On Optimal Artificial-Noise Assisted Secure Beamforming for Fading Eavesdropper Channel

在本篇論文中，我們考慮一個衰退通道實體安全傳輸之系統。在此系統中，假設傳送端知道合法接收端之通道資訊以及只知道竊聽者通道之統計特性。我們利用人工雜訊來增加系統之傳輸速度，而人工雜訊第一個是被Goel和Negi所提出來。我們證明Goel和Negi提出來人工雜訊的選法不是最佳；我們提出在多輸入多輸出且竊聽者只有一根天線之系統中，將人工雜訊放在所有方向上以干擾竊聽者來改進Goel和Negi方法的效能。我們證明在上述條件下最佳傳輸方式是波束合成。同時，我們亦證明在選擇波束方向與合法接收端通道同方向下，所有落在波束方向之零空間之人工雜訊之功率是均勻分布。此外，我們亦提供最佳人工雜訊之共變異數矩陣滿秩之必要條件。模擬結果顯示我們所提出之人工雜訊選法優於Goel和Negi之選法，尤其當合法接收端通道品質相對於竊聽者通道非常差時。利用我們所提出之人工雜訊選擇方式，傳輸速度非零之區域將被放大，此性質可用於改善安全網路的可連通性。In this thesis we consider the secure transmission in fading channels with only the statistics of the eavesdropper’s channel state information known at the transmitter. We optimize the celebrated artificial-noise (AN) assisted beamforming, which was studied by Goel and Negi using heuristically selected AN and beamforming directions. We find that Goel and Negi’s AN selection is strictly sub-optimal. On the contrary, one may inject AN to the beam direction of the message to improve the secrecy rate performance. We prove that for a multiple-input, single-output, single-eavesdropper antenna system, the optimal transmission scheme is a beamformer. With the selected beamformer in the direction of main channel, we then prove that for the AN projecting in the null space of the legitimate channel, uniformly allocating power is optimal. We also provide the necessary condition for the proposed AN selection to be optimal. Simulation results show that our AN selection outperforms Goel and Negi’s, especially when the legitimate channel is poor. In particular, the regime with non-zero secrecy rate is enlarged, which can significantly improve the connectivity of the secure network when the AN assisted beamforming is applied