Operator-theoretic modeling and waveform design for radar in the presence of Doppler

Douglas Cochran, Stephen D. Howard, Bill Moran

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Scopus citations


Optimal radar waveform design for target detection has been addressed in prior research literature under various assumptions regarding noise and clutter. A common model of the radar scene in work of this kind is a linear time-invariant (LTI) operator with additive Gaussian noise that acts on the transmitted signal to produce the received signal. This model is intrinsically ill-suited to dynamic scenes or moving radar platforms because it cannot account for Doppler. This paper introduces scene models based on Hilbert-Schmidt class (HS) operators on the space of finite-energy signals. This category of models generalizes the LTI category in the sense that every LTI operator is also a HS operator, but the HS class includes operators that account for frequency shifts as well as time shifts and are thus suitable for modeling radar scenes involving Doppler. Every HS operator is uniquely expressible as a superposition of elementary time and frequency shift operators, thus providing a convenient interpretation of a scene in terms of these physically meaningful operations on the transmitted signal. Application of this perspective to waveform design for target detection in noise and to optimal receiver processing for a given waveform for target detection in clutter and noise are demonstrated.

Original languageEnglish (US)
Title of host publication2012 IEEE Radar Conference
Subtitle of host publicationUbiquitous Radar, RADARCON 2012 - Conference Program
Number of pages4
StatePublished - 2012
Event2012 IEEE Radar Conference: Ubiquitous Radar, RADARCON 2012 - Atlanta, GA, United States
Duration: May 7 2012May 11 2012

Publication series

NameIEEE National Radar Conference - Proceedings
ISSN (Print)1097-5659


Other2012 IEEE Radar Conference: Ubiquitous Radar, RADARCON 2012
Country/TerritoryUnited States
CityAtlanta, GA

ASJC Scopus subject areas

  • Electrical and Electronic Engineering


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