The Capacity of Memoryless Channels with Sampled Cyclostationary Gaussian Noise

Abstract: Non-orthogonal communications play an important role in future communication architectures. In such scenarios, the received signal is corrupted by an interfering signal which is typically cyclostationary in continuous-time. If the period of interference is synchronized with the sampling period, the sampled interference is a discrete-time (DT) cyclostationary process. However, in the common interference scenario, the period of the interference is not necessarily synchronized with the sampling period. In such cases, the DT interference is an almost cyclostationary process. In this work we characterize the capacity of 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 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 cyclostationary noise. Our results characterize the effects of changes in the sampling rate and sampling time offset on the capacity of the resulting DT channel. In particular, we demonstrate that minor variations in the sampling period can substantially affect capacity.