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首页> 外文期刊>Information Theory, IEEE Transactions on >Waterfilling Theorems for Linear Time-Varying Channels and Related Nonstationary Sources
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Waterfilling Theorems for Linear Time-Varying Channels and Related Nonstationary Sources

机译：线性时变信道的注水定理及相关的非平稳源

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摘要

The capacity of the linear time-varying (LTV) channel, a continuous-time LTV filter with additive white Gaussian noise, is characterized by waterfilling in the time-frequency plane. Similarly, the rate distortion function for a related nonstationary source is characterized by reverse waterfilling in the time–frequency plane. Constraints on the average energy or on the squared-error distortion, respectively, are used. The source is formed by the white Gaussian noise response of the same LTV filter as before. The proofs of both waterfilling theorems rely on a Szegő theorem for a class of operators associated with the filter. A self-contained proof of the Szegő theorem is given. The waterfilling theorems compare well with the classical results of Gallager and Berger. In the case of a nonstationary source, it is observed that the part of the classical power spectral density is taken by the Wigner–Ville spectrum. The present approach is based on the spread Weyl symbol of the LTV filter, and is asymptotic in nature. For the spreading factor, a lower bound is suggested by means of an uncertainty inequality.
机译：线性时变（LTV）通道（具有加性高斯白噪声的连续时间LTV滤波器）的容量的特征是在时频平面中充水。同样，相关非平稳源的速率失真函数的特征是在时频平面中进行反向注水。分别使用平均能量约束或平方误差畸变约束。该源由与以前相同的LTV滤波器的白高斯噪声响应形成。对于与过滤器相关的一类算子，两个注水定理的证明都依赖于塞格定理。给出了塞格定理的一个独立证明。充水定理与Gallager和Berger的经典结果相当。在非平稳源的情况下，可以观察到经典功率谱密度的一部分由Wigner-Ville谱获得。本方法基于LTV滤波器的扩展Weyl符号，并且本质上是渐近的。对于扩展因子，通过不确定性不等式建议下限。

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