An antenna receives this blackbody noise from the environment, but the value that affects the communication system depends both on the pattern shape and the direction of the main beam. We determine the antenna noise temperature by integrating the pattern times the environmental noise temperature distribution:

  (1)

where   is the antenna gain pattern and   is the angle-dependent blackbody radiation of the environment. Changing the antenna pointing changes . Equation (1) is a weighted average of the environment noise temperature, usually referred to as the sky temperature. The second source of noise in the antenna is that of components that have both dissipative losses and reflection losses that generate noise.

A receiving system needs to maximize the signal-to-noise ratio for given resources. System considerations, such as bit error rate, establish the required S/N ratio. We determine the noise power from the product

   (2)

where ko is Boltzmann’s constant   and   is the receiver bandwidth (Hz).  is the effective noise temperature (K). When referring noise temperature to other parts of the network, we increase or decrease it by the gain or loss, since it represents power and not a true temperature. Antenna gain is a measure of the signal level, since we can increase gain independent of the noise temperature, although the gain pattern is a factor by Eq. (1).

The antenna conductor losses have an equivalent noise temperature:

  (3)

where  is the antenna physical temperature and L is the loss (a ratio > 1). From a systems point of view, we include the transmission line run to the first amplifier or mixer of the receiver. We do not include the current distribution losses (aperture efficiencies) that reduce gain in Eq. (3) because they are a loss of potential antenna gain and not noise-generating losses (random electrons). The antenna–receiver chain includes mismatch losses, but these do not generate random electrons, only reflected waves, and have a noise temperature of zero. We include them in a cascaded devices noise analysis as an element with loss only.

Noise characteristics of some receiver components are specified as the noise figure  (ratio), and cascaded devices’ noise analysis can be analyzed using the noise figure, but we will use noise temperature. Convert the noise figures to noise temperature using

  (4)

 is the standard reference temperature 290 K.