本篇論文致力於在中斷機率限制下解決兩端使用者藉由多個轉傳端點進行雙向通訊的效能最 大化。首先,作者藉由近似方法得到中段機率的封閉解,就我們所知,目前只有針對單一轉 運端的模型有中斷機率的近似封閉解。 再來採用連續凸進似技術來解決效能問題,在個別功 率限制或是總和功率限制下,都可解出近乎最佳解。此外對於單一及兩個轉傳端點且在個別 功率限制的效能最大化問題,我們得出最佳解的封閉解。最後我們藉由模擬顯示本篇演算法 的效能。

This paper studies maximizing the system utility (e.g., weighted sum-rate, weighted geometric mean rate, and weighted harmonic mean rate) via power allocation for a two-way relay network (TWRN) with multiple relay nodes and two terminal nodes with rate outage constraints. We assume amplify- and-forward (AF) relaying with analog network coding (ANC) protocol and half-duplex transmmision. Instead of the stringent assumption of the previous works [1], [2], etc., that the knowledge of channel state information (CSIT) is available at the transmitter ends, the knowledge of complete channel state information at the receiver ends (CSIR) and channel distribution information at the transmitter ends (CDIT) is assumed to be available here. To formulate the optimization problem, the outage probabil- ity for TWRN with single relay node and multiple nodes must be derived. However, to the best of our knowledge, there is only approximated outage probability for Single Relay Node being proposed before. We adopt two approximation methods in this paper to derive the approximated outage proba- bility for Two Relay Node, and Multiple Relay Node, while for Single Relay Node, we use the same technique in [3]. However, the approximated outage constraints lead to a nonconvex structure for the considered problem. Based on our previously proposed SCA technique [4], we can obtain near optimal solution for the utility maximization problem for TWRN. Moreover, we derive closed-form solutions for the optimization problem for Single Relay Node and Two Relay Node with weighted-sum rate being the utility function under individual power constraint. Our simulation results demonstrate the accuracy of the approximation and the advantage of our algorithm comparing with some intuitive methods, full or uniform power allocation.

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