Early in the evolution of land mobile radio, it was discovered that the higher the base-station antenna, the greater the radio coverage area. This sent land mobile radio system engineers looking for higher ground and taller towers.

Predicting radio coverage area is an important aspect in the design of a land mobile radio system and proper placement of the base station(s). If the earth were a perfectly smooth sphere, with equal signal attenuation in all directions, such predictions would come down to a simple formula and the plot of the coverage area would be a perfect circle.

But the earth is not perfectly smooth, so radio coverage from a base station to a mobile unit (located anywhere in the coverage area) generally involves plane-earth propagation. In free-space propagation, the path loss increases six decibels (dB) per octave of distance. For example, at a distance of five miles between two dipole antennas operating at a frequency of 160 MHz, the path loss is 90.3 dB. If the distance is doubled to 10 miles, the path loss becomes 96.3 dB. For plane-earth propagation, the path loss increases by 12 dB per octave of distance.

In *Land Mobile Radio Systems, 2nd edition*, author Edward Singer describes a formula for calculating radio range based on the “modified Egli method” (p.201). This formula is based on 90% probability of communication (see Figure 1).

When using the formula, pay close attention to arithmetic signs and treat them algebraically. For example, the receiver sensitivity (S) is expressed in dBW and this will be a negative figure. The minus sign in front of the S in the formula will change this to a positive value. Since this is such a long formula, it is somewhat unwieldy to handle on a calculator. A computer program that runs under DOS or a DOS window can be obtained by e-mailing me at halkinley@charter.net. An example of how to use the formula is in Figure 2.

Plugging the data from Figure 2 into the formula yields a distance (D) of 20.3 miles. It is important to note that the transmitter antenna height used in the formula is “effective height.” Effective height is the ground elevation of the tower site plus the height of the antenna, minus the average terrain elevation. In order to calculate this, the HAAT (height above average terrain) must be known.

The HAAT is calculated as shown in Figure 3. Concentric circles are drawn on a topographic map at two-mile increments from the transmitter site, to a distance of 10 miles. Then, eight radials are drawn at an angular spacing of 45 degrees from the transmitter site to intersect the 10-mile circle. These eight radials are called the cardinal radials. At the point where a radial intersects a circle, the elevation is taken — there are 40 such points.

Then, the 40 elevation readings are added together and then divided by 40 to yield the average terrain elevation around the transmitter site. The elevation of the transmitter site plus the height of the antenna above ground minus the average terrain elevation, is equal to the HAAT of that antenna.

Some interesting points can be gleaned from the formula. The range varies as a function of the square root of the multiplication factor of the effective height of the antenna. For example, if the effective height of the antenna is quadrupled, the range will double . In our example, the tower height must be increased to 675 feet in order to quadruple the effective antenna height. This would double the range to 40.6 miles.

Another way the range can be doubled is by adding 12 dB of gain somewhere, by reducing the losses by 12 dB, or by employing a combination of the two. For example, the transmitter power could be quadrupled (for a 6 dB gain) and the antenna gain increased by 6 dB to yield a total system gain of 12 dB. Theoretically, this would have the same effect as increasing the effective antenna height by a factor of four. However, it may not always work out that way in practice.

In some locations, the terrain might approach that of a smooth sphere. However, much of the earth involves very irregular terrain, from gently rolling hills to very rugged mountains. In order to achieve any significant degree of accuracy in the prediction of radio coverage, the terrain of the coverage area must be taken into account. This involves such a tremendous amount of calculations that computer programs have been developed to handle the task. The Egli model, the Bullington model and the Longley-Rice model are the three most commonly used range-prediction models.

Radio Mobile Deluxe^{1} is propagation study software based on the Longley-Rice^{2} propagation model that assesses irregular terrain in the frequency range of 20 MHz to 20 GHz. This free software can be downloaded from http://www.cplus.org/rmw/english1.html. (The basis for this software can be found at http://elbert.its.bldrdoc/itm.html.) Radio Mobile Deluxe provides an excellent Windows-based interface between users and the Longley-Rice propagation model. In order to use the program, you must have terrain elevation data. The one arcsecond (30 meter) database provides excellent resoluion and can be obtained from several sites. One is ftp://edcsgs9.cr.usgs.gov/pub/data/srtm/United_States_1arcsec/1arcsec. (Don't omit the underscores when typing in this Web address.)

In addition, good information on the ITS irregular terrain model can be found in the NTIA Report 82-100, *A Guide to the Use of the ITS Irregular Terrain Model in the Area Prediction Mode*, April 1982.^{3} The NTIA's Web address is http://www.ntia.doc.gov.

While this column doesn't have the space to provide a complete tutorial on running the Radio Mobile Deluxe software, a few sample coverage plots illustrate some of its capabilities. Figure 4 shows two plots over the same map. The lighter colored plot was based on a received-signal level of one microvolt. The darker plot was based on a received-signal level of three microvolts. This allows the user to determine the effect of system changes on the coverage area.

The radio network depicted in Figure 4 consists of three base stations. The plot in Figure 4 is for the Spartanburg, S.C., station only. The software will produce plots that combine the coverage of any or all of the stations in a network. Figure 5 shows the combined plot of all three stations in the network. The green plot indicates that a mobile unit anywhere in the green area should be able to communicate with at least one of the base stations in the network.

Figure 6 shows a plot that indicates areas of interference (red) where the desired signal (green) is less than 6 dB above the undesired signal. The signal-to-interference ratio (S/I) can be set to other values in the software.

These plots were done using the one-arcsecond terrain elevation database. The plots were overlaid on a map from MapBlast. The Radio Mobile Deluxe software has many other features that are too numerous to describe, or even list, here. Remember that while no propagation software is 100% foolproof, sensible input will provide useable output.

Until next time — stay tuned!

^{1} Radio Mobile Deluxe is freeware developed by Roger Coudé of Canada.

^{2} Longley-Rice is named for Anita Longley and Phil Rice.

^{3} NTIA is the National Telecommunications and Information Administration.