Non-orthogonal communications play an important role in future digital communication architectures. In such scenarios, the received signal is corrupted by an interfering communications signal, which is much stronger than the thermal noise, and is often modeled as a cyclostationary process in continuous-time. To facilitate digital processing, the receiver typically samples the received signal synchronously with the symbol rate of the information signal. If the period of the statistics of the interference is synchronized with that of the information signal, then the sampled interference is modeled as a discrete-time (DT) cyclostationary random process. However, in the common interference scenario, the period of the statistics of the interference is not necessarily synchronized with that of the information signal. In such cases, the DT interference may be modeled as an almost cyclostationary random process. In this work we characterize the capacity of DT memoryless additive noise channels in which the noise arises from a sampled cyclostationary Gaussian process. For the case of synchronous sampling, capacity can be obtained in closed form. When sampling is not synchronized with the symbol rate of the interference, the resulting channel is not information stable, thus classic information-theoretic tools are not applicable. Using information spectrum methods, we prove that capacity can be obtained as the limit of a sequence of capacities of channels with additive cyclostationary Gaussian noise. Our results allow to characterize the effects of changes in the sampling rate and sampling time offset on the capacity of the resulting DT channel. In particular, it is demonstrated that minor variations in the sampling period, such that the resulting noise switches from being synchronously-sampled to being asynchronously-sampled, can substantially change the capacity.

中文翻译：

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具有采样循环平稳高斯噪声的无记忆信道容量

非正交通信在未来的数字通信架构中扮演着重要的角色。在这种情况下，接收到的信号会被比热噪声强得多的干扰通信信号破坏，并且通常被建模为连续时间的循环平稳过程。为了便于数字处理，接收机通常与信息信号的符号率同步地对接收信号进行采样。如果干扰统计周期与信息信号周期同步，则采样干扰被建模为离散时间（DT）循环平稳随机过程。然而，在常见的干扰场景下，干扰的统计周期不一定与信息信号的周期同步。在这种情况下，DT 干扰可以建模为一个几乎循环平稳的随机过程。在这项工作中，我们描述了 DT 无记忆加性噪声通道的容量，其中噪声来自采样的循环平稳高斯过程。对于同步采样的情况，可以以封闭的形式获得容量。当采样与干扰的符号率不同步时，产生的信道不是信息稳定的，因此经典的信息论工具不适用。使用信息谱方法，我们证明了容量可以作为具有加性循环平稳高斯噪声的信道容量序列的极限来获得。我们的结果允许表征采样率和采样时间偏移的变化对产生的 DT 通道容量的影响。特别是，