分時多工下的蝴蝶式無線網路與半雙工中繼器之最佳分集與多工增益權衡

Abstract

在這篇論文中，我們考慮兩個傳輸端，兩個接收端與多個中繼端組成的蝴蝶 式無線網絡。其中，中繼端主要負責結合兩個傳輸端的資訊並且傳送訊息到兩個 接收端。在假設半雙工中繼器在時間比率t 時傳送與在時間比率(1-t)時接收的前 提下，我們完整描述了應用在半雙工中繼器的蝴蝶式無線網路上，通訊協定的效 能上界，討論範圍最多涵蓋到三個中繼端。在給定分時多工參數t 與多工增益參 數r 的分集與多工增益權衡之效能分析下，我們聯合網路上每個割集的效能去找 到此網路的支配割集，進而得到可以被任何通訊結構達到的最佳效能。接下來我 們可以最佳化所有可能的t 值，進而求得真正的最佳分集與多工增益權衡效能。 我們也指出在此網路的多工增益ｒ之下，最佳分時多工t 的結果。令人驚訝的是， 在ｒ值的變化之下分時多工參數t 並不會一直維持在常數。最後，我們針對割集 的分集與多工增益權衡在時間t=1/2 時，分別比較多址通道正交放大後傳送與多 址通道非正交放大後傳送兩者協定的效能。我們顯示出在給定分時多工參數t=1/2 的分集與多工增益效能表現下，這些協定是最好的通訊協定。

In this thesis, we consider a wireless butterfly network that consists of two source nodes, two destination nodes, and a number of intermediate nodes. The intermediate node plays an important role of a relay that cooperates with the two source nodes to transmit information to the two destination nodes. Assuming a half-duplex communication at the relays, i.e., the relays receive in t-fraction of time and transmit in (1-t) fraction of time, we determine completely a performance upper bound for any communication protocols to be applied to the wireless butterfly network with at most three relays. The performance is measured in terms of the diversity-multiplexing gain tradeoff. To be more specific, we first fix the time-division parameter t and the multiplexing gain r. We then determine the DMT performance associated with each cut-set in the network. Finally, with the above we proceed to identify the dominant cut-sets in the network and obtain the best DMT performance that can be achieved by any communication schemes at time-division parameter t and the multiplexing gain r. The true optimal DMT is then obtained after optimizing over all possible choice of t. Our result also indicates the optimal time-division t for iii the network at multiplexing gain r. Surprisingly, the time-division parameter t varies with r and is not always a constant. Finally, having the optimal cut-set DMT in mind, we compare the DMT performances of the MAC-OAF and MAC-NAF protocols against the cut-set DMT at time t=1/2. We show that these protocols are optimal in terms of DMT performance at t=1/2.