WAAS Satellite Changes

[jimh]

The satellite based augmentation system (SBAS) called the Wide Area Augmentation System (WAAS) provided by the Federal Aviation Administration (FAA) for the Space Force NAVSTAR Global Positioning System (GPS) currently has three leased transponders on geostationary satellites. As of May 2022, the three satellites providers, their longitude, and their pseudo random noise (not number) (PRN) codes (and possible NMEA number in parenthesis) are as follows, going from East to West:

EUTELSAT 117 WEST B, 117° West, PRN 131, NMEA 44

GALAXY 30, 125° West, PRN 135, NMEA 48

SES-15, 129° West, PRN 133, NMEA 46

The location of these satellites in comparison to the USA mainland is rather tilted to the west, but this may be a result of the FAA orientation toward aircraft and a desire to support augmentation services in the far western areas of the United States, such as Alaska and Hawaii.

LOOK ANGLES
A "look angle" is the apparent elevation in the sky of a WAAS satellite from your particular location (and also the azimuth angle or heading to the satellite, but in this discussion, the azimuth won't be considered because the antenna used in marine GNSS receivers are omni-directional, that is, they do not need to be pointed at a particular heading in order to receive a satellite signal, as distinct from satellite high-gain dish antennas). All geostationary-orbit satellites are located on the equator. If the satellite longitude and your longitude are the same, the look angle is simply calculated by subtracting your latitude from 90-degrees. As can easily been inferred, the farther your location is north (or south) of the equator, the lower the look angle becomes. For example, if your location were at latitude 50-North, then the highest possible look angle would be 90 - 50 = 40-degrees for a satellite located on your longitude. If your location is not on the same longitude as the satellite, the look angle will be even lower. Calculating look angles involves some spherical trigonometry, but there are several on-line calculators that can solve for the look angle, given a particular ground location and a particular satellite.

Using a typical ground position for my boating, near 45-degree-North, 85-degrees-West, and using the easternmost WAAS satellite (EUTELSAT 117 WEST B at 117-degrees W), the look angle is rather low, 29.3-degrees. If you were a boater in Maine (around 44.8-North, 68.7-West, the look angle will be even lower: 20-degrees.

The lower the look angle, the longer the signal path. Also the signal path through the atmosphere will be corresponding longer. The longer the path length for the signal, the more attenuation of the signal, resulting in a lower signal level at the receiver. For this reason, boaters in the eastern USA should prefer to use PRN code 131, as it is being transmitted from the easternmost satellite and should be the strongest signal. Most GNSS receiver today can automatically choose the WAAS PRN source, but older receivers may need to be manually set to a specific satellite.

BIAS TO THE WEST
Earlier configurations of the WAAS satellites position tended to have more favorable locations for the eastern USA. For example, from November 2010 to November 2017, the INMARSAT4 F3 satellite at 97.6-degree-West longitude was part of WAAS, transmitting as PRN 133. This was the most favorable location as it was the most eastern satellite in the constellation. With this satellite location, the look angle from my boating area increased to 36.7-degrees.

Because the FAA system was designed for enhancement of position information from GPS for aircraft, these relatively low look angles in the eastern USA are more understandable: an aircraft in flight at 30,000-feet altitude does not really have to worry about any ground obstructions blocking a signal.

Because geo-stationary satellites over the eastern USA may have more customers for leasing a transponder, the cost of a leased transponder may be higher in those locations than for geostationary satellites in farther west longitudes. I don't have any data on this, and it is just my speculation.

PRN CODE and NMEA NUMBER
To understand why there is a "NMEA" number for these SBAS satellite PRN codes, I include an earlier article I wrote on this subject 15-years ago, in 2008:


GPS: PRN Codes and NMEA Satellite ID

The GPS system uses a form of spread-spectrum or code-division multiple access (CDMA) communications in which each signal source is modulated by a PRN code. PRN means "pseudo-random noise." (It does not mean "pseudo-random number" as is sometimes mistakenly reported.) The PRN code (along with other encoded sub codes) dithers the L1 carrier (or the coarse-acquisition carrier) of the signal. All receivers listen on the same L1 frequency, but they sort out the satellite signals by demodulating them according to their PRN encoding.

There is an allocation plan for assignment of PRN codes. In as much as the GPS is controlled by the military, not surprisingly the Air Force (now Space Force) is the source of authority. The allocation of PRN codes is:

1 to 63: Reserved for GPS satellites;

64 to 119: Reserved for ground-based augmentation systems (GBAS) and other sources;

120 to 158: Reserved for satellite-based augmentation systems (SBAS) such as the FAA's WAAS;

159 to 210: Reserved for future use

Source: http://www.losangeles.af.mil/shared/med ... 30-036.pdf
Also see: http://www.losangeles.af.mil/library/fa ... sp?id=8618

In the current GPS implementation, all the satellites are using a PRN code in the range 1 to 31. For the WAAS system all PRNs will be in the 120 to 158 range. [When this article was originally published there were ]only two active satellites, and they use PRN 135 and 138. Previously PRN 122 and 134 were active.

In the NMEA 0183 specification, which is proprietary and not available except by purchase, there is a field designator SATELLITE ID. As far as I can tell, again this is based without access to the actual specifications, the SATELLITE ID and the PRN are the same for values of 1 to 32.

Identification of WAAS SIS ("signals in space") sources in NMEA apparently uses a different technique. The SATELLITE ID is set to the PRN minus 87. We can build a table thus:

PRN -- NMEA ID
120 = 33
121 = 34
122 = 35
123 = 36

and so on to

135 = 48
136 = 49
137 = 50
138 = 51

and finally

157 = 70
158 = 71

In trying to understand the reasoning behind this, and again without the benefit of being able to actually see the NMEA-0183 specification, it appears as though the PRN numbering was transformed in order to cause it to become less than 64 for most possible PRN numbers. This may have been necessary to accommodate a limit in the NMEA-0183 specification with regard to the size of binary numbers it could send. This explanation seems plausible because the initial GPS configuration only suggested there would be PRN codes of 63 or less. When WAAS was introduced, there may not have been a specification in NMEA-0183 which provided for identification of signals with PRN numbers higher than 63.

I also speculate that in the NMEA-2000 specification there may be a new specification that provides for identification of the signal source by PRN, using a field size that can directly accommodate larger numbers. Or, perhaps there is an automatic re-translation of the numbers in the range 32 to 71 back to their original PRN of 120 to 158.

When initially looking at the relationship between PRN and NMEA SATELLITE ID, the offset of 87 did not make any sense. The value 87 does not seem intuitive as it is not a power of 2 (binary) or otherwise a natural number. However, once I discovered the notation of SBAS PRN beginning at 120, the translation by subtraction of 87 makes perfect since. It moves most all of the PRN codes into the range 32 to 63, a natural container based on binary math with a limited number of fields available.

If anyone with access to the NMEA-0183 or NMEA-2000 specification would care to comment on this, it would be appreciated.

CALCULATING LOOK ANGLES
The equations to calculate the look angles (azimuth and elevation) to a satellite from a ground position is demonstrated in a nice tutorial at

https://www.youtube.com/watch?v=1gS1zxpEMls

[jimh]

The look angles azimuth and elevation are calculated with spherical trigonometry and involve three-dimension (3D) analysis. The elevation angle can be reduced to a two-dimension (2D) by considering just the triangle formed in the plane of the satellite location, the earth location, and the center of the earth. This plane is shown in Figure 1.

Fig. 1. Angular relationship between satellite location, earth location, and earth center, shown in a 2D plane.

diagramGammaSymbol.png (10.84 KiB) Viewed 1384 times

The angle marked γ is usually referred to as "gamma" and shown with the Greek lower case letter γ. This is the included angle in the triangle at the earth center point.

The point marked Satellite Subpoint is the location on the Earth were the satellite appears directly overhead. In this particular case of using a geostationary satellite, the satellite subpoint will be on the equator and at the specific longitude of the satellite position. This will simplify some of the calculations. For non-geostationary satellites, the satellite would appear to be in motion relative to the earth because of its orbital characteristics, and in order to calculate the subpoint the precise orbital elements and the particular time would be required to predict the exactly location of the satellite subpoint. A geostationary satellite appears at a fixed position in the sky, so the time and orbit elements are not needed to deduce its subpoint.

The angle L is the elevation angle at the earth station location, which is the angle to be calculated from the other parameters available.

Two sides of the triangle have known lengths, re and rs, which are the radius of the earth and the radius of the satellite orbit. The radius of the earth is well known, and the radius of the satellite orbit for a geostationary satellite is also well known, so these two elements are easily found.

[jimh]

In order to calculate the angle γ ( or g ), you have to use trigonometry. With Le and Ls as the latitude of the earth station and the satellite subpoint, and le and ls are the longitude of the earth station and the satellite, the formula is:

cos(γ) = sin(Le)sin(Ls) + cos(le)cos(Ls)cos(ls-le)

Using the ArcCos (cos-1) function you find γ.

Then you can deduce the elevation angle L with this formula:

cos(L) = sin(γ) / [1 + (re/rs) - 2(re/rs)cos(γ) ]0.5

again using the ArcSin (cos-1) function to find L.

[I will try to work an example to demonstrate this works, but so far my results are not good. A simple on-line calculator can be found at

https://www.groundcontrol.com/us/knowledge/look-angle-calculator/

and it saves one a lot of trigonometry.]

[jimh]

Note that in the diagram shown in Figure 1, repeated below



the relationship shown in the drawing occurs in a particular situation with a geostationary satellite orbit which happens to be located on your meridian. In that case satellite subpoint on the earth is on the equator, and your subpoint angular distance, the angle γ (gamma), is just your latitude. The triangle can then be solved with 2D geometry to find the elevation angle.

For example, using the sin-cos calculator at

http://cossincalc.com

and using its notation of angles A, B, C and sides a, b ,c:

Enter these values:

A = your latitude
b = satellite radius, equal to earth radius + satellite orbit altutide
c = earth radius

The earth radius is 3,958.8 miles.

For a geostationary orbit the satellite altitude is 22,236 miles, so satellite radius is then 26194.8-miles

Assuming there is a geostationary satellite on your meridian (i.e., at your longitude), then Angle A is your latitude.

For a satellite on your meridian, the included angle B minus 90 is the satellite elevation angle:

The calculator provides this drawing showing the solution:

Fig. 2. A triangle showing the 2D geometry when a satellite in geostationary orbit is on your meridian.

triangle42-North.png (30.45 KiB) Viewed 1383 times

The included angle B is 131.5-degree, so minus 90-degrees gives the elevation angle: 41.5-degrees. The path length to the satellite, side a, is thus 23,403-miles. This is a much longer path length to the WAAS satellites that occurs with the GPS constellation satellites.

The orbit height of GPS satellites is 12,550-miles, or about half the height of the WAAS geostationary orbit satellites.

[jimh]

NOTE TO MYSELF

How I figured out a way to type the Greek lower case letter gamma using MacOS and enter it in the drawing program GIMP.

In MacOS System Preferences, open the Keyboard.

In the Input Sources tab, click the plus (+) sign at lower left.

Browse through the language sources, and select Greek, then select Greek again in the choices.

Click the box "Show input menu in the menu bar". This allows you to switch input languages for the keyboard.

The letter gamma is found at keyboard "g", for example: γ

[jimh]

Regarding the elevation angle and path lengths calculated for a WAAS satellite, we have also found a typical path length as shown above, in the case of a receiver at 42-degrees latitude. The optimum path length for a WAAS satellite occurs when the receiver is on the equator and at the longitude of the geostationary satellite orbit. At that location the path length is the orbit altitude, which is 22,236 miles. Any other location not on the equator and not at the longitude of the geostationary orbit the path length will be longer.

Regarding the elevation angle and path length for a GPS satellite, as long as the receiver is located at less than 50-degrees latitude, a GPS satellite will at some point pass directly overhead--the same parameter used for the WAAS satellite--and the path length will then be the GPS orbit altitude, or 12,550-miles.

Because in each case the satellite will be directly overhead and the path will be line-of-sight through the atmosphere, we can deduce the path loss with the free space model, where distance influences the path loss by the inverse square law relationship.

For both the GPS satellite and the WAAS satellites, the frequency is the same: the L1 carrier at 1,575.42-MHz. Computing the path loss with those parameters we find:

Path Loss GPS = -182.5 dB
Path Loss WAAS = -187.5 dB

The transmitter power (including antenna gain) for GPS is said to be 56.5 dBm. With a path loss of -182.5 dB, the received signal power should be -126 dBm.

The imputed transmitter power (including antenna gain) for WAAS is 61.5 dBm (based on a receiver signal power to be expected as the same for a GPS satellite at -126 dBm after path loss of -187.5 dB).

Comparing transmitted signal power level (including antenna gain) we have

GPS = 56.5 dBm or 446.6-Watts ERP
WAAS = 61.5 dBm or 1,412.5 Watts ERP