RF Energy Powered Feedback-Aided Cooperation
Hiroki Kawabata and Koji Ishibashi
Advanced Wireless Communication Research Center (AWCC), The University of Electro-Communications,
1-5-1 Chofugaoka, Chofu, Tokyo 182-8585, Japan
Email: hiroki@awcc.uec.ac.jp, koji@ieee.org

Abstract—In this paper, we propose a radio-frequency (RF)energy powered cooperative transmission using RF energy harvesting which scavenges the energy from ambient radio waves.
The outage probability of this system is theoretically analyzed
to show the advantageous region compared with the directtransmission without RF energy harvesting relay when amplifyand-forward (AF) and decode-and-forward (DF) relaying are
employed. Moreover, if the source can get the information about
the residual battery and decoding results of the relay, the source
can recognize the availability of relay and resources. Thus, we
propose feedback-aided cooperation with RF energy harvesting,which can exploit all the available resources in the network, andshow that utilizing the explicit or implicit feedback information
significantly improves the overall performance.

I. I NTRODUCTION
For battery-limited applications such as sensor networks
which autonomously collect environmental information suchas temperature and humidity, robustness and low energy consumption are more important design factors than higher data
rate to realize long time and real-time observations. Typical
wireless channels, however, suffer from multipath fading andshadowing which significantly reduce communication capacity
for a given average transmission power and hinder reliabletransmission. Although an effective option is using multiple
antennas to obtain spatial diversity gain [1], it is practicallydifficult to equip multiple antennas to sensors because of thesize, complexity, and cost. Hence, another concept has been
proposed in the literature; when the source cannot reliably
communicate with the destination, other available nodes cantemporarily work as relays in order to support the communication by expending their own energies regularly supplied
by a pre-charged battery, which is called cooperative diversity
and allows nodes to enjoy spatial diversity gain without equipping additional antennas [2]. Cooperative diversity inherently
consumes the battery of users to support some users havingwith small channel capacities. Thus, it is important to reduce
the energy consumption used to forward the signals. To thisend, energy-efficient relaying has been proposed in [3] basedon decode-and-forward (DF) relaying to enhance the power
amplifier (PA) efficiency at the relay.
Even with the energy-efficient relaying, the cooperation stillconsumes additional energy from pre-charged battery, which
may result in shorter network life since more nodes drain
their batteries at the same time. A remedy for this crucial
battery issue is the use of energy harvesting [4] in combination
with cooperative diversity [5], [6]. Energy harvesting makes
it possible to scavenge energy from solar, vibration, wind,ambient electromagnetic waves and so on in order to recharge
the battery. The performance of cooperative communication
with multiple energy harvesting relays has been studied in [5]and the advantage of using relays was shown where the energy
harvested by the relay was assumed to be a stationary andergodic process with a constant mean. However, the source ofenergy deeply depends on the ambient environment and thus
the energy may not be generated for a long period. In [6],wireless energy transfer such as radio-frequency (RF) energy
harvesting has been considered in scenarios with cooperative
communications besides conventional energy harvesting andit was shown that the outage probability performance canbe improved by harvesting energy from ambient signals.
Furthermore, one-hop amplify-and-forward (AF) relaying withpractical finite pre-charged battery model has been studied
in [7] where only RF energy harvesting was assumed as thesource of energy. Although these seminal works showed theadvantage of energy harvesting, the relay still utilizes precharged battery and consumes its own energy.
The question that may arise here is how much gain we
can obtain when the relay only utilizes the energy harvested
from the received signals. In [8], [9], three phase cooperativetransmission has been investigated where the relay forwards
the received information only with the harvested energy.
However, the effect of finite-size battery of the relay has notbeen considered in the literature. Therefore, in this paper, weinvestigate an RF energy powered cooperative relaying withthe finite-size battery. Specifically, the outage probability ofthis system is theoretically analyzed to show the advantageous region compared with the direct transmission without
RF energy harvesting relay when AF and DF relaying are
employed as relaying function. Moreover, if the source can get
the information about the residual battery and decoding resultsof the relay, the source can recognize the availability of all the
resources in the network. Thus, we propose feedback-aided
cooperation with RF energy harvesting, which can efficiently
exploit all the available resources in the network.
The paper is organized as follows. Section II describes thesystem model treated in the paper and proposed cooperation
is described. In Section III, we derive outage probability ofcooperative transmissions with RF energy harvesting usingstate transition matrix and show the diversity order of the proposed approach. Numerical results confirm theoretical analyses
and clarify the advantageous region of RF energy harvesting
relay without external energy in Section IV. Finally, Section
V concludes this work.

II. S YSTEM M ODELIn this paper, we assume that the network is composed ofthree nodes, source (S), relay (R), and destination (D), andeach node equips a single antenna. Due to the half-duplex
constraint, every node cannot simultaneously transmit andreceive. Thus, when the relay is available, every transmission
is performed in two phases. Also, we assume that relay has the
RF energy harvesting capability and the battery with finite size
𝑃𝑏 ≥ 0 where the residual battery 𝑒 = 0 at the beginning oftransmissions since the relay only utilizes the energy harvested
from received signals.
In the first phase, the source broadcasts its own information
during 𝑇 /2 duration over wireless channels. Then, the received
signal at the time instant 𝑡 = 1, 2, ⋅ ⋅ ⋅ at R and D can berespectively expressed by
√
√
(1)
(1)
(1)
𝑦SR (𝑡) = 𝑃S ℎSR 𝐺SR 𝑥(𝑡) + 𝑛R (𝑡)
√
√
(1)
(1)
(2)
𝑦SD (𝑡) = 𝑃S ℎSD 𝐺SD 𝑥(𝑡) + 𝑛D (𝑡),where 𝑥(𝑡) is a complex transmit signal with unit power,𝑛j∈{R,D} is additive white Gaussian noise (AWGN) with zeromean and variance 𝑁𝑗 = 𝜎 2 , 𝑃S is the transmit powerof source, and ℎ𝑖𝑗 is the channel coefficient between node𝑖 ∈ {S, R} and 𝑗 following a complex Gaussian distribution
with zero mean and unit variance. In the paper, frequency
non-selective block Rayleigh fading is assumed and thus
the coefficients are constant during each transmission block.
Also, 𝐺𝑖𝑗 denotes the path-loss coefficient which is given by
𝐺𝑖𝑗 = (1 + 𝑑𝛽𝑖𝑗 )−1 where 𝑑𝑖𝑗 is the distance between node 𝑖and 𝑗, and 𝛽 denotes the path-loss exponent practically ranging
from 2 to 4. Without loss of generality, 𝛽 is assumed to be
2 in the rest of the paper. Note that the path-loss coefficientis regularly modeled as 1/𝑑𝛽𝑖𝑗 rather than (1 + 𝑑𝛽𝑖𝑗 )−1 [10].
This typical function, however, might be greater than one
when the distance 𝑑𝑖𝑗 is smaller than one while no receiver
can obtain more power than was transmitted. In this case, analternative option is the use of minimum possible path-loss
degradation which ensures the accuracy of path-loss model
for short distances [11], [12].
During the source transmission, the relay switches twomodes (either harvesting or relaying) according to its own
residual battery 0 ≤ 𝑒 ≤ 𝑃𝑏 . Let 𝐸R denote the transmit
energy of the relay and the relay’s battery size is given by
𝑃𝑏 = 𝛼𝐸R where 𝛼 ≥ 1.
When 𝑒 < 𝐸R , the relay works in harvesting mode andscavenges the power from received RF signals and the harvested energy 𝑒ℎ is defined as𝑒ℎ ≜ 𝜂𝑃S ∣ℎSR ∣2 𝐺SR × 𝑇𝐻 ,(3)

where 𝑇𝐻 denotes the time duration for energy harvesting and𝜂(0 < 𝜂 ≤ 1) denotes the conversion efficiency, 100 × 𝜂% of
the received energy can be stored. Thus, the resulting battery
after RF energy harvesting is given by min(𝑃𝑏 , 𝑒 + 𝑒ℎ ). On
the other hand, if 𝑒 ≥ 𝐸R , the relay works in relaying modeand receives the information and forwards it consuming own
battery. Upon forwarding in the second phase, the remaining

Fig. 1. The protocol of the source and the relay in the proposed feedbackaided cooperation.

battery is given by max(0, 𝑒−𝐸R ) which decides the behaviorof relay at the first phase in the next transmission.
A. AF Relaying
In AF relaying, the relay scales and amplifies the received
signals and thus neither decoding nor demodulation is needed.
Then, the received signal at the destination node in the second
phase is written by
√
√
(2)
(1)
(2)
𝑦SRD (𝑡) = 𝑃R ℎRD 𝐺RD 𝐾SR 𝑦SR (𝑡) + 𝑛D (𝑡),(4)where 𝑃R denotes the transmit power of the relay, given as
𝑃R = 𝐸R /𝑇C using the time duration for relaying 𝑇C , and
𝐾SR is an amplification factor which is given by)−1(√
𝑃S ∣ℎSR ∣2 𝐺SR + 𝑁R
.
(5)
𝐾SR =
The node D combines two received signals given by (2) and(4) using maximum ratio combining (MRC).
B. DF Relaying
In the DF relaying, if and only if the relay has correctly
decoded the information, it re-encodes and forwards the information with regenerated symbols 𝑧(𝑡) with unit average power.
Then, the received signal at the destination node is expressed
as
√
√
(2)
(2)
(6)
𝑦RD (𝑡) = 𝑃R ℎRD 𝐺RD 𝑧(𝑡) + 𝑛D (𝑡).
In this paper, we assume that the relay transmits additional
codewords similar to incremental redundancy (IR) or distributed coding to efficiently obtain both diversity and coding
gain upon decoding with (2) and (6).
C. Feedback-Aided Cooperation with RF Energy Harvesting
If the source can get the information about the residual
battery of the relay, the source can exploit the available
wireless resource in the second phase. For example, if theresidual battery of the relay does not exceed 𝐸R , the source
utilizes the second phase to transmit its own information while
the relay continues to harvest the energy. Moreover, if thesource recognize the failure decoding of the DF relay at theend of the first phase, the source can transmit even in thesecond phase while the relay charges its own battery fromthe received RF waves. This approach is called feedbackaided cooperation in the rest of the paper and its protocol
is illustrated in Fig. 1.
In this paper, we consider two different feedback schemes:
explicit and implicit feedback. In case of explicit feedback, therelay transmits a small packet reporting both its residual battery and the decoding result during 𝛿𝑇 /2 time duration. In caseof implicit feedback, the source detects the relay’s behavior(i.e., in transmission or idle) for the short time duration 𝛿𝑇 /2
and recognizes the availability of resources in the network.
Upon 𝛿𝑇 /2 time duration, the source decides either to be idle
or to transmit with the aid of the feedback information. Notethat the explicit feedback consumes additional energy during
𝛿𝑇 /2 time duration but the implicit one.
III. O UTAGE ANALYSIS WITH STATE TRANSITION MATRIXIn this section, the outage probability of cooperative transmissions described in Section II is theoretically analyzed. The
outage event occurs when the instantaneous channel capacity
derived from the instantaneous signal-to-noise ratio (SNR) is
less than the given target rate 𝑅. Thus, the outage probabilityof the system is simply written as
CH+ (1 − 𝑃A )𝑃out,
𝑃out = 𝑃A 𝑃out

(7)

C
H
where 𝑃out
and 𝑃out
respectively indicate the outage probability of relaying mode and harvesting mode. Moreover, 𝑃A
is the probability that the relay is available. This obviously
depends on the statistical behavior of the battery with RFenergy harvesting, which will be thoroughly discussed in thesubsequent subsections. Hereinafter 𝑇 = 1 is assumed forsimplicity without loss of generality.

B. Outage Probability of DF Relaying
C1) With Explicit Feedback: In case of DF relaying, 𝑃out
depends on whether the relay successfully decodes the information or not. Thus, the outage probability between the source
and the relay is calculated by𝑃decode = Pr [log2 (1 + 𝛾SR ) > 𝑅]
( 𝑅
)
2 −1
= 1 − exp −
,
𝛾¯SR

(10)

where 𝛾SR is the instantaneous SNR from the source to therelay. In the DF relaying, the relay may fail to decode even
if it has the enough residual battery. In this case, the source
can utilize the available time slot and the relay can harvest
RF signals. Then, when the relay fails to decode, the channel
capacity is given by 𝐶H = 2−𝛿
2 log2 (1+𝛾SD ). Then, the outage
probability Pr[𝐶H < 𝑅] is similarly calculated by (9).
In case of the relaying mode, the resulting capacity isdenoted by1−𝛿{log2 (1 + 𝛾SD ) + log2 (1 + 𝛾RD )}.
(11)
2
Then, using Jensen’s inequality, the outage probability
Pr [𝐶C < 𝑅] is calculated as][1−𝛿
{log2 (1 + 𝛾SD ) + log2 (1 + 𝛾RD )} < 𝑅
Pr
2
[
]
𝑅
≤ Pr ∣ℎSD ∣2 𝛾¯SD + ∣ℎRD ∣2 𝛾¯RD < 2(2 1−𝛿 − 1)
𝐶C =A. Outage Probability of AF Relaying
1) With Explicit Feedback: When the explicit feedback isavailable and the relay is in the energy harvesting mode, therelay can harvest energy in both phases. Thus, the harvesting
duration is extended to 𝑇𝐻 = (2 − 𝛿)/2 while the relay
consumes extra power 𝛿𝐸R from its own battery for feedback.
Moreover, unless the relay is available, the source transmits
even in the second phase.
Hence, when the relay is available (i.e., relaying mode), theCat high SNR region
outage probability of AF relaying 𝑃out
can be approximately given by [2]
[
]
1−𝛿
C
log2 (1 + 𝛾SD + 𝛾SRD ) < 𝑅
= Pr
𝑃out
2
2

(2 1−𝛿 𝑅 − 1)2 −1 −1𝛾¯SD 𝛾¯SRD .
∼22) With Implicit Feedback: On the other hand, when theimplicit feedback is utilized, the source autonomously detects
the relay’s behavior (in transmission or idle) without consuming extra energy from the battery. Based on the observation
result, the source decides the behavior in the second phase.
Therefore, the outage probability in relaying mode equals tothe equation (8) with 𝛿 = 0 and that in harvesting mode equals
to equation (9).

(8)

On the other hand, when the relay is in the harvesting mode,the outage probability is given by
[
]
2−𝛿
H
log2 (1 + 𝛾SD ) < 𝑅
𝑃out = Pr2()
2
2 2−𝛿 𝑅 − 1= 1 − exp −
,
(9)
𝛾¯SD
where 𝛾SD is the instantaneous SNR from the node S to thenode D, 𝛾SRD is that from the node S to the node D throughthe node R, and 𝑥¯ denotes the mean of random variable 𝑥.

𝑅

−1 −1
𝛾¯RD ,∼ 2(2 1−𝛿 − 1)2 𝛾¯SD

(12)where 𝛾RD is instantaneous SNR from relay to destination.
From (9) and (12), the outage probability of proposedcooperation with DF relaying is given byC𝑃out= (1 − 𝑃decode )Pr [𝐶C < 𝑅] + 𝑃decode Pr [𝐶H < 𝑅] .
(13)2) With Implicit Feedback: When the implicit feedbackis used together with DF relaying, the outage probability is
obtained as similar to the AF relaying and thus the details ofderivation are here omitted due to limitations of space.
C. Available Probability
As described in the previous section, the residual battery
continuously changes according to the received energy andthis defines the available probability of the relay. In orderto analyze this probability, the discretized battery model with(𝐿 + 2) levels is introduced [7], which is expressed as
𝑒𝑥 ≜

𝑥𝑃𝑏
, 𝑥 = 0, 1, . . . , 𝐿 + 1
𝐿+1

(14)

In discretized battery model, harvesting energy 𝑒ℎ and energy
consumption 𝐸R are respectively defined as follow:𝑒ℎ ≜ 𝑒𝑖ℎ

s.t.

𝑖ℎ =

𝐸R ≜ 𝑒𝑖𝑟

s.t.

𝑖𝑟 =

arg max{𝑒𝑖ℎ < 𝑒ℎ }(15)

arg min{𝑒𝑖𝑟 ≥ 𝐸R }.

(16)

TABLE IS IMULATION PARAMETERS
𝑑SR [𝑚]𝑑RD [𝑚]𝑑SD [𝑚]𝑁0
𝐸R𝑖ℎ ∈{0,1,...,𝐿+1}

𝑖𝑟 ∈{0,1,...,𝐿+1}

2.0, 5.0
28.0
30.0
0.0001
1.0

𝛼
𝛽
𝜂
𝐿
𝛿

100
2.0
0.37
100
0.1

The state of the battery is defined by
S𝑘 = State[residual battery is 𝑒𝑘 ],and corresponding transition probability from state S𝑎 to stateS𝑏 is defined as
E𝑎,𝑏 = Event[transit from state S𝑎 to state S𝑏 ].

(18)

Then, all the transition events are classified as follow.
1) E0,0 : The battery remains empty.
2) E0,𝑖 (0 < 𝑖 < 𝐿 + 1): The empty battery is partiallycharged.
3) E0,𝐿+1 : The empty battery is fully charged.
4) E𝑖,𝑖 (0 < 𝑖 < 𝐿 + 1): The non-empty battery remains
constant.
5) E𝑖,𝑗 (0 < 𝑖 < 𝑗 < 𝐿 + 1): The non-empty battery ispartially charged.
6) E𝑖,𝐿+1 (0 < 𝑖 < 𝐿 + 1): The non-empty battery is fully
charged.
7) E𝐿+1,𝐿+1 : The battery remains full.
8) E𝑗,𝑖 (𝑗 > 𝑖): The battery is discharged.
These transition probabilities are simply calculated by exponential distribution as discussed in [7].
Then, using these state transition probabilities, state transition matrix P is expressed as follows.
⎛⎞
𝑃 (E0,0 )𝑃 (E0,1 )⋅⋅⋅𝑃 (E0,𝐿+1 )⎜ 𝑃 (E1,0 )𝑃 (E1,1 )⋅⋅⋅𝑃 (E1,𝐿+1 ) ⎟
⎜
⎟
P=⎜
⎟
..
..
..
.
..
⎝
⎠
.
.
.
𝑃 (E𝐿+1,0 )𝑃 (E𝐿+1,1 )⋅⋅⋅𝑃 (E𝐿+1,𝐿+1 )State transition matrix at 𝑡 = 𝑇𝑜 is expressed as P𝑇𝑜 .
Assuming that (⋅)𝑎,𝑏 is the element of 𝑎 row 𝑏 column, therelay’s available probability at 𝑡 = 𝑇𝑜 is expressed as follows.
𝑃A =

𝐿+1
∑
𝑏=𝑘

(

)
P𝑇𝑜 𝑎,𝑏s.t.

IV. N UMERICAL RESULTS(17)

𝑘 = arg min {𝑒𝑘 > 𝐸R }𝑘∈0,1,...,𝐿+1(19)

D. Diversity Order Analysis of Proposed Cooperation
Based on the above analyses, we further elaborate theachievable diversity order of the proposed approach. From
(8) and (12), the relaying transmissions seem to achieve thediversity order of two. However, since the relay transmits withconstant power 𝑃R regardless of the received SNR, neither
AF nor DF relaying achieves the diversity order of two. In
contrast, the three-phase RF energy harvesting cooperation
proposed in [8], [9] achieves the diversity order of two since
the relay boosts up its own transmit power according to theinstantaneous received power (i.e., harvested energy).

Numerical results are presented in this section to confirm
the statements in the previous section and to evaluate theadvantage of the feedback-aided cooperation. The common
parameters are listed in Table I where the conversion efficiency
𝜂 is assumed to be 0.37 as a practical value [13].
A. Outage Performance Comparisons
Figure2 shows the outage probabilities of direct transmission, AF and DF cooperation without feedback, explicitfeedback-aided AF and DF cooperation, and implicitfeedback-aided AF and DF cooperation where 𝑑SR is assumed
to be 2.0[m]. Note that the battery of the relay is not
charged at all at the beginning of transmissions and thus
the relay does not consume any external energy. Theoreticalcurves derived in the previous section are also drawn in the
figure. As observed from the figure, all the results calculatedby the derived equations show good agreement with thoseobtained by Monte-Carlo simulations. Moreover, the outage
probabilities of proposed feedback-aided cooperation with AF
or DF relaying are superior to that of direct transmission
where DF cooperation with implicit feedback exhibits thebest performance. Comparing the implicit-feedback-aided DF
cooperation with that without feedback, the additional gain is
about 3.0 dB at 10−4 . This fact clearly indicates that the source
and relay can efficiently exploit available resources based on
the feedback information. Also, compared with direct transmission, the implicit-feedback-aided DF cooperation obtains
about 7.0 dB additional gain at 10−4 . Note that the diversity
order of the proposed cooperation approaches to one as the
SNR increases, which is anticipated in the previous section.
Thus, the proposed approach cannot increase the diversity
order although it still provides significant gain at moderately
high SNR region.
In order to show the effect of proximity of the relay, Fig.3
shows the outage performances with 𝑑SR = 5.0[m]. The otherparameters are same as Fig.2. Comparing these figures, theperformance gap between direct transmission and proposed
feedback-aided cooperation becomes smaller as the distance
between the source and the relay increases. It is, hence, clearthat the relay should be placed nearby the source to efficiently
harvest the energy from the received RF waves.
B. Effect of 𝛿
Finally, we evaluate the effect of duration 𝛿 on explicitfeedback-aided and implicit-feedback-aided DF cooperation interms of outage probability. Also, we assume that 𝛾¯SD = 30 dB(𝑃S = 100[mW]) and 𝑑SR = 2.0[m] and the other parametersFig. 2. Outage probability performances of direct transmission, AF and DF
cooperation without feedback, explicit-feedback-aided AF and DF cooperation, and implicit-feedback-aided AF and DF cooperation when 𝑑SR = 2[𝑚]Fig. 4. Outage performance of implicit-feedback-aided DF cooperation withdifferent 𝛿 where 𝑑SR = 2[𝑚] and 𝛾¯SD = 30 dB.

ACKNOWLEDGMENT
This work was supported by JSPS KAKENHI 24760295.
R EFERENCES

Fig. 3. Outage probability performances of direct transmission, AF and DF
cooperation without feedback, explicit-feedback-aided AF and DF cooperation, and implicit-feedback-aided AF and DF cooperation when 𝑑SR = 5[𝑚]are the same as those in the previous subsection. The outage
performances with different 𝛿 are shown in Fig.4. The significant performance degradation is observed when the explicit
feedback is utilized since increasing 𝛿 incurs decreasing theresulting capacity in relaying mode with explicit feedback.
Therefore, the explicit feedback not only consumes the relay’s battery but also causes the degradation of the overall
performance.
V. C ONCLUSIONSIn this paper, the RF energy powered cooperation system
was proposed and its outage probability has been analyzed byusing state transition matrix. We have showed that the implicitfeedback-aided DF relaying was the best option to achieve thehigher reliability without consuming any extra energy.

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