TY - JOUR

T1 - The Capacity of Memoryless Channels with Sampled Cyclostationary Gaussian Noise

AU - Shlezinger, Nir

AU - Abakasanga, Emeka

AU - Dabora, Ron

AU - Eldar, Yonina C.

N1 - Funding Information:
Manuscript received February 26, 2019; revised July 18, 2019; accepted September 30, 2019. Date of publication October 7, 2019; date of current version January 15, 2020. This work was supported by the Israel Science Foundation under Grants 1685/16 and 0100101, and by the Israeli Ministry of Economy through the HERON 5G consortium. This article was presented in part at the 2019 IEEE International Symposium on Information Theory. The associate editor coordinating the review of this article and approving it for publication was G. Durisi. (Corresponding author: Nir Shlezinger.) N. Shlezinger and Y. C. Eldar are with the Faculty of Mathematics and Computer Science, Weizmann Institute of Science, Rehovot 7610001, Israel (e-mail: nirshlezinger1@gmail.com; yonina@weizmann.ac.il).
Publisher Copyright:
© 2019 IEEE.

PY - 2020/1/1

Y1 - 2020/1/1

N2 - 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.

AB - 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.

KW - Channel capacity

KW - interference-limited communications

KW - sampling

UR - http://www.scopus.com/inward/record.url?scp=85078283047&partnerID=8YFLogxK

U2 - 10.1109/TCOMM.2019.2945785

DO - 10.1109/TCOMM.2019.2945785

M3 - Article

AN - SCOPUS:85078283047

VL - 68

SP - 106

EP - 121

JO - IEEE Transactions on Communications

JF - IEEE Transactions on Communications

SN - 1558-0857

IS - 1

M1 - 8861124

ER -