在多用戶無線通訊系統中，個別使用者間都希望傳輸資料到所對應的接收器，若干擾訊號沒有有效的處理，將會導致用戶的總和傳輸速率效能下降。近幾年干擾對齊的概念被提出來克服干擾的問題並且達到最大的總傳輸速率，此種方法是利用多天線所提供的空間上的維度來將所有干擾訊號對齊在同一個干擾子空間中。然而過去有許多干擾對齊方法的文獻，但是在這一些文獻中沒有考慮到使用者欲接收到訊號的強度，也沒考慮雜訊的影響。因此在某些情況下，即使干擾訊號完美對齊在一干擾子空間中，使用者的訊號與干擾雜訊比(Signal to interference and noise ratio, SINR)仍會非常的低。面對此問題，本論文提出一個聯合式預編碼器與解碼器設計的干擾對齊方法，最主要的最佳化問題是考慮最差使用者接收器的訊號與干擾雜訊比，並且使其最大化。然而此問題為一非凸型最佳化問題。因此，我們利用K.K.T.條件推導出解碼器的最佳化條件，接著提出二分法、下界近似法與訊號與干擾雜訊比近似法三種方法來求得最佳的解碼器矩陣。而預編碼器的設計，我們藉著半正定規劃(Semi-definite programming, SDP)與秩數放寬(Rank relaxation)的方法，將問題轉換為凸最佳化問題來求得最佳的預編碼矩陣。最後，根據模擬出的結果得知，無論多天線所提供自由度的多寡，本論文所提出的方法對於最差使用者的訊號與干擾雜訊比皆會比先前文獻[1][2]的方法來的好。In multiuser interference channels, each transmitter desires to communicate its data to the intended receiver, and the multiuser interference will cause severe performance degradation on the sum rate performance if the interference signals are not appropriately mitigated. Recently, the idea of interference alignment has been emerged to utilize the spatial dimension offered by multiple antennas to overcome the interference problem and achieve the maximum sum rate performance. Although there have been some interference alignment approaches for designing precoders and decoders in recent literatures, they do not consider the desired signal strength from one transmitter to the intended receiver and the noise effect. In some cases, users may have the extremely poor SINR performance even if users’ interference signals are all appropriately aligned. Toward this end, this thesis proposes a novel iterative interference alignment approach which jointly designs the precoder and the decoder by maximizing the worst signal-to-interference and noise ratio (SINR) among users with multiple antennas. In fact, the considered optimization problem is non-convex. Based on the Karush-Kuhn-Tucker (K.K.T.) conditions, we first derive the optimality condition for designing the decoder, and propose three methods, named as bisection approach, lower bound approximation approach and SINR approximation approach, to achieve the optimal solution. For the precoder designs, we resort to the semidefinite programming (SDP) and rank relaxation techniques to transform the optimization problem into a convex form to obtain the optimal solution. Numerical results reveal that our proposed algorithms perform much better than the two existing algorithms in [1] and [2] in the generalized multiuser multi-input multi-output (MIMO) interference channels.
