Editing Ambiguity function (section)

==Multistatic ambiguity functions==

The ambiguity function can be extended to multistatic radars, which comprise multiple non-colocated transmitters and/or receivers (and can include [[bistatic radar]] as a special case).

For these types of radar, the simple linear relationship between time and range that exists in the monostatic case no longer applies, and is instead dependent on the specific geometry – i.e. the relative location of transmitter(s), receiver(s) and target. Therefore, the multistatic ambiguity function is mostly usefully defined as a function of two- or three-dimensional position and velocity vectors for a given multistatic geometry and transmitted waveform.

Just as the monostatic ambiguity function is naturally derived from the matched filter, the multistatic ambiguity function is derived from the corresponding optimal ''multistatic'' detector – i.e. that which maximizes the probability of detection given a fixed probability of false alarm through joint processing of the signals at all receivers. The nature of this detection algorithm depends on whether or not the target fluctuations observed by each bistatic pair within the multistatic system are mutually correlated. If so, the optimal detector performs phase coherent summation of received signals which can result in very high target location accuracy.<ref>T. Derham, S. Doughty, C. Baker, K. Woodbridge, [http://sites.google.com/site/thomasderham/Home/AmbiguityFunctionsforSpatiallyCoherentandIncoherentMultistaticRadar.pdf?attredirects=0 "Ambiguity Functions for Spatially Coherent and Incoherent Multistatic Radar,"] IEEE Trans. Aerospace and Electronic Systems (in press).</ref> If not, the optimal detector performs incoherent summation of received signals which gives diversity gain. Such systems are sometimes described as ''MIMO radars'' due to the information theoretic similarities to [[MIMO]] communication systems.<ref>G. San Antonio, D. Fuhrmann, F. Robey, "MIMO radar ambiguity functions," IEEE Journal of Selected Topics in Signal Processing, Vol. 1, No. 1 (2007).</ref>

[[File:Ambiguity function plane.png|thumb|Ambiguity function plane]]