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Volumn 56, Issue 3, 2010, Pages 1166-1186

On the monotonicity, log-concavity, and tight bounds of the generalized marcum and nuttall Q-Functions

Author keywords

Generalized Marcum Qfunction; Log concavity; Monotonicity; Nuttall Q function; Tight bounds

Indexed keywords

COGNITIVE RADIO; COMPREHENSIVE STUDIES; DIFFERENTIAL PHASE-SHIFT KEYING; ERROR PERFORMANCE; LOG LIKELIHOOD RATIO; LOWER AND UPPER BOUNDS; MARCUM Q-FUNCTION; MONOTONICITY; NUMERICAL RESULTS; OUTAGE PROBABILITY ANALYSIS; PROBABILISTIC INTERPRETATION; PROBABILISTIC METHODS; Q-FUNCTIONS; RELATIVE ERRORS; THREE PARAMETERS; TIGHT BOUND; WIRELESS COMMUNICATION SYSTEM;

EID: 77949507230     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2009.2039048     Document Type: Article
Times cited : (121)

References (67)
  • 1
    • 84941524798 scopus 로고
    • A statistical theory of target detection by pulsed radar
    • Apr.
    • J. I. Marcum, "A statistical theory of target detection by pulsed radar," IRE Trans. Inf. Theory, vol.6, no.2, pp. 59-267, Apr. 1960.
    • (1960) IRE Trans. Inf. Theory , vol.6 , Issue.2 , pp. 59-267
    • Marcum, J.I.1
  • 2
    • 0001379710 scopus 로고
    • Studies of target detection by pulsed radar
    • Apr.
    • J. I. Marcum and P. Swerling, "Studies of target detection by pulsed radar," IEEE Trans. Inf. Theory, vol.IT-6, no.2, pp. 227-228, Apr. 1960.
    • (1960) IEEE Trans. Inf. Theory , vol.IT-6 , Issue.2 , pp. 227-228
    • Marcum, J.I.1    Swerling, P.2
  • 5
    • 0032162383 scopus 로고    scopus 로고
    • A unified approach to the performance analysis of digital communications over generalized fading channels
    • Sep.
    • M. K. Simon and M.-S. Alouini, "A unified approach to the performance analysis of digital communications over generalized fading channels," Proc. IEEE, vol.86, no.9, pp. 1860-1877, Sep. 1998.
    • (1998) Proc. IEEE , vol.86 , Issue.9 , pp. 1860-1877
    • Simon, M.K.1    Alouini, M.-S.2
  • 6
    • 0032299730 scopus 로고    scopus 로고
    • A unified approach to the probability of error for noncoherent and differentially coherent modulations over generalized fading channels
    • Dec.
    • 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.
    • (1998) IEEE Trans. Commun. , vol.46 , Issue.12 , pp. 1625-1638
    • Simon, M.K.1    Alouini, M.-S.2
  • 7
    • 3042839204 scopus 로고    scopus 로고
    • Some new results for integrals involving the generalized Marcum Q function and their application to performance evaluation over fading channels
    • Jul.
    • M. K. Simon and M.-S. Alouini, "Some new results for integrals involving the generalized Marcum Q function and their application to performance evaluation over fading channels," IEEE Trans. Wireless Commun., vol.2, no.4, pp. 611-615, Jul. 2003.
    • (2003) IEEE Trans. Wireless Commun. , vol.2 , Issue.4 , pp. 611-615
    • Simon, M.K.1    Alouini, M.-S.2
  • 8
    • 0344875685 scopus 로고    scopus 로고
    • m (a√x,b√x) with application to error probability analysis of diversity receivers
    • Nov.
    • m (a√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.
    • (2003) IEEE Trans. Veh. Technol. , vol.52 , Issue.6 , pp. 1568-1575
    • Gaur, S.1    Annamalai, A.2
  • 9
    • 33947684402 scopus 로고    scopus 로고
    • Averages of the product of two Gaussian Q-functions over fading statistics and applications
    • Jan.
    • 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.
    • (2007) IEEE Commun. Lett. , vol.11 , Issue.1 , pp. 58-60
    • Li, R.1    Kam, P.Y.2
  • 10
    • 60149088811 scopus 로고    scopus 로고
    • A simplified expression for the probability of error for binary multichannel communications
    • Jan.
    • C. O. Driscoll and C. C. Murphy, "A simplified expression for the probability of error for binary multichannel communications," IEEE Trans. Commun., vol.57, no.1, pp. 32-35, Jan. 2009.
    • (2009) IEEE Trans. Commun. , vol.57 , Issue.1 , pp. 32-35
    • Driscoll, C.O.1    Murphy, C.C.2
  • 11
    • 70449411436 scopus 로고    scopus 로고
    • Approximate average bit error probability for DQPSK over fading channels
    • Nov. 5
    • Y. Sun, Á Baricz, M. Zhao, X. Xu, and S. Zhou, "Approximate average bit error probability for DQPSK over fading channels," Electron. Lett., vol.45, no.23, pp. 1177-1179, Nov. 5, 2009.
    • (2009) Electron. Lett. , vol.45 , Issue.23 , pp. 1177-1179
    • Sun, Y.1    Baricz, Á.2    Zhao, M.3    Xu, X.4    Zhou, S.5
  • 14
    • 40949144088 scopus 로고    scopus 로고
    • Diversity-multiplexing tradeoff and outage performance for Rician MIMO channels
    • Mar.
    • W.-Y. Shin, S.-Y. Chung, and Y. H. Lee, "Diversity-multiplexing tradeoff and outage performance for Rician MIMO channels," IEEE Trans. Inf. Theory, vol.54, no.3, pp. 1186-1196, Mar. 2008.
    • (2008) IEEE Trans. Inf. Theory , vol.54 , Issue.3 , pp. 1186-1196
    • Shin, W.-Y.1    Chung, S.-Y.2    Lee, Y.H.3
  • 15
    • 66849141976 scopus 로고    scopus 로고
    • On the mutual information distribution of MIMO Rician fading channels
    • May.
    • Y. Zhu, P. Y. Kam, and Y. Xin, "On the mutual information distribution of MIMO Rician fading channels," IEEE Trans. Commun., vol.57, no.5, pp. 1453-1462, May 2009.
    • (2009) IEEE Trans. Commun. , vol.57 , Issue.5 , pp. 1453-1462
    • Zhu, Y.1    Kam, P.Y.2    Xin, Y.3
  • 16
    • 33847674846 scopus 로고    scopus 로고
    • On the energy detection of unknown signals over fading channels
    • Jan.
    • F. F. Digham, M.-S. Alouini, and M. K. Simon, "On the energy detection of unknown signals over fading channels," IEEE Trans. Commun., vol.55, no.1, pp. 21-24, Jan. 2007.
    • (2007) IEEE Trans. Commun. , vol.55 , Issue.1 , pp. 21-24
    • Digham, F.F.1    Alouini, M.-S.2    Simon, M.K.3
  • 17
    • 38549140152 scopus 로고    scopus 로고
    • Performance analysis of primary user detection in a multiple antenna cognitive radio
    • Glasgow, Scotland, Jun.
    • A. Pandharipande and J.-P. M. G. Linnartz, "Performance analysis of primary user detection in a multiple antenna cognitive radio," in Proc. IEEE Int. Conf. Commun., Glasgow, Scotland, Jun. 2007, pp. 6482-6486.
    • (2007) Proc. IEEE Int. Conf. Commun. , pp. 6482-6486
    • Pandharipande, A.1    Linnartz, J.-P.M.G.2
  • 18
    • 77949504063 scopus 로고
    • Table of functions
    • M-339, ASTIA Document AD 1165451, RAND Corporation, Santa Monica, CA
    • J. I. Marcum, Table of functions, U.S. Air Force Project RAND Res. Memo. M-339, ASTIA Document AD 1165451, RAND Corporation, Santa Monica, CA, 1950.
    • (1950) U.S. Air Force Project RAND Res. Memo.
    • Marcum, J.I.1
  • 19
    • 0004056122 scopus 로고
    • Naval Underwater Systems Center, New London Lab, New London, CT, Tech. Rep. 4297
    • A. H. Nuttall, Some Integrals Involving the Q-Function, Naval Underwater Systems Center, New London Lab, New London, CT, Tech. Rep. 4297, 1972.
    • (1972) Some Integrals Involving the Q-Function
    • Nuttall, A.H.1
  • 20
    • 35448997685 scopus 로고    scopus 로고
    • Joint and marginal eigenvalue distributions of (Non) centralWishart matrices and PDF-based approach for characterizing the capacity statistics ofMIMO Ricean and Rayleigh fading channels
    • Oct.
    • A. Maaref and S. Aissa, "Joint and marginal eigenvalue distributions of (Non) centralWishart matrices and PDF-based approach for characterizing the capacity statistics ofMIMO Ricean and Rayleigh fading channels," IEEE Trans. Wireless Commun., vol.6, no.10, pp. 3607-3619, Oct. 2007.
    • (2007) IEEE Trans. Wireless Commun. , vol.6 , Issue.10 , pp. 3607-3619
    • Maaref, A.1    Aissa, S.2
  • 21
    • 68249160815 scopus 로고    scopus 로고
    • On the monotonicity of the generalized Marcum and Nuttall Q-functions
    • Aug.
    • V. M. Kapinas, S. K. Mihos, and G. K. Karagiannidis, "On the monotonicity of the generalized Marcum and Nuttall Q-functions," IEEE Trans. Inf. Theory, vol.55, no.8, pp. 3701-3710, Aug. 2009.
    • (2009) IEEE Trans. Inf. Theory , vol.55 , Issue.8 , pp. 3701-3710
    • Kapinas, V.M.1    Mihos, S.K.2    Karagiannidis, G.K.3
  • 22
    • 38549093699 scopus 로고    scopus 로고
    • Antenna array processing in fading and interference: An interference-cancellation vs. diversity comparative performance
    • Glasgow, Scotland, Jun.
    • J. M. Romero-Jerez and A. J. Goldsmith, "Antenna array processing in fading and interference: An interference-cancellation vs. diversity comparative performance," in Proc. IEEE Int. Conf. Commun., Glasgow, Scotland, Jun. 2007, pp. 1108-1113.
    • (2007) Proc. IEEE Int. Conf. Commun. , pp. 1108-1113
    • Romero-Jerez, J.M.1    Goldsmith, A.J.2
  • 23
    • 0038681919 scopus 로고    scopus 로고
    • Largest eigenvalue of complex Wishart matrices and performance analysis of MIMO MRC systems
    • Apr.
    • M. Kang and M. S. Alouini, "Largest eigenvalue of complex Wishart matrices and performance analysis of MIMO MRC systems," IEEE J. Sel. Areas Commun., vol.21, no.3, pp. 418-426, Apr. 2003.
    • (2003) IEEE J. Sel. Areas Commun. , vol.21 , Issue.3 , pp. 418-426
    • Kang, M.1    Alouini, M.S.2
  • 24
    • 41849083097 scopus 로고    scopus 로고
    • MIMO multichannel beamforming ser and outage using new eigenvalue distributions of complex noncentralWishart matrices
    • Mar.
    • S. Jin, M. R. McKay, X. Gao, and I. B. Collings, "MIMO multichannel beamforming SER and outage using new eigenvalue distributions of complex noncentralWishart matrices," IEEE Trans. Commun., vol.56, no.3, pp. 424-434, Mar. 2008.
    • (2008) IEEE Trans. Commun. , vol.56 , Issue.3 , pp. 424-434
    • Jin, S.1    McKay, M.R.2    Gao, X.3    Collings, I.B.4
  • 25
    • 64049105980 scopus 로고    scopus 로고
    • Prony and polynomial approximations for evaluation of the average probability of error over slow-fading channels
    • Mar.
    • P. Loskot and N. C. Beaulieu, "Prony and polynomial approximations for evaluation of the average probability of error over slow-fading channels," IEEE Trans. Veh. Technol., vol.58, no.2, pp. 1269-1280, Mar. 2009.
    • (2009) IEEE Trans. Veh. Technol. , vol.58 , Issue.2 , pp. 1269-1280
    • Loskot, P.1    Beaulieu, N.C.2
  • 26
    • 0024627009 scopus 로고
    • The calculation of the probability of detection and the generalized Marcum Q-function
    • Mar.
    • D. A. Shnidman, "The calculation of the probability of detection and the generalized Marcum Q-function," IEEE Trans. Inf. Theory, vol.35, no.2, pp. 389-400, Mar. 1989.
    • (1989) IEEE Trans. Inf. Theory , vol.35 , Issue.2 , pp. 389-400
    • Shnidman, D.A.1
  • 27
    • 0021497526 scopus 로고
    • Evaluating radar detection probabilities by steepest descent integration
    • Sep.
    • C. W. Helstrom and J. A. Ritcey, "Evaluating radar detection probabilities by steepest descent integration," IEEE Trans. Aerosp. Electron. Syst., vol.AES-20, no.5, pp. 624-634, Sep. 1984.
    • (1984) IEEE Trans. Aerosp. Electron. Syst. , vol.AES-20 , Issue.5 , pp. 624-634
    • Helstrom, C.W.1    Ritcey, J.A.2
  • 28
    • 0023384927 scopus 로고
    • Comparison of generalized Q-function algorithms
    • Jul.
    • P. E. Cantrell and A. K. Ojha, "Comparison of generalized Q-function algorithms," IEEE Trans. Inf. Theory, vol.IT-33, no.4, pp. 591-596, Jul. 1987.
    • (1987) IEEE Trans. Inf. Theory , vol.IT-33 , Issue.4 , pp. 591-596
    • Cantrell, P.E.1    Ojha, A.K.2
  • 29
    • 0011274801 scopus 로고
    • Computing the generalized Marcum Q-function
    • Jul.
    • C. W. Helstrom, "Computing the generalized Marcum Q-function," IEEE Trans. Inf. Theory, vol.38, no.4, pp. 1422-1428, Jul. 1992.
    • (1992) IEEE Trans. Inf. Theory , vol.38 , Issue.4 , pp. 1422-1428
    • Helstrom, C.W.1
  • 30
    • 0031996394 scopus 로고    scopus 로고
    • A new twist on the Marcum Q function and its application
    • Febl.
    • 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.
    • (1998) IEEE Commun. Lett. , vol.2 , Issue.2 , pp. 39-41
    • Simon, M.K.1
  • 31
    • 0036864480 scopus 로고    scopus 로고
    • The Nuttall Q function-its relation to the Marcum Q function and its application in digital communication performance evaluation
    • Nov.
    • M. K. Simon, "The Nuttall Q function-its relation to the Marcum Q function and its application in digital communication performance evaluation," IEEE Trans. Commun., vol.50, no.11, pp. 1712-1715, Nov. 2002.
    • (2002) IEEE Trans. Commun. , vol.50 , Issue.11 , pp. 1712-1715
    • Simon, M.K.1
  • 32
    • 39049156865 scopus 로고    scopus 로고
    • Computing and bounding the generalized Marcum Q-function via a geometric approach
    • Seattle, WA, Jul.
    • R. Li and P. Y. Kam, "Computing and bounding the generalized Marcum Q-function via a geometric approach," in Proc. IEEE Int. Symp. Inf. Theory (ISIT), Seattle, WA, Jul. 2006, pp. 1090-1094.
    • (2006) Proc. IEEE Int. Symp. Inf. Theory (ISIT) , pp. 1090-1094
    • Li, R.1    Kam, P.Y.2
  • 33
    • 68249154417 scopus 로고    scopus 로고
    • Tight bounds of the generalized Marcum Q-function based on log-concavity
    • New Orleans, LA, Nov.
    • Y. Sun and S. Zhou, "Tight bounds of the generalized Marcum Q-function based on log-concavity," in Proc. IEEE Global Commun. Conf., New Orleans, LA, Nov. 2008, pp. 1-5.
    • (2008) Proc. IEEE Global Commun. Conf. , pp. 1-5
    • Sun, Y.1    Zhou, S.2
  • 34
    • 0033887180 scopus 로고    scopus 로고
    • Exponential-type bounds on the generalized Marcum Q-function with application to error probability analysis over fading channels
    • Mar.
    • 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.
    • (2000) IEEE Trans. Commun. , vol.48 , Issue.3 , pp. 359-366
    • Simon, M.K.1    Alouini, M.-S.2
  • 35
    • 0344870843 scopus 로고    scopus 로고
    • Cauchy-Schwarz bound on the generalized Marcum Q-function with applications
    • Mar.
    • A. Annamalai and C. Tellambura, "Cauchy-Schwarz bound on the generalized Marcum Q-function with applications,"Wireless Commun. Mob. Comput., vol.1, pp. 243-253, Mar. 2001.
    • (2001) Wireless Commun. Mob. Comput. , vol.1 , pp. 243-253
    • Annamalai, A.1    Tellambura, C.2
  • 36
    • 0036847122 scopus 로고    scopus 로고
    • New bounds for the Marcum Q-function
    • Nov.
    • G. E. Corazza and G. Ferrari, "New bounds for the Marcum Q-function," IEEE Trans. Inf. Theory, vol.48, no.11, pp. 3003-3008, Nov. 2002.
    • (2002) IEEE Trans. Inf. Theory , vol.48 , Issue.11 , pp. 3003-3008
    • Corazza, G.E.1    Ferrari, G.2
  • 37
    • 39049157800 scopus 로고    scopus 로고
    • Simple tight exponential bounds on the firstorder Marcum Q-function via the geometric approach
    • Seattle, WA, Jul.
    • P. Y. Kam and R. Li, "Simple tight exponential bounds on the firstorder Marcum Q-function via the geometric approach," in Proc. IEEE Int. Symp. Inf. Theory (ISIT), Seattle, WA, Jul. 2006, pp. 1085-1089.
    • (2006) Proc. IEEE Int. Symp. Inf. Theory (ISIT) , pp. 1085-1089
    • Kam, P.Y.1    Li, R.2
  • 38
    • 39349110037 scopus 로고    scopus 로고
    • Generic exponential bounds on the generalized Marcum Q-function via the geomatric approach
    • Washington, DC, Nov.
    • R. Li and P. Y. Kam, "Generic exponential bounds on the generalized Marcum Q-function via the geomatric approach," in Proc. IEEE Global Telecommun. Conf., Washington, DC, Nov. 2007, pp. 1754-1758.
    • (2007) Proc. IEEE Global Telecommun. Conf. , pp. 1754-1758
    • Li, R.1    Kam, P.Y.2
  • 39
    • 40149104262 scopus 로고    scopus 로고
    • Tight geometric bound for Marcum Q-function
    • Feb.
    • X. Zhao, D. Gong, and Y. Li, "Tight geometric bound for Marcum Q-function," Electron. Lett., vol.44, pp. 340-341, Feb. 2008.
    • (2008) Electron. Lett. , vol.44 , pp. 340-341
    • Zhao, X.1    Gong, D.2    Li, Y.3
  • 40
    • 50649089585 scopus 로고    scopus 로고
    • A flexible method to approximate Marcum Q-function based on geometric way of thinking
    • Malta, Mar.
    • N. Ding and H. Zhang, "A flexible method to approximate Marcum Q-function based on geometric way of thinking," in Proc. 3rd Int. Symp. Commun. Control Signal Process., Malta, Mar. 2008, pp. 1351-1356.
    • (2008) Proc. 3rd Int. Symp. Commun. Control Signal Process. , pp. 1351-1356
    • Ding, N.1    Zhang, H.2
  • 41
    • 67650172598 scopus 로고    scopus 로고
    • New bounds for the generalized Marcum Q-function
    • Jul.
    • Á Baricz and Y. Sun, "New bounds for the generalized Marcum Q-function," IEEE Trans. Inf. Theory, vol.55, no.7, pp. 3091-3100, Jul. 2009.
    • (2009) IEEE Trans. Inf. Theory , vol.55 , Issue.7 , pp. 3091-3100
    • Baricz, Á.1    Sun, Y.2
  • 42
    • 68049137315 scopus 로고    scopus 로고
    • Tight bounds for the generalized Marcum Q-function
    • Dec.
    • Á Baricz, "Tight bounds for the generalized Marcum Q-function," J. Math. Anal. Appl., vol.360, pp. 265-277, Dec. 2009.
    • (2009) J. Math. Anal. Appl. , vol.360 , pp. 265-277
    • Baricz, Á.1
  • 43
    • 0012660795 scopus 로고
    • 2 and distributions with applications
    • 2 and distributions with applications," J. R. Statist. Soc. B, vol.35, pp. 480-492, 1973.
    • (1973) J. R. Statist. Soc. B , vol.35 , pp. 480-492
    • Ghosh, B.K.1
  • 44
    • 50249098067 scopus 로고    scopus 로고
    • Inequalities for the generalized Marcum Q-function
    • Sep.
    • Y. Sun and ÁBaricz, "Inequalities for the generalized Marcum Q-function," Appl. Math. Comput., vol.203, pp. 134-141, Sep. 2008.
    • (2008) Appl. Math. Comput. , vol.203 , pp. 134-141
    • Sun, Y.1    Baricz, Á.2
  • 45
    • 34347200833 scopus 로고
    • Sulla funzione gamma incompleta
    • Dec.
    • F. G. Tricomi, "Sulla funzione gamma incompleta," Ann. Mater. Pura Appl., vol.31, pp. 263-279, Dec. 1950.
    • (1950) Ann. Mater. Pura Appl. , vol.31 , pp. 263-279
    • Tricomi, F.G.1
  • 48
    • 0003312808 scopus 로고
    • Logarithmic concave measures and related topics
    • M. A. H. Dempster, Ed. London, U.K.: Academic
    • A. Prékopa, "Logarithmic concave measures and related topics," in Stochastic Programming, M. A. H. Dempster, Ed. London, U.K.: Academic, 1980, pp. 63-82.
    • (1980) Stochastic Programming , pp. 63-82
    • Prékopa, A.1
  • 50
    • 85042570155 scopus 로고
    • The noncentral chi-square distribution with zero degrees of freedom and testing for uniformity
    • Aug.
    • A. F. Siegel, "The noncentral chi-square distribution with zero degrees of freedom and testing for uniformity," Biometrika, vol.66, pp. 381-386, Aug. 1979.
    • (1979) Biometrika , vol.66 , pp. 381-386
    • Siegel, A.F.1
  • 51
    • 33947644810 scopus 로고    scopus 로고
    • Poisson representation and Monte Carlo estimation of generalized Marcum Q-function
    • Oct.
    • G. V. Weinberg, "Poisson representation and Monte Carlo estimation of generalized Marcum Q-function," IEEE Trans. Aerosp. Electron. Syst., vol.42, no.4, pp. 1520-1531, Oct. 2006.
    • (2006) IEEE Trans. Aerosp. Electron. Syst. , vol.42 , Issue.4 , pp. 1520-1531
    • Weinberg, G.V.1
  • 53
    • 77949511067 scopus 로고    scopus 로고
    • A simple single integral representation of the bivariate Rayleigh distribution
    • Oct.
    • M. K. Simon and M.-S. Alouini, "A simple single integral representation of the bivariate Rayleigh distribution," IEEE Trans. Commun., vol.45, no.10, pp. 1159-1161, Oct. 1997.
    • (1997) IEEE Trans. Commun. , vol.45 , Issue.10 , pp. 1159-1161
    • Simon, M.K.1    Alouini, M.-S.2
  • 54
    • 0038377173 scopus 로고    scopus 로고
    • Closed form and infinite series solutions for the MGF of a dual-diversity selection combiner output in bivariate Nakagami fading
    • Apr.
    • C. Tellambura, A. Annamalai, and V. K. Bhargava, "Closed form and infinite series solutions for the MGF of a dual-diversity selection combiner output in bivariate Nakagami fading," IEEE Trans. Commun., vol.51, no.4, pp. 539-542, Apr. 2003.
    • (2003) IEEE Trans. Commun. , vol.51 , Issue.4 , pp. 539-542
    • Tellambura, C.1    Annamalai, A.2    Bhargava, V.K.3
  • 55
    • 68049128194 scopus 로고    scopus 로고
    • Turán type inequalities for some probability density functions
    • to be published
    • Á Baricz, "Turán type inequalities for some probability density functions," Studia Sci. Math. Hungar., to be published.
    • Studia Sci. Math. Hungar.
    • Baricz, Á.1
  • 57
    • 0004167764 scopus 로고
    • Stanford CA: Stanford Univ. Press
    • S. Karlin, Total Positivity. Stanford, CA: Stanford Univ. Press, 1968.
    • (1968) Total Positivity
    • Karlin, S.1
  • 58
    • 45049083719 scopus 로고    scopus 로고
    • Properties of the probability density function of the noncentral chi-squared distribution
    • Oct.
    • S. András and Á Baricz, "Properties of the probability density function of the noncentral chi-squared distribution," J. Math. Anal. Appl., vol.346, pp. 395-402, Oct. 2008.
    • (2008) J. Math. Anal. Appl. , vol.346 , pp. 395-402
    • András, S.1    Baricz, Á.2
  • 59
    • 11944251241 scopus 로고    scopus 로고
    • Log-concave probability and its applications
    • M. Bagnoli and T. Bergstrom, "Log-concave probability and its applications," Econom. Theory, vol.26, pp. 445-469, 2005.
    • (2005) Econom. Theory , vol.26 , pp. 445-469
    • Bagnoli, M.1    Bergstrom, T.2
  • 60
    • 77949494519 scopus 로고    scopus 로고
    • Functional inequalities for the incomplete gamma function
    • submitted for publication
    • H. Alzer and Á Baricz, "Functional inequalities for the incomplete gamma function," Rocky Mountain J. Math., submitted for publication.
    • Rocky Mountain J. Math.
    • Alzer, H.1    Baricz, Á.2
  • 61
    • 0040682364 scopus 로고    scopus 로고
    • Inequalities for the chi square distribution function
    • Jul.
    • H. Alzer, "Inequalities for the chi square distribution function," J. Math. Anal. Appl., vol.223, pp. 151-157, Jul. 1998.
    • (1998) J. Math. Anal. Appl. , vol.223 , pp. 151-157
    • Alzer, H.1
  • 62
    • 0001014646 scopus 로고
    • Some inequalities for the chi square distribution function and the exponential function
    • May.
    • M. Merkle, "Some inequalities for the chi square distribution function and the exponential function," Arch. Math., vol.60, pp. 451-458, May 1993.
    • (1993) Arch. Math. , vol.60 , pp. 451-458
    • Merkle, M.1
  • 64
    • 0036880335 scopus 로고    scopus 로고
    • Closed-form formulas for the outage probability of wireless communication systems with a minimum signal power constraint
    • Nov.
    • H.-C. Yang and M.-S. Alouini, "Closed-form formulas for the outage probability of wireless communication systems with a minimum signal power constraint," IEEE Trans. Veh. Technol., vol.51, no.6, pp. 1689-1698, Nov. 2002.
    • (2002) IEEE Trans. Veh. Technol. , vol.51 , Issue.6 , pp. 1689-1698
    • Yang, H.-C.1    Alouini, M.-S.2
  • 65
    • 39749083337 scopus 로고    scopus 로고
    • Soft-decoding of low-density parity check codes for DPSK signals
    • Anaheim, CA, Mar. 25-29
    • K.-P. Ho and H.-C. Wang, "Soft-decoding of low-density parity check codes for DPSK signals," in Proc. Opt. Fiber Commun./Nat. Fiber Opt. Eng. Conf., Anaheim, CA, Mar. 25-29, 2007, pp. 1-3.
    • (2007) Proc. Opt. Fiber Commun./Nat. Fiber Opt. Eng. Conf. , pp. 1-3
    • Ho, K.-P.1    Wang, H.-C.2
  • 66
    • 34247121302 scopus 로고    scopus 로고
    • Inequalities involving modified Bessel functions of the first kind II
    • Aug.
    • ÁBaricz and E. Neuman, "Inequalities involving modified Bessel functions of the first kind II," J. Math. Anal. Appl., vol.332, pp. 265-271, Aug. 2007.
    • (2007) J. Math. Anal. Appl. , vol.332 , pp. 265-271
    • Baricz, Á.1    Neuman, E.2
  • 67
    • 77949537093 scopus 로고    scopus 로고
    • Performance analysis of mobile radio systems over composite fading/shadowing channels with co-located interference
    • Jul.
    • I. Trigui, A. Laourine, S. Affes, and A. Stéphenne, "Performance analysis of mobile radio systems over composite fading/shadowing channels with co-located interference," IEEE Trans.Wireless Commun., vol.8, no.7, pp. 3448-3453, Jul. 2009.
    • (2009) IEEE Trans.Wireless Commun. , vol.8 , Issue.7 , pp. 3448-3453
    • Trigui, I.1    Laourine, A.2    Affes, S.3    Stéphenne, A.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.