Chengxiao Liu, Wei Feng,*, Xiaoming Tao, Ning Ge

a Department of Electronic Engineering, Tsinghua University, Beijing 100084, China

b Beijing National Research Center for Information Science and Technology, Tsinghua University, Beijing 100084, China

Keywords:Cell-free Mobile edge computing Non-terrestrial networks Sixth-generation Wide-area time-sensitive IoT

ABSTRACT In the upcoming sixth-generation (6G) era, the demand for constructing a wide-area time-sensitive Internet of Things (IoT) continues to increase. As conventional cellular technologies are difficult to directly use for wide-area time-sensitive IoT,it is beneficial to use non-terrestrial infrastructures,including satellites and unmanned aerial vehicles (UAVs). Thus, we can build a non-terrestrial network (NTN)using a cell-free architecture. Driven by the time-sensitive requirements and uneven distribution of IoT devices, the NTN must be empowered using mobile edge computing (MEC) while providing oasisoriented on-demand coverage for devices. Nevertheless, communication and MEC systems are coupled with each other under the influence of a complex propagation environment in the MEC-empowered NTN, which makes it difficult to coordinate the resources. In this study, we propose a process-oriented framework to design communication and MEC systems in a time-division manner. In this framework,large-scale channel state information(CSI)is used to characterize the complex propagation environment at an affordable cost,where a nonconvex latency minimization problem is formulated.Subsequently,the approximated problem is provided, and it can be decomposed into sub-problems. These sub-problems are then solved iteratively. The simulation results demonstrated the superiority of the proposed process-oriented scheme over other algorithms, implied that the payload deployments of UAVs should be appropriately predesigned to improve the efficiency of using resources,and confirmed that it is advantageous to integrate NTN with MEC for wide-area time-sensitive IoT.

1. Introduction

In future sixth-generation (6G) networks, the concentration of cutting-edge technologies will change from humans to intelligent machines[1].In contrast to human beings,these machines are usually unevenly distributed in remote areas [1], which are built to accomplish time-sensitive tasks [2,3]. This scenario increases the demand for constructing a wide-area time-sensitive Internet of Things (IoT) in the upcoming 6G era [1–3].

However, terrestrial infrastructures are difficult to deploy in remote areas [4–6], indicating that terrestrial cellular networks have blind sides in terms of coverage ability [7]. Consequently, it is difficult to serve intelligent machines using conventional fourth-generation (4G) and fifth-generation (5G) technologies.Considering this challenge, it is beneficial to employ nonterrestrial infrastructures,including satellites and unmanned aerial vehicles (UAVs), for wide-area time-sensitive IoT. Thus, we can build a non-terrestrial network (NTN). In particular, an NTN is needed to provide oasis-oriented on-demand coverage for machines and accommodate the uneven distribution of machines;thus,the NTN should be designed under a cell-free architecture[8].In addition,driven by the time-sensitive requirements of machines,data from machines must be processed by the NTN as quickly as possible. Therefore, satellite communications (SatCom)-on-themove antennas and edge servers can be carried on UAVs to build high-speed links between satellites and UAVs[9],and rapidly process data with mobile edge computing (MEC) [10], respectively.Thus, an MEC-empowered NTN must be constructed using the cell-free architecture. Nevertheless, communications and MEC are coupled with each other in the NTN with a complex propagation environment that arises new challenges. First, owing to the complex propagation environment in the MEC-empowered NTN,realizing oasis-oriented on-demand coverage under a cell-free architecture is challenging[8].Additionally,as communication and MEC systems are coupled with each other,simultaneous coordination of the resources is slightly complicated[10].Hence,we investigate the design of an MEC-empowered NTN for wide-area timesensitive IoT.

2. Literature review

For wide-area IoT, the narrow-band IoT (NB-IoT) is an enabling technique that was designed under conventional cellular architecture[11],whereas the long-range radio(LoRa)technique was proposed to further expand network coverage [12]. In addition, the design of time-sensitive networks (TSNs) has garnered extensive attention worldwide to serve time-sensitive machines, where industrial automation is a principal application scenario [13–15].Lo Bello and Steiner[13]provided an overview of the applicability of TSNs to various industrial systems. Liang et al. [14] presented a comprehensive survey on wireless networks for the wireless industrial automation–factory automation (WIA-FA) technique and its applications. Luvisotto et al. [15] evaluated the feasibility of wireless high-performance (WirelessHP) technology for industrial wireless networks. These studies promoted the standardization of 5G ultra-reliable low-latency communication (URLLC) [16]and the industrial IoT [17] constructed by the Third Generation Partnership Project (3GPP).

Owing to the coverage holes of terrestrial cellular networks,NTN may become an advantageous technique for 6G networks,where the standardization of NTNs has been launched in 3GPP Release 16[18]. In the future,the design of an NTN for supporting a wide-area time-sensitive IoT will be discussed in 3GPP Release 17[19]. In the existing studies, satellite-enabled IoT has been widely discussed as it can provide ubiquitous coverage for wide-area IoT[20–22].De Sanctis et al.[20]investigated the protocols and architectures for a satellite-based internet for remote objects.Cioni et al.[21] studied the opportunities and challenges of satellite-enabled massive machine-type communications (MMTC). Zhen et al. [22]proposed an optimal preamble design method that could adapt to the group-based random access pattern for satellite-based MMTC. However, satellite-enabled IoT systems undergo a high latency and low efficiency [20–22], which entangles meeting the requirements of intelligent machines [1].

In addition, UAVs have the potential to provide on-demand services for wide-area time-sensitive IoT [23–26]. In Ref. [23], a low-latency routing algorithm was proposed for UAV-enabled IoT,which was designed using a layered network architecture with a UAV swarm. The design of a UAV-enabled IoT-oriented network was proposed in Ref.[24]to support real-time remote virtual reality.In Ref.[25],the uplink(UL)power of IoT devices was optimized to design a UAV-assisted URLLC network. A UAV-assisted ubiquitous trust evaluation system was designed to reliably collect data from IoT devices[26].To further improve the latency performance,UAV-enabled IoT was integrated with MEC [27–32]. In Ref. [27],the three-dimensional deployment of UAVs was optimized to support time-sensitive IoT, where UAVs were mounted as cloudlets.The average latency of users in UAV-aided MEC networks were minimized, as reported in Ref. [28]. In Ref. [29], the trajectories of UAVs were optimized for a smart IoT community,where an augmented reality-based use case was discussed. An energy-efficient multi-domain resource allocation scheme was proposed in Ref.[30] considering stringent latency requirements. In Ref. [31], an online UAV-mounted edge server dispatching scheme was proposed, where latency fairness among users was guaranteed with an efficient resource utilization. Additionally, a multi-UAV task offloading system was established that could transmit data from IoT devices to edge servers in a trustworthy manner [32].Nevertheless, the UAV-enabled network usually lacks persistence and stability [33], which is an inevitable limitation for wide-area time-sensitive IoT.

Therefore, it is advantageous to jointly use satellites and UAVs with MEC for wide-area time-sensitive IoT [10,34,35]. In Ref.[34], Liu et al. presented a task-oriented intelligent architecture for IoT-oriented space–aerial–ground–aqua-integrated networks.Cheng et al. [10] investigated the concurrent design of computing resource allocation and task offloading strategies for IoT-oriented space–aerial–ground integrated networks,where stringent latency constraints were utilized and a learning-based approach was proposed. Cao et al. [35] discussed the coupling of trajectory design and task offloading strategies in an integrated satellite-UAV network under the influence of wind. Despite these achievements,when an NTN is integrated with MEC under a cell-free architecture,new challenges will be encountered. First, because of the complex propagation environment, NTN cannot perfectly acquire the channel state information (CSI), resulting in a complicated design of oasis-oriented on-demand coverage for machines under the cellfree architecture. Second, the resources cannot be readily coordinated in the MEC-empowered NTN because communication and MEC systems are coupled with each other. In our previous study[8], we discussed the cell-free coverage patterns of integrated satellite-UAV networks.In this study,we advance the investigation to the design of an MEC-empowered NTN for wide-area timesensitive IoT. The relationships between the existing technologies and certain research areas are summarized in Table 1 [11,12,14–17,20–22].

3. Study contributions

In this study,we investigated the design of an MEC-empowered NTN for a wide-area time-sensitive IoT. In particular, we focused on the design of NTN, which consists of hierarchically integrated satellites and UAVs considering the overall communication and computing latency as the metric of latency performance. The MEC-empowered NTN is designed under a process-oriented framework in a time-division manner [8] to satisfy the service requirements of wide-area time-sensitive IoT, where a latency minimization problem is formulated using a large-scale CSI.Subsequently, a process-oriented joint resource orchestration scheme is proposed to solve the latency minimization problem. The main contributions of this study are summarized as follows:

(1) A process-oriented framework is presented for an MECempowered NTN. This framework can jointly design communication and MEC systems in a time-division manner for hierarchically integrated satellites and UAVs.Subsequently,an overall communication and computing latency minimization problem is formulated, where large-scale CSI is used to characterize complex propagation environments at an affordable cost.

(2) As the latency minimization problem is a nonconvex stochastic optimization problem, we first prove that the original problem can be transformed into a simplified form. Subsequently,we propose an approximation of the simplified problem,which can be further decomposed into sub-problems according to the properties of the overall communication and computing efficiency function.

(3) We propose a joint power allocation and data stream scheduling scheme to solve sub-problems,where block coordinate descent and successive convex approximation techniques are applied. The process-oriented joint resource orchestration scheme is derived iteratively.

The remainder of this paper is organized as follows. We introduce the system model and the process-oriented framework in Section 4. In Section 5, the solution of the latency minimizationproblem is presented, where a joint power allocation and data stream scheduling scheme is introduced. The simulation results and discussions are presented in Section 6, and the conclusions are drawn in Section 7.

Table 1 Existing technologies and our concentrations.

4. System model

In practical systems,the computing ability of each IoT device is usually weak; thus, devices must upload data to the satellite or UAVs to accomplish computation-intensive yet time-sensitive tasks [10]. After the cloud server successfully receives all the data from devices,the entire process of communication and computing is completed[37,38].We assume that the uth device has Dudata to be uploaded. The communication and computing process is designed under a process-oriented framework to manage the influence of UAV movement on data transmission, which can reduce the complexity of optimizing the entire process [8]. As illustrated in Fig. 2, the entire process is divided into NTsegmentations. The parameters of the MEC-empowered NTN are updated at the beginning of the segmentation, and are assumed to be constant during each segmentation and possibly vary with each other in different segmentations. The update interval of system parameters is denoted as δT, and the overall communication and computing latency can be expressed as Ttotal=NTδT+?a, where ?ais the total propagation time of the electromagnetic wave.In particular,in the tth segmentation,the uth device can send a ratio of ηLt data directly to the satellite,the ratio of ηSu，tdata to the satellite via device–UAV and UAV–satellite links, and the ratio of ηCu，tdata via device–UAV links to on-board MEC servers for computing. Thus, we have Eqs. (1) and (2) as the practical constraints for these ratios. After the data are computed by the MEC servers, the computational results are transmitted from the MEC servers to the satellite via UAV-satellite links. For simplifying the mathematical analysis, we assume that the output data size is proportional to that of the input data for MEC servers[39,40],where the proportion of the data from the uth device is denoted as ζu.

Fig. 1. Illustration of an MEC-empowered hierarchical NTN for wide-area time-sensitive IoT.

Fig. 2. Diagram of the process-oriented framework in the MEC-empowered NTN.

In each segmentation of the process, data from IoT devices are first transmitted to the satellite or UAVs.Under the cell-free architecture,all devices are assumed to share the same frequency band[8], where the bandwidth is denoted as B. When an IoT device is directly connected to the satellite, we assume that the UL rate between the device and satellite is constant [41], which is RL.Moreover,when IoT devices are connected with UAVs,they consist of a multiuser multiple-input-multiple-output(MU-MIMO)UL system for data transmission.Therefore,the receive symbol of the uth user from the kth UAV in the tth segmentation is formulated as follows:

where T is the transpose symbol; j is the imaginary unit; and d0is the distance between adjacent antennas.

In this system,the process of data transmission from devices to UAVs is designed prior to UAV takeoff,which its time scale is considerably larger than the channel coherence time.Therefore,using pilot symbols,the UL CSI in Eq. (4) can be accurately estimated by UAVs within the channel coherence time;however,such a CSI cannot be perfectly acquired prior to UAV takeoff considering the large time scale of the entire process. Consequently, a perfect CSI is difficult to use when designing a data transmission process.In particular,we regard the position-related parameters,that is,lu，kand au，kas slowly varying large-scale channel parameters, which can be perfectly acquired using radio maps in practical systems[5].These parameters are assumed to be constant throughout the entire process. In contrast, su，k，tvaries rapidly owing to the movement of UAVs,and only its distribution is known.Under these assumptions,the efficiency of data transmission in each segmentation of the process can be evaluated using the ergodic rate [8]. In addition, it is reasonable to assume that minimum mean square error(MMSE)detection is used at the receiver [37], where the detection vector for the uth device at the kth UAV in the tth segmentation is denoted as wu，k，t[44]. Consequently, the UL ergodic rate of the uth device at the kth UAV in the tth segmentation can be formulated as follows [45]:

If the MEC server on the UAV is used for computing, we have

5.Joint power allocation and data stream scheduling under the process-oriented framework

5.1. Problem decomposition

Fig. 3. Numerical evaluations of the approximated ergodic rate accuracy.

It is not difficult to certify that the sub-problems in Eqs. (16)–(18) are independent of each other. For simplicity of notation, if we have P，η（） as the solution to Eqs. (16), (17), or (18), the corresponding objective function is expressed as δTP，η（）. Subsequently, we can discuss the solutions to these sub-problems individually.

5.2. Solution to Eq. (16)

Remark 1: The solution to Eq. (16) provides the joint resource orchestration scheme when we use only the satellite to transmit data. Intuitively, we show that the minimum overall latency is achieved by this strategy when Duis sufficiently small. This is because the overall latency may be less than 2?0if we only use the satellite for data transmission; however, the latency is at least 2?0if UAVs are used, as shown in Eqs. (16h), (17h), and(18h). This intuition can be further verified by the simulation results.

5.3. Solution to Eq. (17)

Owing to the coupling of P and η in Eqs. (17b)–(17d), Eq. (17)is nonconvex and difficult to solve directly. To solve this problem, we use the block coordinate descent technique to decompose Eq. (17) into two sub-problems [8], which are formulated as

where i is the iteration index; Eq. (22) is the power allocation subproblem and Eq. (23) denotes the data stream scheduling subproblem. Next, we discuss the solutions to Eqs. (22) and (23).

5.4. Solution to Eq. (22)

It is not difficult to certify that Eq.(22)is nonconvex.According to Theorem 1 in Ref. [48], the problem in Eq. (22) can be solved iteratively using successive convex approximation techniques after applying the Taylor expansion to Eqs. (22b), (22c), and (22d) [49].Denoting the iteration index as j, the problem in Eq. (22) is reformulated as

Property 1: The problem in Eq. (24) is convex, and its optimal solution is a feasible solution to Eq. (22).

Proof: See Appendix A.

Property 1 shows that Eq.(24)can be solved using conventional convex optimization tools [46], which also indicates that the solution to Eq. (22) can be iteratively derived using the solution to Eq. (24). The detailed steps of this method are presented in Algorithm 1.

Algorithm 1. Power allocation algorithm for solving Eq. (22).input: K，M，U，RL， RSk，RC■■?k，θ，z， ｛Du ｝?u，NT，?0，Pmax，γUL，B，ηi-1，Pi-1 1: initialization: Pi，0 =Pi-1， ?=1×10-2， j=1 2: solve Eq. (24), denoting the optimal solution as δ*T，P*k（）,setting Pi，j =P*，δT Pi，j，ηi-1■■■■■■=δ*T 3: while 1-δT Pi，j-1，ηi-1（）δT Pi，j，ηi-1（）■■■■>?do 4: j = j + 1 5: solve Eq. (24), denoting the optimal solution as δ*T，P*（）,setting Pi，j =P*，δT Pi，j，ηi-1■■■■=δ*T output: Pi，j，δT Pi，j，ηi-1

5.5. Solution to Eq. (23)

The problem in Eq. (23) is nonconvex because Eq. (23b) is concave with respect to ηi. Furthermore, it can be solved using the Taylor expansion and successive convex approximation techniques[49]. Denoting the iteration index j, Eq. (23) is reformulated as follows:

Algorithm 2. Data stream scheduling algorithm for solving Eq. (23).input: K，M，U，RL， RSk，RC■■?k，θ，z， ｛Du ｝?u，NT，?0，Pmax，γUL，B，ηi-1，Pi 1: initialization:ηi，0 =ηi-1，?=1×10-2， j=1 2: solve Eq. (30), denoting the optimal solution as δ*T，η*k（）,setting ηi，j =η*，δT Pi，ηi，j■■■■■■=δ*T 3: while 1-δT Pi，ηi，j（）δT Pi，ηi，j-1（）■■■■>?do 4: j = j + 1 5: solve Eq. (30), denoting the optimal solution as δ*T，η*（）,setting ηi，j =η*，δT Pi，ηi，j■■■■=δ*T output:ηi，j，δT Pi，ηi，j

After the problems in Eqs.(22)and(23)are solved,the solution to Eq.(17)can be iteratively derived by jointly using Algorithms 1 and 2 according to the block coordinate descent technique[8].The detailed steps of the proposed joint resource orchestration scheme are summarized in Algorithm 3.

orithm for，?0，Pmax，γUL，B e elements in T riables in the range of ［0，1］,?=1×10-3，i=1 2: solve Eq. (23) using Algorithm 2, denoting the optimal solution as δ*T，η*■■■■■■（）, setting η0 =η*，δT P0，η0=δ*T 3: while 1-δT Pi，ηi，j（）δT Pi，ηi，j-1（）■■■■>?do 4: solve Eq. (23) using Algorithm 2, denoting the optimal solution as δ*T，η*■■■■■■（）setting ηi =η*，δT Pi，ηi =δ*T 5: while 1-δT Pi-1，ηi-1（）δT Pi，ηi（ ）■■■■>?do 6: i = i + 1 7: solve Eq. (22) using Algorithm 1, denoting the optimal solution as δ*T，P*■■（）, setting Pi =P*，δT Pi，ηi-1=δ*T 8: solve Eq. (23) using Algorithm 2, denoting the optimal solution as δ*T，η*■■（）, setting ηi =η*，δT Pi，ηi■■=δ*T output: Pi，ηi，δT Pi，ηi

5.6. Solution to Eq. (18)

Comparing Eq. (18b) with Eq. (17b), we can state the following property:constraints in Eqs. (18c)–(18h) can be satisfied. Consequently,ηCu，t=0 always belongs to the feasible region of Eq. (18) for any u and t.

Using Property 2, Eq. (18) can be simplified to

Remark 2: The most important difference between the solutions to Eqs.(17)and(18)is the possibility of using MEC for computing.Similar to the discussion in Remark 1, the communication and computing process may be accomplished with one segmentation when Duis small, whereas a smaller overall communication and computing latency can be achieved if MEC is not used. The reason is that the overall latency could be lower than 3?0if MEC is not used; however, the latency must be at least 3?0if MEC is used, as expressed by Eqs. (17h) and (18h). This phenomenon can also be observed after the numerical results are derived.

Based on Algorithms 1–3, a process-oriented joint resource orchestration scheme to solve Eq. (13) is derived, as summarized in Algorithm 4.The minimum overall communication and computing latency can be obtained using Algorithm 4.

Algorithm 4. Proposed process-oriented joint resource orchestration algorithm.input:K，M，U，RL， RSk，RC■■T ，Ns3?k，θ，z， ｛Du ｝?u，Ns1 T ，Ns2 T ，?0，?a，Pmax，γUL，B 1: solve Eq. (16) with NT =Ns1 k（）is derived T ; then, Ps1，ηs1 using Eq. (20) and δs1T is derived by Eq. (21)2: solve Eq. (17) NT =Ns2T using Algorithms 1–3. Denote the（）; then, δs2T is derived 3: solve Eq. (18) NT =Ns3T using Algorithms 1–3. Denote the solution as Ps2，ηs2（）; then, δs3 T is derived 4: calculate Tmin =min Ns1 solution as Ps3，ηs3■+?a, where P*，η*（） is derived as the corresponding joint power allocation and data stream scheduling scheme output: Tmin，P*，η*■T δs1 T ，Ns2 T δs2 T ，Ns3T δs3 T

5.7. Convergence analysis

Here, we analyze the convergence of Algorithms 1–3. For the problem in Eq. (24) during the jth iteration step, we have

which shows that the objective function in Eq. (17a) continues to decrease when i increases. Owing to the constraints in Eqs. (17b)–(17h), the objective function must have a lower bound. Consequently, the convergence of Algorithm 3 is proven, and the locally optimal solution to Eq. (17) can be derived.

6. Simulation results and discussions

Subsequently, we compared the proposed algorithm performance with other schemes.First,a simple scheme was considered,where we only used satellites for communication. Furthermore,the following three schemes were considered:

Scheme 1: We allocate the total bandwidth among multiple devices using the bandwidth allocation method proposed in Ref.[37], where the maximum transmission power is used and a greedy data stream scheduling strategy is applied, as presented in Ref. [10].

Scheme 2: The transmission power of each device is set to be equal [8], where power backoff is used to satisfy the constraints of the data stream and a greedy data stream scheduling strategy is applied, as presented in Ref. [10].

Fig. 5. Comparison between different algorithms when D is small.

Fig. 6. Comparison between different algorithms when D is large.

Table 2 Overall communication and computing latencies with different data sizes.

Fig.7. Relationship between the minimum overall communication and computing latency and segmentation numbers.

Fig. 9. Relationship between the overall communication and computing latency and degree of aggregation with different average throughputs of MEC servers.

Fig. 10. Relationship between the overall communication and computing latency and degree of aggregation with different numbers of IoT devices.

Fig. 11. Relationship between the overall communication and computing latency and height of the UAV swarm, where the distance between different UAVs varies.

7. Conclusions

In this study,the design of an MEC-empowered NTN for a widearea time-sensitive IoT was investigated. To jointly design the communication and MEC systems for hierarchically integrated satellites and UAVs, a process-oriented framework was presented in a time-division manner. Under this framework, a latency minimization problem was formulated using the large-scale CSI.Subsequently, the problem could be transformed into a simplified form,and an approximation of the simplified problem was derived. The approximated problem was decomposed into sub-problems based on the properties of the overall communication and computing efficiency function. Additionally, an iterative algorithm was proposed to solve these sub-problems by jointly using block coordinate descent and successive convex approximation techniques. A process-oriented joint resource orchestration scheme was proposed for the MEC-empowered NTN using the solutions to the sub-problems. The simulation results demonstrated that the proposed process-oriented scheme exhibited a higher performance than that of the other comparison algorithms.In addition, simulations proved that the proposed process-oriented scheme could flexibly adapt to varying data sizes.Therefore,the payload deployments of UAVs should be appropriately predesigned to improve the efficiency of resource use in the MEC-empowered NTN.Finally,the results implied that it is advantageous to integrate NTN with MEC for wide-area time-sensitive IoT.

Acknowledgments

This work was supported in part by the National Key R&D Program of China (2018YFA0701601 and 2020YFA0711301), the National Natural Science Foundation of China (61771286,61941104, and 61922049), and the Tsinghua University–China Mobile Communications Group Co., Ltd. Joint Institute.

Compliance with ethics guidelines

Chengxiao Liu, Wei Feng, Xiaoming Tao, and Ning Ge declare that they have no conflict of interest or financial conflicts to disclose.

Appendix A. Supplementary data

Supplementary data to this article can be found online at https://doi.org/10.1016/j.eng.2021.11.002.