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

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_eff 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_TG_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⁻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

(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.