Density of Interferers Equation

The power received at a radiometer due to the emission of *P*_{T} watts from a particular interferer at distance *R* can be predicted using the Friis formula:

(C.1)

where *P*_{R} is the power received at the radiometer in watts, *G*_{T} is the transmitter antenna gain in the direction of the radiometer (dimensionless), *A*_{ef}*f* is the effective aperture of the receive antenna (square meters), and *e*^{−}^{τ} describes the attenuation of the transmitted power by atmospheric gases, clouds, and rain along the path from the transmitter to the receiver. The product *P*_{T}*G*_{T} 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 *P*_{R} produces a brightness-temperature perturbation of

(C.2)

where *k* is Boltzmann’s constant (1.38 × 10^{−}^{23} W − Hz^{−1}K^{−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

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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:
PT GT
Aeff e −τ
PR =
(C.1)
2
4 πR
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 e–τ 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
PR
(K )
δT = (C.2)
kB
where k is Boltzmann’s constant (1.38 × 10–23 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
0

OCR for page 208

aPPendix c 0
(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:
( )
kBe τ 64
PT GT
Wm −2
= δT 2 π
λ
A (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 bright-
ness 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.