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Multi-User Relay Selection for Full-Duplex Radio
Saman Atapattu, Prathapasinghe Dharmawansa, Marco Di Renzo, Chintha
Tellambura, Jamie Evans
To cite this version:
Saman Atapattu, Prathapasinghe Dharmawansa, Marco Di Renzo, Chintha Tellambura, Jamie Evans.
Multi-User Relay Selection for Full-Duplex Radio. IEEE Transactions on Communications, Institute
of Electrical and Electronics Engineers, 2019, 67 (2), pp.955-972. �10.1109/TCOMM.2018.2877393�.
�hal-02395808�
1
Multi-user Relay Selection for Full-Duplex Radio
Saman Atapattu, Member, IEEE, Prathapasinghe Dharmawansa, Member, IEEE,
Marco Di Renzo, Senior Member, IEEE, Chintha Tellambura, Fellow, IEEE, and
Jamie Evans, Senior Member, IEEE
Abstract—This paper investigates a user-fairness relay selection
(RS) problem for decode-and-forward (DF) full-duplex (FD) relay
networks where multiple users cooperate with multiple relays in
each coherence time. We consider two residual self-interference
(RSI) models with or without direct links. We propose a sub-
optimal relay selection (SRS) scheme which requires only the
instantaneous channel state information (CSI) of source-to-relay
and relay-to-destination links. To evaluate performance, the
outage probability of SRS is derived for different scenarios
depending on RSI models and the availability of direct links.
To further investigate, asymptotic expressions are derived for
the high transmit power regime. For comparison purposes, i)
the average throughputs of FD and half-duplex (HD) modes
are derived; ii) non-orthogonal transmission is considered and
its performance is discussed with approximations; and iii) the
impact of imperfect CSI is investigated with the aid of analysis.
While simulation results are provided to verify the analytical
results, they reveal interesting fundamental trends. It turns out
that a significant throughput degradation occurs with FD mode
over HD mode when self-interference is fully proportional to the
transmit power. Since all users can communicate in the same
coherence time with FD mode, these joint RS schemes are useful
for user-fairness low-latency applications.
Index Terms—Full-duplex communications, multiple-user net-
works, outage probability, relay selection, residual self-
interference, throughput.
I. INTRODUCTION
Conventional wisdom had been that a radio node cannot
simultaneously transmit and receive on the same frequency
band. Recently it has been discovered that full-duplex (FD)
radio not only able do that, but also avoids typical spectrum
splitting employed across forward and reverse links and hence
improves spectrum efficiency compared to conventional half-
duplex (HD) radio in which silent times lead to a loss of
spectral efficiency (also known as the multiplexing loss) [1].
For instance, FD nodes relaying can potentially double the
spectral efficiency achieved by the conventional HD relaying,
thereby extending network coverage while improving power
efficiency and robust connectivity [2]. However, since the
self-interference (SI) signal on a FD node can sometimes
be 100 dB above its legitimate received signal strength, the
benefits of FD radio are contingent on proper SI cancellation
[3]. Nevertheless, the measurement and fully suppression of
S. Atapattu and J. Evans are with the Department of Electrical and
Electronic Engineering, the University of Melbourne, Australia (e-mail:
{saman.atapattu, jse}@unimelb.edu.au).
P. Dharmawansa is with the Department of Electronic and Telecom-
munication Engineering, University of Moratuwa, Sri Lanka (e-mail:
prathapa@uom.lk).
M. D. Renzo is with the Laboratoire des Signaux et Systmes, CentraleSu-
plec, Universit Paris-Saclay, France (e-mail: marco.direnzo@lss.supelec.fr).
C. Tellambura is with the Department of Electrical and Computer Engi-
neering, University of Alberta, Canada (e-mail: chintha@ece.ualberta.ca).
SI is challenging even with the recent signal processing
breakthroughs [4].
Although multiple relays can improve error-rate and link-
reliability by exploiting multipath diversity, overall spectral
efficiency can be affected because of the need for one orthog-
onal channel per each relay. This in turn increases bandwidth
utilization, time slots or spreading codes. On the other hand,
because relay selection (RS) schemes activate only one or
few relays from a large set of nodes, resource utilization and
overhead do not scale up as rapidly. Instead, RS enjoys the best
of both techniques, e.g., spectral efficiency and full diversity
gains [5]–[7]. Although RS requires an exchange of channel
state information (CSI) between the nodes, such multiplexing
losses can be recovered under the constraint of very limited
feedback [8]. The RS with FD radios is important because
it provides better diversity-multiplexing gain tradeoff (DMT)
at least at the high multiplexing gain regime where the FD
achieves a better multiplexing gain than that of the HD [9].
Effective FD RS strategies are thus the main focus of this
paper.
A. Related work
FD RS strategies have been considered for one-way commu-
nication [10]–[14], two-way communication [15]–[17], cog-
nitive radio [18], device-to-device (D2D) [19], physical-layer
security [20], energy harvesting [21], [22], and non-orthogonal
multiple access (NOMA) [23], to mention but a few. Outage
probability and asymptotic analysis of several RS schemes
which are based on the available channel state information
(CSI) are derived in [10]. A joint RS and power allocation with
outdated CSI is analyzed in [11]. Outage probability, average
symbol error rate, and ergodic capacity are derived for a joint
relay and transmit/receive antenna mode selection scheme in
[12]. In [13], channel capacities with RS are analyzed under
different adaptation policies including optimum power with
rate-adaptation and truncated channel inversion with a fixed
rate. For nodes distributed as a 2-D homogeneous Poisson
point process, an analytical framework is proposed to study
how RS strategies perform with HD and FD nodes by combin-
ing renewal theory and stochastic geometry in [14]. In [15], an
optimal RS scheme which maximizes the effective signal-to-
interference and noise ratio (SINR) is proposed and analyzed
for a two-way FD relay network. In [17], outage probability
based on max-min scheduling is analyzed for a two-way
multiple-user network where user pairs compete only for one
relay node. A multi-source multi-relay network is considered
with one destination for two-way network in [16], where the
best source is selected based on the instantaneous signal-to-
noise ratio (SNR) of the direct link and the best relay is
2
selected by using the max-min principle based on the selected
source. However, there is no simultaneous transmission from
all source nodes.
Optimal RS for the FD underlay cognitive radio networks
is analyzed with respect to the distributional properties of the
received SNR in [18]. A power-efficient RS scheme is for-
mulated as a combinatorial optimization problem to minimize
the power consumption of the mobile devices in multiple D2D
user pairs in [19]. The secrecy outage probability of a hybrid
RS scheme which switches between FD and HD modes is
studied in [20]. The FD RS for physical-layer security in a
multi-user network is recently considered under the attack of
colluding eavesdroppers in [24]. RS schemes for FD relay
networks with energy harvesting are considered for the power-
splitting protocol in [21] and the time-switching protocol in
[22]. In [23], the impact of RS on cooperative NOMA is also
investigated for both FD and HD modes by considering the
locations of relays where stochastic geometry tools are used.
B. Problem statement
As discussed above, in the existing literature, FD RS prob-
lems are limited to two scenarios: i) single source-destination
pair with multiple intermediate relays; ii) multiple sources
and multiple relays with single destination where only one
selected source communicates with the destination; or iii)
multiple source-destination pairs with single intermediate relay
where only one pair communicates at each coherent time
[25]. However, the model of single source-destination pair per
coherence time has limited applications as wireless systems
evolve from Long Term Evolution (LTE) to fifth generation
(5G), the number of active users per unit area is expected to
increase dramatically, making simultaneous communication is
a more urgent goal, with better resource utilization, supporting
ultra-reliable low-latency communication (URLLC) [26].
In FD relay studies [10], [11], it is commonly assumed
that no direct source-destination link exists because the direct
link is sufficiently weak due to obstacles and/or deep fading.
In HD relaying, however, a direct link is a great advantage
as the destination receives two copies of the same signal.
However, in FD mode, the relayed received signal at the
destination is the previous signal of the source. Unless the
source employs a smart strategy, e.g., coding such as space-
time code (STC), or destination employs a smart receiving
technique, e.g., buffering, this relayed signal interferes with
the direct-link received signal at the same time instance [27]–
[30]. In [31], the outage probability is derived for a basic
three-node FD relay network with direct link over Rayleigh
fading channels under distance-dependent path loss. Those
results reveal that the FD relay network can achieve the full
diversity order only when the self-interference is independent
of transmit power and when there is no direct link. In all
other cases, diversity gains are lost and an outage floor occurs.
Since existing FD RS is limited to single source-destination
pair, FD RS must be developed for multiple source-destination
pairs communicating via intermediate relays. Availability of
direct links and their interference are a special case of this
problem. This typical scenario has general applications in
future wireless systems, and the related FD RS has remained
widely open to date. Therefore, given this state-of-the-art, we
address this problem.
C. Challenges and contributions
With FD RS for multiple user pairs, we find the following
two challenges:
i) When a given relay cannot be shared by more than
one user and limited channel state information (CSI) is
available, the first challenge is to develop an RS scheme
which improves each individual user link as well as user
fairness. User fairness refers to the potential equality
of quality of service (QoS) parameters among different
users. In our problem, maximizing the SINR of the worst-
case link is a possible way to ensure fairness among
the users. For example, randomly choosing a relay, the
simplest RS scheme, does not need CSI but offers no
performance gains. On the other hand, with full CSI
availability, a naive RS strategy is to rank the best relays
and assign them to the users one by one. This scheme
clearly ensures QoS imbalances among users. Focusing
on user fairness, [32], [33] and [34] respectively proposed
and developed RS algorithms to find the set of paths that
maximizes the minimum end-to-end SINR of all users for
a full-CSI HD network and for a full-CSI FD network.
A crucial step in in-band FD communications is the full-
CSI estimation of time-varying self-interference channels
at relays and direct channels at destinations. Thus, in
practice, full-CSI may not be available at a central node
(relay selector) to perform such RS.
ii) The second challenge is the myriad of analytical diffi-
culties inherent in performance evaluation as all possible
user SINRs via multiple relays (see (4)) are non-identical
and also correlated random variables (rvs). In particular:
i) For a given user pair, a common direct link exists with
multiple relay links. Consequently, all possible end-to-end
SINRs via all relays are correlated due to this common
direct link, i.e., entries of each row of (4); and ii) For a
given relay, a common self-interference channel exists for
all users, and all possible end-to-end SINRs from all user
pairs via a given relay are correlated due to this common
SI, i.e., entries of each column of (4). Since the analysis
involves the order statistics of correlated rvs, this multi-
user RS problem is radically different from traditional
RS problems. This correlation among the rvs may also
be another reason for the lack of analysis of multi-user
FD networks thus far in the literature.
To address these challenges, this paper studies the RS
problem for multiple source-destination pairs and multiple
DF relays. In this respect, a recent paper [34] considered
Gaussian SI channels and having no direct links among source-
destination pairs. In contrast, in this paper, we consider the
more general scenario that the SI channel may either be
Gaussian noise or a random (fading) channel, and that direct
links may exist between source-destination pairs. The key
technical contributions are:
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Fig. 1: A full-duplex multiple-user pairs network with multiple
relays.
1) From practical point of view, we may reasonably assume
that the relay selector does not have knowledge of instan-
taneous direct channels and SI channels, but has partial
knowledge of them (statistics). Based on this realistic
assumption, we propose a sub-optimal relay selection
(SRS) scheme, which becomes equivalent to optimal relay
selection (ORS) if there are no source-destination direct
links and the SI channels are Gaussian.
2) We derive closed-form outage probability of FD SRS con-
sidering Rayleigh fading channels and for four different
scenarios based on SI models and the availability of direct
links. Asymptotic analysis is also provided to ascertain
the diversity order and the outage floor.
3) The average throughput of FD SRS is also derived for
comparison purposes. In particular, we compare it with
the HD mode, and also with interfering non-orthogonal
transmissions from source and relay nodes.
The rest of this paper is organized as follows. Section II
discusses the system model and RS scheme. Section III derives
the SRS performance analysis with exact and asymptotic
outage probabilities, and the average throughput. Section V
presents numerical results and discussions, followed by the
conclusions in Section VI. The respective proofs are relegated
to the Appendix.
II. SYSTEM MODEL
A. Network Model and assumptions
This work considers a general multiple source-destination
pairs dual-hop wireless relay network (Fig. 1), where the K
sources S
1
, . . . , S
K
(source-cluster) communicate with their
corresponding destinations D
1
, . . . , D
K
(destination-cluster)
via FD relays R
1
, . . . , R
N
(relay-cluster). Thus, we have K
user pairs, denoted as user k, k ∈ {1, . . . , K}. Each source
node and each destination node are single-antenna nodes. Each
FD relay has one transmit antenna and one receive antenna.
The power budget is fixed at p for each source and relay.
Different power levels can be considered for power allocation
problems, e.g. [35]. We assume that each user is helped by
one and only one relay, and each relay can help at most
one user. Thus, we need N ≥ K
1
. To avoid interference
among users, the users are assigned orthogonal channels using
frequency-division or time-division multiple access. It is also
important to note that almost all FD RS papers in the literature
omit the direct link by assuming that the direct channel is
sufficiently weak to be ignored due to obstacles and/or deep
fading, e.g., [10]–[14]. Unless we use an advanced signal
processing technique at the destination, the direct link signal
is interference to the FD relay signal. While this is a widely
accepted assumption in the literature, in practice, we may
still have an impact from weaker direct links in wireless
environments due to multipath propagation. We thus consider
a more general multiple-user and multiple-FD-relay network
with and without direct links as shown in Fig. 1. To treat the
direct link signal as a useful signal in FD RS, we need different
signal processing techniques and joint resource allocations
which moves this situation beyond the scope of this paper.
We assume independent small-scale multipath Rayleigh
fading for all the links along with large-scale path-loss fading.
Further, the distance between clusters is much larger than the
distance between the nodes in the same cluster. Therefore,
the channel gains and distances in a given hop are identical
while the channel gains and distances of the two hops are not
necessarily identical. The fading coefficient, channel variance
and distance between S
k
and R
n
(the first hop) are f
kn
,
σ
2
f
and l
sr
, respectively. Thus, all the f
kn
’s are independent
and identically distributed (i.i.d.) zero-mean complex Gaussian
with CN(0, σ
2
f
) for n ∈ {1, . . . , N} and k ∈ {1, . . . , K}.
Similarly, these parameters between R
n
and D
k
(the second
hop) are g
kn
, σ
2
g
and l
rd
, respectively, i.e., g
kn
∼ CN(0, σ
2
g
).
Further, those parameters of the direct link of user k are h
k
, σ
2
h
and l
sd
(≤ l
sr
+ l
rd
), respectively, i.e., h
k
∼ CN(0, σ
2
h
). Since
reception and transmission occur simultaneously, the R
n
relay
receives a self-interference via its channel e
n
. Moreover, f
kn
,
g
kn
, h
k
, and e
n
are independent but not necessary identical.
B. Analytical Model
Without loss of generality, the user k helped by R
n
is
elaborated here. We denote the information symbols of the
source S
k
and the relay R
n
as x
s
k
and x
r
n
, respectively,
with unit average energy (E
|x
s
k
|
2
= 1 where E [·] is
the expectation). At time t, the received signal at R
n
is
y
r,n
[t] =
q
p
l
η
sr
f
kn
x
s
k
[t] + i
n
[t] + n
r,n
[t], n = 1, . . . , N ,
where η is the path loss exponent, n
r,n
[t] is the additive
white Gaussian noise (AWGN) at R
n
with zero-mean and σ
2
r
variance, and i
n
[t] is the self-interference term.
1
The scenario K > N should be treated separately due to a number of
reasons. If each relay can help at most one user, in each coherence time, only
N users can be selected, e.g., random-user selection or best-N-users selection.
If each relay can help more than one user, all K users can communicate in
every coherence time by jointly allocating relays and powers. If there are direct
links, any user can communicate with its destination via either the direct link
or a relay link where at least (K − N ) users can use their direct links, given
that the direct-link carries useful information. Given these complexities, the
scenario K > N is beyond the scope of this paper and left as future research.
4
Residual self-interference (RSI) models: If no interference
cancellation is performed at R
n
, we may write i
n
[t] =
√
pe
n
x
r
n
[t] and x
r
n
[t] = ˆx
s
k
[t−1]. Here, the symbol ˆx
s
k
[t−1]
represents the decoded and forwarded information symbol at
the relay R
n
which was transmitted by S
k
in the previous
time-slot at time (t − 1). Then the signal i
n
[t] can dominate
y
r,n
[t] and can cause significant performance degradation [36].
To avoid this, each relay node applies some self-interference
cancellation, which results in RSI denoted as
˜
i
n
[t].
To avoid excessive interference, each relay node applies
some self-interference cancellation, which results in RSI de-
noted as
˜
i
n
[t] [37], [38]. The antenna isolation techniques such
as implementing a solid physical barrier between transmit and
receive antennas, utilizing directional antennas and exploiting
antenna polarization greatly mitigate the transmit power leak-
age especially via the line-of-sight (LoS) path. However, there
still exists RSI which is received due to the non-LoS multi-
path propagation. Among different options, the following two
RSI models which are often used in the literature are adopted
in this paper:
1) RSI Model I:
˜
i
n
[t] is a block-fading complex Gaussian
CN(0, σ
2
i
) variable, and the amplitude of RSI is thus
Rayleigh distributed. This model is valid when the trans-
mit signal from a relay returns to its receive antenna via
different multi-paths, and is used in [10]–[12] and many
more papers.
2) RSI Model II:
˜
i
n
[t] is i.i.d. with zero-mean, σ
2
i
variance,
additive and Gaussian, which has similar effect as AWGN
[2]. Based on the central limit theorem, the Gaussian
assumption holds in practice due to the various sources
of imperfections in the interference cancellation process.
This model is extensively used in the literature, e.g., [2],
[13], [16].
For performance analysis over block fading channels, the RSI
term is treated as a random variable only under Model I.
Further, the variance of the RSI depends on relay transmit
power and the SI cancellation technique. Since all relays have
the same transmit power P and the similar SI cancellation
technique is implemented at each FD radio, it is reasonable to
assume that RSI samples of all relays are i.i.d. By including the
impacts of several stages of cancellation into the RSI variance,
in general, it is modeled as σ
2
i
= ωp
ν
where the two constants,
ω > 0 and ν ∈ [0, 1], depend on the SI cancellation scheme
used at the relay [2]. One can thus investigate the effect of RSI
based on three cases: i) ν = 0; ii) ν = 1; and iii) 0 < ν < 1. In
terms of performance, the cases ν = 0 and ν = 1 represent the
best-case scenario and the worst-case scenario, respectively.
Since the performance of the case 0 < ν < 1 is in-between
those two cases [34], in this paper, we only consider ν = 0
and ν = 1.
We also define α
kn
= |f
kn
|
2
; β
kn
= |g
kn
|
2
; δ
k
=
|h
k
|
2
; and
n
= |
˜
i
n
|
2
. Then, we write channel gains in
the first-hop, second-hop, direct and self-interference links,
respectively, as H
1
= (α
kn
) ∈ R
K×N
; H
2
= (β
kn
) ∈
R
K×N
; D = (δ
k
) ∈ R
K×1
; and I = (
n
) ∈ R
N×1
. With
the DF relay R
n
, the received signal at D
k
is y
d,k
[t] =
q
p
l
η
rd
g
kn
x
r
n
[t] +
q
p
l
η
sd
h
k
x
s
k
[t] + n
d,k
[t], ∀k, where n
d,k
[t]
is the AWGN at D
k
with zero-mean and σ
2
d
variance. Since
D
k
interests on the relay signal x
r
n
[t], the direct link signal
x
s
k
[t] is an interference. Thus, the receive SINRs at relay R
n
(the first hop) and the destination D
k
(the second hop) can be
given, respectively, as
γ
kn,1
=
(
aα
kn
1+c
n
=
x
kn
1+u
n
; Model-I;
aα
kn
1+cσ
2
i
=
x
kn
1+cσ
2
i
; Model-II,
γ
kn,2
=
bβ
kn
1+dδ
k
=
y
kn
1+v
k
; with direct link;
bβ
kn
= y
kn
; without direct link,
(1)
respectively, where a =
p
l
η
sr
σ
2
r
; b =
p
l
η
rd
σ
2
d
; c =
1
σ
2
r
; d =
p
l
η
sd
σ
2
d
; x
kn
= aα
kn
; y
kn
= bβ
kn
; u
n
= c
n
; and v
k
= dδ
k
.
Thus, random variable Z ∈ {x
kn
, y
kn
, u
k
, v
n
}, is Exponential
probability density function (p.d.f.) and cumulative distribution
function (c.d.f.) given by
f
Z
(z) = λe
−λz
and F
Z
(z) = 1 − e
−λz
. (2)
Here, the parameter λ for Z ∈ {x
kn
, y
kn
, u
n
, v
k
} denoted
by λ ∈ {λ
x
, λ
y
, λ
u
, λ
v
}, respectively, takes the value λ
x
=
1
aσ
2
f
; λ
y
=
1
bσ
2
g
; λ
u
=
1
cσ
2
i
; and λ
v
=
1
dσ
2
h
.
The effective end-to-end receive SINR of user k helped by
the DF relay R
n
is given by
2
γ
kn
= min (γ
kn,1
, γ
kn,2
) . (3)
Thus, all possible user SINRs connected via any relay can
be given in matrix form as
Γ = (γ
kn
) ∈ R
K×N
. (4)
C. Max-Min Fairness Relay Selection (RS) Scheme
From Fig. 1, it is seen that each user has N possible paths
(relays). Since a relay cannot be shared between more than
one user, for a given relay assigned to one user, there are
(N − 1) possible relays for any next user. Likewise, there
are (N − K + 1) possible paths for the final user. We can
thus consider several possible RS schemes. But we know that
random RS has no performance improvement and naive RS
causes significant performance degradation for the final user
compared to the other users. Thus, we need an RS scheme,
which guarantees the individual performance as well as user
fairness, capable of choosing the set of paths that maximizes
the minimum end-to-end SINR of all users. Such an algorithm
is proposed for an HD relay network in [39]. Further developed
algorithm in [32] maximizes the minimum receive SINR of all
users, and guarantees an unique solution. The algorithm can
be performed on entries of the matrix Γ.
• Optimal RS (ORS) with global CSI: If a central node
(which may also be one of the nodes in given network)
has global channel knowledge, i.e., f
kn
, g
kn
, h
k
and
˜
i
n
∀k, n, to calculate Γ, the RS matrix for the ORS
scheme Γ
o
, i.e., max-min optimal, can be defined as
Γ
o
= Γ = (γ
o,kn
) ∈ R
K×N
where γ
o,kn
= γ
kn
. (5)
2
For AF relaying, the effective end-to-end receive SINR of user k can be
given by γ
AF
kn
=
γ
kn,1
γ
kn,2
γ
kn,1
+γ
kn,2
+1
. Since this can be upper-bounded as γ
AF
kn
≤
min
γ
kn,1
, γ
kn,2
, the results in this paper can be used as approximations
for AF relaying, especially in moderate and high SINR regions.
