對無線通訊系統而言，由於傳輸廣播 ( broadcast ) 的特性，使得資訊保密及安全性成為重要的討論議題。近年來，除了應用傳統的密鑰 ( secret key ) 交換技術外，許多研究傾向於利用無線通道的特性，實現實體層的密鑰產生技術。然而，在通道變動緩慢的環境下，欲利用正統傳收者之間的通道變動來進行加密，需耗費較長時間來產生長度較長的密鑰，大大降低密鑰產生的速率；此外，接收機熱雜訊影響，也使得正統傳送者及正統接收者容易產生不一致的密鑰。本篇論文考慮一保密無線通訊系統，其中，一個雙天線的正統傳送者 ( legitimate transmitter ) ，欲傳送訊號至單天線的正統接收者 ( legitimate receiver ) ，網絡中存在竊聽者 ( eavesdropper ) 亦具備單天線。與傳統保密無線通訊系統不同，正統傳送者利用通道估測資訊，設計波束成形係數 ( beamforming coefficient ) ，在正統傳收端之間產生虛擬通道 ( virtual channel ) ，使得正統接收者可藉由估測虛擬通道的變化產生密鑰，亦即，藉由不同的波束成形係數產生變動的虛擬通道，即可以在通道變動緩慢的環境下產生足夠長度的密鑰。為了有效避免正統傳收者產生的密鑰不一致，我們捨棄了文獻中利用旁側資訊 ( side information ) 傳遞誤差保護資訊，而是採用錯誤更正碼來增加不同密鑰所對應虛擬通道的歐氏距離 ( Euclidean distance ) ，這樣一來竊聽者也無法從旁側資訊中得到任何正統傳收者之間的通道資訊。在本篇論文中，編碼器的部份，我們使用交織碼調變 ( trellis coded modulation , TCM )，將摺積碼 ( convolutional code ) 和調變星座圖 ( constellation ) 相結合，交織碼調變將編碼及調變後的符元序列之間歐氏距離拉大，並將一般錯誤更正碼要付出多餘的頻寬去傳送校驗位元 ( parity ) ，轉換為利用擴展星座圖來獲得所需的編碼增益 ( coding gain ) ，此特性可有效降低正統傳收者之間密鑰不一致機率；為了進一步提升效能，正統接收者將使用 BCJR 演算法解碼，以較低複雜度獲取最大事後機率之解碼。由模擬結果可以驗證，我們最佳化波束成形係數，並使用交織碼調變及 BCJR 演算法，確實有效地降低了密鑰發生不一致的機率。

Information security becomes more and more important due to broadcasting nature of wireless communications system. In recent years, many research papers tend to exploit fading properties of wireless channel to generate secret key in physical layer, in addition to traditional secret key exchanging technology. However, it may take a longer period of time to generate physical-layer secret key if we would like to exploit the channel variation between legitimate transceivers under slow fading environment, which greatly reduce the rate of key generation. Moreover, the legitimate transmitter and receiver may generate different keys due to the effect of thermal noise. In this thesis, we consider a secure communication system, where the legitimate transmitter is equipped with two antennas and both the legitimate receiver and eavesdropper are equipped with single antenna. Different from the conventional secure wireless communication systems, the secret key generation is dominated by the legitimate transmitter by using beamforming technique to introduce virtual channel between the legitimate transceivers. The beamforming coefficients are designed based on channel estimate at the transmitter. The legitimate received then generate secret key after estimating the variation of the virtual channel. That is, our scheme is able to generate long-length secret key through various beamforming coefficients. To avoid key disagreement between the legitimate transceivers, we adopt error correction codes to enlarge the Euclidean distance of virtual channels corresponding to secret keys, instead of using side information to convey additional channel information. Thus, the eavesdropper is not able to attain any information from the side information. To effectively reduce the probability of key disagreement, we employ trellis coded modulation ( TCM ) scheme at the legitimate transmitter to encode the secret key and BCJR algorithm at the legitimate receiver to obtain the maximum a posteriori solution with low complexity. The TCM encoder enlarges the Euclidean distance among virtual channel sequences by jointly considering convolutional encoder and sorting of constellation map, which leads to coding gain without taking additional spectrum. Simulation results show that our proposed method effectively reduce the probability of secret key disagreement.

論文審定書 i
致謝 ii
摘要 iv
Abstract v
目錄 vii
圖次 viii
第一章 緒論 1
第二章 文獻探討 5
　第一節 運用最佳的向量量化器的實體層密鑰產生技術 5
　第二節 運用虛擬通道法則的實體層密鑰產生技術 13
第三章 系統模型 18
第四章 最小平方通道估測法則與波束成形係數之設計 24
　第一節 最小平方通道估測法則 24
　第二節 波束成形係數的最佳化 28
第五章 交織碼調變與 BCJR 演算法 33
　第一節 交織碼調變 ( trellis-coded modulation ) 33
　第二節 BCJR 演算法 39
第六章 模擬與結果 47
第七章 結論 52
參考文獻 53

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