Abstract

In J. Opt. Soc. Am. A 27, 797 (2010), Yura and Hanson derived what they claim to be “a general expression for the mean level crossing rate for an arbitrary” random process following any desired probability distribution function. On the other hand, the authors themselves assert that in some cases their results “differ somewhat from the result reported in the literature.” This discrepancy “remains unexplained” by the authors “and is laid open for future discussion.” In this note, we explain the reason for such discrepancy and show that the Yura-Hanson formula is indeed a special-case solution. A more general solution is then given that is applicable to arbitrary random processes and that is fully consistent with the Rice mean level crossing rate formula.

© 2012 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. H. T. Yura and S. G. Hanson, “Mean level signal crossing rate for an arbitrary stochastic process,” J. Opt. Soc. Am. A 27, 797–807 (2010).
    [CrossRef]
  2. A. Papoulis and S. U. Pillai, Probability, Random Variables and Stochastic Processes, 4th ed. (McGraw-Hill, 2002).
  3. S. O. Rice, “Statistical properties of a sine wave plus random noise,” Bell Syst. Tech. J. 27, 109–157 (1948).
  4. J. C. S. Santos Filho and M. D. Yacoub, “On the second-order statistics of Nakagami fading simulators,” IEEE Trans. Commun. 57, 3543–3546 (2009).
    [CrossRef]

2010 (1)

2009 (1)

J. C. S. Santos Filho and M. D. Yacoub, “On the second-order statistics of Nakagami fading simulators,” IEEE Trans. Commun. 57, 3543–3546 (2009).
[CrossRef]

1948 (1)

S. O. Rice, “Statistical properties of a sine wave plus random noise,” Bell Syst. Tech. J. 27, 109–157 (1948).

Hanson, S. G.

Papoulis, A.

A. Papoulis and S. U. Pillai, Probability, Random Variables and Stochastic Processes, 4th ed. (McGraw-Hill, 2002).

Pillai, S. U.

A. Papoulis and S. U. Pillai, Probability, Random Variables and Stochastic Processes, 4th ed. (McGraw-Hill, 2002).

Rice, S. O.

S. O. Rice, “Statistical properties of a sine wave plus random noise,” Bell Syst. Tech. J. 27, 109–157 (1948).

Santos Filho, J. C. S.

J. C. S. Santos Filho and M. D. Yacoub, “On the second-order statistics of Nakagami fading simulators,” IEEE Trans. Commun. 57, 3543–3546 (2009).
[CrossRef]

Yacoub, M. D.

J. C. S. Santos Filho and M. D. Yacoub, “On the second-order statistics of Nakagami fading simulators,” IEEE Trans. Commun. 57, 3543–3546 (2009).
[CrossRef]

Yura, H. T.

Bell Syst. Tech. J. (1)

S. O. Rice, “Statistical properties of a sine wave plus random noise,” Bell Syst. Tech. J. 27, 109–157 (1948).

IEEE Trans. Commun. (1)

J. C. S. Santos Filho and M. D. Yacoub, “On the second-order statistics of Nakagami fading simulators,” IEEE Trans. Commun. 57, 3543–3546 (2009).
[CrossRef]

J. Opt. Soc. Am. A (1)

Other (1)

A. Papoulis and S. U. Pillai, Probability, Random Variables and Stochastic Processes, 4th ed. (McGraw-Hill, 2002).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Equations (10)

Equations on this page are rendered with MathJax. Learn more.

νY(y)=σy˙πγexp(h2(y)2),
σy˙2=R¨Y(τ)|τ=0=0ω2SY(ω)dω0SY(ω)dω,
h(y)2erf1(2FY(y)1),
γYfY(y)h˙2(y)dy,
νY(y)=+|y˙|fY,Y˙(y,y˙)dy˙.
X(t)=FX1(FY(Y(t)))h(Y(t)),
fY,Y˙(y,y˙)=[h˙(y)]2fX,X˙(h(y),h˙(y)y˙).
Y(t)=FY1(FX(X(t))),
νY(y)=νX(h(y)),
h(y)FX1(FY(y)).

Metrics