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Spectrum Management for Science in the 21st Century (2010)

Chapter:Appendix C: Density of Interferers Equation

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Suggested Citation:"Appendix C: Density of Interferers Equation." National Research Council. 2010. Spectrum Management for Science in the 21st Century. Washington, DC: The National Academies Press. doi: 10.17226/12800.
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Appendix C
Density of Interferers Equation

The power received at a radiometer due to the emission of PT watts from a particular interferer at distance R can be predicted using the Friis formula:

(C.1)

where PR is the power received at the radiometer in watts, GT is the transmitter antenna gain in the direction of the radiometer (dimensionless), Aeff is the effective aperture of the receive antenna (square meters), and eτ describes the attenuation of the transmitted power by atmospheric gases, clouds, and rain along the path from the transmitter to the receiver. The product PTGT when using the maximum of the transmitter antenna gain is also referred to as the equivalent isotropic radiated power (EIRP) of a source. For multiple uncorrelated radio frequency interference (RFI) sources within a radiometer footprint, the EIRP of the interference is usually approximated as the sum of that of all the individual sources.

The received power PR produces a brightness-temperature perturbation of

(C.2)

where k is Boltzmann’s constant (1.38 × 1023 W − Hz−1K−1) and B is the radiometer bandwidth (Hz). Combining Equations C.1 and C.2 and using the property that the radiometer beamwidth (and hence footprint size) is related to the antenna size

Suggested Citation:"Appendix C: Density of Interferers Equation." National Research Council. 2010. Spectrum Management for Science in the 21st Century. Washington, DC: The National Academies Press. doi: 10.17226/12800.
×

(and hence to the square root of the effective aperture area), the density (in W/m2) of the EIRP within the radiometer field of view can be related to the maximum tolerable brightness perturbation:

(C.3)

where A is the radiometer footprint area (m2); Equation C.3 shows that it is the density of EIRP per area (computed over the radiometer footprint) that determines the interference to the radiometer. EIRP limits on individual transmitters must be combined with information on the expected number of transmitters within a specific area in order to predict or interpret observed interference levels δT.

As an example, a 6.9 GHz Advanced Microwave Scanning Radiometer-Earth (AMSR-E) observation (2,500 km2 footprint area) with a bandwidth of 350 MHz will experience a brightness increase of 1 K if even a single interferer having a 130 milliwatt EIRP (in the direction of the radiometer antenna) is included in the footprint area. That such low radiated interference powers can perturb observed brightness temperatures demonstrates the high sensitivity of Earth Exploration-Satellite Service observations to interference. The fact that multiple interference sources may reside within any radiometer footprint substantially exacerbates the problem. The impact of a specific interference level on a particular geophysical measurement depends on the sensitivity of the measurement to changes in brightness temperature, as discussed in §2.2 in Chapter 2 of this report. The accuracy achieved in current radiometer systems typically makes even small changes in brightness caused by radio frequency interference to have a significant impact on measured products.

Suggested Citation:"Appendix C: Density of Interferers Equation." National Research Council. 2010. Spectrum Management for Science in the 21st Century. Washington, DC: The National Academies Press. doi: 10.17226/12800.
×
Page208
Suggested Citation:"Appendix C: Density of Interferers Equation." National Research Council. 2010. Spectrum Management for Science in the 21st Century. Washington, DC: The National Academies Press. doi: 10.17226/12800.
×
Page209
Next: Appendix D: Analysis of Out-of-Band Emission Impacts to the EESS from §27.53 of the FCC Rules »
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Radio observations of the cosmos are gathered by geoscientists using complex earth-orbiting satellites and ground-based equipment, and by radio astronomers using large ground-based radio telescopes. Signals from natural radio emissions are extremely weak, and the equipment used to measure them is becoming ever-more sophisticated and sensitive.

The radio spectrum is also being used by radiating, or "active," services, ranging from aircraft radars to rapidly expanding consumer services such as cellular telephones and wireless internet. These valuable active services transmit radio waves and thereby potentially interfere with the receive-only, or "passive," scientific services. Transmitters for the active services create an artificial "electronic fog" which can cause confusion, and, in severe cases, totally blinds the passive receivers.

Both the active and the passive services are increasing their use of the spectrum, and so the potential for interference, already strong, is also increasing. This book addresses the tension between the active services' demand for greater spectrum use and the passive users' need for quiet spectrum. The included recommendations provide a pathway for putting in place the regulatory mechanisms and associated supporting research activities necessary to meet the demands of both users.

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