本論文探討保密性波束形成技術在多輸入單輸出且傳送端僅具通道方向資訊的情況下的最佳性。在之前的成果中，已經發現如果輸入端的共變異矩陣的rank為1，那麼由Khisti等人所導出的保密性通道容量上界就可以被一個使用高斯波束形成技術的保密傳輸速率所達到，也就是說該保密傳輸速率為最大的速率。因此根據上述結果，我們想要從數學上和數值上兩個角度切入去驗證rank-1的輸入端的共變異矩陣對該上界來說是不是一個最佳解。在這篇論文中，我們從數學上證明了在一些特別的情況下，rank-1的輸入端共變異矩陣的確是一個最佳解。在一般性的情況下，我們則是使用數值解(也就是interior point algorithm)的方式去驗證，而這個演算法在目標問題是convex-concave問題時才能保證其解的最佳性。最後我們根據模擬結果畫出上界和下界的比較結果。

Abstract i
Contents ii
1 Introduction 1
2 System Model and Review of Prior Work 5
3 Property of the Secrecy Capacity Upper Bound 12
3.1 Unit Rank Input Covariance is Optimal for Upper Bound in Special Cases . 15
4 Saddle-Point Solution of the Secrecy Capacity Upper Bound Based on
Interior Point Algorithm 20
5 Simulation Result 31
6 Conclusion 40

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