Calculating Range of Communication

[jimh]

Calculating Range of Communication

In any radio circuit, an important topic of interest is the anticipated or expected range of communication. There are several elements that affect the range of communication, namely

• transmitter output power
• transmitter transmission line loss
• transmitter antenna gain
• propagation path loss
• receiver antenna gain
• receiver transmission line loss
• receiver sensitivity
• desired signal margin.

I discuss each element briefly with regard to the VHF Marine Band. These parameters will then be analyzed to demonstrate a method to predict communication range.

Regarding signal power level, the comparison will be in decibels relative to one one-thousandths of a Watt or 0.001-Watt. This reference is called dBm (m for milliWatt).

Transmitter Power
For a VHF Marine Band ship station, the transmitter power output (Ptx) is limited to 25-Watts. Typically in order to achieve this power output the transmitter power supply must be maintained at the specified voltage and provide the specified current. The transmitter output must be connected to a properly matched antenna and transmission line. Any deficiency in supply power voltage or current or any mismatch in the antenna impedance and transmission line impedance will tend to reduce the power output. In order to not exceed the maximum power output, a manufacturer will typically aim for just under 25-Watts actual output. The effect of all these influences can reduce the actual power output to more like 20-Watts on average for a typical radio as installed on a typical boat. For better handling in the calculations, the power is converted to be in dBm, which is a ratio expressed is decibels to a power of 1-milliwatt. This produces Ptx = +43 dBm

Transmitter Transmission Line Loss
A general rule of thumb in selecting a transmission line is to aim for a loss in the transmission line (Ltx) of less than -1 dB at the frequency of operation. For 156.8-MHz and for a length of up to 20-feet, use of RG-58C/U transmission line will produce -1 dB or less of line loss. Thus Ltx= -1 dB

Transmitter Antenna Gain
Antenna gain is to be measured with reference to an isotropic radiator, indicated as dBi. Most VHF Marine Band antennas will exhibit about 3 dBi gain in their primary lobe of radiation. While antenna gain is difficult to measure, it can be done, and thus the transmitter antenna gain (Gtx) is a known value. A typical value will be Gtx= +3 dB

Propagation Path Loss
All radio signals lose intensity as they propagate, principally by beam spreading, and secondarily from the medium through which they are traveling. In some instances propagation loss can be increased or decreased by the a signal being reflected by terrain or other objects and recombining with the original signal in an additive or subtractive manner, depending on the phase relationship.

For propagation in a vacuum in completely empty or free space, theoretical analysis of propagation loss predicts that the intensity of the signal will decrease with the distance factor squared (second power exponent), also known as the inverse-square-law rule. In a real world in which the signal propagates through the atmosphere and there is terrain (land or sea) present, the effect of distance on signal strength is greater. Many approximations for propagation loss use a distance factor to the fourth exponent to better account of real-world propagation loss. Propagation loss is an estimated value, but it can be reasonably estimated and used in predicting range of communication. Path loss depends on three elements: frequency, distance, and propagation medium factor. Because the goal of this analysis is to find the maximum distance of communication, the frequency and the propagation medium factor must be known or be approximated as inputs to the calculation. A frequency of 156.8-MHz will be used. For the propagation medium factor, the fourth exponent of distance will be used as an approximation. The PathLoss which can be tolerated is yet to be deduced, as depends on the required it necessary receiver signal power, Prx.

Receiver Antenna Gain
As with transmitting antennas, the gain of a receiving antenna is the same as when transmitter. For this factor a gain of 3 dBi will again be used. Grx = +3 dB

Receiver Transmission Line Loss
Again, a value of -1 dB loss will be used for the receiver transmission line: Lrx = -1 dB

Receiver Sensitivity
All receivers have a limit to their useful sensitivity which is established by the internal electrical noise created by the receiver itself, by the bandwidth necessary to receive a modulated signal, and by the nature of the modulation. For a typical well-designed narrow-band FM receiver, the sensitivity is usually give as the needed signal power or voltage to produce a demodulated signal that is 10-times (10 dB) stronger than any noise or distortion in the recovered signal.

Receiver sensitivity (RxSens) is often stated in terms of microVolts at the 50-Ohm antenna input of the receiver. This power level can be converted to dBm. For advice on how to make the conversion, see a separate article at

Conversion of Receiver Sensitivity
From Microvolts to dBm
https://continuouswave.com/whaler/reference/dBm.html

A typical value for receiver sensitivity is 1-microvolt, and when converted to dBm gives an RxSens = -107 dBm.

Desired Margin
It is also useful to add some margin to the calculation to allow for variations in sensitivity caused by factors such as the presence of local radio-frequency noise interference or to allow for the possibility of signal fading due to variation in propagation loss. A margin for the signal to have a 100-times excess (20-dB) is useful to improve the reliability of the predicted communication range.

Required Minimum Signal Power at Receiver
Next, the necessary minimum signal power at the receiver site (Prx) to produce a useful demodulated signal is calculated. The receiver antenna gain improves sensitivity (allows weaker signals at the antenna) ; line loss decreases sensitivity (requires more signal), and the desired margin also effectively decreases receiver sensitivity (requires more signal) so we algebraically sum as follows:

Prx = RxSens + Margin

Now we find the maximum Path Loss (Lp) that can be tolerated, that is, when the desired Prx will occur based on the transmitter power, antenna gains, transmission line loses, and path losses.

Maximum tolerable propagation loss
 Lp = Ptx + Gtx + Grx + Ltx + Lrx - Prx

We have now found the maximum path loss that can be tolerated. Once this value has been estimated, the distance of communication can be calculated.

Calculating Path Distance As Function of Path Loss

The formula for path loss can be derived from radio theory for propagation in free space for the unit values to be MHz and Miles to be:

Path Loss  = -36.6 - 20log(f) - 20log(d)  (f in MHz, d in miles)

To see how this equation using deciBel ratios was derived, read my article "Marine VHF Radio Communication" and see the section under the heading "Converting Path Loss to Decibel Equation” at

https://continuouswave.com/whaler/reference/VHF.html

The influence of distance on loss is provided by the factor 20log(d), which is a way to express the familiar inverse-square-law of decrease in intensity with distance to a decibel form. To account for the greater loss over actual terrain and in the atmosphere, a formula with greater influence of distance is used, increasing the coefficient of the log(d)factor to 40 or higher:

Path Loss  = -36.6 - 20log(f)  - 40log(d)  (f in MHz, d in miles)

Solving the above for distance (d) gives

Path Loss  + 36.6 + 20log (f)  = 40log(d)
log(d) = (Path Loss  + 36.6 + 20log(f) ) / 40
d = 10^ [ (Path Loss  + 36.6 + 20log(f) ) / 40]

The purpose for the derivation of the above calculation method is to facilitate a simple way to predict a range of communication given a set of conditions for a particular communication circuit. The process can be incorporated into an algorithm or a spreadsheet, permitting the input of the variables and immediate calculation of the estimated range of communication.

To put some real numbers into these calculations, I will demonstrate a typical boat-to-boat VHF Marine Band situation. For the example, I will use the following inputs to deduce the allowed path loss Lpath:

f = 156.8 Mhz
Ptx =  +43 dBm
Ltx = -1 dB
Gtx = 3 dB
Grx = 3 dB
Lrx = -1
RxSen = -107 dBm
Margin = 20
Prx = -87 dBm
Distance Loss coefficient = 40

Prx = Ptx + Gtx + Grx + Ltx  + Lrx + Lpath

Path Loss =   Prx - Ptx  - Gtx - Gtx - Ltx  - Lrx
Path Loss =   -87 - (43) - (3) - (3) - (-1) - (-1)
Path Loss = -134 dB

Now that the maximum tolerable path loss has been calculated, we can use the formula for predicting path loss and solve it for distance. Again, path loss in decibel notation as a function of frequency and miles is

Path Loss  = -36.6 - 20log(f)   - 40log(d)  (f in MHz, d in miles)

Plugging our value for maximum path loss of of -134 dB and frequency 156.8 and solving for d gives

-134 = -36.6 - 20log(156.8) - 40log(d)
40log(d) =134 -36.6 - 43.91 
40log(d)=53.49
d=10^(53.49/40)
d = 21.7-miles

By creating a spreadsheet, the various input values can be changed to suit. Typical changes would be antenna gains, transmission line losses, and the coefficient for the distance factor. The latter change will have the most impact. For example, with all other variable as shown above, if the distance factor is changed to the free space model of 20log(d), the distance calculation becomes enormously longer: 472-miles.

-134 = -36.6 - 20log(156.8) - 20log(d)
20log(d) =134 -36.6 - 43.91 
20log(d)=53.49
d=10^(53.49/20)
d = 473-miles

If we further reduce reducing the signal margin required to zero, the range estimate becomes a rather fantastic 4,728-miles.

Getting back to real-world conditions, we restore the margin to 20 dB and increase the distance factor to 46log(d), which yields a predicted range of only 14.6-miles. This is probably the most reasonable estimate and most likely to actually be achieved in the real world of boat-to-boat communication.

[jimh]

When a radio engineer is faced with the problem of creating a reliable radio circuit between two locations, the distance between the stations is already known and is a fixed constant. The radio engineer begins the design of the communication system with that distance as the principal parameter, and he is tasked with designing a radio system to allow communication at that distance that will have a certain reliability. To create reliable communication, the appropriate elements such as frequency, transmitter power, antenna gain, and transmission line loses are adjusted to deliver the desired received signal power.

In contrast, a recreational boater with a VHF Marine Band radio inherits the limitations of the radio transmitter power, the receiver sensitivity, and frequency spectrum allowed to him. The distance at which those element will provide reliable communication is a function of all fixed limitations, and that is why in the discussion above the goal is to calculate that distance.

The analysis shows that the various maritime radio commissions which created the international VHF Marine Band considered all of these parameters, with the result they enacted regulations that created a maritime radio service for VHF that is designed to provide a range of reliable boat-to-boat communication of at least 15-miles for open seas without intervening land and with appropriate antenna height.

An estimate of 15-miles range also assumes that the heights of the transmitting and receiving antennas are both sufficient to produced a radio horizon that is at least half the the distance separating the two stations. A radio horizon includes compensation for the anticipated refraction of radio waves during propagation through normal earth atmosphere. A separate article gives details about the calculation of a radio horizon.

If we assume a symmetrical situation with regard to the radio horizon, then each boat needs a radio horizon of 7.5-miles. This implies each boat antenna must have a height above the sea of at least 28-feet.

Such heights may not be possible on smaller boats. If we assume a height of antenna to be only 8-feet above the water, then the radio horizon will only be 4-miles, so the total path may be limited to 8-miles. However, at that path distance, then only 1-Watt will be needed to produce a signal with at least a 20 dB fade margin, and a transmitter power of 20-Watts will produce and additional 13 dB of signal margin. This suggests that at a separation of 8-miles, boats using a 20-Watt output radio and antennas with 3-dBi gain at 8-feet above the water will have extremely reliable communication with each other.

[jimh]

A further consideration in calculating a useable radio path is to consider the absence of possible deflecting surfaces in the path which could redirect a portion of the transmitted wavefront, a wave that would normally not arrive at the receiving antenna, and cause that wave to be directed toward the receiving antenna. A wave arriving at the receiving antenna via deflection will always have travelled a longer distance, so the phase of that waves will not be in synchronism with the direct wave. Depending on the phase relationship between the direct and deflected wave, the two waves can combine either to add or subtract in amplitude. The worst case for combining of the two waves occurs when the longer wave has travelled exactly one-half-wavelength further; when this occurs the two waves will tend to sum toward zero, resulting in a significant reduction the received signal strength.

In order to avoid the possibility of this cancellation of the wavefronts occurring, the path between the transmitting antenna and the receiving must be clear of any obstacles in the regions where the deflected wave would tend to travel a distance that is exactly one-half-wavelength longer. This region is known as the First Fresnel Zone.

The width of the Fresnel Zone between two antenna locations as viewed in the vertical plane is an elongated oval, with the maximum width occurring at the half-way point between the two antennas. This is shown in the illustration below.

Fig. 1. The First Fresnel Zone indicated by the dark black line. Note the radius is greatest at the midpoint of the distance separating the two antennas. Credit: Jcmcclurg, as seen at https://commons.wikimedia.org/wiki/File:FresnelSVG1.svg

800px-FresnelSVG1.svg.jpeg (53.32 KiB) Viewed 1001 times

Any obstructions that lie inside the Fresnel Zone could generate deflected signals that would arrive out-of-phase with the direct signal, causing the received signal to decrease.

If a path is analyzed and no obstructions are found inside the First Fresnel Zone, the path is generally considered to be a Line-of-Sight (LOS) path, and path loss can be calculated using the Friis equation. (The Friis equation is explained in the addendum of a separate article) If an obstruction penetrates less than the 50-percent into of the First Fresnel Zone is path can be considered as near-Line-of-Sight (nLOS). If an obstruction penetrates more than 50-percent into the First Fresnel Zone, the path is considered as Non-Line-of-Sight (NLOS).

There are a number of useful on-line calculators that predict the necessary clearance above an obstruction that should be maintained at the path midpoint. A good example is found at

Fresnel Zone Calculator
https://afar.net/fresnel-zone-calculator/

That calculator includes an allowance for the natural refraction of the radio wave in the atmosphere. The K-value of 1.33 is the same as the often seen "four-thirds (4/3) Earth radius" factor applied to mapping of Earth curvature between two points for analysis of radio wave propagation. The value of "Percent of 1st FZ" refers to how much of the First Fresnel Zone is kept clear; the value of 60-percent is a common benchmark for assessing the path to he a line-of-sight path.

Using the AFAR.NET calculator for a situation in marine communication in the VHF Marine Band between two boats separated by a distance of just ten miles, as inputs, and setting the amount of clear Fresnel zone desired to be 60-percent (chosen to get the equivalent of a LOS path), the results are rather alarming: the needed antenna height at each end of the path is a very surprising (and generally unobtainable) 185-feet.

Fig. 2. A Fresnel Zone calculator predicting needed antenna height above the sea for a 10-mile path at 158-MHz. From https://afar.net/fresnel-zone-calculator/

pathAnalysis.jpg (86.8 KiB) Viewed 1001 times

This is a good example of why most boat-to-boat VHF Marine Band paths will not be in the category of line-of-sight, and the free-space path loss prediction formula won't be a good model to calculate path loss. Generally the compensation for path loss due to distance must be significanly increased to account for the presence of terrain (or in this case the open sea).

More detailed explanation of the calculation of the Fresnel Zone can be found in the Wikipedia article on that topic:

https://en.wikipedia.org/wiki/Fresnel_zone