Tian DANG, Chenxi LIU, Xiqing LIU, Shi YAN

State Key Laboratory of Networking and Switching Technology,

Beijing University of Posts and Telecommunications, Beijing 100876, China

Abstract: Fog radio access networks (F-RANs), in which the fog access points are equipped with communication,caching, and computing functionalities, have been anticipated as a promising architecture for enabling virtual reality(VR) applications in wireless networks. Although extensive research efforts have been devoted to designing efficient resource allocation strategies for realizing successful mobile VR delivery in downlink, the equally important resource allocation problem of mobile VR delivery in uplink has so far drawn little attention. In this work, we investigate a mobile VR F-RAN delivery framework, where both the uplink and downlink transmissions are considered. We first characterize the round-trip latency of the system, which reveals its dependence on the communication, caching, and computation resource allocations. Based on this information, we propose a simple yet efficient algorithm to minimize the round-trip latency,while satisfying the practical constraints on caching,computation capability,and transmission capacity in the uplink and downlink. Numerical results show that our proposed algorithm can effectively reduce the round-trip latency compared with various baselines, and the impacts of communication, caching, and computing resources on latency performance are illustrated.

Key words: Virtual reality delivery; Fog radio access network (F-RAN); Round-trip latency; Resource allocation https://doi.org/10.1631/FITEE.2100308CLC number: TN914

1 Introduction

Fifth generation and beyond (5G and beyond)wireless networks have been an indispensable part of our daily life, enabling many novel and “intellicise” applications. As stated in Zhang P et al.(2022),“intellicise” means that 5G and beyond wireless networks can provide these novel applications with endogenous intelligence and primitive conciseness. Among these applications,virtual reality(VR)is regarded as a transformative application, since it can provide immersive experiences for users, and therefore receives significant attention from both academia and industry (Bastug et al., 2017; Hu et al.,2020). However,VR applications require realtime broadband communications. As anticipated by Cisco, VR traffic will be 254.4 petabytes per month by 2022 (Cisco System, 2019), which creates many challenges for current and future wireless networks,such as high data rate and low latency. Against this backdrop,increasing research attention has been paid to delivering immersive VR experiences in wireless networks.

One of the main research problems in mobile VR delivery is the resource allocation problem. Specifically, in scenarios where fog and mobile edge computing (MEC) capabilities are deployed to render VR videos, Yoshihara and Fujita (2019) offloaded the rendering of the background view from the cloud server to the fog nodes and achieved a low-latency VR game. In Zhang Y et al. (2019), the rendering modules were dynamically placed at the distributed MEC servers to reduce the operational cost and communication delay. In Huang et al. (2018),VR videos were designed to be pre-cached at the user destination to reduce the transmission latency and optimize the access probability. In Dai et al.(2020),a transmission latency minimization problem was studied by hierarchically and adaptively caching VR videos at the cloud server and the remote radio heads (RRHs). Moreover, in Du et al. (2020),the offloaded rendering and transmit power control were jointly optimized to minimize energy consumption with a deep reinforced learning approach. An MEC-based VR delivery framework was presented in Sun et al.(2019),in which the caching and computation resources were jointly optimized and the tradeoffs among communications,caching,and computing were revealed. In Zhou et al. (2021), a joint bandwidth,caching,and computation resource allocation was designed to minimize the maximum communication and computing latency.

Recently, fog radio access networks (F-RANs)have been regarded as a promising network architecture for mobile VR delivery, because they deploy caching and computing functionalities near user equipment, thereby greatly alleviating the fronthaul traffic load and reducing the latency (Peng et al.,2016;You et al., 2019). Chiu et al. (2019)examined how to formulate fog node groups according to various communication and computation resources to achieve low-latency VR service. In Park SH et al.(2016), cloud and edge processing were jointly designed to maximize the delivery rate with enhanced RRHs equipped with local caching and baseband processing capabilities. Liu et al. (2018) developed a strategy involving a joint offloading decision,computing, power, and bandwidth allocation that minimized latency and energy consumption. In our previous work(Dang and Peng, 2019),we considered the impact of downlink transmissions only on VR delivery in F-RANs and formulated a tolerant latency maximization problem. We proposed a Lagrangian dual decomposition based approach that jointly optimizes the content placement and task offloading to solve the formulated problem, and illustrated the impact of caching and computing resources on the average tolerant delay with numerical results.

The aforementioned works focused mainly on the resource allocation problem in downlink transmissions. However, the limited resources in uplink transmissions can have a significant impact on the performance of mobile VR delivery. In Park J et al. (2018), uploading delay in the uplink was regarded as the bottleneck in the downlink delay;the proposed uplink spectrum allocation yielded up to 25.1%average end-to-end latency reduction compared to the equal uplink allocation. In Chen et al.(2020), tracking information was transmitted in the uplink over a sub-6 GHz frequency band to provide reliable communication with limited bandwidth,emphasizing that the uplink transmission latency cannot be ignored. Given the significance of the uplink transmissions in mobile VR delivery, it is therefore essential to address the impact of both the uplink and downlink in designing the corresponding resource allocation strategies.

Motivated by the above observations, in this work,we investigate how to effectively and efficiently deliver mobile VR services in F-RANs. Both the uplink and downlink transmissions are considered.Specifically, in the uplink, the tracking information is collected from VR users. In the downlink, VR videos are delivered to the VR users,and the processing tasks are offloaded to either the fog access points(F-APs) or the VR users. In this work,a round-trip latency minimization problem is formulated to allocate the caching, computing, and communication resources. Our contributions are as follows:

1.We characterize the round-trip latency of mobile VR delivery in F-RANs, revealing its dependence on communication resource allocation in both uplink and downlink, as well as caching and computation resource allocations between F-APs and VR users.

2. We formulate a round-trip latency minimization problem,subject to practical constraints on the uplink and downlink transmission capacities,the F-AP caching size,and the computation capabilities of the F-APs and VR users. To solve this NP-hard problem,we decompose it into two subproblems,the mode selection problem and the joint communication and computation resource allocation problem,which are tackled with the branch-and-bound method and convex optimization, respectively. Finally, a simple yet effective algorithm is proposed to iteratively solve these subproblems.

3. We examine the impact of key system parameters on round-trip latency. Compared to various baselines,our proposed algorithm can effectively improve mobile VR delivery performance,especially when the downlink transmission capacity is relatively large.

Unless specified, the notations used throughout this paper are as summarized in Table 1.

2 System model

As illustrated in Fig. 1, the considered F-RANbased mobile VR delivery system consists of one cloud server,one high-power node(HPN),MF-APs,NVR users, and multiple RRHs. The cloud server includes a baseband unit (BBU) pool. The F-APs and VR users are denoted byM={1,2,...,M}andN={1,2,...,N}, respectively. In this system, the cloud server extracts 360°VR videos into monocular videos(MVs) and stereoscopic videos (SVs). The FAPs are equipped with certain caching and computation capabilities and can judiciously cache VR videos and process computing tasks. The VR users are equipped with limited computational capabilities,and access either the RRHs or the F-APs. The RRHs communicate with the VR users through centralized cooperative transmission. The resource management decision is transmitted through the HPN in the control link. In the uplink, the tracking information is uploaded. In the downlink,the requested VR videos are delivered to the VR users.

We now describe the VR delivery process, including the following:

1. Tracking. The VR users upload the tracking information to the associated access points, i.e., FAPs or RRHs, through the uplink.

2. Extraction. Using the tracking information,the F-APs and the cloud server extract the VR videos(i.e., SVs or MVs).

3. Projection. The F-APs and VR users project the MVs into the SVs when the computing tasks are offloaded.

Table 1 Notations used in this paper

4. Rendering. The VR users render the SVs into 360°videos and present them. Note that the projection exists if and only if the computing tasks are offloaded to the F-APs or the VR users.

The service modes considered in this work are summarized into five categories (Fig. 2). Note that there are 3M+ 2 service modes, consisting of two modes through the RRHs and three modes through each F-AP. Letqn,i ∈{0,1}(n ∈N, i ∈{1,2,...,3M+2})denote the service mode selection variable of VR usern, in whichqn,i= 1 indicates that the VR video is delivered to VR usernin service modei, andqn,i= 0 otherwise. The service modes in Fig. 2 are as follows:

1.qn,1= 1. In service mode 1, VR usernaccesses the RRHs and the MV is delivered to the VR user from the cloud server. Meanwhile, the computing task is processed at VR usern.

Fig. 1 VR delivery in F-RANs

Fig. 2 Service modes for mobile VR delivery

2.qn,2= 1. In service mode 2, VR usernaccesses the RRHs and the SV is delivered to the VR user from the cloud server.

3.qn,3m= 1,m ∈M. In service mode 3, VR usernaccesses F-APmand the SV is delivered to the VR user from F-APm. The SV must be pre-cached at F-APm.

4.qn,3m+2=1,m ∈M. In service mode 3m+2,VR usernaccesses F-APmwith the requested MV cached. The computing task is offloaded to F-APmto project the MV to SV. Then, SV is transmitted to VR usern.

2.1 Cache and computation model

Table 2 Summary of service modes for VR users

2.2 Transmission model

2.3 Round-trip latency

To evaluate the performance of mobile VR delivery, we adopt round-trip latency as the metric,given by

wherebandlare the tuples of the data rate and processing frequency allocations, respectively. Note that the round-trip latencyτn,i(b,l) is the convex function ofbandl.

3 Problem formulation and resource allocation scheme

In this section, we first formulate a mixedinteger nonlinear programming(MINLP)problem to minimize the round-trip latency by jointly optimizing the communication, caching, and computation resource allocation. To solve this NP-hard problem,we decompose it into two subproblems: the mode selection problem and the joint communication and computation resource allocation problem. The joint communication and computation resource allocation problem is convex and can be solved with the convex optimization method. The mode selection problem is a 0-1 linear programming problem, which is solved with the proposed branch-and-bound-based algorithm, in which an optimal mode selection can be obtained within finite iterations.

3.1 Problem formulation

The key goal of our work is to jointly optimize the communication, caching, and computing resources to minimize the round-trip latencyτ, satisfying the caching capacity, processing frequency,energy consumption,and transmission capacity constraints. Mathematically, the optimization problem can be formulated as

wherea,c, andddenote the tuples of the user association, caching, and offloading decision, respectively. It is observed that problem (14) is an NPhard MINLP problem. To tackle this problem, we replace the user association, caching, and offloading decisions, i.e.,a,c, andd, with the mode selectionqn,i. Then problem(14)can be transformed to

whereqdenotes the tuple ofqn,i, and C1-C8 are obtained from Eqs. (1)-(8) by replacinga,c, anddwithq. C9 and C10 ensure that only one service mode can be chosen for each VR user.

3.2 Problem decomposition

It is observed that reformulated problem(15)is a non-convex MINLP problem, which is challenging to solve. To make it more tractable, we first decompose problem(15)into two subproblems as follows:

Particularly, subproblem (24) is yielded with givenbandl, and subproblem(25)is obtained with givenq. Note that there is a mutual dependence amongb,l, andqin problem (15); this decomposition implies that the objective values of problems (24) and (25) are the upper bounds for problem (15). To make the upper bounds approach the optimal round-trip latency,we propose Algorithm 1,an iterative algorithm, whereδout> 0 is the termination parameter with a small value. Note that Algorithm 1 is guaranteed to converge (Zhou et al.,2021).

Note that the round-trip latency achieved by Algorithm 1 is sensitive to the initial resource allocation decisions. Therefore,we perform Algorithm 1 repeatedly and select the resource allocation with the lowest round-trip latency.

Algorithm 1 The iterative algorithm for solving problem(15)1: Initialize a feasible resource allocation q0, b0, and l0 and iteration index j =1. The round-trip latency is ?τ0.2: repeat 3:With the given qj?1, problem (25) is a convex optimization problem. Then, bj and lj are achieved by solving problem (25) with the traditional convex optimization approach.4:With the given bj and lj, problem (24) is a 0-1 linear programming problem. Then, qj can be obtained by solving problem(24)with the branchand-bound approach.5:The corresponding round-trip latency can be calculated with qj,bj, and lj and denoted as ?τj.6:Set j =j+1.7: until |?τj ??τj?1|≤δout

3.3 Service mode selection

Subproblem (24) is a 0-1 linear programming problem, which can be traditionally solved with an exhaustive search at the cost of a high computational complexity. To reduce the complexity, we resort to the branch-and-bound method (the branchand-bound method can solve the formulated problem with less computational complexity compared to the traditional exhaustive search method) (Boyd and Mattingley, 2018). Denoteτoptas the optimal objective value of problem (24). Relax the binary variableqinto the continuous variable 0≤qn,i ≤1 to yield the following problem:

It is observed that problem (26) is a linear programming problem, which can be tackled with the traditional simplex method (Nelder and Mead,1965). LetL1denote the objective latency of problem(26),which is a lower bound forτopt. IfL1→∞,the problem is surely infeasible. Otherwise, by rounding the relaxed variables and substituting them into the objective of problem (24), an upper bound forτopt, denoted byU1, can be obtained.τopt,L1,andU1satisfyL1≤τopt≤U1.

Denoteδin> 0 as the termination parameter with a small value. If the difference betweenL1andU1is small enough,which means thatU1?L1≤δin,the required tolerance is satisfied,the algorithm terminates, and we haveτopt=L1. Otherwise, we focus on branching. Pick any index(n,i)and form two subproblems from problem (24) by makingqn,i= 1 and 2:

In this case, problem (24) is called the parent problem of problems (27) and (28). Then, relax problems (27) and (28), and solve them to obtain the lower and upper bounds for the optimal objective value of each subproblem. Denote these bounds asLs1andUs1forqn,i=0 andLs2andUs2forqn,i=1.Ls1andLs2must be at least as large asL1, i.e.,min{Ls1,Ls2} ≥L1. Similarly, the upper bounds satisfy min{Us1,Us2} ≤U1. Then,τoptsatisfiesL2= min{Ls1,Ls2} ≤τopt≤U2= min{Us1,Us2}.We also observe thatU2?L2≤U1?L1.

IfU2?L2≤ δin, the algorithm terminates,and we haveτopt=L2. Otherwise, consider problems(27) and (28) as the parent problems and split them on a new index (n′,i′), which has not been used before. Similarly,the subproblems can be tackled in the same way as shown above,and a set of lower bounds and upper bounds is obtained,the minima of which give a lower bound and an upper bound forτopt. Denote the lower bound and upper bound asLjandUj, respectively. It can be observed thatLjis non-decreasing and thatUjis non-increasing.Thus, these bounds satisfyUj+1?Lj+1≤Uj ?Lj.The iteration must quit whenUj ?Lj ≤δin.

Finally, the branch-and-bound-based algorithm for service mode selection is summarized in Algorithm 2. The convergence of this algorithm is guaranteed, because the algorithm must terminate in fewer than 2(3M+2)Niterations,withUj=Lj.

?

4 Numerical results

4.1 Performance comparison

First, we compare the proposed Algorithm 1 withthecentralized-modes-only(CMO),distributed-modes-only(DMO),andhalfcentralized-half-distributed(HCHD)schemes.Specifically,in the CMO scheme,all VR users access the RRHs, where the mode selection and resource allocation are achieved with Algorithm 1. Similarly,in the DMO scheme, all VR users access the F-APs,

where the mode selection and resource allocation are achieved with Algorithm 1. In the HCHD scheme, half of the VR users access the RRHs and the remaining half access the F-APs,randomly. The joint bandwidth and computing frequency allocation is achieved by solving convex problem(25).

In Fig. 4, we compare the round-trip latency per VR user achieved by our proposed algorithm with that achieved by the optimal solution obtained with an exhaustive search for different values of averageDMk. It is observed that our proposed scheme achieves almost the same performance as the optimal solution, especially whenDMkis relatively small.

4.2 Impact of caching capacity

Fig. 3 Round-trip latency per VR user vs. downlink transmission capacity of F-APs(a)and number of VR users accessing RRHs vs. downlink transmission capacity of F-APs (b) with different resource allocation schemes

The impact of the caching capacity on the round-trip latency is studied in Fig. 5. It is observed that the round-trip latency per VR user can be reduced by increasing the caching capacity of the F-APs. For instance, whenE(DMk) = 16 Mb, the round-trip latency decreases from 51.55 to 46.76 ms when the caching capacity is increased from 0.05 to 0.15 Gb. This situation occurs because more VR videos can be pre-cached at the F-APs with a larger caching capacity, which means that more VR users can be served by the F-APs for lower round-trip latency. This result suggests that the F-APs should be equipped with a larger caching capacity to achieve lower round-trip latency. Furthermore, a larger MV data volume leads to a higher round-trip latency.

4.3 Impact of computing frequency

Fig.6 shows the round-trip latency per VR user and the computing energy consumption vs. the computing frequency of the F-APs. The round-trip latency per VR user decreases based on the computing frequency of the F-APs, because higher computing frequency leads to lower processing latency according to Eq. (13). We also find that the computing energy consumption of the F-APs increases as the computing frequency increases. Furthermore, the round-trip latency per VR user remains unchanged for different values ofEAmfor both small and large computing frequencies, because no computing task is offloaded to the F-APs when the computing frequency is low and the computing energy consumption of the F-APs meets the constraints when the computing frequency is high.

Fig. 4 Round-trip latency per VR user vs. average

Fig. 5 Round-trip latency per VR user vs. caching capacity of F-APs CAm (N =10 and K =10)

4.4 Impact of transmission capacity

Fig.6 Round-trip latency per VR user and computing energy consumption vs. computing frequency of FAPs (K =1, LVn =1.5 GHz, EVn =30 J, CAm =0.1 Gb,and RF =3.5 Gb/s)

Fig.9 shows the round-trip latency per VR user vs. the downlink transmission capacity of the F-APs for 10 VR users and 6 VR services. It is observed that

Fig. 7 Round-trip latency per VR user vs. uplink transmission capacity of F-APs RUmmax

Fig. 8 Round-trip latency per VR user vs. uplink fronthaul capacity RUF

Fig. 9 Round-trip latency per VR user vs. downlink transmission capacity of F-APs Rmaxm (10 VR users,6 VR services)

Fig.10 illustrates the round-trip latency per VR user vs. the downlink fronthaul capacity, with one F-AP and 6 VR services,i.e.,M=1 andK=6. It is observed that the round-trip latency per VR user decreases with increased downlink fronthaul capacity.With 10 VR users, up to 29.1%latency reduction is obtained when the downlink fronthaul capacityRFincreases from 5 to 10 Gb/s. This situation occurs because large downlink fronthaul capacity helps reduce the downlink transmission latency for the VR users that access the RRHs. We also find that more VR users could cause higher round-trip latency due to the constrained resource.

Finally, we evaluate the uplink transmission latency as the averageskvaries, as shown in Fig. 11.In Fig.11,we consider a benchmark scheme,namely“equal uplink bandwidth,” in which the uplink transmission capacity is equally allocated to the VR users.It is observed that the uplink transmission latency increases as the averageskincreases. Considering the case of 10 VR users, up to 32.4% latency increase is created with the averageskincreasing from 0.14 to 0.18 Mb. We also find that the proposed Algorithm 1 always outperforms the equal uplink bandwidth scheme, which demonstrates the effectiveness of our proposed Algorithm 1.

5 Conclusions

In this study, a mobile virtual reality (VR) delivery framework in fog radio access networks was investigated, in which both the uplink and downlink transmissions were considered. Specifically, we characterized the round-trip latency and showed how it was determined by the communication, caching,and computation resource allocations. Then, a simple yet efficient algorithm was proposed to minimize the round-trip latency, while satisfying the practical constraints on caching,computation capabilities,and transmission capacity. Numerical results were provided to verify the effectiveness of our proposed algorithm.

Fig.10 Round-trip latency per VR user vs. downlink fronthaul capacity RF for RUmaxm=0.2 Gb/s (M =1,K =6)

Fig. 11 Uplink transmission latency per VR user vs. average sk (CAm = 0.1 Gb, RUF = 0.06 Gb/s,RUmaxm=0.03 Gb/s)

Contributors

Tian DANG carried out the analysis of the resource allocation optimization and drafted the paper. Chenxi LIU modeled the system and designed the algorithms. Xiqing LIU performed the simulations and helped organize the paper. Shi YAN helped with the optimization analysis and simulations. Tian DAN and Chenxi LIU revised and finalized the paper.

Compliance with ethics guidelines

Tian DANG, Chenxi LIU, Xiqing LIU, and Shi YAN declare that they have no conflict of interest.