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On the Spectral Efficiency of Noncoherent Doubly Selective Block-Fading Channels

机译：非相干双选择性块衰落信道的频谱效率

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In this paper, we consider noncoherent single-antenna communication over doubly selective block-fading channels with discrete block-fading interval $N$ . In our noncoherent setup, neither the transmitter nor the receiver know the channel fading coefficients, though both know the channel statistics. In particular, we consider discrete-time channels whose impulse-response trajectories obey a complex-exponential basis expansion model with uncorrelated coefficients, and we show that such a model holds in the limit $Nrightarrow infty$ for pulse-shaped transmission/reception over certain wide-sense stationary uncorrelated scattering channels. First, we show that, when the inputs are chosen from continuous distributions, the channel's multiplexing gain (i.e., capacity pre-log factor) equals $max (0, 1 - N_{ssr delay} N_{ssr Dopp} /N)$ , for discrete delay spread $N_{ssr delay}$ and discrete Doppler spread $N_{ssr Dopp}$. Next, for the case of strictly doubly selective fading (i.e., $N_{ssr Dopp}>1$ and $N_{ssr delay}>1$), we establish that, for cyclic-prefixed affine pilot-aided transmission (PAT) schemes designed to minimize the mean-squared error (MSE) attained by pilot-aided minimum-MSE channel estimati-n-non, the pre-log factor of the achievable rate is less than the channel's multiplexing gain. We then provide guidelines for the design of PAT schemes whose achievable-rate pre-log factor equals the channel's multiplexing gain and construct an example.
机译：在本文中，我们考虑了具有离散块衰落间隔$ N $的双选块衰落信道上的非相干单天线通信。在我们的非相干设置中，尽管发射机和接收机都知道信道统计信息，但它们都不知道信道衰落系数。特别地，我们考虑离散时间信道，其脉冲响应轨迹服从具有不相关系数的复指数基展开模型，并且我们证明了这种模型在一定范围内对于脉冲状发送/接收具有限制$ Nrightarrow infty $广义的静止不相关散射通道。首先，我们表明，当从连续分布中选择输入时，通道的复用增益（即容量对数因子）等于$ max（0，1-N_ {ssr delay} N_ {ssr Dopp} / N）$ ，对于离散延迟扩展$ N_ {ssr delay} $和离散多普勒扩展$ N_ {ssr Dopp} $。接下来，对于严格双重选择性衰落的情况（即$ N_ {ssr Dopp}> 1 $和$ N_ {ssr delay}> 1 $），我们建立了对于循环前缀仿射导频辅助传输（PAT）如果采用最小化由导频辅助的最小MSE信道估计获得的均方误差（MSE）的方案，则可实现速率的前对数因子小于信道的复用增益。然后，我们为可实现速率对数因子等于通道复用增益的PAT方案设计提供指导，并构建一个示例。

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