具私密訊息及傳送端僅知部分通道資訊之快速衰退多天線高斯廣播通道之安全速率區域

Abstract

在這篇論文中，我們考慮了具私密訊息之快速衰退多天線高斯廣播通道的安全傳輸。系統中有一具備多天線之傳送端，傳送各自獨立的私密訊息給兩個使用者。在傳送端僅知通道統計資訊的條件下，達成消息理論定義下的安全傳輸。我們首先利用same marginal的性質，去歸類在我們系統模型中，有意義的案例；亦即，兩個使用者可以同時達到非零的速率。我們接著透過解出通道輸入變異矩陣與髒指編碼因子，推導可達成的安全速率區域。由於速率區域的式子相當複雜，我們試著從低訊噪比的分析，更深入去探討關於此通道的特性。最後，模擬結果顯示，在消息理論的安全要求下，兩個使用者可以同時達到正的速率。

In this thesis we consider the secure transmission over the fast fading multiple antenna Gaussian broadcast channel with confidential messages (FMGBC-CM), where a multiple-antenna transmitter sends independent confidential messages to two users with informa-tion theoretic secrecy and only the statistics of the receivers’ channel state information are known at the transmitter. We first use the same marginal property of the FMGBC-CM to classify the non-trivial cases, i.e., both the two users have nonzero rates. We then derive the achievable rate region for the FMGBC-CM by solving the channel input covariance matrices and the inflation factor. Due to the complicated rate region formulae, we also resort to low SNR analysis to investigate the characteristics of the channel. Finally, the numerical examples show that under the information-theoretic secrecy requirement both users can achieve positive rates simultaneously.