AI and Deep Learning for THz Ultra-Massive MIMO: From Model-Driven Approaches to Foundation Models

In this paper, we explore the potential of artificial intelligence (AI) to address the challenges posed by terahertz ultra-massive multiple-input multiple-output (THz UM-MIMO) systems. We begin by outlining the characteristics of THz UM-MIMO systems, and identify three primary challenges for the transceiver design: 'hard to compute', 'hard to model', and 'hard to measure'. We argue that AI can provide a promising solution to these challenges. We then propose two systematic research roadmaps for developing AI algorithms tailored for THz UM-MIMO systems. The first roadmap, called model-driven deep learning (DL), emphasizes the importance to leverage available domain knowledge and advocates for adopting AI only to enhance the bottleneck modules within an established signal processing or optimization framework. We discuss four essential steps to make it work, including algorithmic frameworks, basis algorithms, loss function design, and neural architecture design. Afterwards, we present a forward-looking vision through the second roadmap, i.e., physical layer foundation models. This approach seeks to unify the design of different transceiver modules by focusing on their common foundation, i.e., the wireless channel. We propose to train a single, compact foundation model to estimate the score function of wireless channels, which can serve as a versatile prior for designing a wide variety of transceiver modules. We will also guide the readers through four essential steps, including general frameworks, conditioning, site-specific adaptation, and the joint design of foundation models and model-driven DL.

Near-Field Wideband Beamforming for RIS Based on Fresnel Zone

Reconfigurable intelligent surface (RIS) has emerged as a promising solution to overcome the challenges of high path loss and easy signal blockage in millimeter-wave (mmWave) and terahertz (THz) communication systems. With the increase of RIS aperture and system bandwidth, the near-field beam split effect emerges, which causes beams at different frequencies to focus on distinct physical locations, leading to a significant gain loss of beamforming. To address this problem, we leverage the property of Fresnel zone that the beam split disappears for RIS elements along a single Fresnel zone and propose beamforming design on the two dimensions of along and across the Fresnel zones. The phase shift of RIS elements along the same Fresnel zone are designed aligned, so that the signal reflected by these element can add up in-phase at the receiver regardless of the frequency. Then the expression of equivalent channel is simplified to the Fourier transform of reflective intensity across Fresnel zones modulated by the designed phase. Based on this relationship, we prove that the uniformly distributed in-band gain with aligned phase along the Fresnel zone leads to the upper bound of achievable rate. Finally, we design phase shifts of RIS to approach this upper bound by adopting the stationary phase method as well as the Gerchberg-Saxton (GS) algorithm. Simulation results validate the effectiveness of our proposed Fresnel zone-based method in mitigating the near-field beam split effect.

A physics-based perspective for understanding and utilizing spatial resources of wireless channels

To satisfy the increasing demands for transmission rates of wireless communications, it is necessary to use spatial resources of electromagnetic (EM) waves. In this context, EM information theory (EIT) has become a hot topic by integrating the theoretical framework of deterministic mathematics and stochastic statistics to explore the transmission mechanisms of continuous EM waves. However, the previous studies were primarily focused on frame analysis, with limited exploration of practical applications and a comprehensive understanding of its essential physical characteristics. In this paper, we present a three-dimensional (3-D) line-of-sight channel capacity formula that captures the vector EM physics and accommodates both near- and far-field scenes. Based on the rigorous mathematical equation and the physical mechanism of fast multipole expansion, a channel model is established, and the finite angular spectral bandwidth feature of scattered waves is revealed. To adapt to the feature of the channel, an optimization problem is formulated for determining the mode currents on the transmitter, aiming to obtain the optimal design of the precoder and combiner. We make comprehensive analyses to investigate the relationship among the spatial degree of freedom, noise, and transmitted power, thereby establishing a rigorous upper bound of channel capacity. A series of simulations are conducted to validate the theoretical model and numerical method. This work offers a novel perspective and methodology for understanding and leveraging EIT, and provides a theoretical foundation for the design and optimization of future wireless communications.

Error Correction Code Transformer: From Non-Unified to Unified

Channel coding is vital for reliable data transmission in modern wireless systems, and its significance will increase with the emergence of sixth-generation (6G) networks, which will need to support various error correction codes. However, traditional decoders were typically designed as fixed hardware circuits tailored to specific decoding algorithms, leading to inefficiencies and limited flexibility. To address these challenges, this paper proposes a unified, code-agnostic Transformer-based decoding architecture capable of handling multiple linear block codes, including Polar, Low-Density Parity-Check (LDPC), and Bose-Chaudhuri-Hocquenghem (BCH), within a single framework. To achieve this, standardized units are employed to harmonize parameters across different code types, while the redesigned unified attention module compresses the structural information of various codewords. Additionally, a sparse mask, derived from the sparsity of the parity-check matrix, is introduced to enhance the model's ability to capture inherent constraints between information and parity-check bits, resulting in improved decoding accuracy and robustness. Extensive experimental results demonstrate that the proposed unified Transformer-based decoder not only outperforms existing methods but also provides a flexible, efficient, and high-performance solution for next-generation wireless communication systems.

Coded Beam Training for RIS Assisted Wireless Communications

Reconfigurable intelligent surface (RIS) is considered as one of the key technologies for future 6G communications. To fully unleash the performance of RIS, accurate channel state information (CSI) is crucial. Beam training is widely utilized to acquire the CSI. However, before aligning the beam correctly to establish stable connections, the signal-to-noise ratio (SNR) at UE is inevitably low, which reduces the beam training accuracy. To deal with this problem, we exploit the coded beam training framework for RIS systems, which leverages the error correction capability of channel coding to improve the beam training accuracy under low SNR. Specifically, we first extend the coded beam training framework to RIS systems by decoupling the base station-RIS channel and the RIS-user channel. For this framework, codewords that accurately steer to multiple angles is essential for fully unleashing the error correction capability. In order to realize effective codeword design in RIS systems, we then propose a new codeword design criterion, based on which we propose a relaxed Gerchberg-Saxton (GS) based codeword design scheme by considering the constant modulus constraints of RIS elements. In addition, considering the two dimensional structure of RIS, we further propose a dimension reduced encoder design scheme, which can not only guarentee a better beam shape, but also enable a stronger error correction capability. Simulation results reveal that the proposed scheme can realize effective and accurate beam training in low SNR scenarios.

Sparse MIMO for ISAC: New Opportunities and Challenges

Multiple-input multiple-output (MIMO) has been a key technology of wireless communications for decades. A typical MIMO system employs antenna arrays with the inter-antenna spacing being half of the signal wavelength, which we term as compact MIMO. Looking forward towards the future sixth-generation (6G) mobile communication networks, MIMO system will achieve even finer spatial resolution to not only enhance the spectral efficiency of wireless communications, but also enable more accurate wireless sensing. To this end, by removing the restriction of half-wavelength antenna spacing, sparse MIMO has been proposed as a new architecture that is able to significantly enlarge the array aperture as compared to conventional compact MIMO with the same number of array elements. In addition, sparse MIMO leads to a new form of virtual MIMO systems for sensing with their virtual apertures considerably larger than physical apertures. As sparse MIMO is expected to be a viable technology for 6G, we provide in this article a comprehensive overview of it, especially focusing on its appealing advantages for integrated sensing and communication (ISAC) towards 6G. Specifically, assorted sparse MIMO architectures are first introduced, followed by their new benefits as well as challenges. We then discuss the main design issues of sparse MIMO, including beam pattern synthesis, signal processing, grating lobe suppression, beam codebook design, and array geometry optimization. Last, we provide numerical results to evaluate the performance of sparse MIMO for ISAC and point out promising directions for future research.

Near-Field Wideband Beam Training Based on Distance-Dependent Beam Split

Near-field beam training is essential for acquiring channel state information in 6G extremely large-scale multiple input multiple output (XL-MIMO) systems. To achieve low-overhead beam training, existing method has been proposed to leverage the near-field beam split effect, which deploys true-time-delay arrays to simultaneously search multiple angles of the entire angular range in a distance ring with a single pilot. However, the method still requires exhaustive search in the distance domain, which limits its efficiency. To address the problem, we propose a distance-dependent beam-split-based beam training method to further reduce the training overheads. Specifically, we first reveal the new phenomenon of distance-dependent beam split, where by manipulating the configurations of time-delay and phase-shift, beams at different frequencies can simultaneously scan the angular domain in multiple distance rings. Leveraging the phenomenon, we propose a near-field beam training method where both different angles and distances can simultaneously be searched in one time slot. Thus, a few pilots are capable of covering the whole angle-distance space for wideband XL-MIMO. Theoretical analysis and numerical simulations are also displayed to verify the superiority of the proposed method on beamforming gain and training overhead.

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.