The Broadcast Equation

The standard ITM calculates the broadcast profile using an Area method based upon empirical and statistical data cover the broadcast area. This is understandable since in the 70´s because cmputer the size of a ballroom had the power of a modern day brick phone. So means had to be taken to simplify the calculations.

However

With modern multicore Threadripper, GHz clock, chips a more rigorous approach can be adopted. Here we us the pt to pt method to cover our broadcast area. So all the equations given for the pt to pt case are applicable here. We only need to detail how we adapt the approach.

Breaking down the Problem

Using a 100Km radius broadcast area as an example of how we approach the problem: A radius of 100Km around the transmitter is divided in to 100m x 100m terrain height blocks as per the NASA strm data. Assuming one matrix element per square(ie 1 pixel per height block) we require a square matrix of 2000 x 2000 or a circular matrix of 1000 pixel radius.

From the Tx centre we generate pt to pt links between the Tx centre and the points on the circumference of the broadcast area. For a 100Km radius this implies 6283 radial links to reach each 100m x 100m height block on the circumference.

The using a modified version of the pt to pt method we calculate the propagation parameters of each radial. Modified because we also calculate the propagtion to each of the height blocks along the link. Thus for a 100Km broadcast radius each pt to pt link has 1000 height points.

We note that as the radius decreases the number of radials required, so a 1Km radius only requires 68 radials. Obviously if we continue with this approach there are alot of duplicate calculations. So what we do is create a Done / Not Done matrix to avoid duplicates. The broadcast area is initialised with -ve values. If the end pt is -ve the propagation properties are calculated, if there is already a non negative value we skip the calculation. In this we we substantially reduce the computation effort.

Paralling Up

Having established the approach we now take advantage the multicore CPU´s commonly available now. The analysis is (in this case) divided into 8 sectors of 45deg each. Each sector is assigned to a different core. A shared in memory array is used to collect the propagation data supplied by each CPU.

Finally

Once the CPU´s have finished work we have all the propagation information in an array. Using this matrix the presentation of results, field strength, antenna voltage etc...can be derived.

In the basic ITM the antenna has an isotropic radiation pattern. However with our pt to pt radial approach each radial can have a defined Tx power. Thus in order to get the field power, voltage with a real antenna we over lay the Tx isotropic power with the radiation pattern. ie the Tx power reflects the antenna radiation power. A number of standard radiation patterns are provided.