合作式中繼技術是指信源(source)將所傳送的訊息藉由許多合作夥伴中繼轉傳給目的端(destination)，並且可利用多使用者無線系統中所擁有的空間多樣性增益(spatial diversity gains)。在此論文中我們檢驗了合作式網路(cooperative network)中同時存在多合作式中繼站(relay)以及多惡意(malicious)中繼站的情境，並利用賽局理論(game theory)來分別探討這兩種中繼站的最佳行為。為了探討這類議題，我們針對解碼後再傳輸(decode-and-forward)以及放大後再傳輸(amplify-and-forward)這兩種系統分別將所探討的問題公式化為對應的零和賽局(zero-sum game)。接著我們在中繼站有其各自的功率限制之下藉由驗證賽局中的納許均衡(Nash equilibrium)來決定每個中繼站的最佳策略。在解碼後再傳輸的系統中，我們提出了在瑞利衰弱通道(Rayleigh fading channel)中，惡意中繼站的最佳策略是使用最大功率傳送獨立的高斯(Gaussian)訊號，至於合作式中繼站的最佳策略則是獨自將解出的信源訊息重新編碼為高斯訊號後傳送至目的端，不同中繼站之間的互相合作是不必要的。在放大後再傳輸的系統中，我們證明了當網路中只存在一個合作式中繼站時，惡意中繼站無法藉由偷聽信源所傳送的訊息來獲得增益並且應該在兩個傳輸階段都傳送獨立的高斯雜訊去分別干擾合作式中繼站以及目的端的訊號接收，而合作式中繼站的最佳策略則是永遠用最大功率將所收到的訊號放大後傳給目的端，並且在此系統中我們也證明了傳送高斯訊號是信源的最佳策略。我們透過數值模擬來驗證所得到的結論。

Cooperative relaying refers to a technique that allows the source to transmit its messages to the
destination via the relaying of multiple cooperative partners and, in this way, exploits the spatial
diversity gains inherent in multiuser wireless systems. In this work, we examine cooperative networks
with both cooperative and malicious relays and determine the optimal behavior for both
kinds of relays using a game-theoretic approach. To study these issues, we formulate the problems
into zero-sum games for both decode-and-forward (DF) and amplify-and-forward (AF) systems.
Then, we determine the optimal relay strategies by identifying the Nash equilibrium of these problems
under individual power constraints. In the DF case, we show that, with Rayleigh fading, the
optimal strategy for malicious relays is to transmit independent Gaussian noise using full power
at each relay and the optimal strategy for cooperative relays is to independently re-encode the
source’s message into Gaussian signals and forward them to the destination. Inter-cooperation
among relays is not necessary. In the AF case, we prove, for the case with only one cooperative
relay, that malicious relays do not gain by overhearing the source’s message and, thus, should
transmit Gaussian noise in both phases to corrupt the reception at both the cooperative relay and
the destination. The optimal strategy for the cooperative relay in this case is to amplify and forward
the received signal with full power at each relay. In this case, we also show that Gaussian signaling
at the source is optimal. The results are verified through numerical simulations.

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