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Energy Efficiency Optimization Based Joint Relay
Selection and Resource Allocation for SWIPT
Relay Networks
Na Zhao, Rong Chai, Qin Hu
Key Laboratory of Mobile Communication Technology
Chongqing University of Posts and Telecommunications
Chongqing, 400065, P.R. China
Jian-Kang Zhang
Department of Electrical and Computer Engineering
McMaster University, Hamilton, Ontario, Canada
Abstract—In this paper, a joint relay selection and resource
allocation scheme is proposed for simultaneous wireless informa-
tion and power transfer (SWIPT) relay networks with multiple
Source nodes (SNs) and Destination nodes (DNs) pairs and energy
harvesting Relay nodes (RNs). The transmit power, subchannel,
power splitting ratio allocation for SNs/RNs and the relay
selection scheme strategy are jointly optimized to maximize the
total energy efficiency of all the SNs and RNs. The optimization
problem is transformed equivalently into two subproblems, i.e.,
transmit power and power splitting ratio optimization subprob-
lem of one SN-RN-DN path and the optimal relay and subchannel
allocation subproblem. By applying iterative algorithm and
Lagrange dual method, the optimal relay selection and resource
allocation strategy are obtained. Simulation results demonstrate
the efficiency of the proposed scheme.
Index Terms—SWIPT, energy efficiency, resource allocation,
relay selection.
I. INT ROD UC TI ON
In recent years, simultaneous wireless information and
power transfer (SWIPT) has attracted considerable attention
from both academia and industry. In a SWIPT system, the
receiver node is allowed to harvest energy from the received
information, thus achieving the tradeoff between information
transmission and energy harvesting.
To enhance the coverage and capacity of a SWIPT system,
relaying techniques can be applied. In [1], the authors con-
sidered a three-node SWIPT relay network, where the energy
constrained Relay node (RN) conducted information forward
and energy harvest at the same time. Two energy harvesting
schemes, i.e., time switching-based and power splitting-based
schemes were proposed and the analytical expressions of the
outage probability and the ergodic capacity of the proposed
protocols were derived, respectively.
In a SWIPT relay network with multiple Source nodes
(SNs) and RN, relay selection and resource allocation issue
has to be considered as it may affect system performance
significantly. The authors in [2] investigated relay selection
schemes in a relay system with Rayleigh fading channel
and the transmission performance of three relay selection
schemes, namely, time-sharing selection, threshold-checking
selection and weighted difference selection scheme. Reference
[3] considered a SWIPT relay network, where multiple Source-
destination (S-D) pairs communicated with each other via an
energy harvesting relay and several power allocation schemes
were proposed to achieve the tradeoff between system perfor-
mance and complexity. In [4], the authors considered SWIPT
in relay interference channels and developed a distributed
power splitting framework to derive a profile of power splitting
ratios for all relays using game theory. Specifically, non-
cooperative games were formulated in each link which was set
as a strategic player aiming to maximize its own achievable
rate.
However, previous research works do not jointly consider
the optimal design of relay selection, transmit power and chan-
nel allocation, and power splitting ratio, and thus may result in
highly limited system performance. In this paper, we propose
an energy efficient joint relay selection and resource allocation
scheme for SWIPT relay networks. The total energy efficiency
of all the SNs and RNs is examined and the optimization prob-
lem is formulated as maximizing the total energy efficiency
subject to the optimization constraints including the maximum
transmit power, the minimum data rate and relay/subchannel
allocation limitation. Through applying iterative algorithm and
Lagrange dual method, the optimization problem is solved
and the joint optimal relay selection and resource allocation
strategy is obtained.
The rest of this paper is organized as follow. In Section
II, we describe the system model. The optimization problem
formulation is discussed in Section III and the problem solving
process is described in Section IV. We present the simulation
results in Section V. Finally, in Section VI, we conclude this
paper.
II. SYSTEM MO DE L
In this paper, we consider a SWIPT relay system consisting
of multiple S-D pairs. To enhance the transmission perfor-
mance of the S-D pairs, multiple RNs are applied to forward
1
2
1
2
1
2
...
...
...
Fig. 1. System model in SWIPT relay network
Information decoder
Energy harvester
Battery
Power Splitter
1-
Fig. 2. The SWIPT-based receiver architecture at the RNs
the information received from the SNs to the Destination nodes
(DNs). The transmission process from the SNs to the DNs
consists of two time slots each with duration T
2. At the first
phase, the SNs send information to the RNs. At the second
phase, the RNs forward received information to the DNs.
To improve the energy efficiency at the RNs, all the RNs
are equipped with energy harvesting device and are capable of
conducting data forwarding and harvesting energy simultane-
ously. In this paper, we assume RNs adopt dynamic power
splitting (DPS) technique which splits the total power of
received signal into two parts, one for information decoding
and the other for energy harvesting. Fig. 2 shows the receiver
architecture of the RNs with the power splitting ratio being
1−ρand ρ, where ρ∈[0,1], to yield the input of information
decoder and energy harvester, respectively.
In this paper, we assume orthogonal frequency division
multiplexing (OFDM) scheme is applied to SNs and RNs, and
different Source-relay (S-R) links and Relay-destination (R-
D) links are allowed to occupy different subchannels for data
transmission. For simplicity, we assume for one S-D pair, the
same subchannel is allocated to the S-R link and R-D link. We
further assume that all links experience slow and frequency-
flat fading.
III. ENE RG Y EFFIC IE NC Y FOR MU LATI ON
In this paper, we jointly design the transmit power, the
subchannel allocation strategy of the SNs and the RNs, the
harvesting energy strategy of the RNs, and the relay selection
scheme of the SNs to achieve the maximization of the total
energy efficiency of all the SNs and RNs. To this end,
in this section, some of the optimization variables and the
optimization objective function are defined.
A. Subchannel Allocation and Relay Selection Variables
To enable relay transmission between a SN-DN pair, one
optimal RN should be selected among multiple candidate
RNs. Furthermore, for a given SN-DN pair with a particularly
selected RN, one subchannel should be assigned. Jointly
considering relay selection and subchannel allocation schemes
of various SN-DN pairs, we introduce binary joint subchannel
allocation and relay selection variables.
We define β(k)
m,n as the subchannel allocation and relay
selection variable of the mth SN-DN pair when selecting
the nth RN for data forwarding on the kth subchannel, i.e.,
β(k)
m,n = 1 indicates that the mth SN-DN pair selects the
nth relay SU for data forwarding, and both the SN-RN link
and the RN-DN link occupy the kth subchannel for data
transmission, otherwise, β(k)
m,n = 0,m= 1,2,· · · , M, n =
1,2,· · · , N, k = 1,2,··· , K ,Mand Ndenote the number
of SN-DN pairs and the number of RNs, respectively and K
denotes the number of subchannels.
In this paper, we assume each SN-DN pair can only select
at most one RN for data forwarding on one subchannel, we
obtain:
N
n=1
K
k=1
β(k)
m,n ≤1, m = 1,2,· · · , M. (1)
Further assume that each subchannel can only be allocated
to one SN-DN pair, and that each RN can only forward
information for one SN-DN pair, i.e.,
M
m=1
β(k)
m,n ≤1, n = 1,2,· · · , N, k = 1,2,· · · , K. (2)
B. Total Energy Efficiency of SNs and RNs
The total energy efficiency of all the SNs and RNs can be
calculated as:
η=
N
n=1
M
m=1
K
k=1
β(k)
m,nη(k)
m,n,(3)
where η(k)
m,n denotes the energy efficiency of the mth SN-
DN pair when transmitting data packets via the nth RN and
occupying the kth subchannel, and can be expressed as:
η(k)
m,n =R(k)
m,n
P(k)
m,n
(4)
where R(k)
m,n and P(k)
m,n denote respectively the sum rate and
the power consumption of the links between the mth SN-DN
pair when transmitting via the nth RN on the kth subchannel.
R(k)
m,n and P(k)
m,n will be derived in the following subsections.
1) Rate Sum of One SN-DN Pair: R(k)
m,n in (4) can be
calculated as:
R(k)
m,n =R(s,k)
m,n +R(r,k)
n,m ,(5)
where R(s,k)
m,n denotes the data rate of the SN-RN link, and can
be expressed as
R(s,k)
m,n =Blog2(1 + γ(s,k)
m,n ),(6)
where Brefers to the bandwidth of each subchannel and γ(s,k)
m,n
denotes the signal-to-noise ratio (SNR) of the link between the
mth SN and the nth RN on the kth subchannel, and can be
calculated as:
γ(k)
m,n =(1 −ρ(k)
m,n)P(s,k)
m,n h(s,k)
m,n
σ2,(7)
where P(s,k)
m,n denotes the transmit power of the mth SN when
transmitting to the nth RN on the kth subchannel, h(r,k)
m,n
denotes the transmission gain of the link between the mth
SN and the nth RN on the kth subchannel, σ2denotes the
noise power of the link, which is assumed to be a constant in
this paper.
R(r,k)
n,m in (5) denotes the data rate of the link between the
nth RN and the mth DN on the kth subchannel and can be
expressed as:
R(r,k)
n,m =Blog2(1 + γ(r,k)
n,m ),(8)
where γ(r,k)
n,m denotes the SNR of the link between the nth RN
and the mth DN on the kth subchannel, and can be calculated
as
γ(r,k)
n,m =P(r,k)
n,m h(r,k)
n,m
σ2,(9)
where P(r,k)
n,m denotes the transmit power of the nth RN when
transmitting to the mth DN at the kth subchannel, and h(r,k)
n,m
denotes the transmission gain of the corresponding link.
2) Power Consumption of SN-DN Pair: P(k)
m,n in (4) can be
calculated as:
P(k)
m,n =P(s,k)
m,n +P(r,k)
n,m −P(H,k)
m,n + 2Pc,(10)
where Pcdenotes the circuit power consumption of the SN
and the RN, P(H,k)
m,n denotes the energy harvested at the nth
RN when receiving from the mth SN on the kth subchannel
and can be expressed as:
P(H,k)
m,n =δnρ(k)
m,nP(s,k)
m,n h(s,k)
m,n .(11)
where δn∈[0,1] denotes the energy conversion efficiency of
the nth RN, and ρ(k)
m,n denotes the power splitting ratio of the
nth RN when receiving information from the mth SN on the
kth subchannel, m= 1,2,· · · , M, n = 1,2,· · · , N, k =
1,2,· · · , K.
C. Optimization Problem Formulation
The optimization problem of joint transmit power, subchan-
nel and power splitting ratio allocation, and relay selection can
be formulated as:
max
β(k)
m,n,P (s,k)
m,n ,P (r,k)
n,m ,ρ(k)
m,n
η
s.t. C1 : β(k)
m,n ∈ {0,1},
C2 :
N
n=1
K
k=1
β(k)
m,n ≤1,
C3 :
M
m=1
β(k)
m,n ≤1,
C4 : R(s,k)
m,n ≥R(min)
m,
C5 : R(r,k)
n,m ≥R(min)
m,
C6 : 0 ≤P(s,k)
m,n ≤P(max)
m,
C7 : 0 ≤P(r,k)
n,m ≤P(max)
n,
C8 : 0 ≤ρ(k)
m,n ≤1,
(12)
where, C1-C3 represent the constraints on relay selection
and subchannel allocation, C4 and C5 represent the data rate
requirement of the mth SN-DN pair, C6 and C7 represent the
maximum transmit power constraint of the SN and RN respec-
tively, and C8 represents the constraint on energy harvesting.
IV. SOLVING THE OPTIMIZATION PROB LE M
The optimization problem formulated in (12) consists of
both Boolean optimization and nonlinear optimization, the
global optimal solution of which is difficult to obtain directly.
Indeed, it can be shown that the original optimization problem
can be transformed equivalently into two subproblems, i.e.,
resource allocation subproblem of one SN-RN-DN path, and
relay and subchannel allocation subproblem of SN-RN-DN
links.
The resource allocation subproblem of one SN-RN-DN path
is formulated as maximizing the energy efficiency of one SN-
RN-DN pair in terms of the transmit power of the SN and
the RN, and the power splitting ratio at the RN. Given the
local optimal transmit power of the SNs and the RNs, and the
power splitting of the RNs, the relay and subchannel allocation
subproblem can be solved to achieve the maximal energy
efficiency of all the SN-DN pairs. In this section, the two
subproblems are solved respectively.
A. Resource Allocation Subproblem
Let β(k)
m,n = 1,∀m, n, k, the maximization of the total
energy efficiency of all the links is equivalent to optimizing
the energy efficiency of all the SN-RN-SN links individually.
Assuming the mth SN-DN pair selects the nth RN as the
relay and occupies the kth subchannel for data transmission,
the optimization problem of energy efficiency of the SN-RN-
DN path can be formulated as:
max
P(s,k)
m,n ,P (r,k)
n,m ,ρ(k)
m,n
η(k)
m,n
s.t.C1 : R(s,k)
m,n ≥R(min)
m,
C2 : R(r,k)
n,m ≥R(min)
m,
C3 : 0 ≤P(s,k)
m,n ≤P(max)
m,
C4 : 0 ≤P(r,k)
n,m ≤P(max)
n,
C5 : 0 ≤ρ(k)
m,n ≤1.
(13)
The optimization problem formulated in (13) can be solved
using the Main Algorithm described in following subsection.
1) Main Algorithm: As the optimization problem (13) is
a non-convex problem, we firstly transform the objective
function into a convex problem using non-linear fractional
programming [5]. Denoting x∗as the optimal energy efficiency
of the SN-RN-DN link, i.e.,
x∗=R(k)
m,n(P(s,k)
m,n , P (r,k)
n,m , ρ(k)
m,n)
P(k)
m,n(P(s,k)
m,n , P (r,k)
n,m , ρ(k)
m,n),(14)
It can be proved that the resource allocation policy achieves
the maximum energy efficiency x∗if and only if
max
P(s,k)
m,n ,P (r,k)
n,m ,ρ(k)
m,n
R(k)
m,n P(s,k)
m,n , P (r,k)
n,m , ρ(k)
m,n
−x∗P(k)
m,n P(s,k)
m,n , P (r,k)
n,m , ρ(k)
m,n
=R(k)
m,n P(s,k)∗
m,n , P (r,k)∗
n,m , ρ(k)∗
m,n
−x∗P(k)
m,n(P(s,k)∗
m,n , P (r,k)∗
n,m , ρ(k)∗
m,n ),
(15)
where P(s,k)∗
m,n ,P(r,k)∗
n,m and ρ(k)∗
m,n denote the optimal P(s,k)
m,n ,
P(r,k)
n,m and ρ(k)
m,n achieving the maximal energy efficiency.
To solve the optimal energy efficiency x∗, an iterative algo-
rithm can be applied. Main Algorithm shows the optimization
process of maximizing the energy efficiency of one SN-RN-
DN path.
2) Inner Algorithm for Solving Optimal Transmit Power:
For a given x, the optimization problem (13) is transformed
into the following problem:
max
P(s,k)
m,n ,P (r,k)
n,m ,ρ(k)
m,n
R(k)
m,n P(s,k)
m,n , P (r,k)
n,m , ρ(k)
m,n
−xP (k)
m,n(P(s,k)
m,n , P (r,k)
n,m , ρ(k)
m,n)(16)
s.t. C1-C5 in (13)
In the optimization objective function of (16), the power
splitting ratio ρ(k)
m,n is coupling with the transmit power of the
SNs, i.e., P(s,k)
m,n , thus resulting in a non-convex problem. For
simplicity, we apply global search between 0 and 1 to find
the optimal ρ(k)
m,n [6]. For a given ρ(k)
m,n, the Lagrange dual
method can be applied to solve the optimal transmit power.
Algorithm 1 Main Algorithm
1: Initialize the maximum number of iterations lmax and the
maximum tolerance ϵ
2: Set maximum energy efficiency x= 0 and iteration index
l= 0
3: repeat
4: For a given x, applying Inner Algorithm, solve the
resource allocation problem of one path to obtain power
allocation policy P(s,k)′
m,n , P (r,k)′
n,m , ρ(k)′
m,n
5: if R(k)
m,n P(s,k)
m,n , P (r,k)
n,m , ρ(k)
m,n−
xP (k)
m,nP(s,k)
m,n , P (r,k)
n,m , ρ(k)
m,n< ϵ then
6: convergence = true
7: return P(s,k)∗
m,n , P (r,k)∗
n,m , ρ(k)∗
m,n =
P(s,k)′
m,n , P (r,k)′
n,m , ρ(k)′
m,n
and x∗=R(k)′
m,n(P(s,k)′
m,n ,P (r,k)′
n,m ,ρ(k)′
m,n)
P(k)′
m,n(P(s,k )′
m,n ,P (r,k)′
n,m ,ρ(k)′
m,n)
8: else
9: x=R(k)
m,n(P(s,k)′
m,n ,P (r,k)′
n,m ,ρ(k)′
m,n)
P(k)
m,n(P(s,k)′
m,n ,P (r,k)′
n,m ,ρ(k)′
m,n)
10: convergence = false
11: end if
12: until convergence = true or l=lmax
The Lagrangian of the primal problem can be formulated as:
L(λ, µ, υ, ω, P (s,k)
m,n , P (r,k)
n,m )
=Blog2(1 + P(s,k)
m,n h(s,k)
m,n (1 −ρ(k)
m,n)
σ2)
+Blog2(1 + P(r,k)
n,m h(r,k)
n,m
σ2)
−x(P(s,k)
m,n + 2PC+P(r,k)
n,m −δnρ(k)
m,nP(s,k)
m,n h(s,k)
m,n )
+λ(Blog2(1 + P(s,k)
m,n h(s,k)
m,n (1 −ρ(k)
m,n)
σ2)−R(min)
m)
+µ(Blog2(1 + P(r,k)
n,m h(r,k)
n,m
σ2)−R(min)
m)
+υ(P(max)
m−P(s,k)
m,n ) + ω(P(max)
n−P(r,k)
n,m )(17)
where λ,µ,ν,ωare Lagrange multipliers. The dual problem
is given by
min
λ,µ,ν,ω max
P(s,k)
m,n ,P (r,k)
n,m
L(λ, µ, ν, ω, P (s,k)
m,n , P (r,k)
n,m )(18)
s.t. λ, µ, ν, ω ≥0
For a given set of λ, µ, ν, ω, the optimal transmit power
of the mth SN and the nth RN on the kth subchannel can be
obtained as:
P(s,k)∗
m,n =(19)
(1 + λ)B
ln2x+ν−xδnρ(k)
m,nh(s,k)
m,n −σ2
h(s,k)
m,n 1−ρ(k)
m,n
+
,
Algorithm 2 Inner Algorithm
1: Set the iteration indices t= 0, maximum number of
iteration tmax
2: Initialize the Lagrange multipliers λ,µ,ν,ωand resource
allocation policies P(s,k)
m,n , P (r,k)
n,m , ρ(k)
m,nfor t = 0
3: repeat
4: Solve the power allocation by using (18) and (19)
5: Update λ,µ,ν,ωby gradient method
6: t=t+ 1
7: until convergence = true or t=tmax
8: return P(s,k)′
m,n , P (r,k)′
n,m , ρ(k)′
m,n=
P(s,k)
m,n , P (r,k)
n,m , ρ(k)
m,n
P(r,k)∗
n,m =(1 + µ)B
ln2 (x+ω)−σ2
h(r,k)
n,m +
,∀m, n, k (20)
and [z]+= max{0, z}.
As the dual function is differentiable, the gradient method
can be applied to solve the optimal Lagrange multipliers which
leads to
λ(t+ 1) = λ(t)−(21)
ξ1(t)×Blog21 + P(s,k)
m,n h(s,k)
m,n (1 −ρ(k)
m,n)
σ2−R(min)
m+
,
µ(t+ 1) = µ(t)−(22)
ξ2(t)×Blog21 + P(r,k)
n,m h(r,k)
n,m
σ2−R(min)
m+
,
ν(t+ 1) = ν(t)−ξ3(t)×P(max)
m−P(s,k)
m,n +
,(23)
ω(t+ 1) = ω(t)−ξ4(t)×P(max)
n−P(r,k)
n,m +
,(24)
where index t≥0is the iteration index and ξi(t), i ∈
{1,2,3,4}, are positive step sizes. The algorithm for solving
the optimal transmit power is shown in Algorithm 2.
B. Relay and Subchannel Allocation Problem of All SN-DN
Pairs
From subsection IV. A., the optimal transmit power and
power splitting ratio are obtained for any SN-RN-DN pair, and
the optimal energy efficiency of each pair can be calculated.
Denoting η(k)∗
m,n as the optimal energy efficiency of the links
between the mth SN-DN pair via the nth RN on the kth
subchannel, the total energy efficiency of all the SN-DN pairs
can be rewritten as:
η=
M
m=1
N
n=1
K
k=1
β(k)
m,nη(k)∗
m,n .(25)
The optimal relay and subchannel allocation problem of all
SN-DN pairs can then be formulated as:
max
β(k)
m,n
η
s.t. C1 : β(k)
m,n ∈ {0,1},
C2 :
N
n=1
K
k=1
β(k)
m,n ≤1,
C3 :
M
m=1
β(k)
m,n ≤1.
(26)
The optimization problem formulated in (26) is a binary
integer programming, which can be solved conveniently using
software toolbox.
V. SIMULATION RESULTS
In this section, we evaluate the performance of the proposed
joint resource allocation and relay selection algorithm using
simulations. We consider a 1.5m×1.5m area with three SN-
DN pairs, and three RNs. The number of subchannels is chosen
as 5. The bandwidth of each channel is set as B=78kHz.
We assume a static signal processing power consumption
of 1.5w. And an energy harvesting efficiency of δn=0.8. We
set M=1000 for discretizing the range of ρ(k)
m,n into 1000
equally spaced intervals for performing the full search. Refer
to [5], we assume the channels between transceiver pairs to
be subject to mutually independent Rayleigh fading. And we
use the channel model that E|h(s,k)
m,n |=ds,k
m,n−γ1and
E|h(r,k)
n,m |=dr,k
n,m−γ2, where γ1, γ2∈[2,5] is the path
loss, and ds,k
m,n refers to the distance of the mth source node
and the nth relay node, and dr,k
n,m refers to the distance of the
nth relay node and the mth destination node.
Fig. 3 shows the evolution of the energy efficiency versus
the number of iterations obtained from the proposed algorithm
for different levels of the maximum transmit power of the SNs.
It can be observed that the iterative algorithm converges to the
optimal value within 5 iterations for all considered scenarios.
Fig. 4 depicts the average system energy efficiency versus
the maximum transmit power P(max)
mfor different noise power.
It can also be seen from the figure that for small P(max)
m,
the energy efficiency increases with the increase of P(max)
m,
however as P(max)
mhas reached a certain value, the energy
efficiency will not increase. This is because the transmit power
P(s,k)
m,n has achieved its optimal value, thus increasing the
maximum transmit power will not result in the increase of
energy efficiency. Comparing three curves, we can see that
the higher channel noise power, the lower energy efficiency.
Fig. 5 shows the energy efficiency versus the power splitting
ratio for different values of energy conversion efficiency at
the RN. It is observed that as the power splitting ratio ρ(k)
m,n
increases from 0 to 1, the energy efficiency of the single
link increases at first until ρ(k)
m,n reaches the optimal value,
which corresponding to the maximum energy efficiency, and
thereafter the energy efficiency decreases from the maximum
1 2 3 4 5 6 7 8 9 10 11
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
5.5 x 105
Number of iterations
Energy efficiency(bit/Joule)
Pm
(max)=0.1w
Pm
(max)=1,1w
Pm
(max)=2.1w
Fig. 3. Average energy efficiency versus the number of iterations
0.5 1 1.5 2 2.5 3
0.9
1
1.1
1.2
1.3
1.4
1.5 x 106
Pm
(max)(w)
Energy efficiency(bit/Joule)
σ2=0.5e−4
σ2=e−4
σ2=2e−4
Fig. 4. Average energy efficiency versus the maximum transmit power of
SN
to zero. From the figure, we can also observe that the larger
energy conversion efficiency, the higher energy efficiency.
VI. CONCLUSIONS
In this paper, we proposed an energy efficiency based
optimal joint resource allocation and relay selection scheme
for a SWIPT relay system. The optimization problem which
maximized the total energy efficiency of all the SN-DN pairs
subject to the minimum data rate, the maximum transmit
power and relay and subchannel selection constraints was
formulated. By applying iterative algorithm and Lagrange
dual method, the optimization problem was solved to obtain
the optimal transmit power, power splitting ratio, and relay
selection and subchannel allocation strategies. Simulation re-
sults showed that the proposed scheme offers optimal energy
efficiency.
ACK NOW LE DG EM EN T
This work was supported by the 863 project
(2014AA01A701), the special fund of Chongqing key
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
4.75
4.8
4.85
4.9
4.95
5
5.05
5.1
5.15
5.2 x 105
ρ m,n
(k)
Energy Efficiency(bit/Joule)
δ n=0.7
δ n=0.8
δ n=0.9
Fig. 5. Energy efficiency versus power splitting ratio
laboratory (CSTC) and the project of Chongqing Municipal
Education Commission (Kjzh11206).
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