arXiv:1611.02660v2 [] 5 Feb 2018

This article has been accepted by IEEE Transactions on Vehicular Technology.
Copyright (c) 2015 IEEE. Personal use of this material is permitted. However, permission to use this material for any other
purposes must be obtained from the IEEE by sending a request to pubs-permissions@ieee.org.
Z. Ye, C. Pan, H. Zhu and J. Wang,“Tradeoff Caching Strategy of Outage Probability and Fronthaul Usage in Cloud-RAN,”
in IEEE Transactions on Vehicular Technology, vol. PP, no. 99, pp. 1-1.
doi: 10.1109/TVT.2018.2797957
https://doi.org/10.1109/TVT.2018.2797957

1

Tradeoff Caching Strategy of Outage Probability
and Fronthaul Usage in Cloud-RAN
Zhun Ye, Member, IEEE, Cunhua Pan, Member, IEEE,
Huiling Zhu, Senior Member, IEEE, and Jiangzhou Wang, Fellow, IEEE

Abstract—In this paper, tradeoff content caching strategy is
proposed to jointly minimize the cell average outage probability
and fronthaul usage in cloud radio access network (CloudRAN). At first, an accurate closed form expression of the outage
probability conditioned on the user’s location is presented, and
the cell average outage probability is obtained through the
composite Simpson’s integration. The caching strategy for jointly
optimizing the cell average outage probability and fronthaul
usage is then formulated as a weighted sum minimization
problem, which is a nonlinear 0-1 integer problem. Two heuristic
algorithms are proposed to solve the problem. Firstly, a genetic
algorithm (GA) based approach is proposed. Numerical results
show that the performance of the proposed GA-based approach
with significantly reduced computational complexity is close to
the optimal performance achieved by exhaustive search based
caching strategy, and the GA-based approach can improve
the performance by up to 47.5% on average than the typical
probabilistic caching strategy. Secondly, in order to further
reduce the computational complexity, a mode selection approach
is proposed. Numerical results show that this approach can
achieve near-optimal performance over a wide range of the
weighting factors through a single computation.
Index Terms—Caching strategy, Cloud-RAN, joint optimization, outage probability, fronthaul usage.

I. I NTRODUCTION

T

HE combination of network densification and coordinated multipoint transmission is a major technical trend
in the fifth generation (5G) wireless mobile systems to improve
the overall system performance [2]–[5]. In the traditional radio
access network (RAN) architecture, each cell has its own base
station (BS), where the radio functionality is statically assigned
Copyright (c) 2015 IEEE. Personal use of this material is permitted.
However, permission to use this material for any other purposes must be
obtained from the IEEE by sending a request to pubs-permissions@ieee.org.
Part of this work was presented in IEEE International Conference on
Communications (ICC), Paris, 2017 [1].
This work was supported by the China Scholarship Council (CSC), the
Fundamental Research Funds of Shandong University (No. 2015ZQXM008),
a Marie Curie International Outgoing Fellowship within the 7th European
Community Framework Programme under the Grant PIOFGA-2013-630058
(CODEC), the UK Engineering and Physical Sciences Research Council under
the Project EP/L026031/1 (NIRVANA), and the Framework of EU Horizon
2020 Programme under the Grant 644526 (iCIRRUS).
Zhun Ye is with the School of Mechanical, Electrical and Information
Engineering, Shandong University, Weihai, Shandong Province, 264209, P.
R. China, e-mail: zhunye@sdu.edu.cn
Cunhua Pan is with the School of Electronic Engineering and Computer
Science, Queen Mary University of London, London, E1 4NS, United
Kingdom, Email: c.pan@qmul.ac.uk
Huiling Zhu and Jiangzhou Wang are with the School of Engineering
and Digital Arts, University of Kent, Canterbury, Kent, CT2 7NT, United
Kingdom, e-mail: {h.zhu, j.z.wang}@kent.ac.uk

to the base band processing module. Adding more base stations and introducing multiple input multiple output (MIMO)
technology will increase the complexity of the network and
result in higher total cost of ownership (TCO) for the mobile
operators [6], [7].
Consisting of centralized base band processing resources,
known as base band unit (BBU) pool, and distributed remote
radio heads (RRHs) or remote antenna units [8]–[10], cloud
radio access network (Cloud-RAN) becomes a new type
of RAN architecture to support multipoint transmission and
access point densification required by 5G systems [6], [7],
[11], [12]. The scalable, virtualized, and centralized BBU pool
is shared among cell sites, and its computing resources can
be dynamically allocated to different cells according to their
traffic. The RRHs are responsible for the radio processing task,
and they are connected with the BBU pool through fronthauls,
while the BBU pool performs the base band processing task
and it is connected to the core network through backhauls.
Thanks to the novel architecture, Cloud-RAN has many advantages such as cost effective, lower energy consumption,
higher spectral efficiency, scalability and flexibility etc., which
makes itself a promising candidate for the 5G deployment.
Particularly, Cloud-RAN is also a competitive solution for the
heterogeneous vehicular networks, which can provide better
quality of service (QoS) to intense vehicular users in an urban
environment [13], [14]. However, existing fronthaul/backhaul
of Cloud-RAN cannot meet the requirements of the emerging
huge data and signaling traffic in terms of transmission bandwidth requirements, stringent latency constraints and energy
consumption etc. [15]–[17], which has become the bottleneck
of the evolution towards 5G.
Statistics showed that a large amount of the data traffic is
generated from a small amount of most popular content files.
These popular files are requested by a large amount of users,
which results in duplicated transmissions of the same content
files on the fronthaul and backhaul links. Therefore, content
caching in RAN can be a promising solution to significantly
reduce the fronthaul/backhaul traffic [18]–[20]. During offpeak times, popular content files can be transferred to the
cache-enabled access points (macro base station, small cell,
relay node etc.). If the files requested by mobile users are
cached in the access points of the RAN, the files will be transmitted directly from the RAN’s cache without being fetched
from the core network, which can significantly reduce the
fronthaul/backhaul traffic and meanwhile shorten the access
latency of the files, thus improve users’ quality of experience
(QoE). In Cloud-RAN, thanks to the ongoing evolution of

2

fronthaul technology and function splitting between the BBU
and RRHs [16], [21], there comes possibility to realize content
caching in RRHs, which allows users fetching required content
files directly from RRHs and thus can further reduce fronthaul
traffic.
There are two stages related with caching: caching placement stage and caching delivery stage [20]. Caching placement, or known as caching strategy, is the stage to determine
which files should be stored in which cache-enabled access
points, and delivery stage refers to stage of transmitting the
requested files from access points to mobile users through
wireless channels. Among these two stages, caching placement
is performed for a relative long-timescale. Once a caching
placement is carried out, it will not change very frequently.
The reason is that the popularity of the content files will
remain the same for a relative long period such as several
hours, one day, or even longer time. On the other hand,
delivery stage runs in a short-timescale. In a delivery stage,
the wireless transmission scheme should be able to adapt to
the instantaneous channel state information (CSI) which varies
very rapidly.
There are many researches investigating the delivery stage
with the target of data association or/and energy consumption
optimization under a given caching strategy, such as [22]–
[24]. On the other hand, caching strategy is of importance
because it is the initial step to perform caching and obviously
it will have an impact on the performance of the delivery stage.
The researches investigating caching strategies generally focus
on reducing the file access latency [25]–[27], or minimizing
the transmission cost of the backhaul [28], [29], or both of
them [30]. However, the wireless transmission characteristics
such as fading were not considered in the aforementioned
researches, i.e., it was assumed that the wireless transmission
is error-free. The caching strategy will affect the wireless
transmission performance such as outage probability, which
is an important metric of the system’s performance. For
the fronthaul/backhaul traffic or average file access delay
reduction, caching different files in the RAN will be optimal,
however there is no transmit diversity to combat fading in the
file delivery stage, which may decrease the reliability of the
wireless transmission. Hence, caching strategy should be optimized by taking into consideration the wireless transmission
performance.
There are some papers considering wireless fading characteristics when designing caching strategy [31], [32]. The authors only considered small scale Rayleigh fading by assuming
that the user has the same large scale fading at any location.
However, in reality, several RRHs will jointly serve the user
in Cloud-RAN, and obviously the distance between each RRH
and the user will not be the same, so it is important to consider
large scale fading in wireless transmission. In addition, they
focused on single-objective optimization without considering
the fronthaul/backhaul usage.
The aim of caching in RRHs of Cloud-RAN is to significantly reduce the fronthaul traffic. Fronthaul usage, i.e.,
whether the fronthaul is used, is a metric which can reflect not
only the file delivery latency but also the energy consumption
of the fronthaul. For example, lower fronthaul usage implies

there are more possibilities that mobile user can access the
content files in near RRHs, which will shorten the file access
latency, meanwhile the fronthaul cost (i.e., the energy consumption) will be lower. On the other hand, outage probability
is an important performance metric of the system, which
reflects the reliability of the wireless transmission, i.e., whether
the requested content files can be successfully transferred to
the user, and it also reflects the utility of the wireless resources.
If replicas of certain content files are cached in several RRHs,
the outage probability will be reduced due to the transmit
diversity in wireless transmissions, while the fronthaul usage
will become higher because the total number of different files
cached in the RRHs are reduced and there is a high possibility
to fetch files from the BBU pool. On the other hand, caching
different files in the RRHs will reduce the fronthaul usage,
while the outage probability will become relatively higher due
to the decrease of wireless diversity. Therefore, there exists
tradeoff between fronthaul usage and outage probability.
In this paper, we investigate downlink transmission in a
virtual cell in Cloud-RAN, such as a hot spot area, shopping
mall, or an area covered by the Cloud-RAN based vehicular
network etc. The tradeoff caching strategy is proposed to
jointly minimize the cell average outage probability and the
fronthaul usage. A realistic fading channel is adopted, which
includes path loss and small scale Rayleigh fading. The
caching strategy is designed based on the long-term statistics
about the users’ locations and content file request profiles. The
major contributions of this paper are:
1) Closed form expression of outage probability conditioned
on the user’s location is derived, and the cell average outage
probability is obtained through the composite Simpson’s
integration. Simulation results show that the analysis is
highly accurate.
2) The joint optimization problem is formulated as a weighted
sum minimization of cell average outage probability and
fronthaul usage, which is a 0-1 integer problem. Two
heuristic algorithms are proposed to solve the problem:
a) An effective genetic algorithm (GA) based approach
is proposed, which can achieve nearly the same performance as the optimal exhaustive search, while the
computational complexity is significantly reduced.
b) In order to further reduce the computational complexity,
a mode selection approach is proposed. Simulation results show that it can achieve near-optimal performance
over a wide range of weighting factors through a single
computation.
The remainder of this paper is organized as follows. Section
II reviews the related works. System model is described in
Section III. The optimization problem is formulated in Section
IV and the cell average outage probability and fronthaul
usage are analyzed. The proposed GA-based approach and the
mode selection schemes are described in Section V. Numerical
results are given in Section VI and the conclusion is given in
Section VII.
Notations: E(·) denotes statistical expectation, and Re(·)
denotes the real part of a complex number. AL×N = {al,n }
denotes L × N matrix, al,n or A(l, n) represents the (l, n)-

3

th entry of the matrix. R+ denotes the set of positive real
numbers, and Z+ denotes positive integer set. CN (µ, σ 2 )
represents complex Normal distribution with mean µ and
variance σ 2 , and χ2 (k) is the central Chi-squared distribution
with k degrees of freedom.
II. R ELATED W ORKS
From the caching point of view, there exists significant similarities between Cloud-RAN, small cell network, marcocell
network and some vehicular networks etc. There are many
researches investigating the delivery stage under a certain
caching strategy, and the main target was to optimize the data
association (e.g., RRH clustering and transmit beamforming),
such as [22]–[24]. In [22] and [23], optimal base station
clustering and beamforming were investigated to reduce the
backhaul cost and transmit power cost under certain caching
strategy. In addition, the performances of different commonly
used caching strategies, such as popularity-aware caching,
random caching, and probabilistic caching, were compared in
[23]. In [24], assuming there are several small base stations
in an orthogonal frequency division multiple access (OFDMA)
macro cell, the optimal association of the users and small base
stations was investigated to reduce the long-term backhaul
bandwidth allocation. In these researches, the caching strategy
was assumed to be fixed when designing the delivery schemes,
which is because the delivery stage runs in a much shorter
timescale than the caching placement stage.
On the other hand, caching strategy has attracted widely
concern recently, the related researches mainly focused on the
reduction of file access latency [25]–[27], fronthaul/backhaul
transmissions [28], [29], or both of them [30]. In [25], a collaborative strategy of simultaneously caching in BS and mobile
devices was proposed to reduce the latency for requesting
content files. The proposed optimal strategy was to fill the BS’s
cache with the most popular files and then cache the remaining
files of higher popularity in the mobile devices. In [26], a
distributed algorithm with polynomial-time and linear-space
complexity was proposed to minimize the expected overall
access delay in a cooperative cell caching scenario. The delay
from different sources to the user was modeled as uniformly
distributed random variables within a certain range. In [27],
the probabilistic caching strategy was optimized in clustered
cellular networks, where the limited storage capacity of the
small cells and the amount of transferred contents within the
cluster were considered as two constraints to minimize the
average latency. The optimized caching probability of each
content file was obtained.
In [28], a coded caching placement was proposed to minimize the backhaul load in a small-cell network, where multicast was adopted. The file and cache sizes were assumed to
be heterogeneours. In [29], to minimize the total transmission
cost among the BSs and from the core network, each BS’s
cache storage was divided into two parts, the first part of
all the BSs cached same files with higher popularity ranks,
while the second part of all the BSs stored different files.
The cache size ratio of the two parts was optimized through
particle swarm optimization (PSO) algorithm. In [30], caching

strategy was investigated in a Cloud-RAN architecture based
networks, and the average content provisioning cost (e.g., latency, bandwidth etc.) was analyzed and optimized subjecting
to the sum storage capacity constraint. Analytical results of
the optimal storage allocation (how to partition the storage
capacity between the control BS and traffic BS) and cache
placement (decision on which file to cache) were obtained.
However, the aforementioned researches did not take wireless
transmission characteristics into consideration. In practice, the
caching strategy will have an impact on the performance of the
delivery stage, so wireless transmission performance should be
considered in order to optimize the caching strategy.
There are some papers considering wireless fading characteristics when designing/investigating caching strategy [31]–
[34]. Stochastic geometry was used to analyze large scale
networks in [33], [34]. In [33], considering a cache-enabled
two-tier heterogeneous network with one macrocell BS and
several small-cell BSs, outage probability, throughput, and
energy efficiency (EE) were analyzed. Each of the BSs caches
the most popular content files until the storage is full filled.
Numerical results showed that larger small-cell cache capacity
may leads to lower network energy efficiency when the density
of the small cells is low. In [34], the performance of probabilistic caching strategy was analyzed and optimized in a smallcell environment, and the aim was to maximize the successful
download probability of the content files. However, only
probabilistic content placement can be obtained through using
the tool of stochastic geometry [35], that is, the probability of
a certain file should be cached in the access points. In [31],
optimal caching placement was obtained through a greedy
algorithm to minimize the average bit error rate (BER) in a
macro cell with many cache-enabled helpers and each helper
can cache only one file. The user selects one helper with
the highest instantaneous received signal to noise ratio (SNR)
among the helpers which cache the requested file. If none of
the helpers cache the requested file, the user will fetch the file
from the BS. In [32], cache-enabled BSs are connected to a
central controller via backhaul links. The aim was to minimize
the average download delay. Similar to [31], the user selects
the BS with the highest SNR in the candidate BSs caching the
requested files. In [31] and [32], the authors only considered
small scale Rayleigh fading by assuming that the user has the
same large scale fading at any location, which is unpractical. In
addition, they focused on single-objective optimization without
considering the fronthaul/backhaul usage.
Inspired by the aforementioned researches, in this paper,
outage probability is used to reflect the wireless transmission performance, and fronthaul usage is used to reflect
the transmission latency and power consumption etc. Outage
probability and fronthaul usage are jointly considered when
designing the caching strategy, which leverages the tradeoff
between caching the same content files to obtain lower outage probability or caching different content files to reduce
fronthaul usage. Considering the distances from each RRH
to the user are different in a Cloud-RAN environment, a more
practical fading channel model which includes both large and
small scale fading is adopted.

4

III. S YSTEM M ODEL

Ċ

It is assumed that there are N cache-enabled RRHs in a
circular cell with radius R, and the set of RRH cluster is
denoted as N = {1, 2, · · · , N }. The file library with a total
of L content files is denoted as F = {F1 , F2 , · · · , FL }, where
Fl is the l-th ranked file in terms of popularity, i.e., F1 is the
most popular content file. The popularity distribution of the
files follows the Zipf’s law [36], and the request probability
of the l-th ranked content file is
l−β

Pl = PL

n=1

n−β

al,n =

Ċ
File l2

Ċ
Ċ

Ċ
File l2

2
3

1
RRH with cache

Ċ
Ċ

4

Mobile user

,

(1)

where β ∈ [0, +∞) is the skewness factor. The popularity is
uniformly distributed over content files when β = 0 (Pl =
1/L, ∀l) and becomes more skewed towards the most popular
files as β grows, while large popularity skewness is usually
observed in wireless applications.
For simplicity, it is assumed that all content files have the
same size, and the file size is normalized to 1. Even though
the file size will not be equal in practice, each file can be
segmented into equal-sized chunks for placement and delivery
[19], [37]. Considering the BBU pool can be equipped with
sufficient storage space, it is assumed that all the L content
files are cached in the BBU pool 1 . Some of the content files
can be further cached in the RRHs in order to improve the
system’s performance, and a file can be cached in one or more
RRHs depending on the cachingPstrategy. The n-th RRH can
N
cache Mn files, and generally n=1 Mn < L. That is, the
total caching storage space in all the RRHs is smaller than
that in the BBU pool. The caching placement of the content
files in the RRHs can be denoted by a binary placement matrix
AL×N , with the (l, n)-th entry


BBU pool

All L
File l1
content files Ċ

1, the n-th RRH caches the l-th file
0, otherwise

(2)

indicating whether
the l-th content file is cached in the n-th
PL
RRH, and l=1 al,n = Mn , ∀n.
Single user scenario is considered in this paper. However,
the proposed algorithms can be applied in practical multiuser
systems with orthogonal multiple access technique such as
OFDMA system, in which each user is allocated with different
subcarriers and there is no interference [38]–[40]. It is assumed
that the user can only request for one file at one time, and
all the RRHs caching the requested file will serve the user.
If none of the RRHs caches the requested file, the file will
be transferred to all the RRHs from the BBU pool through
fronthauls, and then to the user from all the RRHs through
1 Generally speaking, the backhaul connecting the BBU pool and the core
network will have larger transmission bandwidth than the fronthaul, so only
the fronthaul usage reduction is considered in this paper. In practice, the BBU
pool can not cache all the content files originated in the Internet, however, if
the requested file is not cached in the BBU pool, it can be fetched from the
core network through using backhaul, then it is the same as the file is already
cached in the BBU pool as we only focus on the fronthaul usage rather than
backhaul usage.

Fig. 1. System model and file delivery scheme. Red dashed and green solid
lines represent the file fetching routes when user requests for the l1 -th and
l2 -th content file, respectively.

wireless channels. The service RRH set for the user with
respect to (w.r.t.) the l-th file is denoted as


, ∃n such that al,n = 1
,
, al,n = 0 for ∀n
(3)
with cardinality |Φl |∈ {1, 2, · · · , N }, (l ∈ {1, 2, · · · , L}). The
system model and file delivery scheme are illustrated in Fig.1.
For example, when the user requests for the l1 -th file which
is not cached in any of the RRHs, the file will be transferred
from the BBU pool to all the RRHs through fronthauls and
then transmitted to the user. Then the user’s service RRH set
is Φl1 = {1, 2, 3, 4}. When the user requests for the l2 -th file
which is already cached in RRH 2 and RRH 3 via caching
placement, the service RRH set is Φl2 = {2, 3}.
The wireless channel is assumed to be block-fading, i.e.,
the channel’s gain is kept as constant within the duration
of a block, and different blocks experience independent and
identically distributed (i.i.d.) fading. When being requested,
a file would be transmitted through different blocks of the
wireless channel. Assuming that both the RRH and the user’s
device are equipped with single antenna, the user’s received
signal from the service RRH set when requesting for the l-th
file can be expressed as
Φl =

{n|al,n = 1, n ∈ N }
N

y=

Xq
pT Kd−α
n hn s + noise,

(4)

n∈Φl

where pT is the transmit power of each RRH, K is a constant
depending on the antenna characteristics and the average
channel attenuation, dn is the distance between the n-th RRH
and the user, α is the path loss exponent, hn ∼ CN (0, 1)
represents complex Gaussian small
 scale fading, s represents
the transmitted symbol and E |s|2 = 1, and noise denotes
complex additive white Gaussian noise (AWGN) with zero
mean and variance σ 2 .
The main modeling parameters and notations are summarized in Table I.

5

high, a large value of η should be chosen to reduce the outage
probability, so that the price is to increase the fronthaul usage.

TABLE I
M ODELING PARAMETERS AND N OTATIONS
Symbol
N
L
Pl
β
Mn
AL×N
al,n
Φl
pT
dn

Definition
Number of RRHs
Number of content files
Request probability of the l-th file
Skewness factor of the Zipf’s distribution
The number of files that the n-th RRH can cache
Caching placement matrix
Binary variable indicating whether the l-th file is
cached in the n-th RRH, (l, n)-th entry of AL×N
The service RRH set for the user w.r.t. the l-th file
Transmit power of each RRH
Distance between the n-th RRH and the user

B. Outage Probability Analysis

IV. P ROBLEM F ORMULATION AND A NALYSIS
A. Problem Formulation
Define the normalized fronthaul usage w.r.t. the l-th file as

N
Y
1, al,n = 0 for ∀n
Tl (A) =
(1 − al,n ) =
,
0, ∃n such that al,n = 1
n=1
(5)
which indicates that if there is at least one copy of the
requested file cached in the RRHs, there will be no fronthaul
usage, i.e., Tl = 0, while if the requested file is not cached in
any of the RRHs, there will be fronthaul usage, i.e., Tl = 1.
Note that Tl does not depend on the user’s location.
The caching strategy should be designed according to the
long-term statistics over the user’s locations and content file
requests. The joint optimization problem can be formulated
through a weighted sum of the objectives [41],
min fobj (A) = η

L
X

h
i
(l)
Pl Ex0 Pout (x0 ) +(1 − η)

l=1

|

L
X

{z

}

al,n = Mn ,

Fγ (γ) =

Ji
I X
X
λj−1 Aij
i

i=1 j=1

·

Pl Tl ,

(j − 1)!

(j − 1)!
λij−1

−

e

−λi γ

j−1
X

(j − 1)!
γ j−1−k
k
(j
−
1
−
k)!
λ
i
k=0

| {z }

fronthaul usage

(6b)

!#
,
(9)

where
"

Ji #
(−λi )Ji −j dJi −j
1
Aij =
Mγ (s) 1 −
·s
(Ji − j)! dsJi −j
λi

l=1

al,n ∈ {0, 1}.

(8)

and the cumulative distribution function (CDF) is given by

"

(6a)
s.t.

Ji
I X
X
λji Aij j−1 −λi γ
fγ (γ) =
γ
e
,
(j − 1)!
i=1 j=1

l=1

cell average outage probability

L
X

When the user requests for the l-th file at location x0 , the
SNR of the received signal is given by
X
X
X pT
−α
2
2
Kd
|h
|
=
γ
S
|h
|
=
γn ,
γl (x0 ) =
n
0
n
n
n
σ2
n∈Φl
n∈Φl
n∈Φl
(7)
where γ0 = pσT2 is SNR at the transmitter of each RRH,
Sn = Kd−α
is the large scale fading, and γn = γ0 Sn |hn |2
n
represents the received SNR from the n-th RRH. For a specific
file, without ambiguity, we omit the subscript of file index l
and the user’s location x0 in the following analysis.
In the service RRH set Φ with cardinality |Φ|, the RRHs
with the same distance to the user are grouped together.
Assuming there are I (I ≤ |Φ|) groups, the
PI number of RRHs
in the i-th group is denoted by Ji , and i=1 Ji = |Φ|. The
distance between the user and the RRH in the i-th group is
1
denoted by di (i ∈ {1, 2, 3, · · · , I}). Letting λi = γ Kd
−α ,
0
i
the probability density function (PDF) of the received SNR
can be obtained as

,
s=λi

(10)

(6c)

where η ∈ [0, 1] is a weighting factor to balance the tradeoff
between outage probability and fronthaul usage, Ex0 denotes
(l)
expectation in terms of the user’s location x0 , Pout (x0 ) is the
outage probability when the user requests for the l-th file at
location x0 . Constraint (6b) describes the caching limit of each
RRH, and constraint (6c) indicates the joint optimization as a
0-1 integer problem.
Different values of η will lead to different balances between
outage probability and fronthaul usage. Given η, the caching
strategy can be determined through solving the optimization
problem in (6). In practice, η is chosen by the decision
maker (e.g., RAN’s operator) according to the system’s longterm statistics of outage probability and fronthaul usage. For
example, when the fronthauls’ average payload is heavy, a
small value of η should be chosen to reduce the fronthaul
usage, and the price is to increase the outage probability. On
the other hand, when the cell average outage probability is

and
Mγ (s) =

Y
n∈Φ

1
.
1 − γ0 Sn · s

(11)

The derivations of (8) and (9) are given in Appendix A.
When the distance between any service RRH and the user
is distinct, i.e., dn 6= dm , ∀n 6= m ∈ Φ, (8) and (9) are written
as




X 1 Y
Sn 
γ
fγ (γ) =

 exp −
γ0 Sn
Sn − Sm
γ0 Sn
n∈Φ

m∈Φ
m6=n

(12)
and

Fγ (γ) =



XY

n∈Φ

m∈Φ
m6=n




Sn 
γ
,
 1 − exp −
Sn − Sm
γ0 Sn
(13)

respectively.

6

placement matrix AL×N = {al,n }. However, the problem is
a 0-1 integer nonlinear problem, and it is difficult to obtain a
closed form solution. The following section will focus on how
to solve this problem.

1
0.9

Prob.(γ < abscissa)

0.8
0.7
0.6

scenario 1

V. C ACHING P LACEMENT S CHEME

scenario 2

In this section, two efficient approaches are proposed to
solve the joint optimization problem: one is GA-based approach and the other is mode selection approach.

0.5
0.4
0.3

scenario 3

0.2

A. Genetic Algorithm Based Approach

Simulation
Analysis

0.1
0
0

2

4

6

8

10

12

14

16

18

20

SNR γ (dB)

Fig. 2. CDF of the user’s received SNR at a fixed location.

The accuracy of the derived CDF of (9) (written as (13) in
special case) is illustrated in Fig. 2 through three scenarios.
Assuming there are 6 service RRHs for the user, and the
distances between the service RRHs and the user are denoted
by a vector D. The three different scenarios are (1) scenario 1:
D1 = [0.8R, 0.8R, 0.8R, 0.8R, 0.8R, 0.8R], (R is the cell radius), i.e., all the RRHs are with the same distance to the user;
(2) scenario 2: D2 = [0.6R, 0.7R, 0.7R, 0.8R, 0.8R, 0.8R],
i.e., some of the RRHs have same distance with the user;
(3) scenario 3: D3 = [0.5R, 0.6R, 0.7R, 0.8R, 0.9R, 1.0R],
i.e., all the RRHs are with different distances to the user.
It can be seen from Fig. 2 that the analytical results match
the simulation results, which demonstrates the accuracy of the
derived expression of (9).
The outage probability according to a certain SNR threshold
γth is
Pout (γth ) = Fγ (γth ).
(14)
It is difficult to find a closed form solution of the cell aver(l)
age outage probability w.r.t. the l-th file, i.e., Ex0 [Pout (x0 )].
However, we can use the composite Simpson’s integration
in forms of polar coordinates, where the user’s location is
denoted by (ρ, θ) and x0 = ρejθ .
h
i
(l)
Ex0 Pout (x0 )
Z 2π Z R
(l)
=
Pout (ρ, θ)fx0 (ρ, θ)ρdρdθ
(15)
0
0
≈

U
V
∆h∆k X X
(l)
wu,v ρu Pout (ρu , θv )fx0 (ρu , θv ),
9 u=0 v=0

where R is the cell radius, even integers U and V are
chosen such that ∆h = R/U and ∆k = 2π/V meeting the
requirement of calculation accuracy, ρu = u∆h, θv = v∆k,
fx0 (ρ, θ) is the probability density function of the user’s
location, which is 1/πR2 when the user’s location is uniformly
distributed in the cell, and {wu,v } are constant coefficients
(please refer to [42] and Chapter 4 in [43]).
Substituting (5), (9), (14) and (15) into (6a), the optimization problem is formulated as a function of the caching

Genetic algorithm is inherently suitable for solving optimization problems with binary variables [44]. The algorithm
structure is shown in Fig. 3. Firstly, Np candidate caching
placement matrices are generated, known as the initial population (with population size Np ), and each matrix is called
an individual. Then the objective value of each individual
is evaluated through (6a). Ne individuals with best objective
values are chosen as elites and passed into next generation (children of current generation population) directly. The
rest of the next generation population are generated through
crossover and mutation operations. The crossover function
operates on two individuals (known as parents) and generates
a crossover child, and the mutation function operates on a
single individual and generates a mutation child. The number of individuals generated through crossover and mutation
operations are denoted as Nc and Nm , respectively, where
Ne + Nc + Nm = Np , and the crossover fraction is defined
c
as fc = NcN
+Nm . The selection function selects 2Nc and
Nm individuals from the current generation for the crossover
and mutation function, respectively, where some individuals
will be selected more than once. Stochastic uniform sampling
selection [45] is adopted, and individuals with lower objective
values in current generations will have a higher probability to
generate offsprings. Repeat the evaluation-selection-generation
procedures until termination criterion is reached. Finally, the
best individual in the current population is chosen as the output
of the algorithm. The initial population, crossover function and
mutation function of the proposed GA approach are described
as follows.
1) Initial Population: The initial population is created as a
set of {AL×N }. For each column in each individual, Mn out
of the first L0 entries (i.e., {a1,n , a2,n , · · · , aL0 ,n }) are set to
be one randomly, and all the remaining entries are set to be
zero, where
XN
L0 =
Mn < L
(16)
n=1

is based on the fact that the total different files with higher popularity can be cached in the RRHs are {Fl |l = 1, 2, · · · , L0 }.
There is no benefit to cache files {Fl |l > L0 } with lower
popularity.
2) Crossover Function: The crossover function generates
a child Ac from parents A1 and A2 . A two-point crossover
function is used, which is described in Algorithm 1, in which
steps 9 to 14 are heuristic operations to meet constraint (6b).

7

Current generation
Elites

...

...
Evaluation
Eq. (6a)

Selection
Function

A L´ N

Crossover
Function

Evaluation

Termination
criterion
reached ?

Eq. (6a)
Mutation
Function

Yes

Output the best
individual in
current population

No

Initial population

Next generation

Fig. 3. Genetic algorithm structure.

Algorithm 1: Crossover function
1

2
3
4
5

6
7

8
9
10
11
12
13
14
15

(1)

(2)

Get parent A1 = {al,n } and A2 = {al,n } from selection
(c)
function, initialize their child Ac = {al,n } = 0L×N .
for n = 1, 2, · · · , N do
Generate random integers l1 , l2 ∈ [1, L0 ], l1 6= l2
if l1 < l2 then
(1)
Replace al,n , l = {l1 , l1 + 1, · · · , l2 } of A1 with
(2)
al,n , l = {l1 , l1 + 1, · · · , l2 } of A2 , and then set
(c)
(1)
al,n = al,n , ∀l ∈ {1, 2, · · · , L}.
else
(2)
Replace al,n , l = {l2 , l2 + 1, · · · , l1 } of A2 with
(1)
al,n , l = {l2 , l2 + 1, · · · , l1 } of A1 , and then set
(c)
(2)
al,n = al,n , ∀l ∈ {1, 2, · · · , L}.
end
PL (c)
while l=1 al,n > Mn do
(c)
Set nonzero al,n to 0 in descending order of l.
end
PL (c)
while l=1 al,n < Mn do
(c)
Set zero al,n to 1 in ascending order of l.
end
end

is the largest content diversity (LCD) caching [32], [46], [47].
In MPC, each RRH caches the most popular files, i.e., the nth RRH caches {Fl |l = 1, 2, · · · , Mn }, which will have low
outage probability while high
PN fronthaul usage. In the LCD
scheme, a total of L0 =
n=1 Mn (< L) different most
popular content files are cached in the RRHs, which can have
lowest fronthaul usage while relatively high outage probability.
If the LCD scheme is adopted in Cloud-RAN, the impact of
locations of caching content files on the cell average outage
probability needs to be considered. Assuming the locations of
the user are uniformly distributed in the cell, caching the most
popular files in the RRH nearest to the cell center will achieve
better outage probability performance, which is similar to the
RRH placement problem [48]. Therefore, for Cloud-RAN, we
improve the LCD scheme and propose a location-based LCD
(LB-LCD) scheme which is described in Algorithm 2.
Algorithm 2: Proposed LB-LCD caching strategy
1

2

Sort the RRH set as
Ns = {ni |i = 1, 2, · · · , N, Dn1 ≤ Dn2 ≤ · · · ≤ DnN },
where Dni denotes the distance between the ni -th RRH
and the cell center.
Fill the cache of the RRH set Ns in sequence from n1 to
PN
nN with content files {Fl |l = 1, 2, · · · , n=1 Mn } in
ascending order of l.

3) Mutation Function: The mutation function operates on
a single individual and generates its mutation child. For each
column of the individual, one of the first L0 entries is randomly
selected and the value is set to be the opposite (0 to 1 and
vice versa), then steps 9 to 14 described in Algorithm 1
are executed to meet constraint (6b). The mutation operation
reduces the probability that the algorithm converges to local
minimums.
If Ng generations are evaluated, there is a total of Np Ng
calculations of the objective values. In order to further reduce
the computational complexity of caching strategy, a mode
selection approach is proposed in next subsection.

For example, there are 3 RRHs {1, 2, 3}, and each RRH can
cache 3 files, so that all the RRHs can cache 9 different content
files. The distance between RRH i and the cell center is Di ,
assuming D1 < D2 < D3 . The LB-LCD caching strategy is
illustrated in Table II.

B. Mode Selection Approach
There are two particular caching placement schemes: one
is the most popular content (MPC) caching, and the other one

Proposition 1. The objective value of both the MPC scheme
and the LCD scheme is linear with η. When η is small, i.e.,
minimization of the fronthaul usage is weighted more, the LCD

TABLE II
E XAMPLE OF T HE LB-LCD C ACHING S TRATEGY
RRH
Files
cached

1
F1
F2
F3

2
F4
F5
F6

3
F7
F8
F9

8

scheme is superior to the MPC scheme. When η is large, i.e.,
minimization of the cell average outage probability is weighted
higher, the MPC scheme is superior to the LCD scheme. There
exists a crossover point of the two schemes, the weighting
factor of the crossover point is
1
h
i
(l)
(l)
P
E
P
(x
)
−
P
(x
)
l
x
0
0
.
0
out,M P C
out,LCD
l=1
1+
PL
l=1 Pl (Tl,LCD − Tl,M P C )
(17)
When Mn = M, ∀n, η0 can be further expressed as
η0 =

PL

1

η0 =

PN M
1+

l=1

Pl Ex0

h

(l)
Pout,LCD (x0 )

PN M

l=M +1

i
(l)
− Pout,M P C (x0 ) .

Pl
(18)


Proof. Please refer to Appendix B.

Based on proposition 1, we propose a mode selection
caching strategy. The RAN can make a decision of the tradeoff
according to the statistics of cell average outage probability
and fronthaul usage in the cell, and a tradeoff weighting
factor η is chosen. When η ≤ η0 , select the LB-LCD caching
scheme, while when η > η0 , select the MPC caching scheme.
C. Computational Complexity Analysis
The number of objective function calculations w.r.t. a certain
value of η is evaluated to measure the complexities of the
exhaustive search method, the proposed GA approach and
the proposed mode Q
selection approach.
The complexity of

N
exhaustive search is n=1 MLn . When Mn = M, ∀n, it is
clear that the complexity of exhaustive search is exponential

L N
. The complexity of the
w.r.t. the number of RRHs, i.e., M
proposed GA is Np Ng , where Np and Ng are the population
size and the number of generations evaluated, respectively. Ng
is determined by the convergence behavior of the GA. While
the complexity of the proposed mode selection scheme is only
2. The reason is that, once the value of η0 is solved from (17),
the RAN can choose a mode between MPC and LCD based
on whether η > η0 , and 2 objective function calculations are
involved in solving the equation. Further more, once η0 is
obtained, caching schemes for all values of η are obtained.
The computational complexities of the three approaches are
summarized in Table III.
TABLE III
C OMPUTATIONAL C OMPLEXITY
Scheme
Exhaustive search
Proposed GA-based approach
Proposed mode selection approach

Objective function calculations
QN
L 
n=1 Mn

Np Ng
2

VI. N UMERICAL R ESULTS
In this section, the performances of the proposed two
caching strategies are investigated through some representative

numerical results. Firstly, the accuracy of the cell average
outage probability and fronthaul usage analysis are verified
by evaluating two typical caching schemes, i.e., the MPC and
the LB-LCD schemes. Then the effectiveness of the proposed
GA approach is verified by comparing its performance with
exhaustive search, where the Pareto optimal solutions [41] of
the joint optimization problem are presented. In the proposed
GA approach, placement matrices of the MPC and the LBLCD schemes are added into the initial population to further
improve the performance. Finally, performances of different
caching strategies are compared and the convergence behavior
of the proposed GA is presented.
The MATLAB software is used for the Monte-Carlo simulations and numerical calculations. Throughout the simulation, it
is assumed that each RRH has the same cache size Mn = M .
P
, where P is the
The transmit power of each RRH is pT = N
P
total transmit power in the cell and σ2 = 23 dB. The constant
K in (4) is chosen such that the received power attenuates
20 dB when the distance between the RRH and the user is R
[49]. In such setting, the outage probability does not depend
on the absolute value of R, that is, R can be regarded as
the normalized radius. The main simulation parameters are
summarized in Table IV.
TABLE IV
S IMULATION PARAMETERS
Parameter
Path loss exponent α
P/σ 2
SNR threshold γth
User location distribution
U and V in Simpson’s integration
Population size Np in GA
Selection function
Number of elites Ne
Crossover fraction fc

Value
3
23 dB
3 dB
uniform
6, 6
50
stochastic universal sampling
10
0.85

A. MPC and LB-LCD Caching Placements
PL
(l)
Cell average outage probability ( l=1 Pl Ex0 [Pout (x0 )])
PL
and average fronthaul usage ( l=1 Pl Tl ) of the MPC and LBLCD schemes are shown in Fig. 4 and Fig. 5, respectively.
There are L = 50 files, N = 7 RRHs with one RRH located
at the cell center and the other 6 RRHs evenly distributed on
the circle with radius 2R/3 [23], [50], and each RRH can
cache M = 5 files. Both the simulation and numerical results
are shown in this subsection. In the Monte-Carlo simulations,
there are 104 realizations of the user’s different locations and
content file requests.
Cell average outage probability with different SNR threshold γth and popularity skewness factor β is illustrated in Fig.
4. It can be seen that the outage probability of both the MPC
and the LB-LCD schemes increases with the increase of γth ,
and the outage probability of the MPC scheme is lower than
that of the LB-LCD scheme. The MPC curves of different
values of β coincide. The reason is as follows: according to
the file delivery scheme and the MPC caching strategy, no
matter whether the requested file is cached in the RRHs or
not, the file will be transmitted to the user from all the RRHs,

9

1

1
Simulation
Analysis

Simulation
Analysis

0.9

0.8

0.8

0.7

0.7

Average fronthaul usage

Cell average outage probability

0.9

0.6
0.5

LB-LCD

0.4

β = 0, 0.5, 1, 1.5, 2, 2.5, 3

0.3
0.2
0.1

0.6
0.5

LB-LCD

0.4
0.3
0.2

β = 0, 0.5, 1, 1.5, 2, 2.5, 3

MPC

MPC

0.1
0

0
0

1

2

3

4

5

0

6

0.5

1

1.5

2

2.5

3

Popularity skewness factor β

SNR threshold γth (dB)

Fig. 4. Cell average outage probability. L = 50, M = 5, N = 7.

Fig. 5. Cell average fronthaul usage. L = 50, M = 5, N = 7.

thus the cell average outage probability w.r.t. any l-th file is
(l)
the same, denoting as Ex0 [Pout (x0 )] = Pcell,out , then the cell
average outage probability expected on all the file requests is

which means when β is large enough (β > 2.0), the cell
average outage probability depends mainly on the first 5 most
popular files. These 5 files are cached in the RRH located at
the cell center, and the cell average outage probability w.r.t
any one of the 5 files is the same, so the cell average outage
probability is nearly the same for different values of β (> 2.0),
which approaches the maximum value.
Fig. 5 shows the fronthaul usage of the two caching
schemes. Because the fronthaul usage is independent of γth ,
the curve versus different values of the skewness factor β is
evaluated. The LB-LCD scheme has lower fronthaul usage
than the MPC scheme, which is because that the LB-LCD
scheme caches a total of M N = 5 × 7 = 35 different files
in the RRHs while the MPC scheme caches only M = 5
different files. The average fronthaul usage of both the MPC
and LB-LCD scheme decreases with the increase of β, which
is due to the same reason that as β increases, the popularity
becomes more skewed towards the first few files with higher
ranks, and there is a higher probability that these few files
are cached in the RRHs. As shown in (20), when β = 3, the
fronthaul usage almost depends on the first 5 popular files,
since they are all cached in the RRHs under both the MPC
and the LB-LCD caching strategies, the fronthaul usages of
both schemes approach zero.
It is seen from Fig. 4 and Fig. 5 that the analytical results
are highly consistent with the simulation results. Therefore,
analytical results will be used instead of time-consuming
simulations in the following evaluations.

L
X
l=1

(l)

Pl Ex0 [Pout (x0 )] = Pcell,out ·

L
X

Pl = Pcell,out ,

(19)

l=1

which is not related to β, i.e., no matter how the popularity is
distributed over the files, the cell average outage probability
is kept as a constant.
For the LB-LCD scheme, cell average outage probability
reaches the minimum value when β = 0, and it increases as
β increases and approaches the maximum value when β is
large enough, e.g., β = 2, 2.5, 3. The reason is explained as
follows. According to the file delivery scheme and the LBLCD caching strategy, if the requested file is not cached in
any of the RRHs, the file will be fetched from the BBU
pool, and then transmitted to the user from all the RRHs.
The outage probability will then achieve the minimum value
due to wireless diversity. While if the requested file is cached
in the RRH (only cached in one of the RRHs), the file
will be transmitted to the user from only one RRH, and the
outage probability will be relatively higher. When β = 0,
Pl = 1/L, ∀l, i.e., the request probability is the same for all
the content files, which means that the cell average outage
probability depends evenly on the outage probability of each
file, and the outage probability of the files which are not
cached in the RRHs is lower than that of the files cached
in the RRHs. As β increases, the more skewness of the
popularity will toward the first few files with high ranks, i.e.,
the cell average outage probability depends more on these
files, and there is a higher probability that there is only one
copy for each of these files cached in one certain RRH, and
the corresponding outage probability is high, so the outage
probability increases as β increases and the curve with β = 0
is the lower bound. Note that


5
 0.90, β = 2.0
X
Pl = 0.96, β = 2.5
(20)


l=1
0.99, β = 3.0

B. Tradeoffs between Cell Average Outage Probability and
Fronthaul Usage
Tradeoffs between cell average outage probability and fronthaul usage obtained by exhaustive search and the proposed
GA-based approach are shown in this subsection. There are

three RRHs,
and the polar coordinates of which are R4 , 0 ,

R 2π
R 4π
3 , 3 , and 2 , 3 , respectively. There are L = 9 content
files, and the popularity skewness factor β = 1.5.

10

1

0.6

D

Pareto optimal solutions
all caching placements

0.9

A1

0.5
0.8

0.6~1

exhaustive search
proposed GA

M=1
M=2
M=3

0.7
0.6

Average fronthaul usage

Average fronthaul usage

0.1

0.08

0.5
0.06

B

C

0.4
0.55

A

0.3

0.57

0.59

0.61

0.4

A2

0.6~1

0.3

A3
0.2

B1

0.5

η = 0~0.3

0.6~1
0.3, 0.4

0.5
0.2
0.1

0.4
0.2, 0.3

B C
0

0.1

0.2

0.3

0.4

0.5

0.6

0.2

D

0.45

0.1
0

0.7

0.8

0.9

1

Cell average outage probability

Fig. 6. Cell average outage probability and fronthaul usage tradeoff region.
L = 9, M = 2, N = 3, β = 1.5. Each red point corresponds to a caching
placement, and the 5 points emphasized by small blue circles are the Pareto
optimal solutions of the joint optimization problem.

Fig. 6 is focused on the scenario when the cache size
M is equal to 2. All tradeoffs between cell average outage
probability and fronthaul usage are given by exhaustive search.
Since the popularities of the content files {Pl }, the fronthaul
(l)
usage {Tl } and the outage probability {Pout } are all discontinuous values w.r.t. integer l, the cell average outage probability
and average fronthaul usage region of all caching placements
is a set of discrete points as shown in the figure, where
each red point corresponds to a caching placement. The 5
points emphasized by small blue circles are the Pareto optimal
solutions (nondominated set [41]) of the joint optimization
problem, i.e., there is no other point dominating with the
Pareto optimal solutions in terms of both the cell average
outage probability and fronthaul usage.
The cell average outage probability is minimized when the
files cached in each RRH are the same, and the popularity of
these cached files will have an impact on the average fronthaul
usage. The corresponding points of these caching placements
lie on the line segment AD, i.e., line segment AD represents
the lower bound of the cell average outage probability. The
MPC scheme represented by point A achieves the minimum
fronthaul usage among these caching placements. The reason
is that the MPC scheme caches the most popular files which
can reduce the fronthaul usage to a minimum value among
these caching placements.
The fronthaul usage is minimized when all RRHs cache
different files with higher popularity ranks, and the cache
locations of these files will have an impact on the cell average
outage probability. The corresponding points of these caching
placements lie on the line segment BC, i.e., line segment BC
represents the lower bound of the average fronthaul usage.
The LB-LCD scheme represented by point B achieves the
minimum cell average outage probability among these caching
placements. The reason is that the LB-LCD scheme caches
the files with higher ranks in the RRHs near to the cell center,

Unless otherwise specified,
η is evaluated from 0 to 1
with step 0.1 in the proposed
GA-based approach

0.4, 0.5

0

0.1

0.2

0.3

B2

C
0.15
0.4

η = 0, 0.1

B3 η = 0, 0.1
0.5

0.6

0.7

0.8

0.9

1

Cell average outage probability

Fig. 7. Cell average outage probability and fronthaul usage tradeoff. L =
9, M = {1, 2, 3}, N = 3, β = 1.5. Unless otherwise specified in the figure,
η is evaluated from 0 to 1 with a step 0.1 in the proposed GA-based approach,
i.e., η = {0.1, 0.2, · · · , 1}.

which has the minimum cell average outage probability among
these caching placements.
Fig. 7 shows the Pareto optimal tradeoffs between the
cell average outage probability and the fronthaul usage with
different cache size M . The results obtained through the
proposed GA approach are almost the same as exhaustive
search, which means that the proposed GA approach can
achieve near-optimal performance. The minimum cell average
outage probability is achieved at point A1 when M = 1,
A2 when M = 2, and A3 when M = 3, respectively. The
minimum cell average outage probability represented by the
three points are the same, and the corresponding caching
placements of the three points are the MPC scheme. The
reason is that according to the file delivery scheme and the
MPC caching placement, all the RRHs will serve the user no
matter how many files the RRHs can cache. It is also seen that
the corresponding fronthaul usage of the three points decrease
as M increases, which is obvious because larger cache size
can cache more files thus the fronthaul usage can be reduced.
On the other hand, the minimum fronthaul usage is achieved
at point B1 when M = 1, B2 when M = 2, and B3 when
M = 3, respectively. The corresponding caching placements
of the three points are the LB-LCD scheme. Obviously, the
corresponding fronthaul usage of the three points decreases as
M increases. The fronthaul usage is zero at point B3 when
M = 3, the reason is that all the RRHs can cache a total
of M N = 3 × 3 = 9 files, which is equal to the number
of files in the file library, i.e., all the files are cached in the
RRHs. The corresponding cell average outage probability of
the three points increases as M increases. The reason is that
according to the file delivery scheme and the LB-LCD caching
strategy, more different files can be cached in the RRHs as M
increases, however, there is only one copy of each file and
the outage probability w.r.t. these cached files will be higher,
i.e., more different files cached in the RRHs, higher the cell
average outage probability is.

11

TABLE V
O PTIMAL C ACHING S TRATEGY O BTAINED BY T HE P ROPOSED GA
η=0
fobj = 0.0689
1 3 5
2 4 6
η = 0.3
fobj = 0.1938
1 1 1
2 3 4
η = 0.6
fobj = 0.2077
1 1 1
2 2 2
η = 0.9
fobj = 0.1561
1 1 1
2 2 2

η = 0.1
fobj = 0.1186
1 3 5
2 4 6
η = 0.4
fobj = 0.2087
1 1 1
2 3 4
η = 0.7
fobj = 0.1905
1 1 1
2 2 2
η = 1.0
fobj = 0.1390
1 1 1
2 2 2

η = 0.2
fobj = 0.1651
1 1 4
2 3 5
η = 0.5
fobj = 0.2144
1 1 1
3 2 2
η = 0.8
fobj = 0.1733
1 1 1
2 2 2
L=9
M =2
N =3
β = 1.5

According to the above evaluations, the MPC and LBLCD caching schemes are two special solutions of the joint
optimization problem when η = 1 and η = 0, respectively. The
former can achieve the lowest cell average outage probability
while the latter can achieve the minimum fronthaul usage. The
proposed GA-based approach can achieve different tradeoffs
between the cell average outage probability and fronthaul usage according to different weighting factors, which can achieve
better performance than the MPC and LB-LCD schemes.

C. Performances of the GA-based Approach and Mode Selection Approach
The performances of the proposed GA-based approach and
the mode selection approach are analyzed in this subsection.
Besides the MPC and the LB-LCD caching schemes, two other
widely used caching strategies are evaluated for comparison,
one is random caching, where each RRH caches the content
files independently and randomly regardless of the files’
popularity distribution, the other one is probabilistic caching,
where each RRH caches the files independently and randomly
according to the files’ popularity distribution, i.e., high-ranked
files have higher probability to be cached [23], [51]. There are

1
MPC
LB-LCD
proposed GA
proposed mode selection
random caching
probabilistic caching

0.9
0.8

Objective function value

Note that as the cache size M increases, the GA-based
approach should evaluate more values of η in order to obtain
all the Pareto optimal solutions of the joint optimization
problem. For example, when M = 3, additional values of
η = 0.15 and η = 0.45 are evaluated to obtain the Pareto
optimal solutions represented by point C and D.
Table V shows all the optimal caching placements obtained
by the proposed GA-based approach when M = 2. For
illustration, we use a M × N matrix to represent the caching
placement, with the (m, n)-th entry bm,n ∈ {1, 2, 3, · · · , L}
denotes the file index cached in the m-th cache space of
the n-th RRH. From (18), η0 = 0.3312. It can be seen
that the LB-LCD scheme is the optimal placement when
η = 0, 0.1 < η0 , while the MPC scheme is the optimal solution
when η = 0.6 ∼ 1.0 > η0 , and some files are duplicately
cached in the RRHs when η = 0.2 ∼ 0.5.

0.7

Crossover points of the MPC
and the LB-LCD schemes with
β = 0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0

0.6
0.5
0.4
0.3
0.2
0.1
0
0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Weighting factor η

Fig. 8. Objective function value versus weighting factor η. L = 50, M =
5, N = 7.

L = 50 files 2 , N = 7 RRHs with one RRH located at the cell
center and the other 6 RRHs evenly distributed on the circle
with radius 2R/3, and β = 1.5.
Fig. 8 shows the objective value of different caching strategies with M = 5. It can be seen from the figure that as the
weighting factor η increases, i.e., more focus on minimization
of outage probability, the objective value of MPC decreases
linearly, while the objective value of the LB-LCD scheme
increases linearly. The horizontal coordinate of the crossover
point of the MPC and LB-LCD scheme (η0 ) approaches zero
as the popularity skewness factor β increases. This is because
that when β increases, the requesting probability
l of the first
PNP
M
few popular files increase significantly, then l=M +1 Pl → 0
in (18), thus η0 → 0. That is, as β increases, the MPC
scheme will dominate with most values of η. This can also be
explained as follows. When β increases, the average fronthaul
usage will depend more and more on the few files with higher
ranks. These files can be cached in the RRHs under both
of the MPC and the LB-LCD schemes, thus the MPC and
the LB-LCD schemes are equivalent in terms of fronthaul
usage, while the MPC can achieve lower outage probability.
Therefore the MPC scheme is superior to the LB-LCD scheme.
The crossover point η0 = 0.23 when β = 1.5 calculated
through (18) exactly matches the simulation results. The above
mentioned results are consistent with Proposition 1.
The random caching strategy has a relative poor performance for all values of η, which is because the files cached
in the RRHs are selected randomly, there is neither a high
probability to cache the same file for reducing the outage probability nor to cache different high-ranked files for reducing the
fronthaul usage. While the probabilistic caching strategy can
achieve better performance than the proposed mode selection
approach in the middle range of η, e.g., for η = 0.2 ∼ 0.4,
2 Alougth there is a huge amount of content files in practice, they can
be classified into different categories [46], and the number of files in each
category (or subcategory) is relatively limited, so the proposed algorithms can
be performed on each category, the number of files evaluated in the simulation
will not lose meaningful insights of the tradeoff caching optimization.

12

1

1

0.7
proposed GA
proposed mode selection

0.9
0.6

0.8

0.8

0.7

0.7

0.6

0.6

0.5

0.5

0.4

0.4

0.3

0.3

0.2

0.2

0.1

0.1

Objective function value

Cell average outage probability

proposed GA
proposed mode selection

Average fronthaul usage

proposed GA
proposed mode selection

0.9

Crossover points of the MPC
and the LB-LCD schemes with
M = 1, 2, 3, 4, 5, 6, 7

0.5

LB-LCD

0.4

MPC

0.3

0.2

0.1

0

0
0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0

1

0

0.1

0.2

0.3

0.4

Weighting factor η

where both the cell average outage probability minimization
and the fronthaul usage reduction are treated approximate
equally. Which is because that, in probabilistic caching, each
RRH will cache the high-ranked files with a higher probability,
so there is a high probability for different RRHs to cache
the same high-ranked files, which can reduce the cell average
outage probability, and meanwhile the inherent randomness
in the placement makes it possible to cache different files to
reduce the fronthaul usage. It is also seen that the proposed
GA-based approach can achieve better performance than the
other caching strategies, for instance, the objective function
value of the proposed GA algorithm is 18.25% lower than
a typical probabilistic caching scheme when η = 0.4, and
this improvement goes up to 87.9% when η = 1, the average
improvement over all values of η is 47.5%.
Cell average outage probability and fronthaul usage of
the proposed GA and the proposed mode selection approach
versus weighting factor are shown in Fig. 9. Note that the
mode selection scheme is actually the LB-LCD scheme when
η ≤ η0 and the MPC scheme when η > η0 , respectively.
For the proposed GA approach, the solution is exactly the
LB-LCD scheme when η = 0, as η increases, the cell
average outage probability decreases and the fronthaul usage
increases, and they reach the lower and upper bounds when
η > 0.6, respectively, where the solution is the MPC scheme.
The proposed GA approach can adjust the caching placement
according to different weighting factors η while the mode
selection scheme only chooses a caching placement between
the MPC and the LB-LCD schemes based on whether η > η0 ,
so the proposed GA approach can achieve better performance
than the mode selection scheme. However, the computational
complexity of the mode selection scheme is extremely low.
Fig. 10 shows the performance of the proposed GA and the
mode selection scheme with different cache size M . It can
be seen from the figure that the mode selection scheme can
achieve near-optimal performance over a wide range of the
weighting factor η. The vertex of the mode selection scheme,
i.e., the crossover point of the MPC and the LB-LCD schemes

0.6

0.7

0.8

0.9

1

Fig. 10. Objective function value versus weighting factor η. L = 50, N =
7, β = 1.5.

0.6

Mean objective function value of the population

Fig. 9. Cell average outage probability and fronthaul usage versus weighting
factor η. L = 50, M = 5, N = 7, β = 1.5.

0.5

Weighting factor η

η
η
η
η

0.5

=
=
=
=

0.2
0.4
0.6
0.8

0.4

0.3

0.2

0.1

0
1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

Generation index

Fig. 11. Convergence behavior of the proposed GA approach. L = 50, M =
5, N = 7, β = 1.5.

moves toward the origin as the cache size M increases, i.e.,
the MPC scheme will dominate with most values of η as
M increases. The reason is explained as follows. When M
increases, more content files can be cached in the RRHs. The
fronthaul usage depends mostly on the first few popular files
cached in the RRHs, so the fronthaul usage will tend to be
the same between the two schemes as M increases. The MPC
scheme can achieve lower outage probability, further more,
the cell average outage probability of the LB-LCD scheme
increases as M increases, so the objective value of the MPC
scheme will be much lower than that of the LB-LCD scheme,
and the MPC scheme is superior to the LB-LCD scheme with
most values of η.
Fig. 11 shows the convergence behavior of the proposed GA
approach. It can be seen from the figure that the mean objective
value of the population converges within average 8 generations. The computational complexity is Ng Np = 8×50 = 400.
While the computational complexity of the exhaustive search

13

7
is 50
= 1.92 × 1044 , which is not feasible in practice. As
5
stated earlier, the popularity of the content files will remain the
same for a relative long period, so the convergence behavior
of the caching placement algorithm is not time-critical. Unlike
the delivery stage, which needs to make an instant decision
for coping with the dynamics of mobile networking systems,
e.g., the rapid change of channel state information, it is not
necessary for the caching strategy to make an instant decision
due to the slow change of the statistics data (e.g., the request
probabilities of the files). In addition, if parallel computing is
adopted, the population size of the proposed GA approach can
be increased without introducing additional execution time,
while the converging speed of the GA will be accelerated.
Thus, the GA approach can perform well with a satisfying
converging speed in practice.
VII. C ONCLUSION
In this paper, we have investigated tradeoff caching strategy
in Cloud-RAN for future mobile communications. In order
to jointly minimize the cell average outage probability and
fronthaul usage, the optimization problem is formulated as a
weighted sum of the two objectives, with weighting factor
η (and 1 − η). Analytical expressions of cell average outage
probability and fronthaul usage have been presented and
verified through simulations. Performances of two particular
caching strategies have been analyzed, namely the MPC and
the LB-LCD schemes. When the minimization of the cell
average outage probability is more focused on, the MPC
scheme is superior to the LB-LCD scheme, while the latter
is superior to the former in the opposite situation, i.e., where
the reduction of average fronthaul usage is more focused on.
When the content files’ popularity skewness factor β is larger,
or the cache size of each RRH increase, the MPC scheme
will dominate in a wide range of η. Two heuristic approaches
have been proposed to solve the joint optimization problem:
one is the GA based approach which can achieve nearly the
same optimal performance of exhaustive search, while the
computational complexity is significantly reduced; the other
is the mode selection approach with extremely low computational complexity, which can obtain near-optimal performance
within a wide range of η. Compared with a typical probabilistic
caching scheme, the proposed GA approach can reduce the
objective function value by up to 45.7% on average and the
proposed two mode selection caching strategy can provide an
average improvement of 36.9%. In practice, the RAN can
make a decision of the tradeoff according to the system’s
statistics of fronthaul traffic and outage probability, and then
adopt caching strategy through the proposed schemes.

(A.2)

The moment generation function (MGF) [53] of the random
variable γn is
Z ∞
fγn (γ)esγ dγ
Mγn (s) =
0


Z ∞
1
γ
(A.3)
exp −
esγ dγ
=
γ0 Sn
γ0 Sn
0
1
,
=
1 − γ0 Sn · s
and the range of convergence (ROC) is Re (s) < γ01Sn . Since
the RRHs are distributed at different locations, {γn , n ∈ Φ}
is
Pindependent of each other, the MGF of received SNR γ =
n∈Φ γn is given by
Mγ (s) =

Y

Mγn (s) =

n∈Φ

Y
n∈Φ

1
,
1 − γ0 Sn · s

(A.4)

T
and the ROC is n∈Φ Re (s) < γ01Sn .
Since there are I distinct distances d1 6= d2 6= · · · 6= di 6=
· · · 6= dI between the service RRHs and the user, and the i-th
distance has multiplicity of Ji , (A.4) can be rewritten as
1
J1 
J2

JI ,
1
1
1
1− s
1− s
··· 1 −
s
λ1
λ2
λI
(A.5)
1
,
i
∈
{1,
2,
·
·
·
,
I}
is
the
i-th
pole
of
where λi = γ Kd
−α
0
i
multiplicity Ji of Mγ (s), using partial fraction expansion,
Mγ (s) can be expressed as
Mγ (s) = 

Mγ (s) =

Ji
I X
X
i=1 j=1

Aij



j ,
1
1− s
λi

(A.6)

where {Aij } are the undetermined coefficients. Multiplying
(1− λ1i s)Ji to both sides of (A.6), then calculating the (Ji −j)th order derivate for both sides and let s = λi , we have
"

Ji #
dJi −j
1
Mγ (s) 1 − s
dsJi −j
λi
s=λi


=

dJi −j
dsJi −j

Ji
I X
X



 i=1 j=1

Aij
j
1
1−
·s
λi


Ji 
1

1− s

λi

s=λi


Ji −j
1
=(Ji − j)! −
Aij .
λi

A PPENDIX A
D ERIVATIONS OF (8) AND (9)
For a specific file Fl , the subscript of file index l and
the user’s location x0 are omitted without ambiguity. In (7),
|hn |2 ∼ χ2 (2), and the PDF is given by [52]
f|hn |2 (x) = exp(−x), x > 0.

Then the PDF of γn = γ0 Sn |hn |2 is


γ
1
exp −
, γ > 0, n ∈ Φ.
fγn (γ) =
γ0 Sn
γ0 Sn

(A.1)

(A.7)
Thus Aij is obtained as (10).
The PDF of γ can be obtained by inversely transforming
the MGF in (A.6). Considering a general form of the PDF,
f (γ) = γ n e−aγ ,

γ ≥ 0,

(A.8)

14

where n ∈ {0} ∪ Z+ , a ∈ R+ . The MGF of f (γ) can be
obtained by continuously using the method of integration by
parts.

=
=
=

=

M (s)
Z ∞
γ n e−aγ esγ dγ
0
Z ∞
1
−
γ n de−(a−s)γ
a−s 0


Z ∞
∞
1
−(a−s)γ n−1
n −(a−s)γ
e
γ
dγ
−
−n
γ e
a−s
0
0
..
.
n!
,
(A.9)
(a − s)n+1

and the ROC is Re (s) < a. Denote the pair of the PDF and
its corresponding MGF as
f (γ) = γ n e−aγ ⇐⇒ M (s) =

n!
.
(a − s)n+1

(A.10)

The CDF can be calculated in the same manner,
Z γ
F (γ) =
f (γ)dγ
Z0 γ
=
γ n e−aγ dγ
(A.11)
0"
!#
n
X
n!
1 n!
− e−aγ
γ n−k
.
=
n
a a
(n − k)! ak
k=0

According to (A.6) and (A.10), the PDF of the received
SNR is obtained, as shown in (8). According to (A.11), the
CDF of the received SNR is obtained as shown in (9).

A PPENDIX B
P ROOF OF P ROPOSITION 1
Without loss of generality, it is assumed that Mn =
M, ∀n ∈ N , |N |> 1. According to (6a), it is obvious that
MP C
the objective functions of the MPC and LCD schemes fobj
LCD
and fobj are linearly (thus monotonic) continuous function
of η on closed interval [0, 1].
PL
When η = 0, fobj = l=1 Pl Tl . The objective values of
the two schemes are
MP C
fobj
=

M
X
l=1

LCD
fobj
=

N
M
X
l=1

Pl Tl
↑
0

Pl Tl
↑
0

L
X

+

Pl Tl
↑
1

l=M +1
L
X

+

=

Pl ,

l=M +1

Pl Tl

l=N M +1

L
X

=

↑
1

L
X

Pl .

l=N M +1

(B.1)
PL
Note that
P
=
1
and
P
>
P
>
·
·
·
>
P
,
where
l
1
2
L
l=1
equality holds if and only if β = 0. Thus
MP C
fobj

η=0

LCD
> fobj

.
η=0

(B.2)

h
i
L
P
(l)
When η = 1, fobj =
Pl Ex0 Pout (x0 ) . Denoting
l=1
h
i
(l)
Ex0 Pout (x0 ) as Pcell,out (l), then
MP C
fobj
=

N
M
X

LCD
fobj

=

N
M
X

{z

}

C

LCD
Pl Pcell,out
(l)

l=1

|

MP C
Pl Pcell,out
(l) ,

l=N M +1

l=1

|

L
X

MP C
Pl Pcell,out
(l) +

{z

|

D

L
X

+

}

LCD
Pl Pcell,out
(l) .

l=N M +1

{z

}

E

{z

|

F

}

(B.3)
According to the wireless transmission strategy, D = F , where
D and F correspond to the scenario that all the RRHs serve
the user, while E > C because E denotes there is only one
RRH serving the user, while C corresponds to all the RRHs
serving the user. Thus
MP C
fobj

η=1

LCD
< fobj

.
η=1

(B.4)

MP C
According to (B.2), (B.4) and the linearity of fobj
and
LCD
fobj
, there exists a crossover point η0 ∈ [0, 1] of the two
objective functions. When η < η0 , the LCD scheme is superior
to the MPC scheme, while when η > η0 , the MPC scheme is
superior to the LCD scheme.
Substituting {al,n } of the MPC and LCD schemes into (6a),
respectively, a linear equation of η is formulated, and the
solution is shown as in (17). Because M = Mn , ∀n, (17)
can be further written as (18).
The proof can be extended to the case that Mn is different
with n.

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