臺灣博碩士論文加值系統

此論文分析自相位調變(self-phase modulation)所引發的非線性相位雜訊的離散以
及連續模型。非線性相位雜訊和接收電場的聯合特徵函式被導出並用來求得接收相位
訊號的機率分布。其中，近似以及精確的相位移鍵調變(BPSK)和相位差分調變(DPSK)
信號的機率密度函式的數學解析式被導出；精確模型考慮了非線性相位雜訊以及放大
器雜訊相位的非獨立關係，而近似模型假設非線性相位雜訊和放大器雜訊相位是獨立
的。分別在離散及連續的模型下，精確以及近似的相位移鍵調變和相位差分調變信號
錯誤機率被計算並比較。
非線性相位雜訊的理論由一組光跨距(fiber span)所組成最小實驗架構來驗證，其
中含有一個光放大器以及一段固定距離的光纖。訊號雜訊比罰分(signal-to-noise ratio
penalty)被用來評估計算系統的效能降低，而此效能降低是受到非線性相位雜訊的影
響。實驗的結果顯示 在簡化的匹配濾波器分析下所得出的訊號雜訊比罰分，可以更
普遍的適用在一般的接受器。實驗量測結果與理論分析差距只有在0.15 分貝(dB)。

Both discrete and distributed models of the self-phase modulation (SPM) induced nonlinear
phase noise are derived. The joint characteristic function of the received electric field
and the nonlinear phase noise is provided for both discrete and distributed models. Both
approximated and exact probability density function for BPSK and DPSK systems are
given by an analytical expression. The exact model includes the dependence between the
nonlinear phase noise and the phase of amplifier noise, and the approximated model assumes
the independence between nonlinear phase noise and the phase of amplifier noise. Both
exact and approximated error probabilities for BPSK and DPSK systems are evaluated
in both discrete and distributed models, and compared with each other. A single-span
experimental setup, the minimal setup to study the nonlinear phase noise, is proposed to
verify the theoretical model of SPM-induced nonlinear phase noise by the measurement of
signal-to-noise ratio (SNR) penalty. The experimental results show that the SNR penalty
from the simplified matched-filter based analysis is applicable to more general receivers.The discrepancy between the results of the experiment and the theory is within ±0.15 dB.

Contents ii
List of Figures iv
List of Tables vi
Acknowledgements vii
1 Introduction to Optical Communication Systems 1
1.1 Introduction 1
1.2 DPSK Transmitter 6
1.3 DPSK Receiver 10
1.4 Fiber Channel 11
1.5 Erbium-doped fiber amplifier (EDFA) 12
2 Nonlinear Phase Noise 13
2.1 Nonlinear Kerr effects 13
2.2 SPM-induced nonlinear phase noise 15
2.3 Mathematical model 15
2.3.1 Discrete model of nonlinear phase noise 16
2.3.2 The distributed model of nonlinear phase noise 31
3 Experimental Verification of the Model of Nonlinear Phase Noise 42
3.1 Themathematical model of the experiment 42
3.2 Setup of the experiment 47
3.3 Experimental results 50
4 Conclusion 55
5 Bibliography 57

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