This is a
version of a publication
in
Please cite the publication as follows:
DOI:
Copyright of the original publication:
This is a parallel published version of an original publication.
This version can differ from the original published article.
published by
GFDM-Based
Cooperative
Relaying
Networks
with
Wireless
Energy
Harvesting
Carrillo
Melgarejo
Dick,
Moualeu
Jules
M.,
Nardelli
Pedro,
Fraidenraich
Gustavo,
da Costa Daniel B.
Carrillo
Melgarejo
D.,
Moualeu
J.
M.,
Nardelli
P.,
Fraidenraich
G.,
da
Costa
D.
B.(2019).
GFDM-
Based Cooperative Relaying Networks with Wireless Energy Harvesting. Published in: 2019
16th International Symposium on Wireless Communication Systems (ISWCS), Oulu, Finland,
27-30 Aug. 2019. DOI: 10.1109/ISWCS.2019.8877135
Post-print
IEEE
2019
16th
International
Symposium
on
Wireless
Communication
Systems
(ISWCS)
10.1109/ISWCS.2019.8877135
© Copyright 2019 IEEE
GFDM-Based Cooperative Relaying Networks with
Wireless Energy Harvesting
Dick Carrillo Melgarejo
1
, Jules M. Moualeu
2
, Pedro Nardelli
1
, Gustavo Fraidenraich
3
, and Daniel B. da Costa
4
1
School of Energy Systems, LUT University, Finland
2
School of Electrical and Information Engineering, University of the Witwatersrand, South Africa
3
School of Electrical and Computer Engineering, University of Campinas, Brazil
4
Department of Computer Engineering, Federal University of Cear
´
a, Sobral, Brazil
e-mail: {dick.carrillo.melgarejo,pedro.juliano.nardelli}@lut.fi, jules.moualeu@wits.ac.za,
gf@decom.fee.unicamp.br, danielbcosta@ieee.org
Abstract—In this paper, the concept of wireless power transfer
and wireless information transmission, which have recently
received special attention for improving energy efficiency in
wireless communication systems, are investigated. In particular,
we focus on a cooperative communication network consisting of a
source node, an energy-constrained relay node and a destination
node. In contrast to conventional wireless-powered cooperative
networks, a GFDM waveform–which is an emerging candidate
waveform for the 5G mobile networks and beyond–is considered.
The performance of the proposed GFDM-based relaying network
with energy harvesting is studied in terms of the average BER for
the general M-QAM constellation set. Numerical and simulation
results are provided to give useful insights and to assess the
accuracy of our mathematical derivations.
Index Terms—Energy harvesting, GFDM ,relay networks,
BER, SWIPT.
I. INTRODUCTION
In recent years, many wireless technologies have adopted
the orthogonal frequency division multiplexing (OFDM)
scheme as a popular scheme for encoding digital data over
multiple carrier frequencies. The use of such a waveform
dates back from the introduction of the standard IEEE 802.11
(Wi-Fi) until the 3rd Generation Partnership Project (3GPP)
release 16, which is an evolution of the actual Long-Term
Evolution (LTE) technology that aims to support the fifth
generation (5G) of cellular connectivity [1], [2]. This pref-
erence is based on the fact that OFDM makes efficient use
of the spectrum, is computationally efficient to implement
modulation and demodulation functions with the adoption
of fast Fourier transform (FFT) techniques, and is relatively
simple from a receiver implementation viewpoint over var-
ious adaptive equalization techniques [3]. However, OFDM
has some disadvantages that have been well reported in the
current literature. For instance, high peak-to-average power
ratio (PAPR), sensitivity in intercarrier interference (ICI), and
the inefficiency of the cyclic prefix (CP) that fails when the
delay distribution in the channel is longer than the CP length,
are just some limitations of the aforementioned waveform [4].
In an effort to address these limitations, various techniques
have been proposed to support new wireless technologies
such as 5G and beyond. One, that has particularly received
a lot of interest recently, is the generalized frequency division
multiplexing (GFDM). GFDM is a non-orthogonal waveform
that can transmit multi-symbols per multi-carrier in a two-
dimensional block structure i.e., time and frequency, and which
can be achieved by a circular convolution of each sub-carrier
through pulse shaping [5], [6]. To overcome fading channels,
it dynamically adopts pulse shaping optimization in time and
frequency. All the aforementioned features enable GFDM to
achieve spectrum and energy efficiency when compared to
OFDM. However, GFDM also presents some disadvantages.
For example, in some cases, the effects of ICI and intersym-
bol interference (ISI) are significant since the variable pulse
shaping filters remove orthogonality between the sub-carriers.
One important design objective for 5G and beyond wireless
networks is energy efficiency. To overcome the bottleneck of
energy-constrained wireless devices, a promising solution that
prolongs their battery lifetime–making them self-sustainable
–has recently been proposed through energy harvesting (EH).
Traditional energy harvesting techniques rely on the surround-
ing environment using various natural sources such as wind,
solar, and thermal just to name a few. However, such EH
methods are often unstable due to the unpredictability of
the weather conditions, and therefore, are not suitable to
provide perpetual and ubiquitous energy demands. To this
end, an alternate approach that relies on radio frequency (RF)
signals has been proposed. RF signals, which are widely
considered as information carriers, can also be used as a
vehicle for transporting energy [7]–[9]. In other words, RF
signals become a potential source of wireless power transfer
(WPT) and wireless information transfer (WIT). In light of
this, a simultaneous wireless information and power transfer
(SWIPT) scheme, which is based on the simultaneous transport
of energy and information through the ambient RF signals, has
been regarded as a sustainable approach [10].
Due to the versatility of RF signals to carry both energy
and information, a SWIPT technique is naturally applicable
to dual-hop cooperative relaying networks which have been
widely investigated in the current literature [10]–[12]. In that
context, a relay device is kept active without relying on
conventional power sources. Current studies on SWIPT relay
architectures consider either OFDM or other general waveform
models with multiple-input multiple-output (MIMO) setups.
However, the above-mentioned waveforms lack some degree
of flexibility necessary to address all the requirements for
the 5G technology. To this end, to further support flexibility
in terms of resource allocation while improving the quality
of the user experience and improving the battery lifetime of
an energy-constrained device, a GDFM transmission can be
incorporated in an EH-based cooperative relaying network.
In [13], a GFDM-based cooperative decode-and-forward (DF)
relaying network is proposed. In that work, the relay node
performs WIT and WPT to the destination node using different
GFDM sub-block sets. However, such a setup (with GFDM
and EH receivers at the destination) has some limitations due
to the high implementation cost associated with computational
resources. Thus, this renders work of [13] less attractive for
energy-constrained devices such as internet-of-things (IoT)
devices or wireless sensors.
To the best of the authors’ knowledge, one can affirm that
there is no work on GFDM-based amplify-and-forward (AF)
cooperative EH-relaying with SWIPT. To partly fill this gap,
we propose a GFDM and EH-based cooperative AF relaying
network, wherein the relay node scavenges energy from the
source node in order to forward the source information to the
destination node which employs a minimum mean square error
(MMSE) receiver. Unlike in [13], the energy-constrained relay
node employs an AF protocol, and therefore, does not require
to perform any demodulation of the GFDM signal. Moreover,
we derive an analytic bit error rate (BER) expression of
the proposed system for a general M-quadrature amplitude
modulation (QAM) constellation set. Monte Carlo simulations
are provided in order to assess the accuracy of the proposed
mathematical derivations.
The remainder of this paper is structured as follows. Section
II describes the system model considered in this work. In Sec-
tion III, the performance of the proposed system is investigated
by deriving an expression of the average BER. Numerical
and Monte Carlo simulations are provided in Section IV, and,
finally, Section V gives some concluding remarks.
II. SYSTEM MODEL
Consider a wireless network shown in Fig. 1, consisting of
a base station, S
t
, an energy-constrained relay node, R, and
a mobile user, D. All the nodes are equipped with a single
antenna. It is assumed that no direct link exists between S
t
and D due to poor channel conditions or heavy shadowing.
To this end, the transmission of GFDM symbols takes place
in two time slots. In the first time slot, S
t
transmits to R,
wherein EH by employing a SWIPT scheme is used over a
high signal-to-noise ratio (SNR) regime. Then, R amplifies
the received signal from the source and forwards to D in the
second time slot. It is assumed that all the received signals are
corrupted by additive white Gaussian noise (AWGN) and the
fading channels are assumed to be quasi-static. It is worthwhile
mentioning that the channel state information (CSI) is known
at the receiver. A detailed description of the system model is
First time
slot:
Second time
slot:
S
t
R
D
GFDM
Transmitter
MMSE
receiver
Energy
harvesting
receiver
Relay
Attenuator that avoids
direct connectivity
between S
t
and D
High SNR
regime
Fig. 1. Illustration of a GFDM-based cooperative EH-relay system.
presented subsequently. In what follows, we briefly revisit the
concept of GFDM followed by the one on SWIPT.
A. GFDM system
The system is designed to transmit a complex symbol
block d
s,k
from S
t
to D at the sth time instance and kth
subchannel containing S ˆ K data symbols, s “ 0, . . . S ´ 1,
k “ 0, . . . K´1. We assume that data symbols are independent
and identically distributed (i.i.d.). In this regard, the GFDM
signal can be given by
xrns “
S´1
ÿ
s“0
K´1
ÿ
k“0
d
s,k
g
s,k
rns, (1)
in which g
s,k
rns is the circular time-frequency shifted version
of the prototype filter grns expressed as
g
s,k
rns fi grpn ´ sKq
N
s e
j2πnk{K
, (2)
where N “ S ˆK and p.q
N
is the modulo operator. Note that,
in order to facilitate a circular convolution, the transmitter
filter grns is circular with a period of n mod N . It is also
important to remark that in (2), the GFDM shifting step is K
and 1{K in time and frequency domains, respectively. Next,
the transmitter and receiver blocks are described .
1) Transmitter: The modulated signal in (1) can be further
expressed in a matrix notation form, wherein all the elements
of the transmit symbol block are organized in a single vector
as d “ rd
T
0
, . . . d
T
s´1
s
T
, in which s “ 0, . . . S ´ 1, and d
s
“
rd
s,0
, . . . d
s,K´1
s
T
with variance σ
2
d
. The vector form of xrns
for n “ 0, . . . N ´ 1 can be written as
x “ Ad, (3)
where x “ rxr0s, . . . xrN ´ 1ss
T
and A, of dimension
N ˆ N , is the modulation matrix or self-interference matrix
of GFDM defined as A “ rG
0
, . . . G
S´1
s, in which G
s
,
for s “ 0, . . . , S ´ 1 , is the N ˆ K matrix of g
s,k
rns
coefficients, such that
G
s
“
»
—
—
—
—
–
g
s,0
r0s g
s,1
r0s ¨ ¨ ¨ g
s,K´1
r0s
g
s,0
r1s g
s,1
r1s ¨ ¨ ¨ g
s,K´1
r1s
.
.
.
.
.
.
.
.
.
.
.
.
g
s,0
rN ´ 1s g
s,1
rN ´ 1s ¨ ¨ ¨ g
s,K´1
rN ´ 1s
fi
ffi
ffi
ffi
ffi
fl
.
(4)
A cyclic prefix (CP) of length N
cp
is added to the GFDM
signal x to prevent inter-block interference over a frequency-
selective channel (FSC). Therefore, the transmitted signal is
given by x
cp
“ rxpN ´ N
cp
` 1
:
Nq; xs.
2) Receiver: We assume a zero-mean circular symmetric
complex (ZMCSC) Gaussian Channel h “ rh
1
, h
2
, ¨ ¨ ¨ , h
L
s
T
where h
r
, with 1 ď r ď L, represents the complex baseband
channel coefficient of the rth path. We also consider that
N
cp
ě L, and the channel coefficients related to differ-
ent paths are uncorrelated. The received vector of length
N
t
“ N
cp
` N ` L ´ 1 is given by y
cp
“ h ˚ x
cp
` ν
cp
,
where the symbol p˚q denotes the linear convolution, ν
cp
is
the AWGN vector of length N
t
with variance σ
2
ν
. On the
receiver side, CP is removed. As a consequence, the frequency-
domain equalization (FDE) properties can be exploited, and
the linear convolution in (5) yields to a circular convolution.
The resulting vector becomes
y “ H
ch
Ad ` ν, (5)
where ν is the AWGN vector of length N with variance σ
2
ν
and H
ch
is the N ˆN circular Toeplitz matrix based on vector
h and given as described in [14] by
H
ch
“
»
—
—
—
—
—
—
—
—
—
—
—
–
h
1
0 ¨¨¨ 0 h
L
¨¨¨ h
2
h
2
h
1
¨¨¨ 0 0 ¨¨¨ h
3
.
.
.
.
.
.
¨¨¨
.
.
.
h
L
h
L´1
¨¨¨ ¨¨¨ ¨¨¨ ¨¨¨ 0
0 h
L
¨¨¨ ¨¨¨ ¨¨¨ ¨¨¨ 0
.
.
.
.
.
.
¨¨¨
.
.
.
0 0 h
L
¨¨¨ ¨¨¨ h
1
fi
ffi
ffi
ffi
ffi
ffi
ffi
ffi
ffi
ffi
ffi
ffi
fl
. (6)
In order to estimate the transmitted complex data sym-
bols, we considered a MMSE receiver matrix ppI
N
`
pH
ch
Aq
:
pH
ch
Aqq
´1
pH
ch
Aq
:
, in which the operator p.q
:
rep-
resents the Hermitian-conjugate of a matrix, I
N
is a N ˆ N
identity matrix, and p is the average SNR given as p “ σ
2
d
{σ
2
ν
.
Conditioned on the matrix pH
ch
Aq, the signal-to-interference-
and-noise ratio (SINR) on the nth data symbol can be ex-
pressed as
γ
n
“
1
MMSE
n
´ 1 “
1
“
pI
N
`
p
N
pH
ch
Aq
:
H
ch
Aq
´1
‰
nn
´ 1.
(7)
Note that (7), given in the same form as [15, Eq. 7.49],
is derived based on the second-order statistics of the input
signals, not restricted to binary signals [16]. The ´1 term in
(7) is to account for bias [17].
B. TSR Protocol
Here, we consider an ideal scenario where the information
transfer receiver and the EH at the relay can operate simulta-
neously, and have access to the total received signal and its
energy.
1
In the time-switching relaying (TSR) protocol, the node R
switches between information detection and EH during the
transmission block T. Let υ denote the percentage of the block
time T to perform simultaneously information reception and
energy harvesting on the node R with 0 ď υ ă 1. In second
half of the block time p1 ´ υqT, R re-transmits the received
signal from the source to D using AF.
1) Source-to-relay information and power transfer: In this
work, it is assumed that both information and energy receivers
are designed to operate at the same location [19]. Therefore,
the information transmission and energy transfer are charac-
terized by the same channels M. Other important assumption
on the system model is that the matrix M is composed by the
product of an identity matrix
2
I and a constant channel gain
m defined by M “ mI. For the case of information transfer,
the received vector y at the relay node is given by Eq. (5) and
Eq. (3),
y
r
“ Mx ` ν
r
, (8)
where x is defined in (3), and the noise is defined by the
AWGN vector ν
r
with zero mean and variance equal to σ
2
r
.
For the case of energy transfer, the EH receiver converts the
RF signal y
r
to a direct current (DC) using a rectifier without
the need for the conversion from RF band to baseband [19].
So, the harvested energy at the relay, in units of energy, is
given by
Q
r
“
1
2
ζ E
„
kM xk
2
“ ζ trpMPpMq
:
q, (9)
where ζ P r0, 1s is the conversion efficiency and trp¨q denotes
the trace operator. The matrix P is the covariance of the vector
x given by Erxx
:
s. As aforementioned, d
s,k
is a GFDM-
generated data symbol, and the filter prototype power in (1) is
assumed to be g
s,k
rns “ 1. Thus, the variable P is an identity
matrix, and as a result, the harvested energy Q
r
will depend
only on the channel matrix M. The used energy at the relay
is defined as E
u
and is either varying or constant given by
E
u
“
#
¯
E
u
, if the used energy is constant,
β Q
r
, otherwise,
(10)
where β is the ratio of the harvested energy to the used energy,
with 0 ď β ď 1, and E
u
ď Q
r
. According to previous
definitions, the transmit power at the relay node using the
whole frame transmission size is given by
P
r
“ 2E
u
. (11)
1
In the existing literature, many practical schemes that separate WPT and
WIT have been proposed. One of these schemes is known as power splitting,
which is developed on the power domain [18], while the other scheme based
on the time domain is known as time switching [7].
2
Justified because the source-to-relay system is operating on a high SNR
regime, which is an ideal condition for EH.
As stated in [18], we assume an infinite capacity storage on
relay node. In this work, and without loss of generality, it is
assumed that the power at the energy-constrained relay node
is constant i.e., E
u
“
¯
E
u
.
2) Relay-to-destination transmission: The received vector
at the destination is defined by y
d
given by
y
d
“ H
ch
y
r
` ν
d
. (12)
After substituting (8) in (12), the following is obtained
y
d
“ H
ch
Mx ` H
ch
ν
r
` ν
d
(13)
where ν
d
is the AWGN vector whose entries are i.i.d. with
zero mean and variance equal to σ
2
d
. The signal y
d
should
be constrained by the gain transmission at the relay node, as
elaborated subsequently.
C. Power transmission gain in the relay
Based on the previous consideration, in (12), it is assumed
that the term H
ch
ν
r
is not significant compared to ν
d
i.e.,
σ
2
r
! σ
2
d
3
. In addition, the term H
ch
Mx, that represents the
product of a circular Toeplitz matrix H
ch
with matrix M results
in a circular Toeplitz matrix M
ch
, similar to the matrix defined
in (6).
Another important fact to consider in the system model
is that the EH-relay system considers the TSR protocol,
which was explained before. Based on the aforementioned
discussions, the received signal at the destination node D can
be simplified to
y
d
« M
ch
x ` ν
d
, (14)
where the power gain at the relay node is defined as
g
υ
“
#
p1 ´ υqP
r
, scenario 1,
p1 ´ υqpυqP
r
, scenario 2.
(15)
with scenario 1 representing the case in which the energy
stored in the relay battery is always guaranteed, available, and
potentially the RF-EH system is complemented by other EH
system as for example photo-voltaic source. In this way, the
power gain used to transmit from the relay node depends only
on the frame window available for transmission, which is equal
to 1 ´ υ. In scenario 2, which is a more economical case, the
power gain used for energy transfer depends on the portion
of the frame used for EH and the portion of the frame used
for information transmission i.e., pυq and p1 ´ υq. In both
scenarios, the power gain is always constant, because υ and
P
r
pE
u
q are constant, and E
u
ď Q
r
. Since it is assumed a
constant power transmission in relay, increasing the period for
harvesting implies in a smaller gain for g
υ
.
3
Such an assumption is practical since the relay node is an internet of things
(IoT) device operating on a high SNR regime, and therefore, its receiver noise
power can be negligible in comparison to the additive noise at the destination
node.
III. PERFORMANCE ANALYSIS
A. BER calculation
Assuming a M-QAM constellation, the conditional BER
denoted by P
b
pE|γ
n
q, is approximated using a general math-
ematical formulation [20]. The average BER is given by
P
b
pEq “
1
N
N´1
ÿ
n“0
ż
8
0
P
b
pE|γ
n
q p
γ
pγ
n
q dγ
n
, (16)
where with the help of (14) and the constraint of (15), the
probability density function (PDF) p
γ
pγ
n
q can be approxi-
mated by [21]
p
γ
pγ
n
q «
1
Γpκq θ
κ
p1 ` γ
n
q
´1´κ
exp
ˆ
´
1
p1 ` γ
n
qθ
˙
, (18)
where θ “ σ
2
{µ and k “ µ
2
{σ
2
,
µ “ Erα
n
s “ ´
N
ÿ
j“1
„
1
Ψ
2
j
exp
˜
N
Ψ
2
j
¸
Ei
´
´
N
Ψ
2
j
¯
, (19)
σ
2
“ Erα
2
n
s ´ pErα
n
sq
2
“
N
ÿ
j“1
„
1
NΨ
2
j
`
1
Ψ
4
j
exp
˜
N
Ψ
2
j
¸
Ei
´
´
N
Ψ
2
j
¯
´
1
Ψ
4
j
exp
˜
2N
Ψ
2
j
¸
Ei
2
´
´
N
Ψ
2
j
¯
, (20)
α
n
“
1
γ
n
`1
, Eipxq is the exponential integral function, and
Ψ
2
j
“ 2 p g
υ
Φ
2
|χ
j
|
2
, (21)
with Φ
2
“
ř
N
r“1
σ
2
r
. |χ
j
| being the eigenvalue j of A with
j “ 1, ¨ ¨ ¨ N. Plugging in (18) in (16) and after performing
some mathematical manipulations, the average BER can be
expressed as in (17) at the top of the next page.
From (21), it can be observed that when the gain g
v
increases, the mean and the variance defined in Eq. (19) and
(20), respectively, will vary, and consequently the PDF defined
in (18) will also vary. Hence, the BER defined in (16) is
dependent on g
υ
.
Our model provides detailed explanation of the BER de-
pendency based on the PDF of γ
n
for different values of υ.
Fig. 3 shows the PDF of γ
n
for scenario 1. Here, when υ
increases the PDF is more concentrated in low SINR values,
which explains the poor performance.
The PDF of γ
n
is depicted in Fig. 4. In this figure, it can
be seen that the PDF that is less concentrated in low values
of SINR(γ
n
), is the one that corresponds to υ “ 0.5, which
provides the best BER performance.
IV. NUMERICAL RESULTS
In this section, some numerical results for the BER are
plotted against υ for a fixed SNR“ 20 dB (high power
regime), by considering the GFDM parameters: K “ 32
(subcarriers), S “ 3 (subsymbols), root raised cosine (RRC)
as the prototype filter, roll-off factor“ 0.9, L “ 2, and power
