WSSUS脉冲设计问题的群论方法
A Group-Theoretic Approach to the WSSUS Pulse Design Problem
摘要：
我们考虑多载波传输中的脉冲设计问题，其中脉冲形状适应于WSSUS信道的二阶统计。尽管许多作者已经解决了这个问题，但分析性的见解相当有限。首先证明了该问题等价于量子信息论中的纯态信道保真度问题。然后，利用Weyl-Heisenberg群的酉表示，将原优化泛函与伪微分算子的特征值问题联系起来，得到了欠扩展信道下伪微分算子的局部逼近，其中隐含了脉冲缩放和最优相空间位移的概念.该问题被重新表述为一个微分方程和最佳脉冲发生的谐振子哈密顿的本征态。此外，这种运营商-代数的方法进行了扩展，以提供不同类别的散射环境的精确解。
英文摘要：
We consider the pulse design problem in multicarrier transmission where the pulse shapes are adapted to the second order statistics of the WSSUS channel. Even though the problem has been addressed by many authors analytical insights are rather limited. First we show that the problem is equivalent to the pure state channel fidelity in quantum information theory. Next we present a new approach where the original optimization functional is related to an eigenvalue problem for a pseudo differential operator by utilizing unitary representations of the Weyl--Heisenberg group.A local approximation of the operator for underspread channels is derived which implicitly covers the concepts of pulse scaling and optimal phase space displacement. The problem is reformulated as a differential equation and the optimal pulses occur as eigenstates of the harmonic oscillator Hamiltonian. Furthermore this operator--algebraic approach is extended to provide exact solutions for different classes of scattering environments.
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