Capacity and Error Probability Analysis of Diversity Reception Schemes Over Generalized- $K$ Fading Channels Using a Mixture Gamma Distribution

In this paper, we analyze the error probability and ergodic capacity performance for diversity reception schemes over generalized-K fading channels using a mixture gamma (MG) distribution. With high accuracy, the MG distribution can approximate a variety of composite fading channel models and provide mathematically tractable properties. In contrast to previous analysis approaches that require complicated signal-to-noise ratio (SNR) statistics, it is shown that a distribution of the received SNR for diversity reception schemes is composed of a weighted sum of gamma distributions by exploiting the properties of the MG distribution. Then, based on this result, we can derive the exact average symbol error probability and simple closed-form expressions of diversity and array gains for maximal ratio combining and selection combining. In addition, an expression of the ergodic capacity for these schemes is obtained in independent and identically distributed fading channels. Our results lead to meaningful insights for determining the system performance with parameters of the MG distribution. We show that our analysis can be expressed with any number of receiver branches over various fading conditions. Numerical results confirm that the derived error probability and ergodic capacity expressions match well with the empirical results.