# Presentation: 181185

## A Proposal for a Hybrid Diffraction Model for ITU-R P.1812

- Malcolm  Hamer

- Correspondence Group 3K-1 Workshop
- 11-13  March 2008  London

## Introduction

- Problem of 3-edge Deygout over-predicting loss in mountainous terrain compared to measurements
- Problem with Bullington under-predicting loss on long and smooth earth paths obviating the need for a troposcatter model in ITU-R P.1812
- To date, focus has been on using a distance correction to Bullington
- Synthetic path profiles have been used to see if a hybrid approach is feasible

## Background

- Similar knife-edges
- Different roughness

- Multiple knife-edges  closely spaced
- Bullington performs better than 3-edge Deygout

## Geometric dependencies

- The lower the obstacle and longer the path, the more important earth curvature
- Ratio of obstacle height to height of earth curvature important
- Knife-edges selected by    3-edge Deygout changes as this ratio reduces
- Terminal horizon distance is not necessarily a selected knife-edge

## Study A

- Terminal guard bands
- Random heights in the range from *h**min* to *h**max*
- Maximum height stepped

- Abscissa

- Graph for each distance

## Study B

- Terminal guard bands
*h**max* fixed
- Random heights in the range from *h**min* to *h**max*
- Window width stepped

- Abscissa

- Graph for each distance

## Data Collection

- Model parameter

- Stepped parameter: maximum obstacle height or window width

- Sample number

**L****d50**

- Mean

**L****d50**

**L****d50**

- Bullington

- Deygout

**0.2 km**

**20 km**

## One sample

- A

- B

- Study A

- Study B

- NB relative spreads and slopes for Deygout and Bullington

## Geometry of Study A

- 50 km

- 100 km

- 500 km

- 200 km

- Deygout

- Bullington

- Deygout

- Bullington

## Ld50 results (study A)

- 50 km

- 100 km

- 500 km

- 200 km

## Obstacle Separation Distance

- Obstacle separation distance:

*d**os*

-  Distance between the terminal horizon points
-  In the following plots, the obstacle  separation distance is the actual separation of the obstacles compared to the window width which defines the maximum allowable separation of the added knife edges

## Actual Obstacle Separation, dos (study A)

- 50 km

- 100 km

- 500 km

- 200 km

## Geometry of Study B

- 50 km

- 100 km

- 300 km

- 200 km

- Deygout

- Bullington

- Deygout

- Bullington

## Ld50 results (study B)

*L**d50* results (study B)

- 50 km

- 150 km

- 300 km

- 200 km

## Actual Obstacle Separation, dos (study B)

- Actual Obstacle Separation, *d**os *(study B)

- 50 km

- 150 km

- 300 km

- 200 km

## Lm50 versus Ls50 correlation

- 200 km

- 300 km

- 150 km

- 50 km

## Deygout secondary edges (50 km)

## New interpolation function

- 	(2)

- Suggested starting values:
*r**os* = [1.5]
*d**osd* = [3.0]

- 					(1)

## Methods of implementation

- Method A

- Method B

- where:

*L**d50D*:     Deygout value
*L**d50B*:     Bullington value

- need to implement both Deygout and Bullington

- only need to implement  Deygout

- Obstacle separation distance:

## Results

- Maximum allowed obstacle separation

- Mean of actual obstacle separation

## Step Size Tests

-  Single gaussian, 500m high, randomly placed between terminal guard bands
-  5% random noise  level  proportional to height
-   of 3km
-  Base profile: 5001 points
-  10m step size
-  Progressively down sampled to 5km

## Results

-  Deygout susceptible to step size
-  Bullington unaffected by step size
-  Large spread with Deygout
-  Hybrid methods unaffected by step size
-  Offsets in hybrid methods due to different distance correction terms

## Edge effects

## Terrain Resolution

- Bullington Ld50 shows little variation with step size & is completely insensitive to a wide range of profiles

## Sub path edges

*d**lt* > *d**it50* or *d**lr* < *d**ir50*

*d**lt* <= *d**it50* or *d**lr* >= *d**ir50*

## Model refinement

*d*: 	path length
*d**lt*:	transmitter horizon distance
*d**lr*:	receiver horizon distance
*d**it50*:	Deygout secondary edge on the transmitter side
*d**ir50*:	Deygout secondary edge on the receiver side

## Conclusions

- Separation between terminal horizon points is a useful parameter to encapsulate effects transition from mountainous to smooth earth terrain
- No need to implement both Deygout and Bullington
- Simple to implement
- Easy to tune
- Insensitive to profile step size
- Further work needed at % time
- Needs testing with real profiles in the refined datasets

- Summary for a hybrid model:

## The alternative approaches

- Obstacle Separation

- Deygout

- Bullington

- equivalent

- Loss

*10 + 0.02d*

*d**9* polyn.

- DB corrn.

- MH Hybrid

## The path we tread!