Integrated sensing and communication (ISAC) is a key technology for future 6G networks. Most existing studies focus on monostatic and/or bistatic setups with limited coverage and capabilities. Networked ISAC systems with distributed base stations (BSs) can overcome these limitations. Moreover, movable antenna (MA) architectures offer improved ISAC performance over fixed-position antennas (FPAs) by enabling adaptable antenna movement. In this paper, we utilize the MA to promote communication capability with guaranteed sensing performance via jointly designing beamforming, power allocation, receiving filters and position configuration of transmit/receive MA towards maximizing the sum rate for both downlink (DL) and uplink (UL) users. The optimization problem is highly difficult due to the unique channel model derived from the position coefficient of the MA. To resolve this challenge, via leveraging the cutting-the-edge majorization-minimization (MM) method, we develop an efficient solution that optimizes all variables via convex optimization techniques. Extensive simulation results verify the effectiveness of our proposed algorithms and demonstrate the substantial performance promotion by deploying the MA framework in the networked ISAC system.

In this paper, we propose a Satellite-Terrestrial Integrated Network (STIN) assisted vehicular multi-tier distributed computing (VMDC) system leveraging hybrid terahertz (THz) and radio frequency (RF) communication technologies. Task offloading for satellite edge computing is enabled by THz communication using the orthogonal frequency division multiple access (OFDMA) technique. For terrestrial edge computing, we employ non-orthogonal multiple access (NOMA) and vehicle clustering to realize task offloading. We formulate a non-convex optimization problem aimed at maximizing computation efficiency by jointly optimizing bandwidth allocation, task allocation, subchannel-vehicle matching and power allocation. To address this non-convex optimization problem, we decompose the original problem into four sub-problems and solve them using an alternating iterative optimization approach. For the subproblem of task allocation, we solve it by linear programming. To solve the subproblem of sub-channel allocation, we exploit many-to-one matching theory to obtain the result. The subproblem of bandwidth allocation of OFDMA and the subproblem of power allocation of NOMA are solved by quadratic transformation method. Finally, the simulation results show that our proposed scheme significantly enhances the computation efficiency of the STIN-based VMDC system compared with the benchmark schemes.

With the advancement of intelligent Internet of Things (IoT), the demand for efficient processing of massive computational tasks is constantly increasing. Thanks to the flexibility and scalability, unmanned aerial vehicle (UAV)-assisted multitier distributed computing can achieve collaborative computing of tasks to meet this demand. Therefore, we propose a multi-tier distributed task offloading model assisted by UAVs. Firstly, we formulate a task offloading optimization problem for minimizing system delay and energy consumption in multi-user and multi-UAV scenarios. Secondly, we propose a multi-agent reinforcement learning strategy based on value function decomposition multi-agent deep Q-networks (MADQN) for problem solving. During the centralized training stage, each UAV shares the global reward information and learns the collaboration strategy. In the distributed execution stage, based on local observations, each UAV autonomously adjusts the position, pitch angle, offloading decision and resource allocation, thereby maximizing the system performance. Finally, the simulation results verified the effectiveness of the MADQN algorithm.

In this paper, we propose a Satellite-Terrestrial Integrated Network (STIN) assisted vehicular task offloading leveraging hybrid terahertz (THz) and radio frequency (RF) communication technologies. Task offloading for satellite edge computing is enabled by THz communication using the orthogonal frequency division multiple access (OFDMA) technique. For terrestrial edge computing, we employ non-orthogonal multiple access (NOMA) and vehicle clustering to realize task offloading. We formulate a non-convex optimization problem aimed at maximizing computation efficiency by jointly optimizing bandwidth allocation, task allocation and power allocation. To address this non-convex optimization problem, we decompose the original problem into three sub-problems and solve them using an alternating iterative optimization approach. For the subproblem of task allocation, we solve it by linear programming. The subproblem of bandwidth allocation of OFDMA and the sub-problem of power allocation of NOMA are solved by quadratic transformation method. Finally, the simulation results show that our proposed scheme significantly enhances the computation efficiency of the STIN-based vehicular task offloading compared with the benchmark schemes.

Free space optical (FSO) transmission has emerged as a key candidate technology for 6G to expand new spectrum and improve network capacity due to its advantages of large bandwidth, low-electromagnetic interference, and high-energy efficiency. Resonant beam operating in the infrared band utilizes spatially separated laser cavities to enable safe and mobile high-power energy and high-rate information transmission but is limited by Line-of-Sight (LoS) channel. In this article, we propose a reconfigurable intelligent surface (RIS) assisted resonant beam simultaneous wireless information and power transfer (SWIPT) system and establish an optical field propagation model to analyze the channel state information (CSI), in which LoS obstruction can be detected sensitively and non line-of-sight (NLoS) transmission can be realized by changing the phased of resonant beam in RIS. Numerical results demonstrate that, apart from the transmission distance, the NLoS performance depends on both the horizontal and vertical positions of RIS. The maximum NLoS energy efficiency can achieve 55% within a transfer distance of 10 m, a translation distance of ±4 mm, and rotation angle of ±50°.

In this article, we propose a novel uplink communication system enabled by a transmissive reconfigurable intelligent surface (RIS) transceiver, where orthogonal frequency division multiple access (OFDMA) is applied to multiple users. Specifically, we explore a novel receiver architecture that includes a transmissive RIS and a single horn antenna for reception. Additionally, a channel model based on both planar and spherical waves is developed, accounting for far-field and near-field effects. To achieve the maximum system sum-rate of uplink communications while adhering to Quality-of-Service (QoS) constraints, we propose a joint optimization problem that optimizes power allocation, subcarrier allocation, and transmissive RIS coefficient. However, this problem is nonconvex in view of the strong interdependence among the optimization variables, posing significant challenges for direct solution. Thus, the alternating optimization (AO) algorithm architecture is employed, which decouples optimization variables and divide the problem into two subproblems. The first subproblem focuses on jointly optimizing power allocation and subcarrier allocation, and it is addressed by utilizing the Lagrangian dual decomposition method. Meanwhile, concerning the design of the transmissive RIS coefficient, the second subproblem is tackled by means of the successive convex approximation (SCA) approach. Subsequently, these two subproblems are solved in an alternating manner until the convergence criterion is met. Finally, the numerical results indicate that the proposed algorithm exhibits excellent convergence performance and effectively enhances the system sum-rate compared to other benchmark algorithms.

In this paper, we investigate a state-of-the-art reconfigurable intelligent surface (RIS)-assisted spatial scattering modulation (SSM) scheme for millimeter-wave (mmWave) systems, where a more practical scenario that the RIS is near the transmitter while the receiver is far from RIS is considered. To this end, the line-of-sight (LoS) and non-LoS links are utilized in the transmitter-RIS and RIS-receiver channels, respectively. By employing the maximum likelihood detector at the receiver, the conditional pairwise error probability (CPEP) expression for the RIS-SSM scheme is derived under the two scenarios that the received beam demodulation is correct or not. Furthermore, the union upper bound of average bit error probability (ABEP) is obtained based on the CPEP expression. Finally, the derivation results are exhaustively validated by the Monte Carlo simulations.

With the development of next-generation wireless networks, the Internet of Things (IoT) is evolving towards the intelligent IoT (iIoT), where intelligent applications usually have stringent delay and jitter requirements. In order to provide low-latency services to heterogeneous users in the emerging iIoT, multi-tier computing was proposed by effectively combining edge computing and fog computing. More specifically, multi-tier computing systems compensate for cloud computing through task offloading and dispersing computing tasks to multi-tier nodes along the continuum from the cloud to things. In this paper, we investigate key techniques and directions for wireless communications and resource allocation approaches to enable task offloading in multi-tier computing systems. A multi-tier computing model, with its main functionality and optimization methods, is presented in detail. We hope that this paper will serve as a valuable reference and guide to the theoretical, algorithmic, and systematic opportunities of multi-tier computing towards next-generation wireless networks.

Multi-tier computing can enhance the task computation by multi-tier computing nodes. In this paper, we propose a cell-free massive multiple-input multiple-output (MIMO) aided computing system by deploying multi-tier computing nodes to improve the computation performance. At first, we investigate the computational latency and the total energy consumption for task computation, regarded as total cost. Then, we formulate a total cost minimization problem to design the bandwidth allocation and task allocation, while considering realistic heterogenous delay requirements of the computational tasks. Due to the binary task allocation variable, the formulated optimization problem is non-convex. Therefore, we solve the bandwidth allocation and task allocation problem by decoupling the original optimization problem into bandwidth allocation and task allocation subproblems. As the bandwidth allocation problem is a convex optimization problem, we first determine the bandwidth allocation for given task allocation strategy, followed by conceiving the traditional convex optimization strategy to obtain the bandwidth allocation solution. Based on the asymptotic property of received signal-to-interference-plus-noise ratio (SINR) under the cell-free massive MIMO setting and bandwidth allocation solution, we formulate a dual problem to solve the task allocation subproblem by relaxing the binary constraint with Lagrange partial relaxation for heterogenous task delay requirements. At last, simulation results are provided to demonstrate that our proposed task offloading scheme performs better than the benchmark schemes, where the minimum-cost optimal offloading strategy for heterogeneous delay requirements of the computational tasks may be controlled by the asymptotic property of the received SINR in our proposed cell-free massive MIMO-aided multi-tier computing systems.

Multi-tier computing effectively enables flexible computation and communication resource sharing by offloading computation-intensive tasks to nearby servers along the cloud-to-thing continuum. In essence, multi-tier computing networks can distribute computing, storage, and communication functions anywhere between the cloud and the endpoint to take full advantage of the resources available along this continuum, thus extending the traditional cloud computing architecture to the edge of the network. With multi-tier computing, some application component processing, such as delay-sensitive components, can take place at the edge of the network, while other components, such as time-tolerant and computation-intensive components, can be performed in the cloud. To best meet user requirements, centralized cloud computing with extensive resources, secure environments, and powerful algorithms is still needed, but also must be complemented by distributed fog and edge computing with shared resources, accessible environments, and simple algorithms for real-time decision-making. Given heterogeneous computing resources and collaborative service architectures, future multi-tier computing networks will be capable of supporting a full range of computing and networking services for different environments and applications. This Special Issue aims to provide a forum for the latest advances in multi-tier computing for next-generation wireless network research, innovations, and applications. Multi-tier computing enables low-latency processing by allowing data to be processed at the network edge close to end devices. It also facilitates the distribution of fog/edge nodes to collect data from end devices. Therefore, multi-tier computing effectively complements the cloud computing architecture.

Multi-tier computing effectively enables flexible computation and communication resource sharing by offloading computation-intensive tasks to nearby servers along the cloud-to-thing continuum. In essence, multi-tier computing networks can distribute computing, storage, and communication functions anywhere between the cloud and the endpoint to take full advantage of the resources available along this continuum, thus extending the traditional cloud computing architecture to the edge of the network. With multi-tier computing, some application component processing, such as delay-sensitive components, can take place at the edge of the network, while other components, such as time-tolerant and computation-intensive components, can be performed in the cloud. To best meet user requirements, centralized cloud computing with extensive resources, secure environments, and powerful algorithms is still needed, but also must be complemented by distributed fog and edge computing with shared resources, accessible environments, and simple algorithms for real-time decision-making. Given heterogeneous computing resources and collaborative service architectures, future multi-tier computing networks will be capable of supporting a full range of computing and networking services for different environments and applications. Multi-tier computing enables low-latency processing by allowing data to be processed at the network edge close to end devices. It also facilitates the distribution of fog/edge nodes to collect data from end devices. Therefore, multi-tier computing effectively complements the cloud computing architecture.

This paper investigates the reconfigurable intelligent surface (RIS) assisted spatial scattering modulation (SSM) scheme for millimeter-wave (mmWave) multiple-input multiple-output (MIMO) systems, in which line-of-sight (LoS) and non-line-of-sight (NLoS) paths are respectively considered in the transmitter-RIS and RIS-receiver channels. Based on the maximum likelihood detector, the expression for the conditional pairwise error probability (CPEP) of the RIS-SSM scheme is derived for both cases of correct demodulation of the received beam or not. Furthermore, we derive the closed-form expressions of the unconditional pairwise error probability (UPEP) by employing two different methods: the probability density function and the moment-generating function expressions with a descending order of scatterer gains. To provide more useful insights, we derive the asymptotic UPEP and the diversity gain of the RIS-SSM scheme in the high SNR region. Depending on UPEP and the corresponding Euclidean distance, we further give the union upper bound of the average bit error probability (ABEP). To acquire the effective capacity of the proposed system, a new framework for ergodic capacity analysis is also provided. Finally, all derivation results are validated via extensive Monte Carlo simulations and reveal that the proposed RIS-SSM scheme outperforms the benchmarks in terms of reliability.

This work presents non-orthogonal multiple access (NOMA) enabled energy-efficient alternating optimization framework for backscatter aided wireless powered uplink sensors communications for beyond 5G intelligent transportation system (ITS). Specifically, the transmit power of carrier emitter (CE) and reflection coefficients of backscatter aided roadside sensors are optimized with channel uncertainties for the maximization of the energy efficiency (EE) of the network. The formulated problem is tackled by the proposed two-stage alternating optimization algorithm named AOBWS (alternating optimization for backscatter aided wireless powered sensors). In the first stage, AOBWS employs an iterative algorithm to obtain optimal CE transmit power through simplified closed-form computed through Cardano’s formulae. In the second stage, AOBWS uses a non-iterative algorithm that provides a closed-form expression for the computation of optimal reflection coefficient for roadside sensors under their quality of service (QoS) and a circuit power constraint. The global optimal exhaustive search (ES) algorithm is used as a benchmark. Simulation results demonstrate that the AOBWS algorithm can achieve near-optimal performance with very low complexity, which makes it suitable for practical implementations.

Driven by unmanned aerial vehicle (UAV)’s advantages of flexible observation and enhanced communication capability, it is expected to revolutionize the existing integrated sensing and communication (ISAC) system and promise a more flexible joint design. Nevertheless, the existing works on ISAC mainly focus on exploring the performance of both functionalities simultaneously during the entire considered period, which may ignore the practical asymmetric sensing and communication requirements. In particular, always forcing sensing along with communication may make it is harder to balance between these two functionalities due to shared spectrum resources and limited transmit power. To address this issue, we propose a new integrated periodic sensing and communication (IPSAC) mechanism for the UAV-enabled ISAC system to provide a more flexible trade-off between two integrated functionalities. Specifically, the system achievable rate is maximized via jointly optimizing UAV trajectory, user association, target sensing selection, and transmit beamforming, while meeting the sensing frequency and beam pattern gain requirement for the given targets. Despite that this problem is highly non-convex and involves closely coupled integer variables, we derive the closed-form optimal beamforming vector to dramatically reduce the complexity of beamforming design, and present a tight lower bound of the achievable rate to facilitate UAV trajectory design. Based on the above results, we propose a two-layer penalty-based algorithm to efficiently solve the considered problem. To draw more important insights, the optimal achievable rate and the optimal UAV location are analyzed under a special case of infinity number of antennas. Furthermore, we prove the structural symmetry between the optimal solutions in different ISAC frames without location constraints in our considered UAV-enabled ISAC system. Based on this, we propose an efficient algorithm for solving the problem with location constraints. Numerical results validate the effectiveness of our proposed designs and also unveil a more flexible trade-off in ISAC systems over benchmark schemes.

A fundamental issue in multiaccess edge computing (MEC) is efficiently offloading multiple tasks to multiple helper nodes (MTMH), i.e., MEC servers. However, most of the existing decentralized schemes do not consider interuser interference or merely adopt time division multiple access (TDMA) as the multiple access scheme for MTMH in the heterogeneous scenario, leading to a large latency. To address these issues, we propose DOT, a novel Decentralized Offloading of Tasks scheme in orthogonal frequency division multiple access (OFDMA)-based heterogeneous MEC, to minimize the sum cost in terms of energy consumption and delay. Specifically, we first formulate DOT as an optimization problem considering the interuser interference and dynamics in communication and computation resource allocation. Then, considering the huge dimension of potential offloading decisions and conflicting objectives of different users, the total cost of each user is minimized in a distributed manner by modeling the offloading problem as a potential game. The formulated potential game is proved to be an ordinal potential game and thus admits a Nash equilibrium (NE). Further, we develop an offloading algorithm to achieve the NE by exploiting the finite improvement property. Finally, simulation results demonstrate that DOT can achieve a lower cost compared with other baselines.

In this paper, a novel intelligent reflecting surface (IRS)-assisted wireless powered communication network (WPCN) architecture is proposed for power-constrained Internet-of-Things (IoT) smart devices, where IRS is exploited to improve the performance of WPCN under imperfect channel state information (CSI). We formulate a hybrid access point (HAP) transmit energy minimization problem by jointly optimizing time allocation, HAP energy beamforming, receiving beamforming, user transmit power allocation, IRS energy reflection coefficient and information reflection coefficient under the imperfect CSI and non-linear energy harvesting model. On account of the high coupling of optimization variables, the formulated problem is a non-convex optimization problem that is difficult to solve directly. To address the above-mentioned challenging problem, alternating optimization (AO) technique is applied to decouple the optimization variables to solve the problem. Specifically, through AO, time allocation, HAP energy beamforming, receiving beamforming, user transmit power allocation, IRS energy reflection coefficient and information reflection coefficient are divided into three sub-problems to be solved alternately. The difference-of-convex (DC) programming is used to solve the non-convex rank-one constraint in solving IRS energy reflection coefficient and information reflection coefficient. Numerical simulations verify the superiority of the proposed optimization algorithm in decreasing HAP transmit energy compared with other benchmark schemes.

In this paper, a massive multiple-input multiple-output (MIMO) relay assisted multi-tier computing (MC) system is employed to enhance the task computation. We investigate the joint design of the task scheduling, service caching and power allocation to minimize the total task scheduling delay. To this end, we formulate a robust non-convex optimization problem taking into account the impact of imperfect channel state information (CSI). In particular, multiple task nodes (TNs) offload their computational tasks either to computing and caching nodes (CCN) constituted by nearby massive MIMO-aided relay nodes (MRN) or alternatively to the cloud constituted by nearby fog access nodes (FAN). To address the non-convexity of the optimization problem, an efficient alternating optimization algorithm is developed. First, we solve the non-convex power allocation optimization problem by transforming it into a linear optimization problem for a given task offloading and service caching result. Then, we use the classic Lagrange partial relaxation for relaxing the binary task offloading as well as caching constraints and formulate the dual problem to obtain the task allocation and software caching results. Given both the power allocation, as well as the task offloading and caching result, we propose an iterative optimization algorithm for finding the jointly optimized results. The simulation results demonstrate that the proposed scheme outperforms the benchmark schemes, where the power allocation may be controlled by the asymptotic form of the effective signal-to-interference-plus-noise ratio (SINR).

This paper proposes a novel network framework of intelligent reflecting surface (IRS)-assisted simultaneous wireless information and power transfer (SWIPT) non-orthogonal multiple access (NOMA) networks, where IRS is used to enhance the NOMA performance and the wireless power transfer (WPT) efficiency of SWIPT. We formulate a problem of minimizing base station (BS) transmit power by jointly optimizing successive interference cancellation (SIC) decoding order, BS transmit beamforming vector, power splitting (PS) ratio and IRS phase shift while taking into account the quality-of-service (QoS) requirement and energy harvested threshold of each user. The formulated problem is non-convex optimization problem, which is difficult to solve it directly. Hence, a two-stage algorithm is proposed to solve the above-mentioned problem by applying semidefinite relaxation (SDR), Gaussian randomization and successive convex approximation (SCA). Specifically, after determining SIC decoding order by designing IRS phase shift in the first stage, we alternately optimize BS transmit beamforming vector, PS ratio, and IRS phase shift to minimize the BS transmit power. Numerical results validate the effectiveness of our proposed optimization algorithm in reducing BS transmit power compared to other baseline algorithms. Meanwhile, compared with non-IRS-assisted network, the IRS-assisted SWIPT NOMA network can decrease BS transmit power by 51.13%.

This paper investigates the task offloading problem in a hybrid intelligent reflecting surface (IRS) and massive multiple-input multiple-output (MIMO) relay assisted fog computing system, where multiple task nodes (TNs) offload their computational tasks to computing nodes (CNs) nearby massive MIMO relay node (MRN) and fog access node (FAN) via the IRS for execution. By considering the practical imperfect channel state information (CSI) model, we formulate a joint task offloading, IRS phase shift optimization, and power allocation problem to minimize the total energy consumption. We solve the resultant non-convex optimization problem in three steps. First, we solve the IRS phase shift optimization problem with the sequential rank-one constraint relaxation (SROCR) algorithm and semidefinite relaxation (SDR) algorithm for a given power- and computational resource allocation. Then, we exploit a differential convex (DC) optimization framework to determine the power allocation decision that minimizes the total energy consumption. Given the IRS phase shifts, the computational resources, and the power allocation, we propose an alternating optimization algorithm for finding the jointly optimized results. The simulation results demonstrate the effectiveness of the proposed scheme as compared with other benchmark schemes, and the energy efficient offloading strategy for the proposed fog computing system can be chosen according to the asymptotic form of the effective signal-to-interference-plus-noise ratio (SINR).

This paper investigates the task offloading problem in a hybrid intelligent reflecting surface (IRS) and massive multiple-input multiple-output (MIMO) relay assisted fog computing system, where multiple task nodes (TNs) offload their computational tasks to computing nodes (CNs) nearby massive MIMO relay node (MRN) and fog access node (FAN) via the IRS for execution. By considering the practical imperfect channel state information (CSI) model, we formulate a joint task offloading, IRS phase shift optimization, and power allocation problem to minimize the total energy consumption. We solve the resultant non-convex optimization problem in three steps. First, we solve the IRS phase shift optimization problem with the semidefinite relaxation (SDR) algorithm. Then, we exploit a differential convex (DC) optimization framework to determine the power allocation decision. Given the IRS phase shifts, the computational resources, and the power allocation, we propose an alternating optimization algorithm for finding the jointly optimized results. The simulation results demonstrate the effectiveness of the proposed scheme as compared with other benchmark schemes.

The energy-efficient task offloading problem of a massive multiple-input multiple-output (MIMO)-aided fog computing system is solved, where multiple task nodes offload their computational tasks to be solved via a massive MIMO-aided fog access node to multiple processing nodes in the fog for execution. By considering realistic imperfect channel state information (CSI), we formulate a joint task offloading and power allocation problem for minimizing the total energy consumption, including both computation and communication power consumptions. We solve the resultant non-convex optimization problem in two steps. First, we solve the computational task allocation and computational resource allocation for a given power allocation. Then, we conceive a sequential optimization framework for determining the specific power allocation decision that minimizes the total energy consumption of the fog access node. Given the computational tasks, the computational resources, and the power allocation, we propose an iterative algorithm for the system optimization. The simulation results show that the proposed scheme significantly reduces the total energy consumption compared to the benchmark schemes.

Over-the-air computation (AirComp) is a promising technology that is capable of achieving fast data aggregation in Internet of Things (IoT) networks. The mean-squared error (MSE) performance of AirComp is bottlenecked by the unfavorable channel conditions. This limitation can be mitigated by deploying a reconfigurable intelligent surface (RIS), which reconfigures the propagation environment to facilitate the receiving power equalization. The achievable performance of RIS relies on the availability of accurate channel state information (CSI), which however is generally difficult to be obtained. In this paper, we consider an RIS-aided AirComp IoT network, where an access point (AP) aggregates sensing data from distributed devices. Without assuming any prior knowledge on the underlying channel distribution, we formulate a stochastic optimization problem to maximize the probability that the MSE is below a certain threshold. The formulated problem turns out to be non-convex and highly intractable. To this end, we propose a data-driven approach to jointly optimize the receive beamforming vector at the AP and the phase-shift vector at the RIS based on historical channel realizations. After smoothing the objective function by adopting the sigmoid function, we develop an alternating stochastic variance reduced gradient (SVRG) algorithm with a fast convergence rate to solve the problem. Simulation results demonstrate the effectiveness of the proposed algorithm and the importance of deploying an RIS in reducing the MSE outage probability.

Sparse code multiple access (SCMA) is one of the promising candidates for new radio access interface. The new generation communication system is expected to support massive user access with high capacity. However, there are numerous problems and barriers to achieve optimal performance, e.g., the multiuser interference and high power consumption. In this paper, we present optimization methods to enhance the spectral and energy efficiency for SCMA with individual rate requirements. The proposed method has shown a better network mapping matrix based on power allocation and codebook assignment. Moreover, the proposed method is compared with orthogonal frequency division multiple access (OFDMA) and code division multiple access (CDMA) in terms of spectral efficiency (SE) and energy efficiency (EE) respectively. Simulation results show that SCMA performs better than OFDMA and CDMA both in SE and EE.

Caching popular contents at heterogeneous devices, e.g., fog nodes (FNs) or fog access points (FAPs), constitutes a promising technique of reducing both the traffic and the energy consumption of the backhaul links. In this paper, we propose an energy-efficient caching and node association algorithm for cache-aided fog networks. First, we solve the problem of energy-efficient content caching and delivery in the FNs/FAPs. In both caching scenarios, we investigate the relationship between the caching probability of the file and the energy-efficient content delivery by formulating the associated energy efficiency (EE) optimization problem. Then, we derive a joint modulation mode allocation strategy and caching policy for each content caching node and conceive a joint node association and caching algorithm. Finally, we quantify both the overall EE and throughput for demonstrating that the proposed caching and transmission strategy achieves significant performance improvements.

Fog computing has been promoted to support delay-sensitive applications in future Internet of Things (IoT). For a general heterogeneous fog network consisting of many dispersive fog nodes (FNs), it may well happen that some of them have delay-sensitive tasks to process, i.e., task nodes (TNs), and some have spare resources to help the TNs to process tasks, i.e., helper nodes (HNs). It remains a fundamental challenge to effectively map multiple tasks or TNs into multiple HNs to minimize every task's service delay in a distributed manner, i.e., the multitask multihelper (MTMH) problem. The problem becomes more challenging as tasks are splittable, i.e., tasks can be divided into multiple subtasks and offloaded to multiple HNs to further reduce the service delay via the scheme similar to distributed computing, because it introduces the more complicated task division problem which results in a much larger and more complex solution space. To tackle this challenge, in this article, a generalized Nash equilibrium problem (GNEP), called parallel offloading of splittable tasks (POST), is formulated and studied thoroughly. The structural properties of the problem are characterized and thus the existence of generalized Nash equilibrium (GNE) is proven via the fixed-point theorem. Furthermore, the corresponding distributed task offloading algorithm is developed via the Gauss-Seidel-type method. The simulation results show that the proposed POST algorithm can offer much better performance in terms of the system average delay, individual delay, delay reduction ratio (DRR), and number of beneficial TNs, compared with the existing solution to the counterpart problem for nonsplittable tasks.

Fog computing (FC) has the potential to process computation-intensive tasks in Industrial Internet of Things (IIoT) systems. In parallel with the development of FC, non-orthogonal multiple access (NOMA) has been recognized as a promising technique to significantly improve the spectrum efficiency. In this paper, a NOMA-based FC framework for IIoT systems is considered, where multiple task nodes offload their tasks via NOMA to multiple nearby helper nodes for execution. We formulate a joint task scheduling and subcarrier allocation problem, with an objective to minimize the total cost in terms of the delay and energy consumption, while taking into account the practical communication and computation constraints. Note that the task scheduling includes task, computation resource, and power allocations. Since the task and subcarrier allocations involve binary variables, it is challenging to obtain an optimal solution for such a combinatorial problem. To this end, we solve the task scheduling and subcarrier allocation problem in an online learning fashion. During the online learning process, we propose an iterative algorithm to jointly optimize the subcarrier allocation and task scheduling in each time episode. Simulation results show that the proposed scheme can significantly reduce the sum cost compared to the baseline schemes.

Fog computing has been promoted to support delay-sensitive applications in future Internet of Things (IoT) and wireless networks. For a general heterogeneous fog network consisting of many dispersive Fog Nodes (FNs) with diverse resources and capabilities, some of them have delay-sensitive tasks to process, i.e., Task Nodes (TNs), while some have spare resources to help their neighboring TNs to process tasks, i.e., Helper Nodes (HNs). How to effectively map multiple tasks or TNs into multiple HNs to minimize every task's service delay in a distributed manner is a fundamental challenge, which is key to reap the full benefits of fog computing. The problem becomes more challenging when tasks can be divided into multiple subtasks to further reduce the service delay via distributed computing. To tackle this challenge, in this paper, a generalized nash equilibrium (NE) game called Parallel Scheduling of Multiple Tasks (PSMT) is formulated and studied. The structure properties of the problem are deduced and thus the existence of NE is proven by the fixed point theorem. Further, the corresponding distributed task scheduling algorithm/mechanism is developed via Gauss-Seidel-type method. Simulation results show that the proposed PSMT algorithm can converge in a fast way and offer much better performance in system average delay and number of beneficial TNs, comparing to the Paired Offloading of Multiple Tasks (POMT) solution to the counterpart problem not supporting distributed computing.

Fog computing has risen as an evolving architecture to support delay-sensitive applications in Internet of Things (IoT) and next generation mobile networks. For a typical heterogeneous fog network consisting of many fog nodes, some of them have different computation tasks while some have spare computation resources, which forms a multi-task multi-helper (MTMH) network. How to effectively map multiple tasks into multiple helper nodes to reduce the service delay is a key issue to be resolved. To tackle this issue, a computation offloading problem minimizing every task's delay is considered, from the perspective of individuals. This problem is further formulated into a non-cooperative game, i.e., MTMH computation offloading (MTMHCO) game, to model the competition among tasks for helpers. The existence of Nash equilibrium (NE) is guaranteed and an efficient distributed algorithm is developed to achieve an NE for the MTMHCO game. Theoretical analysis and simulation results show that the proposed algorithm can offer the nearoptimal performance in system average delay and achieve more number of beneficial task nodes, at two orders of magnitude lower complexity than a centralized optimal algorithm.

Fog computing (FC) has the potential to enable computation-intensive applications for the next generation wireless networks. In parallel with the development of FC, nonorthogonal multiple access (NOMA) has been recognized as a promising solution to improve the spectrum efficiency. In this paper, a NOMA-based FC system is considered, where multiple task nodes perform task scheduling via NOMA to a helper node, the helper node with abundant computation resource is required to compute the computation task from the task nodes. We formulate a joint task scheduling, computational resource allocation, and power allocation problem with an objective to minimize the sum cost (i.e., delay and energy consumptions for all task nodes) realizing energy-delay tradeoff. It is challenging to obtain an optimal policy for such a combinatorial optimization problem. To this end, we propose an online learning-based optimization framework to tackle this problem. Simulation results show that the proposed scheme significantly reduces the sum cost compared to the baselines.

Fog computing is a promising paradigm to perform low-latency computation for supporting the internet of things (IoT) applications. It enables provisioning resources and services to be closer for end users. Limited by the computing and storage resources, end users offload the computation-intensive tasks to the nearby fog nodes. However, due to mobility feature of the fog nodes, it's challenging to realize efficient task offloading. We rigorously formulate the task offloading problem for dynamic fog networks as an online stochastic optimization problem, and design offloading policies when the network is in stationary status and non-stationary status. When the fog network is in stationary status, we propose task offloading for the stationary status (TOS) algorithm to minimize the long-term average offloading delay. When the fog network is in non-stationary status, we propose two algorithms as task offloading for the non-stationary status using a sliding window (TON-SW) and task offloading for non-stationary status using a discount factor (TON-D) to minimize the average offloading delay. Besides, learning regret bounds of our algorithms are given. Numerical simulations show that our algorithms achieve a significant performance improvement compared to the upper-confidence bound (UCB) algorithm.

Fog computing has risen as a promising architecture for future Internet of Things, 5G and embedded artificial intelligence applications with stringent service delay requirements along the cloud to things continuum. For a typical fog network consisting of heterogeneous fog nodes (FNs) with different computing resources and communication capabilities, how to effectively schedule complex computation tasks to multiple FNs in the neighborhood to achieve minimal service delay is a fundamental challenge. To tackle this problem, a new concept named processing efficiency (PE) is first defined to incorporate computing resources and communication capacities. Further, to minimize service delay in heterogeneous fog networks, a scalable, stable, and decentralized algorithm, namely dispersive stable task scheduling (DATS), is proposed and evaluated, which consists of two key components: 1) a PE-based progressive computing resources competition and 2) a QoE-oriented synchronized task scheduling. Theoretical proofs and simulation results show that the proposed DATS algorithm can achieve effective tradeoff between computing resources and communication capabilities, thus significantly reducing service delay in heterogeneous fog networks.

By providing shared and flexible communication, computation, and storage resources along the cloud-to-things continuum, fog computing has become an attractive technology to support delay-sensitive applications in Internet of Things (IoT) and future wireless networks. Consider a typical heterogeneous fog network consisting of different types of fog nodes (FNs), wherein some task nodes (TNs) have computation-intensive and delay-sensitive tasks, while some helper nodes (HNs) have spare computation resources for sharing with their neighboring nodes. In order to minimize the delay of every task, these TNs and HNs should be effectively associated in a distributed manner, which is the fundamental multi-task multi-helper (MTMH) problem. To tackle this challenging problem, a potential game called paired offloading of multiple tasks (POMT) is formulated and studied. Theoretical analysis proves the existence of the Nash equilibrium (NE) for this proposed game. Further, the corresponding POMT algorithm is developed for every TN to achieve the NE of the general game. The analytical and simulation results show that our POMT algorithm can offer the near-optimal performance in system average delay and delay reduction ratio (DRR), and achieve more number of beneficial TNs, at two orders of magnitude lower complexity than a centralized optimal algorithm for computation offloading.

Future Internet of Things (IoT) networks enabled with fog computing is promising to achieve lower processing delay and lighter link burden, by effectively offloading the computing tasks of the terminal nodes (TNs) to nearby fog nodes (FNs) at the network edge. Existing researches for the energy consumption in fog-enabled networks mostly focused on the minimization of the overall energy consumed by the task offloading services. However, fair offloading among multiple FNs while maintaining a satisfactory energy efficiency is of great significance for the sustainability of the fog-enabled IoT networks, especially in the scenarios with battery-powered FNs. In this paper, we propose a fair and energy-minimized task offloading (FEMTO) algorithm based on a fairness scheduling metric, taking three important characteristics into consideration, which include the task offloading energy consumption, the FN's historical average energy and the FN priority. The analytical results of the optimal target FN, the optimal TN transmission power, and the optimal subtask size are obtained in a fair and energy-minimized manner. Extensive simulations are carried out for the heterogeneous fog-enabled IoT network, and the numerical results indicate that the proposed FEMTO algorithm effectively determines the FN feasibility and the minimum energy consumption for the task offloading services. Moreover, a high and robust fairness level for the FNs' energy consumptions is obtained by the proposed FEMTO algorithm.

A homogeneous fog network is defined as a group of peer nodes with sharable computing and storage resources, as well as spare spectrum for node-to-node/device-to-device communications and task scheduling. It promotes more intelligent applications and services in different Internet of Things (IoT) scenarios, thanks to effective collaborations among neighboring fog nodes via cognitive spectrum access techniques. In this paper, a comprehensive analytical model that considers circuit, computation, offloading energy consumptions is developed for accurately evaluating the overall energy efficiency (EE) in homogeneous fog networks. With this model, the tradeoff relationship between performance gains and energy costs in collaborative task offloading is investigated, thus enabling us to formulate the EE optimization problem for future intelligent IoT applications with practical constraints in available computing resources at helper nodes and unused spectrum in neighboring environments. Based on rigorous mathematical analysis, a maximal energy-efficient task scheduling (MEETS) algorithm is proposed to derive the optimal scheduling decision for a task node and multiple neighboring helper nodes under feasible modulation schemes and time allocations. Extensive simulation results demonstrate the tradeoff relationship between EE and task scheduling performance in homogeneous fog networks. Compared with traditional task scheduling strategies, the proposed MEETS algorithm can achieve much better EE performance under different network parameters and service conditions.

In this paper, we propose adaptive techniques for multiuser multiple-input and multiple-output (MU-MIMO) cellular communication systems, to solve the problem of energy efficient communications with heterogeneous delay-aware traffic. In order to minimize the total transmission power of the MU-MIMO, we investigate the relationship between the transmission power and the M-ary quadrature amplitude modulation (MQAM) constellation size and get the energy efficient modulation for each transmission stream based on the minimum mean square error (MMSE) receiver. Since the total power consumption is different for MU-MIMO and multiuser single input and multiple output (MU-SIMO), by exploiting the intrinsic relationship among the total power consumption model, and heterogeneous delay-aware services, we propose an adaptive transmission strategy, which is a switching between MU-MIMO and MU-SIMO. Simulations show that in order to maximize the energy efficiency and consider different Quality of Service (QoS) of delay for the users simultaneously, the users should adaptively choose the constellation size for each stream as well as the transmission mode.

In this paper, we propose a cross-layer design framework for transmitting Markov modulated Poisson process (MMPP) traffic over Nakagami-m fading channel with delay demands. The adaptive modulation and coding (AMC) technique is used at the physical layer. The energy efficiency is described as the average throughput over the average transmission power, where both of throughput and transmit power have full consideration of the queuing system. We first derive the closed-form expressions of the delay and the energy efficiency with the stationary distribution of the system. We then derive the energy efficient thresholds to choose the AMC transmission modes. At last, we derive the transmission policy to maximize the energy efficiency with delay constraints. Numerical results are provided to support the theoretical development.

In this paper, we propose adaptive techniques for multiple input and multiple output (MIMO) systems, to solve the problem of energy efficient communications with delay constraint, where the energy efficiency is defined as the number of bits per second correctly received per power consumed. We first investigate the optimal multiple quadrature amplitude modulation (MQAM) constellation size for each transmission stream and the optimal packet size. By exploiting the intrinsic relationship among the constellation size, the packet size, the symbol error rate (SER) and delay, we propose an adaptive transmission mode for different delay demands. For the case of user's buffer overflow, we use the congestion control algorithm to schedule the average queue length, and maintain the optimal delay performance for energy efficiency. Simulations show that to maximize the energy efficiency and offer different Quality of Service (QoS) of delay simultaneously, the transmitter should adaptively choose the constellation size and the packet size as well as the transmission mode. In this framework, the tradeoff between energy efficiency and delay demand are well demonstrated.