Ex 2 GPS Power Calculation

0178-EX-CM-2018 Text Documents

General Motors Research Corporation

2018-09-29ELS_217102

Exhibit #2 GPS Re-Radiation System Technical Description GM proposes to install the seven (7) fixed GPS re-radiation GLI-Metro-G repeaters which will be located indoors in the test crash hall, which is a facility/building located at the General Motors Milford Proving Grounds in Milford, Michigan. The building in question is used exclusively for GM operations to conduct vehicle crash testing and telematics system testing under a variety of constraints and scenarios. A total of two rooftop active antennas (one existing, one new) will be used and locations are as follows: No. Rooftop Antenna Latitude Longitude Location (receives GPS signal from satellites) 1. Active Antenna FCC license acquired already 2. Active Antenna 42°33'52.76"N 83°40'42.19"W Outdoor/Rooftop The locations of the GPS Repeaters (with their attached passive transmitting antennas) for which GMRC seeks approval are given in the following table. Repeater 1 is existing and an FCC license has already been acquired for it; only a change in power level and elimination of L2 is being proposed. GMRC proposes to add Repeaters 2, 3, 4, 5, 6, 7, and 8 to the license. Repeater Transmitting Equipment Latitude Longitude Location 1 GLI-Metro-G Repeater 42°33'56.60"N 83°40'42.70"W Indoor 2 GLI-Metro-G Repeater 42°33'55.53"N 83°40'42.70"W Indoor 3 GLI-Metro-G Repeater 42°33'54.41"N 83°40'42.70"W Indoor 4 GLI-Metro-G Repeater 42°33'53.29"N 83°40'42.70"W Indoor 5 GLI-Metro-G Repeater 42°33'54.53"N 83°40'42.41"W Indoor 6 GLI-Metro-G Repeater 42°33'53.54"N 83°40'42.41"W Indoor 7 GLI-Metro-G Repeater 42°33'52.54"N 83°40'42.41"W Indoor 8 GLI-Metro-G Repeater 42°33'52.54"N 83°40'42.53"W Indoor 1

Below is the system diagram of the crash test facility, showing the GPS repeater locations. Below is the aerial view of the crash test facility with the GPS repeater locations (1 is existing; 2, 3, 4, 5, 6, 7, and 8 are proposed). 2

Emission Calculations Emission calculation per antenna/GPS repeater1 are explained below, and compliance with Redbook section 8.3.27 is demonstrated. The calculations are performed based on the fact that the antennas are directional.2 All of the repeaters re-radiate L1.3 Power Settings The GPS repeater offers an output power setting, which is a whole number from -85 to -65 inclusive. It specifies the output power of the repeater, which is then supplied to the passive transmitting antenna that is attached to the repeater. The proposed output power settings in order to receive good coverage in the crash test facility are as below: Repeater Transmit ERP L1 Units 1 -76 dBm 2 -79 dBm 3 -78 dBm 4 -78 dBm 5 -78 dBm 6 -78 dBm 7 -78 dBm 8 -77 dBm Assessment against 8.3.27 section “e” Section 8.3.27 of the NTIA “Manual of Regulations and Procedures for Federal Radio Frequency Management (Redbook)”, Sept 2017 Revision of the Sept 2015 edition, states the following in section “e”: “The area of potential interference to GPS reception (e.g., military or contractor facility) has to be under the control of the user.” The crash test facility (the building shown earlier) is located inside the GM Milford Proving Grounds, which is a large private access controlled campus surrounded by a fence. Thus this campus, the crash test facility, and indeed the area of potential interference, are under the control of the user. 1 Each GPS re-radiator consists of a repeater with an attached passive transmitting antenna. 2 See “Explanation of Gain Values Used” section for explanation. 3 Previously Repeater 1 re-radiated both L1 and L2, but GMRC proposes to replace this repeater’s antenna with an antenna that supports only L1. 3

Assessment against 8.3.27 section “f” Maximum Permissible EIRP Section “f” imposes a maximum permissible EIRP in dBm called “𝑃𝑇𝑚𝑎𝑥”, which is calculated according to the following formula: 𝑃𝑇𝑚𝑎𝑥 = 𝑃𝑅 + 20 log10 𝑓 + 20 log10(30 + 𝑑) − 27.55 Where: 𝑃𝑇𝑚𝑎𝑥 is the maximum permissible EIRP in dBm 𝑃𝑅 is the power received at 30 meters from the building (i.e. -140 dBm/24 MHz) 𝑓 is frequency in MHz (i.e. 1575.42 for L1, 1227.60 for L2, 1176.45 for L5) 𝑑 is the distance between the radiator and the closest exterior wall of the building in meters. This requirement is met for each repeater. Below are the calculations of maximum permissible EIRP and actual EIRP for each repeater:4 4 The antenna gain values used in these calculations are explained in the “Explanation of Gain Values Used” section later in this document. 4

Antenna 1 - L1 Maximum Permissible EIRP Label Parameter Value Units Notes / Formula A PR -140 dBm Power received at 30 meters from the building B f 1575.42 MHz L1 center frequency Distance between the radiator and the closest exterior C d 7.26 meters wall of the building Maximum permissible EIRP D PTmax -72.2 dBm = A + 20 * log(B) + 20 * log(30 + C) − 27.55 E PTmax 60.6 pW Maximum permissible EIRP = 10(D/10)+9 Antenna 1 - L1 Actual EIRP Label Parameter Value Units Notes / Formula Transmit ERP A from repeater -76 dBm Transmit ERP = 10(A/10)+9 B from repeater 25.1 pW Transmit EIRP C from repeater -73.85 dBm = A + 2.15 Gain of repeater's antenna in direction of closest exterior D Antenna Gain 1.17 dB wall Transmit EIRP from repeater's E antenna -72.7 dBm =C+D Transmit EIRP from repeater's = 10(E/10)+9 F antenna 53.9 pW The actual EIRP for Repeater 1 (-72.7 dBm = 53.9 pW) is less than the maximum permissible EIRP for this repeater (-72.2 dBm = 60.6 pW). 5

Antenna 2 - L1 Maximum Permissible EIRP Label Parameter Value Units Notes / Formula A PR -140 dBm Power received at 30 meters from the building B f 1575.42 MHz L1 center frequency Distance between the radiator and the closest exterior C d 9.24 meters wall of the building Maximum permissible EIRP D PTmax -71.7 dBm = A + 20 * log(B) + 20 * log(30 + C) − 27.55 E PTmax 67.2 pW Maximum permissible EIRP = 10(D/10)+9 Antenna 2 - L1 Actual EIRP Label Parameter Value Units Notes / Formula Transmit ERP A from repeater -79 dBm Transmit ERP = 10(A/10)+9 B from repeater 12.6 pW Transmit EIRP C from repeater -76.85 dBm = A + 2.15 Gain of repeater's antenna in direction of closest exterior D Antenna Gain 4.33 dB wall Transmit EIRP from repeater's E antenna -72.5 dBm =C+D Transmit EIRP from repeater's = 10(E/10)+9 F antenna 56.0 pW The actual EIRP for Repeater 2 (-72.5 dBm = 56 pW) is less than the maximum permissible EIRP for this repeater (-71.7 dBm = 67.2 pW). 6

Antenna 3 - L1 Maximum Permissible EIRP Label Parameter Value Units Notes / Formula A PR -140 dBm Power received at 30 meters from the building B f 1575.42 MHz L1 center frequency Distance between the radiator and the closest exterior C d 5.94 meters wall of the building Maximum permissible EIRP D PTmax -72.5 dBm = A + 20 * log(B) + 20 * log(30 + C) − 27.55 E PTmax 56.4 pW Maximum permissible EIRP = 10(D/10)+9 Antenna 3 - L1 Actual EIRP Label Parameter Value Units Notes / Formula Transmit ERP A from repeater -78 dBm Transmit ERP = 10(A/10)+9 B from repeater 15.8 pW Transmit EIRP C from repeater -75.85 dBm = A + 2.15 Gain of repeater's antenna in direction of closest exterior D Antenna Gain 2.50 dB wall Transmit EIRP from repeater's E antenna -73.4 dBm =C+D Transmit EIRP from repeater's = 10(E/10)+9 F antenna 46.2 pW The actual EIRP for Repeater 3 (-73.4 dBm = 46.2 pW) is less than the maximum permissible EIRP for this repeater (-72.5 dBm = 56.4 pW). 7

Antenna 4 - L1 Maximum Permissible EIRP Label Parameter Value Units Notes / Formula A PR -140 dBm Power received at 30 meters from the building B f 1575.42 MHz L1 center frequency Distance between the radiator and the closest exterior C d 5.94 meters wall of the building Maximum permissible EIRP D PTmax -72.5 dBm = A + 20 * log(B) + 20 * log(30 + C) − 27.55 E PTmax 56.4 pW Maximum permissible EIRP = 10(D/10)+9 Antenna 4 - L1 Actual EIRP Label Parameter Value Units Notes / Formula Transmit ERP A from repeater -78 dBm Transmit ERP = 10(A/10)+9 B from repeater 15.8 pW Transmit EIRP C from repeater -75.85 dBm = A + 2.15 Gain of repeater's antenna in direction of closest exterior D Antenna Gain 2.50 dB wall Transmit EIRP from repeater's E antenna -73.4 dBm =C+D Transmit EIRP from repeater's = 10(E/10)+9 F antenna 46.2 pW The actual EIRP for Repeater 4 (-73.4 dBm = 46.2 pW) is less than the maximum permissible EIRP for this repeater (-72.5 dBm = 56.4 pW). 8

Antenna 5 - L1 Maximum Permissible EIRP Label Parameter Value Units Notes / Formula A PR -140 dBm Power received at 30 meters from the building B f 1575.42 MHz L1 center frequency Distance between the radiator and the closest exterior C d 4.62 meters wall of the building Maximum permissible EIRP D PTmax -72.8 dBm = A + 20 * log(B) + 20 * log(30 + C) − 27.55 E PTmax 52.3 pW Maximum permissible EIRP = 10(D/10)+9 Antenna 5 - L1 Actual EIRP Label Parameter Value Units Notes / Formula Transmit ERP A from repeater -78 dBm Transmit ERP = 10(A/10)+9 B from repeater 15.8 pW Transmit EIRP C from repeater -75.85 dBm = A + 2.15 Gain of repeater's antenna in direction of closest exterior D Antenna Gain 2.50 dB wall Transmit EIRP from repeater's E antenna -73.4 dBm =C+D Transmit EIRP from repeater's = 10(E/10)+9 F antenna 46.2 pW The actual EIRP for Repeater 5 (-73.4 dBm = 46.2 pW) is less than the maximum permissible EIRP for this repeater (-72.8 dBm = 52.3 pW). 9

Antenna 6 - L1 Maximum Permissible EIRP Label Parameter Value Units Notes / Formula A PR -140 dBm Power received at 30 meters from the building B f 1575.42 MHz L1 center frequency Distance between the radiator and the closest exterior C d 4.62 meters wall of the building Maximum permissible EIRP D PTmax -72.8 dBm = A + 20 * log(B) + 20 * log(30 + C) − 27.55 E PTmax 52.3 pW Maximum permissible EIRP = 10(D/10)+9 Antenna 6 - L1 Actual EIRP Label Parameter Value Units Notes / Formula Transmit ERP A from repeater -78 dBm Transmit ERP = 10(A/10)+9 B from repeater 15.8 pW Transmit EIRP C from repeater -75.85 dBm = A + 2.15 Gain of repeater's antenna in direction of closest exterior D Antenna Gain 2.50 dB wall Transmit EIRP from repeater's E antenna -73.4 dBm =C+D Transmit EIRP from repeater's = 10(E/10)+9 F antenna 46.2 pW The actual EIRP for Repeater 6 (-73.4 dBm = 46.2 pW) is less than the maximum permissible EIRP for this repeater (-72.8 dBm = 52.3 pW). 10

Antenna 7 - L1 Maximum Permissible EIRP Label Parameter Value Units Notes / Formula A PR -140 dBm Power received at 30 meters from the building B f 1575.42 MHz L1 center frequency Distance between the radiator and the closest exterior C d 4.62 meters wall of the building Maximum permissible EIRP D PTmax -72.8 dBm = A + 20 * log(B) + 20 * log(30 + C) − 27.55 E PTmax 52.3 pW Maximum permissible EIRP = 10(D/10)+9 Antenna 7 - L1 Actual EIRP Label Parameter Value Units Notes / Formula Transmit ERP A from repeater -78 dBm Transmit ERP = 10(A/10)+9 B from repeater 15.8 pW Transmit EIRP C from repeater -75.85 dBm = A + 2.15 Gain of repeater's antenna in direction of closest exterior D Antenna Gain 2.50 dB wall Transmit EIRP from repeater's E antenna -73.4 dBm =C+D Transmit EIRP from repeater's = 10(E/10)+9 F antenna 46.2 pW The actual EIRP for Repeater 7 (-73.4 dBm = 46.2 pW) is less than the maximum permissible EIRP for this repeater (-72.8 dBm = 52.3 pW). 11

Antenna 8 - L1 Maximum Permissible EIRP Label Parameter Value Units Notes / Formula A PR -140 dBm Power received at 30 meters from the building B f 1575.42 MHz L1 center frequency Distance between the radiator and the closest exterior C d 8.58 meters wall of the building Maximum permissible EIRP D PTmax -71.9 dBm = A + 20 * log(B) + 20 * log(30 + C) − 27.55 E PTmax 64.9 pW Maximum permissible EIRP = 10(D/10)+9 Antenna 8 - L1 Actual EIRP Label Parameter Value Units Notes / Formula Transmit ERP A from repeater -77 dBm Transmit ERP = 10(A/10)+9 B from repeater 20.0 pW Transmit EIRP C from repeater -74.85 dBm = A + 2.15 Gain of repeater's antenna in direction of closest exterior D Antenna Gain 2.50 dB wall Transmit EIRP from repeater's E antenna -72.4 dBm =C+D Transmit EIRP from repeater's = 10(E/10)+9 F antenna 58.2 pW The actual EIRP for Repeater 8 (-72.4 dBm = 58.2 pW) is less than the maximum permissible EIRP for this repeater (-71.9 dBm = 64.9 pW). 12

The following table summarizes the above: Repeater Maximum Actual EIRP Actual EIRP is less than Permissible EIRP (dBm/pW) maximum permissible EIRP? (dBm/pW) 1 -72.2 / 60.6 -72.7 / 53.9 YES 2 -71.7 / 67.2 -72.5 / 56.0 YES 3 -72.5 / 56.4 -73.4 / 46.2 YES 4 -72.5 / 56.4 -73.4 / 46.2 YES 5 -72.8 / 52.3 -73.4 / 46.2 YES 6 -72.8 / 52.3 -73.4 / 46.2 YES 7 -72.8 / 52.3 -73.4 / 46.2 YES 8 -71.9 / 64.9 -72.4 / 58.2 YES Distance to Nearest Exterior Wall Section “f” also requires the following: “Applications requesting power greater than the 𝑃𝑇𝑚𝑎𝑥 calculated at 𝑑 = 0 meters (i.e. 39.3 pW for L1…) must provide the distance from the transmit antenna to the nearest exterior wall so that reviewing agencies can determine if the requested power meets the maximum EIRP described above.” The following table provides the distance from each repeater’s transmit antenna to the nearest exterior wall.5 Repeater Distance to nearest exterior wall (meters) 1 7.26 2 9.24 3 5.94 4 5.94 5 4.62 6 4.62 7 4.62 8 8.58 Explanation of Gain Values Used The antennas attached to the repeaters are directional, i.e. the gain of the antenna varies as a function of azimuth with respect to the antenna. Therefore in the “Maximum Permissible EIRP” section above the gain value that is used for each repeater is the one corresponding to the azimuth of a line drawn from the antenna to the closest exterior wall. The purpose of this section is to explain the antenna’s 5 These are the same figures used in the earlier calculations for “Maximum Permissible EIRP”. 13

gain values as a function of azimuth, and after that to show how this is used to obtain the gain value to use for each repeater. The antenna that is used for each repeater is the L1G1P “GNSS L1/G1/E1 Passive Antenna” from GPS Source. The following polar plot, taken from the antenna’s data sheet6, shows the gain as a function of azimuth: 6 Technical Product Data Sheet L1G1P GNSS L1/G1/E1 Passive Antenna, document number 059-FAN-AKD-AAY-PYZ- 001, dated 12/22/2016, filename “L1G1-Passive-GNSS-Antenna-Wireless-059-FAN-AKD-AAY-PYZ-001.pdf”. Obtained from GPS Source. 14

To simplify the calculations, the above polar plot is simplified to the following “pie slice” depiction: The above simplified polar plot does not understate the gain at any azimuth and in fact overstates it in many cases. This conservative approach ensures that this simplification never falsely indicates compliance with Redbook section 8.3.27. Below is the diagram of the crash test facility, with a dashed arrow drawn from each repeater to the closest exterior wall.7 7 For legibility the arrows are drawn beyond the wall. The length of the arrows is not meaningful. 15

The following table shows the azimuth (with respect to antenna orientation) for each dashed arrow, as well as the corresponding antenna gain value.8 Repeater Azimuth to closest exterior Antenna gain (dB) wall (degrees) 1 135 1.17 2 45 4.33 3 90 2.50 4 90 2.50 5 90 2.50 6 90 2.50 7 90 2.50 8 270 2.50 Supplement – Graphical Depictions of Signal Strength From the “simplified polar plot” of gain shown above, calculations were performed to determine the distance to which a signal strength higher than -140 dBm EIRP extends from the repeater, as a function of both azimuth and of power setting. The calculations are provided later in this document in the section “Appendix – Calculations for Signal Strength Depictions”. The following table summarizes the results of those calculations: Power How far (in meters) signal strength of -140 dBm EIRP extends from repeater Setting 315-45 degrees 45-90 degrees, 90-270 degrees a.k.a. 270-315 degrees Transmit ERP L1 (dBm) -79 35.83 29.01 24.89 -78 40.20 32.55 27.92 -77 45.11 36.53 31.33 -76 50.61 40.98 35.15 From the results in the above table, graphical “pie slice” depictions of signal strength were prepared for various combinations of power setting and azimuth range. Finally, for each repeater appropriate signal strength depiction was laid on top of the crash test facility diagram at that repeater’s proposed location. The results of that exercise are shown in the eight figures that follow. How to read the figures: • Direction of black arrow indicates which way the repeater’s antenna will be pointed. • Pink shaded region indicates the area surrounding the repeater where signal strength is higher than -140 dBm EIRP. 8 These are the gain values used in the “Maximum Permissible EIRP” section above. 16

• Purple bars, 30 meters in length, are placed in various locations to show 30 meter distance from the building. The below eight figures confirm that for each repeater the signal strength is at or below -140 dBm EIRP at 30 meters from the building. Pink shows area where signal strength is higher than -140 dBm EIRP for Repeater 1, set to -76 dBm ERP: Pink shows area where signal strength is higher than -140 dBm EIRP for Repeater 2, set to -79 dBm ERP: 17

Pink shows area where signal strength is higher than -140 dBm EIRP for Repeater 3, set to -78 dBm ERP: Pink shows area where signal strength is higher than -140 dBm EIRP for Repeater 4, set to -78 dBm ERP: 18

Pink shows area where signal strength is higher than -140 dBm EIRP for Repeater 5, set to -78 dBm ERP: Pink shows area where signal strength is higher than -140 dBm EIRP for Repeater 6, set to -78 dBm ERP: 19

Pink shows area where signal strength is higher than -140 dBm EIRP for Repeater 7, set to -78 dBm ERP: Pink shows area where signal strength is higher than -140 dBm EIRP for Repeater 8, set to -77 dBm ERP: Appendix – Calculations for Signal Strength Depictions Below are the calculations for how far the signal strength of -140 dBm EIRP (or higher) reaches from the repeater, as a function of azimuth and repeater power setting. The results of these calculations are used in the earlier section “Supplement – Graphical Depictions of Signal Strength”. 20

Label Parameter Value Units Notes / Formula Received signal strength of A interest -140 dBm Frequency of B interest 1575.42 MHz L1 center frequency Transmit ERP C from repeater -79 dBm Power setting on repeater Transmit EIRP D from repeater -76.85 dBm = C + 2.15 Azimuth range E of interest 315-45 degrees Antenna gain in this azimuth Obtained from "pie slice" depiction of gain F range 4.33 dB shown earlier Transmit EIRP from repeater's G antenna -72.5 dBm =D+F Distance to which signal strength of H interest extends 35.83 meters = 10^(( -A + G - 20*log(B) + 27.55)/20) 21

Label Parameter Value Units Notes / Formula Received signal strength of A interest -140 dBm Frequency of B interest 1575.42 MHz L1 center frequency Transmit ERP C from repeater -79 dBm Power setting on repeater Transmit EIRP D from repeater -76.85 dBm = C + 2.15 Azimuth range E of interest 45-90, 270-315 degrees Antenna gain in this azimuth Obtained from "pie slice" depiction of gain F range 2.50 dB shown earlier Transmit EIRP from repeater's G antenna -74.4 dBm =D+F Distance to which signal strength of H interest extends 29.01 meters = 10^(( -A + G - 20*log(B) + 27.55)/20) 22

Label Parameter Value Units Notes / Formula Received signal strength of A interest -140 dBm Frequency of B interest 1575.42 MHz L1 center frequency Transmit ERP C from repeater -79 dBm Power setting on repeater Transmit EIRP D from repeater -76.85 dBm = C + 2.15 Azimuth range E of interest 90-270 degrees Antenna gain in this azimuth Obtained from "pie slice" depiction of gain F range 1.17 dB shown earlier Transmit EIRP from repeater's G antenna -75.7 dBm =D+F Distance to which signal strength of H interest extends 24.89 meters = 10^(( -A + G - 20*log(B) + 27.55)/20) 23

Label Parameter Value Units Notes / Formula Received signal strength of A interest -140 dBm Frequency of B interest 1575.42 MHz L1 center frequency Transmit ERP C from repeater -78 dBm Power setting on repeater Transmit EIRP D from repeater -75.85 dBm = C + 2.15 Azimuth range E of interest 315-45 degrees Antenna gain in this azimuth Obtained from "pie slice" depiction of gain F range 4.33 dB shown earlier Transmit EIRP from repeater's G antenna -71.5 dBm =D+F Distance to which signal strength of H interest extends 40.20 meters = 10^(( -A + G - 20*log(B) + 27.55)/20) 24

Label Parameter Value Units Notes / Formula Received signal strength of A interest -140 dBm Frequency of B interest 1575.42 MHz L1 center frequency Transmit ERP C from repeater -78 dBm Power setting on repeater Transmit EIRP D from repeater -75.85 dBm = C + 2.15 Azimuth range E of interest 45-90, 270-315 degrees Antenna gain in this azimuth Obtained from "pie slice" depiction of gain F range 2.50 dB shown earlier Transmit EIRP from repeater's G antenna -73.4 dBm =D+F Distance to which signal strength of H interest extends 32.55 meters = 10^(( -A + G - 20*log(B) + 27.55)/20) 25

Label Parameter Value Units Notes / Formula Received signal strength of A interest -140 dBm Frequency of B interest 1575.42 MHz L1 center frequency Transmit ERP C from repeater -78 dBm Power setting on repeater Transmit EIRP D from repeater -75.85 dBm = C + 2.15 Azimuth range E of interest 90-270 degrees Antenna gain in this azimuth Obtained from "pie slice" depiction of gain F range 1.17 dB shown earlier Transmit EIRP from repeater's G antenna -74.7 dBm =D+F Distance to which signal strength of H interest extends 27.92 meters = 10^(( -A + G - 20*log(B) + 27.55)/20) 26

Label Parameter Value Units Notes / Formula Received signal strength of A interest -140 dBm Frequency of B interest 1575.42 MHz L1 center frequency Transmit ERP C from repeater -77 dBm Power setting on repeater Transmit EIRP D from repeater -74.85 dBm = C + 2.15 Azimuth range E of interest 315-45 degrees Antenna gain in this azimuth Obtained from "pie slice" depiction of gain F range 4.33 dB shown earlier Transmit EIRP from repeater's G antenna -70.5 dBm =D+F Distance to which signal strength of H interest extends 45.11 meters = 10^(( -A + G - 20*log(B) + 27.55)/20) 27

Label Parameter Value Units Notes / Formula Received signal strength of A interest -140 dBm Frequency of B interest 1575.42 MHz L1 center frequency Transmit ERP C from repeater -77 dBm Power setting on repeater Transmit EIRP D from repeater -74.85 dBm = C + 2.15 Azimuth range E of interest 45-90, 270-315 degrees Antenna gain in this azimuth Obtained from "pie slice" depiction of gain F range 2.50 dB shown earlier Transmit EIRP from repeater's G antenna -72.4 dBm =D+F Distance to which signal strength of H interest extends 36.53 meters = 10^(( -A + G - 20*log(B) + 27.55)/20) 28

Label Parameter Value Units Notes / Formula Received signal strength of A interest -140 dBm Frequency of B interest 1575.42 MHz L1 center frequency Transmit ERP C from repeater -77 dBm Power setting on repeater Transmit EIRP D from repeater -74.85 dBm = C + 2.15 Azimuth range E of interest 90-270 degrees Antenna gain in this azimuth Obtained from "pie slice" depiction of gain F range 1.17 dB shown earlier Transmit EIRP from repeater's G antenna -73.7 dBm =D+F Distance to which signal strength of H interest extends 31.33 meters = 10^(( -A + G - 20*log(B) + 27.55)/20) 29

Label Parameter Value Units Notes / Formula Received signal strength of A interest -140 dBm Frequency of B interest 1575.42 MHz L1 center frequency Transmit ERP C from repeater -76 dBm Power setting on repeater Transmit EIRP D from repeater -73.85 dBm = C + 2.15 Azimuth range E of interest 315-45 degrees Antenna gain in this azimuth Obtained from "pie slice" depiction of gain F range 4.33 dB shown earlier Transmit EIRP from repeater's G antenna -69.5 dBm =D+F Distance to which signal strength of H interest extends 50.61 meters = 10^(( -A + G - 20*log(B) + 27.55)/20) 30

Label Parameter Value Units Notes / Formula Received signal strength of A interest -140 dBm Frequency of B interest 1575.42 MHz L1 center frequency Transmit ERP C from repeater -76 dBm Power setting on repeater Transmit EIRP D from repeater -73.85 dBm = C + 2.15 Azimuth range E of interest 45-90, 270-315 degrees Antenna gain in this azimuth Obtained from "pie slice" depiction of gain F range 2.50 dB shown earlier Transmit EIRP from repeater's G antenna -71.4 dBm =D+F Distance to which signal strength of H interest extends 40.98 meters = 10^(( -A + G - 20*log(B) + 27.55)/20) 31

Label Parameter Value Units Notes / Formula Received signal strength of A interest -140 dBm Frequency of B interest 1575.42 MHz L1 center frequency Transmit ERP C from repeater -76 dBm Power setting on repeater Transmit EIRP D from repeater -73.85 dBm = C + 2.15 Azimuth range E of interest 90-270 degrees Antenna gain in this azimuth Obtained from "pie slice" depiction of gain F range 1.17 dB shown earlier Transmit EIRP from repeater's G antenna -72.7 dBm =D+F Distance to which signal strength of H interest extends 35.15 meters = 10^(( -A + G - 20*log(B) + 27.55)/20) 32

The following two pages discuss the GLI-Metro-G specifications for transmission of GPS and GLONASS 33

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Document Created: 2018-09-12 16:06:45
Document Modified: 2018-09-12 16:06:45
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