Wimaxorbust Inc. Microwave Radio Terrain Diffraction Modeling
 I. Introduction

II. Model Used

    - Part 1

III. Testing / Results

IV. References

2. Diffraction

Due to my lack of experience in MATLAB, I decided to code the diffraction model in the computer language that I know best: Perl.  I exported the matrix of the landscape into a text file, to be read in by my code.  I imported the matrix as an array of arrays.  Next, I needed to draw a line-of-sight from all points on the matrix to the base station to determine any intersections with other terrain features.  I created a nested loop and drew a topographical line from each point to the base station using a simple line algorithm.  A visualization of this algorithm may be seen below:

5              
  2 1          
      8 3      
          Base Station    
               
               
 

First, the slope from the outward point to the base station was calculated using slope = (elevation_1 - BS_elevation) / radius.  The pink line was traversed from the base station outward.  If the elevation at any point was higher than slope * radius + BS_elevation, then there must be some shadow cast behind that point.  A separate matrix was used to keep track of the number of line-of-sight intersections from each point to the base station.  In the above example, both the "3" and the "8" would cast a shadow on the "5. "  After all of these points were calculated, the idea was to run this matrix through a fast Fourier transform to "blur" geographical edges.  This would leave the output so that only the large, thick features would completely block communications.  Edges would pass most of the signal, simulating the bending of the signal.

However I ran into an unforeseen problem when attempting this algorithm.  After 18 hours of computation on my home computer, not even one map had been solved.  Given that a high level of accuracy had already been attained, this diffraction modeling was abandoned.  I would classify diffraction modeling, at least the way I attempted to implement it, as neither economical nor practical for any wireless company, especially for large areas.  This is simply due to the computational power required for these problems.