Line-Of- Sight (LOS) Radio Link Path Calculations

Background

The design of radio links usually involves three sets of calculations, each following each other. The first, being the design of the tower heights, where the k-factor is the dominant variable. The tower height design considers the path profile and the Earth Bulge, together with the Fresnel zone radius. The path profile is important as it indicates the distance from one of the transmitter sites where obstructions to the line-of-sight radio link may occur. The Earth Bulge is important as it indicates for a given k-factor, how high an obstruction rises above a flat Earth, and the Fresnel zone is important, because it shows for a given designated carrier frequency the zone where 96% of the power of the radio wave is concentrated. The object of this calculation set is to arrange the height of the towers at both ends of the link, so that an obstruction in the path does not enter into the Fresnel zone by a specified amount according to the k-factor used.

The second set of calculations determines the equipment parameters, such as the transmitter power, the size of the antennas, the receiver sensitivity, etc. The salient parameters carried over from the first set of calculations are; the path length, as determined from the path profile and the designated frequency which is to be used. It is this set of calculations which is the subject of this applet.

The third set of calculations determines the reliability of the link, that is, what the expected total outage time per annum is expected to be. These calculations are based on fading models, thermal noise, etc. The most important parameter carried over from the second set of calculations is the Fade Margin allowed for in the path calculations.

Theory

The LOS radio link path calculations involve parameters such as antenna dish size at either end of the link, transmitter power and fade margin, given the variables; length of the link, antenna coupling losses and cable losses at either end of the link, frequency of the carrier and receiver sensitivity. Usually all calculations are performed by adding or subtracting logarithmic values, such as dBm, dBi, or dB. To perform calculations to determine a specific parameter such as antenna dish size, all other parameters and variables must be known or specified, that is; transmitter power, fade margin, link length, antenna and cable coupling losses, frequency of the carrier and receiver sensitivity. This section will derive the equations used to determine either dish diameter, transmitter power, or fade margin, given the relevant specified parameters or variables. The applet presented below permits the individual calculation of antenna dish size (for equal dishes at either end of the link) and gives the summed antenna gains (dBi) for calculation of an individual antenna at one end of a link, given the gain of the other antenna. It also permits a separate calculation for the transmitter power, and it also permits the calculation of the fade margin. A radio link showing the definitions of terms usually used is shown below in Figure 1.

Figure 1 Graphical depiction of terms used in the transmission loss concept.

(Courtesy of CCIR, Recommendation 341-2 - Propagation in Non-Ionized Media, 1986)


 
 

The losses

Free space basic transmission loss Ao.

Path calculations start by first determining the free space basic transmission loss Ao in decibels (dB). This is given by:

Antenna, cable and other losses at each end of the link

Referring to Figure 1, the other losses involved over the link, again expressed in dB, are the losses due to the transmitting and receiving antenna circuits and the losses due to filters, feeders and connectors. These losses may be different at each end of the link, due to the feeder lengths, antenna sizes, etc., being different. Usually, these losses are summed at each end of the link, and the resulting sum is used in the calculations. For site A, this is given by LbA and for site B, LbB. These losses may be included in the applet, and are usually obtained from the manufacturer's data. Typical values are usually under 10 dB for each end of the link with values around 3.5 dB for feeder loss, 4.5 dB for branching loss, 0.5 dB for adapter and connector loss.

Other losses

These include losses not mentioned above, and if are required to be added into the applet should be added into the antenna and coupling/connector losses scrollbar. These losses include: absorption loss (ionospheric, atmospheric gases or precipitation), diffraction loss (as for ground waves), effective reflection or scattering loss, polarization coupling loss, aperture to medium coupling loss or antenna gain degradation due to the presence of substantial scatter phenomena on the pathe, and the effect of wave interference between the direct and indirect rays reflected from the ground or other obstacles or atmospheric layers. For a 30 km path operating at 13 GHz, the atmospheric absorption loss is around 0.6 dB.

The gains

The Antennas

The only gains in the link are those from the antennas. The gain of an antenna is specified in dB over an isotropic antenna, thus dBi. Usually, for a given frequency band of operation, the antenna manufacturer will supply the gain figures and a voltage standing wave ratio (VSWR) for an antenna of a specific diameter. If the antenna at either end of the link is known, then the gain of the antenna at site A would be given by GA , and similarly at site B the antenna gain would be given by GB . The applet permits the antenna gains to be entered into the scrollbars for the different sites. If it is the antenna gains which are to be calculated then the resulting gain figure is for equal antennas at either site, together with the diameter of each of the equal antennas. This is not felt to be a problem, because the answer to a problem which requires that only one antenna gain be found, can easily lead to the determination of that antenna gain by subtracting the known antenna gain from the summed gain answer. The diameter, however, will not be so easily determined, as it is computed from the assumption that each antenna is of equal gain. Should an individual antenna diameter be required to be determined, given the gain, then the following equation may be used:

which results in

Where: D = diameter of the antenna (m), c = 2.99792458 x 108 (m/s), f = band center frequency (Hz), G = antenna gain (dBi), h = antenna efficiency (which is usually taken as 0.65) and is taken as 0.65 in the applet calculation of antenna diameter, l is the wavelength of the band center frequency (m), A = effective area of the antenna (m2) and Ap = the antenna gain factor (dimensionless).

The total loss

Again referring to Figure 1, the total loss in dB, of a radio link may be defined as the difference between the power supplied by the transmitter of a radio link and the power supplied to the corresponding receiver in real installation, propagation and operational conditions. If the transmitter power is given by Ptx (dBm) and the unfaded received signal power is given by Prx(unfaded), then the difference between these two powers must be the sum of the losses and the gains as described above. That is:

on rearranging, the unfaded received signal power is given by:

The Fade Margin

The flat fade margin is the power level that the unfaded received signal Prx(unfaded) , can fall to until it reaches the receiver threshold Pthresh. That is:

The threshold power of the receiver is the level of signal which would produce a 30 dB signal-to-noise ratio out of the baseband of an analogue receiver, or a bit error ratio (BER) = 10-4 out of the baseband of a digital receiver. This figure is usually supplied by the radio equipment manufacturer and can typically be -80 dB. It is a determined quantity and is entered into the applet accordingly. However, the fade margin must be determined. Typical figures are 20 to 35 dB. By equating the unfaded received signal level in the last two equations, the main equations for calculating the transmitter power, the antenna gains and the fade margin result. That is:

It is these last three equations which are used to calculate either the transmitter power, given the remaining parameters and variables, or the antenna gains, or the fade margin.

The Applet

The applet comprises six scrollbars and three radio buttons. After selecting the radio button for the required parameter to be determined, data is entered into each of the remaining scrollbars. The scrollbars for which the required parameter is to be determined are disabled. After entering the required data, the radio button for the parameter to be determined must be selected again. The result will be the required answer. As the distance is increased, the two antennas will be separated. As the antenna gains entered or calculated are increased, the antenna sizes will increase or decrease accordingly. As the transmit power is increased the site A radio hut will change color, with red as the maximum power permitted. As the received signal power increases, the site B radio hut will change colour, again with red near maximum power and black as the maximum received power of 0 dBm is reached (a burnt out receiver). Note the units which are to be entered in the scrollbars, frequency is in GHz and will step in steps of 100MHz, distance will step in steps of 100m, power in 0.1 dBm, antenna gains in 0.1 dB and antenna /coupling losses in steps of 0.1 dB. Each scrollbar will exceed the maximum expected values to be entered for a practical radio link. Apart from the main parameter calculation, there are side calculations in blue at the bottom of the applet. These give the free space basic transmission loss (or path loss) Ao, the unfaded received signal power Prx(unfaded) (dBm), and the sum of the two antenna gains GA + GB (dBi). The resulting parameter for equal antennas is the diameter of the dish, therefore to determine what the gain of the two dishes are, read the bottom right hand side value in dBi. By adjusting values, it is hoped that you get a feel for radio link design. A typical range of transmitter powers to use are 30 to 40 dBm. Typical path lengths are 30 to 40 km.

The source code (version 98/08/05 Rev.1) is available according to the GNU Public License.


Tony Townsend, tonyart@ieee.org