An amplified-and-forward network coded protocol (ANCP) is proved to achieve excellent network performance [6]. In this paper, we first drive the closed-form expression of the system outage probability in the high SNR regime, based on ANCP protocol in a classical butterfly wireless network. However the complex expression is a bottleneck of developing power allocation. Then we approximate the expression with a simplified version and propose power allocation strategies with a closed form, only requiring statistical channel state information (CSI). Finally, it is shown that the closed-form expression almost overlap the curve of the system outage probability by Monte Carlo simulation in the high SNR regime and the simplified version is very close to the simulation curve. Moreover, it is validated that the proposed power allocation strategies achieve a large signal-noise ratio (SNR) gain over the system without power allocation strategies.
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