8.3 ‘Sky’ noise.
We examined signal receivers in earlier sections and considered the effects of noise generated inside the receiver system. A receiver picking up signals from the real world will also usually pick up background noise from objects in its field of view. This process can be summarised as illustrated in figures 8.4a/b.
The receiving antenna will see some Thermal Radiation from the atmosphere in its field of view. Unless the atmosphere is very opaque it will also collect some noise from astronomical sources in the field of view. (Even if the atmosphere were perfectly transparent and there were no bright stars & galaxies in the field of view the receiver would still pick up the 2·7 Kelvins Cosmic Background radiation.) The total noise power reaching the receiver can be represented in terms of the noise temperature contributions from the atmosphere and the astronomical ‘sky’.
For simplicity we can imagine the atmosphere as being a homogeneous layer of depth, d, temperature, 
, and emissivity, 
.
In the Rayleigh-Jeans region of the spectrum (where we can simplify things by treating temperatures as if they were powers) this produces a noise temperature contribution of
where t is the Optical Thickness of the atmosphere
Here we have extended the concept of a Black Body to a new idea, sometimes called a Grey Body by astronomers. This radiates a spectrum which has the same overall shape as a Black Body, but is translucent to some extent. This translucence has two important consequences.
- We may, to some extent, see some radiation from any sources behind the Grey Body
- The intensity of the thermal radiation coming from the Grey Body is reduced by an amount which depends upon how translucent it is.
It can be proven that the emissivity of a translucent body has the same value as its attenuation coefficient. Hence the noise temperature contribution from the extraterrestrial objects in the far sky will be
where 
is the effective average temperature of the far objects in the field of view. The total external natural noise contributions will therefore be
Note that this noise is in addition to any generated inside the receiver itself. We've also ignored any ‘man-made’ noise like the radiation from electric drills, light bulbs, or Tornado aircraft radars! These artificial noise sources can be very powerful at low radio frequencies. For example, the effective environmental radio noise temperature in the centre of a big city is well over a million Kelvins in the MW/LW band!
The actual atmosphere+sky noise contributions will depend on the zenith angle — i.e. the angle between the direction the antenna is looking in and the zenith (straight up). Looking to the zenith the antenna will be facing the smallest possible thickness of atmosphere. Looking towards the horizon, the antenna signal path has to pass through a much longer piece of atmosphere.
Figure 8.5 illustrates how the atmospheric noise temperature depend upon the signal frequency and zenith angle. It also shows the main astronomical ‘sky’ noise contributions (apart from the Sun, which may be in view). This plot is for an antenna at sea level in temperate air (not raining!). Going to a high dry site can significantly reduce the noise level. This is why mm-wave & optical astronomers prefer Hawai'i to Manchester. (Well, it's one of the reasons, anyway!...) Similar sorts of graphs can be drawn for THz, infra-red and optical frequencies.
Figure 8.6 shows a more general plot of the atmosphere’s attenuation properties over a wider frequency range. Note that the vertical scale is a log scale of the attenuation in decibels! It is also worth noting that figures 8.5 and 8.6 assume a ‘standard’ atmosphere at sea level. In practice, rain, snow, or fog can significantly increase the level of atmospheric attenuation - especially in the infrared-to-ultraviolet region.
Summary
You should now understand how we can use antenna gain values to work out the Link Gain we can expect when sending power from place to place. That Planck Black Bodies are equivalent to thermal noise sources and hence produce a ‘white’ spectrum in the Rayleigh-Jeans region. That a translucent object (e.g the atmosphere) can be represented as a Grey Body. You should also now see how the received Noise temperature and atmospheric attenuation depend upon the operating frequency and conditions.
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University of St. Andrews, St Andrews, Fife KY16 9SS, Scotland.
