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. 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. Ambiguity function plane An ambiguity function plane can be viewed as a combination of an infinite number of radial lines. Each radial line can be viewed as the fractional Fourier transform of a stationary random process. Example The Ambiguity function (AF) is the operators that are related to the WDF. (1)If WDF and AF for the signal with only 1 term (2) If + + + When where , , , , , When ≠ WDF and AF for the signal with 2 terms For the ambiguity function: The auto term is always near to the origin See also Matched filter Pulse compression Pulse-Doppler radar Digital signal processing Philip Woodward References Further reading Richards, Mark A. Fundamentals of Radar Signal Processing. McGraw–Hill Inc., 2005. . Ipatov, Valery P. Spread Spectrum and CDMA. Wiley & Sons, 2005. Chernyak V.S. Fundamentals of Multisite Radar Systems, CRC Press, 1998. Solomon W. Golomb, and Guang Gong. Signal design for good correlation: for wireless communication, cryptography, and radar. Cambridge University Press, 2005. M. Soltanalian. Signal Design for Active Sensing and Communications. Uppsala Dissertations from the Faculty of Science and Technology (printed by Elanders Sverige AB), 2014.