雙向多輸入多輸出（MIMO, multiple-input multiple-output）中繼轉送因可顯著改善系統效能與信號覆蓋範圍，近年來相當受到關注；其一特點為藉由中繼點進行信息交換時，可達到與點對點傳輸相同的通道使用率。在這類系統中，中繼點預編碼器設計實為一關鍵技術以充分運用空間多工與分集增益。然而，利用奇異值分解將MIMO通道對角化之常見作法卻難以直接推廣至雙向MIMO中繼轉送系統；這著實使得中繼點預編碼器設計於雙向MIMO中繼轉送系統中成為一極具挑戰性的議題。
在本論文中，我們針對雙向放大轉送MIMO中繼系統發展中繼點預編碼器設計方法，其乃根據中繼點預編碼器與有效MIMO通道奇異值之間的關聯性，建構一基於串接MIMO通道之奇異向量子空間（singular vector subspace）的候選中繼點預編碼器集合，然後從中選擇一預編碼器以符合所採用的設計準則；可依據之設計準則包括但不限於最小均方誤差總和（minimum sum of mean-squared errors）、最大通道容量總和（maximum sum of capacities）、最小條件數總和（minimum sum of condition numbers）、最大條件數總和（maximum sum of condition numbers）等，其中條件數定義為一MIMO通道的最大與最小奇異值比。相較於先前具有最佳效能之迭代設計法，本論文所提出之中繼點預編碼器設計方法可達到近似效能但具有明顯較低的運算複雜度。
此外，基於所提出之中繼點預編碼器設計方法，我們亦在多個中繼點情況下探討天線功率分配（antenna power allocation）與中繼點選擇（relay selection）演算法。我們首先分別針對最小均方誤差總和與最大通道容量總和提出所對應之天線功率分配方法，接著利用前述提出之結果，發展聯合天線功率分配、中繼點選擇以及中繼點預編碼器設計之演算法。經由分析均方誤差下界之漸進行為（asymptotic behavior），我們另提出簡化之中繼點選擇演算法以降低運算複雜度。電腦模擬結果顯示，所提出之演算法皆能達到與最佳迭代演算法相似效能。

Two-way multiple-input multiple-output (MIMO) relaying has attracted much attention for its capability to significantly improve the system performance and signal coverage in wireless communications, where an information exchange is realized through relays using the same amount of channel resources as that for direct transmission. In such systems, relay preocder designs play a key role to fully exploit spatial multiplexing and diversity gains. It should be noted that existing well-known diagonalization techniques for MIMO channels based on singular value decomposition cannot be directly applied to two-way MIMO relaying due to bidirectional transmission and reception at the relays. This limitation makes relay precoder designs in two-way MIMO relaying become a challenging issue.
In this dissertation, we present new relay precoder designs for two-way amplify-and-forward MIMO relay systems with multiple relays and two terminals, where only a single relay is selected to participate in data transmission. For a given relay, we first derive the mean-squared error (MSE) matrices of the received signals at the two terminals, and then show that their behavior strongly depends on the singular values of the effective MIMO channels of the corresponding relay system. Motivated by this property, a set of relay precoders are subsequently constructed based on the singular vector subspaces of the MIMO channels, and one of them is selected for meeting a specific design criterion. Four design criteria are investigated, including the minimum sum of MSEs, the maximum sum of capacities, and the minimum or maximum sum of condition numbers, where the condition number is defined as the ratio of the largest to the smallest singular value of a MIMO channel. As compared with the conventional iterative methods, the proposed relay precoders based on minimizing the sum of MSEs or maximizing the sum of capacities achieve close performance while requiring much lower computational complexity. In contrast, the proposed designs based on minimizing or maximizing the sum of condition numbers provide further complexity reduction, with similar performance at high signal-to-noise ratios (SNRs) but a performance loss at low SNRs.
Furthermore, we investigate antenna power allocation and relay selection algorithms based on the above-mentioned relay precoder designs for a multiple-relay case. Two antenna power allocation schemes are derived; one is based on minimizing the sum of asymptotic MSE lower bounds to approach the minimum sum of MSEs, and the other is obtained according to the distribution of singular values of both effective MIMO channels to approach the maximum sum of capacities, where more power is allocated to subchannels with larger singular values and less power is allocated to those with smaller singular values. It is demonstrated that, at high SNRs, the derived schemes contribute power gains as compared with equal power allocation among antennas. With these results, we then propose two joint algorithms to obtain the selected relays as well as the corresponding relay precoders with antenna power allocation for the minimum sum of MSEs and for the maximum sum of capacities, respectively. The proposed joint algorithms employ exhaustive search for the solutions, and achieve close performance to the conventional iterative methods with exhaustive-search relay selection at high SNRs. To reduce the search complexity, two simplified relay selection algorithms are also developed by utilizing the asymptotic MSE lower bounds, one based on the maximum sum of capacities and the other based on the minimum sum of MSEs. It is shown that the former still maintains close-to-optimal performance at high SNRs, while the latter has a small performance loss.

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