A.P. Trifonov - Dr. Sc. (Eng.), Honored Scientist of RF, Professor, Head of Department of Radiophysics, Voronezh State University. E-mail: trifonov@phys.vsu.ru E.V. Litvinov - Ph. D. (Phys.-Math.), Assistant, Department of Radiophysics, Voronezh State University. E-mail: elitvinov@list.ru

In this paper the analysis of detection algorithm of the symmetrical general form radio-signal with unknown amplitude, arrival time, duration and phase is considered provided by finite-sized а priori area. The asymptotically exact expressions for Type I and Type II error probabilities are get. The heuristic method based on the evaluation of the mean Euler characteristic of principal statistic excursion sets in fixed-size a priori area is used to evaluate Type I error probability. To derive the expression for Type II error probability the well-known expression is used there are take into account conditions of high precision estimation of unknown parameters and the distribution of principal statistic obtained for evaluation of Type I error. It is shown that the precision of derived expressions increases when the detection level rises, it does not depend on the size of a priori area and it is higher then the precision of expressions for Type I and Type II error probabilities evaluated on condition of infinite a priori area. The statistical computer modeling of bell-like signal detection algorithm is used to investigate the applicability limits of derived ex-pressions.

 

1. Akimov P.S., Bakut P.A., Bogdanovich V.A.i dr. Teorija obnaruzhenija signalov / Pod red. P.A. Bakuta. M.: Radio i svjaz. 1984. 440 s.
2. Pronjaev E.V. Obnaruzhenie uzkopolosnogo radiosignala v uslovijakh parametricheskojj apriornojj neopredelennosti // Trudy IXMezhdunar. nauchno-tekhnich. konf. «Radiolokacija, navigacija, svjaz». Voronezh. 2003.
3. Trifonov A.P., SHinakov JU.S. Sovmestnoe razlichenie signalov i ocenka ikh parametrov na fone pomekh. M.: Radio i svjaz. 1986. 264 s.
4. Kulikov E.I., Trifonov A.P. Ocenka parametrov signalov na fone pomekh. M.: Sov. radio. 1978. 296 s.
5. Worsley K.J. Testing for signals with unknown location and scale in a χ2 random field, with an application to fMRI // Advances in Applied Probability. 2001. 33. P. 773−793.
6. Hasofer A.M. Upcrossings of Random Fields // Supplement to Advances in Applied Probability. 1978. 10. P. 14−21.
7. Bykov V.V. Cifrovoe modelirovanie v statisticheskojj radiotekhnike. M.: Sov. radio. 1971. 326 s.