Signal detection in Gaussian noise of unknown level: An invariance application

Scharf, Louis L.; Lytle, Dean W.

doi:10.1109/tit.1971.1054668

Cited by 106 publications

(46 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Il=P.S (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13) where P = 2 + 2 and has Rayleigh distribution, and S has the generalized Chi distribution. Let's denote the product PS by W, then the density function of Kdistributed random variable W is ,lfLw)=-2 ._ 2 K,,-,(cw) , w >() (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14) where a is the shape parameter, c is the scale parameter and Kv(x) is the modified Bessel function of the second kind.…”

Section: Simulation Proceduresmentioning

confidence: 99%

“…So In simulation of detection performance, the clutter samples in the reference window are generated from I 2 and the test cell sample from 101". (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19) Then the signal to clutter power ratio, SCR, is given by…”

Section: Simulation Proceduresmentioning

confidence: 99%

“…In the conventional cell averaging constant false alarm rate detector, (CA-CFAR), the threshold is obtained from the arithmetic mean of the reference window cell samples (5]. When the background is homogeneous and the reference window contains independent and identically Jistributed (1ID) observations governed by the exponential distribution, the CA-CFAR processor maximizes the detection probability, Pd [6,7]. As the length of the reference window increases, the detection probability, of this system approaches that of the classical Neyman-Pearson optimum detector where the background interference information is known a priori.…”

Section: Introductionmentioning

confidence: 99%

“…In the design of most systems, the noise samples and target-plus-noise samples are assumed to be Gaussian random variables and the threshold is obtained from the background noise samples which are assumed to be homogeneous, i.e. the samples are independent identically distributed (iid) random variables [5,7].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Intelligent Use of CFAR Algorithms

Antonik¹,

Bowles²,

Capraro³

et al. 1993

View full text Add to dashboard Cite

Section: Simulation Proceduresmentioning

confidence: 99%

Section: Simulation Proceduresmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Intelligent Use of CFAR Algorithms

Antonik¹,

Bowles²,

Capraro³

et al. 1993

View full text Add to dashboard Cite

“…Application of invariance principle to signal detection problem can be traced back as early as 1971 [4] , or even earlier. About fourteen years ago an important paper [5] appeared in IEEE Transaction on signal processing.…”

Section: Introductionmentioning

confidence: 99%

A Rigorous Proof for the Invariant Study of the Problem in Section VI in "Matched Subspace Detectors"

Nan¹

2009

Journal of Mathematics and Statistics

View full text Add to dashboard Cite

Problem statement: This research provided rigorous proof for the invariant study of the problem in section VI in "matched subspace detectors". About 14 years ago an important research entitled "matched subspace detectors" was published in IEEE transactions on signal processing, Vol. 42, No. 8, August 1994. Since its publication, the study has been widely cited in many areas. The main contribution of the research is to use invariance principle to study the Generalized Likelihood Ratio Test (GLRT) for four kinds of signal detection problems. While the conclusions are all correct, the largest invariant transformation group provided by the geometrical method is questionable. Furthermore the geometrical method in proving the maximal invariants is not helpful. The researchers themselves also frankly acknowledged "a rigorous proof requires an algebraic proof'' (page 2152 in above research). Approach: Hence, this correspondence exactly gave rigorous proof based on algebraic method regarding one problem in the above mentioned research. Results: The algebraic method in this correspondence can be readily applied to other cases in the same research. Conclusion/Recommendations: Through this concrete example, we advocated the algebraic, rigorous method in the invariant study of signal detection problems, while abandoning the geometrical method.

show abstract