section_path: Principles/Radar range equation
section_name: Radar range equation
paragraph_text: Radar range equation
  
  The power P returning to the receiving antenna is given by the equation:
  
  where
  
  In the common case where the transmitter and the receiver are at the same location, R = R and the term R ² R ² can be replaced by R, where R is the range.This yields:
  
  This shows that the received power declines as the fourth power of the range, which means that the received power from distant targets is relatively very small.
  
  Additional filtering and pulse integration modifies the radar equation slightly for pulse-Doppler radar performance, which can be used to increase detection range and reduce transmit power.
  
  The equation above with F = 1 is a simplification for transmission in a vacuum without interference. The propagation factor accounts for the effects of multipath and shadowing and depends on the details of the environment. In a real-world situation, pathloss effects are also considered.