A distinctive function of sixth-generation (6G) networks is the integration of distributed sensing and edge artificial intelligence (AI) to enable intelligent perception of the physical world. This resultant platform, termed integrated sensing and edge AI (ISEA), is envisioned to enable a broad spectrum of Internet-of-Things (IoT) applications, including remote surgery, autonomous driving, and holographic telepresence. Recently, the communication bottleneck confronting the implementation of an ISEA system is overcome by the development of over-the-air computing (AirComp) techniques, which facilitate simultaneous access through over-the-air data feature fusion. Despite its advantages, AirComp with uncoded transmission remains vulnerable to interference. To tackle this challenge, we propose AirBreath sensing, a spectrum-efficient framework that cascades feature compression and spread spectrum to mitigate interference without bandwidth expansion. This work reveals a fundamental tradeoff between these two operations under a fixed bandwidth constraint: increasing the compression ratio may reduce sensing accuracy but allows for more aggressive interference suppression via spread spectrum, and vice versa. This tradeoff is regulated by a key variable called breathing depth, defined as the feature subspace dimension that matches the processing gain in spread spectrum. To optimally control the breathing depth, we mathematically characterize and optimize this aforementioned tradeoff by designing a tractable surrogate for sensing accuracy, measured by classification discriminant gain (DG). Experimental results on real datasets demonstrate that AirBreath sensing effectively mitigates interference in ISEA systems, and the proposed control algorithm achieves near-optimal performance as benchmarked with a brute-force search.

Speculative inference (SPIN) was originally developed as an efficient architecture to accelerate Large Language Models (LLMs). In this work, we propose its distributed deployment to enable cooperative token generation in a multiuser edge system; its advantage is to effectively balance computational loads between resource-constrained devices and servers. The resulting architecture, termed Multi-access SPIN (Multi-SPIN), utilizes on-device small language models to generate and upload candidate token drafts, while an edge server operates the LLM to verify them in parallel batches. Given the severe heterogeneity in users' computation and communication capabilities, the draft length emerges as a critical control variable that influences node-level computation loads and multi-access latency, thereby governing the sum token goodput. Consequently, considering frequency-division multiple access, we investigate the problem of multi-access draft control, a joint optimization of draft-length control and bandwidth allocation to maximize sum token goodput. We examine two cases: (1) homogeneous draft lengths across users to facilitate server-side batching, and (2) heterogeneous draft lengths to introduce a new dimension for goodput enhancement. By developing decomposition methods, we reduce these complex optimizations into tractable sub-problems, which allow efficient draft control algorithms to be derived in closed form. Our analysis shows that the optimal bandwidth allocation compensates users with weaker computation-and-communication capabilities in the homogeneous case due to the batching synchronization requirements, whereas its heterogeneous-case counterpart rewards users with higher acceptance rates by relaxing such requirements. Experiments using Llama-2 and Qwen3.5 model pairs across diverse tasks demonstrate that Multi-SPIN improves goodput by up to 88

Beamforming is conventionally understood as a collective property of many discrete antenna elements in both communication and radar fields, which links angular selectivity to array size, element spacing, and band-specific hardware. Here we uncover a fundamentally different beamforming mechanism achieved by a Rydberg atomic receiver: a Rydberg-atom vapor cell dressed by a local-oscillator field constitutes a continuous quantum aperture. In this regime, spatially-varying quantum coherence across the aperture provides continuous amplitude-phase control, allowing a directional beam pattern to emerge from one sensing volume rather than from an engineered array. We establish the theory of continuous quantum aperture and show that tailoring the local-oscillator field can directly program the aperture response. This enables reconfigurable single-peak, multipeak, and multiband beamforming within a single vapor cell. Experiments on a Rydberg atomic receiver prototype verify that practical beam patterns agree with theoretical predictions across aperture sizes, frequency bands, and local-oscillator configurations. Leveraging this new beamforming mechanism, we further demonstrate interference mitigation, multiuser access, and multiband multiuser access with the single-vapor-cell platform. Our results identify the continuous quantum aperture as a new operating principle of Rydberg atomic receivers and establish single-vapor-cell beamforming as an integrated and reconfigurable platform for spatially selective electromagnetic reception.

Leveraging the quantum advantages of highly excited atoms, Rydberg atomic receivers (RAREs) represent a paradigm shift in microwave detection with extremely high sensitivity and broadband tunability. However, existing studies often model RAREs as isotropic point receivers and neglect the spatial variation of Rydberg atomic states within vapor cells, which can lead to inaccurate characterization of their reception patterns. To address this issue, we theoretically analyze the spatial response of a local-oscillator (LO) field-dressed RARE. Our results reveal that as the vapor-cell length increases, a receiving beam aligned with the LO field is formed, and its beamwidth is inversely proportional to the cell length. This finding enables atomic beamforming with only a single atomic vapor cell to enhance signal-to-noise ratio. Furthermore, we analyze the maximum beamforming gain of a single vapor cell by balancing the fundamental tradeoff between improved spatial selectivity and increased laser attenuation in the atomic medium as the vapor cell length becomes longer. To mitigate the beamforming-gain loss caused by laser attenuation, we further propose a segmental-vapor-cell architecture. In this architecture, multiple short vapor cells are arranged along the optical propagation path and separated by clear-air gaps. This design effectively expands the reception aperture while keeping the total vapor-cell length, and hence attenuation loss, fixed. As a result, it achieves a narrower beamwidth and higher beamforming gain than a conventional single-vapor-cell receiver, as demonstrated by extensive numerical results.

Rydberg Atomic REceivers (RAREs) have demonstrated remarkable capabilities for radio-frequency signal measurement, enabling advanced quantum wireless sensing. Existing RARE-based sensing systems popularly adopt the heterodyne detection methodology, which requires an additional reference source to serve as an atomic mixer. However, this approach entails a bulky transceiver architecture and is limited in the supportable sensing bandwidth. To address these limitations, we propose a self-heterodyne sensing paradigm where the transmitter's self-interference naturally provides the reference signal. We demonstrate that a self-heterodyne RARE functions as an atomic autocorrelator, eliminating the need for external reference sources while supporting substantially wider bandwidth than conventional heterodyne methods. Next, a two-stage algorithm is devised to perform target ranging in self-heterodyne RARE systems. This algorithm is shown to closely approach the Cram & eacute;r-Rao lower bound. Furthermore, we introduce the power-trajectory (P-trajectory) design for RAREs, which maximizes the sensing sensitivity through time-varying transmission power control. An internal noise (ITN)-limited P-trajectory is developed to capture the profile of the asymptotically optimal time-varying power in the presence of ITN only. This design is then extended to the practical P-trajectory by incorporating both the ITN and external noise. Numerical results validate that the proposed self-heterodyne sensing can achieve a similar to 100MHz-level bandwidth with high sensitivity, substantially surpassing existing heterodyne counterparts and paving the way for high-resolution quantum wireless sensing.

The exploitation of sub-MHz (1 MHz) can be beneficial for a plethora of applications like underwater vehicular communication, subsurface exploration, low-frequency navigation etc. The traditional electrical receivers in this band are either hundreds of meters long or, when miniaturized, inefficient and bandwidth-limited, making them inapplicable for practical underwater implementations. Such obstacles can be circumvented by the emerging Rydberg atomic receiving technology, which is capable of detecting fields from DC up to the terahertz regime with compact structure. Against this background, we propose a method to detect sub-MHz electric fields without further calibration. Specifically, a physics-based model of the combined DC and AC-Stark response is established. Based on the model, we modulate the DC-Stark spectrum with the received signal and extract its amplitude by fitting the cycle-averaged, symmetric Stark-split peaks. Then we map this swing directly to the intrinsic atomic polarizability. By such operations, the proposed method can remove the dependence on electrode spacing or field-amplitude references. For performance evaluation, six-level Lindblad simulations and experiments are conducted at a low-frequency field of 30 kHz demonstrate a minimum detectable field of 5.3 mV/cm, with stable readout across practical optical-power variations. The approach manages to expand operating range of Rydberg atomic receivers below 1 MHz, and enables compact, calibration-free quantum front ends for underwater and subsurface receivers.

Harnessing multi-level electron transitions, Rydberg Atomic REceivers (RAREs) can detect wireless signals across a wide range of frequency bands, from Megahertz to Terahertz. This capability enables multi-band wireless communications and sensing (CommunSense). Existing research on multi-band RAREs primarily focuses on experimental demonstrations, lacking a tractable model to mathematically characterize their mechanisms. This issue leaves the multi-band RARE as a black box and poses challenges in its practical applications. To fill in this gap, this paper investigates the underlying mechanism of multiband RAREs and explores their optimal performance. For the first time, an analytical transfer function with a closed-form expression for multi-band RAREs is derived by solving the quantum response of Rydberg atoms. It shows that a multiband RARE simultaneously serves as a multi-band atomic mixer for down-converting multi-band signals and a multi-band atomic amplifier that reflects its sensitivity to each band. Further analysis of the atomic amplifier unveils that the intrinsic gain at each frequency band can be decoupled into a global gain term and a Rabi attention term. The former determines the overall sensitivity of a RARE to all frequency bands of wireless signals. The latter influences the allocation of the overall sensitivity to each frequency band, representing a unique attention mechanism of multi-band RAREs. The optimal design of the global gain is provided to maximize the overall sensitivity of multi-band RAREs. Subsequently, the optimal Rabi attentions are also derived to maximize the practical multi-band CommunSense performance. An experiment platform is built to validate the effectiveness of the derived transfer function, and numerical results confirm the superiority of multi-band RAREs.

The natural integration of distributed sensing and edge artificial intelligence (AI), termed integrated sensing and edge AI (ISEA), is envisioned to be a key enabler of sixth-generation (6G) networks. In this context, leveraging over-the-air computing (AirComp) for simultaneous feature fusion in ISEA systems has attracted growing research interest. Despite its advantages, AirComp-based distributed sensing still faces two challenges: 1) the vulnerability of AirComp to interference resulting from uncoded transmission, and 2) communication bottleneck due to high-dimensional feature uploading. To tackle these challenges, we propose AirBreath sensing, a spectrum-efficient framework that cascades feature compression and spread spectrum to mitigate interference without bandwidth expansion. This work reveals a fundamental tradeoff between these two operations under constrained spectrum resources: a more aggressive compression may reduce sensing accuracy but allows for more aggressive interference suppression via spread spectrum, and vice versa. This tradeoff is regulated by a key variable called breathing depth, defined as the feature subspace dimension and is optimized by designing a tractable surrogate for sensing accuracy, measured by classification discriminant gain (DG). Experiments on real datasets show that AirBreath sensing effectively suppresses interference in ISEA systems, with the proposed algorithm achieving near-optimal performance.

Reconfigurable intelligent surfaces (RISs) have emerged as a promising technology for enhancing wireless communications through dense antenna arrays. Accurate channel estimation is critical to unlocking their full performance potential. To enhance RIS channel estimators, this paper proposes a novel observation matrix design scheme. Bayesian optimization framework is adopted to generate observation matrices that maximize the mutual information between received pilot signals and RIS channels. To solve the formulated problem efficiently, we develop an alternating Riemannian manifold optimization (ARMO) algorithm to alternately update the receiver combiners and RIS phase-shift matrices. An adaptive kernel training strategy is further introduced to iteratively refine the channel covariance matrix without requiring additional pilot resources. Simulation results demonstrate that the proposed ARMO-enhanced estimator achieves substantial gains in estimation accuracy over state-of-the-art methods.

In recent years, densifying multiple-input multiple-output (MIMO) has attracted much attention from the communication community. Thanks to the subwavelength antenna spacing, the strong correlations among densifying antennas provide sufficient prior knowledge about channel state information (CSI). This inspires the careful design of observation matrices (e.g., transmit precoders and receive combiners), that exploits the CSI prior knowledge, to boost channel estimation performance. Aligned with this vision, this work proposes to jointly design the combiners and precoders by maximizing the mutual information between the received pilots and densifying MIMO channels. A two-dimensional ice-filling (2DIF) algorithm is proposed to efficiently accomplish this objective. The algorithm is motivated by the fact that the eigenspace of MIMO channel covariance can be decoupled into two sub-eigenspaces, which are associated with the correlations of transmitter antennas and receiver antennas, respectively. By properly setting the precoder and the combiner as the eigenvectors from these two sub-eigenspaces, the 2DIF promises to generate near-optimal observation matrices. Moreover, we further extend the 2DIF method to the popular hybrid combining systems, where a two-stage 2DIF (TS-2DIF) algorithm is developed to handle the analog combining circuits realized by phase shifters. Simulation results demonstrate that, compared to the state-of-the-art schemes, the proposed 2DIF and TS-2DIF methods can achieve superior channel estimation accuracy.

The imminent emergence of sixth-generation (6G) networks faces critical challenges from spatially heterogeneous traffic and escalating energy consumption, necessitating sustainable scaling strategies for network infrastructure such as base stations (BSs) and reconfigurable intelligent surfaces (RISs). This paper establishes fundamental scaling laws for the Integrated Relative Energy Efficiency (IREE) metric under joint multi-BS and multi-RIS deployment in traffic-mismatched scenarios. Specifically, we propose an Alternating Directional Dual-Radial Basis Function (ADD-RBF) framework that models the channels of BSs and RISs as two type of spatially decoupled RBF neurons to maximize IREE through alternative optimization, with proven universal approximation capability and convergence guarantees. Theoretical analysis reveals a scaling dichotomy: BS proliferation drives logarithmic capacity growth 𝒪(log N^BS) but only polynomial mismatch reduction 𝒪(1/√(N^BS)), whereas RIS deployment achieves exponential mismatch mitigation 𝒪(δ_err^-(N^R+1)) despite its sub-logarithmic capacity gains. Simulation results validate that RISs excel in capturing spatial traffic correlations and alleviating hotspots, making them particularly effective when mismatch dominates, while BSs are preferable under capacity shortages. These findings offer practical guidelines for green 6G network design.

Leveraging the strong atom-light interaction, Rydberg atomic receivers (RAREs) can measure radio waves with extreme sensitivity. Existing research primarily focuses on improving the signal detection capability of RAREs, while traditional signal processing methods at the transmitter side have remained unchanged, which leaves a large gap from the maximum channel capacity. To address this issue, we exploit the transmitter precoding in atomic multiple-input-multiple-output systems to achieve the channel capacity. To begin with, a strong-reference approximation is proposed to linearize the nonlinear magnitude-detection model of atomic receivers, allowing us to express the channel capacity analytically. Then, a new digital precoding technique, termed In-phase-and-Quadrature (IQ) aware precoding is presented, which features independent processing of I/Q data streams using four real-valued matrices. The design is shown to be capacity-achieving for the atomic MIMO system. For the case of large-scale MIMO, we extend the proposed design into the popular hybrid precoding architecture, which cascades a classical high-dimensional analog precoder with a low-dimensional version of the proposed IQ-aware digital precoder. By alternatively optimizing the digital and analog parts, the hybrid design is able to approach the performance of the optimal IQ-aware fully digital precoding. Simulation results validate the superiority of proposed IQ-aware precoding methods over existing techniques in atomic MIMO communication 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 estimation is necessary but challenging due to the large antenna numbers. To overcome this obstacle, this paper reveals that a well-designed observation matrix, that exploits the high spatial correlation of DAS channels, is crucial for realizing near-optimal channel estimation. To materialize this vision, we propose to design the observation matrix by maximizing the mutual information between received pilots and channels. An ice-filling algorithm is proposed to solve the formulated problem. Its key idea is to properly assign the observation vectors with the eigenvectors of the channel covariance matrix in a greedy manner. Theoretical analysis reveals that the proposed algorithm is equivalently a quantized version of the water-filling principle, which guarantees its near-optimal channel estimation performance. Finally, numerical results confirm that our proposed designs outperform existing channel estimation methods significantly.

Densifying multiple-input multiple-output (MIMO) has attracted much attention in recent years. The strong correlations among densifying antennas provide sufficient prior knowledge about channel state information (CSI), which inspires the careful design of observation matrices (e.g., transmit precoders and receive combiners) to boost channel estimation performance. To achieve this, this work proposes to jointly design the combiners and precoders by maximizing the mutual information between the received pilots and densifying MIMO channels. Particularly, a two-dimensional ice-filling (2DIF) algorithm is proposed, which is motivated by the fact that the eigenspace of MIMO channel covariance can be decoupled into two sub-eigenspaces. By properly setting the precoder and the combiner as the eigenvectors from these two sub-eigenspaces, the 2DIF promises to generate nearoptimal observation matrices for channel estimation. Simulation results demonstrate that, the proposed 2DIF method outperforms the state-of-the-art schemes in channel estimation accuracy.

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.

Rydberg Atomic REceivers (RAREs) have shown compelling advantages in precise measurement of radio-frequency signals, empowering quantum wireless sensing. Existing RARE-based sensing systems primarily rely on the heterodyne-sensing technique, which introduces an extra reference source to serve as the atomic mixer. However, this approach entails a bulky transceiver architecture, requiring additional reference sources and transmitter-receiver signal decoupling. To address this problem, we propose a novel concept called selfheterodyne sensing. It utilizes the self-interference generated by the transmitted sensing signal as the reference signal, thus greatly simplifying the transceiver architecture. We derive the transmission model of self-heterodyne sensing and reveal that a self-heterodyne RARE functions as an atomic autocorrelator, where the received signal represents the autocorrelation of the transmitted signal at different delays. This characteristic translates the range of a sensing target into the frequency of the received signal. Inspired by this finding, a two-stage algorithm is devised to estimate the target range via frequency estimation and Newton refinement. Numerical results validate the superiority of the proposed quantum self-heterodyne sensing method.

By deploying a large number of antennas with subhalf- 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 designing the observation matrix to exploit the high spatial correlation of DAS channels is crucial for realizing near-optimal Bayesian channel estimation. Specifically, we prove that the observation matrix design for channel estimation is equivalent to a time-domain duality of point-to-point multipleinput multiple-output precoding, except for the change in the total power constraint on the precoding matrix to the pilot-wise discrete power constraint on the observation matrix. Inspired by Bayesian regression, 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 interpreted as a “quantized” water-filling algorithm, wherein the latter’s continuous power-allocation process is converted into the former’s discrete pilot-assignment process. To support the near-optimality of the proposed designs, we provide comprehensive analyses on the achievable mean square errors and their asymptotic expressions. Finally, numerical results confirm that our proposed designs achieve the near-optimal channel estimation performance and outperform existing approaches significantly.

The advancement of Rydberg atoms in quantum information technology is driving a paradigm shift from classical radio-frequency (RF) receivers to Rydberg atomic receivers. Capitalizing on the extreme sensitivity of Rydberg atoms to external electromagnetic fields, Rydberg atomic receivers are capable of realizing more precise radio-wave measurements than RF receivers to support high-performance wireless communication and sensing. Although the atomic receiver is developing rapidly in quantum-physics domain, its integration with wireless communications is at a nascent stage. In particular, systematic methods to enhance communication performance through this integration are yet to be discovered. Motivated by this observation, we propose in this paper to incorporate Rydberg atomic receivers into multiple-input-multiple-output (MIMO) communication, a prominent 5G technology, as the first attempt on implementing atomic MIMO receivers. To begin with, we provide a comprehensive introduction on the principles of Rydberg atomic receivers and build on them to design the atomic MIMO receivers. Our findings reveal that signal detection of atomic MIMO receivers corresponds to a non-linear biased phase retrieval (PR) problem, as opposed to the linear Gaussian model adopted in classical MIMO systems. Then, to recover signals from this non-linear model, we modify the Gerchberg-Saxton (GS) algorithm, a typical PR solver, into a biased GS algorithm to solve the biased PR problem. Moreover, we propose a novel Expectation-Maximization GS (EM-GS) algorithm to cope with the unique Rician distribution of the biased PR model. Our EM-GS algorithm introduces a high-pass filter constructed by the ratio of Bessel functions into the iteration procedure of GS, thereby improving the detection accuracy without sacrificing the computational efficiency. Finally, the effectiveness of the devised algorithms and the feasibility of atomic MIMO receivers are demonstrated by theoretical analysis and numerical simulation.

One mission of sixth-generation (6G) networks is to deploy large-scale artificial intelligence (AI) models at the network edge to enable intelligent services for edge devices. The resultant platform, known as edge inference, will support a wide range of Internet-of-Things applications, such as autonomous driving, industrial automation, and augmented reality. Given the mission-critical and time-sensitive nature of these tasks, existing studies, which primarily focus on channel outage probability, may fail to ensure E2E inference accuracy and latency. To address this limitation, we propose a theoretical framework that introduces the inference outage (InfOut) probability, quantifying the likelihood that E2E inference accuracy falls below a target threshold. Under latency constraints, this framework reveals a fundamental tradeoff between communication overhead and inference reliability. To optimize this tradeoff, we derive tractable surrogate functions for InfOut probability based on a Gaussian approximation of the receive discriminant gain. Experiments demonstrate the superiority of the proposed design over conventional communication-centric approaches.

Rydberg Atomic REceiver (RARE) is driving a paradigm shift in electromagnetic (EM) wave measurement by harnessing the electron transition phenomenon of Rydberg atoms. Operating at the quantum scale, such receivers have the potential to breakthrough the performance limit of classic receivers, sparking a revolution in physical-layer wireless communications. The objective of this paper is to offer insights into RARE-empowered communications. We first provide a comprehensive introduction to the fundamental principles of RAREs. Then, a thorough comparison between RAREs and classic receivers is conducted in terms of the antenna size, sensitivity, and bandwidth. Subsequently, we overview the recent progresses in RARE-aided wireless communications, covering the frequency-division multiplexing, multiple-input-multiple-output, wireless sensing, and quantum many-body techniques. Moreover, the unique application of RARE in multiband sensing and communication is introduced. Finally, we conclude by providing promising research directions.