Cache-Aided Non-Orthogonal Multiple Access

arXiv:1712.09557v2 [] 29 Jan 2018

Lin Xiang, Derrick Wing Kwan Ng, Xiaohu Ge,
Zhiguo Ding, Vincent W.S. Wong, and Robert Schober
Abstract—In this paper, we propose a novel joint caching and
non-orthogonal multiple access (NOMA) scheme to facilitate
advanced downlink transmission for next generation cellular
networks. In addition to reaping the conventional advantages
of caching and NOMA transmission, the proposed cache-aided
NOMA scheme also exploits cached data for interference cancellation which is not possible with separate caching and NOMA
transmission designs. Furthermore, as caching can help to reduce
the residual interference power, several decoding orders are
feasible at the receivers, and these decoding orders can be
flexibly selected for performance optimization. We characterize
the achievable rate region of cache-aided NOMA and investigate
its benefits for minimizing the time required to complete video
file delivery. Our simulation results reveal that, compared to several baseline schemes, the proposed cache-aided NOMA scheme
significantly expands the achievable rate region for downlink
transmission, which translates into substantially reduced file
delivery times.

I. I NTRODUCTION
Wireless caching is a content-centric networking solution
to meet the large downlink capacity demands introduced by
video streaming in fifth generation (5G) cellular networks [1]–
[6]. Recently, caching at streaming user equipments (UEs),
e.g. smartphones and tablets, has been advocated [7], [8]
to enhance the streaming quality of experience (QoE) while
reducing (i.e., offloading) over-the-air traffic. This poses significant challenges for the design of cache placement and
delivery as the aggregate cache capacity is distributed across
non-cooperating devices with small individual cache memory
sizes. Besides, the actual requests of the UEs are difficult to
predict during cache placement due to the users’ mobility and
the random nature of the users’ requests.
In the literature, coded caching has been proposed as an
effective solution for caching at UEs [7], [8]. By exploiting
the cached data as side information, a coded multicast format is created for simultaneous error-free video delivery to
multiple users, which leads to a multiplicative performance
gain that scales with the aggregate cache memory size of
the UEs. However, coded caching has an exponential-time
computational complexity. Moreover, the caching concepts
proposed in [7], [8] are mainly applicable to noiseless and
error-free communication links, e.g. in wireline networks. For
wireless networks impaired by fading and noise, however, the
performance of coded multicast is limited by the weakest user
with the poorest channel condition within the multicast group.
On the other hand, non-orthogonal multiple access
(NOMA) is an efficient approach for wireless multiuser
transmission that alleviates the adverse effects of fading [9],
[10]. Different from multicast and coded multicast, NOMA
pairs multiple simultaneous downlink transmissions on the
same time-frequency resource via power domain or code domain multiplexing [11]. Strong users with favorable channel
conditions can cancel the interference caused by weak users
with poor channel conditions that are paired on the same timefrequency resource, and hence, achieve a high data rate at
low transmit powers. Therefore, high transmit powers can be
allocated to weak users to achieve communication fairness

[12]. NOMA has also been extended to multicarrier and multiantenna systems; see [13], [14] and references therein.
So far, wireless caching and NOMA were either investigated separately or combined in a straightforward manner
[15]. For the latter case, NOMA was shown to improve the
performance of both caching and delivery in [15]. In this
paper, however, the joint design of caching and NOMA is
advocated to maximize the performance gains introduced by
caching at UEs. We show that the joint design of caching
and NOMA can significantly outperform the straightforward
combination of caching and NOMA. To this end, we consider
a simple distributed caching scheme for video file delivery.
By splitting the video files into several subfiles, superposition
transmission of the requested uncached subfiles is enabled
during delivery. If the cached content is hit, i.e., requested by
the caching UE, the proposed cache-aided NOMA scheme
enables traditional offloading of the video traffic. Otherwise,
the missed cached data, which is not requested by the caching
UE, is still exploitable as side information to facilitate (partial)
interference cancellation for NOMA. The resulting cacheenabled interference cancellation (CIC) can neither be exploited by separate caching and NOMA designs nor by the
scheme in [15].
With CIC, cached data is useful during file delivery even
if the users’ requests cannot be accurately predicted a priori.
Moreover, joint CIC and successive interference cancellation
(SIC) improves the interference mitigation capability at the
UEs and increases the number of possible decoding orders
compared to conventional NOMA. Furthermore, the performance of both strong and weak users can benefit from CIC.
However, adaptive adjustment of the decoding order according
to the cache and channel statuses is critical for reaping the
benefits of cache-aided NOMA. Hence, we investigate the
joint decoding order selection and power and rate allocation
optimization problem for minimization of the file delivery
time for fast video delivery. The main contributions of this
paper are as follows:
•

•

•

We propose a novel cache-aided NOMA delivery scheme
for spectrally efficient downlink transmission. Thereby,
cached data is exploited for cancellation of NOMA
interference. We characterize the achievable rate region
of the proposed scheme.
We jointly optimize the NOMA decoding order and
the rate and power allocations for minimization of the
delivery time. As the formulated optimization problem
is nonconvex, we propose an iterative method to solve it
optimally via solving a sequence of convex problems.
We show by simulation that the proposed scheme leads
to a considerably larger achievable rate region and a
significantly reduced delivery time compared to several
baseline schemes, including the straightforward combination of caching and NOMA.

Notations: C and R+ denote the sets of complex and
nonnegative real numbers,
respectively. E(·) is the expectation

operator. CN µ, σ 2 represents the complex Gaussian distri-

bution with mean µ and variance σ 2 . 1 [·] denotes an indicator
function which is 1 when the event is true and 0 otherwise. For
(n)
decoding the received signals, the notation i → xf means that

cached

cached

WA1

(n)

xf is the nth decoded signal at UE i. Similarly, i → (xf , xf ′ )
means that signals xf and xf ′ are jointly decoded in the
nth decoding step. Finally, C(Γ) , log2 (1 + Γ) denotes
the capacity function of an additive white Gaussian noise
(AWGN) channel, where Γ is the signal-to-interference-plusnoise ratio (SINR).

WA

uncached

uncached

WA2

cached

cached

WB0
WB1

WB

II. S YSTEM M ODEL

uncached

We consider cellular video streaming from a base station
(BS) to two UEs indexed by i and j, respectively. The
BS and the UEs have a single antenna, respectively. UEs i
and j request files WA and WB of sizes VA and VB bits,
respectively, where WA 6= WB . The respective requests are
denoted as (i, A) and (j, B). Each UE is equipped with a
cache of size Ck bits. Thereby, UE k ∈ {i, j} can place
portions of file f ∈ {A, B} into its cache prior to the time of
request, e.g. during the early mornings when cellular traffic
is low. As the cache placement is completed before the users’
requests are known, the users may cache files which they later
do not request. We assume that UE k, k ∈ {i, j}, has cached
ckf ∈ [0, 1] portion of file Wf , f ∈ {A, B}.

UE i

A. Cache Status and File Splitting
Let us define the minimum and maximum portions of
content cached for file Wf by
cf , min ckf
k∈{i,j}

and cf , max ckf ,
k∈{i,j}

(1)

which correspond to the cache status at user
k f , arg min ckf and k f , arg max ckf ,
k∈{i,j}

(2)

k∈{i,j}

f ∈ {A, B}, respectively. Based on (1) and (2), four cache
configurations are possible at the time of request:
Case I: i = k B and j = k A , i.e., i = k A and j = k B ;
Case II: i = k B and j = kA , i.e., i = k A and j = k B ;
Case III: i = k B and j = k A , i.e., i = kA and j = k B ;
Case IV: i = k B and j = k A , i.e., i = k A and j = k B .
In particular, Case I reflects the scenario where the nonrequesting user has cached a larger portion of file Wf than
the requesting user, which constitutes an unfavorable cache
placement for both users but cannot be avoided in practice as
user requests cannot be predicted accurately. In the following,
due to the limited space, we only consider Case I. However,
the derivations for Case I can be extended to Cases II–IV in
a relatively straightforward manner.
Let Zk , (Zk,A , Zk,B ), k ∈ {i, j}, denote the cache
status of UE k, where Zk,f , f ∈ {A, B}, is the cached
content of file Wf . We assume that the video data of file
Wf is sequentially organized. Moreover, based on different
user requests and cache configurations, Wf is split into
three subfiles (Wf 0 , Wf 1 , Wf 2 ) for adaptive file delivery.
As illustrated in Fig. 1, Wf 0 and Wf 2 of size cf Vf and
(1 − cf )Vf bits are the video chunks which are cached and
uncached at both UEs, respectively, whereas subfile Wf 1 of
size (cf − ckf )Vf bits is only cached at UE k f . Hence, we
have Zkf ,f = (Wf 0 ) and Zkf ,f = (Wf 0 , Wf 1 ), f ∈ {A, B}.
As the cached data Zkf ,f is the prefix of Zkf ,f , the considered
caching scheme is referred to as prefix caching in [16].

WA0

uncached

WB2

UE j

Fig. 1. Illustration of file splitting for cache-aided NOMA, assuming the
cache configuration in Case I.

B. NOMA Transmission
For video delivery, we assume a frequency flat quasi-static
fading channel, where the channel coherence time exceeds
the time needed for completion of file delivery. The received
signal at UE k is given by
y k = hk x + z k ,

(3)

where hk ∈ C denotes the channel gain between the BS and
UE k, and is constant during the transmission of file Wf . x
is the transmit signal and zk ∼ CN (0, σk2 ) is the AWGN at
UE k.
The BS is assumed to know the cache statuses Zi and
Zj during video delivery. Hence, the BS only transmits the
uncached subfiles requested by the UEs. Thereby, for file
Wf , subfiles Wf 1 , Wf 2 , f ∈ {A, B}, are encoded employing
four independent codebooks at the BS and the corresponding
codewords are superposed before being broadcasted over the
channel according to the NOMA principle. The resulting BS
transmit signal is given by
√
√
√
√
x = pi,1 xA1 + pi,2 xA2 + pj,1 xB1 + pj,2 xB2 , (4)
where xf s , f ∈ {A, B}, s ∈ {1, 2}, is the codeword corre2
sponding to subfile Wf s , and E |xf s | = 1. Furthermore,
pk,s ≥ 0, k ∈ {i, j}, s ∈ {1, 2}, denotes the transmit power
of xf s .
As the channel is static, we consider time-invariant power
allocation, i.e., the powers, pk,s , are fixed during file delivery.
The total transmit power at the BS is constrained to P , i.e.,
X
X
C1:
pk,s ≤ P.
(5)
k∈{i,j}

s∈{1,2}


We define p , (pi,1 , pi,2 , pj,1 , pj,2 ) and P , p ∈ R4+ | C1
as the power allocation vector and the corresponding feasible
set, respectively.
C. Joint CIC and SIC Decoding

The proposed cache-aided NOMA scheme enables CIC at
the receiver, which is not possible for conventional NOMA.
The joint CIC and SIC receiver performs CIC preprocessing
of the received signal before SIC decoding as illustrated
in Fig. 2. In particular, the interference caused by transmit
signal xA1 (xB1 ), which is requested by UE i (UE j), can
be canceled at UE j (UE i) by exploiting the cached data
Zj,A (Zi,B ). Hence, the residual received signal after CIC

Uncached
UE

fs’

UE

Received
signal

...

+

nr_s’

Decode s1

+ -

x

Encode s1

channel hk
Encode
cache
miss cache
hit

Cached
data

Decode sD

+ -

x

Encode sD

channel hk

+
CIC preprocessing

...

channel
hk

x

Video
playback

SIC decoding

Fig. 2. Joint CIC and SIC decoding at receiver k ∈ {i, j} for cacheaided NOMA. s1 , . . . , sD , D ≤ 4, represent the residual signals xf s ,
f ∈ {A, B}, s ∈ {1, 2}, which are not canceled by CIC but decoded
successively by employing SIC.

preprocessing is given by
√
√
√
yiCIC = hi ( pi,1 xA1 + pi,2 xA2 + pj,2 xB2 ) + zi , (6)
√
√
√
yjCIC = hj ( pi,2 xA2 + pj,1 xB1 + pj,2 xB2 ) + zj . (7)
Remark 1. For the proposed cache-aided NOMA scheme, ckf
portion of file Wf is not transmitted at all, while cf −ckf portion of file Wf can be removed from the received signal of the
non-requesting UE k ′ via CIC, where (k, f ) ∈ {(i, A), (j, B)}
and k ′ 6= k. As such, the proposed scheme can exploit
cf portion of Wf for performance improvement, even for
the unfavorable cache configuration of Case I, whereas a
straightforward combination of caching and NOMA can only
exploit the cached portion ckf of the requested file [15].
As CIC reduces the multiuser interference power, multiple
decoding orders become possible for SIC processing of ykCIC .
For example, there are 4! = 24 possible decoding orders based
on (6) and (7), compared to 2! = 2 for conventional NOMA.
This leads to a substantially increased flexibility in decoding
the video data based on ykCIC .
Optimizing the SIC decoding order and the respective transmission rates and power allocations based on the cache status
and channel conditions enhances the performance of video
delivery. On the other hand, decoding order optimization is a
combinatorial problem, which may increase complexity. However, by careful inspection of the SIC decoding conditions,
we show in Section III that the optimal decoding order is
contained in a small subset of all possible decoding orders,
and hence the associated complexity is limited.
III. ACHIEVABLE R ATE R EGION AND D ELIVERY T IME
M INIMIZATION
In this section, we evaluate the achievable rate region of the
proposed cache-aided NOMA scheme. Based on the derived
results, we then minimize the delivery time during file transfer
by optimizing the decoding order and the power and rate
allocation. Let r , (ri,1 , ri,2 , rj,1 , rj,2 ) be the rate allocation
vector, where rk,s ≥ 0 is the rate for delivering xf s to UE k,
σ2
(k, f ) ∈ {(i, A), (j, B)}, s ∈ {1, 2}. We define αk , |h k|2 ,
k
k ∈ {i, j}, as the effective noise variance at UE k. Without
loss of generality, we assume αi < αj , i.e., UE i has a larger
channel gain than UE j.
A. Derivation of Achievable Rate Region
According to (6) and (7), two subfiles, xf 1 and xf 2 , are
delivered to each user and xB1 (xA1 ) is canceled at UE i
(j) by CIC. Moreover, xA2 and xB2 , which are interference

signals at one user, are commonly received at both users,
whereas xA1 and xB1 are received only at the requesting
users. The interference signals can be decoded and canceled
only if the SIC decoding condition is fulfilled, i.e., the
received SINR for xA2 and xB2 at the non-requesting users,
UE j and UE i, has to exceed that at the requesting users,
UE i and UE j, respectively. In contrast, signals xA1 and xB1
can be decoded without such constraint. Depending on which
signal is decoded first, three cases can be distinguished: for
the first two cases, signals xA1 and xB1 are decoded first at
the requesting users, respectively, whereas, for the third case,
the interference signals xA2 and xB2 are decoded first. For
these cases, as (6) and (7) constitute a non-degraded broadcast
channel, the corresponding achievable rate regions have to be
evaluated for specific power regions individually.
(1)
(1)
1) UE i → xA1 : If UE i decodes xA1 first, signals yi =
√
√
√
(1)
h ( pi,2 xA2 + pj,2 xB2 ) + zi and yj = hj ( pi,2 xA2 +
√i
√
pj,2 xB2 + pj,1 xB1 )+ zj have to be decoded subsequently.
The achievable rate region is provided in Proposition 1.
(1)
Proposition
S 1. When UE i → xA1 , the rate region
R1 (P1 ) R2 (P2 ) is achievable, where




pi,1


r
≤
C
=
C


i,1
i,1




 pi,2 +p
 j,2 +αi




p

[  ri,2 ≤ Ci,2 = C αi,2i


R1 (P1 ) ,
r
pj,s
 rj,s ≤ Cj,s = C
2

p∈P1
pi,2 +αj , s = 1, 







p
+p

 rj,1 + rj,2 ≤ Cj,1,2 = C j,1 j,2 
pi,2 +αj


 
pi,1




 ri,1 ≤ Ci,1 = C  pi,2 +pj,2+αi







p
i,2

[  ri,2 ≤ Ci,2 = C pj,2 +αi


R2 (P2 ) ,
r
p
 rj,1 ≤ Cj,1 = C j,1


p∈P2



 αj
 




p
j,2
 rj,2 ≤ Cj,2 = C

pi,2 +pj,1 +αj

with P1 = P and P2 , {p ∈ P | pj,2 − pj,1 > αj − αi }. For
R1 (P1 ), the decoding orders for UEs i and j are given as
(1)

(2)

(3)

(1)

i → xA1 → xB2 → xA2 and j → (xB1 , xB2 ), respectively.
(1)

(2)

For R2 (P2 ), the decoding orders are i → xA1 → xA2 and
(1)

(2)

(3)

j → xA2 → xB2 → xB1 , respectively.
Proof: Please refer to Appendix A.
Remark 2. In Proposition 1, the interference for decoding xA2
is reduced after xA1 has been decoded and canceled from
yiCIC . Hence, decoding xA1 first is desirable when e.g. WA1
has a smaller size and/or requires a lower delivery rate than
WA2 . The decoding orders for R1 (P1 ) favor the delivery of
xA2 to UE i as it experiences no interference after SIC, and
thus can attain a high data rate ri,2 even for small transmit
powers pi,2 . In contrast, the decoding orders for R2 (P2 )
favor the delivery of xB1 to UE j. This implies that R2 (P2 )
expands R1 (P1 ) along rj,1 .
(1)

(1)

2) UE j → xB1 excluding UE i → xA1 : 1 Decoding
and canceling xB1 first improves the SINR of xB2 at UE
j, which is desirable when subfile WB1 has a smaller size
than WB2 . The resulting signals after xB1 has been canceled
√
√
√
(1)
are yi = hi ( pi,1 xA1 + pi,2 xA2 + pj,2 xB2 ) + zi and
√
√
(1)
yj = hj ( pi,2 xA2 + pj,2 xB2 ) + zj . The corresponding
achievable rate region is given in Proposition 2.
1 The

(1)

(1)

achievable rate region for UE j → xB1 and UE i → xA1 is already
included in R1 (P1 ), and hence, excluded herein.

(1)

(1)

Proposition 2. When UE j → xB1 but UE i →
xA1 is excluded,
the achievable rate region is given by
S
R3 (P3 ) R4 (P4 ), where




p

 ri,s ≤ C αi,si , s = 1, 2 










pi,1 +pi,2


[
ri,1 + ri,2 ≤ C
α
i


R3 (P3 ) ,
r
pj,1
 rj,1 ≤ C


p∈P3
pi,2 +pj,2+αj









pj,2
 rj,2 ≤ C

pi,2 +αj




p


ri,1 ≤ C pj,2i,1





 +αi





p

[  ri,2 ≤ C pi,1 +pi,2
+α
j,2
i 

R4 (P4 ) ,
r
pj,1

 rj,1 ≤ C

p∈P4



 pi,2 +p
 j,2 +αj 




p

 rj,2 ≤ C j,2
αj

with P3 , {p ∈ P | pi,1 < αj − αi } and P4 = P\P3 . The
(1)

(2)

decoding orders achieving R3 (P3 ) are UE i → xB2 →
(1)

(2)

(xA1 , xA2 ) and UE j → xB1 → xB2 . Moreover, the decoding
(1)

(2)

orders for R4 (P4 ) are UE i → xA2 → xA1 and UE
(1)

(2)

(3)

j → xB1 → xA2 → xB2 .

Proof: Please refer to Appendix B.
(1)

(1)

(1)

(1)

When UE j → (xA2 , xB2 ) and UE

i → (xS
the achievable rate region is given by
A2 , xB2 ), S
R5 (P5 ) R6 (P6 ) R7 (P7 ), where




pi,s


,
s
∈
{1,
2}
r
≤
C


i,s
αi 



 




p
+p
i,1
i,2

[  ri,1 + ri,2 ≤ C
α
i


R5 (P5 ) ,
r
pj,1

 rj,1 ≤ C

p∈P5 




 pi,2 +αj





p
j,2

 rj,2 ≤ C
pj,1 +pi,2 +αj




p


 ri,1 ≤ C αi +pi,1j,2 ∆










pi,2

[
ri,2 ≤ C pi,1 +pj,2 +αi 


R6 (P6 ) ,
r
 rj,1 ≤ C pj,1


p∈P6 




 αj




pj,2
 rj,2 ≤ C

pi,2 +pj,1 +αj




pi,1


r
≤
C


i,1



 pj,2 +αi
 




p

[  ri,2 ≤ C pi,1 +pi,2
j,2 +αi


R7 (P7 ) ,
r
 rj,s ≤ C pj,s , s = 1, 2 

p∈P7
αj 







p
+p

 rj,1 + rj,2 ≤ C j,1 j,2 
αj

with P5 , {p ∈ P | pi,1 < pj,1 + αj − αi }, P6 = P7 =
P\P5 , and ∆ , 1 [pi,2 > pi,1 − pj,1 − αj + αi ]. The decod(1)

(2)

ing orders achieving R5 (P5 ) are UE i → xB2 → (xA1 , xA2 )
(1)

(2)

(2)

(1)

(2)

(2)

decoding orders UE i → xA2 → xA1 and UE j → xA2 →
(xB1 , xB2 ).
Proof: Please refer to Appendix C.
Remark 3. Different from conventional NOMA, file splitting
in the proposed cache-aided NOMA scheme enables joint
decoding opportunities. For example, joint decoding of xB1
and xB2 at UE j is possible in R1 (P1 ), as the two signals
are received by UE j over the same AWGN channel with
noise variance pi,2 + αj . Therefore, UE j can choose the
decoding order for these files without restriction. Similarly,
joint decoding of xA1 and xA2 is possible at UE i in
R3 (P3 ) and R5 (P5 ), respectively. We note that employing
file splitting in conventional NOMA would not increase the
achievable rates at UEs. However, if a portion of file is cached
at one of the UEs, the achievable rates of the UEs can be
increased by employing file splitting in the proposed cacheaided NOMA as this enables CIC.
Finally, combining the results in Propositions
1–3, the
S7
overall achievable rate region is R , n=1 Rn (Pn ). Note
that Rn (Pn ) can be written in general form as
[  C2: r ≤ C (p), k ∈ {i, j} , s ∈ {1, 2}
ks
k,s
r
Rn (Pn )=
C3: rk1 +rk2 ≤ Ck,1,2 (p), k ∈ {i, j}
p∈Pn

3) UE j → (xA2 , xB2 ) and UE i → (xA2 , xB2 ): Recall
that decoding the interference signals first is only possible if
the SIC condition is fulfilled. In this case, the achievable rate
region is given in Proposition 3.
Proposition 3.

(1)

and UE j → xB2 → xB1 . Finally, R7 (P7 ) is achieved by the

and UE j → xB2 → xB1 . Moreover, R6 (P6 ) is achieved by
the decoding orders
(
xA1 ,
if ∆ = 1,
(1)
(2)
UE i → xA2 →
(3)
xB2 → xA1 , otherwise,

(8)
where Ck,s and Ck,1,2 are the respective capacity bounds for
decoding signal xf s , s ∈ {1, 2}, and signals {xf 1 , xf 2 } at
user k ∈ {i, j}.
B. Rate and Power Allocation for Fast Delivery
Let T be the time required to complete the delivery of the
requested files. We have
T =

max

k∈{i,j}, s∈{1,2}

βk,s
,
rk,s

(9)

for r ∈ R, where βk,1 , (cf − ckf )Vf and βk,2 , (1 − cf )Vf
for (k, f ) ∈ {(i, A), (j, B)} denote the effective volume
of data to be delivered to user k. To avoid trivial results,
we assume throughout this section that βk,1 + βk,2 > 0,
∀k ∈ {i, j}, i.e., each user requests some video data that
is not cached2 . Consequently, the delivery time optimization
problem is formulated as
P1:
min
T
(10)
r∈R, p∈P, T ≥0

s.t.

C4: rks T ≥ βk,s , k ∈ {i, j} , s ∈ {1, 2} ,

where C4 ensures completion of file delivery at time T .
Problem P1 is generally nonconvex as the capacity functions in C2 and C3 in (8) are not jointly convex with respect to
r and p, and C4 is bilinear. However, the optimal solution of
Problem P1 can be obtained by solving a sequence of convex
problems as will be shown in the following. In particular,
assume that the optimal solution lies in Rn . For each feasible
power allocation, the rate region Rn , cf. (8), reduces to a polyhedron. Consequently, the optimal rate allocation, denoted as
∗
∗
∗
∗
r∗ , (ri,1
, ri,2
, rj,1
, rj,2
), can be obtained as the rate tuple on
3
the dominate face of Rn [17]. For example, for n = 1, we
∗
∗
have ri,1
= Ci,1 and ri,2
= Ci,2 as the rates of UE i are only
constrained by C2. In contrast, as the rates ofUE j are
con
p∗
j,1
∗
strained by both C2 and C3, we have rj,1 = C p∗ +p∗ +αj
j,2

2 Otherwise,

i,2

pk,1 = pk,2 = 0 and rk,1 = rk,2 = 0.
a polyhedron, any point that lies outside the dominant face is
dominated elementwise by some point on the dominant face [17].
3 For

Algorithm 1 Bisection search for ρ∗n .
1: initialization: Given LB, U B, and tolerance ǫ;
2: repeat
3:
ρn ← (LB + U B)/2;
4:
Solve the feasibility problem of (11) for ρn ;
5:
if (11) is infeasible then
6:
U B ← ρn ;
7:
else
8:
LB ← ρn ;
9:
end if
10: until U B − LB < ǫ.

∗
and rj,2
=C



∗
and rj,1
= C

p∗
j,2
∗
pi,2 +αj
p∗
j,1
p∗
i,2 +αj





(1)

(1)

(2)

for decoding order j → xB1 → xB2



p∗
∗
and rj,2
= C p∗ +pj,2
for
∗ +α
j
i,2

j,1

(2)

decoding order j → xB2 → xB1 , and the optimal power
allocation p∗ = (p∗i,1 , p∗i,2 , p∗j,1 , p∗j,2 ). In the same manner, the
optimal rate allocation for all n ∈ {1, . . . , 7} can be obtained.
Substituting the optimal rate allocations and letting ρn =
1/T , P1 can be equivalently reformulated as T ∗ =
minn∈{1,...,7} ρ∗n with
ρ∗n ,
max
ρn
(11)
p∈Pn , ρn ≥0

s.t.

∗
C5: rk,s
(p) ≥ ρn βk,s , k ∈ {i, j} , s ∈ {1, 2} .

The optimal value ρ∗n can be found iteratively by employing
Algorithm 1. In particular, in each iteration, the feasibility
of problem (11) is checked for a given ρn , cf. line 4. For
given ρn , we have ρ∗n ≥ ρn if (11) is feasible, i.e., ρn is a
lower bound on ρ∗n , and ρ∗n ≤ ρn otherwise, i.e., ρn is an
upper bound on ρ∗n . Hence, a bisection search can be applied
to iteratively update the value of ρn until the gap between
the lower and the upper bounds vanishes, whereby ρ∗n is
obtained. Moreover, efficient convex optimization algorithms
can be employed [18] in line 4 of Algorithm 1. This is
because although
C5 is a linear fractional constraint of the

aT p
form log2 1 + bT p+1 ≥ c for a, b ∈ R4+ and c ∈ R+ , it
can be transformed into an equivalent convex constraint of the
T
form (a − (2c − 1) b) p ≥ 2c − 1 such that an equivalent
convex formulation of problem (11) is obtained.
IV. P ERFORMANCE E VALUATION
In this section, the performance of the proposed cacheaided NOMA is evaluated by simulation. Consider a cell of
radius R = 2 km, where the BS is deployed at the center of
the cell and the strong and the weak users, UE i and UE j,
are uniformly distributed on discs of radii Ri = 0.2 km and
Rj = 0.6 km, respectively. For modeling the wireless channel,
the 3GPP path loss model (“Urban Macro NLOS” scenario)
in [19] is adopted. The small-scale fading coefficients are independent and identically distributed (i.i.d.) Rayleigh random
variables. The video files have size VA = VB =500 MBytes.
Moreover, the system has a bandwidth of 5 MHz. The noise
power spectral density is −172.6 dBm/Hz. Finally, we set the
maximal transmit power as P = 35 dBm and the cache status
as ciA = 0.2, ciB = 0.8, cjA = 0.8, and cjB = 0.2.
A. Baseline Schemes
1) Baseline 1 (Cache-aided orthogonal multiple access
(OMA)): As baseline, we consider time-division multiple
access (TDMA) for transmitting the uncached portions of
the requested files. In particular, τ and 1 − τ fractions of
time are allocated for transmission to UE i and UE j,

respectively, where τ ∈ [0, 1]. Consequently, the capacity
region for
o OMA =
n all possible time allocations is given by R
S
P
P
),
r
≤
(1
−
τ
)C(
)
r
≤
τ
C(
. Note
j
i
αi
αj
τ ∈[0,1] (ri , rj )
that, with Baseline 1, caching only facilitates conventional
offloading of the hit cached data.
2) Baseline 2 (Conventional NOMA with and without
caching): If caching is possible, Baseline 2 is a straightforward combination of caching and NOMA, whereby the
requested data hit by the cache is offloaded and only the
remaining data is transmitted by applying NOMA. If caching
is not possible, Baseline 2 reduces to the conventional
NOMA√ scheme. In both cases, the BS transmits signals
√
x = pi xA + pj xB for delivering files WA and WB ,
where
the power allocations pi and pj satisfy PNOMA ,

(pi , pj ) ∈ R2+ | pi + pj ≤ P . The received signals at UEs
i and j are given by, √

√
y i = hi
(12)
pi xA + pj xB + zi ,

√
√
y j = hj
pi xA + pj xB + zj .
For Baseline
oNOMA ) =
n 2, the same capacity region RNOMA(P
S
pj
pi
,
r
≤
C
r
≤
C
is
(r
,
r
)
j
i
i j
αi
pi +αj
p∈PNOMA
achieved by SIC with and without caching [17], where xB
is decoded and canceled before decoding xA at UE i. For
Baselines 1 and 2, the rate and time/power allocation is
optimized for minimization of the delivery time in a similar
manner as for the proposed cache-aided NOMA scheme.

B. Simulation Results
In Fig. 3, we compare the achievable rate regions of
the proposed cache-aided NOMA scheme and the baseline
schemes for αi = 10−3 and αj = 10−2 . For the proposed
scheme, the rate achievable by UE k is given by rk,1 + rk,2 ,
k ∈ {i, j}. Note that the achievable rate regions of all
considered schemes are independent of the values of ckf ,
(k, f ) ∈ {(i, A), (j, B)}. In particular, Baseline 2 with and
without caching achieves the same rate region. From Fig. 3,
we observe that all considered schemes achieve the same
corner points (0, 10.0) and (13.2, 0), since the maximal rate
for each UE is fundamentally limited by its channel status.
Baseline 1 achieves the smallest rate region as it employs
OMA to avoid interference. As NOMA introduces additional
degrees of freedom for the users, Baseline 2 has a larger
achievable rate region than Baseline 1. The expansion of the
rate region is more significant for the weak user than for the
strong user since the strong user consumes a small transmit
power, and hence, causes little interference to the weak user.
The proposed cache-aided NOMA scheme achieves the largest
rate region among all considered schemes as joint CIC and
SIC allows more interference to be canceled compared to
Baseline 2 which can only perform SIC. This translates into
a large sum rate gain for the proposed scheme. With the
proposed scheme, significant performance gains are possible
for both the weak and the strong user due to CIC.
In Fig. 4, we show the optimal average delivery times of
the proposed cache-aided NOMA scheme and Baselines 1
and 2 as functions of the distance of the weak UE to the BS
Rj . The performance is averaged over different realizations
of the user locations and the channel fading. For a given
Rj , as expected from the achievable rate region results in
Fig. 3, Baseline 1 requires the longest time to complete
video file delivery. The proposed cache-aided NOMA scheme
outperforms both Baseline 2 without caching and Baseline 2
with caching. This is due to the exploitation of CIC, which

Achievable rate for UE j [bps/Hz]

V. C ONCLUSION

Optimal average delivery time [min]

Fig. 3. Achievable rate region of the proposed scheme and Baselines 1 and
2 for αi = 10−3 and αj = 10−2 .

Fig. 4. Optimal average delivery time versus the distance between the weak
user and the BS.

is possible only with the proposed joint caching and NOMA
transmission design. However, different from the achievable
rate region, the delivery times of Baseline 1, Baseline 2 with
caching, and the proposed scheme critically depend on the
amount of cached data. As Rj increases, UE j, the weak user,
suffers from an increased path loss, which in turn reduces
the channel gain of UE j. Moreover, since the delivery time
of the weak user dominates the overall delivery time, we
observe from Fig. 4 that the optimal delivery time increases
with Rj for all considered schemes. However, Baseline 1
is the least efficient among the considered schemes, and its
delivery time increases by about 80% as Rj increases from
0.2 km to 2 km. By exploiting NOMA and the resulting
increased degrees of freedom, Baseline 2 effectively reduces
the performance degradation caused by the weak user. For
example, even without caching, the delivery time of Baseline
2 is 40% (50%) lower than that of Baseline 1 when UE j
is located at Rj = 0.2 km (Rj = 2 km). Moreover, when a
cache is available, Baseline 2 can also exploit caching for
offloading of the delivery data, which further reduces the
delivery time compared to Baseline 1 by an additional 12%
(10%) for Rj = 0.2 km (Rj = 2 km). The proposed scheme
enjoys the best performance and its delivery time is about
80% lower than that of Baseline 1 for the considered values
of Rj .

In this paper, a joint caching and NOMA transmission design was presented for spectrally efficient downlink communication. The proposed scheme exploits unrequested cached
data for cancellation of NOMA interference, which is not
possible with separate caching and NOMA transmission. The
achievable rate region of the proposed cache-aided NOMA
scheme was characterized, and the optimal decoding order
and the optimal power and rate allocations for minimization
of the delivery time were investigated. Simulation results
showed that the proposed scheme can significantly expand
the achievable downlink rate region for both the strong and
the weak users. Moreover, the delivery time of both users can
be effectively reduced to achieve fast video delivery. For ease
of illustration, the proposed cache-aided NOMA was only
evaluated for the important case of two paired NOMA users.
The extension of cache-aided NOMA to multiple users will
be considered in future work.
A PPENDIX A
P ROOF OF P ROPOSITION 1
(1)

As i → xA1 , ri,1 ≤ Ci,1 is achievable for decoding xA1 at
UE i. To derive the achievable rate region, we need to check
the decodability of the interfering signals xB2 and xA2 at UE
i and j, respectively. Let us consider the following two power
regions.




p
p
(1) For p ∈ P1 \P2 , we have C pj,1i,2
< C pj,2i,2
+αj
+αi ,
i.e., UE j cannot decode xA2 before decoding xB1 as the SIC
decoding condition is not met. Also, for any (pj,1 , pj,2 ) ∈ R2+ ,
xA2 
cannot be decoded
 before
 decoding xB2 at UE j as
pi,2
pi,2
pi,2
<C
<C
.
C
pj,1 + pj,2 + αj
pj,2 + αj
pj,2 + αi
(13)
On the other hand, for any (pj,1 , pj,2 ) ∈ R2+ , xB2 can be
always decoded and canceled at UE i before xA2 is decoded
as αi < αj ; and hence, ri,2 ≤ Ci,2 is achievable. In contrast,
UE j cannot decode xA2 in any case. Consequently, the
(2)
(3)
feasible decoding orders are UE i → xB2 → xA2 and
(1)
UE j → (xB1 , xB2 ), whereby rate region R1 (P1 \P2 ) is
achieved.




p
p
> C pj,1i,2
>
(2) For p ∈ P2 , we have C αi,2i
+αj


pi,2
C pj,2 +αi , i.e., xA2 can be decoded at UE j before xB1 is
(2)

decoded if and only if UE i → xA2 . Assume xA2 is decoded
last at UE i such that UE j cannot decode xA2 in any case.
Then, rate region R1 (P2 ) is achievable. On the other hand,
suppose xA2 is decoded first at UE i. Then, UE j can achieve
a higher rate for rj,1 by decoding xA2 before decoding xB1 ,
which is only possible after xB2 has been decoded according
to (13). Thus, the rate region R2 (P2S) is achievable.
Therefore, the rate region R1 (P1 ) R2 (P2 ) is achievable,
S
and any rate vector outside the region R1 (P1 ) R2 (P2 )
cannot be achieved by SIC decoding. This completes the
proof.
P ROOF

A PPENDIX B
OF P ROPOSITION 2



p
is achievBy decoding xB1 first, rj,1 ≤ C pi,2 +pj,1
+α
j,2
j
able for UE j. To obtain the achievable rate region, two power
regions have to be considered.

(1) For p∈ P3 , we have 


pi,2
pi,2
C
>C
,
p + pj,2 + αi
p + αj

 j,2

 i,1
pj,2
pj,2
>C
,
C
pi,1 + pi,2 + αi
pi,2 + αj

C
(14)
(15)

which imply that xA2 cannot be decoded at UE j in general,
cf. (14), but xB2 can always be decoded at UE i, cf. (15).
Consequently, UE j can decode xB2 only by treating xA2
as noise whereas UE i will first decode xB2 and cancel
its contribution to the received signal before decoding xA1
and xA2 . Therefore, the achievable rate region is given by
R3 (P3 ).
(2) For p∈ P4 , we have 


pi,2
pi,2
C
<C
,
(16)
p + pj,2 + αi
p + αj
 i,1

 j,2

pj,2
pj,2
C
<C
,
(17)
pi,1 + pi,2 + αi
pi,2 + αj




pj,2
pj,2
C
<C
.
(18)
pi,1 + αi
αj

That is, at UE i, xB2 cannot be decoded first, cf. (17). Hence,
(1)
we only need to consider UE i → xA2 . In this case, UE j is
able to cancel the interference from xA2 before decoding xB2
due to (16). However, at UE i, xB2 cannot be canceled before
(2)
decoding xA1 due to (18), i.e., UE i → xB2 is infeasible.
Therefore, the achievable rate region is given by R4 (P4 ),
where UE i cannot decode xB2 while UE j can decode and
cancel xA1 before decoding xB2 . Therefore, the rate region
in Proposition 2 is achievable, which completes the proof.
A PPENDIX C
P ROOF OF P ROPOSITION 3
(1)

(1)

First, assume UE j → xB2 and UE i → (xA2 , xB2 ). If
p ∈ P5, we have



pj,2
pj,2
>C
,
(19)
C
p +p +α
p + p + αj
 i,1  i,2  i
 i,2  j,1

pi,2
pi,2
pi,2
C
>C
>C
.
(20)
αi
pi,1 + αi
pj,1 + αj

By (19), UE i can decode and cancel xB2 as αi < αj .
(1)

Thus, UE i → xB2 , which leads to the residual received
√
√
(1)
(1)
signals yi = hi pi,1 xA1 + pi,2 xA2 + zi and yj =
√
√
hj
pj,1 xB1 + pi,2 xA2 + zj . By (20), UE j cannot de(1)
code xA2 based on yj . Therefore, the decoding orders UE
(1)

(2)

(1)

(2)

i → xB2 → (xA1 , xA2 ) and UE j → xB2 → xB1 are feasible
and achieve rate region R5 (P5 ).
However, if p ∈ P6 , UE i cannot decode xB2 first due to
(1)
(19). Then, for the assumption of UE i → (xA2 , xB2 ), we
(1)

only need to consider
the case
We have

 UEi → xA2 . 
pi,2
pi,2
C
>C
,
pj,1 + αj
pi,1 + αi

(21)

i.e., UE j can cancel xA2 before decoding xB1 . On the other
hand, UE i cannot cancel xB2
xA1 unless


 before decoding
pj,2
p
<
C
.
∆ = 0, whereby we have C pi,2 +pj,2
+α
p
+α
j,1
j
i,1
i
Hence, rate region R6 (P6 ) is achievable.
(1)

(1)

Next, assume
UE j →
and UE i → xA2 , which

 xA2 
p
pi,2
requires C pj,1 +pi,2
>
C
, or equivaj,2 +αj

pi,1 +pj,2 +αi 
p
pj,2
>
lently, p ∈ P7 . In this case, as C αi > C pj,1j,2
+αj



pj,2
pi,1 +αi



, UE i cannot decode xB2 . Hence, the decoding
(1)

(2)

(1)

(2)

orders UE i → xA2 → xA1 and UE j → xA2 → (xB1 , xB2 )
are feasible and achieve rate region R7 (P7 ).
(1)

(1)

Finally, for UE j → xA2 and UE i → xB2 , feasible power
and rate allocations do not exist. In particular, for such a rate
region to exist, the following inequalities would have to hold,




pi,2
pi,2
>C
,
(22)
C
p + pj,2 + αj
p + αi
 j,1

 i,1

pj,2
pj,2
C
>C
,
(23)
pi,1 + pi,2 + αi
pj,1 + αj
(1)

(1)

which ensure feasibility of UE j → xA2 and UE i → xB2 ,
respectively. Eqs. (22) and (23) are equivalent to pi,1 − pj,1 >
pj,2 + αj − αi and pi,1 − pj,1 < αj − αi − pj,2 , respectively,
which lead to pi,2 + pj,2 < 0. That is, (22) and (23) cannot
be met for feasible powers. Therefore, the rate region in
Proposition 3 is achievable, which completes the proof.
R EFERENCES
[1] X. Wang, M. Chen, T. Taleb, A. Ksentini, and V. Leung, “Cache in the
air: Exploiting content caching and delivery techniques for 5G systems,”
IEEE Commun. Mag., vol. 52, no. 2, pp. 131–139, Feb. 2014.
[2] V. W. S. Wong, R. Schober, D. W. K. Ng, and L.-C. Wang, Key
Technologies for 5G Wireless Systems. Cambridge University Press,
2017.
[3] X. Ge, S. Tu, M. Guoqiang, C.-X. Wang, and T. Han, “5G ultra-dense
cellular networks,” IEEE Wireless Commun., vol. 23, no. 1, pp. 72–79,
Feb. 2016.
[4] L. Xiang, D. W. K. Ng, T. Islam, R. Schober, V. W. S. Wong, and
J. Wang, “Cross-layer optimization of fast video delivery in cache- and
buffer-enabled relaying networks,” IEEE Trans. Veh. Technol., vol. 66,
no. 12, pp. 11 366–11 382, Dec. 2017.
[5] L. Xiang, D. W. K. Ng, R. Schober, and V. W. Wong, “Cache-enabled
physical-layer security for video streaming in backhaul-limited cellular
networks,” to be published in IEEE Trans. Wireless Commun..
[6] ——, “Secure video streaming in heterogeneous small cell networks
with untrusted cache helpers,” to be published in IEEE Trans. Wireless
Commun..
[7] M. A. Maddah-Ali and U. Niesen, “Fundamental limits of caching,”
IEEE Trans. Inf. Theory, vol. 60, no. 5, pp. 2856–2867, May 2014.
[8] ——, “Decentralized coded caching attains order-optimal memory-rate
tradeoff,” IEEE/ACM Trans. Netw., vol. 23, no. 4, pp. 1029–1040, Aug.
2015.
[9] Y. Saito, Y. Kishiyama, A. Benjebbour, T. Nakamura, A. Li, and
K. Higuchi, “Non-orthogonal multiple access (NOMA) for cellular
future radio access,” in Proc. IEEE Veh. Technology Conf. (VTC Spring),
Dresden, Germany, Jun. 2013, pp. 1–5.
[10] Z. Ding, X. Lei, G. K. Karagiannidis, R. Schober, J. Yuan, and
V. Bhargava, “A survey on non-orthogonal multiple access for 5G
networks: Research challenges and future trends,” IEEE J. Sel. Areas
Commun., vol. 35, pp. 2181–2195, Oct. 2017.
[11] 3GPP TR 36.859, “Study on downlink multiuser superposition transmission (MUST) for LTE (Release 13),” Dec. 2015.
[12] Z. Ding, P. Fan, and H. V. Poor, “Impact of user pairing on 5G
nonorthogonal multiple-access downlink transmissions,” IEEE Trans.
Veh. Technol., vol. 65, no. 8, pp. 6010–6023, Aug. 2016.
[13] Y. Sun, D. W. K. Ng, Z. Ding, and R. Schober, “Optimal joint power
and subcarrier allocation for full-duplex multicarrier non-orthogonal
multiple access systems,” IEEE Trans. Commun., vol. 65, no. 3, pp.
1077–1091, Mar. 2017.
[14] Z. Ding, R. Schober, and H. V. Poor, “A general MIMO framework for
NOMA downlink and uplink transmission based on signal alignment,”
IEEE Trans. Wireless Commun., vol. 15, no. 6, pp. 4438–4454, Aug.
2016.
[15] Z. Ding, P. Fan, G. K. Karagiannidis, R. Schober, and H. V. Poor,
“NOMA assisted wireless caching: Strategies and performance analysis,” arXiv preprint arXiv:1709.06951, 2017.
[16] J.-P. Hong and W. Choi, “User prefix caching for average playback
delay reduction in wireless video streaming,” IEEE Trans. Wireless
Commun., vol. 15, no. 1, pp. 377–388, Jan. 2016.
[17] D. Tse and P. Viswanath, Fundamentals of Wireless Communication.
Cambridge University Press, 2005.
[18] S. Boyd and L. Vandenberghe, Convex Optimization.
Cambridge
University Press, 2004.

[19] 3GPP TR 36.814, “Further advancements for E-UTRA physical layer
aspects (Release 9),” Mar. 2010.

