Content uploaded by Yaru Fu

Author content

All content in this area was uploaded by Yaru Fu on Apr 21, 2021

Content may be subject to copyright.

1

Caching Efﬁciency Maximization for

Device-to-Device Communication Networks: A

Recommend to Cache Approach

Yaru Fu, Lou Sala¨

un, Xiaolong Yang, Wanli Wen, and Tony Q. S. Quek

Abstract—Edge side caching assisted device-to-device (D2D)

communication has been acknowledged as a promising technique

to alleviate the heavy burden of backhaul transmission link and

to reduce the network latency. However, the effectiveness of

caching strategies at the network edge is highly dependent on

the distribution of individual user’s content preference. To fully

attain the beneﬁts of edge caching, some proactive mechanisms

shall be considered. Among which, recommendation performs

noticeably well due to its capability of reshaping the content

request probabilities of different users, which in turn affects

the cache decision signiﬁcantly. In this work, we quantitatively

investigate how recommendation can be applied to enhance

the caching efﬁciency of D2D enabled wireless content caching

networks. And for that, the cache hit ratio maximization problem

for a generic network model is formulated taking into account

the requirements of each user’s personalized recommendation

quality, recommendation quantity and cache capacity. Then, we

show that the optimal recommendation and caching policies

which jointly maximize the cache efﬁciency is NP-hard to com-

pute. Further, a time-efﬁcient sub-optimal algorithm is designed,

which works in an iterative manner and has provable convergence

guarantee as well as polynomial time complexity. Monte-Carlo

simulation results demonstrate the convergence performance of

our proposed joint decision algorithm and its cache efﬁciency

improvements compared to extensive benchmarks.

Index Terms—Content caching, device-to-device (D2D) com-

munications, caching hit ratio, recommendation mechanism, NP-

hardness.

This work was supported in part by the Hong Kong President’s Adviso-

ry Committee on Research and Development (PACRD) under Project No.

2020/1.6, in part by the National Natural Science Foundation of China (NSFC)

under Grants No. 61971239 and No. 61771427, in part by the National

Key Research and Development Project under Grant No. 2020YFC1511701,

in part by the National Research Foundation, Singapore and Infocomm

Media Development Authority under its Future Communications Research

& Development Programme. Any opinions, ﬁndings and conclusions or

recommendations expressed in this material are those of the author(s) and

do not reﬂect the views of National Research Foundation, Singapore and

Infocomm Media Development Authority. (Corresponding author: Xiaolong

Yang.)

Y. Fu is with the School of Science and Technology, The Open University

of Hong Kong, Hong Kong, 999077, China (Email: yfu@ouhk.edu.hk).

L. Sala¨

un is with Bell Labs, Nokia Paris-Saclay, 91620 Nozay, France (e-

mail: lou.salaun@nokia-bell-labs.com).

X. Yang is with the School of Information and Communication Engineering,

Beijing Information Science and Technology University, Beijing, 100101,

China, and with the Key Laboratory of Modern Measurement and Control

Technology, Ministry of Education, Beijing Information Science and Technol-

ogy University, Beijing 100101, China. (e-mail: xiaolongyang@bistu.edu.cn).

W. Wen is with the College of Communication Engineering, Chongqing

University, Chongqing 400044, China (e-mail: wanli wen@cqu.edu.cn).

Tony Q. S. Quek is with the Dept. of Information Systems Technology and

Design, Singapore University of Technology and Design, Singapore (e-mail:

tonyquek@sutd.edu.sg).

I. INTRODUCTION

The rapid evolution of wireless communication technologies

as well as the termination techniques has trigged the explosive

growth of mobile data trafﬁc. In accordance with the cutting

edge Ericsson mobility report [1], the mobile data trafﬁc per

month is forecast to increase to 160 Exabytes (EBs) in 2025

from 38 EBs each month in 2019, pushing the endurance

to the limits of our current cellular networks architecture.

To address this issue, caching at the network edge side has

been acknowledged as one of the promising solutions [2],

[3]. More precisely, the popular contents can be stored by

the cache entities in mobile terminals and shared with neigh-

bor subscribers via device-to-device (D2D) communications,

making a substantial part of preferred content items ubiquitous

to the consumers. From this point of view, the construction

of the complicated wireless transmission links is not always

necessary for each content requesting. As a consequence, the

average content delivery latency and the backhaul transmission

load are reduced and alleviated. In recent years, D2D caching

networks have received extensive attentions [4]–[13]. To be

more speciﬁc, the performance comparison of D2D caching

and small cell base station (BS) caching is investigated in [4]

with the information of content popularity and spatiotemporal

request correlation taken into account. Thereof, the authors

reveal that D2D caching provides higher opportunity to serve

more users requests simultaneously via short-distance cache-

enabled D2D communication, especially when the user density

is high. In [5], the social-aware rate based content sharing

mode selection scheme for D2D caching system is studied

to maximize the weighted link capacity. The formulated op-

timization problem has been transformed to a submodular

welfare problem, which was solved by a distributed algorithm.

The joint cache placement and content delivery is investigated

in [6] to maximize the content successful ofﬂoading ratio.

Simulation results shown the efﬁcacy of joint optimization.

The authors in [7] investigate the cache placement for D2D-

assisted cellular networks to maximize the achievable caching

revenue by a multi-winner auction approach. Thereof, several

decision-making algorithms with different time complexities

are developed. It is explicitly demonstrated by [8] that with

the prior information of users’ preference distribution, the

optimized caching placement for D2D networks achieves

signiﬁcant improvement on content access delay and trafﬁc

ofﬂoading gain. It is noteworthy that the contents can be

partially cached in [8], which is totally different from the

2

caching mechanism in [4]–[7], [9]–[13], where the caching

decision indicator of each item is a Boolean variable. Since

the cache placement algorithms for D2D caching network

always have huge computational complexity due to the large

size of users set and the contents library, clustering algorithms

are adopted in [9] and [10] to reduce problem’s dimensions

via bundling users into different small-size groups. With the

obtained clusters, cache decision is made to optimize various

objectives. Speciﬁcally, [9] targets at minimizing the average

content delivery latency while [10] aims to maximize the cache

hit ratio of users within each cluster. Recent works [11]–[13]

apply machine learning techniques into D2D caching networks

to do cache placement and user preference estimation.

Recommendation, on the other hand, has the capability of

reshaping the content request probabilities of different users,

which deeply inﬂuence the caching efﬁciency. It was precisely

demonstrated that the video view of YouTube and Netﬂix

induced by recommendation account respectively for 50% and

80% of the total views [14]–[16]. Thereby, considering caching

and recommendation independently cannot reach their full

beneﬁts. Recommendation and caching are synergistic with

each other. Indeed, recommendation inﬂuences the content

request behaviors of users, which in turn affects the cache

decision making. In a nutshell, to construct user-friendly and

network-friendly wireless content caching systems, a coop-

erative working mechanism should be considered between

cache decision making and recommendation optimization.

Nevertheless, in existing wireless architectures, the recom-

mendation and content caching are in the charge of two

independent entities, i.e., the third-party content provider and

the telecommunication operators, respectively. Fortunately, the

fusion of roles like content providers and telecom operators

is speeding up and becomes more and more evident, making

the joint optimization become a reality. Chatzieleftheriou et

al. in [17] ﬁrst propose the application of recommendation in

wireless content caching networks and consider the interplay

between caching and recommendation. This idea is extended

to generic cache-assisted small cell networks in [18], and it

is demonstrated that through recommendation-aware caching,

higher cache hit ratio can be obtained. Recognizing that users’

association affects the cache hit, a joint user association,

caching, and recommendation decision-making problem is

investigated in [19]. Simulation results show the validity

of user association in terms of improving system’s cache

efﬁciency. Later, many studies are made to investigate the

joint recommendation and cache optimization under extensive

performance metrics [20]–[25]. To be more speciﬁc, the suc-

cessful ofﬂoading probability maximization problem is studied

via jointly optimizing caching at the BS and personalized

recommendation at users in [20], [21]. Thereof, the authors

characterize the successful ofﬂoading ratio as the probability

that a requested ﬁle of a user can be retrieved from the content

provider triumphantly, i.e., the received signal-to-interference-

ratio (SIR) is no less than a pre-determined threshold. In [22],

[23], the cache hit ratio maximization problem for content

caching based networks with recommendation is investigated.

Speciﬁcally, in [22], a cache-aware recommendation algorithm

is proposed for the current economic ecosystem, wherein

the collaboration between network and content provider was

not required. Moreover, departing from the assumption of

hard cache hits in various existing works, [23] introduces

the concept of soft cache hits, in which, some related and

locally cached items will be recommended to user given that

his/her requested contents are not available. It is shown that

soft cache hit achieves enhanced caching gains. In contrast

to [17]–[23], where single content request mode is adopted,

the authors of [24] optimized the recommendation to obtain

the minimum caching cost of a sequential-content-access

based caching network. Nevertheless, the cache placement

optimization is neglected in [24], which is done by [25].

All the aforementioned works [17]–[25] focus on scenarios

where caching is conducted at the BSs. For user side caching,

[26] studies the data ofﬂoading ratio maximization problem

for cache enabled mobile social networks, whereas, cache

placement can only be implemented at important users (IU),

which is deﬁned as the users who act as a helper to provide

contents for their adjacent subscribers. The authors applied the

notion of recommendation, in this case however, the effect of

recommendation mechanism on content request of users is not

quantitatively characterized in the problem formulation, as it

is done in this work.

In summary, new research is called to enable

recommendation-aware D2D-enabled wireless edge caching

networks. This motivates us to explore how recommendation

can be used to enhance the gains of caching approaches in

edge side cache networks with D2D communications. To the

best of our knowledge, investigating the caching efﬁciency

maximization problem for D2D enabled wireless content

caching systems from a perspective of recommend-to-cache

has never been addressed by existing works. We distinguish

the primary contributions of this work as follows:

•We consider a generic D2D communication assisted

wireless content caching networks, wherein the role of

content provider for each user is modeled through the

social-aware value, which is further characterized by the

preference similarity as well as the distance between two

distinct users.

•We quantitatively illustrate how recommendation and

caching affect the system caching efﬁciency mathemat-

ically. Based on it, the caching efﬁciency maximization

oriented joint recommendation and caching problem is

formulated with the consideration of individual user’s

recommendation quality, recommendation quantity and

cache capacity requirements.

•We reveal the NP-hardness of the formulated maximiza-

tion problem with rigorous mathematical proof. To make

it tractable, we decouple the NP-hard problem into two

sub-problems and whereafter, two-side swapping oriented

algorithms are proposed to solve the sub-problems in

sequence. With the foregoing analysis, a time-efﬁcient

suboptimal solution is designed, which works in an

iterative manner and has provable convergence guarantee.

The computational complexity of the proposed algorithm

is scrupulously analyzed as well.

•Monte-Carlo simulation is implemented to validate the

3

D2D area

MBS

D2D area

Wireless

communication

link

User

D2D link

User

Cloud Server

Backhaul

link

Cache

Fig. 1. System model of the device-to-device (D2D) assisted wireless content

caching network. Thereof, users’ content requests are jointly determined by

their inherent preference as well as the system recommendation mechanism.

convergence performance of our designed algorithm and

highlight its caching efﬁciency enhancements when com-

pared to that of various baselines.

The rests of this paper are organized as follows: In Section

II, the architecture of our D2D assisted wireless content

caching network is introduced. Both the mechanisms on rec-

ommendation and the deﬁnitions on caching efﬁciency are

presented in Section III. Therein, the computing method of

social-aware value between D2D users is elaborated as well.

With the above mentioned preliminaries, the caching efﬁcien-

cy maximization oriented joint recommendation and caching

decision problem is formulated in Section IV. In Section V,

we reveal that the formulated maximization problem is NP-

hard with rigorous mathematical proof. To solve the intractable

problem efﬁciently, a time-efﬁcient sub-optimal algorithm is

designed in Section VI. Numerical results are presented in

Section VII to show the validity of our joint recommendation

and caching strategy. In the end, we summarize this work and

propose several possible future research directions.

II. SY ST EM MO DE L

In this section, we ﬁrst introduce the architecture of our

cache aided device-to-device (D2D) communication network.

Afterwards, the caching model at each subscriber is elaborated.

A. Network Description

As illustrated in Fig. 1, we consider a D2D assisted wireless

content caching system, in which a macro base station (MBS)

servers Kuniformly distributed users within its disk region.

It is assumed that the users have the capabilities of content

caching, i.e., each user is equipped with a cache entity of

different size. Denote by K={1,2, . . . , K}the index set of

all the subscribers. In addition, let Bkbe the cache capacity

of subscriber k, where k∈ K. Our system includes Ncontent

items, which can be distinct for different macro cells. Deﬁne

N={1,2, . . . , N }as the index set of all the items. For n∈

N, let Lnin bits denote the size of content n. Moreover, we

deﬁne D†

kas the index set of all users that are located within

user k’s D2D communication region, where k∈ K. Without

otherwise stated, in the following parts of this work, the set

D†

kof user kincludes kitself. Furthermore, we declare that

both the MBS and the users are equipped with single antenna.

Each user can request his/her intended content from its

local cache given that the requested content of user khappens

to be cached in its local storage, the construction of D2D

communication link or wireless communication link is not

needed. Otherwise, user kwill broadcast the request to its D2D

neighbors1. Suppose that some of the neighbors have this item

in their storages, user kwill download this content through the

neighbor that induces the largest social-aware value2via D2D

communication link instead of creating complicated wireless

channels with MBS. A wireless communication link will be

established between MBS and user kgiven that the intended

item is not cached by the local storage and all the possible

D2D providers of user k, i.e., this content will be retrieved

from the cloud server by MBS. To be more speciﬁc, after

receiving the requests from users, MBS ﬁrst downloads the

required contents from the cache of cloud content provider

and then feedbacks the items to the corresponding users.

It is noticeable that the communication between MBS and

the content servers is conducted via backhaul link. Besides,

it is assumed that the content provider’s servers can offer

any requested items from the users, which can be seen as a

backup content delivery mode. Intuitively, the cache enabled

D2D communication is capable of alleviating the workload of

backhaul links.

B. Caching at Users

In this subsection, we discuss the caching model at different

users. For k∈ K and n∈ N , deﬁne the binary indicator ck ,n

as the caching decision of user kin terms of content item n.

Speciﬁcally, ck,n = 1 means user khas item nin its cache

and ck,n = 0 otherwise. Under the cache size constraint, we

have

n∈N

ck,nLn≤Bk, k ∈ K.(1)

Before ending this section, we declare that the radio resource

adopted by D2D communication as well as that used by

wireless communication are orthogonal with each other. Since

the radio resource for wireless communication links as well

as the capacity of backhaul links are limited3, our system is

inclined to pose less content requests to the MBS via jointly

optimizing the caching deployment and the recommendation

decision for each subscriber. It is worth mentioning that even

though the cache capacity of mobile user is in general not very

large, the cache storage of all the mobile devices can generate

1Note that the D2D communication coverage region of a user is limited.

Thereby, the user can only communicate with its neighbors located within its

D2D region.

2The deﬁnition of social aware rate between two distinct users will be

speciﬁed in Section III-B

3Even though D2D communication also needs to use radio resource, the

communication cost is relative small due to its short distance when compared

to that of the communications between users and MBS, which always have

large distance-dependent path loss.

4

a large virtual and unitive cache space. How to reap the full

beneﬁts of the cache space is the emphasis of this article. In

addition, the radio resource management with ﬁxed caching

and recommendation decision for our system can be conducted

via following the conventional resource management schemes

in cache based D2D systems [27].

III. REC OM ME NDATI ON MECHANISM AND CACHE

EFFIC IE NC Y

In this section, we ﬁrst illustrate the notion of user pref-

erence distribution. Then, the concept of social-aware value

between users is introduced. Subsequently, we present our de-

signed recommendation mechanism4as well as the associated

content request distribution of each user, wherein the user-

speciﬁc recommendation quality is taken into account. Finally,

the considered effectiveness metric for our cache aided D2D

system is explained.

A. User Preference Distribution

We assume that the Ncontent items belong to Mthemes,

indexed by M={1,2, . . . , M}. It is important to note that

the Mthemes can be regarded as the feature sets that capture

different items in content library N. In addition, the deﬁnition

of theme can be diverse. For instance, the generalized concept

“video” can be classiﬁed as different categories, e.g., variety

entertainment, movie, talk show, music, etc. Nevertheless, the

category “movie” can be further divided into several sub-

themes, e.g., love, science ﬁction, comedy, animated cartoon,

history, and war movies, etc. The contents library in this work

can be either a main class or a distinct category. The speciﬁcs

of such classiﬁcation is not the main focus of this paper.

For n∈ N and m∈ M, deﬁne f†

n(m)∈[0,1] as the score

of item nin feature m, which represents how much item n

is correlate to theme m. For each content item, we normalize

these scores over all the themes and obtain the normalized

feature value of item non theme mas follows:

fn(m) = f†

n(m)

M

m=1 f†

n(m), m ∈ M.(2)

In addition, let fn= (fn(1), fn(2), . . . , fn(M)) be the feature

vector of item n.

Similarly, for user k, a feature vector over all the themes

is characterized as well. For k∈ K and m∈ M, let

f†

k(m)∈[0,1] represent the score of user kin category m,

which indicates how much user klikes the contents of theme

m. Thereby, we can obtain the feature vector of user k, which

is denoted by fk= (fk(1), fk(2), . . . , fk(M)), whose m-th

component is calculated as follows:

fk(m) = f†

k(m)

M

m=1 f†

k(m), m ∈ M.(3)

4Unless otherwise stated, the recommendation studied in this paper is

task-based [28]. More precisely, the recommendation is performed to return

optimized objective value in a speciﬁc task. Considering a time period of

a few hours or half of a day, the preference for each content per user can

be treated as ﬁxed. In other words, the individual user’s recommendation

decision, and the cache placement are done once for such interval of time to

optimize system’s caching efﬁcacy.

In this work, we assume that the aforementioned feature

vectors are prior information since they can be estimated

by content provision sites in accordance with the histori-

cal information of users’ contents requests and downloads,

as suggested by [11], [29], [30]. Particularly, via modeling

the user’s request behavior by probabilistic latent semantic

analysis (pLSA) and estimating the associated parameters by

the expectation maximization algorithm, the authors in [11]

predict the users’ preference distribution based on a Movielens

data set. Details are omitted here to avoid redundancy.

As far as the heterogeneity of different users, we assume

that each user has personalized preferences to the content items

in N. For k∈ K and n∈ N , deﬁne apref

k,n ∈[0,1] as the

preference of user kto item n, which can be acknowledged

as the probability that user kasks for item n. Based on [18],

the inherent preference of user kin terms of item ncan be

jointly modeled by the feature vectors of kand n, i.e., fkand

fn, respectively. We adopt in this work the same generation

procedure as in [18] to construct the individual preference

distribution of user kover all the contents. It is characterized

by the cosine similarity index of the aforementioned two

vectors fkand fn, and is expressed as follows:

˜apref

k,n =M

m=1 fk(m)fn(m)

M

m=1 (fk(m))2M

m=1(fn(m))2

, k ∈ K, n ∈ N .

(4)

We normalize the values of ˜apref

k,n over all the items in Nfor

each user k, where k∈ K. Then, the preference distribution

of user kin terms of content nis quoted below:

apref

k,n =˜apref

k,n

N

n=1 ˜apref

k,n

, n ∈ N ,(5)

where ˜apref

k,n is given in (4). For notation simplicity, apref

k=

(apref

k,1, apref

k,2, . . . , apref

k,N )is used to represent the preference dis-

tribution vector of user k, where k∈ K.

B. Social-aware Value

In practical D2D systems, the individual users are in general

intend to cache the content items that are ranked in their top

preferences. In other words, users are not willing to cache the

contents that are more attractive to other neighbor users but not

highly desired by themselves. This is reasonable, especially

when considering the selﬁsh nature of human behaviour. To

address this issue, in this work, we assume that user k

only provides possible D2D-oriented supports for its socially

connected users. For k∈ K, the socially-aware subscribers of

user kshould satisfy the following criteria:

i. Located within the D2D communication region of mobile

user k.

ii. The social-aware value associated with user kis no less

than a pre-determined threshold, which is denoted by ¯

Vk

for k∈ K. The threshold is chosen by the user itself,

which indicates how selﬁsh the user is.

The social-aware rate between user kand user k′, denoted by

Vk,k′, is characterized by two elements, namely the distance

between this pair of users and the preference correlation

5

User 1

1

2

3

4

5

5

4

1

3

2

User 2

1

2

3

5

4

User 3

ܸ

ଵǡଷ

User 4

2

3

1

4

5

ܸ

ଵǡସ

ܸ

ଷǡସ

ܸ

ଶǡଷ

Fig. 2. An example of socially-aware D2D communication system with

4 users and 5 contents, where the table represents the contents preference

ranking of each subscriber.

of these two users, which are deﬁned as dk,k′and Sk,k′,

respectively. With above deﬁnitions, Vk,k′is given as follows:

Vk,k′,Sβ

k,k′/dα

k,k′,(6)

where k, k′∈ K.αand βrepresent the weights of preference

similarity and the distance, respectively. In addition, they

satisfy α+β= 1. It is worth noting that, for user k′, the

shorter distance to user kand the higher preference correlation

with user k, the larger value of social-aware rate Vk,k′. An

example with 4 users and 5 contents is illustrated in Fig. 2.

From which, it is easy to see that V1,3is larger than V2,3due

to the shorter distance and higher similarity between user 1

and user 3 when compared to that between user 2 and user 3.

In this work, we apply the cosine similarity as in [31] to

determine the preference correlation between users kand k′,

which is quoted below

Sk,k′,apref

kapref

k′

||apref

k|| × ||apref

k′||,(7)

where ||x|| indicates the l2-norm of vector x.

Since user kcan only receive contents from the subscribers

that are socially correlated with himself or herself via D2D

communications, we deﬁne the social neighbor set of user k

as Dk. With aforementioned analysis, we have

Dk={k′|k′∈ D†

k,and Vk,k′≥¯

Vk′}, k ∈ K.(8)

C. Recommendation Model

As above mentioned analysis, each user has an inher-

ent preference distribution to the content items in N, i.e.,

apref

k, where k∈ K. Each user will request its desired

contents following this distribution without other external

factors, e.g., recommendation. Otherwise, the requests will be

jointly determined by both the inherent preference and the

recommendation mechanism. In the following paragraph, the

recommendation model used in this article is introduced.

Given that the system conducts recommendations, the con-

tent request probability of each user will be deﬁnitely affected,

as discussed in [14]–[16]. Nevertheless, the investigation on

how the recommendation mechanism quantitatively affects the

content request of users is still in its infancy due to the

high complexity of human behavior. The authors in [18],

[32] have proposed some intuition or experiment oriented

methods. To be more speciﬁc, in [18] the ultimate content

request distribution of each user is designed as a convex

combination of the individual inherent preference distribution

and the recommendation probability distribution. Meanwhile,

the authors in [32] mapped the recommendations for user k

to a new distribution denoted by arec

k,n, where n∈ N , and

the request probability of user kon item nis shaped as

max{arec

k,n, apref

k,n}. The recommended items for each user have

boosted request probabilities while the request probabilities

of the non-recommended items are decreased to guarantee

the request distribution remains normalized in the above

discussed two methods. In reality, the users may reject the

recommendations, especially when they do not identify the

quality of the recommended contents before they consume the

items. To characterize this feature, in this work, we follow

the model introduced in [17], and widely used, e.g. in [20],

[21]. We assume that user kaccepts the recommendations

with a probability denoted by xk∈[0,1]. In this aspect,

the rejection probability of user kto the recommendations

is (1 −xk)∈[0,1]. In this work, it is assumed that xkis

a prior information and different mobile users have different

values of xkdue to their heterogeneities in personality.

D. User Content Request Distribution

In the subsection, we reveal how recommendation affects

the content request probability of each subscriber mathemat-

ically by following the footsteps in [17]. For k∈ K and

n∈ N , deﬁne rk,n ∈ {0,1}as the binary indicator to

represent whether content nis recommended to user kor not.

In particular, rk,n = 1 if the content item nis recommended

to user kand 0 otherwise. In addition, let Rkbe the index

set of all the items that have been recommended to user k.

Therein, the cardinality of Rkis assumed to be Rk. It is

notable that Rkcan be taken as the recommendation quantity

of user k. This kind of setting is necessary, especially for the

screen size limited customers, e.g., mobile phones, iPad and

lap-top, etc. Since scrolling down for a long recommendation

list is not user friendly. Besides, we deﬁne areq

k,n as the

ultimate request probability of user kwith respect to item

nthat is jointly determined by its inherent preference as well

as the recommendation mechanism. Speciﬁcally, the request

probability of user kto the recommended item n∈ Rkis

expressed as follows:

ˆareq

k,n =rk,n apref

k,n

j∈Rkapref

k,j

=rk,napref

k,n

j∈N rk,j apref

k,j

,(9)

where k∈ K and n∈ N . Meanwhile, the request probability

distribution of user kto the non-recommended item n∈ N \

Rkis quoted below:

˜areq

k,n =(1 −rk,n )apref

k,n

j∈N \Rkapref

k,j

=(1 −rk,n)apref

k,n

j∈N (1 −rk,j )apref

k,j

.(10)

Summarizing the above mentioned two-fold analysis into a

uniform formula, we obtain the request probability of user k

6

in terms of item nas follows:

areq

k,n =xkˆareq

k,n + (1 −xk)˜areq

k,n

=xk

rk,napref

k,n

j∈N rk,j apref

k,j

+ (1 −xk)(1 −rk,n)apref

k,n

j∈N (1 −rk,j )apref

k,j

,

(11)

where k∈ K and n∈ N . Thereof, ˆareq

k,n and ˜areq

k,n are well

deﬁned in (9) and (10), respectively.

Remark 1. Based on (11), it is easy to check that the contents

request distribution of user k,areq

k,n for n∈ N , remains

normalized, where k∈ K.

E. Personalized Recommendation Quality

In this subsection, we give the deﬁnition of recommendation

quality, which is an important personalized metric in recom-

mendation system. Speciﬁcally, even though the recommenda-

tion system can reshape the content request probability of each

user, the inherent preference distribution of users should also

be taken into consider to avoid the psychological inversion of

users [33]. To alleviate this issue, a user-speciﬁc psychological

threshold is set for each subscriber to measure the quality of

the recommendation, which is denoted by Qk, where k∈ K.

Under the recommendation quality constraint, we have

n∈N

rk,napref

k,n ≥Qk, k ∈ K,(12)

where apref

k,n is deﬁned in (5). In addition, we assume the value

of Qkis a prior information for k∈ K, which can be estimated

from the interactive response system provided by content

service companies. A simpliﬁed example, the customers will

be labeled according to their historical behavior [34], the ones

that have relatively picky labels will be assign a Qkwith

higher value, while the users with casual personality will

be given a lower threshold. Moreover, this value can also

be pre-determined by user itself to represent its personalized

requirement. Details about the methodologies on setting the

value of Qkare not explicitly discussed here.

F. System Effectiveness

In this subsection, we discuss the system performance

metric of this work. On one hand, for the mobile users, the

associated requirement is that their requested contents can

be provided by the edge caches. On the other hand, the

less content requests from users the lighter burden of the

wireless communication links and the backhaul transmission

links, which in turn reduces the content access latency and

improves users quality of experience. The above mentioned

two aspects can be well satisﬁed with a high content hit ratio

(CHR), which is deﬁned as the probability that the required

contents of subscribers are cached by their socially connected

mobile terminals. As a consequence, in this work, we deﬁne

CHR as our system performance measurement.

With aforementioned deﬁnitions, the CHR of user kin terms

of requesting content item nis quantiﬁed below:

CHRk,n =areq

k,n ×I(

k′∈Dk

ck′,n),(13)

where k∈ K,n∈ N . In addition, I(x)is an indicator

function, and it is deﬁned as follows:

I(x) = 1if x > 0

0otherwise.(14)

Moreover, the deﬁnition of areq

k,n is given in (11). According

to (13), we can see that, from user k’s own selﬁsh point of

view, caching the items within its effective D2D region that

has large value of areq

k,n increases CHR of user kdramatically.

However, the decision will be deﬁnitely affected when taking

the other socially connected users’ content request probability

into account. In addition, the caching decision of user kwill

also be signiﬁcantly affected by the caching states of the users

within its social neighbor set, referred to as Dk. Thereby, how

to apply the cache resource of all the mobile devices in a

federated and effective manner should be well investigated.

IV. JOI NT RECOMMENDATION AND CACHE DECISION

PROB LE M FOR MU LATI ON

In this work, we target at maximize the CHR of al-

l subscribers via jointly optimizing content caching and

recommendation decisions for each individual user. Let

ck= (ck,1, ck,2, . . . , ck,N )and c= (c1,c2, . . . , cK)be

the cache decision of user kand the cache decision vec-

tor of the network, respectively. Similarly, deﬁne rk=

(rk,1, rk,2, . . . , rk,N )and r= (r1,r2, . . . , rK)as the rec-

ommendation strategy vectors of user kand the system,

respectively. With the deﬁnitions, the CHR maximization ori-

ented joint cache placement and recommendation decision for

cache enabled D2D communication network is mathematically

formulated as follows:

maximize

r,c

k∈K

n∈N

CHRk,n P(1)

subject to

C1:

n∈N

ck,nLn≤Bk, k ∈ K,

C2:

n∈N

rk,napref

k,n ≥Qk, k ∈ K,

C3:

n∈N

rk,n =Rk, k ∈ K,

C4:rk,n ∈ {0,1}, k ∈ K, n ∈ N ,

C5:ck,n ∈ {0,1}, k ∈ K, n ∈ N ,

where CHRk,n in the objective function is well given in

(13). In addition, C1indicates that the cache capacity of user

kcannot exceed its storage budget. Besides, C2represents

users recommendation quality requirements as aforementioned

analysis. Moreover, C3shows the constraint for the recommen-

dation quantity per user, where Rkrepresents the maximum

number of the recommended items for user k, where k∈ K.

Furthermore, C4and C5depict the binary property of the

decision variables. For simplicity, we denote the formulated

CHR maximization problem as P(1), which is a non-convex

integer optimization problem, whose complexity is mathemat-

ically examined in next section.

7

V. PROBLEM COMPLEXI TY AN ALYS IS

In this section, we prove the NP-hardness of the content hit

ratio maximization problem P(1) with rigorous mathematical

proof. Details are presented in the following Theorem:

Theorem 2. P(1) is NP-hard.

Proof: The idea of the proof is to construct a polynomial-

time reduction mapping any instance of an NP-hard problem

to an instance of P(1). We say that P(1) is NP-hard according

to the transitivity of reduction [35]. The NP-hard problem

considered here is the multiple knapsack problem (MKP),

which has been well studied in [36]. It is deﬁned as follows:

maximize

y

K

k=1

N

n=1

pnxk,n (MKP)

subject to

C′

1:

N

n=1

wnxk,n ≤Wk, k ∈ K,

C′

2:

K

k=1

xn,k ≤1, n ∈ N ,

C′

3:xn,k ∈ {0,1}, n ∈ N , k ∈ K,

where Kdenotes the number of knapsacks, and Nis the

number of items. Parameters wnand pnrepresent the weight

and proﬁt of item n, respectively. Besides, Wkdenotes the

capacity of the k-th knapsack in constraint C′

1. The decision

variable xn,k is set to 1if and only if item nis assigned to

the k-th knapsack. Constraint C′

2ensures that each item nis

assigned to at most one knapsack.

Given an instance of MKP with the aforementioned param-

eters, we construct an instance of P(1) with Kusers and

Nitems. For each user k∈ K and item n∈ N , we set:

apref

k,n ,pn

∑N

i=1 pi,xk,1,Dk,K,Ln,wn,Bk,Wk,

Qk,1, and Rk,N. Note that the user preference

distribution is normalized, i.e., n∈N apref

k,n = 1, for all k∈ K,

to be consistent with deﬁnition (5). Problem P(1) can be now

written as:

maximize

r,c

k∈K

n∈N

CHRk,n (MKP)

subject to

C†

1:

n∈N

wnck,n ≤Wk, k ∈ K,

C†

2:

n∈N

rk,n

pn

N

i=1 pi

≥1, k ∈ K,

C†

3:

n∈N

rk,n =N, k ∈ K,

C†

4:rk,n ∈ {0,1}, k ∈ K, n ∈ N ,

C†

5:ck,n ∈ {0,1}, k ∈ K, n ∈ N .

Constraints C†

2,C†

3and C†

4imply that rk,n = 1, for all

users kand items n. Hence, the objective function of P(1)

becomes:

k∈K

n∈N

CHRk,n =

k∈K

n∈N areq

k,n ×I(

k′∈K

ck′,n),(15)

=

k∈K

n∈N pn

N

i=1 pi

×I(

k′∈K

ck′,n),(16)

=K

N

i=1 pi

n∈N pn×I(

k′∈K

ck′,n).(17)

Equation (15) comes from the fact that Dk,K. We then

derive (16) from the deﬁnition of areq

k,n, the choice of apref

k,n,xk,

as well as from rk,n = 1 due to constraints C†

2to C†

4. We

multiply the objective function (17) by N

i=1 pi/K to get the

following equivalent problem:

maximize

r,c

n∈N pn×I(

k′∈K

ck′,n)P′(1)

subject to

C†

1:

n∈N

wnck,n ≤Wk, k ∈ K,

C†

5:ck,n ∈ {0,1}, k ∈ K, n ∈ N .

Since the social neighbor sets contain all users, i.e., Dk,

K, each item only needs to be cached by one user in an optimal

solution of P′(1). More precisely, we claim that there exists

an optimal solution c∗

k,n satisfying k∈K c∗

k,n ≤1, for all

n∈ N . Indeed, let us consider an optimal solution such

that c∗

k1,n =c∗

k2,n = 1, for some n∈ N and k1, k2∈ K.

We have I(k′∈K c∗

k′,n)=1. By setting c∗

k2,n = 0, the

indicator function remains the same, i.e., I(k′∈K c∗

k′,n) = 1.

Therefore, when only one user cache item n, the objective

value remains optimal and C†

1,C†

5are still satisﬁed. Finding

the optimal value of P′(1) is thus equivalent to ﬁnding the

optimal value of the following problem P′′(1).

maximize

r,c

k∈K

n∈N

pnck,n P′′(1)

subject to

C†

1:

n∈N

wnck,n ≤Wk, k ∈ K,

C†

5:ck,n ∈ {0,1}, k ∈ K, n ∈ N ,

C6:

k∈K

ck,n ≤1, n ∈ N ,

where C6has been added to ensure that each item is cached

by at most one user. We see that problem P′′(1) is equivalent

to MKP by rewriting ck,n as xk,n. Hence, we have constructed

a polynomial time reduction from any instance of the MKP to

an instance of P(1). We derive that P(1) is NP-hard due to

the NP-completeness of MKP [36].

VI. CACHING AND REC OM ME NDATIO N OPTIMIZATION

ALGORITHMS DESIGN

In this section, the joint caching and recommendation opti-

mization for P(1) is studied, where we target at solving it in

8

a time-efﬁcient manner since obtaining the optimal solution is

NP-hard. Towards this end, we ﬁrst decouple P(1) into two

subproblems, i.e., cache placement with ﬁxed recommendation

strategy and the recommendation decision under given caching

policy, respectively. Whereafter, the corresponding algorithm

for each subproblem is designed. Based on the two-tire anal-

ysis, a joint cache placement and recommendation decision

algorithm is proposed, which is proceed in an iterative manner

and has guaranteed convergence performance. In addition,

we prove that our proposed joint decision algorithm has

polynomial-time computational complexity.

A. Optimization of Caching Decision

In this subsection, the caching placement for problem P(1)

is investigated with the prior information of recommendation

decision, i.e., r. Given r,P(1) is reduced to the following

problem P(2) with objective function

max

c

n∈N

k∈K

areq

k,n ×I(

k′∈Dk

ck′,n),(18)

and subjects to the constraints C1and C5. In the objective

function of P(2), the content request probability areq

k,n is known

with ﬁxed raccording to (11), where k∈ K and n∈ N .

In addition, from (18), we see that Iis a function of c. For

simplicity, we rewrite I(k′∈Dkck′,n)as I(c). Note that P(2)

is an integer non-convex programming as well since I(c)

is non-convex5, which is still intractable to solve. To avoid

combinatorial complexity in obtaining the optimal solution,

we propose a suboptimal caching decision algorithm based

on the concept of two-sided exchange, which ensures a non-

decreasing system CHR from any arbitrary initial state. This

will beneﬁt the convergence performance of our joint decision-

making algorithm.

Before detailing the proposed algorithm, some deﬁnitions

are clariﬁed. Denote by Ekthe index set of the cached items

of subscriber k, where k∈ K. Note that Ekcan be mapped

to the caching decision vector of user k, i.e., ck. In detail,

ck,n = 1 if and only if n∈ Ek. For simplicity, we deﬁne the

mapping Ψ:Ek→ckas follows:

Ψ(Ek),ck,(ck,1, ck,2, . . . , ck,N ), k ∈ K.(19)

In addition, we deﬁne Vk=N \ Ekas the complementary set

of Ek, and let E={Ek|k∈ K} represent the caching policy

of the entire system. Similarly, another mapping Λ:E → cis

deﬁned such that

Λ(E),c,(c1,c2, . . . , cK).(20)

Thereby, we now can write CHRk,n in the objective function

of P(2) as the function of Λ(E)and r. Besides, denote by

CHR(r,Λ(E)) the cache hit ratio of the system under the

caching strategy Λ(E)and given r. Speciﬁcally, we have

CHR(r,Λ(E)) =

k∈K

n∈N

CHRk,n(r,Λ(E)).(21)

With aforementioned discussions, we specify the deﬁnition

of the swap-blocking pair of subscriber kas follows:

5The detailed deﬁnition about the indicator function Iis given in (14).

Deﬁnition 3. Given a pair of items (ik, jk)where ik∈ Ekand

jk∈ Vk, respectively. We say (ik, jk)is a swap-blocking pair

suppose that C1under E′

kas well as the following condition

CHR(r,Λ(E(k, ik, jk))) >CHR(r,Λ(E)) (22)

are satisﬁed, where E(k, ik, jk),{Ej|j∈ K \ {k},Ek=E′

k},

in which E′

k,Ek\ {ik} ∪ {jk}.

We claim that the concept of swap-blocking adopted in

our problem derives from matching theory [37]–[39]. In ac-

cordance with Deﬁnition 3, the achievable cache hit ratio of

our system will increase given that the two-side exchange of

items in a swap-block pair is approved. Since the caching

policy of one subscriber affects the decisions of the other

users mutually, the caching deployments for all users should

be designed jointly. The proposed cache decision approach is

an iterative algorithm, where we assume that the initial cache

strategies of all users are based on the top-cache policy. In

particular, for subscriber k, it will cache the top-ranked items

based on its inherent preference distribution, apref

k, to make its

cache storage full, i.e., the following constraint

Bk−min

n∈Vk

Ln<

n∈N

ck,nLn≤Bk

is satisﬁed.

In order to achieve a high content hit ratio, it is sensible to

approve the swapping of a pair items, denoted by (i‡

k∗, j‡

k∗),

that induces the largest objective value of problem P(2), i.e.,

(i‡

k∗, j‡

k∗),argmax

(ik,jk)⊂Sk,k∈K

CHR(r,Λ(E(k, ik, jk))),(23)

in which

Sk,{(ik, jk)|ik∈ Ek, jk∈ Vk}, k ∈ K.(24)

We repeat the two-side exchange oriented steps until no

swapping pair can be found. For the sake of simplicity, we

summarize the pseudo-code of the proposed cache decision

approach to P(1) under given recommendation policy in

Algorithm 1.

Algorithm 1 Cache placement algorithm

1: Given the pre-determined recommendation strategy r, the initial

cache decision vector c, and the auxiliary sets Skas expressed

in (24). In addition, denote by K†=K.

2: repeat

3: Determine the pair (i‡

k∗, j‡

k∗)based on (23), i.e.,

(i‡

k∗, j‡

k∗) := argmax

(ik,jk)⊂Sk,k∈K†

CHR(r,Λ(E(k, ik, jk))).

4: if (i‡

k∗, j‡

k∗)is a swap-blocking pair then

5: Let Ek∗,Ek∗\ {i‡

k∗}∪{j‡

k∗}.

6: Update ck∗in accordance with (19), i.e., ck∗:= Ψ(Ek∗).

7: else

8: Keep the current caching policy.

9: end if

10: Update Sk∗,Sk∗\ {(i‡

k∗, j‡

k∗)}

11: if Sk∗=∅then

12: Denote K†,K†\ {k∗}.

13: end if

14: until No swap-blocking pair can be found

15: return the caching strategy ckfor k∈ K.

9

B. Optimization of Recommendation Decision

We investigate the optimization for recommendation deci-

sion, r, with ﬁxed caching strategy, c, in this subsection. It

is worth noting that, given c, the indicator function I(c)is

determined, which can be acknowledged as the availability of

content item nto subscriber kvia D2D-enabled edge caching,

where k∈ K and n∈ N . Thereby, how to conduct the

recommendations is vital to maximize the CHR of the system

since raffects the coefﬁcients of I(c).

In accordance with the deﬁnition of content request proba-

bility in (11), the recommendation optimization for subscriber

kis independent with the other users’ strategies. Therefore,

the recommendation decision for all the subscribers with ﬁxed

ccan be divided into Kparallel subproblems. Each user

solves its own recommendation decision making subproblem.

Without loss of generality, we choose user kas an example.

For user k, (s)he needs to optimize rkto maximize its caching

hit ratio. Deﬁne Uk=N \ Rkas the supplementary set of the

recommended contents set of user k, i.e., Rk. We assume the

top-Rkmost preferred items based on the inherent preference

in (5) are selected as the initial recommended contents of

mobile user k, where k∈ K. Deﬁne the mapping Φ:Rk→rk

as follows:

Φ(Rk),rk,(rk,1, rk,2, . . . , rk,N ).(25)

To be more speciﬁc, rk,n = 1 if n∈ Rkand 0 otherwise.

Denote by CHRk(Φ(Rk),c)the cache hit ratio of user k

whose recommended items fall into Rk, therein the caching

decision is c. With aforementioned deﬁnitions, we have

CHRk(Φ(Rk),c),

n∈N

areq

k,n ×I(c).(26)

Based on (11), it is easy to see that the request distri-

bution of user k, i.e., areq

k,n, is a non-convex function of

the recommendation vector rk. Therefore, to simplify the

algorithm, we propose a matching theory oriented method

to do the recommendation decision optimization, which has

similar properties to the methodology used in the caching

decision problem. Hereafter, we ﬁrst give the deﬁnition of

a swap-blocking pair for user kvia exchanging the items

between sets Rkand Uk, and it is given as follows:

Deﬁnition 4. For any pair of contents (i, i′)where i∈ Rk

and i′∈ Uk, we say (i, i′)is a swap-blocking pair provided

that C2under R′

kas well as the following condition

CHRk(Φ(R′

k),c)>CHRk(Φ(Rk),c)(27)

are satisﬁed, in which R′

k,Rk\ {i} ∪ {i′}.

Intuitively, the exchange of items iand i′, which come from

sets Rkand Uk, respectively, resulting in an increased CHR

value for user k. Based on this observation, the recommenda-

tion optimization algorithm is designed, whose main idea is

to do the swapping one by one until no swap-blocking pair

can be found for each subscriber. For brevity, the two-side

swapping oriented recommendation decision methodology for

user kis concluded in Algorithm 2.

Algorithm 2 Recommendation decision algorithm for user k

1: Given the caching placement strategy cand the initial recom-

mendations set Rk. Deﬁne an auxiliary set as G={(i, i′)|i∈

Rk, i′∈ Uk}.

2: repeat

3: Select (i, i′)⊂ G.

4: if (i, i′)is a swap-blocking pair then

5: Let Rk=Rk\ {i}∪{j}.

6: Update rkbased on (25), i.e., rk:= Φ(Rk).

7: else

8: Keep the current recommendation pattern.

9: end if

10: Adjust G=G \ {(i, i′)}.

11: until No swap-blocking pair can be found for user k

12: return the recommendation decision of user k, i.e., rk.

C. The Joint Optimization for Cache Placement and Recom-

mendation Decision

In this subsection, we discuss the joint cache placement and

recommendation decision algorithm based on the aforemen-

tioned two-fold analysis. Wherein, the convergence as well as

the complexity of the proposed approach are investigated.

At ﬁrst, some deﬁnitions are presented. For k∈ K and

n∈ N , deﬁne ck,n (t)as the cache decision of user kin

terms of content item nin the t-th iteration. In addition,

denote by ck(t) = (ck,1(t), ck,2(t), . . . , ck,N (t)) the caching

strategy of subscriber kin iteration t. Besides, let c(t) =

(c1(t),c2(t), . . . , cK(t)) be the caching policy of our method

in the t-th iteration. Moreover, it is assumed that c(0) is

set by the top-cache scheme as discussed in Section VI-A.

Similarly, we deﬁne r(t)as the recommendation decision in

the t-th iteration and set r(0) by the aforementioned top-

recommendation strategy. Furthermore, denote by CHR(r,c)

the objective function of P(1) under the optimized decisions

(r,c).

With the deﬁnitions, the joint optimization algorithm is

expressed as follows: in the t-th iteration, with the obtained

recommendation strategy r(t−1) in the (t−1)-th iteration,

we obtain the optimized caching policy c(t)in accordance

with Algorithm 1, in which the initial cache decision vector

(in line 1 of Algorithm 1) is set to be c(t−1). Based on

the resultant c(t), we determine the updated recommendation

scheme r(t)according to Algorithm 2, wherein the initial

recommendation policy in line 1 of Algorithm 2 is assumed to

be r(t−1). These kinds of settings guarantee the optimized

strategy results in a monotonously increased objective value.

We repeat the aforementioned steps until that the value of

CHR(r(t),c(t)) can not be further increased or the maximum

iteration number is reached. In the interest of conciseness, the

pseudo-code of our designed joint decision methodology is

summarized in Algorithm 3.

Lemma 5. The convergence of Algorithm 3 is warranted.

Proof: With foregoing analysis, it is easy to see that the

CHR of P(1) during the iteration is a monotonic increasing

sequence. According to (13), the objective value of P(1) is

upper bounded by K, the convergence is guaranteed [40].

In addition, the complexity of Algorithm 3 is elaborated in

the following proposition.

10

Algorithm 3 Joint cache and recommendation optimization

algorithm

1: Deﬁne the maximum iteration number as T. Determine r(0) by

the top-recommendation strategy, and initialize c(0) based on the

top-cache scheme. Let t= 1.

2: repeat

3: Obtain the caching police c(t)under ﬁxed recommendation

policy r(t−1) according to Algorithm 1. Therein, we claim

that, the initial caching strategy of Algorithm 1 is set as c(t−

1).

4: Update the recommendation strategy r(t)with the obtained

caching strategy c(t)of last step in the light of Algorithm

2. It is notable that, in this step, the initial recommendation

decision in line 1 of Algorithm 2 is set to be r(t−1).

5: Update t=t+ 1.

6: until CHR(r(t),c(t)) cannot be further increased or the maxi-

mum iteration number is reached, i.e., t>T

7: return the joint cache and recommendation decision strategy

(r,c)

Proposition 6. Since Algorithm 3 is constituted by the recom-

mendation optimization and the cache decision approaches,

i.e., Algorithm 2 and Algorithm 1, respectively, its complexity

shall be determined by these two algorithms. Speciﬁcally, the

complexity of Algorithm 1 is relates to the set size of Skfor

k∈ K due to the application of two-side swapping, which

can be attained as O(KN 2). Similarly, the time complexity of

Algorithm 2 is obtained as O(RkN).

Before ending this section, we declare that the binary vari-

ables are in general coupled in the optimization problems for

recommendation-aware caching networks, these problems are

very challenging to be solved. A commonly used methodology

is to decouple the variables, explore the solutions for each

individual subproblem, and alternatively optimize the differ-

ent types of variables. This research methodology has been

widely utilized by [17]–[21] and this work. More precisely,

the dynamic programming algorithm and a simpler heuris-

tic scheme are proposed to solve the cache placement and

recommendation decision subproblems, respectively, in [17].

Nevertheless, our cache decision subproblem is still a non-

convex and non-linear integer programming problem, which

cannot be solved by the proposed method in [17] directly.

Thereby, a match theory oriented algorithm is designed, which

ensures a non-decreasing system CHR from any arbitrary

initial state. This will beneﬁt the convergence performance

of our joint decision-making algorithm. Similarly, our recom-

mendation decision-making subproblem is also a non-convex

integer problem since the objective function is non-convex to

r. Thus, to avoid combinatorial complexity in obtaining the

optimal solution, a two-side swapping method is designed,

which has similar properties to the method used in the caching

decision problem. Note that both the pure cache placement and

the pure recommendation decision-making subproblems are

linear integer programming problems in [17], which, however,

are non-convex integer problems in this paper.

VII. NUMERICAL RES ULTS

Monte-Carlo simulation is conducted in this section to show

the performance of our designed joint recommendation and

caching algorithm. The system parameters are summarized as

follows. The cell radius is set to be 250 m, where 20 users

uniformly distributed within its disk region, i.e., K= 20. The

D2D communication radius per user is assumed to be 25 m.

In addition, the contents number is set to be N= 50, which

are characterized by M= 10 themes. The feature vectors

of both users and contents are generated via a random walk

method. Without loss of generality, we assume each content

item has the same data size, which is normalized as 1, that

is Ln= 1 for n∈ N . As a consequence, the cache capacity

of user kcan be set to be an integer number, and we assume

that the users have the same size storage, i.e., Bk=Bfor

k∈ K. Moreover, we consider the usage scenario where each

user has the same acceptance probability, the recommendation

size, the recommendation quality requirement and the social-

aware rate threshold, i.e., xk=X,Rk=R,Qk=Qand

¯

Vk=Vare satisﬁed for k∈ K, respectively. We declare

that our designed algorithm also appropriates for the scenarios

where Bk,xk,Rk,Qk,¯

Vkare disparate for k∈ K. Without

otherwise stated, in the simulation, we assume that X= 0.618,

Q= 0.08 and let αin (6) be α= 0.686, respectively [41],

[42]. Furthermore, for the sake of obtaining complete picture

of the research focus, we model the preference distribution of

each user as follows:

apref

k=win

kain

k+1−win

kaout,(28)

where ain

krepresent the personalized content preference distri-

bution of subscriber k, the components of which are obtained

based on Section III-A, while aout represents the external

content preference distribution in accordance with the content

popularity, whose elements are generated according to the Zipf

distribution [8]. win

k∈[0,1] depicts the weight of the inherent

content preference distribution. Note that let win

k= 1 for

k∈ K, the preference distribution is exactly the one as deﬁned

in Section III-A.

In addition, for performance comparison, the following

baselines are taken into considered:

•Baseline 1: Top cache and no recommendation. In this

scheme, user kcaches the top preferred items based

on its inherent preference distribution, apref

k, to make its

cache storage full. In addition, no recommendation will

be conducted for each subscriber.

•Baseline 2: Top cache and top recommendation. In this

method, the caching policy is the same as that in Baseline

1, while user kwill be recommended by the top-Rk

contents based on apref

k, where k∈ K.

•Baseline 3: Homogeneous cache and top recommen-

dation. In this strategy, each user will cache the top

ranked items in accordance with all the users aggregated

preference to stuff up their caches. Thereof, the recom-

mendation scheme is the same as Baseline 2.

•Baseline 4: Homogeneous cache and homogeneous rec-

ommendation. The caching scheme of Baseline 4 is

identical with that of Baseline 3, while each user k∈ K

will be recommended the top-Rkitems based on the

aggregated preference of all subscribers.

•Revised CawR: In this strategy, the proposed CawR algo-

11

0 50 100 150

Iteration Index

8

10

12

14

16

18

Cache Hit Ratio

(a) V= 0.04.

0 50 100 150

Iteration Index

6

8

10

12

14

16

Cache Hit Ratio

(b) V= 0.06.

Fig. 3. Convergence behavior of our designed algorithm under different

values of V. Thereof, the content preference of each user is generated by the

method in Section III-A.

rithm in [18] is adopted with the difference that the cache

placement scheme is replaced by our devised method,

i.e., Algorithm 1. This is because the cache decision

procedure implemented in CawR is not applicable to our

case as stated at the end of Section VI.

Two system metrics are evaluated in this section: 1) the

convergence performance of our designed joint caching and

recommendation algorithm, and 2) the content hit ratio of

different schemes. Further, we consider different social-aware

rate thresholds, i.e., V, for each of the aforementioned metrics

since Vaffects the social neighbor set per user, which in turn

inﬂuences system’s CHR.

A. Convergence Performance

In this subsection, the convergence performance of our joint

decision algorithm is evaluated under extensive parameters

settings, as illustrated in Fig. 3 and Fig. 4. Thereof, the number

of the recommended item per subscriber is set to be R= 2. In

addition, the users preference distribution of Fig. 3 is obtained

by the manner introduced in Section III-A while that of Fig.

4 is following by (28) with win

k= 0. We use the cache hit

ratio value during the iterations to show this performance. To

be more speciﬁc, the x-axis depicts the number of iterations

while the y-axis represents the cache hit ratio of the system.

In Fig. 3(a) and Fig. 3(b), the D2D social aware rate

threshold is set to be V= 0.04 and V= 0.06, respectively.

From each of the sub-ﬁgures, we see that, our proposed algo-

rithm converges quickly under different settings. In addition,

a smaller value of cache capacity induces to a higher rate

of convergence since the size of swapping set decreases with

the decreasing of B. Besides, as expected, we see that a

large cache capacity induces to an enhanced cache efﬁciency.

Moreover, for any given cache capacity budget, the CHR of

the system is decreased with the increasing of V. This is due

to the fact that a large value of Vreduces the set size of the

possible content provider for each user, which in turn lower

the probability of cache hit for D2D enabled content caching

networks.

In Fig. 4, we examine how the heterogeneity of user’s

content preference impacts the convergence performance of

our designed algorithm. The extreme usage scenario where

win

k= 0 is considered, which indicates that the content

0 50 100 150

Iteration Index

8

10

12

14

16

18

Cache Hit Ratio

(a) V= 0.04.

0 50 100 150

Iteration Index

8

9

10

11

12

13

14

15

Cache Hit Ratio

(b) V= 0.06.

Fig. 4. Convergence behavior of our proposed algorithm under different

values of V, where the preference distribution per subscriber is characterized

by Zipf. Speciﬁcally, the Zipf component is set to be 0.5.

0 2 4 6 8 10 12

Cache Capacity Budget

0

5

10

15

20

Cache Hit Ratio

(a) V= 0.02 and win

k= 1.

0 2 4 6 8 10 12

Cache Capacity Budget

0

5

10

15

20

Cache Hit Ratio

(b) V= 0.03 and win

k= 1.

Fig. 5. Cache hit ratio versus cache capacity budget per user, where the

preference distribution of each user is characterized by the method in Section

III-A.

preference distributions of all users are homogeneous. Similar

conclusions as that of Fig. 3 are attained, details are not

redundantly expressed here. In addition, with the same setting

of V, the performance of our method under win

k= 0 is better

than that of the scenario where win

k= 1 because the diversities

among users are eliminated in the ﬁrst case, resulting in a high

cache hit probability for our joint decision algorithm.

B. Content Hit Ratio

Fig. 5 and Fig. 6 illustrate the cache hit ratios of our

proposed algorithm as well as the extensive baselines versus

the cache capacity budget per user. Thereof, the preference

distribution parameter win

kin (28) are set to be 1 and 0,

respectively. In addition, the recommendation size is assumed

to be R= 5. We distinguish the observations from the two

ﬁgures in these following paragraphs.

First, we consider Fig. 5, in Fig. 5(a) and Fig. 5(b), V

is set to be 0.02 and 0.03, respectively. As expected, the

cache hit ratio of all the schemes increases with the increasing

of cache capacity budget. In addition, for any given V, our

designed scheme always achieves the optimal performance

as regards cache hit ratio owning to the jointly optimized

decisions. Besides, CawR is not the best, in particular when

the cache capacity budget is high. This is because without

globally optimal cache placement, the termination of CawR

after a single recommendation amendment step is not ensured,

which leaves space for further performance improvements as

shown by our iterative joint optimization algorithm. Moreover,

Baseline 2 and Baseline 4 have better performance than that

12

0 2 4 6 8 10 12

Cache Capacity Budget

5

10

15

20

Cache Hit Ratio

(a) V= 0.02 and win

k= 0.

0 2 4 6 8 10 12

Cache Capacity Budget

5

10

15

20

Cache Hit Ratio

(b) V= 0.03 and win

k= 0.

Fig. 6. Cache hit ratio versus cache capacity budget per user, where the

preference distribution of each subscriber is captured by Zipf with component

set as 1.1.

2 4 6 8 10

Cache Capacity Budget

0

0.2

0.4

0.6

0.8

1

Traffic Offloading Ratio

(a) V= 0.02 and win

k= 1.

2 4 6 8 10

Cache Capacity Budget

0

0.2

0.4

0.6

0.8

1

Traffic Offloading Ratio

(b) V= 0.03 and win

k= 1.

Fig. 7. Trafﬁc ofﬂoading ration versus cache capacity budget per user.

of Baseline 3 since both of them adopt the top cache and top

recommendation mechanisms. Baseline 3 performs worse than

the other three recommendation-aware strategies because its

recommendation is not seize the momentum of caching policy,

restricting to fully reap the gains of caching to some extent.

Furthermore, it is worth noting that, a large value of Vreduces

the achievable cache hit values of all the strategies (except

Baseline 4) since the possible content providers of each user

are downsized. As far as Baseline 4, all the users cache the

same items and be recommended by the same contents, the

changing of Vwill not affect the content provider probabilities

of the adjacent users.

Then, we apply Fig. 6 to explore the effects of heterogeneity

among users on the cache efﬁciency of all six approaches, i.e.,

we set win

k= 0. It can be seen that our developed scheme

outperforms the four baselines in all simulated scenarios, as

well as the Revised CawR benchmark. It is noteworthy that

with win

k= 0, three recommendation enabled benchmarks,

i.e., Baselines 2, 3 and 4 are reduced to one policy in

accordance with their deﬁnitions. Besides, the schemes with

recommendation outperform Baseline 1, therein no recom-

mendation is conducted, demonstrating the effectiveness of

recommendation mechanism. Besides, with the increasing of

V, the cache hit ratio of our scheme decreased slightly and that

of the other strategies remain unchanged due to their working

mechanisms. Moreover, via comparing Fig. 5 to Fig. 6, we see

that under the same system parameters, our proposed algorithm

with homogenous users preference distribution achieves higher

cache hit ratio when compared with that of the heterogenous

case, which stays consistent with the foregoing analysis.

Fig. 7 plots the BS trafﬁc ofﬂoading ratios (TOR) of differ-

2 4 6 8 10

Cache Capacity Budget

0

5

10

15

20

Cache Hit Ratio

Fig. 8. Cache hit ratio of our propose scheme versus cache capacity budget

under different recommendation threshold, Q.

ent approaches, wherein the deﬁnition of TOR is followed by

equation (22) in [7]. More speciﬁcally, we stipulate V= 0.02

and V= 0.03 for Fig. 7(a) and Fig. 7(b), respectively. In both

two ﬁgures, the x-axis and y-axis depict the cache capacity

budget per user and the value of TOR, respectively. A higher

value of TOR represents a larger number of contents that are

delivered by D2D communication, which further expresses a

reduced BS trafﬁc load. Based on Fig. 7, we observe that

the TOR of each scheme increases with the increasing of

cache capacity budget per user. In addition, we see that the

proposed decision-making scheme induces the highest TOR.

For example, when V= 0.02 and B= 3, the TOR of our

developed optimization strategy is 70.9%,29.1%,151.0%,

431.4%, and 36.5% more than Baseline 1, Baseline 2, Baseline

3, Baseline 4, and Revised CawR, respectively, showing the

capability of our algorithm in terms of alleviating BS’s trafﬁc

pressure. Furthermore, via comparing Fig. 7(a) with Fig. 7(b),

a larger value of Vresults in an decreased value of TOR

for each scheme. This is because, increasing Vdegrades

the capability of D2D communication between users. This

observation is consistent with the analysis in Fig. 5.

Subsequently, we investigate the effect of recommendation

quality threshold, i.e., Q, on the performance of our devised

joint optimization algorithm in terms of cache hit ratio, as

demonstrated by Fig. 8. Therein, the recommendation quantity

per user and the social-aware rate threshold are set to be R=

10 and V= 0.03, respectively. In addition, we assume win

k=

1. Note that similar trends are attainable for other parameters

settings, which are not plotted here for simplicity. From Fig. 8,

we notice that a higher value of Qinduces a reduced cache hit

ratio due to the fact that increasing the value of Qdownsizes

the total number of feasible recommendation combinations,

which can be seen from C2of P(1) as well. This, in turn,

degrades the performance of our optimization approach.

At last, we examine in Fig. 9 the effect of recommendation

size on cache efﬁciency among different schemes. Thereof,

the cache capacity budget per subscriber is assumed to be 2.

Speciﬁcally, in Fig. 9(a) and Fig. 9(b), we consider win

k= 1

and win

k= 0, respectively. We ﬁrst focus on Fig. 9(a).

It can be seen that, our proposed scheme always has the

highest cache hit ratio among all the strategies, while the

Revised CawR is usually the second best performing strategy.

Besides, with the increasing of recommendation size, all

the recommendation-aware methods have the reduced cache

efﬁciency values, which is in consistent with the ﬁndings

13

234567

Recommendation Size

0

5

10

15

20

Cache Hit Ratio

(a) V= 0.02 and win

k= 1.

234567

Recommendation Size

6

8

10

12

14

16

18

20

Cache Hit Ratio

(b) V= 0.02 and win

k= 0.

Fig. 9. Cache hit ratio versus recommendation size per user.

in [17]–[19]. The reason is two-fold. On one hand, a large

number of recommendations making the preference distribu-

tion more ﬂat, which is unproﬁtable to the cache efﬁciency’s

enhancement. On the other hand, increasing the number of the

recommended items induces boosted request probabilities for

these contents to some extent. Nevertheless, the cache size

is limited, which can not fully bear the recommendations,

resulting in a decrease cache hit probability. Moreover, it

is noticeable that the performance loss of our algorithm is

not so much remarkable with the increasing of R, since for

the proposed algorithm, the caching policy and the recom-

mendation decision are iteratively optimized. This in return

demonstrates how the recommendation and caching optimiza-

tion in the proposed scheme can be useful for improving

caching efﬁciency. Meanwhile, from Fig. 9(b), we see that,

all the recommendation enabled schemes outperform Baseline

1. Furthermore, when compared Fig. 9(b) with Fig. 9(a), it

is noticeable that, the homogeneous preference distribution

accompanied by an enhanced cache efﬁciency for Baselines

3, Baseline 4, and Revised CawR. Since Baseline 2 reduces

to be Baselines 3 and 4, its performance is decrease when each

user has homogenous preference distribution.

VIII. CONCLUSION

In this work, we examined how recommendation can be

implemented to enhance the caching efﬁciency of D2D en-

abled wireless content caching networks. Towards this end, a

cache hit ratio maximization problem was formulation. To be

more speciﬁc, we quantitatively characterized how cache hit

ratio can be jointly affected by recommendation and caching.

In addition, the user speciﬁc recommendation quantity, rec-

ommendation quality as well as cache capacity budget were

taken into account. We demonstrated the NP-hardness of the

maximization problem with rigourous mathematical proof.

To make the NP-hard problem tractable, we decoupled the

original problem into two subproblems, whereafter the corre-

sponding approaches were designed. Based on that, an iterative

algorithm was proposed to obtain the joint decision policies,

which had provable convergence guarantee and polynomial

time complexity. Extensive numerical results revealed the

effectiveness of our designed versatile algorithm compared to

various baselines. Notice that the successful implementation

of wireless edge caching is crucially depends on joint content

delivery, cache placement, or/and recommendation decisions,

future work will involve the joint optimization for the forego-

ing three aspects.

REF ER EN CE S

[1] Ericsson, “The Ericsson mobility report,” Nov 2019. [Online]. Available:

https://www.ericsson.com/en/mobility-report.

[2] D. Liu, B. Chen, C. Yang, and A. F. Molisch, “Caching at the

wireless edge: design aspects, challenges, and future directions,” IEEE

Communications Magazine, vol. 54, no. 9, pp. 22–28, Sep. 2016.

[3] J. Rao, H. Feng, C. Yang, Z. Chen, and B. Xia, “Clustered device-to-

device caching based on ﬁle preferences,” in Proc. IEEE International

Conference on Communications (ICC), May. 2016.

[4] Z. Chen and M. Kountouris, “D2D caching vs. small cell caching:

Where to cache content in a wireless network?” in Proc. IEEE Signal

Processing Advances in Wireless Communications (SPAWC), Jul. 2016.

[5] D. Wu, L. Zhou, and Y. Cai, “Social-aware rate based content sharing

mode selection for D2D content sharing scenarios,” IEEE Transactions

on Multimedia, vol. 19, no. 11, pp. 2571–2582, Dec. 2017.

[6] B. Chen, C. Yang, and Z. Xiong, “Optimal caching and scheduling for

cache-enabled D2D communications,” IEEE Communications Letters,

vol. 21, no. 5, pp. 1155–1158, Jan. 2017.

[7] T. Zhang, X. Fang, Y. Liu, G. Y. Li, and W. Xu, “D2D-enabled

mobile user edge caching: A multi-winner auction approach,” IEEE

Transactions on Vehicular Technology, vol. 68, no. 12, pp. 12 314–

12 328, Dec 2019.

[8] T. Zhang, H. Fan, J. Loo, and D. Liu, “User preference aware caching

deployment for device-to-device caching networks,” IEEE Systems Jour-

nal, vol. 13, no. 1, pp. 226–237, Mar. 2019.

[9] X. Zhang, Y. Wang, R. Sun, and D. Wang, “Clustered device-to-

device caching based on ﬁle preferences,” in Proc. IEEE International

Symposium on Personal, Indoor and Mobile Radio Communications

(PIMRC), Oct. 2016.

[10] K. S. Khan, Y. Yin, and A. Jamalipour, “On the application of agglomer-

ative hierarchical clustering for cache-assisted D2D networks,” in Proc.

IEEE Annual Consumer Communications & Networking Conference

(CCNC), Jan. 2019.

[11] B. Chen and C. Yang, “Caching policy for cache-enabled D2D commu-

nications by learning user preference,” IEEE Transactions on Commu-

nications, vol. 66, no. 12, pp. 6586–6601, Dec. 2018.

[12] G. S. Paschos, A. Destounis, and G. Iosiﬁdis, “Learning to cooperate in

D2D caching networks,” in Proc. IEEE Signal Processing Advances in

Wireless Communications (SPAWC), Jul. 2019.

[13] W. Jiang, G. Feng, S. Qin, T. S. P. Yum, and G. Cao, “Multi-agent

reinforcement learning for efﬁcient content caching in mobile D2D

networks,” IEEE Communications Magazine, vol. 18, no. 3, pp. 1610–

1622, Mar. 2019.

[14] R. Zhou, S. Khemmarat, and L. Gao, “The impact of YouTube rec-

ommendation system on video views,” in Proc. 10th ACM SIGCOMM

Internet Measurement Conference (IMC), pp. 404–410, May. 2010.

[15] D. K. Krishnappa, M. Zink, C. Griwodz, and P. Halvorsen, “Cache-

centric video recommendation: An approach to improve the efﬁciency

of YouTube caches,” ACM Transactions on Multimedia Computing,

Communications, and Applications (TOMM), vol. 11, no. 4, pp. 48:1–

48:20, Jun. 2015.

[16] C. A. Gomez-Uribe and N. Hunt, “The Netﬂix recommender system:

Algorithms, business value, and innovation,” ACM Transactions on

Management Information Systems (TMIS), vol. 6, no. 4, pp. 1–19, Dec.

2015.

[17] L. E. Chatzieleftheriou, M. Karaliopoulos, and I. Koutsopoulos,

“Caching-aware recommendations: Nudging user preferences towards

better caching performance,” in Proc. IEEE International Conference

on Computer Communications (INFOCOM), May. 2017.

[18] ——, “Jointly optimizing content caching and recommendations in small

cell networks,” IEEE Transactions on Mobile Computing, vol. 18, no. 1,

pp. 125–138, Jan. 2019.

[19] L. E. Chatzieleftheriou, G. Darzanos, M. Karaliopoulos, and I. Kout-

sopoulos, “Joint user association, content caching and recommendations

in wireless edge networks,” ACM SIGMETRICS Performance Evaluation

Review, vol. 46, no. 3, pp. 12–17, Dec. 2018.

[20] K. Qi, B. Chen, C. Yang, and S. Han, “Optimizing caching and

recommendation towards user satisfaction,” in Proc. IEEE International

Conference on Wireless Communications and Signal Processing (WC-

SP), pp. 1–7, Dec. 2018.

14

[21] D. Liu and C. Yang, “A learning-based approach to joint content

caching and recommendation at base stations,” in Proc. IEEE Global

Communications Conference (GLOBECOM), Dec. 2018.

[22] S. Kastanakis, P. Sermpezis, V. Kotronis, and X. Dimitropoulos,

“CABaRet: Leveraging recommendation systems for mobile edge

caching,” in Proc. ACM SIGCOMM workshops: Workshop on Mobile

Edge Communications, Aug. 2018.

[23] P. Sermpezis, T. Spyropoulos, L. Vigneri, and T. Giannakas, “Femto-

caching with soft cache hits: Improving performance through recom-

mendation and delivery of related content,” IEEE Journal on Selected

Areas in Communications, vol. 36, no. 6, pp. 1300–1313, Jun. 2018.

[24] T. Giannakas, P. Sermpezis, and T. Spyropoulos, “Show me the cache

optimizing cache-friendly recommendations for sequential content ac-

cess,” in Proc. IEEE International Symposium on a World of Wireless

Mobile and Multimedia Networks (WoWMoM), Jun. 2018.

[25] Y. Fu, Z. Yang, T. Q. S. Quek, and H. H. Yang, “Towards cost

minimization for wireless caching networks with recommendation and

uncharted users’ feature information,” IEEE Transactions on Wireless

Communications, Aug 2020.

[26] Y. Wang, M. Ding, Z. Chen, and L. Luo, “Caching placement with

recommendation systems for cache-enabled mobile social networks,”

IEEE Communications Letters, vol. 21, no. 10, pp. 2266–2269, Oct.

2017.

[27] K. N. Doan, T. V. Nguyen, H. Shin, and T. Q. S. Quek, “Socially-aware

caching in wireless networks with random D2D communications,” IEEE

Access, vol. 7, pp. 58 394–58 406, May 2019.

[28] Y. Zhang, M. Zhang, Y. Liu, C. Tat-Seng, Y. Zhang, and S. Ma, “Task-

based recommendation on a web-scale,” in Proc. IEEE International

Conference on Big Data (Big Data), pp. 827–836, Oct. 2015.

[29] E. Bastug, M. Bennis, E. Zeydan, M. A. Kader, I. A. Karatepe, A. S.

Er, and M. Debbah, “Big data meets telcos: A proactive caching

perspective,” Journal of Communications and Networks, vol. 17, no. 6,

pp. 549–557, Dec. 2015.

[30] Y. Dong, Q. Ke, Y. Cai, B. Wu, and B. Wang, “Teledata: data mining,

social network analysis and statistics analysis system based on cloud

computing in telecommunication industry,” in Proceedings of the third

ACM international workshop on cloud data management, pp. 41–48,

2011.

[31] D. Wu, L. Zhou, and Y. Cai, “Social-aware rate based content sharing

mode selection for D2D content sharing scenarios,” IEEE Transactions

on Multimedia, vol. 19, no. 11, pp. 2571–2582, Dec. 2017.

[32] M. Verhoeyen, J. D. Vriendt, and D. D. Vleeschauwer, “Optimizing

for video storage networking with recommender systems,” Bell Labs

Technical Journal, vol. 16, no. 4, pp. 97–113, Mar. 2012.

[33] D. Jannach and G. Adomavicius, “Price and proﬁt awareness in recom-

mender systems,” in Proceedings of the RecSys Workshop, Como, Italy,

August 2017.

[34] A. Vinciarelli and G. Mohammadi, “A survey of personality computing,”

IEEE Transactions on Affective Computing, vol. 5, no. 3, pp. 273–291,

May. 2014.

[35] M. R. Garey and D. S. Johnson, Computers and intractability. W. H.

Freeman New York, 2002, vol. 29.

[36] H. Kellerer, U. Pferschy, and D. Pisinger, Knapsack Problems. Berlin

Heidelberg: Springer-Verlag, 2004.

[37] E. Bodine-Baron, C. Lee, A. Chong, B. Hassibi, and A. Wierman, “Peer

effects and stability in matching markets,” in International Symposium

on Algorithmic Game Theory, pp. 117–129, 2011.

[38] D. Gale and L. S. Shapley, “College admissions and the stability of

marriage,” The American Mathematical Monthly, vol. 69, no. 1, pp. 9–

15, 1962.

[39] H. Sasaki and M. Toda, “Two-sided matching problems with externali-

ties,” Journal of Economic Theory, vol. 70, no. 1, pp. 93–108, 1996.

[40] R. G. Bartle and D. R. Sherbert, Introduction to Real Analysis. John

Wiley & Sons, Inc., 2010.

[41] Y. Fu, Q. Yu, T. Q. S. Quek, and W. Wen, “Revenue maximization

for content-oriented wireless caching networks (CWCNs) with repair

and recommendation considerations,” IEEE Transactions on Wireless

Communications, vol. 20, no. 1, pp. 284–298, Jan. 2021.

[42] X. Yang, Y. Fu, W. Wen, T. Q. S. Quek, and F. Song, “Mixed-timescale

caching and beamforming in content recommendation aware Fog-RAN:

A latency perspective,” IEEE Transactions on Communications, 2020.

[Online]. Available: DOI:10.1109/TCOMM.2020.3044074

Yaru Fu (S’14-M’18) received her BEng (Hons.)

in Telecommunication Engineering from Northeast

Electric Power University (NEEPU), MSc (Hons.) in

Communication and Information System from Nan-

jing University of Posts and Telecommunications

(NUPT) and Ph.D in Electronic Engineering from

City University of Hong Kong (CityU) in 2011,

2014, and 2018, respectively. Then, she joined in

the Institute of Network Coding (INC), the Chinese

University of Hong Kong (CUHK) as a Post-doctoral

Research Assistant. From Sep. 2018 to Jun. 2020,

she served as a Research Fellow (Class 2) in Singapore University of Technol-

ogy and Design. From Feb. 2016 to May. 2016, she was a visiting researcher

in Telecom Paris Tech (TPT) and Laboratory of Information, Networking

and Communication Sciences (Lincs). She was also an Intern with Nokia

Bell Labs, Paris, France. Now, she is a Research Assistant Professor with

the School of Science and Technology, The Open University of Hong Kong,

China. Her research interests include intelligent wireless communications and

networking, caching and recommendation, distributed storage systems, IoT,

and URLLC.

Lou Sala¨

un received the engineering diploma and

the M.Sc. degree from Centrale-Sup´

elec, Gif-sur-

Yvette, France, in 2016, specializing in computer

system, applied mathematics, signal processing, and

telecommunications, and the Master of Research de-

gree from University of Paris-Saclay, Saclay, France,

in 2016, specializing in computer science and soft-

ware engineering. He obtained his Ph.D. degree in

2020, on resource allocation and optimization for

the non-orthogonal multiple access from T´

el´

ecom

Paris, Paris, France, jointly working with Nokia

Bell Laboratories, Nozay, France. He is currently working as a Research

Engineer at Nokia Bell Laboratories. His research interests include algorithmic

computer science, optimization, telecommunications, resource allocation, and

distributed computing.

Xiaolong Yang received his Ph.D degree in Infor-

mation and Communication Engineering from the

School of Information and Electronics, Beijing Insti-

tute of Technology in 2020. From Dec. 2018 to Dec.

2019, he served as a visiting student in Singapore

University of Technology and Design, supervised by

Prof. Tony Q. S. Quek. Now, he is an Assistant Pro-

fessor with the School of Information and Communi-

cation Engineering, Beijing Information Science and

Technology University, Beijing, China. His research

interests include intelligent wireless communications

and networks, caching, mobile edge computing, URLLC, and recommendation

system.

Wanli Wen (S’15-M’20) received the B.S. degree

from Anhui University of Finance and Economics,

Bengbu, China, in 2011, the M.S. degree in Commu-

nication and Information Systems from Hangzhou

Dianzi University, Hangzhou, China, in 2014, and

the PhD degree in Information and Communication

Engineering from Southeast University, Nanjing,

China, in 2019. Currently, he is a postdoctoral re-

search fellow in Singapore University of Technology

and Design. His research interests include mobile

edge computing, caching, federated learning, and

physical layer security.

15

Tony Q.S. Quek (S’98-M’08-SM’12-F’18) received

the B.E. and M.E. degrees in electrical and electron-

ics engineering from the Tokyo Institute of Technol-

ogy in 1998 and 2000, respectively, and the Ph.D.

degree in electrical engineering and computer sci-

ence from the Massachusetts Institute of Technology

in 2008. Currently, he is the Cheng Tsang Man Chair

Professor with Singapore University of Technology

and Design (SUTD). He also serves as the Director

of the Future Communications R&D Programme, the

Head of ISTD Pillar, and the Deputy Director of the

SUTD-ZJU IDEA. His current research topics include wireless communica-

tions and networking, network intelligence, internet-of-things, URLLC, and

big data processing.

Dr. Quek has been actively involved in organizing and chairing sessions,

and has served as a member of the Technical Program Committee as well as

symposium chairs in a number of international conferences. He is currently

serving as an Editor for the IE EE TR ANS ACT ION S ON WI REL ES S COMM U-

NI CATIO NS and an elected member of the IEEE Signal Processing Society

SPCOM Technical Committee. He was an Executive Editorial Committee

Member for the IE EE TRANSACTIONS ON WIREL ES S COMMUNICATIONS,

an Editor for the I EEE T RANSACTIONS ON COMMUNICATIONS, and an

Editor for the I EEE WIR EL ESS COMMUNICATIONS LETT ER S.

Dr. Quek was honored with the 2008 Philip Yeo Prize for Outstanding

Achievement in Research, the 2012 IEEE William R. Bennett Prize, the 2015

SUTD Outstanding Education Awards – Excellence in Research, the 2016

IEEE Signal Processing Society Young Author Best Paper Award, the 2017

CTTC Early Achievement Award, the 2017 IEEE ComSoc AP Outstanding

Paper Award, the 2020 IEEE Communications Society Young Author Best

Paper Award, the 2020 IEEE Stephen O. Rice Prize, the 2020 Nokia Visiting

Professor, and the 2016-2020 Clarivate Analytics Highly Cited Researcher.

He is a Distinguished Lecturer of the IEEE Communications Society and a

Fellow of IEEE.