LTV信道的脉冲整形、局部化和近似特征结构
Pulse Shaping, Localization and the Approximate Eigenstructure of LTV Channels
摘要：
在这篇文章中，我们展示了WSSUS信道的脉冲整形理论与时变信道的近似本征结构概念之间的关系。我们认为脉冲整形的一般信令方案，称为魏尔-海森堡信令，其中包括OFDM与循环前缀和OFDM/OQAM。从最佳WSSUS平均信干噪比的观点来看，脉冲设计问题是局部化和“正交性”之间的相互作用。本地化问题本身可以用本地化算子的特征值来表示，并且与LTV信道算子的近似特征结构的概念密切相关。事实上，在L_2水平上，两者是等价的，我们将证明这一点。“正交性”的概念又可以与紧框架的概念相关。如何在这两方面取得适当的平衡仍然是一个悬而未决的问题。然而，关于某些本地化措施的可实现值和SINR的基本限制的几个陈述已经可以被做出，如将在本文中示出的。
英文摘要：
In this article we show the relation between the theory of pulse shaping for WSSUS channels and the notion of approximate eigenstructure for time-varying channels. We consider pulse shaping for a general signaling scheme, called Weyl-Heisenberg signaling, which includes OFDM with cyclic prefix and OFDM/OQAM. The pulse design problem in the view of optimal WSSUS--averaged SINR is an interplay between localization and "orthogonality". The localization problem itself can be expressed in terms of eigenvalues of localization operators and is intimately connected to the concept of approximate eigenstructure of LTV channel operators. In fact, on the L_2-level both are equivalent as we will show. The concept of "orthogonality" in turn can be related to notion of tight frames. The right balance between these two sides is still an open problem. However, several statements on achievable values of certain localization measures and fundamental limits on SINR can already be made as will be shown in the paper.
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