1 Resource Constrained Vehicular Edge Federated Learning with Highly Mobile Connected Vehicles

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Resource Constrained Vehicular Edge Federated

Learning with Highly Mobile Connected Vehicles

Md Ferdous Pervej, Graduate Student Member, IEEE, Richeng Jin, Member, IEEE, and Huaiyu Dai, Fellow, IEEE

Abstract—This paper proposes a vehicular edge federated

learning (VEFL) solution, where an edge server leverages highly

mobile connected vehicles’ (CVs’) onboard central processing

units (CPUs) and local datasets to train a global model. Con-

vergence analysis reveals that the VEFL training loss depends

on the successful receptions of the CVs’ trained models over the

intermittent vehicle-to-infrastructure (V2I) wireless links. Owing

to high mobility, in the full device participation case (FDPC),

the edge server aggregates client model parameters based on a

weighted combination according to the CVs’ dataset sizes and

sojourn periods, while it selects a subset of CVs in the partial

device participation case (PDPC). We then devise joint VEFL

and radio access technology (RAT) parameters optimization

problems under delay, energy and cost constraints to maximize

the probability of successful reception of the locally trained

models. Considering that the optimization problem is NP-hard,

we decompose it into a VEFL parameter optimization sub-

problem, given the estimated worst-case sojourn period, delay

and energy expense, and an online RAT parameter optimization

sub-problem. Finally, extensive simulations are conducted to

validate the effectiveness of the proposed solutions with a prac-

tical 5G new radio (5G-NR) RAT under a realistic microscopic

mobility model.

Index Terms—Connected vehicle (CV), energy efﬁciency (EE),

federated learning (FL), vehicular edge network (VEN).

I. INTRODUCTION

WHILE modern connected vehicles (CVs) are an essen-

tial part of an intelligent transportation system (ITS),

higher automation on the road demands more exploration.

One way to achieve higher automation is to put more sensors

on the onboard units of these CVs to facilitate real-time

sensing and onboard computing [1]. Machine learning (ML)

has shown its potential in various ITS applications, such as

object detection, trafﬁc sign classiﬁcation, congestion predic-

tion, velocity/acceleration prediction, etc., to name a few [2].

However, the sensing capabilities and onboard computation

powers of CVs are still limited. Moreover, ofﬂoading raw data

to an edge server raises immense privacy risks and requires

humongous bandwidth. Therefore, a privacy-preserving dis-

tributed ML solution is urgently needed for modern vehicular

This research was supported in part by the Zhejiang Provincial Natural

Science Foundation of China under Grant No. LQ23F010021, in part by the

Ng Teng Fong Charitable Foundation in the form of ZJU-SUTD IDEA Grant

under Grant No. 188170-11102, in part by the National Key Research and

Development Program of China under Grant 2018YFB1801104, and in part by

the US National Science Foundation under grants CNS-1824518 and ECCS-

2203214. (Corresponding author: Richeng Jin.)

M. F. Pervej and H. Dai are with the Department of Electrical and

Computer Engineering, NC State University, Raleigh, NC 27695, USA (e-

mails: {mpervej, hdai}@ncsu.edu).

R. Jin is with the Zhejiang–Singapore Innovation and AI Joint Research

Lab, the Department of Information and Communication Engineering, Zhe-

jiang University, Hangzhou, China, 310007, and also with Zhejiang Provin-

cial Key Lab of Information Processing, Communication, and Networking

(IPCAN), Hangzhou, China, 310007 (e-mail: richengjin@zju.edu.cn).

edge networks (VENs) to ensure higher automation levels

on the road where the moving CVs must make operational

decisions swiftly.

With its privacy-preserving and distributed learning abilities,

federated learning (FL) [3] is, thus, an ideal solution for VENs.

Note that FL follows the parameter server paradigm, where the

server distributes a global ML model to the clients, who then

perform local model training in parallel on their devices and

send their locally trained model parameters to the server [4].

Thus, the CVs do not need to share their raw data, i.e., data

remains private. Besides, system and data heterogeneity of the

CVs can be handled by carefully designing model aggregation

rules and local training loss functions.

Unlike traditional stationary clients, however, devising a

vehicular edge FL (VEFL) framework is challenging for mul-

tiple reasons. Firstly, limited radio coverage makes the sojourn

periods of the highly mobile CVs very short. Therefore,

the CVs can perform local model training only for a few

iterations before moving out of the coverage area. Secondly,

modern CVs’ onboard central processing units (CPUs) are

responsible for many operational computations. Besides, the

CVs are owned by different clients who may not readily join

the FL process. Therefore, a service level agreement (SLA)

between a CV that wishes to utilize its limited resource for

FL model training and the edge server should exist. Note that

an SLA is a commitment between the server and the CV that

both parties agree to uphold. Thirdly, a proper radio access

technology (RAT) solution is required since the server can

aggregate trained models only if these models are successfully

received at the aggregation time. However, the high mobility of

the CVs makes communication over the intermittent wireless

vehicle-to-infrastructure (V2I) links even more challenging.

As such, we shall carefully orchestrate the interplay between

the server and the RAT solution to perform VEFL. Moreover,

the underlying RAT requires mandatory resource management.

Finally, system and data heterogeneity among the CVs is a

norm in VENs since automotive makers produce products with

different features.

A. Related Work

We have seen many remarkable contributions to joint FL and

wireless network parameter optimizations [4]–[8]. However,

these studies did not consider the fundamental constraint in

VEN, i.e., client’s high mobility, which results in a very short

sojourn period. Some recent works [9]–[18] also considered

FL for different tasks in VENs. However, only a handful of

studies [19]–[22] addressed the constraints present in VENs.

Zeng et al. proposed a dynamic federated proximal algorithm

to design a controller for autonomous vehicles in [19]. The

arXiv:2210.15496v4 [eess.SY] 23 Apr 2023

authors considered moving connected and autonomous vehi-

cles as FL clients and devised their algorithm accounting for

the communication and computation delay constraints. The

communication delay was derived using a simplistic channel

model with one channel realization. Each vehicle had a unique

orthogonal resource block to ofﬂoad its trained model to the

server.

Xiao et al. jointly consider vehicular client selection, trans-

mission power selection, CPU frequency selection and local

model accuracy optimization under delay and energy con-

straints in [20]. More speciﬁcally, the authors assumed data

quality is known, and optimized local model precision before

the server performs global aggregation. Besides, the authors

considered a transmission control protocol/internet protocol

based channel model with a unique radio resource for each

client for ofﬂoading its trained model. Taik et al. considered a

clustered vehicular FL in [21]. The authors used the traditional

federated averaging (FedAvg) algorithm, where the vehicular

cluster head performed model aggregation from the cluster

members and then forwarded the aggregated model to the

server. Liu et al. used a proximal FL algorithm, which is

very similar to the widely used FedProx algorithm [23], for

vehicular edge computing in [22]. The impact of mobility and

wireless links was not considered in [22].

Asynchronous communication and model aggregation

mechanisms were also proposed in some recent works [24]–

[26]. More speciﬁcally, [24] considered a semi-synchronous

FL for the Internet of vehicles, where the authors dynami-

cally adjusted the server’s waiting time between two global

rounds in proportion to the total participating clients. A

hierarchical asynchronous FL was considered in [25]. A semi-

asynchronous hierarchical FL for transportation system was

proposed in [26]. Particularly, [26] assumed a synchronous

model aggregation for the local-edge level and a semi-

synchronous model aggregation for the edge-cloud level.

B. Motivations and Our Contributions

While [9]–[18] showed the efﬁcacy of FL in different vehicular

applications and [19]–[22] addressed some typical resource-

constraints in VENs, these studies had their own limits.

Particularly, due to the intermittent wireless V2I links, VEFL

is not as straightforward as broadcasting the global model

and then aggregating locally trained model parameters under

perfect wireless communication links between the server and

clients. A practical RAT, such as the 5G new radio (5G-NR),

is required for the parameter server to broadcast the global

model in the downlink and then receive the model from the

vehicular clients in the uplink. Moreover, the parameter server

must devise the VEFL strategy to accommodate the underlying

RAT’s characteristics. As such, a joint study should address

the constraints of the parameter server, mobile clients and the

underlying RAT. It is worth pointing out that 3rd generation

partnership project (3GPP) release 18 will include different

artiﬁcial intelligence and ML solutions for its data-driven

network applications [27]. Besides, different work groups

within 3GPP are working actively to include ML in the next-

generation standard. Moreover, ML-application-based RAT

design is also a part of standardization for release 18 [28].

In this work, we, therefore, present a VEFL framework

with a joint study of the impact of the mobility of the

clients, i.e., the CVs, with a practical 5G-NR-based RAT

solution and under strict delay, energy, computation resource,

radio resource and cost constraints. More speciﬁcally, our

contributions are summarized as follows:

•Leveraging 5G-NR RAT, we propose a VEFL framework

where an edge server utilizes a ﬁxed bandwidth part

(BWP) [29] and an uplink heavy frame structure to re-

ceive the locally trained ML models over the intermittent

V2I links from highly mobile CVs which participate in

the model training and charge the server based on SLAs.

•We consider a full device participation case (FDPC) and

a more practical partial device participation case (PDPC),

where all CVs and only a subset of CVs participate in the

model training, respectively. As FDPC is less ﬂexible, to

combat high mobility, i.e., short sojourn period, the server

aggregates local model parameters based on a weighted

combination reﬂecting the CVs’ expected sojourn periods

and dataset sizes.

•In both cases, corresponding joint VEFL and RAT param-

eter optimization problems are formulated to maximize

the probability of successful trained models reception

at the server under strict delay, energy and cost con-

straints. Since channel state information (CSI) can vary

in each slot and is unknown beforehand, the original

joint problem is decomposed into a VEFL parameter

optimization sub-problem, given the upper bounds of the

communication delay, energy expense and cost, and a

RAT parameter optimization sub-problem that aims to

maximize long-term energy-efﬁciency (EE).

•The non-convex VEFL parameter optimization sub-

problems are solved using standard relaxations and the

difference between convex (DC) approach. The fractional

non-convex long-term EE optimization problem is ﬁrst

transformed into a tractable form using the Dinkelbach

method, which is further converted into a per-slot online

optimization problem leveraging Lyapunov drift-plus-

penalty-based stochastic optimization.

•Finally, using simulation of urban mobility (SUMO)

[30], we simulate a microscopic mobility scenario in

Downtown Raleigh, NC, USA, and use four popular

ML datasets to show the effectiveness of our proposed

solutions.

The rest of the paper is organized as follows: Section II

introduces our proposed VEFL system model. Section III

provides the convergence analysis and our joint problem for-

mulation. Section IV presents the solution to the problem. We

discuss our simulation results in Section V. Finally, Section

VI concludes the paper.

II. VEFL SYSTEM MODEL

We consider a VEN conﬁned within a region of interest (RoI),

as shown in Fig. 1. The edge server—embedded into the next

generation Node B (gNB)—wishes to perform a distributed

ML task leveraging the moving CVs’ onboard CPUs and local

datasets. Similar to [31], [32], SLAs between the CVs and the

Fig. 1. Vehicular FL system model

edge server, which require the edge server to pay the CVs for

contributing to the VEFL task, are assumed1. Note that the

terms server and gNB are used interchangeably when there

is no ambiguity. We consider a general learning task, which

can be object detection, trafﬁc sign classiﬁcation/detection,

velocity/acceleration prediction, trafﬁc congestion prediction,

travel time prediction, fuel consumption prediction, etc., for

our VEFL. Moreover, the VEN operates in a discrete time-

slotted manner. The slots are denoted by T={t}|T|

t=1. Partic-

ularly, the gNB has a ﬁxed BWP for the VEFL to provide

radio connectivity to the moving client CVs. The server can

only leverage the trained ML model on the CVs’ onboard

CPUs within the communication range of the gNB. Denote

the communication radius of the gNB by r.

The CVs enter and leave the RoI following some distribu-

tions, i.e., the CV set may not be the same in all time slots

due to high mobility. Denote the CV set during time slot t

by Vt={v}Vt

v=1. Moreover, the server knows the maximum

possible velocity on the roads inside this RoI. Denote the

maximum possible velocity of the RoI by umax. Assuming the

gNB is located at the center of the coordinate system of the

RoI, its coverage circle is given by

x2+y2=r2,(1)

where xand yare the horizontal and vertical coordinates,

respectively.

A. CV Mobility Model

Denote the coordinate of v∈Vt, during slot t, by

xloc

v(t),yloc

v(t)as shown in Fig. 2. Also, let us denote CV

v’s velocity and acceleration during time tby uv(t)and

˙uv(t), respectively. We consider the widely used car-following

mobility (CFP) model, known as the intelligent driver model

(IDM) mobility model, to model microscopic mobility for the

CVs [35]. In IDM, the mobility is controlled by the following

instantaneous acceleration equation [35]:

˙uv(t) = ¯

u11−[uv(t)/umax]4−¯

u1[s∗

v/∆dv(t)]2,(2)

where ¯

u1is the maximum acceleration or a constant that

depends on the design. ∆dv(t)is the front bumper to the back

1However, the implementation of SLAs in a practical VEN implicates the

core network and the user plane and control plane protocol stacks [33], [34],

which are beyond the scope of this paper.

bumper distance of CV vand the vehicle directly in front

of it, during time t. Furthermore, s∗

vis the desired dynamical

distance and is calculated as follows:

s∗

v=ssaf +uv(t)·tdst + [uv(t)·∆uv(t)]/(2√¯

u1¯

u2),(3)

where ssaf is the safety distance between vand the CV directly

in front of it, tdst is the desired time headway that gives the

minimum possible time to the CV directly in front of v,∆uv(t)

is the velocity difference between vand the vehicle in front of

it, and ¯

u2is a positive number that deﬁnes the comfortable

braking deceleration. Note that, in (2), the ﬁrst term, i.e.,

u11−[uv(t)/umax]4, is the instantaneous acceleration of CV

v, which essentially is the desired acceleration on a free road.

The second term is the deceleration induced by the CV in

front of it [35].

Moreover, we assume the server does not need to know the

entire trajectory of the vehicle. Therefore, the server will only

estimate the guaranteed sojourn period tsoj

v,t. To ﬁnd tsoj

v(t),

ﬁrst, we write the horizontal and vertical lines that intersect

the gNB’ radio coverage circle boundary as follows:

y=yloc

v(t),(4) x=xloc

v(t).(5)

Note that (4) and (5) are represented by the purple and

orange color chords, respectively, in Fig. 2. We can then

ﬁnd the x-coordinates of the gNB coverage boundary

by solving (1) and (4) as xbnd,1

v(t) = qr2−yloc

v(t)2and

xbnd,2

v(t) = −qr2−yloc

v(t)2. As such, we can ﬁnd the

horizontal distances of these boundary points and the current

location of the CV (xloc

v(t),yloc

v(t)) as dy

x1=xloc

v(t)−xbnd,1

v(t)

and dy

x2=xloc

v(t)−xbnd,2

v(t). Similarly, we can ﬁnd the y-

coordinates of the gNB coverage boundary by solving (1) and

(5) as ybnd,1

v(t)=qr2−xloc

v(t)2and ybnd,2

v(t)=−qr2−xloc

v(t)2.

Then, the corresponding vertical distances of these

boundary points and the current location of the CV

(xloc

v(t),yloc

v(t)) are calculated as dy1

x=yloc

v(t)−ybnd,1

v(t)

and dy2

x=yloc

v(t)−ybnd,2

v(t).

As such, from time t, the minimum expected sojourn period

of vunder the gNB’s coverage is bounded below by

tsoj

v(t)≥mindy

x1,dy

x2,dy1

x,dy2

x/umax.(6)

Note that (6) is based on a linear trajectory and uniform

velocity umax, which is the worst-case estimation of the sojourn

period of the CV.

B. V2I Radio Access Technology Model

We assume that the VEN operates in TDD mode and has

a ﬁxed W Hz BWP for providing RAT connectivity over

the universal mobile telecommunications system (UMTS) air

interface (Uu interface) for the VEFL. Note that TDD facili-

tates channel reciprocity and thus offers less control overhead.

Besides, we assume that all transceivers can mitigate the

Doppler effect satisfactorily2. For model distribution in the

downlink, as the gNB sends the same data to all selected

CVs, it can use the entire spectrum and high transmission

power to broadcast the model. Therefore, similar to [4], [8],

2Although Doppler shift is a well-known problem, if the underlying RAT

mitigates it adequately, it is less critical for our proposed VEFL framework.

,

(

(), 

())

y = y

(t)

x = x

(t)

d



d



d



d



y

,

Fig. 2. Finding coverage boundary points

Symb 0 Symb 1 Symb 2 Symb 3 Symb 4 Symb 5 Symb 6 Symb 7 Symb 8 Symb 9 Symb 10 Symb 11 Symb 12 Symb 13

DL Fexible UL UL UL UL UL UL UL UL UL UL UL UL

1 Slot = 14 OFDM Symbols

Fig. 3. OFDM Symbols within a slot [36]

= 1 = 2 = 3 = 4 = 5 = 6 = 7 = 8 = 9 =10 =11 =12

==

1TTI =

𝑡(k)= ( ̆

k+1 -̆

k) × 

1= 3 ̆

2= 10

Fig. 4. Time slot orchestration in the proposed VEFL

[19], we ignore the downlink communication. The W Hz

bandwidth is divided into orthogonal physical resource blocks

(pRBs). Denote the pRB set of the allocated BWP by the set

Z={z}Z

z=1. Note that due to orthogonal pRBs, there is no

intra-cell interference. Besides, as we consider a single cell,

the proposed VEN is interference-free.

The gNB considers the 5G-NR frame structure in which the

radio frame is 10 ms long with 10 subframes. Within each 1 ms

subframe, there are 2¯nslots, where ¯nis the sub-carrier spacing

numerology [36]. The pRB allocation granularity is the slot,

i.e., the pRBs can be allocated to different users in each slot t.

Each slot carries 14 OFDM symbols in the time domain and

12 sub-carriers in the frequency domain. Moreover, the OFDM

symbols can be conﬁgured based on the duplexing mode. As

this is uplink-heavy transmission, we consider a downlink-

control uplink transmission slot format as shown in Fig. 3. As

such, we consider the effective uplink data rate per slot, which

will be ﬂeshed out in what follows.

We consider a single-input-multiple-output (SIMO) case,

where the gNB has Nantennas, and each CV has a single

antenna. Note that our framework can also be extended to

other multiple-antenna communication models3. During slot

t, denote the channel between CV vand the nth antenna of

the gNB over pRB zby hn,v,z(t). Then, we denote the entire

channel response at VU vfrom the gNB over PRB zas

hv,z(t) = pψv(t)ρv(t)˘

hv,z(t)∈CN×1,(7)

where pψv(t),ρv(t)and ˘

hv,z(t) = [h1,v,z(t),...,hN,v,z(t)]T∈

CN×1are large scale fading, log-Normal shadowing and fast

fading channel responses from the Nantennas, respectively.

The path losses are modeled based on the urban macro (UMa)

model [37].

To that end, denote CV v’s unit powered intended signal for

the gNB by sv(t)∈Cand allocated uplink transmission power

for pRB zby P

v,z(t). Assuming receiver beamforming vector

gv,z(t)∈CN×1, the effective uplink signal received at the gNB,

over pRB z, is calculated as follows:

yv,z(t) = Iv,z(t)·qP

v,z(t)gv,z(t)Hhv,z(t)sv(t) + η,(8)

where Iv,z(t)∈ {0,1}is an indicator function that takes value

1 when pRB zis allocated to CV v, and η∼CN(0,ς2)is the

circularly symmetric zero mean Gaussian distributed random

variable with variance ς2.

3However, the TDD-based massive MIMO requires rigorous channel esti-

mation/equalization, beam management, etc., which deserve separate studies.

Then, we calculate the received signal-to-noise ratio (SNR)

at the gNB for CV v’s uplink transmission as follows:

Γv,z(t) = Iv,z(t)·P

v,z(t)gv,z(t)Hhv,z(t)2/(ως 2),(9)

where ωis the pRB size. The gnB can conﬁgure CV-speciﬁc

CSI reference signal (RS) to estimate the channels. Since

5G-NR has the ﬂexibility of conﬁguring CSI-RS periodically,

semi-persistently or aperiodically and may also perform up-

link channel information multiplexing on the physical uplink

shared channel [38], this work primarily focuses on the overall

VEFL framework considering CSI is known at the gNB4.

Therefore, the gNB can use maximal ratio combining receiver

beamforming to get gv,z(t) = hv,z(t)/khv,z(t)k, which gives the

following uplink SNR over pRB z.

Γv,z(t) = (Iv,z(t)·P

v,z(t)khv,z(t)k2)/(ως 2).(10)

To this end, we can calculate the achievable data rate at the

gNB from CV v’s uplink as follows:

rv(t) = ω(1−υ)·Iv(t)∑Z

z=1Eh[log2(1+Γv,z(t))],(11)

where Iv(t)∈{0,1}is an indicator function that takes value 1

when CV v∈Vtis scheduled for transmissions in slot tand the

expectation is over the channel hv,z(t). Besides, υis the loss

due to control signaling overhead. For our case, if the ﬂexible

symbol in Fig. 3is allocated for uplink, we set υ=1/14.

Moreover, if it is not assigned to uplink, we set υ=2/14.

C. Preliminaries of VEFL

Denote the server’s global ML model by ω

ω. Denote the dataset

available at CV vby Dv={xi,yi}|Dv|

i=1, where xiand yiare the

ith sample feature and the corresponding label, respectively.

Therefore, during time t, the entire dataset can be denoted as

Dt={Dv}Vt

v=1. The edge server aims to optimize

min

ωF(ω

ω) = ∑Vt

v=1pvfv(ω

ω),(12)

where pv∈[0,1]is the linear combination weight for CV v

with ∑Vt

v=1pv=1. While the typical FedAvg set pv=|Dv|/|Dt|

[3], we will explore more on how to properly set these weights

in what follows. Besides, fv(ω

ω)is the local empirical loss

function of CV v.

The server distributes the global model during the VEFL

global rounds k=1,...,Kas shown in Fig. 4. Denote the slots

corresponding to the global rounds by the set Tg={˘

tk}K

k=1,

where ˘

t1represents the VEN slot tat which k=1. For

4Channel estimation delay is a part of the RAT and is less critical for our

proposed VEFL framework as the server only uses the worst-case estimated

channel, discussed in Section IV, to determine the approximate upper bound

for the uplink model ofﬂoading delay.

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1ResourceConstrainedVehicularEdgeFederatedLearningwithHighlyMobileConnectedVehiclesMdFerdousPervej,GraduateStudentMember,IEEE,RichengJin,Member,IEEE,andHuaiyuDai,Fellow,IEEEAbstractThispaperproposesavehicularedgefederatedlearning(VEFL)solution,whereanedgeserverleverageshighlymobileconnectedvehicles...

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1 Resource Constrained Vehicular Edge Federated Learning with Highly Mobile Connected Vehicles

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