高斯-馬可夫衰減通道下雙極傳輸的管道傳輸極限上界

Abstract

在此篇碩士論文中，我們針對隨時間改變衰減的高斯-馬可夫傳輸管道，作管道傳輸極限 (capacity) 的探討。首先，我們根據實際通訊系統的傳送端與接收端是否分別具有「頻道狀態資訊」 (channel state information)，定義出四種不同的管道傳輸極限公式。接著，我們推導高斯-馬可夫傳輸管道下的管道輸出與輸入信號間的管道轉換機率 (channel transition probability) 公式。由於，在傳送端與接收端均無「頻道狀態資訊」的情況下，管道傳輸極限的計算相當困難，因此我們轉而探討其「獨立上界」 (independent bound)。我們導出在不同的管道記憶級數 (memory order) 下的獨立上界公式，並依公式計算出獨立上界的數值解加以討論。

In this thesis, we focus on the capacity for the time-varying Gauss-Markov fading channels. We first remark on four different definitions of channel capacities according to whether the transmitter and the receiver have or have not the channel state information (CSI). We then provide detailed derivations for the channel transition probability of the Gauss-Markov channels. As the true capacity formula for blind-CSI in both transmitter and receiver is hard to obtain, we derive its independent upper bound instead, and establish a close-form expression of the independent bound for any memory order $M$. Discussions are finally given by numerical evaluation of the independent bounds.