1 / 15

# Incoherent Detection

Incoherent Detection. ECE 7251: Spring 2004 Lecture 38 4/21/04. Prof. Aaron D. Lanterman School of Electrical &amp; Computer Engineering Georgia Institute of Technology AL: 404-385-2548 &lt;lanterma@ece.gatech.edu&gt;. A Problem with a Nuisance Parameter.

Download Presentation

## Incoherent Detection

An Image/Link below is provided (as is) to download presentation Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

### Presentation Transcript

1. Incoherent Detection ECE 7251: Spring 2004 Lecture 38 4/21/04 Prof. Aaron D. Lanterman School of Electrical & Computer Engineering Georgia Institute of Technology AL: 404-385-2548 <lanterma@ece.gatech.edu>

2. A Problem with a Nuisance Parameter • Discussion based on Van Trees, Sec. 4.4.1 • W(t) is WGN with power • Signal is an amplitude-modulated sinusoid with a slowly-varying normalized envelope f(t) and an unknown, random phase angle

3. pull into threshold The Integrated Likelihood Ratio

4. where Some Trignometry

5. Rephrased Test Statistic • In a communication system, we may have some training data with which we can estimate the phase; try a Von Mises density • In a radar system, don’t have anything; pick to be uniform

6. For a Uniform Density on  • Since I0 is monotone, it (and a bunch of other stuff) can be shoved over into the threshold

7. Quadrature Demodulator Interpretation

8. Under H1: Statistics of Lcand Ls (1)

9. Statistics of Lcand Ls (2) • EFTR:Convince yourself that under H1, and under H0, and under either hypothesis,

10. Probability of False Alarm

11. Probability of Detection

12. Assorted Algebra and Trignometry

13. Probability of Detection

14. Marcum’s Q function (not to be confused with our previous univariate Gaussian Q-function)! Marcum’s Q Function and • Let

15. Comparing with the Coherent Case • Suppose we are comparing a coherent detection system with to an incoherent detection system with • According to Poor, p. 71 (citing Helstrom, 1968), the ROC curves of the two systems are approximately equal if

More Related