雙向式傳輸中繼(two-way relay)系統近年來受到了大家廣泛的討論。它的優點在於可提高通道的使用效率。在雙向中繼系統考慮使用多個中繼點一起傳輸，藉由增加中繼點個數所造成的空間多樣性，可以降低錯誤傳輸機率。因此，在雙向且多中繼點系統中，如何去聯合中繼點最佳的權重設計及功率分配使得系統的效能提升，成為了一個重要的議題。
在本篇研究中，針對於討論雙向放大轉送中繼系統並且基於最小化相加均方誤差(sum of mean-square-error)，提出了一個聯合中繼權重設計和功率分配的演算法。我們可以將上述最小化相加均方誤差描述成聯合中繼權重設計和功率分配的最佳化問題，但原最佳化問題無法直接求解，因此，我們將原最佳化問題分解成兩個子最佳化問題。針對於解決第一個子問題，首先假設在功率已知的情形下，子問題一可簡化成單一權重設計的問題，因此，可以求解出各中繼點最佳的權重設計。另外，透過由子問題一所求解出的權重設計帶回原最佳化問題，此時成為了僅考慮功率分配的問題，稱此為第二個子問題，利用梯度演算法(gradient decent algorithm)去找可達到最小相加均方誤差的功率分配方式來解決子問題二。此外，考慮在限制中繼點個數的情況下，我們另外提出了一個有效的多中繼點選擇法，它可以有效的使所選到的中繼點組合可達到較小的相加均方誤差。利用透過電腦模擬的結果顯示，我們所提出之聯合中繼權重設計和功率分配的演算法，無論是在降低相加均方誤差或降低位元錯誤率上都會比均等功率分配(未做功率分配)的方法還要顯著。另外，模擬結果亦顯示，在我們所提出的多中繼點選擇法之下且在相較於隨機選擇的方法，在相加均方誤差的表現較好且相當的靠近最佳選擇法。

Two-way relaying, exploiting relays to realize information exchange between two source nodes over a shared wireless channel, has received much attention in recent years due to its high efficiency of channel utilization. Considering a two-way relay system with multiple relays, how to design the relays’ weighting factors and allocate the power of the two source nodes and the relays to enhance the network capacity has become a critical issue. In this thesis, we propose a joint weighting design and power allocation (WD-PA) algorithm in a two-way amplify-and-forward relay system to minimize the sum of mean-square-errors (sum-MSE) of the received signals at the two source nodes. The algorithm alternates between two parts: obtaining relays’ optimal weighting factors for a specific PA, which is derived as a closed-form solution, and searching a PA that could minimize the sum-MSE via a gradient-descent algorithm. In addition, for a required number of relays, we also propose a simple but efficient multi-relay selection scheme to obtain an appropriate relay set which is more possible to attain the smallest sum-MSE. Computer simulation results show that the proposed WD-PA algorithm has better sum-MSE and sum bit-error-rate (sum-BER) performance than that of the equal power allocation scheme. The results also demonstrate that using the proposed relay selection scheme, the sum-MSE of a two-way relay system is further reduced as compared to that with a random relay selection method, especially in high signal-to-noise ratio regions.

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