Modelling and QoS-Achieving Solution in full-duplex Cellular Systems

Modelling and QoS-Achieving Solution in
full-duplex Cellular Systems
Ali Y. Al-Zahrani
Department of Electrical and Computer Engineering
University of Jeddah
Jeddah 21589, Saudi Arabia
Email: ayalzahrani1@uj.edu.sa
ABSTRACT
The global bandwidth scarcity and the ever-growing demand for fast wireless ser-
vices have motivated the quest for new techniques that enhance the spectral efficiency
(SE) of wireless systems. Most conventional SE increasing methods (e.g., adaptive
modulation and coding) have already been exhausted. Single-channel full-duplex
(SCFD) communication is a new attractive approach in which each node may simul-
taneously receive and transmit over the same frequency channel, and thus, it has
the potential to double the current SE figures. In this paper, we derive a model for
the signal-to-interference-plus-noise ratio (SINR) in a SCFD-based cellular system
with imperfect self-interference cancellation. Furthermore, given a set of uplink and
downlink quality of service requirements, we answer the following two fundamental
questions. First, is this set achievable in the SCFD-based cellular system? Second,
if the given set is achievable, what is the optimal achieving policy? To that end, we
provide a unified model for the SCFD-based cellular system, and give insights in the
matrix of interference channel gains. Simulation results suggest that depending on
the locations of the users, a combination of full-duplex and half-duplex modes over
the whole network is more favourable policy.
KEYWORDS— full-duplex, cellular network, self-interference, inter-cell interfer-
ence, resource allocations and interference cancellation
International Journal of Computer Networks & Communications (IJCNC) Vol.10, No.5, September 2018
117DOI:10.5121/ijcnc.2018.10507

1 Introduction
The ever-increasing demand for wireless services stresses on finding new methods that
increase the spectral efficiency. A recent method to enhance the spectral efficiency
is called single-channel full-duplex (SCFD) transmission. In SCFD, any wireless de-
vice is permitted to simultaneously receive and transmit information over the same
frequency channel. Traditionally, devices are able to transmit and receive either at
different instants or over different frequency bands [1].
Although SCFD transmission has the potential to double the spectral efficiency
[2], its successful implementation faces a major technical difficulty, that is self-
interference problem. self-interference is the interference caused by the terminal
on itself due to in-band and simultaneous transmission and reception (i.e., transmit-
ting a high power signal and receiving a weak power desired signal) [2,3].
self-interference can be classified according to its path into two types: direct-path
self-interference in which the transmit signal propagates directly from the transmit-
ting antenna to the receiving antenna, and reflected-path self-interference in which
the transmit signal is reflected by the surrounding environment to the receiving an-
tenna [4, 5]. Canceling the former is relatively simple using propagation-domain
techniques such as antenna polarization and antenna directionality [3,6–9] whereas
the latter needs additionally more sophisticated adaptive methods in both analog
and digital domains [10–16]. The degree of complexity depends on the bandwidth of
the transmit signal. In general, the narrower the signal’s bandwidth is the simpler a
design would be.
Since the transmitted signal is known to the terminal, one might suggest cancel-
ing the self-interference using any digital cancellation technique [19]. Although the
digital baseband interference cancellation helps alleviate the self-interference, it is
actually insufficient. The analog circuits in the front end of the transceiver and the
limited dynamic range of the analog-to-digital converter (ADC) distort the transmit-
ted signals. Thus, the digital interference cancellation becomes imperfect due to the
difference between the original signal and its distorted copy. Despite the progress
in the antenna designs and analog/digital cancellation techniques [3,6–16], the self-
interference is still above the noise floor, and hence can affect the detection of the
desired received signals. Therefore, the goal of completely doubling the spectral ef-
ficiency is hard to achieve without a tight interference control.
Because SCFD eliminates the in-band half-duplex constraint, which is a funda-
mental constraint in the conventional wireless networks [1], modeling and redesigning
many aspects of wireless networks must be considered in case of SCFD. In this paper,
we model the problem of inter-cell interference in multi-cell SCFD wireless systems
118

with imperfect self-interference cancellation. Then, we redesign the inter-cell inter-
ference control techniques under certain quality of service (QoS) requirements.
In cellular networks, there are two types of wireless full-duplex communications:
symmetric and asymmetric [2, 21]. In symmetric full-duplex communication, the
full-duplex transmission occurs between two nodes (usually the base station (BS)
and one user equipment (UE)). This kind of SCFD is sometimes called bidirectional.
On the other hand, the asymmetric half-duplex includes three nodes (usually BS,
downloader UE and uploader UE). In this research, we propose a unified model that
captures both kinds of SCFD [2,22].
In half-duplex transmission-based networks, spectrum sharing as well as inter-
ference management and power control have been studied very well. References
[20,23,24], for example, studied these issues in latest applications such as heteroge-
neous and device to device (D2D) networks. On the other hand, the area of SCFD-
based wireless networks has just got enough attention that produced some construc-
tive research results. However, very few papers in this domain consider large SCFD-
based cellular systems with imperfect self-interference cancellation. The authors
in [25] studied the end-to-end capacity of SCFD relaying with two modes: amplify-
and-forward and decode-and-forward. They evaluated the self-interference threshold
below which the full-duplex transmission outperforms the half-duplex transmission.
In their work, they considered the isolated system of 3 nodes only, that is one link
of two hops (source-relay-destination). In [26], a single cell full-duplex system aided
with the multi-input-multi-output (MIMO) technology was considered. The authors
exploited the large number of antennas at the BS for self-interference cancellation.
Optimal dynamic power allocation schemes for different scenarios were developed
in [4] with an objective of maximizing the sum rate of a SCFD bidirectional link.
However, the inter-cell interference was not considered. In [21], a simple decode-
and-forward full-duplex MIMO relaying, the transmitter/receiver dynamic range
limitations were modeled. More importantly, a tight upper and lower bounds on
the end-to-end achievable rate were derived. In addition, the authors proposed a
transmission policy that maximizes the lower bound.They also derived a theoretical
approximation of the achievable rate which helps to gain insights into the system
design tradeoffs. The authors in [22] analyzed the effects of adopting SCFD enabled
BSs in an OFDM multicell network with legacy UEs. However, in their work, the
perfect self-interference cancellation was assumed. In [17] the unique advantages of
FD radios are identified and the multi-input multi- output (MIMO) communication is
leveraged to translate the FD spectral efficiency gain at the PHY level to throughput
and power efficiency gain at the network layer. The authors in [18] studied two sce-
narios of full-duplex (FD) multiple-input?multiple-output cognitive radio networks:
119

: Desired signal
: Intercell interference
: Self interference
Figure 1: A full-duplex cellular network
FD cognitive ad hoc networks and FD cognitive cellular networks. Two optimization
problems were addressed: one is to minimize the sum of mean-squared errors (MSE)
of all estimated symbols whereas the other is to minimize the maximum MSE of
estimated symbols, both problems are subject to power constraints at the secondary
users and interference constraints projected to each primary users
The rest of this paper is organized as follows. In the next section, the setup of
the full-duplex cellular system is developed, and the mathematical model of a crucial
performance metric (SINR) is derived. In section 3, the feasibility of a given set of
target SINRs is addressed, and an optimal achieving policy is provided. Finally, the
conclusion of this research and possible future directions are discussed in section 5.
2 full-duplex System Model
We consider N full-duplex links each of which is located in a separate cell as shown
in Figure 1. The transmitter typically sends a signal x(t) to its intended receiver as
shown in Fig.(2). However, this signal is distorted by the RF analog circuits in the
transmitter front end. Moreover, after passing through the channel and corrupted
by the noise and diﬀerent interfering signals, the pre-ADC received signal u(t) im-
pinging the receiver antenna is distorted again by RF analog circuits and the ADC
120

UE_Tx Rf
Front Chain Chu
iu
(t)+n(t)
BS_Rx Rf
Front Chain yu
(t)=uu
(t)+eu
(t)
BS_Tx Rf
Front Chain xd
(t)Chd
Chud
Chdu
UE_Rx Rf
Front Chainyd
(t)=ud
(t)+ed
(t)
id
(t)+n(t)
Baseband channel BS baseband sideUE baseband side
+
+
Chu
Chd
Figure 2: A full-duplex baseband-equivalent system for both uplink and downlink
signals
in the receiver front end.Figure 2 shows the discrete-time baseband-equivalent model
for full-duplex (FD) link. This model, which is closely related to the model proposed
in [21], captures the effects of analog circuits and the limited dynamic range in both
sides of the link. The effect of the transmitter distortion is captured by injecting
an independent zero-mean Gaussian noise c(t) whose variance equals the power of
the intended signal x(t) times a constant parameter κ. This noise closely approxi-
mates the combined effects of additive power-amp harmonics, non-linearities in the
digital-to-analog converter (DAC) and power-amp, and oscillator phase noise [21].
Therefore, the baseband equivalent of the radiated signal is
s(t) = x(t) + c(t); suchthat



c(t) ∼ N(0, κ|x(t)|2
)
c(t) ⊥ x(t)
c(t) is white.
(1)
On the other hand, the effect of the receiving RF front end and the ADC is captured
by injecting an independent zero-mean Gaussian noise e(t) whose variance equals the
power of the pre-ADC received signal u(t) times a constant parameter β. Therefore,
the baseband signal after ADC would be
y(t) = u(t) + e(t); s.t.



e(t) ∼ N(0, β|u(t)|2
)
e(t) ⊥ u(t)
e(t) is white.
(2)
Note that κ 1 and β 1 are system parameters. The pre-ADC received signal
u(t) includes the desired signal, self-interference and inter-cell interference plus noise.
121

Thus, the pre-ADC received uplink and downlink signals at the nth
BS antenna and
its associated UE antenna would be respectively as follows
uu
n(t) = hu
nn(t) xu
n(t) + cu
n(t) + hud
nn xd
n(t) + cd
n(t) + iu
n(t) + nu
n(t); (3a)
ud
n(t) = hd
nn(t) xd
n(t) + cd
n(t) + hdu
nn xu
n(t) + cu
n(t) + id
n(t) + nd
n(t); (3b)
where the superscript d and u indicate downlink and uplink, respectively. hd
nn(t)
and hu
nn are the desired downlink and uplink channel responses. hdu
nn is the channel
response of the uplink to downlink self-interference (i.e., self-interference at UE)
whereas hud
nn is the channel response of the downlink to uplink self-interference(i.e.,
self-interference at BS). The additive white Gaussian noise processes at both receiving
ends are represented by nu
n(t) and nd
n(t). Finally, iu
n(t) and id
n(t) are the inter-cell
interference signals impinging the antennas of the nth
BS and its associated UE,
respectively. They can be expressed as
id
n(t) =
k∈N
k=n
hdd
nk(t)sd
k(t) + hdu
nksu
k(t) (4a)
iu
n(t) =
k∈N
k=n
hud
nk(t)sd
k(t) + huu
nksu
k(t) . (4b)
Using equations (2) and (3), the received baseband signals at both ends would
then be (after some arrangement)
yd
n(t) = hd
nn(t)xd
n(t)
Desired signal
+ hdu
nnxu
n(t)
self-interference
+ hd
nn(t)cd
n(t) + hdu
nncu
n(t) + ed
n + nd
n(t)
Aggregate noise due to Rf front ends distortions
+id
n(t);
(5a)
yu
n(t) = hu
nn(t)xu
n(t)
Desired signal
+ hud
nnxd
n(t)
self-interference
+ hu
nn(t)cu
n(t) + hud
nncd
n(t) + eu
n + nu
n(t)
Aggregate noise due to Rf front ends distortions
+iu
n(t).
(5b)
At every cell, we assume that the desired channels and the self-interference channels
are estimated correctly. Therefore, the ﬁrst term in the above two equations is the
desired signal. The self-interference in the second term is known and thus can be
canceled. The third term captures the aggregate distortions introduced by the front
end chains. The last term is the inter-cell interference.
&
122

After self-interference cancellation1
, the SINR at both ends can thus be written
as follows(suppressing the argument (t))
γd
n =



pd
ngd
nn
κpd
ngd
nn+κpu
ngdu
nn+β|ud
n|2+σ2
nd
n
+Id
n
for symmetric communication
pd
ngd
nn
κpd
ngd
nn+(1+κ)pu
ngdu
nn+β|ud
n|2+σ2
nd
n
+Id
n
for asymmetric communication
(6a)
γu
n =
pu
ngu
nn
κpu
ngu
nn + κpd
ngud
nn + β|uu
n|2 + σ2
nu
n
+ Iu
n
(6b)
where pd
n = |xd
n|2
and pu
n = |xu
n|2
are the downlink and uplink transmit power,
respectively. g = |h|2
is generally the power gain of a given channel h. While σ2
nn
is
the additive noise power, Id
n and Iu
n are the total inter-cell interference power affecting
the downlink signal and the uplink signal, respectively. According to (3), β|ud
n|2
and
β|uu
n|2
can be evaluated as follows
β|ud
n|2
= β (1 + κ)pd
ngd
nn + (1 + κ)pu
ngdu
nn + σ2
nd
n
+ Id
n (7a)
β|uu
n|2
= β (1 + κ)pu
ngu
nn + (1 + κ)pd
ngud
nn + σ2
nu
n
+ Iu
n . (7b)
In the last two equations, since κ 1 and β 1, any term which includes κβ is
considered significantly small, and hence it could be ignored. Therefore, the SINR
of both links is updated in the following equations
γd
n =
pd
ngd
nn
(κ + β)pd
ngd
nn + (PI + κ + β)pu
ngdu
nn + (1 + β)σ2
nd
n
+ (1 + β)Id
n
(8a)
γu
n =
pu
ngu
nn
(κ + β)pu
ngu
nn + (κ + β)pd
ngud
nn + (1 + β)σ2
nu
n
+ (1 + β)Iu
n
(8b)
where PI is an indicator parameter which equals 0 in case of symmetric communi-
cations and 1 for asymmetric communications. Since gd
nn gud
nn due to the incurred
path loss, the distortion (κ + β)pd
ngd
nn is usually ignored in all previously conducted
research on conventional half-duplex systems, with an implicit assumption that this
distortion arrives very faded and at the noise floor. Therefore, this part of distortion
may be regarded as part of the additive noise: (κ + β)pd
ngd
nn + (1 + β)σ2
nd
n
= σ2
o. A
similar argument can be made on the uplink. Thus, the SINR at both ends can be
1
In case of asymmetric communication (i.e., one UE transmits an uplink stream to the BS, while
another UE receives a downlink stream from the BS), then only BS can perform self-interference
cancellation, and the downlink user will regard the signal from the uplink user as an interference.
&
123

rewritten as
γd
n =
pd
ngd
nn
(1 + β)Id
n + (PI + κ + β)pu
ngdu
nn + σ2
o
γu
n =
pu
ngu
nn
(1 + β)Iu
n + (κ + β)pd
ngud
nn + σ2
o
(9)
This model includes the case of perfect self-interference cancellation. Authors
in [15] claimed that they cancelled the self-interference to the noise level. In this
case, κ, β = 0.
3 A Required QoS: Feasibility and Solutions
Any required quality of service (QoS) which basically consists of the minimum re-
quired data rate and the maximum probability of error, can be mapped into a certain
SINR target. This section derives a criterion on whether a given set of target SINRs
is achievable or not. To that end, we will ﬁrst consider the case of one cell network
(i.e., N = 1), afterward, a multi-cell case will then be derived by extension.
3.1 Single-Cell system
In the case of a single-cell full-duplex wireless system, Id
and Iu
are considered of
zero values. Let Γd
and Γu
be the target SINRs required for the downlink stream
and uplink stream, respectively. We are interested to answer two questions: 1) Is
this pair of required SINRs feasible (i.e., achievable)? 2) If it is feasible, what is
the best policy for achieving it? To answer these questions, let’s start from a basic
objective inequality in which the actual received SINRs at both ends are required to
be greater than or equal to the target SINRs
γd
≥ Γd
,
γu
≥ Γu
.
(10)
Substituting (9) into (10) produces
pd
≥
Γd
gd
((PI + κ + β)pu
gdu
+ σ2
o),
pu
≥
Γu
gu
((κ + β)pd
gud
+ σ2
o).
(11)
&
124

The above system of inequalities in (11) can be expressed in a matrix form as follows
p ≥ DGp + Dσ, (12)
where p = [pd
pu
]T
≥ 0. The 2 × 2 matrix D is a diagonal matrix which is equal to
diag Γd
gd , Γu
gu , whereas G is the self-interference channel gain matrix, that is:
G =
0 (P + κ + β)gdu
(κ + β)gud
0
. (13)
Finally, the noise vector equals σ = [σ2
o σ2
o]T
.
The central solution of (12) is
p ≥ [I − DG]−1
Dσ, subject to p ≥ 0, (14)
where I is the identity matrix. Notice that DG is a nonnegative matrix, and hence
the spectral radius2
ρ(DG) is an eigenvalue of DG [27]. According to the Perron-
Frobenius theory [27], the solution in (14) is a nonnegative transmit power vector if
and only if the spectral radius ρ(DG) is less than unity, mathematically,
[I − DG]−1
Dσ ≥ 0 ⇔ ρ(DG) < 1. (15)
Satisfying the nonnegative power constraint in (14) actually depends on the values
of Γd
and Γu
. Therefore, the pair of target SINRs is feasible iﬀ ρ(DG) < 1.
The solution p∗
= [I − DG]−1
Dσ is Pareto optimal since all other feasible solu-
tions require at least same power element-wise (i.e., p ≥ p∗
∀ p ≥ 0 satisfying (14)).
The policy in one cell system is as follows. Over the control channel, the UE sends the
BS the uplink target SINR Γu
and the estimated channel gain of the self-interference
gdu
. Since downlink and uplink transmissions occur over the same frequency band,
the downlink and uplink channels are reciprocal, and hence, gd
, gu
can be easily es-
timated at the BS. Using p∗
= [I − DG]−1
Dσ, the BS computes the best transmit
power for both uplink and downlink transmissions. Then, it dictates its associated
UE to act accordingly.
3.2 Multicell System
In a system of N cells, the required QoS for both uplink and downlink streams in
the nth
cell can be mapped into a pair of target SINRs Γd
n and Γu
n. To achieve the
&
125

pd
ngd
nn
(1 + β)
k∈N
k=n
gdd
nkpd
k + (1 + β)
k∈N
k=n
gdu
nkpu
k + (PI + κ + β)pu
ngdu
nn + σ2
o
≥ Γd
n, ∀n ∈ N
pu
ngu
nn
(1 + β)
k∈N
k=n
gud
nkpd
k + (1 + β)
k∈N
k=n
guu
nkpu
k + (κ + β)pd
ngud
nn + σ2
o
≥ Γu
n, ∀n ∈ N.
(16)
target QoS for both streams, the actual SINRs of both links have to equal at least
the target required SINRs Γd
n and Γu
n; that is,
Note that the ﬁrst two terms in the denominators account for inter-cell interference.
These two inequalities can be compacted in a matrix form that models the whole
system
p ≥ DGp + ν, (17)
where p = [pd
pu
]T
= [pd
1, ..., pd
N , pu
1, ..., pu
N ]T
is the vector of all downlink and
uplink transmit powers. The 2N × 2N matrix D is a diagonal matrix that equals
(1 + β)diag
Γd
1
gd
11
, ....,
Γd
N
gd
NN
,
Γu
1
gu
11
, ...,
Γu
N
gu
NN
while ν = [νd
νu
]T
is a normalized noise
vector, where νd
=
Γd
1σ2
o
gd
11
, ....,
Γd
N σ2
o
gd
NN
and νu
=
Γu
1 σ2
o
gu
11
, ....,
Γu
N σ2
o
gu
NN
. The 2N ×2N matrix
G is the gains matrix of the interference channels whose diagonal elements equal to
zero, and can be simpliﬁed as
G =
Gdd
Gdu
Gud
Guu , (18)
where the zero-diagonal submatricies Gdd
and Guu
are the downlink to downlink
interference channel gain and uplink to uplink interference channel gain, respectively.
Moreover, Gdu
represents the uplink to downlink interference channel gains whose
diagonal is the normalized self-interference: (PI +κ+β)gdu
nn
1+β
, for n = 1...N. Finally, Gud
represents the downlink to uplink interference channel gains whose diagonal is the
normalized self-interference: (κ+β)gud
nn
1+β
, for n = 1...N. In case of a sophisticated self-
interference cancellation that the residual interference is brought down to the noise
level, then the diagonal elements of Gdu
and Gud
are equal to zero. A breakdown of
2
Spectral radius of a matrix A is the maximum absolute value of A’s eigenvalue elements (i.e.,
ρ(A) = max{|λi|}i=N
i=1 ).
&
126

G is shown in (19).
0 gdd
12 · · · gdd
1N
(PI +κ+β)gdu
11
1+β
gdu
12 · · · gdu
1N
gdd
21 0 · · · gdd
2N gdu
21
(PI +κ+β)gdu
22
1+β
· · · gdu
2N
...
...
...
...
...
...
...
...
gdd
N1 gdd
N2 · · · 0 gdu
N1 gdu
N2 · · ·
(PI +κ+β)gdu
NN
1+β
(κ+β)gud
11
1+β
gud
12 · · · gud
1N 0 guu
12 · · · guu
1N
gud
21
(κ+β)gud
22
1+β
· · · gud
2N guu
21 0 · · · guu
2N
...
...
...
...
...
...
...
...
gud
N1 gud
N2 · · ·
(κ+β)gud
22
1+β
guu
N1 guu
N2 · · · 0












































D
U
D U
.
(19)
Since all nodes transmit over the same frequency channel, the channel between
any two nodes can be considered reciprocal (e.g., hdu
ij = hdu
ji ). Therefore, Gdd
=
[Guu
]T
and Gud
is a symmetric matrix whereas Gdu
is symmetric matrix only in case
of symmetric communications. Thus,
GT
=
Guu
Gud
Gdu
Gdd . (20)
Note that G is irreducible matrix, and DG is a nonnegative matrix. Below we
rewrite (17) as
p ≥ [I − DG]−1
ν, (21)
where, I is the identity matrix. Applying Perron-Frobenius theory, the target SINRs
Γ can be achieved with nonnegative solution p∗
if and only if the spectral radius
ρ(DG) is less than unity, mathematically,
p∗
= [I − DG]−1
ν ≥ 0 ⇔ ρ(DG) < 1. (22)
Accordingly, if the set of target SINRs is feasible, then p∗
= [I − DG]−1
ν represents
the centralized policy which requires all system’s information to be collected at a
central entity for processing. This is obviously impractical in a large multi-cell sys-
tem. In this case, we should ﬁnd a distributed solution that ends up with the same
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127

solution as that of the centralized one.
Notice that (17) (with equality) represents the iterative distributed solution using
the best response algorithm, i.e.,
p(τ + 1) = DGp(τ) + ν, (23)
In other words, the behaviour of the nodes in cell n is
pd
n(τ + 1) = Γd
n
(1 + β)Id
n(τ) + (PI + κ + β)pu
n(τ)gdu
nn + σ2
o
gd
nn
pu
n(τ + 1) = Γu
n
(1 + β)Iu
n (τ) + (κ + β)pd
n(τ)gud
nn + σ2
o
gu
nn
.
(24)
Equivalently, this can be written3
as:
pd
n(τ + 1) = Γd
n
pd
n(τ)
γd
n(τ)
pu
n(τ + 1) = Γu
n
pu
n(τ)
γu
n(τ)
.
(25)
Thus, plugging the current transmit power levels and the current measured SINRs in
the above equations will generate the required transmit power in the next iteration
(τ + 1).
Let the right hand side (RHS) of (17) be F(p) = DGp + ν. Then, the solution
of (23) is actually the fixed point of F(p). Moreover, F(p) possesses the following
properties:
• positivity i.e., F(p) > 0 ∀ p ≥ 0,
• monotonicity i.e., if p1 > p2 ⇒ F(p1) > F(p2),
• scalability i.e., for any a > 1, aF(p) > F(ap).
According to Yates [28], F(p) is called a standard interference function. In addition,
if the problem is feasible, then F(p) has a unique fixed point. Furthermore, as the
iteration count τ → ∞, the power vector p in (23) converges to the unique fixed
point p∗
. Therefore, the distributed algorithm in (23) will surely converge to the
Pareto optimal solution.
3
This is done by multiplying the denominator and numerator by the corresponding transmit
power pn(τ).
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128

0 0.5 1 1.5 2 2.5 3
x 10
10
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Energy efficiency (bits/Hz/joul)
EmpiricalCDFF(x):Probability(EE<=x)
Dr=20, No.Cells: 27
Full duplex
Half duplex
Student Version of MATLAB
(a)
10
7
10
8
10
9
10
10
10
11
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
log(energy efficiency (b/Hz/J))
EmpiricalCDFF(x):Probability(log(EE)<=x)
Dr=20, No.Cells: 27
Full duplex
Half duplex
(b)
Figure 3: Energy efficiency of a system with 27 cells, each with radius of 20 m: a)
linear scale, b) normalized dB scale
4 Simulation Results and Discussions
In this section, we show the results of a simulation experiment conducted on a cellular
network whose architecture is similar to that in Fig(1). We simulated a full-duplex
transmission scheme and a half-duplex transmission scheme under same conditions.
If users’ target SINRs are feasible, each user in both scenarios will be able to
transmit with the required throughput. Therefore, the spectral efficiency in the full-
duplex system will be twice of that in the half-duplex system because the FD system
requires half the bandwidth. However, this merit comes with a cost; full-duplex
system must radiate more power to offset the effect of large amount of interference
compared to that in half-duplex system. Therefore, to capture the net efficiency, we
propose to use the energy efficiency (EE) in terms of bits/Hz/Joule, which is ratio
of the spectral efficiency to the radiated power.
Figures 3 through 5 show the empirical cumulative distribution function (CDF)
of the energy efficiency in bits/Hz/Joule for both transmission schemes: half-duplex
and full-duplex. In all figures, the full-duplex scheme generally outperforms the half-
duplex scheme. Furthermore, in worst case scenarios (the lower tail), where users
happen to be in bad locations, both schemes will radiate more power to achieve the
required QoS. However, in these bad moments, the full-duplex requires to radiate
even more power because as the interference increases in the system, the outcome
of increasing the power diminishes (i.e., the slope of the energy efficiency curve
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129

0 2 4 6 8 10 12
x 10
8
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Dr=50, No.Cells: 27
Full duplex
Half duplex
Figure 4: Energy efficiency of a system with 27 cells, each with radius of 50 meter
decreases with respect to the transmit power). On the other hand, as the users
move to more favourable locations, the energy efficiency of the full-duplex scheme
increasingly outperforms that of half-duplex. This is clearly noticeable from the
increasing gap between the CDFs as the EE increases.
In the ideal single-cell system, the ratio of the energy efficiency in full-duplex
to that in half-duplex (i.e., EEF D
EEHD
) is theoretically supposed to approach 2. In the
simulated multi-cell system, however, we got an average ratio of about 1.47. This low
ratio (i.e., EEF D
EEHD
= 1.47) is due to the large amount of inter-cell interference generated
in full-duplex system compared to that in half-duplex system. The average ratio
would have been increased had worst located users operated in half-duplex mode;
thereby considerably reducing the amount of interference in the network. This result
suggests the following:
• as users move to better locations, the ratio EEF D
EEHD
increases and approaches 2.
• operating completely in full-duplex mode for all cells at all times is not always
a wise decision, rather, a combination of both modes over the cells (hybrid
mode) might be a better choice.
• the transmission mode (half or full) is a new dimension into the problem of
radio resource management (RRM). In other words, the RRM algorithm should
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130

0 0.5 1 1.5 2 2.5 3 3.5
x 10
10
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Dr=20, No.Cells: 60
Full duplex
Half duplex
(a)
0 2 4 6 8 10 12 14 16 18
x 10
8
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Dr=50, No.Cells: 60
Full duplex
Half duplex
(b)
Figure 5: Energy efficiency of a system with 60 cells: a) 20 meter cell radius, b) 50
meter cell radius
decide the transmission mode in each cell, over each subchannel, and at each
time slot.
• in a hybrid mode, as users move to better locations, as the number of cells
operating in full-duplex increases.
• certain criteria/threshold on deciding the transmission mode for each cell must
be figured out.
5 Conclusion and Future Work
The full-duplex communication has attracted enormous attention due to its potential
to double the link spectral efficiency. However, co-channel interference is a major
challenge that obstructs a successful deployment of full-duplex multi-cell systems.
In this paper, we derived the general expression of the SINRs of both uplink and
downlink for different scenarios in large cellular SCFD-based networks. Furthermore,
we addressed the feasibility of achieving certain QoS requirements in central and
distributed setups. It was shown that if the spectral radius of the product of a
diagonal matrix and interference channel gains matrix is less than one, then the set of
target SINRs is achievable. Moreover, in the case of feasibility, the central achieving
policy is the solution of a simple linear equation while the distributed solution can
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131

be found by applying the best response algorithm until reaching to the fixed point.
Simulation results show that as users become in better locations, the efficiency of the
full-duplex transmission approaches twice the efficiency of half-duplex transmission.
On the other hand, when users are in worst locations (i.e., cell edge), the efficiency
of full-duplex is indifferent to the half-duplex. Moreover, the hybrid transmission
mode a cross the whole network is shown to be the best operational mode. As an
extension of this research, we plan to study the case of infeasible target SINRs and
find the best policy that maximizes the fairness among all SCFD equipped UEs. In
addition, identifying specific criteria for deciding the best transmission mode (full or
half ) is still an open problem.
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Author
Ali Al-Zahrani received his B.S. in Electrical Engineer-
ing with honor from King Fahad University of Petrolume and
Minirals (KFUPM), Dhahran, Saudi Arabia, in 2002. He fur-
ther received his M.S. and PhD in Electrical and Computer
Engineering from Carleton University, Ottawa, Canada in
2010 and 2015, respectively. Ali is now an Assistant Professor
in the Department of Electrical and Computer Engineering at
the University of Jeddah, Saudi Arabia. He worked as an engi-
neer at the Saudi Basic Industries Corporation (SABIC) from
2002 to 2007. His research interests include radio resource al-
location, interference management in wireless communication
systems and massive MIMO.
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Modelling and QoS-Achieving Solution in full-duplex Cellular Systems

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