紧支持扩频的LTV信道的近似特征结构
Approximate Eigenstructure of LTV Channels with Compactly Supported Spreading
摘要：
在这篇文章中，我们得到了信道的近似本征结构的估计，其扩展函数只支持在一组有限测度$|U|$上。因为在典型的应用中，如无线通信，扩展函数是一个随机过程，对应于一个随机的希尔伯特-施密特信道算子$\BH$，我们根据$p$ -从Weyl符号演算的变体到$a$的偏差的范数--扩展函数本身的范数。这推广了最近在$p=2$和$a=1$情况下获得的结果。我们提供了一个通用的方法，这一主题，并考虑然后运营商与$|U|<\infty$更详细。我们展示了脉冲整形和模糊函数加权范数的关系。最后，我们得到了几个必要条件，$|U|$，使逼近误差低于一定的水平。
英文摘要：
In this article we obtain estimates on the approximate eigenstructure of channels with a spreading function supported only on a set of finite measure $|U|$.Because in typical application like wireless communication the spreading function is a random process corresponding to a random Hilbert--Schmidt channel operator $\BH$ we measure this approximation in terms of the ratio of the $p$--norm of the deviation from variants of the Weyl symbol calculus to the $a$--norm of the spreading function itself. This generalizes recent results obtained for the case $p=2$ and $a=1$. We provide a general approach to this topic and consider then operators with $|U|<\infty$ in more detail. We show the relation to pulse shaping and weighted norms of ambiguity functions. Finally we derive several necessary conditions on $|U|$, such that the approximation error is below certain levels.
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