本論文研究了無線通信系統中用戶之間相互干擾的模型. 在傳統的干擾模型中, 對於一個目標用戶, 其他共用信道的用戶的信號被認為是干擾, 且干擾被假設成是一個高斯隨機過程. 我們摒棄這種對干擾的分布的假設, 研究一個更實際的干擾模型. 我們稱之為非高斯假設的干擾模型. 在我們的模型中, 目標用戶和干擾用戶可以使用不同的發射功率和符號速率, 並且他們的信號不要求同步. 我們推導了非高斯假設的干擾模型下, 二進制移相鍵控 (BPSK) 的匹配濾波最佳接收的平均誤比特概率表達式. 並且我們評定了傳統的高斯干擾模型的有效性. / 對於非高斯干擾模型的研究, 我們先從時不變信道入手. 利用誤比特率作為系統性能的指標, 我們探討了兩類功率控制問題. 研究的結果顯示高斯干擾模型和非高斯假設的干擾模型有一些本質上的區別. 第一類功率控制問題是最小化所有用戶中的最大誤比特率. 我們發現在非高斯假設的干擾模型中, 當某些條件符合時, 最優化的誤比特率可以為零, 而在高斯干擾模型下, 最優化的誤比特率在任何條件下都不可能達到零. 同時, 我們發現在非高斯假設的干擾模型中, 在某些情況下, 有限的功率就能實現誤比特率的優化. 但在高斯干擾模型中, 無論什麼情況, 要實現最優的誤比特率就要使用無限的功率. 第二類功率控制問題是最小化所有用戶的發射功率總和, 且每個用戶滿足給定的誤比特率要求. 我們探究了非高斯假設的干擾模型下, 誤比特率函數的性能, 並且提出了尋找最優解的迭代算法. 通過仿真比較兩種干擾模型對功率控制的影響, 我們發現高斯干擾模型比非高斯假設的干擾模型要求更大的功率去實現相同的誤比特率要求. / 接著, 我們研究衰落信道下的非高斯假設的干擾模型 . 分析的重點集中在兩個用戶構成的系統: 一個目標用戶和一個干擾用戶. 我們分別探究了在瑞利(Rayleigh), Nakagami 和萊斯 (Rician) 衰落信道下的誤比特率性能. 首先我們從理論上分析了誤比特率隨著衰落嚴重程度的變化趨勢. 然後我們利用數值分析全面比較了高斯干擾模型和非高斯假設的干擾模型在衰落信道下的表現. 仿真結果表明, 高斯干擾模型准確預測誤比特率的能力非常有限, 它不能有效地反映誤比特率對應於信號噪聲功率比 (SNR), 信號干擾功率比 (SIR), 符號速率和衰落嚴重程度的變化. / This thesis studies the interference model of a wireless communication system. In the traditional Gaussian interference model (GIM), for a desired user, the combined interference from other simultaneous users is assumed to be a Gaussian process. We dispense with this Gaussian assumption on the interference and study a more realistic interference model. We call it the non-Gaussian interference model (NGIM). Our model allows for different transmission powers, symbol rates and symbol timing asynchronism between the desired user and interfering users. We derive precise expressions for the average bit error probability (BEP) of binary phase shift keying (BPSK) under the NGIM and access the validity of the GIM. / We start the study by first focusing on the NGIM for non-fading channels. We use the BEP as utility metric to investigate two types of power control problems under the new model and our work demonstrates some qualitative differences between the GIM and NGIM. The first power control problem is to minimize the maximal BEP of all users. We find that in the NGIM, the minimum of the maximal BEP of all users can be zero under certain conditions while in the GIM, the optimal value can never be zero. We also find that under the NGIM, in some cases, the optimal value is achieved by infinite power while under the GIM, the optimal value is always achieved by in&#xc9;IÆpg℗ / We then extend the study to the NGIM for fading channels. We analyze the BEP performance of a two-user system over the Rayleigh, Nakagami and Rician fading channels, respectively. We provide some theoretical results concerning the BEP behavior with respect to the fading severity under the NGIM. Comprehensive numerical study and comparison of the BEP performance between the GIM and the NGIM are also presented. The results show that the GIM has limitation in predicting the exact BEP performance in fading channels. It fails in accurately tracking the variation of the BEP with respect to the signal-to-noise ratio (SNR), signal-to-interference ratio (SIR), symbol rate and fading severity. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Chen, Yi. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2012. / Includes bibliographical references (leaves 98-104). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Motivation --- p.1 / Chapter 1.2 --- Overview --- p.4 / Chapter 1.3 --- Outline --- p.7 / Chapter 2 --- Power Control for NGIM --- p.9 / Chapter 2.1 --- Introduction --- p.9 / Chapter 2.2 --- System Model and Error Probability Calculation --- p.11 / Chapter 2.2.1 --- BEP in the NGIM --- p.13 / Chapter 2.2.2 --- BEP in the GIM --- p.15 / Chapter 2.3 --- The Minimal BEP Problem --- p.16 / Chapter 2.4 --- The Minimal BEP for non-M-Matrix Character Matrix --- p.21 / Chapter 2.5 --- The Minimal Power Problem --- p.26 / Chapter 2.6 --- Simulation Results --- p.31 / Chapter 3 --- BEP of NGIM in fading channels --- p.35 / Chapter 3.1 --- Introduction --- p.36 / Chapter 3.2 --- System Model --- p.39 / Chapter 3.3 --- The moments of ξ --- p.43 / Chapter 3.3.1 --- T[subscript i] ≥ T[subscript j] --- p.43 / Chapter 3.3.2 --- T[subscript i] < T[subscript j] --- p.44 / Chapter 3.4 --- BEP under fading channels --- p.45 / Chapter 3.4.1 --- Rayleigh --- p.46 / Chapter 3.4.2 --- Nakagami --- p.48 / Chapter 3.4.3 --- Rician --- p.50 / Chapter 3.5 --- Numerical Results --- p.51 / Chapter 3.6 --- Discussion of multiple interferers --- p.55 / Chapter 4 --- Probability of M-matrix --- p.65 / Chapter 4.1 --- System model --- p.65 / Chapter 4.2 --- BEP Floor --- p.66 / Chapter 4.3 --- Probability of M-matrix in Rayleigh fading channels --- p.68 / Chapter 4.4 --- Discussion --- p.71 / Chapter 5 --- Summary --- p.75 / Appendices --- p.77 / Chapter A --- NGIM in non-fading channels --- p.77 / Chapter A.1 --- Derivation of the variance of W[subscript i subscript j] --- p.77 / Chapter A.2 --- Proof of Lemma 2.9 --- p.78 / Chapter A.3 --- Proof of Lemma 2.10 --- p.78 / Chapter A.4 --- Proof of Lemma 2.11 --- p.79 / Chapter A.5 --- Proof of Lemma 2.14 --- p.80 / Chapter A.6 --- Proof of Lemma 2.15 --- p.80 / Chapter A.7 --- Proof of Lemma 2.16 --- p.81 / Chapter B --- NGIM in fading channels --- p.84 / Chapter B.1 --- Calculation of the moments of ξ --- p.84 / Chapter B.2 --- BEP in Rayleigh fading --- p.86 / Chapter B.3 --- Lower bound of BEP difference in Rayleigh fading --- p.87 / Chapter B.4 --- BEP in Nakagami fading --- p.88 / Chapter B.5 --- Proof of Theorem 3.2 --- p.89 / Chapter B.6 --- Proof of Theorem 3.3 --- p.91 / Chapter B.7 --- BEP in Rician fading --- p.93 / Chapter B.8 --- Proof of Theorem 3.4 --- p.94 / Bibliography --- p.98

Timing jitter and phase noise are important design considerations in most electronic systems, particularly communication systems. The desire for faster transmission speeds and higher levels of integration, combined with lower signal levels and denser circuit boards has placed greater emphasis on managing problems related to phase noise, timing jitter, and timing distribution. This thesis reports original work on phase noise modelling in electronic systems. A new model is proposed which predicts the up-conversion of baseband noise to the carrier frequency in RF amplifiers. The new model is validated by comparing the predicted phase noise performance to experimental measurements as it applies to a common emitter (CE), bipolar junction transistor (BJT) amplifier. The results show that the proposed model correctly predicts the measured phase noise, including the shaping of the noise about the carrier frequency, and the dependence of phase noise on the amplifier parameters. In addition, new work relating to timing transfer in digital communication systems is presented. A new clock recovery algorithm is proposed for decoding timing information encoded using the synchronous residual time-stamp (SRTS) method. Again, theoretical analysis is verified by comparison with an experimental implementation. The results show that the new algorithm correctly recovers the source clock at the destination, and satisfies the jitter specification set out by the ITU-T for G.702 signals.