section_path: Principles/Limiting factors/Noise
section_name: Noise
paragraph_text: Noise
  
  Signal noise is an internal source of random variations in the signal, which is generated by all electronic components.
  
  Reflected signals decline rapidly as distance increases, so noise introduces a radar range limitation. The noise floor and signal-to-noise ratio are two different measures of performance that affect range performance. Reflectors that are too far away produce too little signal to exceed the noise floor and cannot be detected. Detection requires a signal that exceeds the noise floor by at least the signal-to-noise ratio.
  
  Noise typically appears as random variations superimposed on the desired echo signal received in the radar receiver. The lower the power of the desired signal, the more difficult it is to discern it from the noise. The noise figure is a measure of the noise produced by a receiver compared to an ideal receiver, and this needs to be minimized.
  
  Shot noise is produced by electrons in transit across a discontinuity, which occurs in all detectors. Shot noise is the dominant source in most receivers. There will also be flicker noise caused by electron transit through amplification devices, which is reduced using heterodyne amplification. Another reason for heterodyne processing is that for fixed fractional bandwidth, the instantaneous bandwidth increases linearly in frequency. This allows improved range resolution. The one notable exception to heterodyne (downconversion) radar systems is ultra-wideband radar. Here a single cycle, or transient wave, is used similar to UWB communications, see List of UWB channels.
  
  Noise is also generated by external sources, most importantly the natural thermal radiation of the background surrounding the target of interest. In modern radar systems, the internal noise is typically about equal to or lower than the external noise. An exception is if the radar is aimed upwards at clear sky, where the scene is so "cold" that it generates very little thermal noise. The thermal noise is given by k T B, where T is temperature, B is bandwidth (post matched filter) and k is the Boltzmann constant. There is an appealing intuitive interpretation of this relationship in a radar. Matched filtering allows the entire energy received from a target to be compressed into a single bin (be it a range, Doppler, elevation, or azimuth bin). On the surface it appears that then within a fixed interval of time, perfect, error free, detection could be obtained. This is done by compressing all energy into an infinitesimal time slice. What limits this approach in the real world is that, while time is arbitrarily divisible, current is not. The quantum of electrical energy is an electron, and so the best that can be done is to match filter all energy into a single electron. Since the electron is moving at a certain temperature (Planck spectrum) this noise source cannot be further eroded. Ultimately, radar, like all macro-scale entities, is profoundly impacted by quantum theory.
  
  Noise is random and target signals are not. Signal processing can take advantage of this phenomenon to reduce the noise floor using two strategies. The kind of signal integration used with moving target indication can improve noise up to 2 {\displaystyle {\sqrt {2}}} for each stage. The signal can also be split among multiple filters for pulse-Doppler signal processing, which reduces the noise floor by the number of filters. These improvements depend upon coherence.