多重存取萊斯衰減通道之通道容量分析

Abstract

本篇論文中探討的是非同調多重存取萊斯衰減通道的通道容量。在此通道中，所傳送的訊號會遭遇相加高斯雜訊以及萊斯衰減；也就是說，此衰減通道程序為高斯分佈並且有一個可目視的路徑成分。在傳送端使用者之間不允許相互合作通訊，因此各使用者假設在統計特性上獨立。

我們的任務是根據已知的單使用者衰減通道的漸進通道容量，推廣到多使用者多重存取的總通道容量。我們只探討單一天線的情況：所有傳送端的使用者及接收端都僅使用單一天線。如果使用者間的獨立限制被放寬，我們可以得到自然的通道容量上限，也就是多傳送天線單一接收天線的通道容量。而如果只有一個使用者傳送其餘皆不傳送，我們可以得到通道容量的下限，也就是單傳送天線單接收天線的通道容量。我們在本論文中改善此上下限，並且得到此通道的確切漸進通道容量。

在本論文中用到的主要概念是輸入信號的機率分佈逃脫到無限，意思是當可用的功率趨近無限大時，輸入信號也要使用隨之趨近無限大的符號。我們提出在多重存取衰減通道中，至少要有一個使用者使用輸入信號分佈逃脫到無限。由此我們得到的結果是此漸進總通道容量等於之前所提的下限：也就是單使用者單傳送天線單接收天線的通道容量。我們推斷出在多重存取的系統中，為了得到最佳的總通道容量，我們必須停止擁有較差通道的使用者傳送，並且只允許有最好通道的使用者傳送。

In this thesis the channel capacity of the noncoherent multiple-access Rician fading channel is investigated. In this channel, the transmitted signal is subject to additive Gaussian noise and Rician fading, i.e., the fading process is Gaussian in addition to a line-of-sight component. On the transmitter side the cooperation between users is not allowed, i.e., the users are assumed to be statistically independent.

Based on the known result of the asymptotic capacity of a single-user fading channel, our work is to generalize it to the multiple-user sum-rate capacity. We study the single-antenna case only: all transmitters and the receiver use one antenna. We get a natural upper bound on the capacity if the constraint of independence between the users is relaxed, in which case the channel becomes a multiple-input single-output (MISO) channel. Also, a lower bound can be obtained if all users apart from one are switched off, which corresponds to a single-input single-output (SISO) channel. We improve these bounds and get an exact formula of the asymptotic capacity.

The main concept we use in this thesis is escaping to infinity of input distributions, which means that when the available power tends to infinity, the input must use symbols that also tend to infinity. We propose that in the multiple-access fading channel, at least one user's distribution must escape to infinity. Based on this we obtain the result that the asymptotic sum-rate capacity is identical to the previously mentioned lower bound: the single-user SISO capacity. We conclude that in order to achieve the best sum-rate capacity in the multiple-access system, we have to switch off the users with bad channels and only allow those with the best channel to transmit.