Interference Alignment with Power Splitting Relays
in Multi-User Multi-Relay Networks
Man Chu∗ , Biao He† , Xuewen Liao∗ , Zhenzhen Gao∗ , and Shihua Zhu∗
∗ Department

arXiv:1705.06791v2 [] 23 May 2017

†

of Information and Communication Engineering, Xi’an Jiaotong University, China
The Center for Pervasive Communications and Computing, University of California at Irvine, Irvine, CA 92697, USA
Email: cmcc 1989414@stu.xjtu.edu.cn, biao.he@uci.edu, {yeplos, zhenzhen.gao, szhu}@mail.xjtu.edu.cn

Abstract—In this paper, we study a multi-user multi-relay
interference-channel network, where energy-constrained relays
harvest energy from sources’ radio frequency (RF) signals
and use the harvested energy to forward the information to
destinations. We adopt the interference alignment (IA) technique
to address the issue of interference, and propose a novel transmission scheme with the IA at sources and the power splitting
(PS) at relays. A distributed and iterative algorithm to obtain
the optimal PS ratios is further proposed, aiming at maximizing
the sum rate of the network. The analysis is then validated by
simulation results. Our results show that the proposed scheme
with the optimal design significantly improves the performance
of the network.

I. I NTRODUCTION
Energy harvesting has been envisioned as a promising
technique to provide perpetual power supplies and prolong
the lifetime of energy-constrained wireless networks, since
wireline charging and battery replacement are not always
feasible or unhazardous. In particular, simultaneous wireless
information and power transfer (SWIPT) has drawn a significant amount of attention with its advantage of transporting
both energy and information at the same time through radio
frequency signals.
The concept of SWIPT was first put forward by Varshney
in his pioneer work [1], in which he investigated the tradeoff
between information delivery and energy transfer. Recently
developed practical receiver designs for SWIPT include power
splitting (PS) and time switching (TS) [2]. For TS, the receiver
switches over time between information decoding and energy
harvesting. Differently, the receiver with PS splits the received
signal power between information decoding and energy harvesting. It has been shown that the TS is theoretically a special
case of the PS with binary PS ratios. Thus, the PS usually
outperforms the TS in terms of the rate-energy tradeoffs. With
the in-depth study on SWIPT, the research problem of how
to combine SWIPT with other key technologies has gained
much attention [3]. For the combination of the SWIPT and
relays, both single-relay and multi-relay networks have been
considered to acquire the efficient SWIPT scheme in [4][5].
In addition, the interference channel (IC) has been taken into
account for the SWIPT with relays in, e.g., [6] and [7]. The
authors in [6] analyzed the outage performance for SWIPT
both with and without relay coordination in multi-user IC

networks. In [7], the SWIPT with relays in IC networks was
studied from a game-theoretic perspective. However, none of
the aforementioned studies has directly addressed the issue
of interference for SWIPT with relays in IC networks. In
practice, interference alignment (IA) is recognized as an
efficient technique to address the issue of interference for
wireless transmissions. With the IA, the interferences are
aligned into certain subspaces of the effective channel to the
receiver, and the desired signals are aligned into interferencefree subspaces [8]. Without the consideration of relays, the
authors in [9] studied the antenna selection with IA for the
SWIPT in the IC network. While to the best of authors’
knowledge, few work has been investigated in the literature
on SWIPT with the IA in multiple AF (amplify and forward)
relay networks.
In this paper, we study an IC network where multiple
sources transmit messages to multiple users through multiple AF relays, where the energy-constrained relays harvest
energy from the RF signals and use that harvested energy to
forward the information to destinations. We propose a novel
transmission scheme by adopting the IA and the PS design. We
further propose a distributed and iterative algorithm to obtain
the optimal PS ratios at relays that maximize the sum rate
of the network. Our results show that the proposed scheme
effectively improves the performance of the network, and it
significantly outperforms benchmark schemes.
II. S YSTEM M ODEL
We consider a K × K × K dual-hop IC network consisting
of K sources, K relays, and K destinations, as shown in
Figure 1. Each source Si intends to transmit messages to its
respective destination Di with the help of its dedicated AF
relay Ri , i ∈ {1, · · · , K}. We assume that there are no direct
links between the sources and the destinations. The numbers
of antennas at each source, relay, and destination are denoted
by M , N , and L, respectively. The sets of sources, relays and
destinations are denoted by NS , NR , and ND , respectively. In
addition, the set of all source-relay-destination (S-R-D) links,
Si → Ri → Di , i = 1, · · · K, is denoted by K.
We adopt the quasi-static block Rayleigh fading model and
assume that all channels are independent of each other. The
N × M normalized channel matrix from Si to Rj is denoted

H11

S1

G11

R1

G12

H12

G1K

H1K

G21

H 21
H 22

S2

D1

G22

R2

H 2K

D2

G2K

GK 1

H K1

GK 2

HK2

SK
H KK

RK

GKK

DK

Fig. 1. Illustration of multi-user multi-relay interference MIMO network.

by Hij , and the L × N normalized channel matrix from Ri
to Dj is denoted by Gij , i, j ∈ {1, · · · , K}. We assume that
each node has the local channel state information (CSI) to
enable the distributed IA. Moreover, the distance between Si
and Rj is denoted by rij , and the distance between Ri and Dj
is denoted by mij . The correspondingly path-loss effects are
−τ
modelled by rij
and m−τ
ij , respectively, where τ ≥ 2 denotes
the path-loss exponent [10].
Half-duplex relays are considered in this work, and the two
hop transmissions operate in two time slots. In the first slot, the
sources simultaneously transmit the information and energy to
the relays. In the second slot, the relays forward the received
information to the destinations by the harvested power in the
first slot. We assume that the wireless power transfer is the
only energy access for the relays. Besides, every time slot is
assumed to be unit interval for simplicity.
III. I NTERFERENCE A LIGNMENT WITH P OWER -S PLITTING
R ELAYS
In this section, we proposed the transmission scheme for
the dual-hop IC with the IA and the PS relays.
A. IA Between Sources and Relays
In the first time slot, the IA is employed for the transmissions from sources to relays. That is, all interference signals
from unintended sources are aligned into certain interference
subspaces at any relay Ri .
As per the mechanism of IA, the following conditions
should be satisfied to have the perfect IA:
UH
i Hji Vj

= 0, ∀j 6= i,

rank(UH
i Hii Vi )

= di

M + N ≥ (K + 1) × di ,

(1)
(2)
(3)

where Vi ∈ CM ×di denotes the unitary precoding matrix at
Si , Ui ∈ CN ×di denotes the unitary decoding matrix at Ri ,
and di denotes the number of data streams from Si . Here,
the perfect IA means that the interferences are aligned into
the null space of the effective channel to the relay and can be
eliminated completely. We can interpret (1) as the condition of
having the interference-free space of the desired dimensions,
and (2) and (3) as the conditions that the desired signal is
visible and resolvable within the interference-free space [11].
When the number of links is larger than 3, i.e., K > 3,
the closed-form expressions for the precoding and decoding
matrixes cannot be obtained. Hence, we use the channel
reciprocity characteristic with the distributed and iterative IA
to determine the IA matrices in this work.
The received signal at Ri (without multiplexing the decoding matrix UH
i ) in the first time slot is given by
q
−τ
IA
pi rii
Hii Vi xi
yR
=
i
K
q
X
−τ
+
pj rji
Hji Vj xj + nAi ,
(4)
j=1,j6=i

where pi denotes the transmit power at Si , xi ∈ Cdi ×1 denotes
the normalized desired signal for Di with E{||xi ||2 } = 1, and
nAi denotes the additive white Gaussian noise (AWGN) at the
receiver antennas of Ri .
B. PS Relays
In this work, the PS scheme is adopted at the relays for
the SWIPT. The block diagram of the receiver at the relay is
shown in Figure 2. For the received signal at Ri , a fraction
0 ≤ ρi ≤ 1 of the power is used for information processing
and forwarding, and the remaining fraction 1−ρi of the power
is used for energy harvesting. We refer to ρi as the PS ratio
at Ri . We assume that the processing power required by the
transmit/receive circuits at the relay is negligible compared
with the power used for signal transmission [10].
Then, the signals received by the energy-harvesting unit at
Ri is given by
q
p
−τ
EH
yRi
=
(1 − ρi )
pi rii
Hii Vi xi
+

K
X

q

−τ
pj rji
Hji Vj xj + nAi


,

(5)

j=1,j6=i

and the harvested energy at Ri is given by


K
X
2
−τ
QRi = η (1 − ρi )  pj rji
||Hji Vj ||  ,

(6)

j=1

where η denotes the energy conversion efficiency. Note that
the harvested energy due to the noise nAi is very small and
thus ignored.
At the information processing unit of Ri , the decoding
matrix UH
i is multiplexed to the received signal to eliminate

(1 − ρi )Xi ρi pi Yii ρi pi b1ii +σ2

γDi (ρ) = PK

j=1,j6=i

(1 − ρj )Xj

ρj pj Yji +cji σ 2
ρj pj bjj +σ 2

1 

…

x

RF Unit and
Antenna

EH

x

IP

IF

.

(12)

j=1,j6=i

nA

=


σ2
η

denotes the power normalization coefficient at Ri . The received signal at Di is given by
q
IP 2
QRi m−τ
yDi =
ii Gii βRi yRi
K
q
X
IP 2
+
QRj m−τ
ji Gji βRj yRj + nDi

Power
Splitting

+

2

+ (1 − ρi ) Xi cii ρi pi bσii +σ2 +

U , nR

q
q
−τ H
QRi m−τ
G
β
ρi pi rii
Ui Hii Vi xi
ii
R
i
ii
K
q
X q
−τ H
QRj m−τ
ρj pj rjj
Uj Hjj
+
ji Gji βRj
j=1,j6=i

Fig. 2. Power splitting model at the relay.

Vj xj +

K q
X

QRj m−τ
ji Gji βRj nRj + nDi , (11)

j=1

the interferences. The processed signals at the information
processing unit of Ri is then given by
IP 1
yR
=
i

q

−τ H
ρi pi rii
Ui Hii Vi xi +

√

ρ i UH
i nAi + nRi , (7)

2
where nRi ∼ CN (0, σR
I ) denotes the AWGN introduced
i N
by the information processing unit at the relay. In practice, the
power of antenna noise nAi is usually much smaller than the
processing noise, and hence, the antenna noise has negligible
impact on the signal processing. Then, the antenna noise nAi
is ignored for simplicity in the rest of analysis in the paper [7],
[12], and the processed signal at Ri is simplified as

IP 2
yR
=
i

q

−τ H
ρi pi rii
Ui Hii Vi xi + nRi .

(8)

C. AF Signals to Destinations
In the second time slot, the relays amplify and forward the
processed signals to destinations by the harvested energy in
the first time slot. Since the utilization of IA for the second
hop would significantly increase the system overhead and
the energy consumption at the energy-constrained relays in
practice, the IA is not adopted for the second-hop transmission.
The transmitted signal at Ri in the second time slot is then
given by
F
yR
=
i

p
IP 2
QRi βRi yR
,
i

(9)

where QRi denotes the transmit power of Ri as given in (6)
and
βR i = q

1
2

−τ
2
ρi pi rii
||UH
i Hii Vi || + σRi

(10)

2
where nDi ∼ CN (0, σD
I ) denotes the AWGN at Di .
i N
In order to simplify the expression, we define Xi =
PK
2
2
−τ
−τ −τ
j=1 pj rji ||Hji Vj || , Yii = mii rii ||Gii H̃ii || , Yji =
2

2

2

−τ
−τ
−τ
m−τ
ji rii ||Gji H̃jj || , bii = rii ||H̃ii || , cji = mji ||Gji || ,
H
and the effective channel matrix H̃ii = Ui Hii Vi . In addi2
2
tion, we assume that σD
= σR
= σ 2 for any i ∈ {1, · · · , K},
i
i
without loss of generality [7]. The signal to interference
plus noise power ratio (SINR) at Di , denoted by γDi (ρ) is
then given by (12) as shown at the top of this page, where
T
ρ = [ρ1 , ρ2 , · · · , ρK ] denotes the vector of all relays’ PS
ratios. Finally, the rate of the transmission to Di is given
by 21 B log2 (1 + γDi (ρ)), where B denotes the frequency
bandwidth and 1/2 is due to the use of two time slots.

IV. O PTIMIZATION OF P OWER S PLITTING R ATIO
We note that the PS ratio ρ plays a pivotal in determining
the network performance. Thus, we optimize the design of ρ
in this section.
A. Problem Formulation
The objective of our design here is to determine a series
of PS ratios, ρ1 , · · · , ρK , to maximize the total transmission
rate of the network. The sum-rate maximization problem is
formulated as:
K
X
1
(P1) max Rsum (ρ) =
B log2 (1 + γDi (ρ)),
ρ
2
i=1
s.t.

ρ ∈ A,
H
Ui UH
i = I, Vi Vi = I,

E{||xi ||2 } = 1, ∀i ∈ {1, · · · , K},

(13)

where A = {ρ | 0 ≤ ρi ≤ 1, ∀i ∈ {1, · · · , K}} is the feasible
region of all PS ratios.
We find that the optimization problem in (13) is not convex,
and the closed-form solution of the globally optimal ρ cannot



(z2 z3 + t) ρi 3 − z3 pi bii + z2 z3 σ 2 − 2t ρi 2 + 2z1 z3 − z2 z3 σ 2 + t + pi bii σ 2 ρ2 + z1 z3
∂γDi (ρ¯i , ρi )
= 0.
=
i2
h
∂ρi
−1
z2 + η (1 − ρi ) Xi cii σ 2 (ρi pi bii ) + σ 2

K
X

z1 =

η (1 − ρj ) Xj pi bii + σ 2

j=1,j6=i
K
X

z2 =

η (1 − ρj ) Xj Yji

K
X
σ2
ρj pj
+
.
η
(1
−
ρ
)
X
c
j
j
ji
ρj pj bjj + σ 2
ρj pj bjj + σ 2

be obtained. Thus, we develop a distributed and iterative
scheme, such that each Ri decides its own PS strategies
aiming at maximizing the individual achievable transmission
rate through the ith link, i.e., Si → Ri → Di , and the global
optimal ρ that maximizes the sum rate of all links can be then
obtained iteratively by the cooperation between the relays. The
design problem is formulated as:
K
X
i=1

max
ρ

1
B log2 (1 + γDi (ρ¯i , ρi )),
2

s.t. ρ ∈ A,
H
Ui UH
i = I, Vi Vi = I,

E{||xi ||2 } = 1, ∀i ∈ {1, · · · , K},

(14)

where ρ¯i = {ρj | 1 ≤ j ≤ K, ∀j 6= i} denotes the vector of
all links’ PS ratios except for the ith link.
B. Optimal Design
We first determine the optimal ρi at Ri that maximizes
the received SINR at Di for any given ρ¯i . The problem is
formulated as:
ρi

s.t. ρ ∈ A,

γ̃Di (ρ¯i , ρi )
η (1 − ρi ) Xi ρi pi Yii ρi pi b1ii +σ2
K
P
j=1,j6=i

=

I, Vi ViH

(18)

to find the optimal ρ. The main idea of our iterative algorithm
is briefly summarized as follows. Assume that the result
of nth iteration is ρ(n) = [ρ1 (n), ρ2 (n), · · · , ρK (n)]. The
solution of (n + 1)th PS ratio ρi (n + 1) is then acquired
by using Newton iteration method with the knowledge of
{ρ1 (n + 1), ρ2 (n + 1), · · · , ρi−1 (n + 1), ρi+1 (n), · · · , ρK (n)}.
We define a parameter ε to evaluate whether the algorithm is
convergent or not. The iteration converges if and only if the
condition of kρ(n + 1) − ρ(n)k2  ε is satisfied.
In what follows, we determine the wise iterative initial
values to reduce the number of the iterations to find the
optimal ρ. To this end, we obtain the optimal PS ratios under
the asymptotic scenario of high SNR, which in fact serve
as the wise initial values of our iterative algorithm under
general scenarios. We note that (12) can be simplified when
the received SINRs at relays are high, i.e., ρi pi bii  σ 2 and
ρj pj bjj  σ 2 . The second item and the third item of the
denominator of γDi (ρ¯i , ρi ) approximate to zero under the high
SINR consideration. Then, γDi (ρ¯i , ρi ) can be rewritten as

=

max γDi (ρ¯i , ρi ),
Ui UH
i

(17)

j=1,j6=i

j=1,j6=i

(P2)

 ρj pj Yji + cji σ 2
− Xi cii σ 2 + pi bii σ 2 .
ρj pj bji + σ 2

(16)

= I,

2

E{||xi || } = 1, ∀i ∈ {1, · · · , K}.

(15)

We find that γDi |ρi =0 = 0 and γDi |ρi =1 = 0, and hence,
γDi (ρ¯i , ρi ) is not a monotonous function of ρi in the range
of [0, 1]. We will later show the uniqueness of the extreme
value point of γDi (ρ¯i , ρi ) for 0 ≤ ρi ≤ 1, and verify that the
extreme point is the optimal PS ratio maximizing the SINR.
Let the first-order derivative of γDi (ρ¯i , ρi ) with respect to
ρi be equal to zero, we have (16) shown at the top of this
paper, where t = Xi cii σ 2 , z3 = Xi pi Yii , and z1 and z2
are given in (17) and (18), respectively. From (16), we find
∂γDi (ρ¯i ,ρi )
∂γDi (ρ¯i ,ρi )
that
|ρi =0 > 0 and
|ρi =1 < 0. Thus,
∂ρi
∂ρi
∂γDi (ρ¯i ,ρi )
= 0. We
∂ρi
∂γDi (ρ¯i ,ρi )
ρi to
= 0
∂ρi

there exists a ρi ∈ [0, 1] that satisfies

note that the closed-form solution of
cannot be obtained. Instead, we propose an iterative algorithm

.

(19)

η (1 − ρj ) Xj ρj pj Yji ρi pi b1ii +σ2 + σ 2

The first-order derivative of γ̃Di (ρ¯i , ρi ) with respect to ρi is
given by
γ̃Di (ρ¯i , ρi )
∂ρi


Xi Yii pi sji + σ 2 −ρi 2 pi bii − 2ρi σ 2 + σ 2
=
,
2
[ρi pi bii (sji + σ 2 ) + σ 2 sji + σ 2 ]
where sji =

K
P

(20)

η (1 − ρj )Xi ρj pj Yji ρj pi b1jj +σ2 . We find

j=1,j6=i
γ̃Di (ρ¯i ,ρi )
|ρi =0 >
∂ρi

γ̃

(ρ¯ ,ρ )

that
0 and Di∂ρii i |ρi =1 < 0. Thus, there
exists a ρi ∈ [0, 1] satisfying that γ̃Di (ρ¯i , ρi ) in (20) is equal
to zero. In addition, we need to solve the following equation
to acquire the initial PS ratios.


fˆ(ρi ) = Xi Yii pi sji + ρi 2 −ρi 2 pi bii − 2ρi ρi 2 + ρi 2 = 0.
(21)

−τ
Since bii = rii
||H̃ii ||2 , it is always true that pi bii > 0. Note
that the solution of (21) is uncorrelated with ρ¯i . Hence, each
ρi can be calculated independently. We further find that (21)
has two real roots, since ∆ = 4σ 2 (σ 2 + pi bi ) > 0. Moreover,
according to the curve of the
√ function as depicted in Figure 3,
2
− ∆
< 0 should be abandoned, and
the solution of ρi = −2σ
2pi bii
the optimal PS √ratio under the high SINR condition is given
2
+ ∆
by ρoi = −2σ
.
2pi bii

TABLE I
A LGORITHM TO SOLVE (P2)

1. Initialization: Set iteration number n = 0; Determine the
initial PS ratios ρ(0) = {ρ1 (0), ρ2 (0) · · · ρK (0)} by (22).
2. Iteration: Obtain the nth iteration results ρ(n + 1) by
solving (16) for each ρi with the Newton iteration method
and {ρ1 (n + 1) · · · ρi−1 (n + 1), ρi+1 (n) · · · ρK (n)}.
3. Check if kρ(n + 1) − ρ(n)k2  ε is satisfied. If it is
satisfied, go to Step 4. Otherwise, update the iteration

fˆ ( ri )

number n = n + 1 and return to Step 2.
4. Obtain the optimal PS ratios as ρ∗ = ρ(n + 1).
0.8

0.75

0.7

r2

0

r1

1

ri

0.65

0.6

0.55

Fig. 3. The curve of fˆ(ρi ) versus ρi .

0.5

0.45

0.4

th

Therefore, the initial PS ratio for the i link of our iterative
algorithm is given by
√
−2σ 2 + ∆
ρi (0) = ρoi =
.
(22)
2pi bii
Different from the system of linear equations, it is difficult
to provide a convergence condition for our proposed iterative
algorithm. However, it can be found that ρi (n + 1) is the
only root of equation γDi (ρ¯i , ρi ). Thus, the result of every
iteration increases the objective function, i.e., γDi (ρi (n +
1)) > γDi (ρi (n)). Considering the monotonic increase of the
objective function and the fact that the maximum achievable
γDi is finite, the proposed algorithm converges to a certain
point, at which the iteration stops. The detailed steps of the
proposed algorithm are given in Table I.
V. N UMERICAL R ESULTS
In this section, we show the performance of the proposed
scheme by simulations. Unless otherwise stated, we set the
distance between each source and its dedicated relay rii = 1,
the distance between each relay and its respective destination
mii = 1, the path-loss exponent τ = 3, the energy conversion
efficiency η = 0.5, the variance of AWGN at receivers σ 2 =
0.01, and the convergency criteria ε = 10−3 . We randomly
generate 10,000 channel realizations to obtain the average sum
rate of the network.

0.35
1

2

3

4

5

6

7

8

9

10

Fig. 4. Illustration of the convergence of the proposed algorithm. The system
parameters are M = N = L = 4 and K = 3.

We first demonstrate the convergence speed of the proposed
iterative algorithm. Figure 4 plots the obtained PS ratio versus
the iteration number for different initial values. As shown in
the figure, the algorithm always converges to the same value
of the PS ratio, i.e., the optimal PS ratio, for any given initial
values. Comparing the results for different initial points, we
find that our proposed initialized PS scheme outperforms all
other schemes, in terms of the use of iterations to obtain the
optimal PS ratio.
We now present the performance comparison between our
proposed scheme and benchmark schemes. We consider three
benchmark schemes, which are the transmission with randomly select PS ratios, the transmission with fixed PS ratios
of ρi = 0.5, and the transmission scheme without the IA as
proposed in [7]. Figures 5 and 6 plot the average sum rate versus the transmit power at the source and the number of links,
respectively. As shown in both figures, our proposed scheme
always significantly outperforms all benchmark schemes. We
note that the benchmark scheme without the IA always has

0.45

0.55
0.5

0.4

0.45
0.35

0.4
0.3

0.35
0.25

0.3

0.2

0.25
0.2

0.15

0.15
0.1

0.1
0.05
0

5

10

15

20

25

30

35

40

0.05
3

Fig. 5. Sum rate of the network versus transmit power at the source. The
system parameters are M = N = L = K = 4.

the worst performance, which implies that the introduction
of the IA improves the network performance even if the PS
ratios are not optimally designed. The great advantage of our
proposed scheme is due to not only the introduction of the
IA to eliminate the interference to relays but also the welldesigned PS ratios that balance the information processing and
energy harvesting to forward the information.
We next discuss the impact of the transmit power at the
source on the performance of the network. As depicted in
Figure 5, the average sum rate increases as the transmit power
increases. From all curves, we note that the speed of the
increase of sum rate decreases as the transmit power increases,
and it becomes very slow when the transmit power is high.
Such an observation can be explained as follows. In this work,
we have not employed the IA for the second hop due to
the practical consideration of the system overhead and the
high energy consumption at relays. Then, the increase of
transmit power at relays may harm the network performance
due to the interference. Thus, the relays actually cannot always
increase the transmit power for the second hop, even if the
harvested energy increases. Furthermore, we find that the
performance gap between our proposed scheme and the other
benchmark schemes increases as the transmit power at the
source increases. This is because that the proposed scheme
wisely takes advantage of the increase of the available energy
resource at sources by the IA and the PS design, while the
other schemes cannot take fully advantage of the increase of
resource due to lack of either interference management or the
PS design.
Finally, we evaluate the impact of the number of links on
the performance of the network. As illustrated in Figure 6,
as the number of links increases, the sum rate of the network
increases first until achieving a peak value, and then decreases.

3.5

4

4.5

5

5.5

6

6.5

7

Fig. 6. Sum rate of the network versus number of links. The system
parameters are M = N = L = 4.

We explain this observation as follows. When the number
of links is small, the increase of the number of links can
significantly increase the multiplexing gain of the network with
the relatively small interference. When the number of links
becomes large, further increasing the number of links would
make the interference issue become serious, as the IA has not
been employed at the relays for the second-hop transmission
in the proposed scheme. From the discussions of Figures 5
and 6, we note that adopting the IA at the second hop has
a considerable potential to further improve the performance
of the network. However, as mentioned previously, the employment of the IA at relays would considerably increase the
system overhead and the energy consumption of the energyconstrained relays. Thus, it is not always feasible to employ
the IA at the wireless-powered relays in practice.
VI. C ONCLUSION
In this paper, we have introduced a novel transmission
scheme for multi-user multi-relay IC networks, where the
IA is employed at the sources and the PS is designed at
the AF relays. We have proposed a distributed and iterative
algorithm to determine the optimal PS ratios that maximize
the sum rate of the network. In order to reduce the number
of iterations to obtain the optimal PS ratios, we have further
derived the closed-form expressions for the optimal PS ratios
under the high SNR condition, which serve as the initial values
of the iteration for the proposed algorithm. Our results have
shown that the proposed scheme significantly outperforms the
benchmark schemes to improve the network performance.
ACKNOWLEDGMENT
This work is supported by National Natural Science Foundation of China (NSFC) under grant 61461136001.

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