OFDM系统中基于对偶分解理论的资源分配算法
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摘要
论文研究了对偶方法和分解理论在OFDM系统资源分配中的应用,并以此为基础,针对速率自适应问题和比例公平性问题提出若干简单高效的次优算法。
OFDM系统中的资源分配算法在近十年来得到了广泛的关注,研究者们使用线性规划、凸优化和博弈论等数学工具,对该领域中存在的各类问题,如速率自适应问题、边值自适应问题和用户公平性问题等,进行了深入的研究。从理论上,研究者对资源分配问题已经有了较成熟的理解。而随着近年来WiMAX系统的成熟,OFDM技术越来越贴近于应用,为其开发低复杂度的实用算法,成为一项非常有现实意义的工作。现有的研究工作中,不乏一些低复杂度的次优算法,但是一方而它们缺少坚实的理论支撑,另一方面,它们对资源分配问题做了过多的简化,性能损失较大。这表明,性能和复杂度的矛盾,仍然是资源分配算法开发过程中有待解决的问题。
本文将对偶分解方法应用于OFDM的资源分配问题,为高效低复杂度的算法开发提供了一种全新的思路。我们首先利用拟凸分析理论,奠定了对偶分解方法在资源分配问题中的应用的理论基础。然后针对不同的问题,使用对偶分解方法分别得出了最优分配方案,这些方案具有很好的性能,但是复杂度也很高。最后,我们通过对最优方案的分析和理解,对其进行简化,得到了复杂度较低的实用算法,而且仍然保持了很好的性能。
针对速率自适应问题,我们首先提出了一种可保证平均数据速率要求的联合子载波和功率分配算法。该算法利用无线信道的时间相干性,约减了最优方案中的迭代次数,从而降低了运算量,并且使算法可以采用分布式的实现结构。在该分布式结构下,用户具有一定的自主性,可以根据本地的信息判断占用某个子载波的可能性,从而判断是否需要反馈该子载波,这种机制显著地减小了反馈开销。而该算法又是在最优方案上进行合理简化的,因此继承了最优算法的联合优化特点,保持了很好的吞吐量性能。我们将用计算机仿真验证该算法的这些特性。
类似的思想也可以应用于解决OFDM系统中保证比例公平性的资源分配问题。有所不同的是,比例公平性问题中子载波分配和功率分配间的联系更为密切,这使得算法收敛的速度变慢。为解决这一问题,我们以平滑后的平均数据速率来代替瞬时数据速率,以减弱算法迭代过程中的振荡现象。在该算法中平滑窗口等参数会显著影响算法性能,我们对其进行评估,并给出了最优的参数设计。
我们还考虑了速率自适应问题中保证瞬时数据速率的资源分配算法。为此,我们采用了另一种简化思路,对最优方案的意义进行了进一步的挖掘,启发式地提出了一种高效低复杂度的算法,该算法可提供和现有算法相仿的中断概率,但其吞吐量性能有了相当高的提升。
本文所采用的对偶分解理论,以及以理论分析指导算法开发的思路,对OFDM系统资源分配算法的研究具有重要的参考意义。而文中针对具体问题所提出的算法,也具有一定的实用价值。
This thesis focuses on applying the dual optimization and decomposition theory to the resource allocation in OFDM systems.And some algorithms are developed heuristically.
The resource allocation in OFDM systems attracts many interests in the past decade. In this field,many problems are formulated,such as rate adaptive problem,margin adaptive problem and fairness problem,et al.For these problems,some mathematic theories,such as linear programming,convex optimization and game theory,are used to obtain optimal solutions and theoretic understanding.As the WiMAX emerged as a practical system in the recent years,it becomes an important task to develop lowcomplexity allocation algorithms for practice.Though there has been already much effort on this,the available practical algorithms have some common shortages.One is the lack of solid theoretic foundation.Another is that so much simplification was made that the performance was degraded significantly.Hence we draw the conclusion that the conflict between the performance and complexity is still a big problem.
This thesis applys the dual decomposition theory to the allocation problem in OFDM systems,and provides a completely novel method for practical algorithm development. Firstly,the quasi-convex analysis is used as the foundation of applying the dual method to a category of allocation problems.Then an optimal solution is obtained.Based on the analysis and understanding of the optimal solution,we make reasonable simplifications and derive some practical algorithms,which are efficient and with low-complexity.
For the rate adaptive problem,we propose a jointly subcarrier and power allocation algorithm to guarantee average data rate requirements.Utilizing the time coherence in wireless channel,the algorithm reduces the iterations in the optimal solution to get low-complexity.Also this make it possible to implement the algorithm in a distributed architecture.Based on local information,the users can decide whether to feedback a certain subcarrier to the base station,which reduces the feedback overhead.At the same time,the algorithm's characteristic of joint optimization brings high efficiency.The simulation is used to evaluate the algorithm.
The same methodology can be used to solve the resource allocation problem to guarantee proportional fairness.However,there is some difference.The allocation of subcarrier and power are coupled more tightly,which will remarkably slow the convergency progress of the iterations.To solve this problem,we use average data rate instead of the instantaneous date rate.The average window size,and other parameters,will affect the algorithm's performance.This thesis studies these parameters carefully and provides optimal design.
The allocation algorithm to guarantee instantaneous data rate requirements is also considered in this thesis.A method different with the above is used to develop the algorithm.We observe the optimal solution and get a new explanation,by which a highly efficient algorithm with low-complexity is presented heuristically.The algorithm provides high throughput as well as low outage probability.
The methodology used in this thesis is innovative and important for the development of allocation algorithms in OFDM systems.And the algorithms presented in this thesis are very meaningful for practice.
OFDM系统中的资源分配算法在近十年来得到了广泛的关注,研究者们使用线性规划、凸优化和博弈论等数学工具,对该领域中存在的各类问题,如速率自适应问题、边值自适应问题和用户公平性问题等,进行了深入的研究。从理论上,研究者对资源分配问题已经有了较成熟的理解。而随着近年来WiMAX系统的成熟,OFDM技术越来越贴近于应用,为其开发低复杂度的实用算法,成为一项非常有现实意义的工作。现有的研究工作中,不乏一些低复杂度的次优算法,但是一方而它们缺少坚实的理论支撑,另一方面,它们对资源分配问题做了过多的简化,性能损失较大。这表明,性能和复杂度的矛盾,仍然是资源分配算法开发过程中有待解决的问题。
本文将对偶分解方法应用于OFDM的资源分配问题,为高效低复杂度的算法开发提供了一种全新的思路。我们首先利用拟凸分析理论,奠定了对偶分解方法在资源分配问题中的应用的理论基础。然后针对不同的问题,使用对偶分解方法分别得出了最优分配方案,这些方案具有很好的性能,但是复杂度也很高。最后,我们通过对最优方案的分析和理解,对其进行简化,得到了复杂度较低的实用算法,而且仍然保持了很好的性能。
针对速率自适应问题,我们首先提出了一种可保证平均数据速率要求的联合子载波和功率分配算法。该算法利用无线信道的时间相干性,约减了最优方案中的迭代次数,从而降低了运算量,并且使算法可以采用分布式的实现结构。在该分布式结构下,用户具有一定的自主性,可以根据本地的信息判断占用某个子载波的可能性,从而判断是否需要反馈该子载波,这种机制显著地减小了反馈开销。而该算法又是在最优方案上进行合理简化的,因此继承了最优算法的联合优化特点,保持了很好的吞吐量性能。我们将用计算机仿真验证该算法的这些特性。
类似的思想也可以应用于解决OFDM系统中保证比例公平性的资源分配问题。有所不同的是,比例公平性问题中子载波分配和功率分配间的联系更为密切,这使得算法收敛的速度变慢。为解决这一问题,我们以平滑后的平均数据速率来代替瞬时数据速率,以减弱算法迭代过程中的振荡现象。在该算法中平滑窗口等参数会显著影响算法性能,我们对其进行评估,并给出了最优的参数设计。
我们还考虑了速率自适应问题中保证瞬时数据速率的资源分配算法。为此,我们采用了另一种简化思路,对最优方案的意义进行了进一步的挖掘,启发式地提出了一种高效低复杂度的算法,该算法可提供和现有算法相仿的中断概率,但其吞吐量性能有了相当高的提升。
本文所采用的对偶分解理论,以及以理论分析指导算法开发的思路,对OFDM系统资源分配算法的研究具有重要的参考意义。而文中针对具体问题所提出的算法,也具有一定的实用价值。
This thesis focuses on applying the dual optimization and decomposition theory to the resource allocation in OFDM systems.And some algorithms are developed heuristically.
The resource allocation in OFDM systems attracts many interests in the past decade. In this field,many problems are formulated,such as rate adaptive problem,margin adaptive problem and fairness problem,et al.For these problems,some mathematic theories,such as linear programming,convex optimization and game theory,are used to obtain optimal solutions and theoretic understanding.As the WiMAX emerged as a practical system in the recent years,it becomes an important task to develop lowcomplexity allocation algorithms for practice.Though there has been already much effort on this,the available practical algorithms have some common shortages.One is the lack of solid theoretic foundation.Another is that so much simplification was made that the performance was degraded significantly.Hence we draw the conclusion that the conflict between the performance and complexity is still a big problem.
This thesis applys the dual decomposition theory to the allocation problem in OFDM systems,and provides a completely novel method for practical algorithm development. Firstly,the quasi-convex analysis is used as the foundation of applying the dual method to a category of allocation problems.Then an optimal solution is obtained.Based on the analysis and understanding of the optimal solution,we make reasonable simplifications and derive some practical algorithms,which are efficient and with low-complexity.
For the rate adaptive problem,we propose a jointly subcarrier and power allocation algorithm to guarantee average data rate requirements.Utilizing the time coherence in wireless channel,the algorithm reduces the iterations in the optimal solution to get low-complexity.Also this make it possible to implement the algorithm in a distributed architecture.Based on local information,the users can decide whether to feedback a certain subcarrier to the base station,which reduces the feedback overhead.At the same time,the algorithm's characteristic of joint optimization brings high efficiency.The simulation is used to evaluate the algorithm.
The same methodology can be used to solve the resource allocation problem to guarantee proportional fairness.However,there is some difference.The allocation of subcarrier and power are coupled more tightly,which will remarkably slow the convergency progress of the iterations.To solve this problem,we use average data rate instead of the instantaneous date rate.The average window size,and other parameters,will affect the algorithm's performance.This thesis studies these parameters carefully and provides optimal design.
The allocation algorithm to guarantee instantaneous data rate requirements is also considered in this thesis.A method different with the above is used to develop the algorithm.We observe the optimal solution and get a new explanation,by which a highly efficient algorithm with low-complexity is presented heuristically.The algorithm provides high throughput as well as low outage probability.
The methodology used in this thesis is innovative and important for the development of allocation algorithms in OFDM systems.And the algorithms presented in this thesis are very meaningful for practice.
引文
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