper + corr

- Means

- The correction increases the Bullington means towards the 3-edge means.
- SD is less affected, but where it differs it is most often reduced.

## Comparison with P1546 : 100 MHz

## Comparison with P1546 : 600 MHz

## Comparison with P1546 : 2000 MHz

## Another look at : Antennas 10 m, 1 GHz

- Another look at : Antennas 10 m, 1 GHz

- It is a good fit to the concentrated line in the random-path results for all combinations of frequency and antenna heights.Thus the 'line' in the scatter diagrams represents smooth paths.

## Calculating  from smooth paths

- Two points can be identified:Max F06 distance;Max LOS distance,at which the correction is easily calculated and not frequency-dependent.

- Calculating  from smooth paths

## Calculating  from smooth paths: 10 m antennas

- The lower graph shows the residual corrections needed.

- Calculating  from smooth paths: 10 m antennas

## Calculating  from smooth paths: 20 m antennas

- Calculating  from smooth paths: 20 m antennas

## Calculating  from smooth paths: 30 m antennas

- Calculating  from smooth paths: 30 m antennas

## Correction from smooth paths: 40 m antennas

## Correction from smooth paths: conclusion

- It is not suitable for calculating the correction within P.1812 since it requires, even for smooth paths, searches through profile points.
- So it still needs closed-form equations to produce a fit.
- At present a correction based on Df06 and Dlos has not been developed further.  The correction already given based on three anchor points performs adequately.

## Conclusions

- "3K-1_March08_BullLongPathCorrection.doc"

- is a candidate solution to prevent the Bullington method under-predicting losses, particularly for long paths.
- This is not intended to conclude whether it is appropriate to replace the 3-edge method by Bullington in the first place.