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Noncoherent Capacity of Underspread Fading Channels

机译：扩频衰落信道的非相干容量

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摘要

We derive bounds on the noncoherent capacity of wide-sense stationary uncorrelated scattering (WSSUS) channels that are selective both in time and frequency, and are underspread, i.e., the product of the channel's delay spread and Doppler spread is small. The underspread assumption is satisfied by virtually all wireless communication channels. For input signals that are peak constrained in time and frequency, we obtain upper and lower bounds on capacity that are explicit in the channel's scattering function, are accurate for a large range of bandwidth, and allow to coarsely identify the capacity-optimal bandwidth as a function of the peak power and the channel's scattering function. We also obtain a closed-form expression for the first-order Taylor series expansion of capacity in the infinite-bandwidth limit, and show that our bounds are tight in the wideband regime. For input signals that are peak constrained in time only (and, hence, allowed to be peaky in frequency), we provide upper and lower bounds on the infinite-bandwidth capacity. Our lower bound is closely related to a result by Viterbi (1967). We find cases where the bounds coincide and, hence, the infinite-bandwidth capacity is characterized exactly. The analysis in this paper is based on a discrete-time discrete-frequency approximation of WSSUS time- and frequency-selective channels. This discretization takes the underspread property of the channel explicitly into account.
机译：我们推导了在时间和频率上都具有选择性且未充分扩展的广义固定不相关散射（WSSUS）通道的非相干容量的界限，即通道的延迟扩展和多普勒扩展的乘积很小。几乎所有的无线通信信道都满足了欠扩展的假设。对于在时间和频率上受到峰值限制的输入信号，我们获得了信道散射函数中明确显示的容量上限和下限，对于较大的带宽范围都是准确的，并且可以粗略地将容量最佳带宽识别为峰值功率的函数和信道的散射函数。我们还获得了无限带宽限制下一阶泰勒级数展开式的封闭形式表达式，并证明了在宽带状态下边界是紧密的。对于仅在时间上受到峰值限制的输入信号（因此，使其在频率上具有峰值），我们提供了无限带宽容量的上限和下限。我们的下界与Viterbi（1967）的结果密切相关。我们发现边界重合的情况，因此精确地描述了无限带宽的容量。本文的分析基于WSSUS时间和频率选择通道的离散时间离散频率近似。这种离散化明确考虑了通道的未扩展属性。

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