Electromagnetic information theory (EIT) is one of the emerging topics for 6G communication due to its potential to reveal the performance limit of wireless communication systems. For EIT, one of the most important research directions is degree of freedom (DoF) analysis. Existing research works on DoF analysis for EIT focus on asymptotic conclusions of DoF, which do not well fit the practical wireless communication systems with finite spatial regions and finite frequency bandwidth. In this paper, we provide mathematical definitions of the DoF for continuous electromagnetic fields. Moreover, we theoretically prove that the channel DoF is upper-bounded by the proposed functional DoF of electromagnetic fields. Furthermore, we use the theoretical analyzing tools from the Slepian concentration problem and extend them to three-dimensional space domains and four-dimensional space-time domains under electromagnetic constraints. Then we provide asymptotic DoF conclusions and non-asymptotic DoF analyzing scheme, which suits practical scenarios better, under different scenarios like three-dimensional antenna array. Finally, we use numerical analysis to provide some insights about the optimal spatial sampling interval of the antenna array, the DoF of three-dimensional antenna array, the impact of unequal antenna spacing, the orthogonal space-time patterns, etc.

Electromagnetic information theory (EIT) is an emerging interdisciplinary subject that integrates classical Maxwell electromagnetics and Shannon information theory. The goal of EIT is to uncover the information transmission mechanisms from an electromagnetic (EM) perspective in wireless systems. Existing works on EIT are mainly focused on the analysis of EM channel characteristics, degrees-of-freedom, and system capacity. However, these works do not clarify how to integrate EIT knowledge into the design and optimization of wireless systems. To fill in this gap, in this paper, we propose an EIT-based statistical channel model with simplified parameterization. Thanks to the simplified closed-form expression of the EMCF, it can be readily applied to various channel modeling and inference tasks. Specifically, by averaging the solutions of Maxwell’s equations over a tunable von Mises distribution, we obtain a spatio-temporal correlation function (STCF) model of the EM channel, which we name as the EMCF. Furthermore, by tuning the parameters of the EMCF, we propose an EIT-based covariance estimator (EIT-Cov) to accurately capture the channel covariance. Since classical MMSE estimators can exploit prior information contained in the channel covariance matrix, we further propose the EIT-MMSE channel estimator by substituting EMCF for the covariance matrix. Simulation results show that both the proposed EIT-Cov covariance estimator and the EIT-MMSE channel estimator outperform their baseline algorithms, thus proving that EIT is beneficial to wireless communication systems.

Electromagnetic information theory (EIT) is an emerging interdisciplinary subject that integrates classical Maxwell electromagnetics and Shannon information theory. The goal of EIT is to uncover the information transmission mechanisms from an electromagnetic (EM) perspective in wireless systems. Existing works on EIT are mainly focused on the analysis of degrees-of-freedom (DoF), system capacity, and characteristics of the electromagnetic channel. However, these works do not clarify whether EIT can improve wireless communication systems. To answer this question, in this paper, we provide a novel example of how to improve channel estimators by integrating EM knowledge into the classical MMSE channel estimator. Specifically, the EM knowledge is first encoded into a spatial correlation function (SCF) of the channel, which we term the EM kernel. This EM kernel plays the role of side information to the channel estimator. Since the EM kernel takes the form of Gaussian processes (GP), we propose the EIT-based Gaussian process regression (EIT-GPR) to derive the channel estimations. Furthermore, we propose EM kernel learning to fit the EM kernel to channel observations. Simulation results show that EIT benefits the channel estimator and enables it to outperform traditional isotropic MMSE algorithm, thus proving the practical values of EIT.

Electromagnetic information theory (EIT) is one of the important topics for 6G communication due to its potential to reveal the performance limit of wireless communication systems. For EIT, the research foundation is reasonable and accurate channel modeling. Existing channel modeling works for EIT in non-line-of-sight (NLoS) scenario focus on far-field modeling, which can not accurately capture the characteristics of the channel in near-field. In this paper, we propose the near-field channel model for EIT based on electromagnetic scattering theory. We model the channel by using non-stationary Gaussian random fields and derive the analytical expression of the correlation function of the fields. Furthermore, we analyze the characteristics of the proposed channel model, including how the parameters of the scattering field affect the degrees of freedom (DoF).

Electromagnetic information theory (EIT) is one of the emerging topics for 6G communication due to its potential to reveal the performance limit of wireless communication systems. For EIT, the research foundation is reasonable and accurate channel modeling. Existing channel modeling works for EIT in non-line-of-sight (NLoS) scenario focus on far-field modeling, which can not accurately capture the characteristics of the channel in near field. In this paper, we propose the near-field channel modeling scheme for EIT based on electromagnetic scattering theory. We model the channel by using non-stationary Gaussian random fields and derive the analytical expression of the correlation function of the random fields. Furthermore, we analyze the characteristics of the proposed channel model, e.g., channel degrees of freedom (DoF). Finally, we design a channel estimation scheme for near-field scenario by integrating the electromagnetic prior information of the proposed model. Numerical analysis verifies the correctness of the proposed scheme and shows that it can outperform existing schemes like least square (LS) and orthogonal matching pursuit (OMP).

The concept of continuous-aperture multiple-input multiple-output (CAP-MIMO) technology has been proposed recently, which aims at achieving high spectrum efficiency by deploying extremely dense antennas or even continuous antennas in a given aperture. The fundamental question of CAP-MIMO is whether it can achieve much better performance than the traditional discrete MIMO system. In this paper, we propose a non-asymptotic performance comparison scheme between continuous and discrete MIMO systems based on the analysis of mutual information. We show the consistency of the proposed scheme by proving that the mutual information between discretized transceivers converges to that between continuous transceivers. Numerical analysis verifies the theoretical results, and suggests that the mutual information obtained from the discrete MIMO with widely adopted half-wavelength spaced antennas almost achieves the mutual information obtained from CAP-MIMO.

Traditional channel capacity based on the discrete spatial dimensions mismatches the continuous electromagnetic fields. For the wireless communication system in a limited region, the spatial discretization may results in information loss because the continuous field can not be perfectly recovered from the sampling points. Therefore, electromagnetic information theory based on spatially continuous electromagnetic fields becomes necessary to reveal the fundamental theoretical capacity bound of communication systems. In this paper, we propose analyzing schemes for the performance limit between continuous transceivers. Specifically, we model the communication process between two continuous regions by random fields. Then, for the white noise model, we use Mercer expansion to derive the mutual information between the source and the destination. For the close-form expression, an analytic method is introduced based on autocorrelation functions with rational spectrum. Moreover, the Fredholm determinant is used for the general autocorrelation functions to provide the numerical calculation scheme. Further works extend the white noise model to colored noise and discuss the mutual information under it. Finally, we build an ideal model with infinite-length source and destination which shows a strong correpsondence with the time-domain model in classical information theory. The mutual information and the capacity are derived through the spatial spectral density.

Reconfigurable intelligent surfaces (RISs) are envisioned as a potentially transformative technology for future wireless communications. However, RISs’ inability to process signals and the attendant increased channel dimension have brought new challenges to RIS-assisted systems, including significantly increased pilot overhead required for channel estimation. To address these problems, several prior contributions that enhance the hardware architecture of RISs or develop algorithms to exploit the channels’ mathematical properties have been made, where the required pilot overhead is reduced to be proportional to the number of RIS elements. In this paper, we propose a dimension-independent channel state information (CSI) acquisition approach in which the required pilot overhead is independent of the number of RIS elements. Specifically, in contrast to traditional signal transmission methods, where signals from the base station (BS) and the users are transmitted in different time slots, we propose a novel method in which signals are transmitted from the BS and the user simultaneously during CSI acquisition. With this method, an electromagnetic interference random field (IRF) will be induced on the RIS, and we propose the structure of sensing RIS to capture its features. Moreover, we develop three algorithms for parameter estimation in this system, in which one of the proposed vM-EM algorithm is analyzed with the fixed-point perturbation method to obtain an asymptotic achievable bound. In addition, we also derive the Cramér-Rao lower bound (CRLB) and an asymptotic expression for characterizing the best possible performance of the proposed algorithms. Simulation results verify that our proposed signal transmission method and the corresponding algorithms can achieve dimension-independent CSI acquisition for beamforming.

Shannon-Hartley theorem can accurately calculate the channel capacity when the signal observation time is infinite. However, the calculation of finite-time mutual information, which remains unknown, is essential for guiding the design of practical communication systems. In this paper, we investigate the mutual information between two correlated Gaussian processes within a finite-time observation window. We first derive the finite-time mutual information by providing a limit expression. Then we numerically compute the mutual information within a single finite-time window. We reveal that the number of bits transmitted per second within the finite-time window can exceed the mutual information averaged over the entire time axis, which is called the exceed-average phenomenon. Furthermore, we derive a finite-time mutual information formula under a typical signal autocorrelation case by utilizing the Mercer expansion of trace class operators, and reveal the connection between the finite-time mutual information problem and the operator theory. Finally, we analytically prove the existence of the exceed-average phenomenon in this typical case, and demonstrate its compatibility with the Shannon capacity.