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On the Sensitivity of Continuous-Time Noncoherent Fading Channel Capacity

机译：连续时间非相干衰落信道容量的灵敏度

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摘要

The noncoherent capacity of stationary discrete-time fading channels is known to be very sensitive to the fine details of the channel model. More specifically, the measure of the support of the fading-process power spectral density (PSD) determines if noncoherent capacity grows logarithmically with the signal-to-noise ratio (SNR) or slower than logarithmically. Such a result is unsatisfactory from an engineering point of view, as the support of the PSD cannot be determined through measurements. The aim of this paper is to assess whether, for general continuous-time Rayleigh-fading channels, this sensitivity has a noticeable impact on capacity at SNR values of practical interest. To this end, we consider the general class of band-limited continuous-time Rayleigh-fading channels that satisfy the wide-sense stationary uncorrelated-scattering (WSSUS) assumption and are, in addition, underspread. We show that, for all SNR values of practical interest, the noncoherent capacity of every channel in this class is close to the capacity of an additive white Gaussian noise channel with the same SNR and bandwidth, independently of the measure of the support of the scattering function (the 2-D channel PSD). Our result is based on a lower bound on noncoherent capacity, which is built on a discretization of the channel input–output relation induced by projecting onto Weyl–Heisenberg sets. This approach is interesting in its own right as it yields a mathematically tractable way of dealing with the mutual information between certain continuous-time random signals.
机译：已知固定离散时间衰落信道的非相干容量对信道模型的精细细节非常敏感。更具体地说，对衰落过程功率谱密度（PSD）的支持程度可确定非相干容量是按信噪比（SNR）对数增长还是比对数慢。从工程的角度来看，这样的结果是不令人满意的，因为不能通过测量来确定PSD的支持。本文的目的是评估对于一般的连续时间瑞利衰落信道，这种灵敏度是否会对实际感兴趣的SNR值的容量产生显着影响。为此，我们考虑了一般的带限连续时间瑞利衰落信道，它们满足广义的平稳不相关散射（WSSUS）假设，并且扩展不足。我们表明，对于所有实际需要的SNR值，此类中每个通道的非相干容量都接近于具有相同SNR和带宽的加性高斯白噪声通道的容量，而与散射支持的度量无关功能（二维通道PSD）。我们的结果基于非相干容量的下限，它是基于投影到Weyl-Heisenberg集上引起的通道输入-输出关系的离散化而建立的。这种方法本身很有趣，因为它产生了一种数学上易处理的方式来处理某些连续时间随机信号之间的互信息。

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