One of the key missions of sixth-generation (6G) mobile networks is to deploy large-scale artificial intelligence (AI) models at the network edge to provide remote-inference 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, it is essential to design edge inference systems that are both reliable and capable of meeting stringent end-to-end (E2E) latency constraints. Existing studies, which primarily focus on communication reliability as characterized by channel outage probability, may fail to guarantee E2E performance, specifically in terms of E2E inference accuracy and latency. To address this limitation, we propose a theoretical framework that introduces and mathematically characterizes the inference outage (InfOut) probability, which quantifies the likelihood that the E2E inference accuracy falls below a target threshold. Under an E2E latency constraint, this framework establishes a fundamental tradeoff between communication overhead (i.e., uploading more sensor observations) and inference reliability as quantified by the InfOut probability. To find a tractable way to optimize this tradeoff, we derive accurate surrogate functions for InfOut probability by applying a Gaussian approximation to the distribution of the received discriminant gain. Experimental results demonstrate the superiority of the proposed design over conventional communication-centric approaches in terms of E2E inference reliability.

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 multi-band 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 multi-band RARE simultaneously serves as amulti-band atomic mixerfor down-converting multi-band signals and amulti-band atomic amplifierthat 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 aglobal gainterm and aRabi attentionterm. 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.

Semantic communication (SemCom) has emerged as a promising paradigm for achieving unprecedented communication efficiency in sixth-generation (6G) networks by leveraging artificial intelligence (AI) to extract and transmit the underlying meanings of source data. However, deploying SemCom over digital systems presents new challenges, particularly in ensuring robustness against transmission errors that may distort semantically critical content. To address this issue, this paper proposes a novel framework, termed generative feature imputing, which comprises three key techniques. First, we introduce a spatial-error-concentration packetization strategy that spatially concentrates feature distortions by encoding feature elements based on their channel mappings—a property crucial for both the effectiveness and reduced complexity of the subsequent techniques. Second, building on this strategy, we propose a generative feature imputing method that utilizes a diffusion model to efficiently reconstruct missing features caused by packet losses. Finally, we develop a semantic-aware power allocation scheme that enables unequal error protection by allocating transmission power according to the semantic importance of each packet. Experimental results demonstrate that the proposed framework outperforms conventional approaches, such as Deep Joint Source-Channel Coding (DJSCC) and JPEG2000, under block fading conditions, achieving higher semantic accuracy and lower Learned Perceptual Image Patch Similarity (LPIPS) scores.

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.

Deploying artificial intelligence (AI) algorithms at the network edge is essential for enabling next-generation network applications. In edge inference systems, features are extracted from distributed sensors and transmitted to an edge server for remote inference. However, traditional communication systems are primarily designed for reliable bit-level transmission and do not account for the unique characteristics of AI-based inference. A key property of AI inference is robustness: the ability to tolerate distortions in input features without significantly degrading performance. Leveraging this property, we propose a robustness-aware framework for energy-efficient edge inference that reduces energy consumption during feature transmission. By allowing nonzero bit error rates (BERs) in the transmitted features, our approach exploits the inherent robustness of AI models to reduce energy consumption while preserving inference accuracy. We begin by quantifying the robustness of inference using the classification margin and analyzing the relationship between classification accuracy and the average BER across distributed sensors. Based on this analysis, we formulate an optimization problem that seeks to minimize the total energy consumption of the sensors while satisfying classification accuracy requirements under radio resource constraints. To solve this problem, we decompose it into subproblems involving sensor selection, power control, and bandwidth allocation. These are efficiently addressed using a low-complexity alternating iterative algorithm. Simulation results demonstrate that the proposed robustness-aware inference framework can effectively tolerate bit errors during feature transmission, achieving significant energy reductions while maintaining target classification accuracy. Our design consistently outperforms benchmark schemes.

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.

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.

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.

The advancement of Rydberg atoms in quantum information technology is driving a paradigm shift from classicalradio-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 intomultiple-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 biasedphase 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.

Thesixth-generation(6G) mobile networks will feature the widespread deployment ofartificial intelligence(AI) algorithms at the network edge, which provides a platform for supporting robotic edge intelligence systems. In such a system, a large-scaleknowledge graph(KG) is operated at an edge server as a “remote brain” to guide remote robots on environmental exploration or task execution. In this paper, we present a new air-interface framework targeting the said systems, called knowledge-based roboticsemantic communications(SemCom), which consists of a protocol and relevant transmission techniques. First, the proposed robotic SemCom protocol defines a sequence of system operations for executing a given robotic task. They include identification of all task-relevantknowledge paths(KPs) on the KG, semantic matching between KG and object classifier, and uploading of robot’s observations for objects recognition and feasible KP identification. Next, to supportultra-low-latency (observation) feature transmission(ULL-FT), we propose a novel transmission approach that exploits classifier’s robustness, which is measured byclassification margin, to compensate for a highbit error probability(BEP) resulting from ultra-low-latency transmission (e.g., short packet and/or no coding). By utilizing the tractableGaussian mixture(GM) model, we mathematically derive the relation between BEP and classification margin under constraints on classification accuracy and transmission latency. The result sheds light on system requirements to support ULL-FT. Furthermore, for the case where the classification margin is insufficient for coping with channel distortion, we enhance the ULL-FT approach by studying retransmission and multi-view classification for enlarging the margin and further quantifying corresponding requirements. Finally, experiments using deep neural networks as classifier models and real datasets are conducted to demonstrate the effectiveness of ULL-FT in communication latency reduction while providing a guarantee on accurate feasible KP identification.

The advancement of Rydberg atoms is driving a paradigm shift from classical receivers to atomic receivers. Capitalizing on the extreme sensitivity of Rydberg atoms to external disturbance, atomic receivers can measure radio waves more precisely than classical receivers to support high-performance wireless communication. Although the atomic receiver is developing rapidly in the field of quantum physics, its integration with wireless communications is at a nascent stage. Particularly, systematic methods to enhance communication performance through this integration are largely uncharted. Motivated by this observation, we propose to incorporate atomic receivers into multiple-input multiple-output (MIMO) communications to implement atomic-MIMO receivers. We establish the framework of atomic-MIMO receivers by exploiting the principle of quantum sensing. Our model reveals that the signal detection of atomic-MIMO systems is intrinsically a nonlinear phase-retrieval problem, as opposed to the linear model in classical MIMO systems. To perform atomic-MIMO signal detection, we propose an Expectation-Maximization-Gerchberg-Saxton (EM-GS) algorithm based on the maximum likelihood (ML) criteria. Its novelty lies in treating the unobserved phase information as a latent variable and thereby decoupling the intricate ML problem into a sequence of tractable linear regression problems with analytical solutions. Experimental results validate the effectiveness of detecting atomic-MIMO signals using the EM-GS algorithm.

The sixth-generation (6G) mobile networks will feature the widespread deployment of artificial intelligence (AI) algorithms at the network edge, which provides a platform for edge intelligence. In this paper, we propose a new air-interface framework targeting the edge inference systems, called ultra-low-latency (observation) feature transmission (ULL-FT). It consists of a novel transmission approach that exploits classifier’s robustness, which is measured by classification margin, to compensate for a high bit error probability (BEP) resulting from ultra-low-latency transmission (e.g., short packet and/or no coding). By utilizing the tractable Gaussian mixture (GM) model, we mathematically derive the relation between BEP and classification margin under constraints on classification accuracy and transmission latency. The result sheds light on system requirements to support ULL-FT. Finally, experiments using deep neural networks (DNN) as classifier models and real datasets are conducted to demonstrate the effectiveness of ULL-FT in communication latency reduction while providing a guarantee on classification accuracy.

Estimating mutual correlations between random variables or data streams is essential for intelligent behavior and decision-making. As a fundamental quantity for measuring statistical relationships, mutual information has been extensively studied and utilized for its generality and equitability. However, existing methods often lack the efficiency needed for real-time applications, such as test-time optimization of a neural network, or the differentiability required for end-to-end learning, like histograms. We introduce a neural network called InfoNet, which directly outputs mutual information estimations of data streams by leveraging the attention mechanism and the computational efficiency of deep learning infrastructures. By maximizing a dual formulation of mutual information through large-scale simulated training, our approach circumvents time-consuming test-time optimization and offers generalization ability. We evaluate the effectiveness and generalization of our proposed mutual information estimation scheme on various families of distributions and applications. Our results demonstrate that InfoNet and its training process provide a graceful efficiency-accuracy trade-off and order-preserving properties. We will make the code and models available as a comprehensive toolbox to facilitate studies in different fields requiring real-time mutual information estimation.

To support emerging applications ranging from holographic communications to extended reality, next-generation mobile wireless communication systems require ultrafast and energy-efficient baseband processors. Traditional complementary metal-oxide-semiconductor (CMOS)-based baseband processors face two challenges in transistor scaling and the von Neumann bottleneck. To address these challenges, in-memory computing-based baseband processors using resistive random-access memory (RRAM) present an attractive solution. In this article, we propose and demonstrate RRAM-implemented in-memory baseband processing for the widely adopted multiple-input–multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) air interface. Its key feature is to execute the key operations, including discrete Fourier transform (DFT) and MIMO detection, using linear minimum mean square error (L-MMSE) and zero forcing (ZF), in one-step. In addition, RRAM-based channel estimation module is proposed and discussed. By prototyping and simulations, we demonstrate the feasibility of RRAM-based full-fledged communication system in hardware, and reveal it can outperform state-of-the-art baseband processors with a gain of$91.2\times $in latency and$671\times $in energy efficiency by large-scale simulations. Our results pave a potential pathway for RRAM-based in-memory computing to be implemented in the era of the sixth generation (6G) mobile communications.

For thesixth-generation(6G) mobile networks, in-situ model downloading has emerged as an important use case to enable real-time adaptiveartificial intelligence(AI) on edge devices. However, the simultaneous downloading of diverse and high-dimensional models to multiple devices over wireless links presents a significant communication bottleneck. To overcome the bottleneck, we propose the framework ofmodel broadcasting and assembling(MBA), which represents the first attempt on leveragingreusable knowledge, referring to shared parameters among tasks/models, to enable parameter broadcasting to reduce communication overhead or latency. The MBA framework comprises two key components. The first, the MBA protocol, defines the system operations including parameter selection from an AI library, power control for broadcasting, and model assembling at devices. The protocol features the use ofShapley valueas a metric for measuring parameters’ reusability. The second component is the joint design ofparameter-selection-and-power-control(PS-PC), which provides guarantees on devices’ model performance and aims to minimize the downloading latency. The corresponding optimization problem is simplified by decomposition into the sequential PS and PC sub-problems without compromising its optimality. The PS sub-problem is solved efficiently by designing two efficient algorithms. On one hand, the low-complexity algorithm of greedy parameter selection features the construction of task-oriented candidate model sets and a greedy selection metric for choosing the sets of model blocks for broadcasting, both of which are designed under the criterion of maximum reusable knowledge among tasks. On the other hand, the optimal tree-search algorithm gains its efficiency via the proposed construction of a compact binary tree pruned using model architecture constraints and an intelligent branch-and-bound search on the tree that fathoms nodes via solving a linear program that integer-relaxes the PS sub-problem. Last, given optimal PS, the optimal PC policy is derived in closed form by transforming the PC sub-problem into the conventional problem of energy-efficient transmission. Through extensive experiments conducted on real-world datasets, our results demonstrate the substantial reduction in downloading latency achieved by the proposed MBA design compared to traditional unicasting-based model downloading.

To tackle the issue of heterogeneous input raw data samples obtained by different devices and enhance the feature extraction capability of edge devices, we propose a vertically split neural network based edge-device collaborative artificial intelligence (AI) inference framework. The local results calculated by various light-size sub-networks at edge devices are transmitted and aggregated at the server for the downstream inference task. Nevertheless, the transmission of such high-dimensional local results involves severe communication overhead. To resolve this issue, the technique of over-the-air computation (AirComp) is adopted to enable low-latency aggregation. The same entry of all devices’ local results is transmitted over a same wireless resource block and aggregated via the waveform superposition property. Furthermore, to simultaneously support the aggregation of all dimensions of the local results, we consider a broadband channel and leverage orthogonal frequency division multiplexing (OFDM) to divide the system bandwidth into multiple subcarriers which are then assigned for different dimensions. Consequently, an extra degree of freedom is introduced to design the aggregation of all dimensions. We then propose a scheme of joint subcarrier allocation, power allocation, and receiver beamforming to minimize the aggregation distortion and enhance inference performance. Extensive experiments are conducted to verify the superiority of the proposed design over benchmarks.

The real-time transmission of videos with both high resolution and high frame rate is challenging, due to the limited storage space and significant communication overhead. To meet the real-time requirement, these issues are usually tackled by video quality reduction, which compromises the user experience. While previous methods, such as video compressed sensing, have attempted to address these issues, they often employ a fixed compression rate without considering the varying channel gain and do not adequately address the real-time transmission requirements. To mitigate these shortcomings, we propose an adaptive compressed sensing framework that optimizes the compression rate based on the channel state. This approach equivalently optimizes the video quality while ensuring real-time transmission by reducing communication overhead and thus latency. The feasibility and performance of our method are validated and discussed through extensive experiments on both classic and custom datasets.

We consider the scenario of inference at the wireless edge, in which devices are connected to an edge server and ask the server to carry out remote classification, that is, classify data samples available at edge devices. This requires the edge devices to upload high-dimensional features of samples over resource-constrained wireless channels, which creates a communication bottleneck. The conventional feature pruning solution would require the device to have access to the inference model, which is not available in the current split inference scenario. To address this issue, we propose the progressive feature transmission (ProgressFTX) protocol, which minimizes the overhead by progressively transmitting features until a target confidence level is reached. A control policy is proposed to accelerate inference, comprising two key operations: importance-aware feature selection at the server and transmission-termination control. For the former, it is shown that selecting the most important features, characterized by the largest discriminant gains of the corresponding feature dimensions, achieves a sub-optimal performance. For the latter, the proposed policy is shown to exhibit a threshold structure. Specifically, the transmission is stopped when the incremental uncertainty reduction by further feature transmission is outweighed by its communication cost. The indices of the selected features and transmission decision are fed back to the device in each slot. The control policy is first derived for the tractable case of linear classification, and then extended to the more complex case of classification using a convolutional neural network. Both Gaussian and fading channels are considered. Experimental results are obtained for both a statistical data model and a real dataset. It is shown that ProgressFTX can substantially reduce the communication latency compared to conventional feature pruning and random feature transmission strategies.

Federated edge learning(FEEL) is a widely adopted framework for training anartificial intelligence(AI) model distributively at edge devices to leverage their data while preserving their data privacy. The execution of a power-hungry learning task at energy-constrained devices is a key challenge confronting the implementation of FEEL. To tackle the challenge, we propose the solution of powering devices usingwireless power transfer(WPT). To derive guidelines on deploying the resultantwirelessly powered FEEL(WP-FEEL) system, this work aims at the derivation of the tradeoff between the model convergence and the settings of power sources in two scenarios: 1) the transmission power and density of power-beacons (dedicated charging stations) if they are deployed, or otherwise 2) the transmission power of a server (access-point). The development of the proposed analytical framework relates the accuracy of distributed stochastic-gradient estimation to the WPT settings, the randomness in both communication and WPT links, and devices’ computation capacities. Furthermore, the local-computation at devices (i.e., mini-batch size and processor clock frequency) is optimized to efficiently use the harvested energy for gradient estimation. The resultant learning-WPT tradeoffs reveal the simple scaling laws of the model-convergence rate with respect to the transferred energy as well as the devices’ computational energy efficiencies. The results provide useful guidelines on WPT provisioning to yield a guaranteer on learning performance. They are corroborated by experimental results using a real dataset.

By deploying machine-learning algorithms at the network edge, edge learning can leverage the enormous real-time data generated by billions of mobile devices to train AI models, which enable intelligent mobile applications. In this emerging research area, one key direction is to efficiently utilize radio resources for wireless data acquisition to minimize the latency of executing a learning task at an edge server. Along this direction, we consider the specific problem of retransmission decision in each communication round to ensure both reliability and quantity of those training data for accelerating model convergence. To solve the problem, a new retransmission protocol called data-importance aware automatic-repeat-request (importance ARQ) is proposed. Unlike the classic ARQ focusing merely on reliability, importance ARQ selectively retransmits a data sample based on its uncertainty which helps learning and can be measured using the model under training. Underpinning the proposed protocol is a derived elegant communication-learning relation between two corresponding metrics, i.e., signal-to-noise ratio (SNR) and data uncertainty. This relation facilitates the design of a simple threshold based policy for importance ARQ. The policy is first derived based on the classic classifier model of support vector machine (SVM), where the uncertainty of a data sample is measured by its distance to the decision boundary. The policy is then extended to the more complex model of convolutional neural networks (CNN) where data uncertainty is measured by entropy. Extensive experiments have been conducted for both the SVM and CNN using real datasets with balanced and imbalanced distributions. Experimental results demonstrate that importance ARQ effectively copes with channel fading and noise in wireless data acquisition to achieve faster model convergence than the conventional channel-aware ARQ. The gain is more significant when the dataset is imbalanced.

Edge machine learning involves the deployment of learning algorithms at the network edge to leverage massive distributed data and computation resources to trainartificial intelligence(AI) models. Among others, the framework offederated edge learning(FEEL) is popular for its data-privacy preservation. FEEL coordinates global model training at an edge server and local model training at devices that are connected by wireless links. This work contributes to the energy-efficient implementation of FEEL in wireless networks by designing jointcomputation-and-communication resource management($\mathrm {C}^{2}$RM). The design targets the state-of-the-art heterogeneous mobile architecture where parallel computing using both CPU and GPU, calledheterogeneous computing, can significantly improve both the performance and energy efficiency. To minimize the sum energy consumption of devices, we propose a novel$\mathrm {C}^{2}$RM framework featuring multi-dimensional control including bandwidth allocation, CPU-GPU workload partitioning and speed scaling at each device, and$\mathrm {C}^{2}$time division for each link. The key component of the framework is a set of equilibriums in energy rates with respect to different control variables that are proved to exist among devices or between processing units at each device. The results are applied to designing efficient algorithms for computing the optimal$\mathrm {C}^{2}$RM policies faster than the standard optimization tools. Based on the equilibriums, we further design energy-efficient schemes for device scheduling and greedy spectrum sharing that scavenges “spectrum holes” resulting from heterogeneous$\mathrm {C}^{2}$time divisions among devices. Using a real dataset, experiments are conducted to demonstrate the effectiveness of$\mathrm {C}^{2}$RM on improving the energy efficiency of a FEEL system.