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

This article deals with the derivation and analysis of the statistical properties of the instantaneous channel capacity 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.