TY - JOUR

T1 - Expected number of maxima in the envelope of a spherically invariant random process

AU - Abdi, Ali

AU - Nader-Esfahani, Said

N1 - Funding Information:
Manuscript received October 21, 1999; revised January 10, 2003. This work has been supported in part by Grant no. 612-1-204 of the University of Tehran. Parts of this work have been presented in IEEE Int. Symp. Inform. Theory, Whistler, B.C., Canada, 1995, and Ulm, Germany, 1997. A. Abdi is with the Department of Electrical and Computer Engineering, New Jersey Institute of Technology, Newark, NJ 07102 USA (e-mail: ali.abdi@njit.edu). S. Nader-Esfahani is with the Department of Electrical and Computer Engineering, University of Tehran, Tehran, Iran. Communicated by T. Fuja, Associate Editor At Large. Digital Object Identifier 10.1109/TIT.2003.810662

PY - 2003/5

Y1 - 2003/5

N2 - In many engineering applications, specially in communication engineering, one encounters a bandpass non-Gaussian random process, with a slowly varying envelope. Among the available models for non-Gaussian random processes, spherically invariant random processes (SIRP's) play an important role. These processes are of interest mainly due to the fact that they allow one to relax the assumption of Gaussianity, while keeping many of its useful characteristics. In this paper, we have derived a simple and closed-form formula for the expected number of maxima of a SIRP envelope. Since Gaussian random processes are special cases of SIRP's, this formula holds for Gaussian random processes as well. In contrast with the available complicated expression for the expected number of maxima in the envelope of a Gaussian random process, our simple result holds for an arbitrary power spectrum. The key idea in deriving this result is the application of the characteristic function, rather than the probability density function, for calculating the expected level crossing rate of a random process.

AB - In many engineering applications, specially in communication engineering, one encounters a bandpass non-Gaussian random process, with a slowly varying envelope. Among the available models for non-Gaussian random processes, spherically invariant random processes (SIRP's) play an important role. These processes are of interest mainly due to the fact that they allow one to relax the assumption of Gaussianity, while keeping many of its useful characteristics. In this paper, we have derived a simple and closed-form formula for the expected number of maxima of a SIRP envelope. Since Gaussian random processes are special cases of SIRP's, this formula holds for Gaussian random processes as well. In contrast with the available complicated expression for the expected number of maxima in the envelope of a Gaussian random process, our simple result holds for an arbitrary power spectrum. The key idea in deriving this result is the application of the characteristic function, rather than the probability density function, for calculating the expected level crossing rate of a random process.

KW - Characteristic function

KW - Envelope

KW - Gaussian processes

KW - Level crossing problems

KW - Maxima of the envelope

KW - Spherically invariant processes

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U2 - 10.1109/TIT.2003.810662

DO - 10.1109/TIT.2003.810662

M3 - Article

AN - SCOPUS:0038530712

SN - 0018-9448

VL - 49

SP - 1369

EP - 1371

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

IS - 5

ER -