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Optimal Power Allocation in Cache-Aided
Non-Orthogonal Multiple Access Systems
Khai Nguyen Doan∗, Wonjae Shin‡, Mojtaba Vaezi†, H. Vincent Poor†and Tony Q. S. Quek∗
∗Information Systems Technology and Design, Singapore University of Technology and Design, Singapore
Email: nguyenkhai doan@mymail.sutd.edu.sg, tonyquek@sutd.edu.sg
†Department of Electrical Engineering, Princeton University, Princeton, NJ, USA
Email: {mvaezi, poor}@princeton.edu
‡Department of Electronics Engineering, Pusan National University, Pusan, South Korea
Email: wjshin@pnu.ac.kr
Abstract—This work combines non-orthogonal multiple access
(NOMA) and caching, two prominent techniques for future com-
munication networks. Specifically, a cache-aided cellular network
with Rayleigh fading channels is analyzed. By exploiting the
channel distribution, users requests, and cache contents in given
time, an optimal power allocation policy for the superposed signal
is derived. The goal is to maximize the system success probability,
i.e., the probability that all users can successfully decode their
desired signals. The analysis highlights the benefits of introducing
caching to NOMA-based systems. Simulation results confirm the
analysis and demonstrate the efficiency of the proposed power
allocation.
I. INTRODUCTION
Future communication networks must satisfy a dramatic
increase in data demand due to the growth of electronic
devices [1]. The system capacity and user quality of service
(QoS) can be improved by deploying networks with a higher
density of access points. This, in turn, causes massive load
on the backhaul [2]. Caching, i.e., pushing contents to user’s
devices [3]–[6], appears to be a promising solution for this
challenge. This technique offers the users a chance to retrieve
the desired contents from their own devices, thus, helping
avoid unnecessary transmissions.
Non-orthogonal multiple access (NOMA) is another po-
tential candidate to improve the system capacity and user
experience. This technique has shown to be more efficient
than its counterpart, orthogonal multiple access (OMA), in
term of reducing the spectrum usage and enhancing the power
efficiency [7]–[10]. In the power domain, NOMA supports the
communication of multiple users using the same radio resource
in time and frequency by superimposing the users signal [11],
[12]. Then, the successive interference cancellation (SIC) can
be applied at the receiver for signal decoding.
Currently, there are very few works investigating potential
benefits of caching in the context of NOMA systems. One
example is [13] which considers a network consisting of a
base station (BS) and several content servers where the system
operation relies on a combination of caching and NOMA.
Caches are implemented at the content servers and NOMA
is applied whenever data needs to be delivered from the BS
to content servers or from content servers to mobile users.
However, the power allocation policy is to guarantee that the
most popular file can be successfully delivered from the BS
to a predefined number of content servers instead of being
optimized to reduce the delivery outage probability at the
user side. In addition, the use of cache contents to eliminate
interference is not considered when applying SIC. From our
point of view, finding an optimal power allocation to suppress
the outage probability or equivalently, maximize the success
probability, is important. Since it plays a key role in improving
the user’s QoS, while ensuring the fairness. Specifically, the
success probability is defined as the probability that all users
can successfully decode their desired signals. In addition, with
the involvement of caching, this problem has not been fully
addressed. For example, in NOMA without caching, the power
is conventionally allocated in an inverse order of channel
gains between users and the BS. Nevertheless, with the aid
of caching, users can remove signals other than their desired
ones from the superposed signal using the cache contents.
Therefore, the conventional power allocation scheme may
not be optimal anymore, and this inspires finding a more
appropriate method.
In this paper, we derive an optimal power allocation policy
for the cache-aided NOMA system to maximize the success
probability. Importantly, the success probability, by its def-
inition, can ensure the fairness among users. Besides, our
design exploits the knowledge of channel gain distribution, the
requests and cache contents of users in an instant time. This
is done with the assumption that, users are paired and in the
worst case, we can afford to allocate orthogonal subchannels
to user pairs. In addition, numerical results are given to gain
more insight to the system operation as well as the relation
between caching and NOMA.
The remainder of this work is organized as follows. Sec-
tion II describes the system model under consideration. Sec-
tion III presents the optimal power allocation. Finally, Sec-
tion IV describes our experimental setup and simulation results
to validate our theoretical results.
II. SY ST EM MO DE L
We consider a system consisting of Kusers served by a
BS as in Fig. 1. Each user’s device has a cache with finite
capacity and we assume that users cache a file as a whole
without partitioning. As will be seen in the next section, the
total number of files that a user can cache does not directly
978-1-5386-4328-0/18/$31.00 ©2018 IEEE
Fig. 1. A BS serving Kmobile users who are equipped with caches. Users
are paired and allocated orthogonal subchannels.
involve in the power allocation decision. Thus, we just assume
that this quantity is finite instead of specifying it for simplicity.
Typically, with caching, users fetch and store a set of files
during the off-peak time called caching phase. In this work,
we assume that the caching phase has already taken place to
consider the next stage called requesting phase. In this phase,
each user is assumed to request for a file in the library. In
addition, we assume that the BS has information about files
stored on each device. For example, when sending the request
messages to BS, users can add information saying which files
currently present in their caches.
With NOMA, when a superposed signal is transmitted from
the BS to users, the SIC scheme is used at each mobile
user to decode the desired signal. As discussed in [10] and
the references therein, SIC may increase the complexity at
the receivers as there are more users occupying the same
subchannel. Therefore, it is reasonable to restrict the number
of users associated with each subchannel to two. In this work,
we assume that users are paired and orthogonal subchannels
are allocated to user pairs.1
Considering a single subchannel occupied by two users,
let us denote h1(and h2) to be the channel coefficient
between user 1 (and user 2) and the BS where |h1|(and
|h2|) follows Rayleigh distribution with parameter σ2
1(and σ2
2).
Then, |h1|2and |h2|2will follow an exponential distribution
with parameter λ1= 2/σ2
1and λ2= 2/σ2
2, respectively. We
denote d1and d2to be the distance from user 1 and 2 to the
BS, respectively. Then, the signal received at user 1 and 2 will
be
y1=h1
dγ
1x1√α+x2√1−α+n1(1)
and
y2=h2
dγ
2x1√α+x2√1−α+n2(2)
1For this model, the subchannels can be allocated dynamically by grouping
users having the same requested file and allocate them a single subchannel
to trigger the broadcasting feature of wireless networks. The situation of two
users per subchannel as our consideration is actually the worst case when
there are no more than two users requesting the same content.
respectively. x1and x2are the signals corresponding to
requested files of user 1 and 2, respectively, αis the portion
of the transmission power Pallocated to the signal of the
user 1, γis the path loss coefficient, and n1is Gaussian
noise with mean 0and variance σ2. Denote 1and 2as the
minimum SINR for which the requested files of user 1 and
2, respectively, can be decoded. Let the SNR be ρ=P
σ2.
Without loss of generality, we assume that ζ1
ζ2>1where
ζ1=λ11β1,ζ2=λ22β2,β1=dγ
1
ρand β2=dγ
2
ρ. Note
that the larger ζ1(or ζ2) is, the harder for user 1 (or user
2) to successfully decode its desired signal. Therefore, this
assumption implies that, without caching, user 1 has a worse
condition to be satisfied.
In SIC without caching, many users may need to decode a
sequence of signals before obtaining their desired ones. In this
case, the failure can occur if users fail to decode one of those
signals. However, with caching, users can remove or reduce
the interference without decoding using cache contents, which
increases the success probability. In this case, the optimal
power allocation policy will not only depend on the channel
information but also the requests and cache contents of users in
an instant time. Therefore, we aim to design a power allocation
policy that can take into account all of this information to
maximize the success probability.
III. OPTIMAL POWE R ALL OC ATION
In our work, the power allocation consists of two stages. The
first stage is to share the total transmission power to user pairs.
Then, the second stage is to allocate portions of a given power
amount to users in each pair. However, due to the dependence
between these stages, we will first present the second stage
in subsection III-A, then, the first stage in subsection III-B.
Note that this two-stage process is optimized as each stage is
optimized separately. This is because user pairs are isolated in
term of interference due to orthogonal subchannels allocation.
A. A user pair with a single subchannel
In this subsection, we deal with a user pair occupying a
single subchannel. Note that the SIC decoding order depends
on which signal is given more power, i.e., 0.5≤α≤1or
0≤α≤0.5, and so does the objective function. Therefore, we
will need to optimize two probability functions in both ranges
of α. As mentioned in the previous section, a limited number
of situations can arise. In some of these cases, the optimal
power allocation is trivial whereas in some other cases, the
problem is involved. We first consider the trivial cases before
listing the others.
1) When both users can find their requested files in their
caches, thus, no transmission is required.
2) When only one of the user’s demand can be found in the
cache, hence to maximize the success probability, all of
power Pwill be used for the transmission to the unsatisfied
user, i.e., α= 0 assuming user 2 is the one has not been
satisfied yet. Then the desired file is successfully decoded
when
|h2|2β2≥2(3)
or equivalently,
|h2|2≥2β2(4)
Since |h2|2has exponential distribution, the success prob-
ability will be
Pr |h2|2≥2β2= exp (−λ22β2)(5)
3) When users request for the same file, e.g. file f, but neither
of them have cached it. Then, a single signal corresponding
to that file is broadcasted with power P. Similar to the
above, the desired file is successfully decoded at each user
when
|h1|2β1≥f(6)
|h2|2β2≥f(7)
where fis the minimum SINR to successfully decode the
file f, and the success probability is given by
Pr |h1|2≥fβ1,|h2|2≥fβ2
= exp (−λ1fβ1−λ2fβ2)
(8)
Without loss of generality, we assume that user 1 request
for file f1and user 2 requests for f2. Then, four cases which
are more complicated are listed as follows
•Case 1: User 1 has cached f2, user 2 has had a cache miss.
•Case 2: User 1 has had a cache miss, user 2 has cached f1.
•Case 3: User 1 has cached f2, user 2 has cached f1.
•Case 4: Both users have had cache misses.
where a user experiences a cache miss when it does not cache
its own desired file and that of the other user. We will analyze
each case separately and derive the optimal power allocation.
Starting with the first case, since user 1 has already cached the
requested file of user 2, it can remove the interference without
decoding. Hence, user 1 can decode its desired content when
|h1|2αβ1≥1(9)
Then, we have the following conditions for successful
decoding at user 2 for α≥0.5and α < 0.5, respectively,
|h2|2α.|h2|2(1 −α) + β2≥1(10a)
|h2|2(1 −α)β2≥2(10b)
and
|h2|2(1 −α).|h2|2α+β2≥2(11)
The success probability in the former and later cases are
expressed by
fCase1
1(α) =
exp −ζ1
α−max λ21β2
(1+1)α−1,ζ2
1−α
, α > 1−1
1+1
0, otherwise
(12)
and
fCase1
2(α) = (exp −ζ1
α−ζ2
1−(1+2)α, α < 1
1+2
0,otherwise
(13)
respectively. To this end, the optimal power allocation policy
is given in Theorem 1.
Theorem 1: For case 1, the success probability is maximized
when
α=(xCase1
1, if fCase1
1xCase1
1≤fCase1
2xCase1
2
xCase1
2, otherwise
(14)
where xCase1
1and xCase1
2depend on the ratio ζ=ζ1
ζ2>1in
the following way
xCase1
1= max 1−1
√ζ+ 1,1−1
1 + 1+1
2!(15)
xCase1
2= min 1
1 + 2 1−1
pζ(1 + 2)+1!,0.5!
(16)
The above results are obtained by maximizing the success
probability in two cases when 0.5≤α≤1and 0≤α≤0.5
separately. For the former case, we minimize the argument
of the exponential function in (12) whose solution is the first
argument of the max function in (15). Then, by combining
it with the constraints α > 1−1
1+1and 0.5≤α≤1,
we obtain (15). Similarly for the case 0≤α≤0.5whose
solution is (16). To this end, we can plug (15) and (16) into the
corresponding objective function for comparison and choose
the better one, which leads to the result in Theorem 1. The
full proof of this as well as the subsequent ones are omitted
due to the space limitation. However, they can be found in a
longer version of this work.
Next, for case 2, the condition for user 2 to successfully
decode its own signal is
|h2|2(1 −α)β2≥2(17)
and the remaining conditions for the success event when αis
above and below 0.5, respectively, are
|h1|2α.|h1|2(1 −α) + β1≥1(18)
and
|h1|2(1 −α).|h1|2α+β1≥2(19a)
|h1|2αβ1≥1(19b)
Correspondingly, the two success probability expressions
are
fCase2
1(α) = (exp −ζ1
(1+1)α−1−ζ2
1−α, α > 1−1
1+1
0,otherwise
(20)
and
fCase2
2(α) =
exp −max λ12β1
1−(1+2)α,ζ1
α−ζ2
1−α
, α < 1
1+2
0,otherwise
(21)
respectively. Then, the optimal power allocation is given in
Theorem 2.
Theorem 2: For case 2, the success probability is maximized
when
α=(xCase2
1, if fCase1
1xCase2
1≤fCase2
2xCase2
2
xCase2
2, otherwise
(22)
where xCase2
1and xCase2
2depend on the ratio ζ=ζ1
ζ2>1in
the following way
xCase2
1= 1 −1
pζ(1 + 1) + 1+ 1(23)
xCase2
2= min 1
2
1+1+2
,0.5!(24)
In case 3, each user has cached the desired file of the
other, hence, the interference can be eliminated at both users
regardless of α’s value. In addition, because of no interference,
this case is similar to the context of OMA excepting that each
user can use the whole spectrum. The success conditions can
be written as
|h1|2αβ1≥1(25)
|h2|2(1 −α)β2≥2(26)
Then, the success probability is
fCase3(α) = exp −ζ1
α−ζ2
1−α(27)
and the optimal power expression is suggested in Theorem 3.
Theorem 3: For case 3, the success probability is maximized
when
α= 1 −1
√ζ+ 1 (28)
with ζ=ζ1
ζ2>1.
Note that the power allocation in Theorem 3 always satisfies
α≥0.5. This implies that if both users can use their cached
content to eliminate the interference, the user having a worse
condition should be allocated more power. In case 4, the
success conditions and the success probability expressions
when αis above and below 0.5, respectively, are
|h1|2α.|h1|2(1 −α) + β1≥1(29a)
|h2|2α.|h2|2(1 −α) + β2≥1(29b)
|h2|2(1 −α)β2≥2(29c)
with success probability function
fCase4
1(α) =
exp −ζ1
(1+1)α−1−max λ21β2
(1+1)α−1,ζ2
1−α
, α > 1−1
1+1
0,otherwise
(30)
and
|h1|2(1 −α).|h1|2α+β1≥2(31a)
|h1|2αβ1≥1(31b)
|h2|2(1 −α).|h2|2α+β2≥2(31c)
with success probability function
fCase4
2(α) =
exp max λ12β1
1−(1+2)α,ζ1
α−ζ2
1−(1+2)α
, α < 1
1+2
0,otherwise
(32)
The optimal power allocation for this case is given in
Theorem 4.
Theorem 4: For case 4, the success probability is maximized
when
α=
xCase4
1, if fCase4
1xCase4
1≤fCase4
2xCase4
2
min xCase4
2,1
2
1+2+1 , otherwise
(33)
where xCase4
1and xCase4
2depend on the ratio ζ=ζ1
ζ2>1in
the following way
xCase4
1= 1 −1
pζ(1 + 1) + 1+ 1 (34)
xCase4
2= min 1
1 + 2 1−1
pζ(1 + 2)+1!,0.5!
(35)
Generally, in the cache-aided NOMA system, if a user
has cached the desired content of other user occupying the
same subchannel, the information can be used to remove the
interference. Therefore, the QoS is enhanced even without
cooperation among users. This can be considered as another
type of cache hit which is not commonly considered in
the caching literature. On the other hand, caching further
contributes to the spectrum and power efficiency improvement
target of NOMA by exploiting user’s preferences. Therefore,
it is a good idea to combine these two advanced techniques
in the future networks.
B. Multiple user pairs with multiple subchannels
Previously, we present optimal ways to share a given power
Pto user in a pair. However, the performance can be further
improved by optimizing P. Therefore, in this subsection, we
present an optimal power allocation policy across user pairs.
We denote Pmax to be the total consumable power for the
transmission, and Pito be the power allocated to the user pair
in the i-th subchannel satisfying PK/2
i=1 Pi=Pmax. Recall
that we previously denote β1=dγ
1σ2
Pand similarly for β2.
In this subsection, we will use Piin place of Pto indicate
which subchannel (or user pair) is being considered since we
are dealing with a multi-subchannel-multi-user scenario.
From the obtained results in the previous subsection, it can
be figured out that except for the case when both users are
satisfied by their own caches, in all of the remaining cases,
the success probability for a user pair in the i-th subchannel
will have the form
gi(Pi) = exp −Ψi
Pi(36)
where Ψi,∀i= 1, . . . , K/2can be obtained by following
results in subsection III-A to allocate power to users in each
pair. The parameters Ψirepresents the dependence of the
power allocation in this stage on that of the previous stage.
Consequently, the success probability of every user in all K/2
subchannels is given by
G(P) = exp
−
K/2
X
j=1
Ψj
Pj
(37)
where vector Pcontains Pi,∀i= 1, . . . , K/2. Therefore,
maximizing G(P)is equivalent to solving the following
convex optimization problem
min
P
K/2
X
i=1
Ψi
Pi
(38)
s.t.
K/2
X
i=1
Pi=Pmax (39)
Pi≥0,∀i= 1, . . . , K/2(40)
whose closed-form solution can be obtained from KKT con-
ditions as follow
Pi=√Ψi
PK/2
j=1 pΨj
Pmax,∀i= 1, . . . , K/2(41)
In summary, there is a two-stage power allocation presented
in this work. Given that each subchannel is occupied by two
users, the quantities Ψi,∀i= 1, . . . , K/2can be defined
following results derived in the previous subsection. Then, the
total power Pmax can be shared to every user pair according
to (41).
IV. ILL US TR ATIVE RES ULT S
This section is devoted to present simulation results illustrat-
ing the combination of caching and NOMA analyzed above. In
this part, we assume the Zipf distribution for the file popularity
as has been shown and widely investigated in previous works,
i.e. the probability that file giis requested by a user is given
by pi=isPN
n=1 1
ns−1
where the parameter scorresponds
to the skewness and Nis the total number of available files in
the catalog. This implies that p1> p2> . . . > pN. Therefore,
in the context of no cooperation between users, the optimal
caching policy is to cache from the most to the least popular
file. In the experiments corresponding to Fig. 2 and 3, we
consider a single subchannel with two users assuming that
the power Phas been allocated to that pair, and the power
coefficient αis defined according to results in subsection III-A.
Fig. 4 investigates the whole system with K= 20 users and
10 subchannels where Pmax is the total power to be shared to
every user pair. Default values for some components are given
in the below table,
Parameters Values
Maximum number of file each user can cache 1
Total number of files 5
P10
Pmax 200
σ21
(d1, d2) (2,1)
(λ1, λ2) (2,1)
(1, 2) (1,1)
γ2
s0.5
and any change will be stated explicitly in each experiment.
Besides that, OMA will be considered as a second candidate
for the performance comparison. Regarding this, we assume
that the spectrum is divided evenly between users, and the
power is optimally allocated which is similar to that of
NOMA in the above case 3.2In addition, when the two users
request the same content file, the whole spectrum will be
used to broadcast signal to both, hence NOMA and OMA
are indifferent in such a situation.
0 2 4 6 8 10 12 14 16 18 20
Total transmission power (P)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Success probability
NOMA with caching
NOMA without caching
OMA with caching
OMA without caching
Fig. 2. The improvement in success probability with respect to (w.r.t.)
transmission power for both NOMA and OMA schemes with and without
caching applied.
Fig. 2 illustrates the variation of our defined success prob-
ability w.r.t. the increase in transmission power. The two
involved candidates are NOMA and OMA in which NOMA
outperforms its counterpart completely. However, the gap
between them shrinks when caching is introduced. This is
because with caching, NOMA and OMA only differentiate
from each other in the last four cases mentioned in subsection
III-A. Moreover, these cases occur with low probability when
2The expression (28) is optimal for OMA scheme only when the subchannel
is divided evenly between two users. This is because the noise power σ2in
the definition of ζwill be cancelled without resulting in any scaling constant
making αunchanged. In other words, if the bandwidth given to the first user
is Ltimes larger than that of the second user, the first user will suffer from L
times more noise power, then ζshould be replaced by Lζ in (28) for OMA.
the skewness factor of the Zipf distribution is large. That is to
say, if the user preference concentration is high, their requests
can be satisfied by their own caches in most of the time without
the use of either NOMA or OMA.
0 0.5 1 1.5 2 2.5
Zipf distribution skewness (s)
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Success probability
NOMA with caching
NOMA without caching
OMA with caching
OMA without caching
Fig. 3. The effect from the user’s preferences on the success probability.
Fig. 3 shows how user’s preference is exploited to increase
the success probability by NOMA and OMA with and without
caching. As sis increased, users will request lower-index files
with higher probability. Obviously, as the support of caching,
both candidate’s performance is picked up remarkably, which
emphasizes the benefit of integrating caching into NOMA and
OMA. Besides that, with or without caching, the two indicated
schemes are closer to each other as the user’s preferences
concentration increases. Because for larger s, there is higher
chance for two users to request the same file where NOMA
and OMA act the same in this context.
0 5 10 15 20 25 30 35 40
Cache capacity
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Success probability
Power allocated optimally
Power allocated equally
10 files
40 files
Fig. 4. The influence of the cache capacity enhancement on the multi-user
system performance in the small and large file-library-size (10 and 40 files,
respectively) scenarios.
Figure 4 illustrates the success probability in a whole system
with 20 users where users are paired and assigned different
subchannels. The two schemes applied to allocate power to
each user pair are the optimal one given in (41) and the flat
power allocation scheme where power is split equally between
user pairs. The results show that the success probability is
improved significantly with the optimal scheme, especially,
when the file catalog is large, which approaches the practice.
V. CONCLUSION
In this work, we have combined caching and NOMA in
a cellular network with Rayleigh fading channels. In order
to ensure the fairness among users, we derive an optimal
power allocation policy to maximize the success probability in
closed form. The analytical and simulation results reveal that
NOMA introduces another type of cache hit occuring when
a user caches the desired content of the others occupying
the same subchannel. This helps users to remove or reduce
the interference in the superposed signal even without user
cooperation, which increases the success probability. This
feature, in addition to the advantages of caching, shows that
the combination of these two techniques is a promising idea
for future networks.
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