Ambiguity function: Difference between revisions

Revision as of 17:40, 10 February 2023

Latest revision as of 01:56, 19 January 2025

(3 intermediate revisions by 3 users not shown)

Line 1:

{{Short description|Function of propagation delay and Doppler frequency}}

In pulsed [[radar]] and [[sonar]] signal processing, an '''ambiguity function''' is a two-dimensional function of [[propagation delay]] <math>\tau</math> and [[Doppler frequency]] <math>f</math>, <math>\chi(\tau,f)</math>. It represents the [[distortion]] of a returned pulse due to the receiver [[matched filter]]<ref>[[Philip Woodward|Woodward P.M.]] ''Probability and Information Theory with Applications to Radar'', Norwood, MA: Artech House, 1980.</ref> (commonly, but not exclusively, used in [[pulse compression]] radar) of the return from a moving target. The ambiguity function is defined by the properties of the [[Pulse (signal processing)|pulse]] and of the filter, and not any particular target scenario.

Line 50 ⟶ 51:

An ambiguity function of this kind would be somewhat of a misnomer; it would have no ambiguities at all, and both the zero-delay and zero-Doppler cuts would be an [[Dirac delta function|impulse]]. This is not usually desirable (if a target has any Doppler shift from an unknown velocity it will disappear from the radar picture), but if Doppler processing is independently performed, knowledge of the precise Doppler frequency allows ranging without interference from any other targets which are not also moving at exactly the same velocity.

This type of ambiguity function is produced by ideal [[white noise]] (infinite in duration and infinite in bandwidth).<ref>Signal Processing in Noise Waveform Radar By Krzysztof Kulpa (Google Books)</ref> However, this would require infinite power and is not physically realizable. There is no pulse <math>s(t)</math> that will produce <math>\delta(\tau) \delta(f)</math> from the definition of the ambiguity function. Approximations exist, however, and noise-like signals such as binary phase-shift keyed waveforms using [[Maximum length sequence|maximal-length sequences]] are the best known performers in this regard.<ref>G. Jourdain and J. P. Henrioux, "Use of large bandwidth-duration binary phase shift keying signals in target delay Doppler measurements," J. Acoust. Soc. Am. 90, 299–309 (1991).</ref>

== Properties ==

Line 188 ⟶ 189:

* Ipatov, Valery P. ''Spread Spectrum and CDMA''. Wiley & Sons, 2005. {{ISBN|0-470-09178-9}}

* Chernyak V.S. ''Fundamentals of Multisite Radar Systems'', CRC Press, 1998.

* Solomon W. Golomb, and [[Guang Gong]]. [http://www.cambridge.org/us/academic/subjects/computer-science/cryptography-cryptology-and-coding/signal-design-good-correlation-wireless-communication-cryptography-and-radar Signal design for good correlation: for wireless communication, cryptography, and radar]. Cambridge University Press, 2005.

* M. Soltanalian. [http://theses.eurasip.org/theses/573/signal-design-for-active-sensing-and/download/ Signal Design for Active Sensing and Communications]. Uppsala Dissertations from the Faculty of Science and Technology (printed by Elanders Sverige AB), 2014.

* Nadav Levanon, and Eli Mozeson. Radar signals. Wiley. com, 2004.

* Augusto Aubry, Antonio De Maio, Bo Jiang, and Shuzhong Zhang. "[https://ieeexplore.ieee.org/document/6563125 Ambiguity function shaping for cognitive radar via complex quartic optimization]." IEEE Transactions on Signal Processing 61 (2013): 5603-5619.

* Mojtaba Soltanalian, and Petre Stoica. "[httphttps://ieeexplore.ieee.org/xpldocument/login.jsp?tp=&arnumber=6142119/ Computational design of sequences with good correlation properties]." IEEE Transactions on Signal Processing, 60.5 (2012): 2180-2193.

* G. Krötzsch, M. A. Gómez-Méndez, Transformada Discreta de Ambigüedad, Revista Mexicana de Física, Vol. 63, pp.&nbsp;505–515 (2017). "[https://rmf.smf.mx/pdf/rmf/63/6/63_6_505.pdf Transformada Discreta de Ambigüedad]".

*[http://djj.ee.ntu.edu.tw/TFW_Writing2.pdf 2 National Taiwan University, Time-Frequency Analysis and Wavelet Transform 2021, Professor of Jian-Jiun Ding, Department of Electrical Engineering]