Twoway relaying is an effective way of improving system spectral efficiency by making use of physical layer network coding. However, energy efficiency in OFDMbased bidirectional relaying with asymmetric traffic requirement has not been investigated. In this study, we focused on subcarrier transmission mode selection, bit loading, and power allocation in a multicarrier single amplifiedandforward relay system. In this scheme, each subcarrier can operate in two transmission modes: oneway relaying and twoway relaying. The problem is formulated as a mixed integer programming problem. We adopt a structural approximation optimization method that first decouples the original problem into two suboptimal problems with fixed subcarrier subsets and then finds the optimal subcarrier assignment subsets. Although the suboptimal problems are nonconvex, the results obtained for a singletone system are used to transform them to convex problems. To find the optimal subcarrier assignment subsets, an iterative algorithm based on subcarrier ranking and matching is developed. Simulation results show that the proposed method can improve system performance compared with conventional methods. Some interesting insights are also obtained via simulation.
1. Introduction
C
onventional oneway relay transmission is less spectrally efficient with respect to twoway relay transmission owing to halfduplex constraints. To overcome this disadvantage, bidirectional relaying has been proposed, which utilizes physical layer network coding (PNC) technology, enabling two users to communicate with each other with the help of an intermediate relay. In previous studies, two main protocols were used: a broadcast threephase protocol and a twophase protocol, which form the foundation for future studies on bidirectional communication
[1]
. In
[1
–
4]
, the problem of capacity, achievable rate regions, and outer bounds of the bidirectional relaying system were addressed. The techniques and methodology developed in the literature for oneway relaying have been found to also work for bidirectional relaying: randomized spacetime block coding in
[5
–
6]
, relay buffering in delaytolerant networks
[7]
, and diversitymultiplexing tradeoff
[8]
.
In practice, there exist some systems that have distinct data rate requirement for uplink and downlink paths. The methods previously developed for these systems assumed symmetric traffic conditions. However, when these methods are applied to asymmetric traffic conditions, lower energy efficiency is experienced. Several studies on bidirectional relay systems with asymmetric traffic have attempted to solve this issue
[9
–
13]
. An asymmetric modulation scheme that is capable of making full use of the stronger link to improve the overall transmission rate and ensures the reliability of the weaker link was proposed in
[9]
. In
[10]
, a hierarchical modulation (HM)based scheme and a hybridconstellationbased relay scheme are considered to enhance the performance of asymmetric bidirectional relaying. In
[11]
, a closedform asymptotic expression is given for the system outage probability for an amplifyandforward (AF) bidirectional protocol with imperfect CSI estimation and asymmetric traffic requirement. A new method that allocates the transmission time and the rates in both directions for asymmetric traffic conditions was introduced in
[13]
.
Multicarrier modulation such as orthogonal frequencydivision multiplexing (OFDM), which divides the data into many substreams, has a natural advantage for finding a way to satisfy asymmetric traffic requirements from the standpoint of the frequency domain, which is an approach that has not been properly investigated. Resource allocation in bidirectional OFDM relay systems had been previously investigated
[12
,
15
,
20]
. In
[12]
, the authors studied power allocation, mode selection, and subcarrier assignments with qualityofservice (QoS) considerations for OFDM bidirectional decodeandforward (DF) relay systems. By using a dual method, the problem was efficiently solved. A twostep approach to power allocation for OFDM signals over a twoway AF relay was proposed in
[15]
, in which the authors show that the received SNRs of the two users are equal under fixed total power constraints at each subcarrier for OFDM bidirectional AF relaying. In
[20]
, power allocation for bidirectional AF multiplerelay multipleuser networks was formulated as a geometric programming (GP) problem by maximizing the instantaneous sum rate or minimizing the symbol error rate.
In this study, we focus on a twohop system with an AF relay node, in which the received signal is linearly scaled by a scaling coefficient and then forward to its destination, which can be another user or a base station. The objective of our proposed optimization is to minimize the total power consumption under the asymmetric traffic requirement constraint. In a situation where two users with different data requirements exist, more subcarriers will naturally be assigned to the user with the higher data rate requirement. The extra subcarriers will have to work in oneway transmission mode. This ultimately means that some subcarriers will operate in oneway transmission mode, whereas others will operate in twoway transmission mode. A combinational optimal problem with transmission mode selection, power allocation, and bit loading is formulated. Unfortunately, the problem is a mixed integer program and NP hard. Owing to this difficulty, we extend the proof for directional relaying in
[14]
and the structure property for symmetric twoway relaying in
[15]
. We develop a suboptimal algorithm to solve the proposed NPhard problem. In the first step, we decouple the original problem into two suboptimal problems with fixed subcarrier subsets. In the second step, we find the optimal subcarrier assignment subsets that minimize the total power consumption.
The main contribution of this work can be broadly classified into two parts:

1) We formulate a joint optimization problem of transmission mode selection, power allocation, and bit loading for OFDM bidirectional AF relaying. Our objective is to minimize the energy consumption per bit. The problem is a mixed integer programming problem and NP hard. Because of nonconvexity, the method developed for DF relaying in[12]is not pragmatic. Therefore, we develop a twostep algorithm to find the asymptotically optimal solution.

2) We investigate the influence of the asymmetric ratio on system energy efficiency; the simulation reveals that there is an asymmetric traffic ratio that minimizes the energy consumption per bit. This is an interesting result for the transmission design.
2. System model
Consider a twohop relay network that consists of two user nodes (
S_{a}
and
S_{b}
) and one AF relay node (
R
) without line of sight between
S_{a}
and
S_{b}
. All the nodes are equipped with one antenna, and the number of subcarriers is
N
. The channels operate under the assumption of reciprocity, which means that the channels from user
S_{i}
(
S_{i}
=
S_{a}
,
S_{b}
) to the relay and from the relay to user
S_{i}
are the same. The block diagram of the network is shown in
Fig. 1
.
The OFDM bidirectional relay channel, where terminals S_{a} and S_{b} exchange messages via a relay node R.
The channel fading coefficient between
S_{a}
and relay
R
and that between user
S_{b}
and relay
R
at subcarrier
n
are denoted by
h_{n}
and
g_{n}
, respectively, and they are modeled as independent Rayleigh distribution variables that remain constant over the entire block transmission.
To model the asymmetric traffic, we define an asymmetric traffic ratio
α
as the ratio of the transmission data rate requirements of users
S_{b}
to
S_{a}
. We assume that user
S_{a}
has a higher data rate requirement in this paper; hence, 0<
α
≤1, and
R_{b}
=
αR_{a}
.
3. Problem formulation
We use subscripts 1, 2 to denote oneway relaying and twoway relaying, respectively. We first introduce the following sets of variables:

Pk,n,1indicates the power of subcarriernat nodekfor oneway relay transmission,k∈{a,r}.

Pk,n,2indicates the power of subcarriernat nodekfor twoway relay transmission,k∈{a,b,r}.

ra,n,1indicates the data rate of subcarriernatSafor oneway relay transmission.

rk,n,2indicates the data rate of subcarriernat nodekfor twoway relay transmission,k∈{a,r}.
 3.1 OneWay Relay Network
For oneway relaying, in the first slot, user
S_{a}
transmits
x_{a,n}
to
R
, and the received signal at relay node is denoted as
In the second time slot, relay
R
amplifies
y_{r,n}
with a scaling factor
ω_{n,1}
and retransmits it to the destination.
where
. Thus, we have
, and
η_{r}
and
η_{b}
are the additive Gaussian noises at relay node
R
and the destination
S_{b}
with zero mean and variance
σ^{2}
, respectively. Hence, the received SNR at
S_{b}
is
The instantaneous rate per subcarrier of user
S_{a}
for oneway relaying is given as
where
C(x)
= (
1/2)log
(
1
+
x
).
 3.2 TwoWay Relay Network
A twophase protocol for twoway relay transmission includes the MAC phase and the BC phase. In the first slot, users
S_{a}
and
S_{b}
simultaneously transmit to relay
R
, and the received signal at subcarrier
n
is
In the second slot, relay
R
scales the received signal with the scaling factor
ω_{n,2}
and broadcasts it to
S_{a}
and
S_{b}
. The received signal at
S_{a}
and
S_{b}
can be expressed as
where
; thus, we have
. where
η_{a}
,
η_{b}
, and
η_{r}
are the additive Gaussian noises at user nodes
S_{a}
and
S_{b}
, and relay
R
with zero mean and variance
σ^{2}
, respectively. Because the user nodes know perfectly well what they have sent, selfinterference cancellation could be used to remove interference. The residual signals
_{a,n}
and
_{b,n}
are
The received SNRs at
S_{a}
and
S_{b}
can be written as
For the twoway relaying transmission mode, the achievable rates of users
S_{a}
and
S_{b}
over subcarrier
n
can be respectively written as
 3.3 EnergyEfficient OFDM Bidirectional AF Relaying with Asymmetric Traffic
In this study, we seek an optimal solution for the asymmetric traffic requirement for two users with multisubcarrier modulation, such as OFDM. Based on the valid assumption that a highdaterate user may require more subcarriers for transmission, we investigate the transmission model selection and rate allocation for each subcarrier such that the total system power consumption is minimum. Mathematically, the joint optimization problem can be formulated as (P1):
where
R_{a}
and
R_{b}
are the minimal data rate requirements for
S_{a}
and
S_{b}
, respectively;
r_{max}
is the maximal data rate at each subcarrier;
ρ
= {
ρ_{n}
,
ρ_{n}
^{*}
} is the set of binary assignment variables that indicates whether a oneway relaying or a twoway relaying transmission mode is adopted at subcarrier
n
; P = {
P_{a,n,1},P_{r,n,1},P_{a,n,2},P_{b,n,2},P_{r,n,2}
} is the set of power variables; and R = {
r_{a,n,1},r_{a,n,2},r_{b,n,2}
} is the set of rate variables.
It noteworthy that the constraints in (10b) and (10c) are nonconcave functions with respect to the power allocation vectors and the scaling factor, and hence cannot be solved by techniques relying on the Karush–Kuhn–Tucker (KKT) conditions. Moreover, the existence of a binary assignment variable makes an optimal solution intractable.
4. Proposed schemes for optimal transmission
The problem in P1 is a combinational optimal problem. The search for the optimal solution can be decoupled into two separate subproblems: (1) optimal power allocation for both oneway relaying and twoway relaying under fixed subcarrier assigned subsets and (2) discrete optimization of the subcarrier assigned subsets. At first glance, we have to assign 0 or 1 to
ρ_{n}
, which requires an exhaustive search over all possible permutations of (
n
= 1, 2...,
N
), with exponential complexity, where each subcarrier has five possibilities of bit loading for the case of {0,2,4,6,8} that used in the simulation, whose computational complexity is 10
^{N}
. Fortunately, by using the optimal linear processing structure of channel pairing
[14
,
16
,
17]
, an exhaustive search can be avoided, thus yielding a simple algorithm for searching the optimal subcarrier number for twoway relay transmission.
 4.1 Optimal Bit Loading and Power Allocation for Fixed Subcarrier Assignment Subset
Assuming that the two subcarrier subsets are given and the same data rate per subcarrier (see remark 1) applies for each user in the twoway relay transmission mode, the optimal problem P1 is decoupled into two suboptimal problems, i.e.,
and
where
,
N_{1}
is the number of subcarrier subsets allocated for twoway relay transmission.
The assumption of the same data rate per subcarrier for twoway relay transmission makes problem P1 solvable. Although we can not guarantee the solution is optimal, form (17), the energy consumption will sharply increase as the number of bits increases. Only when the subcarrier channel for oneway relay transmission is poor does an asymmetric data rate in twoway relay transmission mode lead to lower energy consumption, e.g. for the case of two subcarrier pairs, the power of using the best subcarrier pair to transmit in asymmetric mode is less than the method we proposed.
Remark 1
: For twoway relaying, energyefficient bit loading at each user is given by
Proof
: With some mathematical manipulations, we can decouple (11) into an
N
parallel minimal optimal problem as follows:
To investigate the optimal data rate
r_{a,n,2}
and
r_{b,n,2}
at each subcarrier, we assume a fixed total power
P_{T}(n)
=
P_{a,n,2}
+
P_{b,n,2}
+
P_{r,n,2}
. Therefore, the persubcarrier energyefficiency optimal problem becomes a series of sum rate maximization problems that are identical to the optimal problem in
[15]
. The optimal result indicates that the received SNRs for all users are the same, which therefore validates (13).
It can be verified that the data rate constraints are nonconvex, and thus, the suboptimal problems (11) and (12) are nonconvex functions, which have been the subject of significant research by several authors
[15
–
21]
. For the case of individual power constraints at the source node and the relay, they either follow an iterative procedure with the assumption that for the optimization of the power allocation at one node the power allocation at the other node is given
[17
–
18]
, using a dualdecomposition method to decouple the problem
[18]
, or they utilize the symmetric attributes of the power allocation at each node per subcarrier [19]. For the cases of total system power constraints, the following three approaches are noteworthy:
[17]
adopted a tight approximation for the SNR setting.
[20]
utilized geometric programming (GP) to optimize the power allocation by maximizing the instantaneous sum rate and minimizing the SER for oneway relay transmission.
[15]
proposed a twostep method for twoway relaying that first allocates power optimally across the subcarriers and then determines the optimal power allocation at each subcarrier.
As is illustrated in
[15]
and
[21]
, by means of dual decomposition, the persubcarrier problems are nonconvex, and it is difficult to find a closedform solution. We propose a method based on the fact that closedform solutions for the persubcarrier energyefficiency problem can be derived if an equality data rate is imposed on each subcarrier. The persubcarrier optimization problem for (11) is written as
By using the Lagrange multiplier method, we can easily derive the optimal solution as
[22]
where
γ_{n}
= 2
^{2ra,n,2}
 1 = 2
^{2rb,n,2}
1. Then, the total power consumption per subcarrier is
By taking
E
_{n}
_{,2}
=
P
_{T}
_{,}
_{n}
_{,2}
/ 2
C
(
γ_{n}
), we can rewrite the optimal problem (11) as
Remark 2
: The problem in (18) is a convex optimization problem.
Proof:
Because
E
_{n}
_{,2}
is convex with respect to
γ_{n}
, and
γ_{n}
is an increasing function of
r_{a,n,2}
or
r_{b,n,2}
,
is also convex with respect to
r_{a,n,2}
or
r_{b,n,2}
.·
As in (15), we get the persubcarrier optimization problem for (12) as
By using the Lagrange multiplier method, we can easily derive the optimal solution as
Then, the total power consumption per subcarrier is
where
γ_{n}
= 2
^{2ra,n,1}
1,
E
_{n}
_{,1}
=
P
_{T}
_{,}
_{n}
_{,1}
/
C
(
γ_{n}
), Thus, we can rewrite the optimal problem (12) as
Remark 3
: The problem in (22) is a convex optimization problem.
Proof:
Because
E_{n,1}
is convex with respect to
γ_{n}
, and
γ_{n}
is an increasing function of
r_{a,n,1}
,
is also convex with respect to
r_{a,n,1}
.·
Because problems (18) and (22) are convex optimization problems, we can find the optimal solution relying on the KKT conditions. With the KKT conditions, the data rate at each subcarrier can be expressed as a function of the Lagrange multiplier
λ
, which enables an effective searching method such as the bisection method for the optimal solution.
 4.2 Finding the Suboptimal Subcarrier Assignment Subset for OneWay and TwoWay Relaying Transmissions
In previous sections, we analyzed the optimal problem with a fixed subcarrier assignment subset. Here, we develop a suboptimal solution to find a subcarrier assignment subset for both oneway and twoway relaying transmissions. To facilitate the solution, we define a ranking and match operator.
Definition 1
: For twohop multicarrier modulation transmission, the ranking operator at each hop with respect to the subcarriers’ channel gain is defined as
and
in descending order, respectively.
For a length
N
vector
s
={
s
[1],…
s
[
n
],..
s
[
N
]}, the ranking operator
is another length
N
vector, whose elements are obtained by permuting the elements of
s
, with
Rank
[
n
1]≥
Rank
[
n
2] for arbitrary
n
1<
n
2.
By indexing and matching the subcarriers, the maximum transmission rate is achieved
[14]
[16]
. Then, we can find a simple way to assign subcarriers to different transmission modes (oneway relay transmission mode or twoway relay transmission mode). Throughout the rest of this paper, we shall replace
n
with (
n
) to denote indexed subcarriers.
Lemma 1
: (see
[14]
, lemma 3)
For both oneway relaying and twoway relaying modes, priority is given to subcarriers with better channel conditions based on the ranking index
Proof:
This lemma is the direct result of the ranking and match operator. For equal transmission rates, the power consumption per bit for oneway relaying
E_{(n),1}
and twoway relaying
E_{(n),2}
are monotonically decreasing functions with respect to
h(n)
and
g(n)
, and because
h(n)
and
g(n)
are decreasing with respect to
(n)
, we conclude the result that
E_{(n),1}
and
E_{(n),2}
are increasing functions with respect to
(n)
·
Lemma 2
: Twoway relay transmission has a higher priority of channel occupancy than oneway relay transmission.
Proof:
Because
E_{(n),1}
−
E_{(n),2}
> 0, twoway relay transmission consumes less power per bit than oneway relay transmission. The twoway relay transmission mode therefore has a higher privilege to use subcarriers with good channel conditions. ·
Lemma 3
: For the cases of two subcarrier transmission systems, the rate requirement for oneway relaying is
r_{1}
and that for twoway relaying is
r_{2}
, and the matched subcarrier with good channel conditions should be assigned to oneway relay transmission when
γ
_{1}
> 2
γ
_{2}
.
Proof:
For fixed transmissions
r_{1}
and
r_{2}
, we investigate the total system power consumption. Two schemes are possible: scheme 1 allocates
h
(1) and
g
(1) to oneway relay transmission and
h
(2) and
g
(2) to twoway relay transmission; scheme 2 exchanges the matched subcarriers for oneway and twoway relay transmissions. If the total power consumption of scheme 1 is less than that of scheme 2, scheme 1 is suggested.
The total power consumption of scheme 1 is
The total power consumption of scheme 2 is
The difference of power consumptions between scheme 1 and scheme 2 is
When
P_{T}
(1)
P_{T}
(2) < 0, scheme 1 is preferred, and we have
where
,
B
=
σ
^{2}
(2/
h
_{(2)}
g
_{(2)}
2/
h
_{(1)}
g
_{(1)}
) , and because
h_{(1)}
>
h_{(2)}
and
g_{(1)}
>
g_{(2)}
, we can conclude
A
> 0 and
B
> 0. Because
is a monotonically increasing function, for the inequality to hold, we must have
γ
_{1}
> 2
γ
_{2}
. ·
Lemmas 1–3 imply that we can adopt a linear search procedure to seek optimal subcarrier assignment subsets. Initially,
N_{1}
(
R_{b}
/
r
_{max}
≤
N
_{1}
≤
N
(
R_{a}

R_{b}
)/
r
_{max}
) pairs of matched subcarriers ((
L(1),L(2),...,L(n),...L(N_{1})
), where
L(n)
= {
h_{(n)},g_{(n)}
)}, are scheduled for twoway relay transmission and the rest for oneway relay transmission, and we execute the link exchange iteration process (based on Lemma 3) and reassign the power until the overall power cannot be further reduced. Then we find the optimal
N_{1}
^{*}
that results in the minimal power consumption; the detailed algorithm follows.
Discussion:
Executing the link exchange iteration at each
N_{1}
will result in a global optimal solution, the time complexity is O(
N
^{3}
log(
N
)). Because of the computational complexity is relatively high, especially for a large number of subcarriers, we develop a suboptimal solution that seeks the optimal subset number
N_{1}
^{*}
first and performs the subcarrier pair exchange iteration. Furthermore, if we execute the process stated in step (b) for all subcarrier pairs, the convergence speed will be accelerated, and the time complexity is reduced to O(
N
^{2}
).
5. Simulation results
We perform the computer simulation for OFDM bidirectional AF relay transmission with asymmetric traffic to evaluate the system performance and the influence of energy efficiency on different asymmetric levels. The proposed scheme is compared with the traditional oneway relay method, which needs four time slots for two users to transmit the information (two time slots for each user). Note that the Rayleigh distribution is assumed in this study; the subcarrier number used is
N
= 64; multiple quadrature amplitude modulation (MQAM) is employed for each subcarrier; and the possible bit loading for each subcarrier is {0, 2, 4, 6, 8}, which means that
r_{max}
= 8. The corresponding modulations are no modulation, 4QAM, 16QAM, 64QAM, and 256QAM. The noise variance is set to 1.2e−10. We assume the relay is located at the center of the line between two users. We first compare the total power consumption of bidirectional relaying with the traditional oneway relaying method under different asymmetric traffic ratios, as depicted in
Fig. 2
. The data rate for
S_{a}
is
R_{a}
=40 bit/s in
Fig. 2
(a) and
R_{a}
=60 bit/s in
Fig. 2
(b); for a different asymmetric traffic ratio
α
, the data rate of
S_{b}
is
R_{b}
=
α
·
R_{a}
bit/s. The simulation results show that for both the oneway relay transmission system and the bidirectional relay transmission system, the power consumption is a monotonically increasing function in response to the asymmetric traffic ratio. This is because as the asymmetric traffic ratio increases, for fixed data rate
R_{a}
, more data needs to be sent. From
Fig. 2
, it is clear that the bidirectional OFDM relaying method needs less energy for transmission compared with the classical oneway OFDM relaying method. This is an interesting result, indicating that the bidirectional OFDM relaying method has an advantage over the classical oneway OFDM relaying method, which was depicted in Lemma 2.
Total energy consumption versus the data rate requirements of the two users.
We present the subcarrier number allocated for twoway relay transmission in
Fig. 3
. It is observed that the data rate requirement has a significant impact on the subcarrier allocation. What’s more, the figure shows that more subcarriers need to be assigned to the twoway relay transmission mode as the asymmetric traffic ratio increases.
Subcarrier number allocated for twoway relay transmission, R_{a}=40, and 60bit/s.
To investigate the energy efficiency of the proposed scheme, we simulate the power consumption per bit with different asymmetric traffic ratios.
Fig. 4
indicates that the energy consumption per bit of the bidirectional OFDM relaying method is less than that of the oneway OFDM relaying method. For the oneway OFDM relaying method, the curve decreases at first and then rises, because when the traffic ratio is small, the best subcarrier pairs can be used to transmit for user
S_{b}
, and the energy consumed per bit decreases, so the curve decreases. However, as the traffic ratio increases, some subcarriers with bad channel conditions are used for transmission, which decreases the energy efficiency, so the curve rises. For the bidirectional OFDM relaying method, the energy consumption per bit transmission almost decreases as the traffic ratio increases. This is because twoway relay transmission has higher energy efficiency than oneway relay transmission under the same conditions. Nevertheless, when the traffic ratio is high, some subcarrier pairs with bad link quality take part in the transmission. Although twoway relay transmission has higher energy efficiency, the average energy consumption for the extra bit in bad subcarrier pairs may exceed the average system energy consumption. This will counteract the effect of the twoway relay transmission, thereby decreasing the system energy efficiency. This is represented as an increase in the traffic ratio (
α
= 0.7–0.9). These results indicate that even when the uplink and downlink paths have the same data rate, asymmetric traffic transmission strategies can still improve the energy efficiency of the system.
Energy consumption per bit with different asymmetric traffic ratios, R_{a}=40bit/s.
6. Conclusion
In this paper, we described the joint optimization problem of power allocation, bit loading, and subcarrier transmission mode selection with asymmetric traffic in an OFDMbased bidirectional AF relay transmission system. By using the attributes for twoway relay transmission and subcarrier pairing, we decouple the primary problem into two subproblems. We first optimize the power allocation for both oneway relay transmission and twoway relay transmission under fixed subcarrier subsets, and find the optimal subsets under subcarrier pairing. The simulation results showed that our proposed scheme outperforms the traditional oneway OFDM relaying method. Furthermore, the best energy efficiency for OFDM bidirectional AF relaying is obtained at a fixed symmetric traffic ratio, which makes this a useful technique for bidirectional relaying design.
BIO
Nianlong Jia received his BE and M.S. from Chongqing University in 2006 and 2009, respectively. He is currently studying for his PhD in the college of communication engineering from Chongqing University of China. His research interests span in the areas of wireless cooperative communications and cognitive radio technology.
Wenjiang Feng received his PhD in electrical engineering from the University of Chongqing University in 2000. Currently, he is a professor at the college of communication engineering in Chongqing University. His research interests fall into the broad areas of communication theory, wireless communication.
Yuanchang Zhong received his BE, M.S. and his PhD in electrical engineering from Changchun University of Science and Technology, college of communication engineering from the University of Chongqing University and Mechanical Electronic Engineering from the University of Chongqing University in 1988, 2002 and 2009 respectively. Now he is a professor at the college of communication engineering in Chongqing University. His research interests fall into the broad areas of wireless communication, measurement control and wireless communication.
Hong Kang received his BE, M.S. from Chongqing University in 2009 and 2011, respectively. Now she is a teacher in Chongqing College of Electronic Engineering. The research interest is cooperative wireless communication.
Kim Sang Joon
,
Mitran Patrick
,
Tarokh Vahid
2008
“Performance bounds for bidirectional coded cooperation protocols,”
IEEE Transactions on Information Theory
54
(11)
5235 
5241
DOI : 10.1109/TIT.2008.929913
Vaze Rahul
,
Truong Kien T.
,
Weber Steven
,
Heath Robert W.
2011
“TwoWay transmission capacity of wireless adhoc networks,”
IEEE Transactions on Wireless Communications
10
(6)
1966 
1975
DOI : 10.1109/TWC.2011.041311.101488
Oechtering Tobias J.
,
Boche Holger
2008
“Bidirectional regenerative halfduplex relaying using relay selection,”
IEEE Transactions on Wireless Communications
2
(3)
1879 
1888
DOI : 10.1109/TWC.2008.060673
Cui Hongyu
,
Zhang Rongqing
,
Song Lingyang
,
Jiao Bingli
2013
“Capacity analysis of bidirectional AF relay selection with imperfect channel state information,”
IEEE Wireless Communications Letters
2
(3)
255 
258
DOI : 10.1109/WCL.2013.020513.120933
Verde Francesco
,
Scaglionet Anna
“Decentralized spacetime block coding for twoway relay networks,”
in Proc. of 11th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC)
June, 2010
1 
5
Zhou Bo
,
Liu Yuan
,
Tao Meixia
“Adaptive scheduling for OFDM bidirectional transmission with a buffered relay,”
in Proc. of IEEE Conf. on Communications and Networking Conference (WCNC)
April, 2013
3248 
3253
Meshgi Hadi
,
Zhao Dongmei
“Opportunistic scheduling in a bidirectional communication link with relaying,”
in Proc. of IEEE Conf. on ICC
June, 2012
5365 
5370
Kim Tùng T.
,
Poor H. Vincent
2011
“DiversityMultiplexing tradeoff in adaptive twoway relaying,”
IEEE Transactions on Information Theory
57
(7)
4235 
4254
DOI : 10.1109/TIT.2011.2145190
Wei Hao
,
Zheng Baoyu
,
Ji Xiaodong
2013
“A novel design of physical layer network coding in strong asymmetric twoway relay channels,”
EURASIP Journal on Wireless Communications and Networking
Feng Minghai
,
She Xiaoming
,
Chen Lan
“Enhanced bidirectional relaying schemes for multihop communications,”
in Proc. of IEEE Conf. on GLOBECOM
December, 2008
1 
6
Li Jing
,
Ge Jianhua
,
Zhang Chensi
2013
“Impact of channel estimation error on bidirectional MABCAF relaying with asymmetric traffic Requirements,”
IEEE Transactions on Vehicular Technology
62
(4)
1755 
1769
DOI : 10.1109/TVT.2012.2235868
Liu Yuan
,
Mo Jianhua
,
Tao Meixia
2013
“QOSAware transmission policies for OFDM bidirectional decodeandforward relaying,”
IEEE Transaction on Wireless Communications
12
(5)
2206 
2216
DOI : 10.1109/TWC.2013.031313.120709
Hausl Christoph
,
Rossetto Francesco
“Optimal time and rate allocation for a networkcoded bidirectional twohop communication,”
in Proc. of European Wireless Conference
April, 2010
1015 
1022
Zhang Wenyi
,
Mitra Urbashi
,
Chiang Mung
2011
“Optimization of amplifyandforward multicarrier twohop transmission,”
IEEE Transaction on Communications
59
(5)
1434 
1445
DOI : 10.1109/TCOMM.2011.022811.100017
Jang YongUp
,
Jeong EuiRim
,
Lee Yong H.
2010
“A twostep approach to power allocation for OFDM signals over twoway amplifyandforward relay,”
IEEE Transactions on Signal Processing
58
(4)
2426 
2430
DOI : 10.1109/TSP.2010.2040415
Dong Min
,
Hajiaghayi Mahdi
,
Liang Ben
2012
“Optimal fixed gain linear processing for amplifyandforward multichannel Relaying,”
IEEE Transactions on Signal Processing
60
(11)
6108 
6113
DOI : 10.1109/TSP.2012.2210711
Hammerström Ingmar
,
Wittneben Armin
2007
“Power allocation schemes for amplifyandforward MIMOOFDM relay links,”
IEEE Transactions on Wireless Communications
6
(8)
2798 
2802
DOI : 10.1109/TWC.2007.06071
Fang Zheng
,
Hua Yingbo
,
Koshy John C.
“Joint source and relay optimization for a nonregenerative MIMO relay,”
in Proc. of 4th IEEE Workshop on Sensor Array and Multichannel Processing
July 1214, 2006
239 
243
Ko Youngwook
,
Ardakani Masoud
,
Vorobyov Sergiy A.
2012
“Power allocation strategies across N orthogonal channels at both source and relay,”
IEEE Transactions on Communications
60
(6)
1469 
1473
DOI : 10.1109/TCOMM.2012.040212.100193
Liu Ted C.K.
,
Xu Wei
,
Dong Xiaodai
,
Lu WuSheng
“Adaptive power allocation for bidirectional amplifyandforward multiplerelay multipleuser networks,”
in Proc. of IEEE Conf. on Globecom
December 610, 2010
1 
6
Ho Chin Keong
,
Zhang Rui
,
Liang YingChang
“Twoway relaying over OFDM: optimized tone permutation and power allocation,”
in Proc. of IEEE Conf. on Communications
May 1923, 2008
3908 
3912
Huang Rong
,
Feng Chunyan
,
Zhang Tiankui
,
Wang Wei
“Energyefficient relay selection and power allocation scheme in AF relay networks with bidirectional asymmetric traffic,”
in Proc. of 14th International Symposium on Wireless Personal Multimedia Communications (WPMC)
October 37, 2011
1 
5