时变信道的近似特征结构
On the Approximate Eigenstructure of Time-Varying Channels
摘要：
本文考虑用符号近似描述双色散信道。我们专注于信道运营商与compressible支持的扩展，这是广泛用于代表快衰落多径通信信道。引入了近似特征结构的概念，它度量了信道运算在给定L_p范数下近似为纯乘法的精度E_p。这样的近似Weyl符号演算的两个变种进行了研究，这在几个模型的时变移动信道中有重要的应用。通常，这种信道具有在有限非零大小的公共支集U上定义的随机扩展函数（逆Weyl变换），使得近似本征结构必须相对于扩展过程的某些范数来测量。我们推导出几个明确的关系的大小|U|的支持。证明了扩展函数的L_q范数与E_p之比的特征与模糊度的加权范数和Wigner函数有关。我们提出了与局部化算子的联系，并给出了模糊函数和维格纳函数在U中局部化能力的新界。我们的分析推广和改进了最近的结果的情况下p=2和q=1。
英文摘要：
In this article we consider the approximate description of doubly--dispersive channels by its symbol. We focus on channel operators with compactly supported spreading, which are widely used to represent fast fading multipath communication channels. The concept of approximate eigenstructure is introduced, which measures the accuracy E_p of the approximation of the channel operation as a pure multiplication in a given L_p-norm. Two variants of such an approximate Weyl symbol calculus are studied, which have important applications in several models for time--varying mobile channels. Typically, such channels have random spreading functions (inverse Weyl transform) defined on a common support U of finite non--zero size such that approximate eigenstructure has to be measured with respect to certain norms of the spreading process. We derive several explicit relations to the size |U| of the support. We show that the characterization of the ratio of E_p to some L_q-norm of the spreading function is related to weighted norms of ambiguity and Wigner functions. We present the connection to localization operators and give new bounds on the ability of localization of ambiguity functions and Wigner functions in U. Our analysis generalizes and improves recent results for the case p=2 and q=1.
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