中繼網路中適應性分佈式波束成型之收斂分析

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研究生：	陳長慶 Chen, Chang-Ching,
論文名稱：	中繼網路中適應性分佈式波束成型之收斂分析 Adaptive Distributed Beamforming for Relay Networks: Convergence Analysis
指導教授：	林澤 Lin, Che
口試委員:	洪樂文陸曉峯
學位類別：	碩士 Master
系所名稱：	電機資訊學院 - 通訊工程研究所 Communications Engineering
論文出版年：	2011
畢業學年度：	99
語文別：	英文
論文頁數：	66
中文關鍵詞：	中繼網路、分佈式波束成型、收斂分析
外文關鍵詞：	Relay network, Distributed beamforming, Convergence analysis
相關次數：	點閱：2 下載：0
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這份研究主要著重於無線中繼網路(wireless relay network)中，可藉由隨機搜尋架構(random search framwork)轉換成局部隨機搜尋演算法(local random search algorithm)的適應性分佈式波束成型格式(adaptive distributed beamforming scheme)的收斂分析。將適應性分佈式波束成型格式轉換成局部隨機搜尋演算法之後，我們證明了只要滿足下列兩個充份條件，則該演算法具備殆必收斂(almost sure convergence) 的特性。此兩個充份條件分別為：
壹、演算法的目標函數為一連續函數，且該函數在我們考慮的可行集合(feasible set)中的所有局部最大值(local maxima)皆為全局最大值(global maxima)。
貳、原點(origin)必須為隨機擾動(random perturbation)的機率測度(probability measure)的台集(support)的內點(interior point)。
如果目標函數為非負函數，則我們可以更進一步證明其相對應的適應性分佈式波束成型格式具備均值收斂(convergence in mean)的特性。此外，這篇論文中所提出的收斂證明可以應用的範圍更為廣泛。因為對於任何適應性分佈式波束成型格式，只要在可行集合中的目標函數以及隨機擾動的機率測度滿足我們所提出的兩個充份條件，則我們的收斂證明即可直接應用。接著，我們考慮了不同功率限制(獨立功率限制以及總和功率限制)條件下的放大前送(amplify-and-forward, AF)以及解碼前送(decode-and-forward, DF)中繼網路的情況並以訊雜比(signal-to-noise ratio, SNR)作為目標函數。我們證明了上述所有情況中的訊雜比函數都會滿足我們提出的第一個充份條件，也證明了在上述情況中使用局部隨機搜尋演算法，其收斂時間會隨著中繼網路中的中繼節點個數增加而成線性成長。我們更進一步地延伸此隨機搜尋架構去分析中繼節點非同步地產生隨機擾動情況下的適應性分佈式波束成型格式。最後，我們利用模擬結果驗證了我們的分析。

For wireless relay networks, this work focuses on the convergence analysis of adaptive distributed beamforming schemes that can be reformulated as local random search algorithms via a random search framework. Once reformulated in our random search framework, it is proved that under two sufficient conditions: a) the objective function of the random search algorithm is continuous and all its local maxima are global maxima in the considered feasible set, and b) the origin is an interior point within the support of the probability measure for the random perturbation, the corresponding adaptive distributed beamforming schemes converge almost surely. If the objective function is non-negative, it can be further proved that the corresponding adaptive distributed beamforming schemes converge in mean. This proof of convergence is general since it can be applied to analyze randomized adaptive distributed beamforming schemes with any type of objective functions with different feasible sets and probability measures as long as both the sufficient conditions are satisfied. Examples of objective functions along with different feasible sets that satisfy the first sufficient condition are demonstrated by analyzing the signal-to-noise ratio (SNR) functions for the adaptive distributed beamforming problems in the decode-and-forward and the amplify-and-forward relay networks under two different power constraint assumptions, i.e. an individual and a total power constraint, respectively. It is also shown that the convergence time of the considered local random search algorithms in both relay network settings scale linearly with respect to the number of relays in the network. Finally, this framework is extended to analyze adaptive distributed beamforming schemes in an asynchronous scenario where relays can only update their beamforming coefficients asynchronously. Simulation results are provided to validate our analyses.

Abstract in Chinese    i
Abstract    ii
Acknowledgement    iii
Contents    iv
     Introduction    1
  System Model    6
1 System Description.................................. 6
1.1 Decode-and-Forward Relay Network .................... 7
1.2 Amplify-and-Forward Relay Network....................8
2 Problem Reformulation................................ 9
  General Proof of Convergence    11
1 Sufficient Conditions ................................. 12
2 Convergence Analysis ................................ 13
  Analysis of Objective SNR Functions in Decode-and-Forward Relay Networks with Different Power Constraints    16
1 DF Relay Network with an Individual Power Constraint. . . . . . . . . . . . . . . 16
2 DF Relay Network with a Total Power Constraint . . . . . . . . . . . . . . . . . . 18
  Analysis of Objective SNR Functions in Amplify-and-Forward Relay Networks with Different Power Constraints    21
1 AF Relay Network with an Individual Power Constraint. . . . . . . . . . . . . . . 22
2 AF Relay Network with a Total Power Constraint . . . . . . . . . . . . . . . . . . 27
  Proof of Linear Scalability    29
  Asynchronous Scheme    34
1 Model Description .................................. 34
2 Reformulation..................................... 34
3 An Alternative Proof ................................. 35
  Simulation Results and Discussions    37
1 Simulation....................................... 37
1.1 Simulation Settings.............................. 37
1.2 Simulation Results .............................. 38
2 Discussions...................................... 42
Conclusion    46
Appendix    48
1 Proof of Proposition1................................. 48
2 Proof of Theorem1.................................. 50
3 Proof of Lemma1................................... 52
4 Proof of Lemma2................................... 55
5 Proof of Theorem2.................................. 60
6 Proof of Theorem3.................................. 61
7 Proof of Theorem4.................................. 62

                                

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