MIMO Capacity Analysis and Channel Estimation for Electromagnetic Information Theory

Electromagnetic information theory (EIT) is an interdisciplinary subject that serves to integrate deterministic electromagnetic theory with stochastic Shannon's information theory. Existing EIT analysis operates in the continuous space domain, which is not aligned with the practical algorithms working in the discrete space domain. This mismatch leads to a significant difficulty in application of EIT methodologies to practical discrete space systems, which is called as the discrete-continuous gap in this paper. To bridge this gap, we establish the discrete-continuous correspondence with a prolate spheroidal wave function (PSWF)-based ergodic capacity analysis framework. Specifically, we state and prove some discrete-continuous correspondence lemmas to establish a firm theoretical connection between discrete information-theoretic quantities to their continuous counterparts. With these lemmas, we apply the PSWF ergodic capacity bound to advanced MIMO architectures such as continuous-aperture MIMO (CAP-MIMO) and extremely large-scale MIMO (XL-MIMO). From this PSWF capacity bound, we discover the capacity saturation phenomenon both theoretically and empirically. Although the growth of MIMO performance is fundamentally limited in this EIT-based analysis framework, we reveal new opportunities in MIMO channel estimation by exploiting the EIT knowledge about the channel. Inspired by the PSWF capacity bound, we utilize continuous PSWFs to improve the pilot design of discrete MIMO channel estimators, which is called as the PSWF channel estimator (PSWF-CE). Simulation results demonstrate improved performances of the proposed PSWF-CE, compared to traditional minimum mean squared error (MMSE) and compressed sensing-based estimators.

Electromagnetic Information Theory for Holographic MIMO Communications

Holographic multiple-input multiple-output (HMIMO) utilizes a compact antenna array to form a nearly continuous aperture, thereby enhancing higher capacity and more flexible configurations compared with conventional MIMO systems, making it attractive in current scientific research. Key questions naturally arise regarding the potential of HMIMO to surpass Shannon's theoretical limits and how far its capabilities can be extended. However, the traditional Shannon information theory falls short in addressing these inquiries because it only focuses on the information itself while neglecting the underlying carrier, electromagnetic (EM) waves, and environmental interactions. To fill up the gap between the theoretical analysis and the practical application for HMIMO systems, we introduce electromagnetic information theory (EIT) in this paper. This paper begins by laying the foundation for HMIMO-oriented EIT, encompassing EM wave equations and communication regions. In the context of HMIMO systems, the resultant physical limitations are presented, involving Chu's limit, Harrington's limit, Hannan's limit, and the evaluation of coupling effects. Field sampling and HMIMO-assisted oversampling are also discussed to guide the optimal HMIMO design within the EIT framework. To comprehensively depict the EM-compliant propagation process, we present the approximate and exact channel modeling approaches in near-/far-field zones. Furthermore, we discuss both traditional Shannon's information theory, employing the probabilistic method, and Kolmogorov information theory, utilizing the functional analysis, for HMIMO-oriented EIT systems.

Near-Optimal Channel Estimation for Dense Array Systems

By deploying a large number of antennas with sub-half-wavelength spacing in a compact space, dense array systems(DASs) can fully unleash the multiplexing-and-diversity gains of limited apertures. To acquire these gains, accurate channel state information acquisition is necessary but challenging due to the large antenna numbers. To overcome this obstacle, this paper reveals that exploiting the high spatial correlation of DAS channels is crucial while designing the observation matrix for optimal/near-optimal channel estimation. Firstly, we prove that the observation matrix design is equivalent to a time-domain duality of multiple-input multiple-output precoding, which can be ideally addressed by the water-filling principle. For practical realizations, a novel ice-filling algorithm is proposed to design amplitude-and-phase controllable observation matrices, and a majorization-minimization algorithm is proposed to address the phase-only controllable case. Particularly, we prove that the ice-filling algorithm can be viewed as a ``quantized" water-filling algorithm. To support the sub-optimality of the proposed designs, we provide comprehensive analyses on the achievable mean square errors and their asymptotic expressions. Finally, numerical simulations verify that our proposed channel estimation designs can achieve the near-optimal performance and outperform existing approaches significantly.

Holography inspired self-controlled reconfigurable intelligent surface

Among various promising candidate technologies for the sixth-generation (6G) wireless communications, recent advances in microwave metasurfaces have sparked a new research area of reconfigurable intelligent surfaces (RISs). By controllably reprogramming the wireless propagation channel, RISs are envisioned to achieve low-cost wireless capacity boosting, coverage extension, and enhanced energy efficiency. To reprogram the channel, each meta-atom on RIS needs an external control signal, which is usually generated by base station (BS). However, BS-controlled RISs require complicated control cables, which hamper their massive deployments. Here, we eliminate the need for BS control by proposing a self-controlled RIS (SC-RIS), which is inspired by the optical holography principle. Different from the existing BS-controlled RISs, each meta-atom of SC-RIS is integrated with an additional power detector for holographic recording. By applying the classical Fourier-transform processing to the measured hologram, SC-RIS is capable of retrieving the user's channel state information required for beamforming, thus enabling autonomous RIS beamforming without control cables. Owing to this WiFi-like plug-and-play capability without the BS control, SC-RISs are expected to enable easy and massive deployments in the future 6G systems.

Near-Field Channel Modeling for Electromagnetic Information Theory

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, e.g., the sparsity of the model in wavenumber domain. Based on the sparsity of the model, we design a channel estimation scheme for near-field scenario. 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).

Electromagnetic Hybrid Beamforming for Holographic Communications

It is well known that there is inherent radiation pattern distortion for the commercial base station antenna array, which usually needs three antenna sectors to cover the whole space. To eliminate pattern distortion and further enhance beamforming performance, we propose an electromagnetic hybrid beamforming (EHB) scheme based on a three-dimensional (3D) superdirective holographic antenna array. Specifically, EHB consists of antenna excitation current vectors (analog beamforming) and digital precoding matrices, where the implementation of analog beamforming involves the real-time adjustment of the radiation pattern to adapt it to the dynamic wireless environment. Meanwhile, the digital beamforming is optimized based on the channel characteristics of analog beamforming to further improve the achievable rate of communication systems. An electromagnetic channel model incorporating array radiation patterns and the mutual coupling effect is also developed to evaluate the benefits of our proposed scheme. Simulation results demonstrate that our proposed EHB scheme with a 3D holographic array achieves a relatively flat superdirective beamforming gain and allows for programmable focusing directions throughout the entire spatial domain. Furthermore, they also verify that the proposed scheme achieves a sum rate gain of over 150% compared to traditional beamforming algorithms.

Successive Bayesian Reconstructor for FAS Channel Estimation

Fluid antenna systems (FASs) can reconfigure their locations freely within a spatially continuous space. To keep favorable antenna positions, the channel state information (CSI) acquisition for FASs is essential. While some techniques have been proposed, most existing FAS channel estimators require several channel assumptions, such as slow variation and angular-domain sparsity. When these assumptions are not reasonable, the model mismatch may lead to unpredictable performance loss. In this paper, we propose the successive Bayesian reconstructor (S-BAR) as a general solution to estimate FAS channels. Unlike model-based estimators, the proposed S-BAR is prior-aided, which builds the experiential kernel for CSI acquisition. Inspired by Bayesian regression, the key idea of S-BAR is to model the FAS channels as a stochastic process, whose uncertainty can be successively eliminated by kernel-based sampling and regression. In this way, the predictive mean of the regressed stochastic process can be viewed as the maximum a posterior (MAP) estimator of FAS channels. Simulation results verify that, in both model-mismatched and model-matched cases, the proposed S-BAR can achieve higher estimation accuracy than the existing schemes.

Coded Beam Training

In extremely large-scale multiple input multiple output (XL-MIMO) systems for future sixth-generation (6G) communications, codebook-based beam training stands out as a promising technology to acquire channel state information (CSI). Despite their effectiveness, when the pilot overhead is limited, existing beam training methods suffer from significant achievable rate degradation for remote users with low signal-to-noise ratio (SNR). To tackle this challenge, leverging the error-correcting capability of channel codes, we introduce channel coding theory into hierarchical beam training to extend the coverage area. Specifically, we establish the duality between hierarchical beam training and channel coding, and the proposed coded beam training scheme serves as a general framework. Then, we present two specific implementations exemplified by coded beam training methods based on Hamming codes and convolutional codes, during which the beam encoding and decoding processes are refined respectively to better accommodate to the beam training problem. Simulation results have demonstrated that, the proposed coded beam training method can enable reliable beam training performance for remote users with low SNR, while keeping training overhead low.

Successive Bayesian Reconstructor for Channel Estimation in Flexible Antenna Systems

Flexible antenna systems (FASs) can reconfigure their locations freely within a spatially continuous space. To keep favorable antenna positions, the channel state information (CSI) acquisition for FASs is essential. While some techniques have been proposed, most existing FAS channel estimators require several channel assumptions, such as slow variation and angular-domain sparsity. When these assumptions are not reasonable, the model mismatch may lead to unpredictable performance loss. In this paper, we propose the successive Bayesian reconstructor (S-BAR) as a general solution to estimate FAS channels. Unlike model-based estimators, the proposed S-BAR is prior-aided, which builds the experiential kernel for CSI acquisition. Inspired by Bayesian regression, the key idea of S-BAR is to model the FAS channels as a stochastic process, whose uncertainty can be successively eliminated by kernel-based sampling and regression. In this way, the predictive mean of the regressed stochastic process can be viewed as the maximum a posterior (MAP) estimator of FAS channels. Simulation results verify that, in both model-mismatched and model-matched cases, the proposed S-BAR can achieve higher estimation accuracy than the existing schemes.

Enhancing Energy Efficiency for Reconfigurable Intelligent Surfaces with Practical Power Models

Reconfigurable intelligent surfaces (RISs) are widely considered a promising technology for future wireless communication systems. As an important indicator of RIS-assisted communication systems in green wireless communications, energy efficiency (EE) has recently received intensive research interest as an optimization target. However, most previous works have ignored the different power consumption between ON and OFF states of the PIN diodes attached to each RIS element. This oversight results in extensive unnecessary power consumption and reduction of actual EE due to the inaccurate power model. To address this issue, in this paper, we first utilize a practical power model for a RIS-assisted multi-user multiple-input single-output (MU-MISO) communication system, which takes into account the difference in power dissipation caused by ON-OFF states of RIS's PIN diodes. Based on this model, we formulate a more accurate EE optimization problem. However, this problem is non-convex and has mixed-integer properties, which poses a challenge for optimization. To solve the problem, an effective alternating optimization (AO) algorithm framework is utilized to optimize the base station and RIS beamforming precoder separately. To obtain the essential RIS beamforming precoder, we develop two effective methods based on maximum gradient search and SDP relaxation respectively. Theoretical analysis shows the exponential complexity of the original problem has been reduced to polynomial complexity. Simulation results demonstrate that the proposed algorithm outperforms the existing ones, leading to a significant increase in EE across a diverse set of scenarios.