Energy and Overhead Aware Adaptive Forwarding
Strategy for Multi-Hop Device-to-Device
Communications
Bleron Klaiqi, Xiaoli Chu, and Jie Zhang
Dept. of Electronic and Electrical Engineering, University of Sheffield,
Sheffield, S1 3JD, UK
Email: {b.klaiqi, x.chu, jie.zhang}@sheffield.ac.uk
Abstract—Device-to-device (D2D) communications in cellular
networks enable direct transmissions between user equipments
(UEs). If the source UE (SUE) and the destination UE (DUE)
are far away from each other or the channel between them
is too weak for direct transmission, then multi-hop D2D communications, where relay UEs (RUEs) forward the SUE’s data
packets to the DUE, can be used. In this paper, we propose
an energy-efficient adaptive forwarding strategy for multi-hop
D2D communications to optimally choose between the best RUE
forwarding (BRF) mode and the cooperative RUEs beamforming
(CRB) mode, depending on which of them provides the higher
instantaneous energy efficiency. We analyse the associated average energy efficiency considering the overhead for obtaining
channel state information, forwarding mode selection and cooperative beamforming. Simulation results show that multi-hop
D2D communications with the proposed adaptive forwarding
strategy exhibit a significantly higher energy efficiency than the
BRF, CRB, direct D2D communications and conventional cellular
communications.
Index Terms—D2D communications, energy efficiency, multihop, cooperative beamforming, overhead, cellular networks.
I. I NTRODUCTION
Different from conventional cellular communications, where
user equipments (UEs) communicate via the base station (BS),
device-to-device (D2D) communications enable UEs to communicate directly with other UEs in its vicinity using cellular
resources [1]-[3]. D2D communications show potential for
three types of gains: proximity gain, reuse gain and hop gain
[4].
In practice, D2D UEs might not be close to each other
or the channel conditions between them could be so poor
that direct D2D communications would be impossible. Under
these circumstances, relays could assist the communication
between D2D UEs [5]-[8]. In [5], a distributed best relay
selection method for D2D communications underlaying cellular networks was proposed, where the best relay among the
ones that will not cause much interference to the cellular
network was selected. Multi-hop UE relaying for sending
emergency messages from disconnected areas was studied in
[6]. For L3 relay assisted D2D communications underlaying
LTE-A cellular networks, a gradient-based distributed resource
This work was partially supported by the EC H2020 Project DECADE
(MSCA-RISE-2014-645705).
allocation scheme was proposed in [7]. In [8], energy and
spectral efficiency of multi-hop D2D communication using
single relay is analysed.
In the works mentioned above, the overhead for obtaining
channel state information (CSI) and for performing relay selection in multi-hop D2D communications has been neglected.
D2D communications have not been considered in the existing
works that analyze the overhead costs for implementing cooperative relaying in practical systems and the related energy
consumption [9]-[13]. Nevertheless, these schemes select the
number of relays based on the size of decoding relay set,
which requires the knowledge of decoding set size and the
availability of a lookup table (containing the optimal number
of selected relays for any possible size of decoding set and
location of cooperating relays) at the source [9]-[11][13] or at
the destination [12].
In this paper, we propose a distributed adaptive forwarding
strategy that optimally switches between the best relay UE
(RUE) forwarding (BRF) and cooperative RUEs beamforming
(CRB). The adaptive forwarding strategy considers the overhead energy consumption for obtaining CSI, forwarding mode
selection and cooperative beamforming as well as the maximum transmission power constraint and channel coherence
time. The proposed forwarding strategy is realized in two main
steps. In the first step, the best RUE with the strongest secondhop channel in the main-cluster that contains all correctly
decoding RUEs is selected using timers at RUEs. In the second
step, if the sub-cluster formed by RUEs with first-hop channels
at least as strong as that of the best RUE in the main-cluster
is not empty, then the best RUE in the sub-cluster is selected
to perform cooperative beamforming with the best RUE in the
main-cluster; otherwise, BRF is performed. In other words, in
the second step CBR is performed only if the instantaneous
energy efficiency is improved compared to BRF, where only
the best RUE in the main-cluster forwards the data.
The remainder of the paper is organized as follows. The
system model is presented in Section II. The proposed adaptive
forwarding strategy for multi-hop D2D communications is
described in Section III. Section IV analyses the energy
efficiency for multi-hop D2D communications utilizing the
proposed forwarding strategy, conventional cellular communi-
cations, and direct D2D communications. The simulation results are presented in Section V. Finally, the paper is concluded
in Section VI.
II. S YSTEM M ODEL
We consider D2D communications overlaying a cellular
network as depicted in Fig. 1. The source UE (SUE) intends
to transmit data packets to the destination UE (DUE). The
data transmission from SUE to DUE can be realized in three
different ways: conventional cellular communications via the
BS, direct D2D communications between SUE and DUE, and
multi-hop D2D communications through half-duplex decodeand-forward (DF) relay UEs (RUEs). The channel power gains
between any two nodes are exponentially distributed and are
represented as follows: hB is the channel power gain between
SUE and BS; h0 is the channel power gain between SUE and
DUE; hi (i=1,. . .,N ) denotes the channel power gain from
SUE to RU Ei ; gB is the channel power gain between BS and
DUE; and gi (i=1,. . .,N ) denotes the channel power gain from
RU Ei to DUE. We assume reciprocal channels and singlecellular
direct D2D
multi-hop D2D
ℎ1
SUE
ℎ |D| ℎ0
RUE2
r
ℎ𝐵
RUE1
𝑔2
RUE |D|
RUE𝑁
𝑔|D|
𝑇𝐶𝑂𝐻
𝑇𝑂𝑀
Training
(SUE->RUE)
𝑡0
Training
(DUE->RUE)
𝑡1
𝑇𝐸𝑀
Forwarding
Strategy
Selection
𝑡2
Data
Transmission
(SUE->RUE)
𝑡3
Data
Transmission
(RUE->DUE)
𝑡3 + 𝑇𝐸𝑀 /2 𝑡3 + 𝑇𝐸𝑀
Fig. 2: Timing diagram for multi-hop D2D communications
with the proposed forwarding strategy selection.
A. Training
ℎ2
ℎ𝑁
We propose an adaptive forwarding strategy for multihop D2D communications to dynamically switch between the
best RUE forwarding (BRF) mode and the cooperative RUEs
beamforming (CRB) mode in a distributed manner depending
on which of them provides the higher instantaneous EE. The
proposed forwarding strategy is summarized in Algorithm 1
and is explained in the following.
As shown in Fig.2, multi-hop D2D communications with
the proposed forwarding strategy have three main activities:
training for acquisition of CSIs for both hops at each RUE,
forwarding mode selection, and data transmission.
𝑔1
𝑔𝑁
𝑔𝐵
DUE
BS
Fig. 1: Different communication modes between SUE and
DUE.
antenna nodes that are subject to the additive white Gaussian
noise (AWGN) with power spectral density of N0 . Perfect
channel estimation at each node is assumed. The communication between each pair of nodes is performed with fixed
rate R (bits/symbol) and bandwidth B (Hz). We consider the
scenario with orthogonal channel allocation between cellular
and D2D communications [8]. All UEs and the BS are subject
UE
to the maximum transmission power constraints of PM
AX and
BS
PM AX , respectively.
III. M ULTI -H OP D2D C OMMUNICATIONS WITH THE
P ROPOSED A DAPTIVE F ORWARDING S TRATEGY
In multi-hop D2D communications, SUE transmits its data
to DUE with the help of DF RUEs that forward the decoded
data to DUE.
During the training stage, NT training symbols are transmitted from SUE to RUEs and from DUE to RUEs at time instants
t0 and t1 , respectively. The N available RUEs estimate the
corresponding channels. It is assumed that RU Ei (i=1,. . .,N )
are relatively close to each other resulting in approximately the
same distance to SUE (dSR ) and to DUE (dRD ), respectively.
The energy consumption for the training stage can be
calculated as follows
ETM = PTS,M + PTD,M NT TS ,
(1)
R/B
d
where PTS,M = h̄M1−2
P , h̄M = 1/ PLD dξSR
, and
ln(1−δout ) N
D,M
ξd
1−2R/B
= ḡM ln(1−δout ) PN , ḡM = 1/ PLD dRD ; h̄M and
PT
ḡM denote the corresponding mean channel power gains; PLD
is a path loss constant for D2D communications and ξd is the
path loss exponent;
All RU Ei (i=1,. . .,N ) with the channel power gains
hi no less than the threshold for successful decoding
UE
θth = (2R/B − 1)PN /PM
AX become part of the main-cluster
D = {RU E1≤i≤N : hi ≥ θth }.
B. Adaptive Forwarding Strategy
At time t2 , the procedure for forwarding strategy selection
is initiated, and each UE belonging to the main-cluster D
starts a timer τj = λ/gj , where λ is a constant parameter
in unit of time [14]. The RU E1:|D| with the shortest timer
τ1:|D| , i.e., the strongest channel to DUE, becomes part of the
forwarding set F = {RU E1:|D| } and transmits NT training
symbol to SUE with transmission power PTR,M = PTS,M . SUE
performs channel estimation to obtain the first-hop CSI of
RU E1:|D| and calculates the minimum transmit
power to
I
reach RU E1:|D| , PD,1:|D|
= 2R/B − 1 PN /h1 . Due to
the broadcast property
of wireless channels, other RU Ej ∈
D \ {RU E1:|D| } may still correctly decode data transmitI
ted with power PD,1:|D|
and can potentially improve EE
through CRB. Therefore, all RU Ej ∈ D \ {RU E1:|D| }
put their timers on hold when they overhear the transmission
from RU E1:|D| . Since RU Ej ∈ D \ {RU E1:|D| } do not
I
know PD,1:|D|
and hence do not know whether they can
improve EE or not, SUE broadcasts a triggering symbol
with
I
power PD,1:|D|
. All RU Ej ∈ D \ {RU E1:|D| } that can
correctly
decode this symbol constitute the RUE sub-cluster
R/B
S = RU Ej ∈ D \ {RU E1:|D| } : hj ≥ (2 P I −1)PN and
D,1:|D|
resume their timers.
The best RUE in the sub-cluster S, RU E1:|S| , with the
shortest timer τ1:|S| becomes part of F if it improves the
instantaneous EE and the time consumed for overhead to
perform relay selection and cooperative beamforming is not
bigger than t3 − t2 . In this case, CRB is selected as the
forwarding strategy and RU E1:|S| transmits a notification
ξ
1−2R/B
PLD (2r) d PN to satsymbol with power PNR,M = ln(1−δ
out )
isfy target outage probability δout at the maximum distance
2r, where r is the radius of main cluster D. As soon as
receiving the notification symbol
from RU E1:|S| , the other
RU Ej ∈ S \ {RU E1:|S| } with unexpired timers reset
their timers and do not participate in the cooperative data
transmission. If RU E1:|S| cannot improve the instantaneous
EE or the time consumed for related overhead exceeds t3 − t2 ,
then BRF is chosen as the forwarding strategy.
The energy consumption for the proposed adaptive forwarding strategy is given by
R,M
R,M
M
I
ES,F = NT PT
+ PD,1:|D| + (|F| − 1)PN
TS . (2)
Algorithm 1: Multi-hop D2D communications utilizing
the proposed adaptive forwarding strategy.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
C. Data Transmission
At time t3 , the data transmission stage starts. The effective transmission time for multi-hop D2D communications is
TEM = TCOH − TOM , where TOM denotes the corresponding
time consumption for overhead and is given by
(
λ/g1:|D| , BRF
M
TO = (3NT + |F|) TS +
,
(3)
λ/g1:|S| , CRB
In the first TEM /2 time interval, SUE transmits data packets
I
with transmission power PD,1:|D|
. These data packets are
decoded only by RU Ej ∈ F. In the second TEM /2 time
interval, RU Ej ∈ F forward the decoded data packets to
DUE.
The overall energy consumed for data transmission in multihop D2D communications using adaptive forwarding strategy
is given by
!
TEM
M
I
II
II
ED,F = PD,1:|D| + PD,1:|D| + PD,1:|S|
,
(4)
2
25
26
27
28
29
30
31
32
33
34
35
36
37
i = 1, l = 1, D = ∅, S = ∅;
SUE and DUE transmit NT training symbols with
powers PTS,M and PTD,M , respectively. Each
RU E1≤i≤N , estimates the corresponding hi and gi ;
UE
θth = (2R/B − 1)PN /PM
AX ;
while i ≤ N do
if hi ≥ θth then
D = D ∪ {RU Ei };
end
i = i + 1;
end
All RU Ej ∈ D, start timers τj = λ/gj ;
RU E1:|D| transmits NT symbols to SUE with power
PTR,M = PTS,M ;
DRES = D \ {RU E1:|D| };
Each RU El ∈ DRES , puts its timer on hold once it
overhears the transmission from RU E1:|D| ;
SUE transmits a triggering symbol with minimum power
I
to reach RU E1:|D| , PD,1:|D|
;
while l ≤ |D| do
I
if RU El ∈ DRES && hl ≥ (2R/B − 1)PN /PD,1:|D|
then
S = S ∪ {RU El };
end
l = l + 1;
end
F = {RU E1:|D| };
if |S| > 0 then
All RU Ei ∈ S resume their timers;
τ1:|S| = min τi ;
i
τO = τ1:|S| + (NT + 2)TS ;
M
M
if EEF
∪{RU E1:|S| } ≥ EEF && τO ≤ t3 − t2 then
F = F ∪ {RU E1:|S| };
RU E1:|S| transmits a notification symbol with
power PNR,M ;
All RU Ei ∈ S \ {RU E1:|S| } reset their timers;
end
end
I
;
SUE transmits data with power PD,1:|D|
if |F| == 1 then
RU E1:|D| forwards data to DUE with power
II
PD,1:|D|
;
else
RU E1:|D| and RU E1:|S| cooperatively beamform
II
II
data towards DUE with powers PD,1:|D|
and PD,1:|S|
,
respectively;
end
where PTS,C =
where
II
PD,1:|D|


1
R/B
g1:|D| (2
g1:|D|
− 1)PN , BRF
=
2R/B − 1 PN , CRB

2
(g1:|D| +g1:|S| )
II
=
PD,1:|S|

0, BRF
g1:|S|

(g1:|D| +g1:|S| )
2
2R/B − 1 PN , CRB
, (5)
, (6)
are the optimal transmission powers in the second-hop. For
CRB, RUEs transmit with optimal powers obtained in [15].
From (5) and (6) is seen that RU E1:|D| and RU E1:|S| need
to know each other’s channel power gains in order to calculate
the optimal transmission powers for CRB. RU E1:|D| and
RU E1:|S| can obtain each other’s second-hop channel power
gains in a distributed manner through overhearing the notification symbols sent upon expiration of their timers. Assume that
at time ts , RU E1:|S| overhears the notification symbol sent
from RU E1:|D| , then RU E1:|S| acquires g1:|D| = λ/(ts − t2 )
[11], where t2 is the time instant when all RU Ej ∈ D start
their timers. Similarly, g1:|S| can be calculated. Propagation
delays within the main cluster D are negligible compared to
RUE selection time.
IV. E NERGY E FFICIENCY A NALYSIS
A. Multi-Hop D2D Communications Based on Proposed
Adaptive Forwarding Strategy
Without loss of generality we assume that |S| > 0. In order
to ensure a minimum effective transmission time, overhead
time consumption for multi-hop D2D communications needs
to be bounded, i.e., TOM ≤ TM AX . The outage in multihop D2D communications occurs when the second-hop link
cannot support target rate R with maximum transmission
UE
power PM
AX or the time consumed for overhead exceeds
TM AX .
The instantaneous EE for multi-hop D2D communications
with the proposed adaptive forwarding strategy is given by
M
EEF
=
RTEM
M + EM
2 ETM + ES,F
D,F

M

1, BRF & g1:|D| ≥ θth & TO ≤ TM AX
1, CRB& g1:|D| + g1:|S| ≥ θth & TOM ≤ TM AX


0, otherwise
PTD,C =
c
h̄B = 1/ PLC dξSB
and
ξc
S,C
= 1/ PLC dBD ; PT and
1−2R/B
P ,
h̄B ln(1−δout ) N
1−2R/B
ḡB ln(1−δout ) PN ,
ḡB
PTD,C
are the required training transmit power levels from BS
to SUE and from BS to DUE, respectively, to satisfy target
rate R with outage probability δout ; TS = 1/B is symbol
duration; PN = N0 B denotes the noise power; h̄B and ḡB
are the mean channel power gains from SUE to BS and from
BS to DUE, respectively; PLC is a path loss constant for
cellular communications and ξc is the corresponding path loss
exponent; dSB and dBD denote the distances from SUE to BS
and from BS to DUE, respectively.
Once DUE has estimated its channel to the BS, it feeds
back the estimated CSI to BS using NF B symbols with
the minimum transmission
power that supports target rate R,
R/B
PFD,C
=
2
−
1
P
/g
N
B.
B
The energy consumption for the CSI feedback is given by
EFCB = PFD,C
B NF B TS .
(9)
During data transmission SUE transmits
data to BS with the
S,C
adaptive power, PD
= 2R/B − 1 PN /hB . BS forwards
BS
the received
data to DUE with transmission power PD =
R/B
2
− 1 PN /gB .
The overall energy consumption for the data transmission
is given by
C
S,C
C
BS TE
,
(10)
ED
= PD
+ PD
2
where TEC = TCOH − TOC is the effective transmission
time for cellular communications; TCOH denotes the channel
coherence time; TOC = (NT + NF B )TS is the time consumed
for overhead in the cellular mode. The factor 1/2 comes from
the two-hop half-duplex transmission.
The outage in the cellular communications mode occurs
when one of the links cannot support target rate R with
UE
maximum transmission power PM
AX .
The instantaneous EE for conventional cellular communications is given by

C
RTE

C +E C +E C , {hB ≥ θth } & {gB ≥ θth }
C
2
E
(
T
FB
D)
EE =
,
0, otherwise
.
(11)
C. Direct D2D Communications
(7)
The factor 1/2 is due to the two-hop half-duplex transmission.
B. Cellular Communications
In conventional cellular communications, SUE transmits
data to DUE via the BS. Prior to data transmission, NT
training symbols are broadcast from the BS to enable SUE
and DUE to estimate their channels to the BS.
The training broadcasting energy for reaching both SUE and
DUE is given by
n
o
ETC = max PTS,C , PTD,C NT TS ,
(8)
In direct D2D communications, SUE directly transmits
data to DUE. First, SUE transmits NT training symbols
R/B
PN . h̄0 =
to DUE with the power PTS,D = h̄0 1−2
ln(1−δ
out )
ξd
1/ PLD dSD is the mean channel power gain between SUE
and DUE; dSD denotes the distance from SUE to DUE.
The energy consumption for training can be calculated as
ETD = PTS,D NT TS ,
(12)
Then, DUE performs channel estimation and uses NF B
symbols to feed back CSI to SUE with power PFD,D
=
B
2R/B − 1 PN /h0 .
The energy consumption for the CSI feedback is given by
EFDB = PFD,D
B NF B TS ,
(13)
After reception of CSI, SUE is able to adapt its transmission
power to the minimum level required to support target rate R,
S,D
PD
= PFD,D
B , leading to the following energy consumption
for data transmission:
S,D D
D
ED
= PD
TE ,
TED
(14)
TOD
where
= TCOH −
is the effective transmission time
for direct D2D communications; TOD = (NT + NF B )TS is the
time consumed for overhead in direct D2D mode.
The outage in direct D2D communications occurs when the
channel between SUE and DUE cannot satisfy target rate R
UE
with PM
AX .
The instantaneous EE for this mode is given by
(
D
RTE
D +E D +E D , h0 ≥ θth
D
E
T
FB
D
.
(15)
EE =
0, otherwise
Fig. 3: Average EE versus dSR for different communication
modes and the proposed forwarding strategy with dSD =
200m, dSB = dBD = 300m, |D| = 10, and |S| = 5.
V. S IMULATION R ESULTS
The performance of the proposed adaptive forwarding strategy for multi-hop D2D communications in terms of average
EE is evaluated through simulation. Average EE is obtained
by averaging of instantaneous EE over 104 different channel
realizations. Main system parameters are listed in Table I.
During training, NT = 1 symbol is transmitted at the target
rate R with outage probability δout = 0.1. We consider 16QAM modulation (R = 4) and, the channel coherence time of
TCOH = 120 symbols, and TM AX = 0.25TCOH . DUE uses
NF B = 2 symbols to feedback CSI to BS or SUE. The radius
of main-cluster D is set to r = 5m.
and increases with increasing dSR . Cellular communication
is more energy-efficient than direct D2D communication due
to the lower path-loss that results in lower transmission power
required to satisfy target rate R and lower outage probability.
Fig. 4 plots the average EE versus dSD for dSR = 0.1dSD
and dSB = dBD = 300m. We can observe that the proposed
forwarding strategy achieves the highest average EE. The EE
for direct D2D and multi-hop D2D communications decreases
with increasing dSD due to increasing transmission power
and higher outage probability. For dSD ≥ 135m, direct
D2D communication is even less energy-efficient than cellular
communication.
TABLE I: System parameters
Bandwidth, B
10 MHz
Noise power spectral density, N0
-174 dBm/Hz
BS
Maximum BS Tx power, PM
AX
43 dBm
UE
Maximum UE Tx power, PM
AX
23 dBm
Path-loss for cellular communications
128.1 + 37.6 log10 [d(km)] dB
Path-loss for D2D communications
148 + 40 log10 [d(km)] dB
Fig. 3 shows the comparison of the average EE versus dSR
among the proposed adaptive forwarding strategy, conventional cellular communications, direct D2D communications,
BRF, and CRB for dSD = 200m and dSB = dBD = 300m.
The proposed adaptive forwarding strategy achieves the highest average EE and outperforms both conventional forwarding
strategies (BRF and CRB) for dSR < 100m, and is as energy
efficient as BRF for larger dSR . This is because the proposed
forwarding strategy selects optimally between BRF and CRB
based on their instantaneous EE. For all the three forwarding
strategies, the average EE initially increases with increasing
dSR due to reduction of transmission power and outage
probability in the second hop; after reaching the maximum,
the average EE decreases because the energy consumption
in the first hop dominates the overall energy consumption
Fig. 4: Average EE versus dSD for different communication
modes and the proposed forwarding strategy with dSB =
dBD = 300m, dSR = 0.1dSD , |D| = 10, and |S| = 5.
Fig. 5 plots average EE versus SUE or DUE to BS distance
(dSB or dBD ), where dSB = dBD [8] and dSD = 150m. For
dSB = dBD < 190m, it can be seen that cellular communica-
tion is more energy-efficient than other communication modes
due to lower transmission power and reduced outage probability. However, the average EE of cellular communications
decreases quickly with increasing dSB = dBD . For dSB =
dBD > 190m, the proposed forwarding strategy is more
energy-efficient than cellular communications and becomes the
most energy-efficient among all communication modes under
comparison. Furthermore, for dSB = dBD > 350m, direct
D2D communications outperforms cellular communications.
Fig. 5: Average EE versus dSB or dBD for different communication modes and the proposed forwarding strategy with
dSD = 150m, dSR = 0.4dSD , |D| = 10, and |S| = 5.
VI. C ONCLUSIONS
In this paper, we have proposed an adaptive forwarding
strategy for multi-hop D2D communications. In the proposed
strategy, the best RUE in the main-cluster, formed by all
successful decoding RUEs, either forwards the data alone, i.e.,
via BRF or cooperatively through CRB with the best RUE in
the sub-cluster, consisting of RUEs with first-hop channel not
weaker than that of best RUE in the main-cluster. The decision
to switch between BRF and CRB is made from best RUE in the
sub-cluster and based on instantaneous energy efficiency. We
performed EE analysis under maximum transmission power
and channel coherence time constraints, considering the related overhead. The simulation results revealed that multi-hop
D2D communications with the proposed adaptive forwarding
strategy is more energy-efficient than best RUE forwarding,
cooperative RUE beamforming, direct D2D communications
and conventional cellular communications.
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