Dual-hop communication systems are known to extend coverage and reduce transmit power in scenarios where one-hop communication is not possible. The $\alpha -\eta -\mu$ fading distribution is a general fading distribution that can be reduced to other fading distributions like Rayleigh, Nakagami- $m$ , $\alpha$ - $\mu$ , and $\eta$ - $\mu$ . In this paper, we study the statistics of the end-to-end signal to noise ratio (SNR) of a dual-hop amplify and forward system with semi-blind relay over independent but not necessarily identical $\alpha -\eta -\mu$ fading channels. Specifically, we derive an expression for the $n$ th moment of the end-to-end SNR. The derived expression is then utilized to find the average value, the amount of fading, and the ergodic capacity of the end-to-end SNR. Numerical results are provided and compared to simulations to validate the derived expressions.
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