Recommendation ITU-R RA.769 lists the levels of detrimental interference (and also the methodology used to derive them) that would contribute an additional 10% to the random uncertainty arising from thermal noise in the receiver system. Assuming the unwanted emission has statistics that approximate Gaussian noise within an integration period of 2000 seconds, the effect on scientific output – on *channel capacity* of a radio telescope – can be calculated. In any radio astronomical observation, the telescope will either be tracking a celestial source, or will be scanning or stepping around that moving source. The angle between the RAS telescope boresight and the direction of the interference will continually be changing. Even if the level of interfering signal reaching the site of the telescope is constant to a high degree, with no scintillation due to ionospheric and tropospheric propagation effects, it will be modulated by the response of the RAS telescope, as the interfering signal moves between peaks and nulls in the sidelobe pattern. Propagation variations, changes of polarization caused by a variety of effects, motion of the satellite in distance and angle, modulation on the transmitted signal and other factors will contribute to a varying and unpredictable level of received interfering signal. Such variations can to some extent be approximated by a random process, and so the statistical impact on RAS observations can be estimated. If the unwanted emission appearing at the RAS receiver cannot be approximated by truly random fluctuations, then the effect is more complicated, harder to mitigate, and will, in general, be much more damaging to the scientific data. An essential part of a scientific observation is the characterization of the uncertainty in that observation. With thermal noise, the uncertainty is well understood, but if a component of uncertainty comes from processes beyond the control of the observer, then the scientific value of an observation will be substantially compromised.

The fluctuations in the receiver detector output due to interfering power entering via the RA sidelobes, add quadratically to the fluctuations resulting from the RAS receiver noise, to give the amplitude of the resultant detector fluctuations that define the RAS sensitivity.

A discussion of the process is given in the ITU *Handbook on Radio Astronomy*, Section 4. The handbook also explains how the criteria defining Recommendation ITU-R RA.769 have been chosen to represent a broad range of radio astronomy observations rather than the extreme of sensitivity.

If

* s_{r}* represents the normal receiver fluctuations after the detector, in a given receiver bandwidth and integration time,

*represents the fluctuations after the detector as a result of interference,*

**s**_{i}then

**s _{ri}**, the resultant fluctuations of the receiver system, in the same bandwidth and integration time is given by:

* s_{ri}* = (

**s**_{r}^{2}+

**s**_{i}^{2})**0.5

The observing time * t* necessary to reach a given level of sensitivity increases as the square of the resultant amplitude of noise fluctuations. The Relative Channel Capacity is defined here as the reciprocal of the factor by which observing time of an observation has to be increased in order to reach the same level of sensitivity as would have been obtained in the absence of interference. With

*as the necessary observing time in the absence of interference, and*

**t**_{r}*the necessary observing time to reach the same level of degradation in the presence of interference,*

**t**_{ri}Relative Channel Capacity = (* t_{r}*/

*)*

**t**_{ri}= (

*/*

**s**_{r}*)*

**s**_{ri}^{2}

=

**s**_{r}^{2}/(

**s**_{r}^{2}+

**s**_{i}^{2})

In the figure below the Relative Channel Capacity is plotted as a function of interfering signal, * s_{i}*, with 0 dB on the horizontal scale corresponding to interfering noise fluctuations having 10% of the power of the thermal fluctuations

*. The 0 dB level then corresponds to the Recommendation ITU-R RA.769 threshold for detrimental interference to the RAS.*

**s**_{r}*Reduction in RAS Channel capacity caused by interference*

Initially, with levels just a very few dB above Recommendation ITU-R RA.769, the added uncertainty to the observations can be compensated by the increasing the observing time, which corresponds to a reduction in channel capacity. A 5 dB excess above Recommendation ITU-R RA.769 gives a reduction in capacity of 10%, meaning that 10% less useful data is being produced by the telescope. At a level of 10 dB above Recommendation ITU-R RA.769, where * s_{i}* =

*, the Channel Capacity is halved. Note however that by the time the unwanted signal equals thermal noise, half of the uncertainty in the observations comes from outside the observer’s control. Radio Astronomers will no longer be able to characterize accurately the precision of their measurements, and in effect, at that point, the observational data will have become worthless. The real situation is likely to be even worse than the above scenario;*

**s**_{r}*.*

**in practice, interference will never have the statistical characteristics assumed above, so when the level of received interference reaches a level of 10 dB above Recommendation ITU-R RA.769 levels, useful observations become impossible, with total loss of service**The figure uses values of system noise, integration time and receiver bandwidth as defined in Recommendation ITU-R RA.769. Many astronomical observations are made today with systems having significantly lower system noise and using longer integration times than assumed in Recommendation ITU-R RA.769. In such cases, the “0 dB” point on the horizontal axis of the figure would correspond to a level several dB below the current Recommendation ITU-R RA.769 definition.