### ASA 129th Meeting - Washington, DC - 1995 May 30 .. Jun 06

## 2pSP10. Effect of ergodicity failure on detection performance prediction.

**George E. Ioup
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*Dept. of Phys., Univ. of New Orleans, New Orleans, LA 70148
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**Lisa A. Pflug
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*Naval Res. Lab., Stennis Space Center, MS 39529
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**Juliette W. Ioup
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*Univ. of New Orleans, New Orleans, LA 70148
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Formulas based on the noise variance and the first four signal moments to
predict the performance at the minimum detectable level of ordinary and higher
order correlation central ordinate threshold detectors have been derived. The
passive prediction formulas have been reported and will be published. The
active prediction results have also been presented. These prediction formulas
agree remarkably well with computer-based Monte Carlo simulations. A breakdown
in the agreement has been observed for simulations containing a small number of
sample points---in the observation window for the passive case and in the
signal for the active case. This breakdown can be traced to the inapplicability
of the ergodicity assumption for various time averages over a small number of
sample points, since key steps in the derivations contain the interchange of
expectations and summations for nonlinear terms. Small sample number time
averages lead to correlation central ordinate value probability density
functions which are non-Gaussian. Prediction errors in the formulas as great as
2 dB are observed for simulations with 32 sample points. These errors decrease
as the number of sample points is increased. Both passive and active examples
are given. [Research supported by ONR/NRL-SSC.]