Comparison of Generalized Q-Function Algorithms

IEEE Transactions on Information Theory

Volumn 33, Issue 4, 1987, Pages 591-596

  Cantrell, Pierce E ^a   Ojha, Anand K ^a  

^a TEXAS A AND M UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

MATHEMATICAL TECHNIQUES - INTEGRAL EQUATIONS;

CUMULATIVE DISTRIBUTION FUNCTIONS; GENERALIZED Q-FUNCTION ALGORITHMS; POWER SERIES EXPANSIONS;

SIGNAL PROCESSING;

EID: 0023384927     PISSN: 00189448     EISSN: 15579654     Source Type: Journal    
DOI: 10.1109/TIT.1987.1057323     Document Type: Article

References (26)

1. J.I. Marcum, “A statistical theory of target detection by pulsed radar: mathematical appendix,” IRE Trans. Inform. Theory, vol. IT-6, pp. 59–267, April 1960.
2. C.W. Helstrom, Statistical Theory of Signal Detection, 2nd ed. New York: Pergamon, 1968.
3. H.L. Van Trees, Detection, Estimation and Modulation Theory – Part I. New York: Wiley, 1968.
4. C.S. Brice and L.C. Andrews, “New expressions for the pdf and cdf of the filtered output of an analog cross correlator,” IEEE Trans. Inform. Theory, vol. IT-28, pp. 668–677, July 1982.
5. P.E. Cantrell, “Computation of the transient M/M/l queue cdf, pdf, and mean with generalized Q-functions,” IEEE Trans. Commun., vol. COM-34, pp. 814–817, Aug. 1986.
6. P.B. Patnaik, “The noncentral x2 and F distributions and their applications,” Biometrika, vol. 36, pp. 202–232, 1949.
7. H. Urkowitz, “Energy detection of unknown deterministic signals,” Proc. IEEE, vol. 55, pp. 523–531, April 1967.
8. S.O. Rice, “Mathematical analysis of random noise,” Bell Syst. Tech. J., vol. 24, pp. 46–159, Jan. 1945.
9. S.O. Rice, “Communications in the presence of noise-Probability of error for two encoding schemes,” Bell Syst. Tech. J., vol. 29, pp. 60–93, Jan. 1950.
10. S.O. Rice, “Uniform asymptotic expansions for saddle point integrals-Application to a probability distribution occurring in noise theory,” Bell. Syst. Tech. J., vol. 47, pp. 1971–2013, Nov. 1968.
11. L.E. Brennan and I.S. Reed, “A recursive method of computing the Q-function,” IEEE Trans. Inform. Theory, vol. IT-11, pp. 312–313, April 1965.
12. W.F. McGee, “Another recursive method of computing the Q-function,” IEEE Trans. Inform. Theory, vol. IT-16, pp. 500–501, July 1970.
13. G.M. Dillard, “Recursive computation of the generalized Q-function,” IEEE Trans. Aerosp. Electron. Syst., vol. AES-9, pp. 614–615, July 1973.
14. D.A. Shnidman, “Efficient evaluation of probabilities of detection and the generalized Q-function,” IEEE Trans. Inform. Theory, vol. IT-22, pp. 746–759, Nov. 1976.
15. G.H. Robertson, “Computation of the noncentral chi-square distribution,” Bell Sys. Tech. J., vol. 48, pp. 201–207, Jan. 1969.
16. D.E. Johansen, “New techniques for machine computation of the Q-function, truncated normal deviates, and matrix eigenvalues,” Appl. Res. Lab., Sylvania Electron. Syst., Waltham, MA, AD-265–309, AFCRL Rep. 556, July 1961.
17. S. Parl, “A new method of calculating the generalized Q-function,” IEEE Trans. Inform. Theory, vol. IT-26, pp. 121–124, Jan. 1980.
18. A.K. Ojha, “Comparative performance of algorithms for machine computation of the Q-function,” M.S. Thesis, Dept. of Elec. Eng., Texas A&M Univ., College Station, TX, May 1985.
19. F.E. Nathanson, Radar Design Principles. New York: McGraw-Hill, 1969.
20. D.A. Shnidman, “Evaluation of the Q-function,” IEEE Trans. Commun., vol. COM-22, pp. 342–346, March 1974.
21. P.E. Cantrell, “On the calculation of the generalized Q-function via Parl's method,” IEEE Trans. Inform. Theory, vol. IT-32, pp. 817–824, Nov. 1986.
22. S. Parl, “A bound on ,” private communication, Dec. 1984.
23. H. Chernoff, “A measure of the asymptotic efficiency for test of a hypothesis based on a sum of observations,” Ann. Math. Stat., vol. 23, pp. 493–507, 1962.
24. J.L. Freeman, “Computational analysis of the Q-function for intermediate to large parameter range,” Senior Honors Thesis, Dept. Elec. Eng., Texas A&M Univ., College Station, TX, May 1986.
25. D.E. Knuth, The Art of Computer Programming, Vol. 1, 2nd ed. Reading, MA: Addison-Wesley, 1973.
26. P.E. Cantrell and J.L. Freeman, “Generalized Q-function calculations for large orders,” to be published.