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Page 1 of 8 Level Crossing Rate in Terms of the Characteristic Function: A New Approach for

Summary: Page 1 of 8
Level Crossing Rate in Terms of the Characteristic Function: A New Approach for
Calculating the Fading Rate in Diversity Systems
Ali Abdi1, Member, IEEE, and Mostafa Kaveh2, Fellow, IEEE
1Dept. of Elec. and Comp. Eng., New Jersey Institute of Technology, Newark, NJ 07102
2Dept. of Elec. and Comp. Eng., University of Minnesota, Minneapolis, MN 55455
Emails: ali.abdi@njit.edu kaveh@ece.umn.edu
Abstract __ The level crossing rate (LCR) of a random process conveys useful information about the
underlying process, and is of interest in diverse engineering fields. In wireless communications, it is
related to the system characteristics such as handoff, outage probability, fading rate, average duration
of fades, velocity (or maximum Doppler shift) of the mobile, and the effect of diversity on fading. The
LCR formula was originally derived by Rice in terms of the joint probability density function (PDF) of
the underlying process and its time derivative. In this paper we express the LCR in terms of the joint
characteristic function (CF). This new formula is useful for many cases where the joint CF is simpler
to derive than the associated joint PDF. As an application and for a DS-CDMA system, the fading rate
at the output of a RAKE receiver with either maximal ratio combiner or postdetection equal gain
combiner, operating over a frequency-selective fading channel with different path statistics, is easily
calculated using the new CF-based LCR formula.
Keywords: Characteristic function, DS-CDMA systems, Fading channels, Level-crossing problems,
RAKE receivers.


Source: Abdi, Ali - Department of Electrical and Computer Engineering, New Jersey Institute of Technology


Collections: Engineering