This paper studies a class of stochastic and time-varying Gaussian intersymbol interference (ISI) channels. The $i^{th}$ channel tap during time slot $t$ is uniformly distributed over an interval of centre $c_i$ and radius $ r_{i}$. The array of channel taps is independent along both $t$ and $i$. The channel state information is unavailable at both the transmitter and the receiver. Lower and upper bounds are derived on the White-Gaussian-Input (WGI) capacity $C_{\scriptscriptstyle{WGI}}$ for arbitrary values of the radii $ r_i$. It is shown that $C_{\scriptscriptstyle{WGI}}$ does not scale with the average input power. The proposed lower bound is achieved by a joint-typicality decoder that is tuned to a set of candidates for the channel matrix. This set forms a net that covers the range of the random channel matrix and its resolution is optimized in order to yield the largest achievable rate. Tools in matrix analysis such as Weyl's inequality on perturbation of eigenvalues of symmetric matrices are used in order to analyze the probability of error.
翻译:本文研究的是一组随机和有时间变化的 Gaussian 间联干扰( ISI) 频道。 在时间档中, 美元 美元 的频道开关在美元美元和半径美元之间的间隔内统一分布。 频道开关的阵列是独立的, 包括美元和美元。 发射机和接收机都无法提供频道状态信息。 白- 百日咳- 投影( WGI) 能力从白- 百日咳- 投影( WGI) 能力中得出下限和上界值 $C{ scrstrampttystem{ WGI} $, 任意值为 r_ 美元 美元。 显示 $C{ scamptystem{ WGI} 美元与平均输入力不相称。 提议的下界是联合典型解码, 该解码与频道矩阵的一组候选人相匹配。 设置一个网, 涵盖随机频道矩阵矩阵范围, 其分辨率得到优化, 以产生最大可实现的速率 。 。 矩阵分析工具, 如 Weyl 的精确度误差值 用于 的精确度分析 。