Dynamic Harvest-and-Forward: New Cooperative
Diversity with RF Energy Harvesting
Koji Ishibashi
Advanced Wireless Communication Research Center (AWCC),The University of Electro-Communications,
1-5-1 Chofugaoka, Chofu, Tokyo 182-8585, Japan
Email: koji@ieee.org

Abstract—In this paper, we propose a new cooperative diversity technique with radio frequency (RF) energy harvesting
named dynamic harvest-and-forward (DHF) cooperation. This
cooperation enables to obtain diversity gain with consuming
neither extra energy nor extra bandwidth by exploiting therelay’s proximity advantage over the destination. We analyze
the proposed approach in terms of outage probability and showthat the DHF cooperation can achieve the diversity order of two(full diversity) in typical three node cooperation scenario. We
also investigate the effect of geometrical arrangement and showthat the advantageous region of DHF cooperation over the directtransmission without the energy harvesting relay.

I. I NTRODUCTION
Typical wireless channels 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]–[3], it is practically difficult to equip multiple antennas in some applications
such as sensor networks because of the size, complexity,
and cost. In order to overcome this issue, another concept
has been proposed in the literature; when the source cannot
reliably communicate with the destination, other available
nodes can temporarily work as relays in order to support
the communication by expending their own energies regularly
supplied by pre-charged batteries, which is called cooperative
diversity and allows nodes to enjoy spatial diversity gain
without equipping additional antennas [4]–[8]. Cooperative
diversity inherently consumes the battery of users to support
some users having with small channel capacities. Thus, it isimportant to reduce the energy consumption used to forward
the signals. To this end, amplify-and-forward (AF) relaying has
been actively studied in the literature because of the simple
functionality. In the AF relaying, the relay only re-transmits
the scaled or amplified version of the received signals andthus neither decoding nor demodulation is needed. However,when power amplifier (PA) efficiency is considered, decodeand-forward (DF) relaying may be beneficial since the AF
relaying has to transmit noisy signals [9]. Considering thisPA issue, the energy-efficient relaying has been studied in[10]. The cooperation yet consumes additional energy frompre-charged battery, which may results in shorter network life
since more nodes drain their batteries at the same time.

A remedy for this crucial battery issue is the use ofenergy harvesting [11]. Energy harvesting technologies enabledevices to harness energy from ambient sources such as solar,
vibration, themoelectric effects, and so on. Since this might
be an ultimate solution of the crucial energy constraint, it
has gained much attention from researchers. Especially, radio
frequency (RF) energy harvesting does not depend on availability of ambient energy sources where ambient RF radiation
is captured by the receiver antennas and converted into a
direct current (DC) voltage through appropriate circuits suchas rectennas [12], [13]. Therefore, this RF energy transfer isconsidered as one of the most attractive candidate technologies
to realize self-sustaining networks.
The performance of cooperative communication with multiple energy harvesting relays has been studied and the advantage of using relays was shown in [14] where energies
harvested by the relays were assumed to be a stationary andergodic process with a constant mean. However, the sourceof energy deeply depends on the ambient environment andthus the energy may not be generated for a long period. In[15], wireless energy transfer such as RF energy harvesting has
been considered in scenarios with cooperative communications
besides conventional energy harvesting and it was shown thatthe outage probability performance can be improved by harvesting energy from ambient RF signals. Furthermore, one-hop
AF relaying with practical finite pre-charged battery model
has been studied in [16] where only RF energy harvesting
was assumed as the source of energy. Although these seminal
works showed the advantage of energy harvesting, the relay
still utilizes the pre-charged battery and consumes its own
energy.
Wireless-powered cooperative communications have been
investigated quite recently in [17], [18]. In [17], the dynamic
wireless power transfer and information transmission in the
typical three node network where all the transmitters areactivated on the fly by highly efficient wireless power transferfrom the base station (BS) to transmitters in order to send
the information from the transmitters to the BS. Also, in[18], throughput and ergodic capacity of one-hop DF relaying
with RF energy harvesting has been investigated where therelay harvests the energy from the source’s signals. Thesewireless-powered cooperative protocols are composed of thefollowing three phases: 1) RF energy harvesting, 2) source-to-relay transmission, and 3) cooperative phase. The latter twophases have the same length of duration as similar to conventional two-phase cooperative protocols [4]–[8]. However,conventional two-phase approaches require extra orthogonal
channel to meet a half duplex constraint and reduce an overall
bandwidth efficiency of the network.
Regularly, cooperative communications become beneficial
when the relay is placed nearby the source since the channel
quality between the source and relay defines whether therelay can successfully decode the source’s information or not.
Also, from the energy harvesting point of view, if the relay
is close to the source, the relay can obtain the sufficientenergy from the source’s transmission in a short time. Fromthese observations, dynamic decode-and-forward (DDF) [19]–[22] cooperation is more appropriate for energy harvesting
cooperation. In this protocol, if the receivers (i.e., relay anddestination) have a knowledge of network configuration, therelay can dynamically superimpose cooperating signals on theoriginal signal from the source using the same channel uponsuccessfully decoding the source’s information. As a result,the destination can achieve the diversity gain without extra
channel resources.
In this paper, we propose a new cooperative diversity technique based on DDF cooperation with RF energy harvesting
named dynamic harvest-and-forward (DHF) cooperation. This
cooperation allows us to obtain diversity gain with consuming
neither extra energy nor extra bandwidth by exploiting therelay’s proximity advantage over the destination. We analyze
this approach in terms of outage probability and show that the
DHF cooperation can achieve the diversity order of two (fulldiversity) in three node cooperation scenario.
The paper is organized as follows. Section II describes
the system model including geometrical relationship between
transmitters which is treated throughout the paper. Section
III explains the proposed DHF cooperative protocol and we
derive outage probability of DHF cooperation in Section
IV. Numerical results in Section V show the advantage of
proposed approach and clarify the advantageous region of RFenergy harvesting relay without consuming extra energy andbandwidth. Finally, Section VI concludes this work.
II. S YSTEM M ODEL
Figure 1 illustrates the geometrical model consideredthroughout the paper. The network is composed of three nodes:
source (S), relay (R) and destination (D). Three nodes are
assumed to be located in two-dimensional plane as in the figure
where θ is the angle of the line S − R − D and dAB denotes thethe Euclidean distance between nodes A and B. We supposethat S intends to transmit its own message to D and that R
has agreed to forward S’s message before the transmission.
All the channel links are disturbed by large-scale pathloss, small-scale quasi static frequency nonselective Rayleighfading, and additive white Gaussian noise (AWGN) with zeromean and noise variance σ 2 = N0 /2 where N0 denotes theone-sided power spectrum density. Thus, the complex fading
coefficients hSR , hSD , and hRD in Fig. 1 are uncorrelated

R
dRD

dSR
θ

hRD

hSR

GR
hSD

S

dSD

D
GS

Fig. 1. Geometrical system model with three nodes: source, relay, anddestination.

and circularly symmetric complex Gaussian random variables
with zero mean and unit variance where these coefficients are
assumed to be ideally available at the receiver sides. In thispaper, the large-scale path loss between A and B is modeledas
Gt Gr λ2f (A, B) ≜,(1)
(4πdAB )2
where Gt and Gr are antenna gains at transmitter and receiver,respectively, and λ is the wavelength.
From the motivation of this work, the geometrical gain due
to the proximity of the relay over the destination is significantly important in the scenario with RF energy harvesting.
To clarify this effect, we here introduce the relative path loss
gain. We assume that the source transmits its own signal withaverage power PS . Let GS denote the geometrical gain at Dfrom S relative to the link S → R, which is simply given by()2
f (S, D)PS
dSR
GS =
≜
.
(2)
f (S, R)PSdSD
Similarly, if the relay forwards the received information withthe average power PR , the geometrical gain at D from R
relative to S → R channel link can be given by
(
)2
dSR
PR
GR ≜
.
(3)
dRD
PS
By triangle equality, we haved2SR + d2RD − 2dSR dRD cos θ = d2SD .

(4)

Let ζ denote the ratio of dRD to dSR , i.e., ζ = dRD /dSR . Then,the gain GR can be rewritten as
GR =

1
1 PR
≜ 2 µ,
ζ 2 PSζ(5)where µ is the transmit power ratio. Note that we assumeµ < 1 since the transmit power of S should be even higher
than that of R which works only with small harvested energy.
Also, the gain GS can be expressed as
GS =

1
.
1 + ζ 2 − 2ζ cos θ

Without loss of generality, we assume 0 ≤ θ ≤ π.

(6)

From the above equation, the transmit power ratio µ is writtenbyηδ1 h2SRµ= 2.
(9)dSR (1 − δ2 )(1 − δ1 )T
S

R

Transmitting

EnergyHarvesting

Decoding

Relaying

δ1T

δ2(1−δ1)T(1−δ2)(1−δ1)T

Clearly, this proposed approach does not reduce the bandwidth efficiency unlike conventional AF or DF cooperation.
Moreover, the relay works only with the harvested energy andthus does not need any extra energy for cooperation.
IV. O UTAGE P ROBABILITY A NALYSIS

Fig. 2. Dynamic three-phase protocol.

III. DYNAMIC H ARVEST- AND -F ORWARD P ROTOCOL
Based on the model described in the previous section,
we here explain our new cooperative protocol with RF energy harvesting. Our dynamic cooperation is composed ofthree phases depending on relay’s behavior: energy harvesting
phase, decoding phase, and relaying phase, as illustrated inFig. 2.
In each transmission block of time duration T , the firstδ1 T amount of time (0 < δ1 < 1) is assigned to harvest
the energy from received RF waves. The remaining (1 − δ1 )transmission block is further divided into two parts by δ2
where 0 < δ2 < 1. During the first δ2 (1 − δ1 )T duration, therelay intends to decode the source’s message. Because of theproximity advantage of the relay over the destination, the relay
successfully decode immediately with high probability. Then,the remaining duration (1 − δ2 )(1 − δ1 )T would be utilized
for cooperative transmission similar to DDF protocol [19]–[22] where the relay forwards the message only by means ofharvested energy EH . At the destination, the received signals
are maximally combined. Hereinafter, T = 1 is assumed forsimplicity without loss of generality.
When the source transmit with average power PS , the energy
harvested at the relay EH is denoted as
EH = ηδ1

h2SR
PS ,
d2SR

(7)

where η is a conversion efficiency from alternative current(AC) to direct current (DC) and its practical value is 0.37
according to [13]. It is worth noting that the distances arenormalized by dSR and thus dSR = 1 in the rest of the paper.
Upon the harvesting phase, the relay activates its own
receiver circuit and starts to decode the information with
δ2 (1 − δ1 ) time duration where δ2 can be dynamically chosen
according to every decoding result. Note that we assume thatthe processing gain to decode the information is negligible.
Due to the proximity advantage of the relay, it might successfully decode the information before the destination does.
Finally, the relay forwards the decoded information during
the remaining time fraction (1−δ2 )(1−δ1 ) and its transmission
power is given byPR =ηδ1 h2SR PS
EH= 2.
(1 − δ2 )(1 − δ1 )dSR (1 − δ2 )(1 − δ1 )(8)

In this section, we analyze the outage probability of proposed DHF protocol. The outage event is defined as follows;
unless the system achieves the capacity equals to or greaterthan the given desired transmission rate R, this event is called
outage. The outage probability explains the probability that
this event occurs and also can be seen as a complementary
cumulative distribution function (CCDF) of the non-ergodic
capacity.
Upon energy harvesting phase δ1 , the relay starts to decode
the information. The time duration of decoding phase isdefined by the instantaneous signal-to-noise ratio (SNR) at R.
The instantaneous SNR at R is written byPS
h2SR 2≜ h2SR ΓSR ,dSR N0(10)

where ΓAB is an average SNR of the link A → B.
For given R and δ1 , the condition to successfully decode
the information during the decoding phase isδ2 (1 − δ1 ) log2 (1 + h2SR ΓSR ) ≥ R.

(11)

Thus, the fraction of remaining time δ2 for decoding is given
by
R
δ2 =
.
(12)
(1 − δ1 ) log2 (1 + h2SR ΓSR )Clearly, the relay cannot cooperate when δ2 ≥ 1. Namely,
there is no remaining time for cooperation. This probability isreferred to as cooperation probability and denoted by Pr[δ2 ≥1]. Considering the distribution of h2SR , the probability can beeasily calculated as[ ( R)]
2 1−δ1 − 1
Pr[δ2 ≥ 1] = exp −
.
(13)
ΓSR
The average SNR of the link S → D is simply expressed as
ΓSD = GS ΓSR from the relationship given by (6). Unless therelay is available at the relaying phase, the resulting achievablerate is calculated by
CD (hSD , ΓSD ) = log2 (1 + h2SD GS ΓSR ).

(14)

Then, the outage probability of this transmission becomes
]
[ R
2 −1
.
(15)
Pr[CD < R] = 1 − exp −GS ΓSR
If the relay is available, the source solely transmits during
the first (δ1 + δ2 (1 − δ1 )) amount of time and the source andFig. 3. The effect of δ1 with different geometrical arrangement ζ where R =1.0, θ = π, and η = 0.37. Also ΓSD is set to be 30 dB when ζ = −30 dB.

relay cooperatively transmit during remaining fraction of time.
The achievable rate during relaying phase is calculated by
CC (hSD , hRD , ΓSD , ΓRD )= log2 (1 + h2SD GS ΓSR + h2RD GR ΓSR )= log2 (1 + h2SD GS ΓSRηδ1+h2 h2 ΓSR ) (16)
ζ 2 d2SR (1 − δ1 )(1 − δ2 ) SR RD
Hence, the overall achievable rate of proposed protocol withrelaying phase is simply given by
CH = (δ1 + δ2 (1 − δ1 ))CD + (1 − δ1 )(1 − δ2 )CC ,(17)

where apparent variables are dropped off in the above equation
for simplicity. Unfortunately, the outage probability Pr[CH <R] does not admit the closed form and we should resort toMonte Carlo calculation.
Finally, the overall outage probability of the system can becalculated by
Pout = Pr[δ2 ≥ 1] Pr[CD < R]+(1 − Pr[δ2 ≥ 1]) Pr[CH < R]. (18)
V. N UMERICAL R ESULTS
In this section, we present some numerical results to demonstrate the advantage of our proposed DHF cooperation. In thefollowing, we assume that R = 1.0 and η = 0.37.
A. Effect of δ1
Figure 3 exhibits the effect of δ1 with different geometricalarrangement ζ in terms of outage probability where θ = π.
Also ΓSD is set to be 30 dB when ζ = −30 dB. Note that,when ζ decreases, it can be intuitively interpreted as that D isplaced farther away than R since the distances are normalized
by the distance between S and R, i.e., dSR = 1.
When ζ = −20 dB and −30 dB (namely, the destination isplaced nearby the relay), the smaller δ1 achieves the better
performance since the relay can obtain sufficient energy from

Fig. 4. The outage probability performance of direct transmission and DHF
cooperation with δ1 = 0.3 where R = 1.0, θ = π, η = 0.37, and ζ =−30 dB.

the source’s transmission in a short duration to reliably forward
the received information. However, when ζ becomes large,
the longer duration of energy harvesting phase is needed as
obvious from the figure (e.g., the case of ζ = −3 dB). As
larger δ1 is chosen, the cooperation probability (13) decreases.
Therefore, the relay is not available with high probability eventhough the required energy is harvested, as observed at theregion of δ1 > 0.5 in the figure.
In order to obtain the optimum performance of DHF cooperation, the relay has to dynamically determine the adequate
duration of energy harvesting phase δ1 based on parametersof all the channel links. However, it imposes the additional
consumption of resources in the network and contradicts the
motivation of this work. Therefore, judicious choice of δ1 isfrom 0.2 to 0.4 since these values provide the reasonable
performance at the region that the availability of relay iseffective. Therefore, δ1 = 0.3 is chosen as an example in
the following.
B. Comparison of Outage Probability Performance
Figure 4 shows the outage probability performance of directtransmission without RF energy harvesting relay and DHF
cooperation with δ1 = 0.3 where we assume that θ = π andζ = −30 dB.
As observed from the figure, the proposed approachachieves diversity order of two at high SNR region while theperformance of DHF cooperation is almost identical to that of
direct transmission at low SNR region. Unlike conventional
cooperative communications, our approach does not consume
any energy in the network and thus the performance of DHF
cooperation is not inferior to that of direct transmission evenat low SNR region.
C. Effect of ζ
Finally, the effect of ζ with fixed δ1 is shown in Fig. 5
where δ1 = 0.3 and θ = π. Also, PS and N0 are assumed

Fig. 5. The effect of geometrical arrangement ζ where R = 1.0, δ1 = 0.3,
θ = π, and η = 0.37. Also, PS and N0 are 10 [mW] and 0.01, respectively.

to be 10 [mW] and 0.01, respectively. Until ζ = −10 dB,
the performance seems almost constant. However, once ζ
exceed −10 dB, the outage probability steeply rises. Thisobservation indicates the relationship between the available
harvested energy and the geometrical region where the relay
effectively works. It is worth noting that, in this paper, dSR isnormalized (fixed) but, when the distance dSR becomes longer,
it is necessary to increase the source’s transmit power PS inorder to achieve the similar performance.
VI. C ONCLUSION
In this paper, we have proposed effective diversity techniquewith RF energy harvesting named DHF cooperation. The
outage probability of DHF cooperation has been analyzed.
Numerical results showed that this cooperation enables toobtain full diversity gain (i.e., diversity order of two) with
consuming neither extra energy nor extra bandwidth by exploiting the relay’s proximity advantage over the destination.
Moreover, the advantageous region of DHF cooperation wasdemonstrated based on the geometrical model.
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