Analysis and design of COFDM multicarrier modulation techniques in view of transmission stability in time variant channels

该项目的中心目标是考虑到无线和其他时变环境中的传输稳定性，对编码正交频分复用（COFDM）进行数学分析和优化。所得到的COFDM设计应该包括COFDM参数的自适应的、信道相关的选择，所述COFDM参数诸如码冗余、符号持续时间、保护间隔长度和载波频率。多年来，OFDM在xDSL应用中存在的时不变环境中主导多载波传输系统。在这样的固定设置中，载波信号是信道运营商的近似本征函数，这是可以通过包括循环前缀来增强的现象。最近，COFDM已经被应用于信道通常是时变的移动的通信。在这种情况下，其结构最优性尚未完全了解。在数学方面，OFDM在Gabor分析的伪装下得到了广泛的研究，其中详细讨论了稳定性问题，合成和分析算法以及载波原型功能设计。例如，包括循环前缀被用双正交Riesz基本序列替换正交合成和分析系统的更一般的数学概念所覆盖。此外，最近的结果，在Gabor分析，旨在运营商的时间频率分析，应导致有关的见解缓慢时变运营商存在于无线系统中。当考虑编码时，Gabor分析对COFDM设计的适用性变得更加明显。所传输的数据中固有的冗余导致可能的传输信号的减少。编码和调制的综合分析可能导致选择先验而不是完整系统，即，经过充分研究的Gabor帧可能导致信道容量的更好利用。

The central goal of this project is the mathematical analysis and optimization of coded orthogonal frequency division multiplexing (COFDM) in view of transmission stability in wireless and other time variant environments. The resulting COFDM design should include an adaptive, channel dependent, choice of COFDM parameters such as code redundancy, symbol duration, guard interval length, and carrier frequencies. For years, OFDM has dominated multicarrier transmission systems in time invariant environments as present in xDSL applications. In such stationary set-ups, the carrier signals are approximate eigenfunctions of the channel operator, a phenomenon that can be enhanced by including a cyclic prefix. Recently, COFDM has been applied to mobile communications where the channel is generally time varying. Its structural optimality in this setting is not fully understood. Within mathematics on the other side, OFDM has been extensively studied under the disguise of Gabor analysis, where stability issues, synthesis and analysis algorithms, and carrier prototype function design are discussed at length. For example, including a cyclic prefix is covered by the more general mathematical concept of replacing an orthogonal synthesis and analysis system with biorthogonal Riesz basic sequences. Further, recent results in Gabor analysis aimed at the time frequency analysis of operators should lead to insights relating to slowly time varying operators as present in wireless systems. The applicability of Gabor analysis for COFDM design becomes even more evident when taking coding into account. The redundancy inherent in the transmitted data leads to a reduction of possible transmission signals. An integrative analysis of coding and modulation might lead to the choice of an a-priori over complete system, i.e., the well-studied Gabor frames might lead to a better utilization of channel capacity.