Open Access

A Generalized Algorithm for the Generation of Correlated Rayleigh Fading Envelopes in Wireless Channels

  • Le Chung Tran1Email author,
  • Tadeusz A Wysocki2,
  • Alfred Mertins3 and
  • Jennifer Seberry4
EURASIP Journal on Wireless Communications and Networking20052005:710469

Received: 23 January 2005

Published: 12 December 2005


Although generation of correlated Rayleigh fading envelopes has been intensively considered in the literature, all conventional methods have their own shortcomings, which seriously impede their applicability. A very general, straightforward algorithm for the generation of an arbitrary number of Rayleigh envelopes with any desired, equal or unequal power, in wireless channels either with or without Doppler frequency shifts, is proposed. The proposed algorithm can be applied to the case of spatial correlation, such as with multiple antennas in multiple-input multiple-output (MIMO) systems, or spectral correlation between the random processes like in orthogonal frequency-division multiplexing (OFDM) systems. It can also be used for generating correlated Rayleigh fading envelopes in either discrete-time instants or a real-time scenario. Besides being more generalized, our proposed algorithm is more precise, while overcoming all shortcomings of the conventional methods.


correlated Rayleigh fading envelopes antenna arrays OFDM MIMO Doppler frequency shift

Authors’ Affiliations

Telecommunications and Information Technology Research Institute (TITR), School of Electrical, Computer and Telecommunications Engineering, University of Wollongong
School of Electrical Computer and Telecommunications Engineering, Faculty of Informatics, University of Wollongong
Signal Processing Group, Department of Physics, University of Oldenburg
School of Information Technology and Computer Science, Faculty of Informatics, University of Wollongong


© Le Chung Tran et al. 2005

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.