非記憶型多重存取廣義衰減之衰減數

Abstract

本篇論文中探討的是非同調多重存取廣義規律衰減通道的通道容量。其中傳送端的使 用者允許擁有任意數量的天線,但接收端僅允許擁有一條天線。在此通道中,所傳送的訊 號會遭遇相加高斯雜訊以及非記憶型廣義衰減的影響,也就是說,此衰減不被特定的機率 分布所限制,如雷利(Rayleigh)分布及萊斯(Rician)分布。雖然我們假設對於時間來說 為非記憶性,但我們允許對於空間上的記憶,也就是說,對於不同天線的衰減分布是相關 的。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。 我們的研究是根據已知的單使用者廣義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,且允許傳送端使用者擁有多餘一條的天線數。我們知道在此通道下, 增加可使用功率對於通道容量的成長是極沒效率的,僅以雙對數形式增長,此外,在高訊 雜比時,漸進總通道容量中的第二項數值,我們稱之為衰減數。我們成功證明在此通道下 的衰減數與單使用者的衰減數相同。 此研究結論在考量三種功率限制下皆成立,分別為尖峰值功率限制,時間平均功率限 制,以及允許功率分享的時間平均功率限制。其中第三項限制是不實際的因為它代表我們 允許使用者分享功率卻不允許合作,但它有助於我們的推導且我們可證明結果皆一致。 我們的證明是基於互消息的對偶型上界與輸入信號的機率分布逃脫到無限的觀念,其精 神為當可用的功率趨近於無限大時,輸入信號必定會使用趨近於無限大的符號。

In this thesis, the sum-rate capacity of a noncoherent, regular multiple-access general fading channel is investigated, where each user has an arbitrary number of antennas and the receiver has only one antenna. The transmitted signal is subject to additive Gaussian noise and fading. The fading process is assumed to be general and memoryless, i.e., it is not restricted to a specific distribution like Rayleigh or Rician fading. While it is memoryless (i.e., independent and identically distributed IID) over time, spacial memory is allowed, i.e., the fading affecting different antennas may be dependent. On the transmitter side cooperation between users is not allowed, i.e., the users are assumed to be statistically independent. Based on known results about the capacity of a single-user fading channel, we derive the exact expression for the asymptotic multiple-user sum-rate capacity. It is shown that the capacity grows only double-logarithmically in the available power. Futhermore, the second term of the high-SNR asymptotic expansion of the sum-rate capacity, the so-called fading number, is derived exactly and shown to be identical to the fading number of the single-user channel when all users apart from one is switched off at all times. The result holds for three different power constraints. In a first scenario, each user must satisfy its own strict peak-power constraint; in a second case, each user’s power is limited by an average-power constarint; and in a third situation — somewhat unrealistically — it is assumed that the users have a common power supply and can share power (even though they still cannot cooperate on a signal basis). The proof is based on a duality-based upper bound on mutual information and on the concept of input distributions that escape to infinity, meaning that when the available power tends to infinity, the input must use symbols that also tend to infinity.