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An analytical series expansion solution to the problem of noncoherent detection
Uppsala University, Disciplinary Domain of Science and Technology, Technology, Department of Engineering Sciences, Signals and Systems Group.
Uppsala University, Disciplinary Domain of Science and Technology, Technology, Department of Engineering Sciences, Signals and Systems Group.
2004 (English)In: IEEE Transactions on Information Theory, ISSN 0018-9448, E-ISSN 1557-9654, Vol. 50, no 12, 3369-3375 p.Article in journal (Refereed) Published
Abstract [en]

The well-known noncoherent detection problem concerns optimal detection of an amplitude-modulated sinusoid, with an unknown phase angle, corrupted by additive Gaussian noise. The classical solution to this problem is the noncoherent detector which is known to be optimal if the envelope belongs to a specific set of functions or satisfies the narrow-band approximation i.e., that the bandwidth of the envelope is narrow in comparison with the (carrier) frequency of the sinusoid. In this work, an analytical series expansion solution to the likelihood ratio for the noncoherent detection problem is derived. This solution offers a generalization of the noncoherent detector in which the conditions imposed on the envelope stated above have been relaxed. Analytical expressions for the joint probability density functions (pdfs) of the in-phase and quadrature components, jointly expressed in polar coordinates, are also derived under the signal-plus-noise and the noise-only hypotheses, respectively. Numerical simulations of the detector performance are presented in the form of receiver operating characteristics (ROC) and minimum probability of error curves. The results from a comparison of the general analytical solution with the classical noncoherent detector show significant differences between the two detectors when the narrow-band approximation does not hold.

Place, publisher, year, edition, pages
2004. Vol. 50, no 12, 3369-3375 p.
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:uu:diva-90173DOI: 10.1109/TIT.2004.838396OAI: oai:DiVA.org:uu-90173DiVA: diva2:162436
Available from: 2003-03-17 Created: 2003-03-17 Last updated: 2017-12-14Bibliographically approved
In thesis
1. Optimal Detectors for Transient Signal Families and Nonlinear Sensors: Derivations and Applications
Open this publication in new window or tab >>Optimal Detectors for Transient Signal Families and Nonlinear Sensors: Derivations and Applications
2003 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis is concerned with detection of transient signal families and detectors in nonlinear static sensor systems. The detection problems are treated within the framework of likelihood ratio based binary hypothesis testing.

An analytical solution to the noncoherent detection problem is derived, which in contrast to the classical noncoherent detector, is optimal for wideband signals. An optimal detector for multiple transient signals with unknown arrival times is also derived and shown to yield higher detection performance compared to the classical approach based on the generalized likelihood ratio test.

An application that is treated in some detail is that of ultrasonic nondestructive testing, particularly pulse-echo detection of defects in elastic solids. The defect detection problem is cast as a composite hypothesis test and a methodology, based on physical models, for designing statistically optimal detectors for cracks in elastic solids is presented. Detectors for defects with low computational complexity are also formulated based on a simple phenomenological model of the defect echoes. The performance of these detectors are compared with the physical model-based optimal detector and is shown to yield moderate performance degradation.

Various aspects of optimal detection in static nonlinear sensor systems are also treated, in particular the stochastic resonance (SR) phenomenon which, in this context, implies noise enhanced detectability. Traditionally, SR has been quantified by means of the signal-to-noise ratio (SNR) and interpreted as an increase of a system's information processing capability. Instead of the SNR, rigorous information theoretic distance measures, which truly can support the claim of noise enhanced information processing capability, are proposed as quantifiers for SR. Optimal detectors are formulated for two static nonlinear sensor systems and shown to exhibit noise enhanced detectability.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2003. 99 p.
Keyword
Signalbehandling, optimal detection, transient signals, noncoherent detection, unknown arrival time, ultrasonic nondestructive testing, nonlinear sensor, stochastic resonance, Signalbehandling
National Category
Signal Processing
Research subject
Signal Processing
Identifiers
urn:nbn:se:uu:diva-3343 (URN)91-506-1664-1 (ISBN)
Public defence
2003-04-11, K23, Magistern, Uppsala, 13:15
Opponent
Supervisors
Available from: 2003-03-17 Created: 2003-03-17Bibliographically approved

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