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On the Definition of Diversity Order Based on Renyi Entropy for Frequency Selective Fading Channels

Department of Information and Communication Engineering, Dongguk University-Seoul, 30 Pildong-ro 1 Gil, Jung-gu, Seoul 100-715, Korea
Author to whom correspondence should be addressed.
Academic Editors: Luis Javier Garcia Villalba, Anura P. Jayasumana and Jun Bi
Entropy 2017, 19(4), 179;
Received: 23 November 2016 / Revised: 11 April 2017 / Accepted: 18 April 2017 / Published: 20 April 2017
(This article belongs to the Special Issue Information Theory and 5G Technologies)
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Outage probabilities are important measures of the performance of wireless communication systems, but to obtain outage probabilities it is necessary to first determine detailed system parameters, followed by complicated calculations. When there are multiple candidates of diversity techniques applicable for a system, the diversity order can be used to roughly but quickly compare the techniques for a wide range of operating environments. For a system transmitting over frequency selective fading channels, the diversity order can be defined as the number of multi-paths if multi-paths have all equal energy. However, diversity order may not be adequately defined when the energy values are different. In order to obtain a rough value of diversity order, one may use the number of multi-paths or the reciprocal value of the multi-path energy variance. Such definitions are not very useful for evaluating the performance of diversity techniques since the former is meaningful only when the target outage probability is extremely small, while the latter is reasonable when the target outage probability is very large. In this paper, we propose a new definition of diversity order for frequency selective fading channels. The proposed scheme is based on Renyi entropy, which is widely used in biology and many other fields. We provide various simulation results to show that the diversity order using the proposed definition is tightly correlated with the corresponding outage probability, and thus the proposed scheme can be used for quickly selecting the best diversity technique among multiple candidates. View Full-Text
Keywords: diversity; diversity order; Renyi entropy; frequency selective fading; outage probability diversity; diversity order; Renyi entropy; frequency selective fading; outage probability

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Chae, S.; Rim, M. On the Definition of Diversity Order Based on Renyi Entropy for Frequency Selective Fading Channels. Entropy 2017, 19, 179.

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