Our propagation modeling technology is based on incorporating terrain diffraction, clutter losses and distance path loss. Although we have the capability to incorporate all three of these losses in our model, many of these loss models are computationally expensive and are not necessary in all cases. For example, if the signal was not propagating through an area with great terrain variations, the return on investment of computing power is minimal.  

Variations in terrain can play a significant role in signal propagation. Many times terrain can block the line of sight between the sending antenna and the receiving antenna. In this case, the signal that is received is only the signal that was diffracted from the terrain. In the interest of simplifying the diffraction calculations, terrain can be modeled as a perfect electric conductor (PEC) edge, as shown in Figure 1, and then approximate the effects of diffraction using the Sommerfield solution for a PEC edge.

Figure 1. Terrain Modeled as Perfect Electric Conductor

Since calculating terrain diffraction is a mathematically intensive, Dekalb Telecom has simplified the terrain diffraction calculations by utilizing linear approximations to estimate terrain diffraction at most points. Our terrain diffraction algorithm works by calculating the wedge points, essentially terrain that intersects the line of sight, between the sending antenna and each one of the pixels at the edge of the cell site map.  Once the terrain diffraction was calculated at the edge of the map, terrain diffraction can be estimated on the interior of the map. Notice the lines on the bottom left side of Figure 2 which shows the interpolated terrain diffraction for cell site A. Movie 1 demonstrates how our terrain diffraction determines the wedge points for 90° sweep of cell site A. Our terrain diffraction model reduces the amount of time required to do the diffraction calculations from approximately 640 hours to 2 hours for each map.

Figure 2. Terrain diffraction for cell site A.

Movie 1. Demonstration of linear interpolation of terrain diffraction for cell site A.

For our case study, all of the transmitters are in the valley of Santa Clara, California, and we’re only concerned with matching our predictions against data collected on the road. There are very few roads (and very few people) high up in the mountains, so it is simplest to simply ignore the terrain diffraction.

Since we are ignoring the terrain, our algorithm only takes into account the clutter. It is worth noting that only 7 of the 17 listed clutter types are actually present in the 8 cell sites that are being analyzed:

To measure the amount of clutter and the impact of the clutter in the 4 sites with measured data the algorithm iterates over the perimeter of the map. At each point on the perimeter the algorithm calculates the polar-coordinate ray between the map border and the transmitter. After calculating the ray, the algorithm starts at the transmitter and steps towards the map border along the ray. At each grid point along the ray path with a non-zero signal strength the algorithm records the clutter, the distance from transmitter, and the signal strength. The clutter is entered into the matrix A, which is a 17-column matrix with each column corresponding to a clutter type. (10 of the columns end up being all-zero.) The signal strength and the distance from the transmitter are entered into a column vector called b. After the entire border has been traversed, the process is repeated for the other 3 cell sites. (The A and b matrices from all of the 4 cell sites are vertically concatenated together.) At this point the algorithm deletes the all-zero columns of A to prevent the creation of a singular matrix. Once A has been pruned, we can finally perform the matrix algebra to solve for x, a column vector with the clutter coefficients:

x = (A­^TA)^-1 * A^Tb

Now the process of traversing the perimeter is repeated to generate the actual predictions. As the algorithm steps outwards from the transmitter towards a point on the border the clutter coefficients are used to adjust for the clutter along the way:

 P_R = P_T + G_T + G_R – 20log₁₀(r) - 20log₁₀(f) + 20log₁₀(c/4π) – a*x(1) – b*x(2) – c*x(3) - …

In this equation, a is the number of type-1 clutter pieces between the transmitter and the current location.

b is the number of type-2 clutter pieces, c is the number of type-3 clutter pieces, etc.