本論文考慮無線多重存取竊聽通道(wireless multiple access wiretap channel)，其中包含了多個傳輸端與一個接收端(如基地台)進行通訊，然而同時存在多個竊聽者欲竊聽每一個傳輸端所傳送的秘密資訊。
在竊聽者無法截取任何資訊的條件下，我們將最大化傳輸端所能傳送的可達保密傳輸速率之總和(achievable secrecy sum rate)。我們設計每一個傳輸端的傳送信號之共變異矩陣(covariance matrix)，在各別功率限制下最大化可達保密傳輸速率之總和。這類型最佳化問題一般皆為非凸面問題(nonconvex problem)，因此難以取得其全域最佳解(global optimal solution)。在本論文中，我們分別討論三種不同的情況：MISOSE (傳輸端有多根天線，接收端與每一個竊聽者只有一根天線)、MISOME (傳輸端與每一個竊聽者有多根天線，接收端只有一根天線)和MIMOSE (傳輸端與接收端有多根天線而每一個竊聽者只有一根天線)，分別尋求取得最佳或近似解的有效方法。
我們的主要結果為當竊聽者為只有一根接收天線時，此對應保密傳輸速率總和最大化問題，可藉由適當的問題重新推演(problem reformulation)而成為一有效可解的問題；然而當竊聽者有多根天線時，我們僅能取得次佳的近似解。
廣泛的模擬結果將展現我們所提出方法的效能，同時呈現不同天線數、傳輸端數量、竊聽者數量和接收端等因素對此保密傳輸速率最大化問題的影響。

In this thesis, we consider a multiple access wiretap channel where multiple transmitters want to communicate with a receiver (e.g., base station) in the presence of eavesdroppers. The eavesdroppers aim to eavesdrop the secret messages sent by the transmitters.
We consider the so called achievable secrecy sum rate, which is the achievable sum rate under which the receiver can reliably decode the message whereas all the eavesdroppers cannot retrieve any information. We focus on the achievable secrecy sum rate maximization problem where the transmit signal covariance matrices of transmitters are optimized subject to individual power constraints. This class of optimization problems is nonconvex; therefore, it’s difficult to obtain its global optimal solution in general. In this thesis, we study three different scenarios, namely, the MISOSE (multiple-input, single-output, single eavesdropper-antenna), the MISOME (multiple-input, single-output, multiple eavesdropper-antennas) and the MIMOSE (multiple-input, multiple-output, single eavesdropper-antenna). For each scenario, we investigate efficient methods for handling the associated optimization problem. We will show that, when each of the eavesdroppers has a single antenna, the secrecy sum rate maximization problem can be reformulated, and solved efficiently. However, when each eavesdropper has multiple antennas, we can only obtain suboptimal solutions.
Extensive simulation results are presented to demonstrate the effectiveness of the proposed methods. These results will show how the number of antennas, number of transmitters, and number of eavesdroppers affect the achievable secrecy sum rate.

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