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 letter, 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 direct-sequence code-division multiple-access 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.
Bibliographical noteFunding Information:
Paper approved by M. Z. Win, the Editor for Equalization and Diversity of the IEEE Communications Society. Manuscript received December 10, 2000; revised April 25, 2001 and September 4, 2001. This work was supported in part by the National Science Foundation under the Wireless Initiative Program, Grant 9979443.
- Characteristic function
- DS-CDMA systems
- Fading channels
- Level-crossing problems
- RAKE receivers