Minimum Transmission Protocol for Full-Duplex Systems With Energy Harvesting

Abstract

A bi-node full-duplex (FD) communications system, in which both nodes are assumed to have the capability of energy harvesting (EH), is investigated. In the proposed model, node B harvests radio frequency (RF) energy that dissipated by node A, to which the former will transmit its signal back simultaneously. Furthermore, by exploiting node B’s critical information, including its channel state information (CSI) and the usage of its battery, a minimum transmission (MT) protocol is proposed by employing two kinds of EH-manners. Note that node B is allowed to always transmit, provided that its residual energy is high enough to ensure a successful decoding at node A. In addition, the proposed protocol with capabilities of both EH and signal transmission can be developed by employing a Markov-chain model, following which we can derive both the stationary distribution and the outage probability of node A. Finally, numerical results validate the proposed theoretical analysis.

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Communications Letters
IEEE COMMUNICATIONS LETTERS, VOL. XX, NO. X, XXX 201X 1
Minimum Transmission Protocol for Full-Duplex
Systems with Energy Harvesting
Qian Zeng, Yuhong Zheng, Bin Zhong, Zhongshan Zhang
Abstract— A bi-node full-duplex (FD) communications system,
in which both nodes are assumed to have the capability of
energy harvesting (EH), is investigated. In the proposed model,
node B harvests radio frequency (RF) energy that dissipated
by node A, to which the former will transmit its signal back
simultaneously. Furthermore, by exploiting node B’s critical
information, including its channel state information (CSI) and
the usage of its battery, a minimum transmission (MT) protocol
is proposed by employing two kinds of EH-manners. Note that
node B is allowed to always transmit, provided that its residual
energy is high enough to ensure a successful decoding at node
A. In addition, the proposed protocol with capabilities of both
EH and signal transmission can be developed by employing
a Markov-chain model, following which we can derive both
the stationary distribution and the outage probability of node
A. Finally, numerical results validate the proposed theoretical
analysis.
Index Terms— Full-Duplex, Energy Harvesting, Markov
Chain, Minimum Transmission Protocol, Throughput.
I. INTRO DUC TIO N
ENERGY harvesting (EH) on radio frequency (RF) signals
has been regarded as a new way for charging the mobile
terminal’s battery, revealing an interesting application potential
in the fifth-generation (5G) wireless communications systems
[1]. Either half-duplex (HD) or full-duplex (FD) mode can be
implemented in the terminals with EH capability [2], [3]. For
example, an EH source may work with an FD-mode energy-
providing relay together to forward the useful signal to the
destination, with their energy source offered by exploiting the
dissipated RF energy [4].
As everyone knows, the energy storage of the battery will
play a critical role in enabling a reliable and steady commu-
nication. To model the stationary distribution of a battery’s
energy storage, Markov chain can be readily employed [5].
For instance, the authors in [2] investigated the scenario of
multiple HD-mode-and-EH-capable relays by modelling the
charging/discharging process of the discrete-level battery as a
This work was supported by the key project of the National Natural Science
Foundation of China (No. 61431001), Beijing Natural Science Foundation
(L172026), the open research fund of National Mobile Communications
Research Laboratory-Southeast University (No.2017D02), Key Laboratory
of Cognitive Radio and Information Processing, and Ministry of Education
(Guilin University of Electronic Technology) (Corresponding author: Zhong-
shan Zhang.)
Qian Zeng, Yuhong Zheng with School of Computer & Communication Engineer-
ing, University of Science and Technology Beijing, Beijing, China 100083 (e-mail:
zengqian617@foxmail.com, zhengyuhongzyhzyh@163.com).
Bin Zhong is with School of Information and Electrical Engineering, Hunan Uni-
versity of Science and Technology, Xiangtan, Hunan Province, China 411201 (e-mail:
zhongbin@hnust.edu.cn).
Zhongshan Zhang is with the School of Information and Electronics, Beijing Institute
of Technology, Beijing 100081, China (email: zhangzs@bit.edu.cn).
finite-state Markov Chain. Furthermore, for a two-way FD-
mode relay-selection network [6], the authors in [3] im-
plemented both time division duplex static power splitting
(TDDSPS) and FD static power splitting (FDSPS) schemes,
showing that the EH capability offered by the relays will
be beneficial to improving the sum throughput. In addition,
the authors in [7] configured the secondary receiver in the
cognitive radio network (CRN) to be an EH-enabled access
point (AP), followed by characterizing the battery’s dynamic
charging/discharging behavior as a finite-state Markov chain.
Despite the performance gain attained in the existing stud-
ies, there still exist several shortcomings. In particular, when
investigating the EH process, the authors either focused on
monitoring the battery’s storage by neglecting the employment
of Markov chain [4], or failed to track the energy-storage
of the mobile nodes [3], not to mention the FD-mode bi-
node scenario (i.e., comprising both nodes A and B) [7].
To mitigate the above-mentioned drawbacks, the authors in
this letter propose an EH protocol for the FD-mode terminals
by modelling their energy storage as a Markov chains [5].
In particular, two FD-mode nodes are considered, in which
one node is capable of transmitting RF signal to its peer and
simultaneously receiving the returned signal, while the other
node is capable of harvesting the RF energy. Furthermore, two
protocols, say minimum transmission time switching (MTTS)
and minimum transmission static power splitting (MTSPS),
will be proposed by employing Markov chain to model the
information-transmission condition as well as the battery’s
energy storage.
The remainder of this letter is organized as follows: the
system model is provided in Section II, followed by describing
the proposed protocols in Section III. In Section V, both
the MTTS and MTSPS protocols will be validated. Finally,
Section VI concludes this letter.
II. SYS TEM MO DEL
Considering a scenario comprising two FD-mode nodes
with EH capability. Note that self-interference (SI)-
cancellation is beyond the scope of this letter, and the
interested readers are suggested to refer to [8], [9] for
details. Like in [10], SI is always assumed to be sufficiently
suppressed by implementing an appropriate SI-cancellation
technique in this letter. In particular, node A is assumed
to have a constant energy supplying (i.e., its transmit RF
works at the power level of PA), which energy dissipation
will be harvested by node B. Therefore, node B, as equipped
with a discrete-level battery, is capable of transmitting its

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signal back to node A with a power of PB. Of course, both
nodes will suffer from the impact of additive white Gaussian
noise (AWGN), which is assumed to have zero mean and
variance σ2
i,i∈ {A, B}, but its impact on the system’s
performance is much weaker than that of the interference
[11]. Without loss of generality, the uplink and downlink
channels are assumed to be reciprocal. Obeying the frequency
non-selective Rayleigh block fading, the gain of each channel
can be denoted by h. We can thus give out the expression
of an average Signal-to-Noise-Ratio (SNR), i.e., λH, at the
receiver.
Denoting by HiSI ,i∈ {A, B }the residual SI channel, we
may express its variance as PihiS I =σ2
iSI [12]. Furthermore, a
perfect channel state information (CSI) is assumed to be avail-
able at the receiver. This assumption is reasonable, because the
channel estimation errors can be made low enough by relying
on some high-quality CSI estimation techniques such as [13].
III. ENE RG Y HA RVE STI NG A N D INF O RM ATI ON
TRA NS MIS SIO N PROTOC OLS
In this section, two new protocols, say the MTTS and
the MTSPS protocols, are proposed for both ensuring an EH
capability in node B and guaranteeing a successful information
reception in node A.
A. Minimum Transmission Policy
Since both energy and useful information are carried in the
RF signal, node B can always be charged by exploiting the RF
energy that dissipated by node A1. In the proposed scheme,
node A keeps transmitting signal to node B, regardless of its
channel quality. Anyway, node B can always receive signals
by neglecting the correctness of the received information. In
fact, even if the received information is incorrect, the received
RF signal can still be exploited by node B for the purpose
of EH. Meanwhile, by obtaining the instantaneous CSI, node
B will transmit its signal back to node A, provided that the
energy storage in the former is high enough to complete this
transmission. The above-mentioned policy is known as the
minimum transmission policy.
Since node B is assumed to operate in the FD mode, EH
can be implemented more conveniently [3], [4], [7]. Evidently,
the FD-enabled node may readily optimize its power budget
within a T-duration by taking its residual energy into account.
B. Minimum Transmission in Time-Switching Way
In the proposed MTTS protocol, we denote by α(0 <α <1)
the fraction of time in a T-duration that allows node B to per-
form EH. Evidently, the remaining time (1 −α)Tbeyond EH
will be left for performing signal transmission [3]. According
to [15], the harvested energy by a node during αT can be
expressed as ER=βPAhαT , where β(0< β < 1) stands for
the energy conversion efficiency [14], PB=ET
(1−α)T, and ET
denotes the energy storage in this node’s battery.
1The EH process is not elaborated on in this letter just for space-saving
consideration. The interested reader may refer to [14] for details.
When node B starts transmitting signal back to node A,
the SNR conceived by the latter will be γA=PBh
PAhASI
+σ2
A
=
PBh
σ2
ASI
+σ2
A
. The outage probability of the signal transmission
can be given by PoutA =P(γA< γth ), where γth denotes the
signal transmission threshold, γth = 2RT−1, and RTis the
fixed transmission rate measured in bps/Hz.
Following the above-mentioned analysis, the battery’s
minimum energy storage can be expressed as ET min =
γth(σ2
ASI
+σ2
A)(1−α)T
h, which specifies the minimum but enough
energy required by node B for successfully transmitting its
signal. Consequently, the throughput of node A can be given
by TT S =RT(1 −PoutA ) (1 −α).
C. Minimum Transmission in Static Power-Splitting Way
As revealed in [3], the EH and information transmission pro-
cesses can be performed within a single T-duration. Here we
must emphasize that node B may not only be recharged with
µPA, but also transmit information back to node A at power-
level (1 −µ)PA, where µ(0< µ <1) denotes the fraction of
power that will be taken as the harvested energy. According
to [15], the harvested energy is ER=βµPAhT , while the
RF transmission power will be PB=ET
T. Furthermore, the
minimum energy storage for performing signal transmission is
ET min =γth(σ2
ASI
+σ2
A)T
h, leading to the throughput TSP S =
RT(1 −PoutA).
IV. AVER AG E THROUGHPUT ANALYSI S
In this part, we analyze the discrete charging/power storage
process, which can be described by a finite-state Markov
process, in the battery according to both the EH condition
and the transmit power requirement of the node of interest.
After obtaining the steady-state probability of the process, we
can readily derive the average throughput of node A.
A. Energy Storage and Usage Analysis
A practical discrete-level model is employed for analyzing
the status of the battery [5], whose capacitance is denoted by
C. Meanwhile, the number of discrete levels is assumed to be
L. In particular, the i-th energy level of the battery of interest
can be characterized as εi=iC/L,i∈(0,1,· · · , L). Thus, the
amount of the harvested energy (i.e., ER) in each T-duration
and the transmit energy (i.e., ET) offered by this battery
can be discretized as εRand εT, respectively. Consequently,
the harvested energy and transmitted energy at node B can
be denoted by εR,εiand εT,εj, respectively [5]. We
can express the battery’s energy storage in the beginning of
transmission block m:
EB[m] =min {EB[m−1]+εRV[m]+(V[m]−1)εT, C }(1)
where V[m]is a binary variable. If there exists signal under
transmission, we set V[m] =0, otherwise V[m]= 1.
B. Markov Chain for FD Transmission
Denote by Sithe energy-containing status of the battery, we
may use Pi,j to specify the transition probability from Sito Sj.
Note that Pi,j can be employed for generalizing the battery’s
energy state transition into a Markov chain [5]. Furthermore,

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we denote by εRand εTthe possible EH amount and that for
signal transmission, respectively, during transition period εt,
where 0≤εt≤tK with C/L =Kand t∈[0, L]. The state
transition probability can thus be expressed:
1) S0to S0: The battery’s energy is empty at start and at
the end (but it may be charged during T,0≤t≤L),
P0,0=P(εR< K)
+
L−1
X
t=1
Ph(tK< εR<(t+1)K)\((t−1)K < εT< t K)
i
+Ph(C < εR)\((L−1) K < εT< C )
i(2)
where P(εt< X ) = Ft(x) = 1 −e−λtxrepresents the
cumulative distribution function (CDF) of an exponential
random variable X.
2) S0to Sj(0< j < L): The empty battery is partially
charged, and there may transmit back signal, 0≤t≤L−j,
P0,j =Ph(jK < εR<(j+ 1) K)\(jK < εT)
i
+
L−j−1
X
t=1
P"((t+j)K < εR<(t+j+ 1) K)
\((t−1) K < εT< tK )#
+Ph(C < εR)\((t−1) K < εT< tK )
i
(3)
3) Sito Si(0< i < L): Similar to (1), but the battery is
never empty with 0≤t≤L−j,
Pi,i =Ph(εR< K)\(K < εT)
i
+
L−i−1
X
t=1
Ph(tK< εR<(t+1)K)\((t−1)K < εT< tK )
i
+Ph((L−i)K <εR)\((L−i−1)K < εT<(L−i)K)
i(4)
4) Sito Sj(0< i < j < L): The node with under-charge
non-empty battery may transmit signal back, 0≤t≤L−j,
Pi,j =P"((j−i)K < εR<(j−i+ 1) K)
\(jK < εT)#
+
L−i−1
X
t=1
P"((t+j−i)K < εR<(t+j−i−1) K)
\((t−1) K < εT< tK )#
+Ph((t+j−i)K < εR)\((t−1) K < εT< tK )
i(5)
5) Sjto Si(0≤i < j ≤L): The discharged non-empty
battery is considered, with the EH process being un-
necessary while the signal can definitely be transmitted
back. When the battery is fully-charged at the beginning,
only the energy cost is considered, otherwise, the EH
should be considered, 0≤t≤L−j,
Pj,i =P((j−i−1) K < εT<(j−i)K), j =L(6a)
P
j,i =Ph((L−j)K<εR
)\((t+j−i−1)K<εT<(t+j−i)K)
i
+
L−j−1
X
t=0
P"(tK < εR<(t+ 1) K)\
((t+j−i−1) K < εT<(t+j−i)K)
#,
otherwise
(6b)
6) The transitions Sito SL(0< i < L), S0to SLand SL
to SLare easy to follow, and
Pi,L =Ph((L−i)K < εR)\P(C < εT)
i(7)
P0,L =hP(C < εR)\P(C < εT)
i(8)
PL,L =P(C < εT)(9)
5 10 15 20 25 30
Transmit Power (dBm)
0
0.5
1
1.5
2
2.5
3
Average Throughput (bps/Hz)
Analytical (MTTS)
Analytical (MTSPS)
Simulation (MTTS)
Simulation (MTSPS)
L
L
L
= 200
L= 10
= 20
= 30
Fig. 1. Average throughput versus transmit power, where L= 10, 20, 30,
200. PA∈[5,30] dBm, C= 20, RT= 3 bps/Hz and δ2
ASI = -90 dBm.
Let us denote by Z=Pi,j the Markov chain’s state transition
matrix in terms of energy contained by the battery. As the
transition matrix Zis both irreducible and row stochastic,
the stationary distribution of the battery’s capacitance can be
expressed as π=PT−I+A−1b[5], where Ai,j = 1,∀i, j
and b=1 1 · · · 1T.
C. Average Throughput
The average throughput of the proposed model can be
characterized in (10):
Rave =RT(1 −Pout (εT≥EB[m]+εH)) ,(10)
For more details, please refer to
Pout (εT≥EB[m]+εH) =
L
X
i=0 πi
L−i
X
t=0
f′(t)!
=
L−1
X
i=0 πi
L−i
X
t=0
f′(t)!+πLFT(C)
(11)
and
L−i
X
t=0
f′(t)= f′(0)+f′(L−i)+
L−i−1
X
t=1
f′(t)
=Ph(εR<K)\(iK<εT)
i+
Ph((L−i)K<εR)\(C<εT)
i
+
L−i−1
X
t=1
Ph(tK < εR<(t+ 1) K)\((t+i)K < εT)
i.
(12)
V. NUME RIC AL RE S ULT S
In this section, we validate the proposed MTTS and MTSPS
protocols by comparing their analytical and Monte Carlo
simulation results. In the following, Tin MTTS (MTSPS)
is set to be 0.5, with µ=β=α= 0.5and δ2
A=−90 dBm.
In Fig. 1, the average throughput versus PAis illustrated,
showing that the analytical analysis in (10) matches the
corresponding Monte Carlo simulation result (thus validates
the proposed analytical analysis). It can be seen intuitively that
a larger Limplies a higher average throughput of the proposed
model (in other words, all curves in Fig. 1 tend to converge to

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Communications Letters
IEEE COMMUNICATIONS LETTERS, VOL. XX, NO. X, XXX 201X 4
5 10 15 20 25 30
Channel Mean (dB)
0
0.5
1
1.5
2
2.5
3
Average Throughput (bps/Hz)
Analytical (MTTS)
Analytical (MTSPS)
Simulation (MTTS)
Simulation (MTSPS)
dBm
= -90
ASI
2
ASI dBm
= -30
2
Fig. 2. Average throughput versus channel mean, where δ2
ASI = -30, -90
dBm, L= 20, PA= 15 dBm, C= 20 and RT= 3 bps/Hz.
1 2 3 4 5 6 7 8 9 10
Transmission Rate (bps/Hz)
0
1
2
3
4
5
6
7
8
9
Average Throughput (bps/Hz)
Analytical (MTTS)
Analytical (MTSPS)
Simulation (MTTS)
Simulation (MTSPS)
L
A
P
dBm
dBm= 15
= 30
= 30/10 (upper/lower line)
= 30
L
L= 10
A
P
Fig. 3. Average throughput versus RT, where L= 10, 30. PA= 15, 30
dBm, δ2
ASI = -90 dBm, C= 20 and λH= 20 dB.
RT). The reason is that, considering the same C, the larger
Lleads to more states about the battery’s capacitance, while
the less energy is needed for state transition. Thus, it reduces
the occurrence of cases in which some energy is received but
cannot be upgraded (i.e., be increased to the next-level state).
Comparing to MTTS, the proposed MTSPS protocol enables
us to achieve a higher average throughput by increasing both
PAand L, provided that a longer EH duration is allowed at
node B. Furthermore, the larger the PA, the faster the average
throughput approaches RT.
In Fig. 2, considering variant residual SI (i.e., after perform-
ing SI cancellation), the average throughput of an FD node
with λHis illustrated. The curves with different residual-SI
levels are depicted, showing that the residual SI will impose a
negligible impact on the throughput, provided that the SI can
be sufficiently suppressed (i.e., to become lower than a given
threshold).
In Fig. 3, it describes the average throughput under a variety
of RT. The impacts of both Land PAon the average
throughput are evaluated. Evidently, the average throughput is
not a monotonically increasing function of RT(but it is that
of parameters PAand L). The higher the PA, the later the
occurrence of the point, beyond which the average throughput
will drop. Furthermore, the higher the PA, the less the impact
of Lon the average throughput. In this case, the proposed
MTTS and MTSPS protocols with L={10,30}under PA=
30 dB would give out almost the same performance. Although
the simulation and analytical results may become inconsistent
as RTincreases, this inconsistency can always be mitigated
by appropriately increasing C.
VI. CO N CL USI ONS
In this letter, two EH and information transmission protocols
(i.e., MTTS and MTSPS) were proposed for improving both
energy and transmission efficiencies of a system that comprises
two FD-mode nodes. Relying on the capability of concurrent
transmission and reception in the FD-mode nodes, the EH
node is capable of transmitting the signal back to its peer,
provided that its energy storage is high enough for completing
the current transmission. Furthermore, the process of both
energy transmission and signal reception in the proposed
protocols was modelled, in which a discrete-level battery is
modelled as a Markov chain. Finally, the expression for the
average throughput of the proposed system was given out for
validating the proposed protocols.
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