On the first- and second-order statistics of the capacity of N*Nakagami-m channels for applications in cooperative networks

Gulzaib Rafiq,Bjøn Olav Hogstad,Matthias Pätzold

doi:10.1186/1687-1499-2012-24

Gulzaib Rafiq, Bjøn Olav Hogstad + Show 1 more

Open Access

https://doi.org/10.1186/1687-1499-2012-24

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Abstract

This article deals with the derivation and analysis of the statistical properties of the instantaneous channel capacitya of N*Nakagami-m channels, which has been recently introduced as a suitable stochastic model for multihop fading channels. We have derived exact analytical expressions for the probability density function (PDF), cumulative distribution function (CDF), level-crossing rate (LCR), and average duration of fades (ADF) of the instantaneous channel capacity of N*Nakagami-m channels. For large number of hops, we have studied the first-order statistics of the instantaneous channel capacity by assuming that the fading amplitude of the channel can approximately be modeled as a lognormal process. Furthermore, an accurate closed-form approximation has been derived for the LCR of the instantaneous channel capacity. The results are studied for different values of the number of hops as well as for different values of the Nakagami parameters, controlling the severity of fading in different links of the multihop communication system. The results show that an increase in the number of hops or the severity of fading decreases the mean channel capacity, while the ADF of the instantaneous channel capacity increases. Moreover, an increase in the severity of fading or the number of hops decreases the LCR of the instantaneous channel capacity of N*Nakagami-m channels at higher levels. The converse statement is true for lower levels. The presented results provide an insight into the influence of the number of hops and the severity of fading on the instantaneous channel capacity, and hence they are very useful for the design and performance analysis of multihop communication systems.

Highlights

Multihop communication systems fall under the category of cooperative diversity systems, in which the intermediate wireless network nodes assist each other by relaying the information from the source mobile station (SMS) to the destination mobile station (DMS) [1,2,3]
6 Conclusion In this article, we have presented a statistical analysis of the capacity of N*Nakagami-m channels
We have studied the influence of the severity of fading and the number of hops on the probability density function (PDF), cumulative distribution function (CDF), level-crossing rate (LCR), and average duration of fades (ADF) of the channel capacity

Summary

Introduction

Multihop communication systems fall under the category of cooperative diversity systems, in which the intermediate wireless network nodes assist each other by relaying the information from the source mobile station (SMS) to the destination mobile station (DMS) [1,2,3]. The analysis of the LCR and ADF has mostly been carried out for the received signal envelope, which provides useful information regarding the statistics of burst errors occurring in fading channels [22]. It is important to study the LCR and ADF in addition to the PDF and CDF of the instantaneous channel capacity in order to meet the increasing demand for high data rates in mobile communication systemsb. Though a lot of artilces have been published in the literature dealing with the performance and analysis of multihop communication systems, the statistical properties of the instantaneous capacity of N*Nakagami-m channels have not been investigated so far. For the calculation of the LCR and the ADF of the channel capacity, we need to find an expression for the joint PDF p 2 ̇ 2 (z, z) of the squared process. The mean channel capacity is defined using the instantaneous channel capacity C(t) as follows

N log2

Asymptotic analysis

Theory

Conclusion