This paper analyzes the outage performance of a twoway relay network in the presence of interference from multiple interferers. We investigate a twoway relay network where a single user communicates with a selected other user via a relay during three phases. We propose a user selection scheme and analyze an outage probability. Numerical results verify our analysis by comparison with computer simulation and show effects of the number of users and the number of interferers on its the outage probability.
Ⅰ.Introduction
In a wireless network, relay communication improves reliability and coverage
[1]

[3]
. Recently, there have been growing interests of twoway relay networks in order to improve spectral efficiency. In practical environment, the performances of relay networks are degraded by interference
[4]

[5]
. However, Furthermore, the performance analysis of multiuser twoway relay network in the presence of interference has not been investigated.
In this paper, we investigate a multiuser twoway relay network where both the users and the relay receive interfering signals from multiple interferers and timedivisionbroadcast protocol is used. In our model, a multiuser diversity is exploited by user selection which the relay selects a user based on signaltointerferenceplusnoiseratio (SINR). The analysis is verified by the simulation.
This paper is organized as follows. We describe the system model in section II, and analyze the outage probability in section III. Numerical results are shown in section IV and conclusion is given in section V.
Notation :
f_{X}
(·) denotes the probability density function (PDF) of a random variable
X
. The complex normal distribution with mean
a
and variance
b
is denoted by
CN
(
a
,
b
) and the gamma distribution with a shape parameter
c
and a scale parameter
d
is denoted by
G
(
c
,
d
).
Ⅱ. System Model
Consider a multiuser twoway decodeandforward relay network which consists of multiple users
A
,
B
_{1}
,
B
_{2}
, ⋯,
B_{K}
, and a relay
R
as shown in
Fig. 1
. The user
A
communicates with one among
B
_{1}
,
B
_{2}
, ⋯,
B_{K}
via the relay
R
during three phases. Suppose that each terminal has a single antenna and operates in a halfduplex mode. Assume that each terminal is impaired by multiple interferers and each interferer has transmit power
P_{I}
. Assume that each terminal is also impaired by the additive white Gaussian noise (AWGN) with zero mean and unit variance. Assume that there is no direct link between the user
A
and the user
B_{k}
.
System model of a multiuser twoway DF relay network having multiple interferers 그림 1. 다중 간섭이 존재하는 다중 유저 양방향 복호 후 전송 릴레이 네트워크 시스템 모델
Assume that each channel from a terminal to another terminal and other each channel from an interferer to a terminal are independent. Assume that each channel is reciprocal and has Rayleigh quasistatic fading such that the channel coefficients remain unchanged during three phases. Let
h_{a,R}
~
CN
(0, Ω
_{a,R}
) denote the independent channel coefficient from the user
a
to the relay
R, a
∈
A, B_{k}
. Let
g_{IA,i,A}
~
CN
(0,Ω
_{IA,i,A}
),
g_{IR,j,R}
~
CN
(0,Ω
_{IR,j,R}
), and
g_{IBm,i,Bk}
~
CN
(0,Ω
_{IBk,m,Bk}
) denote the independent channel coefficient from
i
th interferer affecting the user
A
to the user
A
, from
j
th interferer affecting the relay
R
to the relay
R
, and from
m
th interferer affecting the user
B_{k}
to the user
B_{k}
, respectively.
In the first phase, the user
A
transmits its signal
x_{A}
with transmit power
P_{A}
to the relay
R
. The received signal at the relay
R
is given by
where
is transmitted signal from the
m
th interferer affecting the relay
R
in the first phase,
is the AWGN at the relay
R
in the first phase, and
N_{R}
is the number of interferers affecting the relay
R
.
In the second phase, the user
B_{k}
transmits its signal
x_{Bk}
with transmit power
P_{Bk}
to the relay
R
. The received signal at the relay
R
is given by
where
is transmitted signal from the
m
th interferer affecting the relay
R
in the second phase, and
is the AWGN at the relay
R
in the second phase.
In the third phase, the relay
R
broadcasts its signal
x_{R}
=
x_{A}
⊕
x_{Bk}
with power
P_{R}
where ⊕ is the XOR operation. The received signals at the user
A
and the user
B_{k}
are given by
and
respectively, where
x_{IA,i,A}
and
x_{Ij,Nk,Bk}
are transmitted signal from the
i
th interferer affecting the user
A
and the
j
th interferer affecting the user
B_{k}
, respectively,
n_{A}
and
n_{Bk}
are the AWGN at the user
A
and the user
B_{k}
, respectively, and
N_{A}
and
N_{k}
are the number of interferers affecting the user
A
and the user
B_{k}
, respectively.
The SINR at the relay
R
in the first phase and the second phase are given by
and
respectively.
The SINRs at the user
A
and the user
B_{k}
in the third phase are given by
and
respectively.
Assume that perfect channel state information is available at the relay
R
aiming to find one user
B_{k∗}
who has maximum SINR
γ_{R,Bk}
. Let
D
denote the set of users whose signals are decoded successfully at the relay
R
in the second phase. The relay
R
selects the user which has the largest SINR among the users in the set
D
, that is,
III. Outage Probability
For simplicity, assume that
P_{Bk}
=
P_{B}
,
N_{k}
=
N_{B}
, and Ω
_{Bk,R}
= Ω
_{B,R}
∀
k
, Ω
_{IBk,i,Bk}
= Ω
_{IB,B}
, ∀
i,k
, and Ω
_{IA,iA}
= Ω
_{IA,A}
, ∀
i
, Ω
_{IR,m,R}
= Ω
_{IR,R}
∀
m
.
The probability that the cardinality of the set
D
is
l
is given by
where
Outage event occurs if
γ
_{A,R}
,
γ
_{Bk,R}
,
γ
_{R,A}
, or
γ
_{R,Bk}
is less than a target SINR threshold
γ_{th}
The outage probability is given by
where
and
and the random variables
Z
~
G
(
N_{R}
,
P_{I}
Ω
_{IR,R}
),
V
~
G
(
N_{A}
,
P_{I}
Ω
_{IA,A}
), and
W_{k}
~
G
(
N_{B}
,
P_{I}
Ω
_{IB,B}
) are Gamma random variables.
IV. Numerical Results
In this section, numerical results verify our analysis by comparison with computer simulation where we suppose that
A
,
R
, and
B_{k}
have same transmit power
P
and the target SINR threshold
γ_{th}
is 7 dB.
Fig. 2
shows the outage probability versus the transmit power for the number of interferers,
N
= 2 and various the number of users,
K
. In this figure, the interference transmit power is fixed at 0 dBm. It is shown that the outage probability decreases as the transmit power increases. It is shown that outage probability when
K
= 2 is lower than that when
K
= 1. It is also shown that the outage probability when
K
= 4 is slightly lower than that when
K
= 2 in the low transmit power, and is almost same with that when
K
= 2 in the high transmit power which implies that the outage probability is less affected by the number of multiple users
K
as
K
is bigger than 2. This is because the outage performance mainly depends on the link between the user
A
and the relay
R
as the transmit power increases.
Outage probability versus P for various K. N = 2 . 그림 2. K 가 바뀔 때의 P 에 대한 불능확률. N = 2
V. Conclusion
In this paper, we consider the multiuser twoway DF relay network where a single user communicates with a selected other user via a relay. We propose a user selection criterion and derive expression of outage probability. Considering the user selection, SINR at the relay in the second phase is just used for the decoding set composition and SINR at the one user who is included in the decoding set in the third phase is used for final user selection. Analysis is verified by computer simulation.
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