Computing and bounding the first-order Marcum Q-function: A geometric approach

IEEE Transactions on Communications

Volumn 56, Issue 7, 2008, Pages 1101-1110

  Kam, Pooi Yuen ^a   Li, Rong ^a  

^a NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

Author keywords

Complex Gaussian distribution; Geometric interpretation; Marcum Q function; Probability bounds; Rician distribution

Indexed keywords

CHLORINE COMPOUNDS; CLUSTER ANALYSIS; RANDOM VARIABLES;

COMPLEX GAUSSIAN DISTRIBUTION; EXPONENTIAL BOUNDS; EXPONENTIAL FUNCTIONS; FINITE-RANGE; FIRST ORDERS; FRUITFUL APPROACH; GAUSSIAN RANDOM VARIABLES; GEOMETRIC APPROACHES; GEOMETRIC INTERPRETATION; GEOMETRIC INTERPRETATIONS; MARCUM Q-FUNCTION; PROBABILITY BOUNDS; Q FUNCTIONS; RICIAN DISTRIBUTION; UPPER AND LOWER BOUNDS;

CONTROL THEORY;

EID: 49049087909     PISSN: 00906778     EISSN: None     Source Type: Journal    
DOI: 10.1109/TCOMM.2008.060360     Document Type: Article

References (27)

1. J. I. Marcum, "A statistical theory of target detection by pulsed radar," IEEE Trans. Inform. Theory, vol. IT-6, pp. 59-267, Apr. 1960.
2. J. I. Marcum, "Table of Q functions," Rand Corporation, Santa Monica, CA, ASTIA Document AD 1165451, Jan. 1950.
3. J. G. Proakis, Digital Communications, 4th ed. New York: McGraw-Hill, 2001.
4. M. K. Simon and M.-S. Alouini, Digital Communication over Fading Channels: A Unified Approach to Performance Analysis, 2nd ed. Hoboken, NJ, USA: John Wiley & Sons, Inc., 2004.
5. D. A. Shnidman, "Evaluation of the Q function," IEEE Trans. Commun. vol. 22, no. 3, pp. 342-346, Mar. 1974.
6. D. A. Shnidman, "Efficient evaluation of probabilities of detection and the generalized Q-function," IEEE Trans. Inform. Theory, vol. IT-22, pp. 746-751, Nov. 1976.
7. S. Parl, "A new method of calculating the generalized Q function," IEEE Trans. Inform. Theory, vol. IT-26, pp. 121-124, Jan. 1980.
8. P. E. Cantrell, "On the calculation of the generalized Q function via Parls method," IEEE Trans. Inform. Theory, vol. IT-32, pp. 817-824, Nov. 1986.
9. P. E. Cantrell and A. K. Ojha, "Comparison of generalized Q-function algorithms," IEEE Trans. Inform. Theory, vol. IT-33, pp. 591-596, July 1987.
10. D. A. Shnidman, "The calculation of the probability of detection and the generalized Marcum Q-function," IEEE Trans. Inform. Theory, vol. 35, pp. 389-400, Mar. 1989.
11. D. A. Shnidman, "Note on "The calculation of the probability of detection and the generalized Marcum Q-function"," IEEE Trans. Inform. Theory, vol. 37, p. 1233, July 1991.
12. C. W. Helstrom, "Computing the generalized Marcum Q-function," IEEE Trans. Inform. Theory, vol. 38, pp. 1422-1428, July 1992.
13. C. W. Helstrom, Elements of Signal Detection and Estimation. Englewood Cliffs, NJ: Prentice-Hall, 1995.
14. M. K. Simon, "A new twist on the Marcum Q-function and its application," IEEE Commun. Lett., vol. 2, no. 2, pp. 39-41, Feb. 1998.
15. R. F. Pawula, "A new formula for MDPSK symbol error probability," IEEE Commun. Lett., vol. 2, pp. 271-272, Oct. 1998.
16. M. Chiani, "Integral representation and bounds for Marcum Q-function," IEEE Electronics Lett., vol. 35, no. 6, pp. 445-446, Mar. 1999.
17. M. K. Simon and M.-S. Alouini, "A unified approach to the probability of error for noncoherent and differentially coherent modulations over generalized fading channels," IEEE Trans. Commun., vol. 46, no. 12, pp. 1625-1638, Dec. 1998.
18. m (α√x, b√x) with application to error probability analysis of diversity receivers," IEEE Trans. Veh. Technol., vol. 52, no. 6, pp. 1568-1575, Nov. 2003.
19. M. K. Simon and M.-S. Alouini, "Exponential-type bounds on the generalized Marcum Q-function with application to error probability analysis over fading channels," IEEE Trans. Commun., vol. 48, no. 3, pp. 359-366, Mar. 2000.
20. A. Annamalai and C. Tellambura, "Cauchy-schwarz bound on the generalized Marcum Q-function," Wirel. Commun. Mob. Comput., vol. 1, pp. 243-253, 2001.
21. G. E. Corazza and G. Ferrari, "New bounds for the Marcum Q-function," IEEE Trans. Inform. Theory, vol. 48, pp. 3003-3008, Nov. 2002.
22. E. Kreyszig, Advanced Engineering Mathematic, 7th ed. New York: Wiley, 1993.
23. W. C. Lindsey, "Error probabilities for Rician fading multichannel reception of binary and n-ary signals," IEEE Trans. Inform. Theory vol. 10, no. 4, pp. 339-350, Oct. 1964.
24. C. H. Ong, "Computation and simulation of bounds on Marcum's Q-function," B. Eng. thesis, National University of Singapore, Singapore, 2003/04, supervised by P. Y. Kam.
25. N. C. Beaulieu, "A useful integral for wireless communication theory and its application to rectangular signaling constellation error rates," IEEE Trans. Commun., vol. 54, no. 5, pp. 802-805, May 2006.
26. R. Li and P. Y. Kam, "Averages of the product of two Gaussian Q-functions over fading statistics and applications," IEEE Commun. Lett., vol. 11, no. 1, pp. 58-60, Jan. 2007.
27. P. Y. Kam and R. Li, "Generic exponential bounds and erfc-bounds on the Marcum Q-function via the geometric approach," in Proc. IEEE Global Telecommun. Conf., San Francisco, CA, USA, Nov. 27-Dec. 1, 2006, session WLC10-1.