臺灣博碩士論文加值系統

在本篇論文中,我們針對一個廣義非同調規律、單輸入多輸出、 且具有迴授系統的記憶性衰減通道,作漸近通道容量(asymptotic channel capacity)的探討。我們假設通道的衰減過程可以是任意地 穩定態且均勻遍歷(ergodic)的隨機過程,同時此隨機過程的能量與 微分熵量比率(differential entropy rate)皆是有限的。而對於迴授系 統的通道部份,則假設其是無任何雜訊影響的,即有無限的通道容 量,但是具有因果關係的(causal)。

研究結果顯示,具有迴授系統的漸近通道容量依然隨著能量呈雙 對數(double-logarithmically) 的速度成長。此外,我們也證明,在漸 進通道容量展開式中的第二項,通稱為衰衰減數(fading number),與 沒有迴授系統時,兩者的衰減數是一樣的。

In this thesis, the channel capacity of a general noncoherent regular single-input multiple-output fading channel with memory and with feedback is investigated. The fading process is assumed to be a general stationary and ergodic random process of finite energy and finite differential entropy rate. The feedback is assumed to be noisefree (i.e., it is of infinite capacity), but causal.

We show that the asymptotic capacity grows double-logarithmically in the power and that the second term in the asymptotic expansion, the fading number, is un- changed with respect to the same channel without feedback.

Chinese Abstract I
Abstract I
Acknowledgments II
1 Introduction 1
2 Channel Model 3
3 Mathematical Preliminaries 5
3.1 Differential Entropy ............................... 5
3.1.1 h+(X)................................... 5
3.1.2 hλ(·).................................... 5
3.1.3 Differential Entropy and Expectation of Logarithms . . . . . . . . . . 6
3.2 Markov’s Inequality ............................... 6
3.3 CausalInterpretation............................... 7
4 Capacity and Fading Number without Feedback 9
5 Capacity and Fading Number with Feedback 11
6 Proof of Theorem 5.4 16
6.1 Main Line Through the Proof.......................... 16
6.2 Detailed Derivations forThreeTerms in(6.24) . . . . . . . . . . . . . . . . 29
6.2.1 FirstTerm ................................ 29
6.2.2 SecondTerm ............................... 30
6.2.3 ThirdTerm................................ 30
7 Discussion and Conclusion 34
A Upper Bound (6.46) 35
B Upper Bound (6.81) 38
C Upper Bounds (6.97) and (6.102) 42
C.1 δ1(κ,ξmin)..................................... 42
C.2 δ2(κ,ξmin)..................................... 44
D Causal Interpretations for Independence 46
Bibliography 48

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