A Generalized Algorithm for the Generation of Correlated Rayleigh Fading Envelopes in Wireless Channels
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A Generalized Algorithm for the Generation of Correlated Rayleigh Fading Envelopes in Wireless Channels Le Chung Tran Telecommunications and Information Technology Research Institute (TITR), School of Electrical, Computer and Telecommunications Engineering, University of Wollongong, Wollongong NSW 2522, Australia Email: [email protected]
Tadeusz A. Wysocki School of Electrical Computer and Telecommunications Engineering, Faculty of Informatics, University of Wollongong, Wollongong NSW 2522, Australia Email: [email protected]
Alfred Mertins Signal Processing Group, Department of Physics, University of Oldenburg, 26111 Oldenburg, Germany Email: [email protected]
Jennifer Seberry School of Information Technology and Computer Science, Faculty of Informatics, University of Wollongong, Wollongong NSW 2522, Australia Email: [email protected] Received 23 January 2005; Revised 6 July 2005; Recommended for Publication by Wei Li 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. Keywords and phrases: correlated Rayleigh fading envelopes, antenna arrays, OFDM, MIMO, Doppler frequency shift.
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INTRODUCTION
In orthogonal frequency-division multiplexing (OFDM) systems, the fading affecting carriers may have cross-correlation due to the small coherence bandwidth of the channel, or due to the inadequate frequency separation between the carriers. In addition, in multiple-input multiple-output (MIMO) systems where multiple antennas are used to transmit and/or 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.
receive signals, the fading affecting these antennas may also experience cross-correlation due to the inadequate separation between the antennas. Therefore, a generalized, straightforward and, certainly, correct algorithm to generate correlated Rayleigh fading envelopes is required for the researchers wishing to analyze theoretically and simulate the performance of systems. Because of that, generation of correlated Rayleigh fading envelope
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