在多使用者的無線通訊系統中，使用者之間的訊號干擾會嚴重影響到系統的效能。在本篇論文中，我們考慮多使用者的感知網路(cognitive radio)與中繼站系統(relay system)，藉由傳輸功率控制，將系統中最低的使用者訊號對干擾及雜訊比(signal-to-interference-plus-noise ratio)最大化，並且必須滿足線性與非線性的系統條件。首先，在感知網路中，非法使用者(secondary users)會利用合法使用者(primary users)的頻譜進行資料傳送。如此一來，非法使用者會對於合法使用者產生訊號干擾，而影響到合法使用者的通訊品質。因此，在合法使用者的非線性中斷機率(outage probability)限制以及非法使用者的線性最大傳輸功率限制之下，我們藉由設計傳輸功率控制方法將最低的非法使用者訊號對干擾及雜訊比最大化。針對此非凹面(nonconvex)最佳化問題，根據Nonlinear Perron-Frobenius定理，我們提出疊代演算法並且證明此演算法會收斂至最佳的傳輸功率。另外，考慮放大轉發式(amplified-and-forward)的中繼站系統，我們假設來源端(source)和中繼站是多天線而目的端(destinations)都是單天線。在來源端和中繼站的最大傳輸功率限制之下，透過傳輸功率控制、來源端波束賦形(beamforming)以及中繼站預先編碼器(precoder)的設計，將系統中最低的訊號對干擾及雜訊比最大化。我們提出疊代設計方法，輪流設計來源端和中繼站收斂至區域最佳解。固定中繼站，我們利用Nonlinear Perron-Frobenius定理和上傳下傳偶性(uplink-downlink duality)，設計出最佳的傳輸功率控制方法以及來源端波束賦形。固定來源端，我們利用半定放寬(semi-definite relaxation)和隨機化方法(randomization technique)，處理中繼站預先編碼器設計時的rank-one限制。最後，電腦模擬顯示所提出的演算法和設計方法擁有快速收斂的特性。

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