1

Resource Optimization and Power Allocation in
In-band Full Duplex (IBFD)-Enabled
Non-Orthogonal Multiple Access Networks

arXiv:1706.05583v1 [] 17 Jun 2017

Mohammed S. Elbamby, Student Member, IEEE, Mehdi Bennis, Senior Member, IEEE,
Walid Saad, Senior Member, IEEE, Mérouane Debbah, Fellow, IEEE, and Matti Latva-aho, Senior Member, IEEE

Abstract—In this paper, the problem of uplink (UL) and
downlink (DL) resource optimization, mode selection and power
allocation is studied for wireless cellular networks under the
assumption of in-band full duplex (IBFD) base stations, nonorthogonal multiple access (NOMA) operation, and queue stability constraints. The problem is formulated as a network
utility maximization problem for which a Lyapunov framework
is used to decompose it into two disjoint subproblems of auxiliary
variable selection and rate maximization. The latter is further
decoupled into a user association and mode selection (UAMS)
problem and a UL/DL power optimization (UDPO) problem
that are solved concurrently. The UAMS problem is modeled
as a many-to-one matching problem to associate users to small
cell base stations (SBSs) and select transmission mode (half/fullduplex and orthogonal/non-orthogonal multiple access), and an
algorithm is proposed to solve the problem converging to a
pairwise stable matching. Subsequently, the UDPO problem is
formulated as a sequence of convex problems and is solved using
the concave-convex procedure. Simulation results demonstrate
the effectiveness of the proposed scheme to allocate UL and
DL power levels after dynamically selecting the operating mode
and the served users, under different traffic intensity conditions,
network density, and self-interference cancellation capability. The
proposed scheme is shown to achieve up to 63% and 73% of gains
in UL and DL packet throughput, and 21% and 17% in UL
and DL cell edge throughput, respectively, compared to existing
baseline schemes.
Index Terms—Interference management, Lyapunov optimization, matching theory, power optimization, resource allocation,
successive interference cancellation

Manuscript received January 27, 2017; revised April 21, 2017; Accepted May 22, 2017. This research has been supported by TEKES grant
2364/31/2014, the Academy of Finland CARMA project, the U.S. National
Science Foundation under Grant CNS-1460316, and the ERC Starting Grant
305123 MORE (Advanced Mathematical Tools for Complex Network Engineering). The authors would like to thank Kien-Giang Nguyen and Trung
Kien Vu for their constructive comments
Mohammed S. Elbamby, Mehdi Bennis, and Matti Latva-aho are with the

Centre for Wireless Communications, University of Oulu, Finland,
email: {mohammed.elbamby,mehdi.bennis,matti.latva-aho}@oulu.fi.
Mehdi Bennis is also with the Department of Computer Engineering, Kyung
Hee University, South Korea.
Walid Saad is with the Wireless@VT, Bradley Department of Electri-

cal and Computer Engineering, Virginia Tech, Blacksburg, VA, USA,
email: walids@vt.edu.
Mérouane Debbah is with the Large Networks and System
Group (LANEAS), CentraleSupélec, Université Paris-Saclay, Gifsur-Yvette, France, and also with the Mathematical and Algorithmic Sciences Lab, Huawei France, Paris, France, email: merouane.debbah@huawei.com.

I. I NTRODUCTION AND RELATED WORK
Due to the rapid increase in the demand for wireless data
traffic, there has been substantial recent efforts to develop
new solutions for improving the capacity of wireless cellular
networks, by enhancing the access to the scarce radio spectrum resources [1]. In view of the scarcity of the frequency
resources, smart duplexing, resource allocation, and interference management schemes are crucial to utilize the available
resources in modern cellular networks and satisfy the needs
of their users.
In-band full duplex (IBFD) communication has the potential of doubling the resource utilization of cellular networks
through transmitting in the uplink (UL) and downlink (DL)
directions using the same time and frequency resources. However, this comes at the cost of experiencing higher levels of
interference, not the least of which is the self-interference
(SI) leaked from the transmitter to the receiver of a IBFD
radio. Moreover, IBFD cellular networks suffer from additional interference generated from having base stations and
users transmitting on the same channel. These interference
types, namely, DL-to-UL interference and UL-to-DL interference significantly degrade the performance of IBFD networks.
Figure 1 (a) illustrates desired and interference signals in a
FD-enabled base station.
Recent results have shown significant advances in the SI
cancellation of wireless IBFD radios, putting full duplex
(FD) operation in wireless cellular networks within reach. By
employing a combination of analog and digital cancellation
techniques [2], [3], it was shown that as much as 110 dB of
SI cancellation is achieved. Another approach to avoid SI is
to emulate a FD base station using two spatially separated
and coordinated half duplex (HD) base stations [4]. The
performance of FD is investigated in [5], [6] using tools from
stochastic geometry. In [5], the combined effect of SI and FD
interference is analyzed. Throughput analysis are conducted
in [6] with respect to network density, interference and SI
levels. A system-level simulation study of the performance of
IBFD ultra-dense small cell networks is conducted in [7]. The
study concludes that FD may be useful for asymmetric traffic
conditions. However, none of these studies take into account
user selection and power allocation, which are key factors to
mitigate interference in a IBFD environment.
To further increase the utilization of frequency resources,
the possibility of multiple users sharing the same channel

2

2
U3
U4

1
UL

U1

DL

U2

3

U5
U6
Time frame

...

SI

DL SBS

UL SBS

U1
FD SBS

U2

(a) Full duplex mode

p5<p6
h5>h6

p3h3>p4h4

U4

U3
Decoded assuming
U4 data is noise

Decoded after U3

(b) UL NOMA mode

U6

U5
Decodes U6 data first

treats U5 data as noise
(c) DL NOMA mode

Figure 1. An illustration of (a) FD (b) UL NOMA and (c) DL NOMA
operations, UDI: UL-to-DL interference, DUI: DL-to-UL interference and SI:
self-interference.

by exploiting differences in the power domain has recently
been proposed in the context of non-orthogonal multiple
access (NOMA) [8]. Different from orthogonal multiple access
(OMA) schemes, NOMA allows multiple users to occupy
the same channel, whereas multi-user detection methods,
such as successive interference cancellation (SIC) are used
to decode users’ messages [9]. In DL NOMA, users with
higher channel gains can decode and cancel messages of
users with lower channel gains before decoding their own
messages, whereas users with lowest channel gains decode
their messages first, treating other users’ messages as noise.
In UL NOMA, base station performs successive decoding and
cancellation of different users data, ranked by their channel
strength. The UL and DL NOMA operation is illustrated
for a two-user case in Figure 1 (b) and (c), respectively.
The decoding order as well as the power allocation are key
factors that affect the performance of NOMA. Since NOMA
comes with an additional receiver complexity for the decoding
phase, practical limitations on the maximum number of users
operating in NOMA must be considered. The combination of
UL NOMA and SIC has been shown to also enhance the celledge user throughput in [10].
User scheduling and power optimization are crucial factors
in achieving the promised gains of both FD and NOMA
schemes. Intra-cell and inter-cell cross-link interference occur
due to IBFD operation. Therefore, smart resource and interference management schemes are needed to reap the gains of FD
and NOMA operation. In [11], a hybrid HD/FD scheduler is
proposed that can assign FD resources only when it is advantageous over HD resource assignment. An auction-based algorithm to pair UL and DL users in a single-cell IBFD network
is proposed in [12]. User scheduling and power allocation
algorithms are presented for IBFD networks in [13] and for DL
NOMA networks in [14], [15], [16]. In the proposed approach
of [14], a many-to-many matching algorithm is used to assign
channel to users in a single cell scenario. The performance

of NOMA in the UL is investigated in [17] using an iterative
channel allocation algorithm. All of the above works focus on
single-cell optimization and hence, avoid handling the intercell interference. A distributed sub-optimal algorithm for the
problem of user selection and power allocation in a multi-cell
full duplex network discussed in [18] showing that IBFD can
achieve up to double the throughput of HD in indoor scenarios and 65% in outdoor scenarios. However, the proposed
algorithm relies on information exchange between neighboring
base stations. It also does not take into account queue state
information (QSI), which has a significant impact on the user
packet throughput. Several algorithms are proposed in [19],
[20], [21] to optimize user pairing/scheduling, and power
allocation. These algorithms are either centralized or intercell interference is overlooked. In [22], the authors consider a
multi-cell UL and DL NOMA system where they propose a
user grouping and power optimization framework. The optimal
power allocation is derived for a single macro cell and limited
number of users. The problem of UL/DL decoupled user
association is studied in [23] for multi-tier IBFD networks
where many-to-one matching algorithms are proposed to solve
the problem. However, dynamic user scheduling and power
allocation are not considered in the optimization problem.
Studying the operation of both FD and NOMA was first
considered in [24], where the problem of subcarrier and power
allocation in a multicarrier and single-cell FD-NOMA system
is optimized. Taking into account the user traffic dynamic
in the optimization problem is also missing in the literature.
A summary of the state of the art contributions to FD and
NOMA resource and power optimization problems is provided
in Table I.
A. Paper Contribution
The main goal of this paper is to study the problem of user
association and power allocation in a multi-cell IBFD-enabled
network operating in NOMA. Our objective is to investigate
the benefits of operating in HD or FD, as well as in OMA
or NOMA modes, depending on traffic conditions, network
density, and self-interference cancellation capabilities. We
propose a Lyapunov based framework to jointly optimize the
duplex mode selection, user association and power allocation.
The problem is formulated as a network utility maximization
where the main objective is to minimize a Lyapunov drift-pluspenalty function that strikes a balance between maximizing a
system utility that is a function of the data rate, and stabilize
the system traffic queues. The optimization problem is decomposed into two subproblems that are solved independently
per SBS. User association and mode selection (UAMS) is
formulated as a many-to-one matching problem. A distributed
matching algorithm aided by an inter-cell interference learning
mechanism is proposed which is shown to converge to a
pairwise stable matching. The matching algorithm allows
SBSs to switch their operation between HD and FD and select
either OMA or NOMA schemes to serve its users. Following
that, UL/DL power optimization (UDPO) is formulated as a
sequence of convex problems and an iterative algorithm to
allocate the optimal power levels for the matched users and
their SBSs is proposed.

3

Simulation results show that using the proposed matching
algorithm, a network can dynamically select when to operate in
HD or FD and when to use OMA or NOMA to serve different
users. It is also shown that significant gains in UL and DL user
throughput and packet throughput can be achieved using the
proposed scheme, as compared to different baseline schemes.
The rest of this paper is organized as follows: Section II
describes the system model. The optimization problem is formulated and decomposed into disjoint subproblems using the
Lyapunov framework in Section III. Section IV discusses the
proposed matching algorithm and power allocation scheme.
The performance of the proposed framework is analyzed in
Section V. Finally, Section VI concludes the paper and outlines
future open research lines.
Notations: Lower case symbols represent scalars, boldface
symbols represent vectors, whereas upper case calligraphic
symbols represent sets. 1{condition} is the indicator function,
which equals to 1 whenever condition is true and 0 otherwise,
+
|X | denotes the cardinality of a set X , [x] = max{x, 0}, and
∇f (x) is the gradient of the function f (x).
II. S YSTEM M ODEL
We consider a time division duplexing (TDD) system in
a network of small cells, where a set B of B SBSs operate
in either FD or HD mode, with SI cancellation capability of
ζ, whereas a set U of U users are available in the network
and are restricted to HD operation. An open-access policy is
considered where users associate to any SBS in the UL or
DL. Furthermore, we assume that base stations and users can
operate in NOMA scheme, where multiple users can share the
same time-frequency resource in either UL or DL. To cancel
the resulting multi-user interference, SBSs or users operating
in NOMA can perform SIC at the receiver side. In this regard,
we assume that the decoding ordering is done in an descending
order of channel strength in DL NOMA. Moreover, we adopt
the ascending order of channel strength in UL NOMA, which
was analytically shown in [26] to outperform OMA.
UL and DL service rates of user u are defined as:
X
UL
ruUL (t) =
xUL
bu (t)Rbu (t),
b∈B

=

X

UL
xUL
bu (t)fb log2 (1 + Γbu (t))

(1)

ΓDL
bu (t) =

N0 +

pDL
bu (t)hbu (t)
,
NOMA-DL
+ IuUL-DL (t) + Ibu
(t)

IuDL-DL (t)

(4)

DL
where pUL
=
u is the UL transmit power of user u, and pb
P
DL
u∈U pbu is the total DL transmit power of SBS b, hx,y (t) =
|gx,y (t)|2 is the channel gain between the two nodes x and y,
gx,y (t) is the propagation channel between the two nodes x
and y, and the interference terms in (3) and (4) are expressed
as follows1 :
X
IbUL-UL (t) =
pUL
u0 (t)hbu0 (t),
u0 ∈U \{u}

X

IbDL-UL (t) =

pDL
b0 (t)hb0 b (t),

b0 ∈B\{b}

X

IuDL-DL (t) =

pDL
b0 (t)hb0 u (t),

b0 ∈B\{b}

IuUL-DL (t) =

X

pUL
u0 (t)hu0 ,u (t),

u0 ∈U

X

NOMA-UL
Ibu
(t) =

pUL
u0 (t)hbu0 (t),

0

u :xUL
=1,
bu0
hbu0 <hbu
NOMA-DL
Ibu
(t) =

X

pDL
bu0 (t)hbu (t),

u0 :xDL
=1,
bu0
hbu0 >hbu

pDL
b (t)/ζ is the leaked SI and N0 is the noise variance. To
guarantee a successful NOMA operation in the DL, a user
u0
u0 DL
should decode the data of user u with an SINR level Γbu (t)
that is at least equal to the user u received SINR ΓDL
bu (t).
Otherwise, the data rate of user u is higher 0 than what user
u0 can decode. Accordingly, the inequality ΓubuDL (t) ≥ ΓDL
bu (t)
must hold, where:
0

ΓubuDL (t) =
pDL
bu (t)hbu0 (t)
.
NOMA-DL
DL
DL-DL
pbu0 (t)hbu0 (t)+N0 +Iu0
(t)+IuUL-DL
(t)+Ibu
(t)
0
0
DL
UL
=
Let QUL (t) = [QUL
1 (t), ..., QU (t)], and Q (t)
DL
DL
[Q1 (t), ..., QU (t)] denote the UL and DL traffic queues at
time instant t, with Qlu (t), l ∈ {UL, DL} representing the
UL/DL queues of a given user u. Then, the queue dynamics
for user u are given by:

b∈B
+

ruDL (t)

=

X

=

X

Qlu (t + 1) = [Qlu (t) − rul (t)] + Alu (t),

DL
xDL
bu (t)Ru (t),

b∈B

xDL
bu (t)fb

log2 (1 +

ΓDL
bu (t))

(2)

b∈B
UL
DL
where xUL
, xDL
are indicator variables
bu (t) ∈ X
bu (t) ∈ X
that user u is associated to SBS b at time instant t in UL
UL
or DL, respectively, fb is the allocated bandwidth, and Rbu
DL
and Rbu are the UL and DL data rates between SBS b and
user r. The UL and DL signal to interference plus noise ratios
between SBS b and user u at time instant t, are given by:

ΓUL
bu (t) =

pUL
u (t)hbu (t)
,
UL-UL
DL-UL
NOMA-UL
N0 +Ib
(t)+Ib
(t)+Ibu
(t)+pDL
b (t)/ζ
(3)

(5)

where Alu is the data arrival for user u in the link direction
l at time instant t, which is assumed to be independent and
identically distributed with mean λlu /µlu > 0, and bounded
above by the finite value Almax . λlu and 1/µlu are the mean
packet arrival rate and mean packet size, which follow Poisson
+
and exponential distributions, respectively. Here [.] indicates
that the actual served rate cannot exceed the amount of traffic
in a queue. To satisfy queue stability requirements, SBSs need
to ensure that traffic queues are mean rate stable. This is
equivalent to ensuring that the average service rate is higher
or equal to the average data arrival, i.e., Ālu ≤ r̄ul .
1 Note that the term I
UL-DL includes the intra-cell interference, to account
for the interference due to FD operation.

4

Table I
S UMMARY OF EXISTING LITERATURE IN FD AND NOMA- BASED RESOURCE ALLOCATION PROBLEMS .
Reference

Network scenario

Implementation

FD scheduling

[11]
[12]
[13]
[18]
[19]

local
local
local
local
central

[20]
[21]

single-cell
single-cell
single-cell
multi-cell
multi-cell (subcarrier is
reused once)
multi-cell
multi-cell

[23]

multi-cell

central/local

HD/FD mode selection
FD user pairing and channel allocation
OFDMA channel allocation
suboptimal HD/FD user selection
mode selection and subcarrier
allocation
matching subcarriers to user pairs
local scheduling, ignores inter-cell
interference
UL/DL decoupled user association

central
local

Power
allocation
×
√

Queue
dynamics
×
×
×
×
×

√
√
√
√
√

×
×

×

×

(a) FD
Reference

Link scenario

Network scenario

Scheduling and power allocation scheme

[14]
[17]
[16]
[15]
[22]

DL
UL
DL
DL
UL + DL

single-cell
single-cell
single-cell
single-cell
multi-cell

[25]
[26]
[24]

DL
UL
UL+DL+FD

multi-cell
heterogeneous
single-cell

matching algorithm
iterative subcarrier and power allocation
subchannel assignment and power allocation
user selection and power optimization
optimal power allocation
for limited number of users
matching algorithm and power allocation
user clustering and power allocation
joint subchannel and power allocation

Queue
dynamics
×
×
×
×
×
×
×
×

(b) NOMA

III. P ROBLEM F ORMULATION
In small cell networks, the network utility is affected by
various factors such as user association, UL/DL mode selection, OMA/NOMA mode selection, and UL and DL power
DL
levels. Let X UL = [xUL
= [xDL
bu ] be the UL and
bu ] and X
UL
UL
DL user association matrices, p = [pUL
,
1 ..., pU ] be the UL
DL
DL
DL
power vector, and pb = [pb1 , ..., pbU ] be the DL power vector
of SBS b. Therefore, a joint optimization problem of user
association, mode selection and power allocation to maximize
a continuous utility function of time-averaged UL and DL
service rates, is cast as follows:

maxDL

UL

X ,X ,
pUL ,{pDL
b }


U {r̄uUL }, {r̄uDL }
=

X

(6a)


fUL (r̄uUL ) + fDL (r̄uDL )

u∈U
UL
DL
DL
subject to ĀUL
u ≤ r̄u , Āu ≤ r̄u , ∀u ∈ U,

p̄UL
u
δuUL
δbDL

DL
≤ δ̄uUL , p̄DL
b ≤ δ̄b ,
UL
≤ Pmax
, ∀u ∈ U,
DL
≤ Pmax , ∀b ∈ B,
X
DL
xUL
bu + xbu ≤ 1, ∀u
b∈B

X
u∈U

X

∀u ∈ U,

(6b)
(6c)
(6d)
(6e)

∈ U,

 X

DL
xUL
.
x
bu
bu ≤ 1, ∀b ∈ B.

(6f)
(6g)

Constraint (6b) ensures the stability of UL and DL traffic
queues. Constraints (6c) limit the effect of aggregate interference by maintaining the average transmit powers of SBSs
and users constrained by threshold values δbUL and δuDL . Here,
DL
UL
denote the maximum UL and DL powers. Note
and Pmax
Pmax
that maintaining the average transmit power below a threshold
value allows SBSs to limit their leaked interference within predefined limits without the need to exchange information with
others, which, in turn, allows for distributed implementation.
u0 DL
DL
DL
Constraint (6i), where Yuu0 = 1hbu0 >hbu xDL
bu xbu0 (Γbu −Γbu )
is to guarantee a successful SIC in the DL. Constraint (6f)
states that a user is associated to a single SBS at a time in
either UL or DL. (6g) ensures that an SBS cannot operate
in both FD and NOMA at the same time instant, i.e., if
it serves one user in one direction it can serve at most
one user in the other direction. Finally, the number of users
an SBS can simultaneously serve in UL or DL NOMA is
limited to a quota of q users by constraint (6h)2 . We note
that the restriction in (6g) is imposed to avoid high intra-cell
interference resulting from operating in both FD and NOMA,
in which case assuming that users can perform SIC of multiple
users transmitting in both directions might be impractical as
the number of users scheduled under NOMA increases.
We define sets of UL and DL auxiliary variables for each
user, denoted as {γuUL }, {γuDL }, ∀u ∈ Ub such that the problem
in (6) is transformed from a utility function of time-averaged
rates into an equivalent optimization problem with a timeaveraged utility function of instantaneous rates. Subsequently,

u∈U

xlbu ≤ q, ∀b ∈ B, ∀l ∈ {UL, DL}.

(6h)

u∈U

Yuu0 ≥ 0 ∀u, u0 ∈ U,

(6i)

2 Note that, in theory, the number of users that can be served simulateaneously using NOMA is unrestricted. However, we impose a quota to avoid
high complexity SIC in the receiver side if a high number of users are
scheduled.

5

the problem can be solved in an online manner at each time instant without prior knowledge of the statistical information of
the network variables. In this regard, we define the equivalent
optimization problem as follows:
max

XbUL ,XbDL ,pUL ,{pDL
b }
UL
DL
{γu
},{γu
}

U ({γuUL }, {γuDL })

=
subject to

X

(7a)


fUL (γuUL ) + fDL (γuDL )

u∈U
UL
γ̄u ≤ r̄uUL , γ̄uDL ≤ r̄uDL , ∀u ∈ U,
UL
DL
γuUL ≤ rmax
, γuDL ≤ rmax
, ∀u ∈ U,

(7b)

(6b) − (6i).

(7d)

(7c)

The transformed problem in (7) is equivalent to the original problem in (6). To show this [27], suppose that U1∗
and U2∗ are the optimal utility values of problems (6) and
(7), and Xb∗UL , Xb∗DL , p∗UL , {p∗DL
b } are the optimal stationary and randomized configurations that solve (6) and correspond to users’ optimal expected
rates {r̄u∗UL }, {r̄u∗DL }. Then,

∗
∗UL
∗DL
U1 = U {r̄u }, {r̄u } .
At all time instants, the values Xb∗UL , Xb∗DL , p∗UL , {p∗DL
b }
as well as the auxiliary variables {γuUL = r̄u∗UL }, {γuDL = r̄u∗DL }
satisfy the constraints of problem (7) and correspond to the
utility value U ({γuUL }, {γuDL }) = U1∗ . As this value is not
necessarily optimal in problem (7), then U2∗ ≥ U1∗ .
DL
UL
Then, let XbUL , XbDL , pUL , {pDL
b }{γu }, {γu } be the configurations that solve the transformed problem (7). These
values satisfy the original problem (6) and correspond to a
utility value that is not greater than U1∗ . Therefore:

U1∗ ≥ U {r̄uUL }, {r̄uDL }

≥ U {γ̄uUL }, {γ̄uDL }
≥ U ({γuUL }, {γuDL })
= U2∗ ,
where the second inequality is due to the constraint (7b)
and the continuity of the utility function, the third inequality
follows from Jensen’s inequality, and the last step is due to the
configurations being the optimal solution for (7). Therefore,
one gets that U2∗ = U1∗ and any solution to (7) is also a
solution to (6).
Next, we invoke the framework of Lyapunov optimization [28], the time-average inequality constraints can be
satisfied by converting them into virtual queues and maintaining their stability. Therefore, we define the following
virtual queues H UL (t) = [H1UL (t), ..., HUUL (t)], H DL (t) =
[H1DL (t), ..., HUDL (t)], Z UL (t) = [Z1UL (t), ..., ZUUL (t)], and
Z DL (t) = [Z1DL (t), ..., ZbDL (t)] that correspond to the constraints over the auxiliary variables and transmit power levels,
respectively. Accordingly, the virtual queues are updated as
follows:
+

Hul (t + 1) = [Hul (t) − rul (t)] + γul (t),
+

ZuUL (t + 1) = [ZuUL (t) − δuUL (t)] + pUL
u (t),
+

ZbDL (t + 1) = [ZbDL (t) − δbDL (t)] + pDL
b (t).

(8)

Let
a
combination
of
the
queues
be
UL
DL
y(t) , [QUL (t), QDL (t), H UL (t), H DL (t),
Z
(t),
Z
(t)],

we define the Lyapunovfunction L y(t) and the drift-pluspenalty function ∆ y(t) as:
 1 n UL
2
2
Q (t) + QDL (t)
L y(t) =
2
o
2
2
2
2
+ H UL (t) + H DL (t) + Z UL (t) + Z DL (t)
,
(11)
n
o



∆ y(t) = E L y(t+1) −L y(t) −vU ({γuUL },{γuDL })|Y (t) ,
(12)
where v is a non-negative parameter that controls the tradeoff
between achieving the optimal utility and ensuring the stability
of the queues.
Proposition 1. At time instant t, the Lyapunov drift-pluspenalty satisfies the inequality in (13) under any
h control
P
2
strategy and queue state, where C = 21 u∈U AUL
max +
i P
2
DL 2
UL 2
UL 2
DL 2
+ b∈B 2Pmax
is a
ADL
max + 2Pmax + 3rmax + 3rmax
finite parameter.
Proof: By squaring equations (5), (8), (9) and (10),
+
and from the fact that ([a − b] + c)2 ≤ a2 + b2 + c2 −
2a(b−c), ∀a, b, c ≥ 0, we can show that:


2
2
2
2
Qlu (t+1)−Qlu (t) ≤ Alu (t)+rul (t)−2Qlu (t) rul (t)−Alu (t) ,


2
2
2
2
Hul (t+1)−Hul (t) ≤ γul (t)+rul (t)−2Hul (t) rul (t)−γul (t) ,


2
2
2
UL 2
UL
UL
UL
ZuUL (t+1)−ZuUL (t) ≤ pUL
u (t)+δu (t)−2Zu (t) δu (t)−pu (t) ,


2
2
2
DL 2
DL
DL
DL
ZbDL (t+1)−ZbDL (t) ≤ pDL
b (t)+δb (t)−2Zb (t) δb (t)−pb (t) .
After replacing the squared queue values in the drift-pluspenalty function in (12) by the above inequalities, and
given the hfact that the variables in the following term
P
2
2
2
2
2
1
UL 2
+ ADL + δuUL + pUL
+ γuUL + γuDL +
u
u∈U Au
2 E{
i P u h
i
2
2
2
2
2ruUL + 2ruDL + b∈B δbDL + pDL
} are bounded above
b
by constant values that are independent of t, replacing this
term by the upper bound constant C yields equation (13).
A. Problem Decomposition Using the Lyapunov Framework
Next, the problem in (13) is solved by choosing the control
action that minimizes the terms in the right-hand side at
each time instant t. Since the optimization parameters in
each of the two terms in (13) are disjoint, each term can be
decoupled and solved independently and concurrently based
on the observation of the system and virtual queues.
1) Auxiliary variables selection: The term #1 in the driftplus-penalty equation is related to the auxiliary variable selection. By decoupling the problem per user, the optimal values
of the auxiliary variables are selected by solving the following
maximization problem:

(9)
(10)

max v.fUL (γuUL (t)) − HuUL (t)γuUL (t)

UL ,γ DL
γu
u

(14a)

6


∆ Y (t) ≤ C

(13)
fixed at time t

}|
z Xh
i{
UL
DL
DL
(QUL
(t))A
(t)
+
(Q
(t))A
(t)
}
+ E{
u
u
u
u
u∈U
impact of auxiliary variables and virtual queues

}|
 z Xh
i {
v.fUL (γuUL (t)) − HuUL (t)γuUL (t) + v.fDL (γuDL (t)) − HuDL (t)γuDL (t) }
− E{
#1

u∈U
impact of scheduling and QSI

}|
{
 z Xh
UL
UL
DL
DL
DL
− E{
(QUL
(t)
+
H
(t))r
(t)
+
(Q
(t)
+
H
(t))r
(t)
u
u
u
u
u
u
u∈U
impact of power allocation and power queues

z
}| h
i
i {
X
UL
UL
UL
DL
DL
DL
+ Zu (t)(δu (t) − pu (t)) } − E{
Zb (t)(δb (t) − pb (t)) }
b∈B

+ v.fDL (γuDL (t)) − HuDL (t)γuDL (t)
subject to

γuUL (t)

≤

UL
rmax
,

γuDL (t)

≤

DL
rmax

(14b)

We choose to maximize linear UL and DL utility functions,
i.e., fUL (γuUL ) = (γuUL ) and fDL (γuDL ) = (γuDL ). In this case,
the parameter v balances the tradeoff between maximizing
the instantaneous rate and maintaining fairness between users
by prioritizing users with higher queue sizes to ensure queue
stability. Since (14) is a linear function, the optimal value of
the auxiliary variables will equal their maximum value when
v − Hul (t) is not negative, and zero when it is negative, i.e.:
(
l
rmax
Hul (t) ≤ v,
l
γu (t) =
(15)
0
otherwise.
2) User scheduling and power allocation problem:
By substituting
ruUL and ruDL from (1) and (2), and
P
DL DL
pDL
=
x
p
b
u∈U bu bu , the term #2 in the drift-plus-penalty
equation can be reformulated as:
X  Xh
UL
UL
UL
(QUL
u (t) + Hu (t))xbu (t)Rbu (t)
u∈U

b∈B

DL
DL
DL
+ (QDL
u (t) + Hu (t))xbu (t)Rbu (t)

+ ZuUL (t)(δuUL (t) − pUL
(t))
u
i
Xh
X
DL
+
ZbDL (t)(δbDL (t) −
xDL
bu (t)pbu (t)) ,

i

(17a)
(17b)

Definition 2. A many-to-one matching Υ is defined as a
mapping from the set B ∪ U into the set of all subsets of

b∈B

Therefore, the decomposed problem can be expressed as:
max
DL

XbUL ,Xb ,pUL ,{pDL
b }

X  Xh
u∈U

i
DL
ΨUL
(t)
+
Ψ
(t)
bu
bu

b∈B

+

 X
+
ΩDL
b (t),

ΩUL
u (t)

b∈B

subject to (6d) − (6i),

IV. U SER A SSOCIATION AND P OWER A LLOCATION
In this section, the proposed solutions for the UAMS and
UDPO problems are presented. First, the UAMS problem
objective is to solve the user association and mode selection,
which is formulated as a matching game between users and
SBSs assuming a fixed power allocation. Subsequently, a
local matching algorithm inspired from the Gale and Shapley
algorithm [29], [30] is proposed. To solve the problem locally,
knowledge of inter-cell interference is needed. Therefore, a
learning based inter-cell interference estimation method is
devised. Subsequently, the UDPO problem of allocating UL
and DL powers is formulated as a DC (difference of convex
functions) programing problem and is solved iteratively.

1) Matching preliminaries: Matching theory is a framework that solves combinatorial problems of matching members of two disjoint sets of players in which each player is
interested in matching to one or more player in the other set
[30], [31]. Matching is performed on the basis of preference
profiles of players. Here, both SBSs and users are assumed to
have preferences towards each other to form matching pairs.
Preferences of the sets of SBSs and users (B, U), denoted b
and u , represent each player ranking of the players in the
other set.

i
X Xh
X
DL
UL
=
ΨUL
ΩDL
bu (t) + Ψbu (t) + Ωu (t) +
b (t). (16)
u∈U b∈B

The above problem is a combinatorial problem of associating users to SBSs and selecting whether to operate in HDOMA, HD-NOMA, or FD-OMA mode, and allocating UL and
DL power, which has an exponential complexity. To solve this
problem, we decouple the user association and mode selection
problem from the power allocation problem. First, a low
complexity matching algorithm is proposed that matches users
to SBSs and selects the transmission mode. Given the outcome
of the matching algorithm, a power allocation problem is
proposed to optimally allocate UL and DL powers.

A. User-SBS Matching

u∈U

b∈B

#2

7

B ∪ U, where B = [1, . . . , B] and U = [1, . . . , U ] are two
disjoint sets of SBSs and users, respectively, such that for each
b ∈ B and u ∈ U: 1) Υ(b) ⊆ U; 2) Υ(u) ∈ B; 3) Υ(b) ≤ q;
4) Υ(u) ≤ 1; 5) Υ(u) = {b} ⇔ u ∈ Υ(b). Note from 3)
that an SBS is matched to at most a quota of q users, whereas
from 4) that users are matched to at most one SBS.
Definition 3. Preferences of Both SBSs and users are transitive, such that if b u b0 and b0 u b00 , then b u b00 , and
similarly, if u b u0 and u0 b u00 , then u b u00 .
Definition 4. Given a matching Υ and a pair (u, b) with u ∈
/
Υb and b ∈
/ Υu , (u, b) is said to be blocking the matching Υ
and form a blocking pair if: 1) T b Υb , T = {u} ∪ Υb , 2)
b  u b0 , Υ u = b0 .
2) Preference profiles: Matching allows defining preference
profiles that capture the utility function of the players. Accordingly, to construct preference profiles that leads to maximizing
the system-wide utility, SBSs and users rank each other with
the objective of maximizing the utility function in (17). Notice
from (17) that the utility function is a sum of weighted rate
maximization terms, i.e., (Ψlbu ) and power control terms, that
DL
are ΩUL
u (t) and Ωb (t). Essentially, the preference of user u
should reflect the user preference to maximize its own UL and
DL rate, which is expressed as:
X
X
b  u b0 ⇔
Ψlbu >
Ψlb0 u .
(18)
l∈{UL,DL}

l∈{UL,DL}

On the other hand, each SBS aims to maximize the rate of
its serving users as well as maintaining the UL and DL power
queues stable through optimizing its user and mode selection.
Therefore, SBSs rank the subsets of proposing users (including
the individual users). The proposed preference of SBS b over
two subsets of users M ⊆ U and M0 ⊆ U is defined as:
M b M0
⇔ ΩDL
b (M) +

X

h
i
Ψlbu (M) + Ωlu (M) >

u∈M
l∈{UL,DL}
0
ΩDL
b (M ) +

X

h
i
Ψlbu (M0 ) + Ωlu (M0 ) . (19)

u∈M0
l∈{UL,DL}

3) Matching algorithm: A matching algorithm to solve the
many-to-one matching problem is introduced. The algorithm is
a modified version of the deferred acceptance (DA) matching
algorithm [30]. In each round of the proposed algorithm, each
unmatched user proposes to the top SBS in its preference list,
SBSs then accept or reject the offers. Due to the fact that
an SBS accepts only users who maximize its own utility and
rejects others, it eliminates the possibility of having blocking
pairs, since it would have formed blocking pairs with these
users otherwise. The detailed matching algorithm is presented
in Algorithm 1.
Remark 5. For a fixed preference profile, Algorithm 1 is
guaranteed to find a two-sides stable matching between SBSs
and users [29].

Algorithm 1 User-SBS Matching Algorithm (a modified DA
algorithm [30])
1: Initialization: all users start unmatched, SBSs initialize empty lists of
proposals.
2: Users construct their own preference lists following (18).
3: repeat each unmatched user with nonempty preference list propose to
its most preferred SBS.
4: foreach SBS j do.
5:
SBS observes the subset of users that are in its proposal list, denoted
as Mj .
6:
if |Mj | = 1,
7:
The user in Mj is accepted.
8:
elseif |Mj | = 2,
9:
Both users in the list are accepted only if Mj b M0j , ∀M0j ⊆
Mj .
10:
Otherwise, the user in the most preferred M0j is accepted and the
other is rejected.
11:
elseif |Mj | > 2,
12:
SBS identifies the feasible subsets M0j ⊆ Mj that satisfy
constraints (6g), (6h), and (6i).
13:
SBS calculates its preference of all the feasible subsets.
14:
SBS accepts the users in the highest preferred subset, other users
are rejected.
15:
end if
16:
An accepted user is marked as matched.
17:
A rejected user removes SBS j from its preference list.
18: end foreach
19: until all users are either matched or not having SBSs remaining in their
preference lists.
20: Output: a stable matching Υ.

The above remark states that if the preference profiles of
some of the players are not affected by the current matching of
other players, the DA-based matching algorithm will converge
to a stable matching. However, since the preference profiles
are function of the instantaneous service rates, there exist
interdependencies between the player’s preferences, which is
known as matching externalities. With these externalities, DAbased algorithms are not guaranteed to find a stable matching.
Moreover, the dependency of the preference on other players’
current matching makes it necessary for SBSs to communicate
with each other to calculate the system-wide utility. The
overhead due to this communication grows as the number of
users and SBSs increase, rendering the matching algorithm
impractical. To this end, a utility estimation procedure through
inter-cell interference learning is carried out in the following
subsection.
4) Dealing with externalities: Having the instantaneous rate
in the term Ψbu causes the preferences of players to vary as
the matching changes, due to having both the intra-cell and
inter-cell interference as per equations (1)-(4). Consequently,
externalities are introduced to the matching problem, which
makes it a computationally hard task to find a stable matching.
Instead, we propose an inter-cell interference learning method
that allows SBSs and users to locally estimate their utility at
each time instant t. Hence, externalities due to varying intercell interference are avoided.
Under this procedure, all SBSs and users keep record of the
inter-cell interference experienced at each time instant. Let the
measured inter-cell interference at SBS b and user u in the time
instant t−1 be I˜b,inter (t−1) and J˜u,inter (t−1), respectively, and
Iˆb,inter (t) and Jˆu,inter (t) are the estimated inter-cell interference
at time instant t. A time-average estimation of the inter-cell

8

Therefore, the matching Υ∗ is not blocked by any pair, i.e., is
pairwise-stable.

interference is performed as follows:
Iˆb,inter (t) = ν1 (t)I˜b,inter (t−1)+(1−ν1 (t))Iˆb,inter (t−1), (20)
Jˆu,inter (t) = ν2 (t)J˜u,inter (t−1)+(1−ν2 (t))Jˆu,inter (t−1), (21)
where ν1 and ν2 are learning parameters.
Once the learning procedure has been established, the
preference profiles of players are built using the estimated
terms. First, we assume that players build their preference
profiles over SBSs using the estimated inter-cell interference
to calculate the estimated weighted rate term, denoted as Ψ̂lbu .
This assumption avoids the complexity of taking into account
the intra-cell interference in calculating users’ utility, in which
the preference will vary significantly according to the SBS
current mode selection as well as the SIC order if NOMA is
selected. Hence, the user preference can be expressed as:
X

b  u b0 ⇔

X

Ψ̂lbu >

l∈{UL,DL}

Ψ̂lb0 u .

(22)

l∈{UL,DL}

On the other hand, as a set of more than one user can propose
to an SBS, the preference of a subset of users over another has
to take into account the actual intra-cell interference, as well as
the estimated inter-cell interference. Therefore, the estimated
UL and DL SINR values of user u at SBS b are expressed as:
UL
Γ̂bu (t)

=

pUL
u (t)hbu (t)

N0 + Iˆb,inter (t) + Ib,intra (t) + pDL
b (t)/ζ
DL
DL
pbu (t)hbu (t)
Γ̂bu (t) =
,
N0 + Jˆu,inter (t) + Ju,intra (t)

Theorem 8. Algorithm 1 converges to a pairwise-stable
matching Υ∗ in a finite number of rounds.
Proof: Since each user can propose to an SBS only once,
removing it from its preference list if it is rejected, it is easy
to see that a user u has a preference list of maximum length
of B. As more rounds are conducted, the preference lists grow
smaller. This means that each user performs a maximum of
B proposals. After which the algorithm will converge to a
pairwise-stable matching Υ∗ .
B. UL/DL Power Optimization Problem (UDPO)
After users are associated to SBSs and transmission modes
are selected, power allocation is performed to optimize the
UL and DL power levels for each scheduled UE and SBS. We
assume that a central-controller performs the optimal power
allocation. The central-controller requires channel knowledge
of only the scheduled users. This substantially reduces the
complexity of the channel reporting, as compared to a fully
centralized solution. Given the user association obtained from
the matching algorithm, equation (16) can be rewritten as
follows:
X X h

,

(23)
(24)

b∈B u∈Υb (t)

⇔ ΩDL
b (M) +

X

h
i
Ψ̂lbu (M) + Ωlu (M) >

u∈M
l∈{UL,DL}
0
ΩDL
b (M ) +

X

h
i
Ψ̂lbu (M0 ) + Ωlu (M0 ) . (25)

u∈M0
l∈{UL,DL}

5) Analysis of matching stability:
Definition 6. Matching Υ is pairwise stable if it is not blocked
by any pair that does not exist in Υ.
Lemma 7. Algorithm 1 converges to a pairwise-stable matching Υ∗ .
Proof: Suppose that there exists an arbitrary pair (u, b)
which does not exist in Υ∗ in which T b Υ∗b , T = {u}∪Υ∗b ,
and b u b0 , Υ∗u = b0 . Since b u b0 , this implies that user
u has proposed to b and got rejected at an intermediate round
i before being matched to b0 . Accordingly, Υib b {u} ∪ Υib .
As Υ∗b b Υib , this implies that u ∈
/ Υ∗b since the preference lists are transitive, which contradicts our supposition.

b∈B

X X h
UL
DL
=
wuUL (t)Rbu
(t) + wuDL (t)Rbu
(t)
b∈B

u∈Υb (t)

+ ZuUL (t)(δuUL (t) − pUL
u (t))

X
DL
DL
DL
+ Zb (t)(δb (t) −
pbu (t)) ,

where Ib,intra and Ju,intra are the actual intra-cell interference
resulting from FD or NOMA operation. Subsequently, the
preference of SBS b over two subsets of users M and M0
is defined as:
M b M0

i X
DL
UL
ΨUL
(t)
+
Ψ
(t)
+
Ω
(t)
+
ΩDL
bu
bu
u
b (t)

i
(26)

u∈Υb (t)

where wul = Qlu + Hul . The power optimization problem is
expressed as3 :
max DL

p={pUL ,{pb }}

X Xh

i
DL
UL
DL
ΨUL
bu (p)+Ψbu (p)+Ωu (p) +Ωb (p),

b∈B u∈Υb

(27a)
pUL
u
pDL
b

≤
≤

UL
Pmax
,
DL
Pmax ,

∀u ∈ Υ,

(27b)

∀b ∈ Υ.

(27c)

Yuu0 ≥ 0 ∀u, u0 ∈ Υ,

(27d)

The above problem is a non-concave utility maximization
problem, due to the interference terms in the UL and DL
rate expressions. This makes it complex to solve, even with
a central controller, with complexity that increases with the
number of SBSs and users. To obtain an efficient solution, we
transform the problem into a DC programming optimization
problem and solve it iteratively [32]. First, we substitute the
service rate terms in the objective function:
3 For the sake of brevity, we omit the time index t from this power
optimization subproblem, as it is performed each time instant.

9

=

X X h
wuUL fb log2 (1+ΓUL
bu (p))
b∈B

Theorem 9. Algorithm 2 generates a sequence of p(it ) that
converges to a local optimum p∗ .

u∈Υb (t)

concave

+wuDL f log2 (1+ΓDL
bu (p))

i
DL
+ ΩUL
(p)
+
Ω
(p)
,
bu
b

(28)

Then, the SINR expressions from (3) and (4) is rewritten as:
pUL
u hbu
,
N0 + Ibu,UL (p)
pDL
bu hbu
ΓDL
(p)
=
,
bu
N0 + Ibu,DL (p)

ΓUL
bu (p) =

(29)
(30)

NOMA-UL
where Ibu,UL = IbUL-UL + IbDL-UL + Ibu
+ pDL
b /ζ and
DL-DL
UL-DL
NOMA-DL
.
Ibu,DL = Iu
+ Iu
+ Ibu
By substituting (29) and (30) in (28), the objective function
becomes:

X X h
=
wuUL fb log2 (N0 + pUL
u hbu + Ibu,UL (p))
b∈B

u∈Υb (t)

convex

z }| {
z }| {
Proof: Let the utility function fp (p) =Flu (p) + Glu (p)
affine
z }| {
+ Ωlu (p) be the function to be maximized. At iteration
it , the convex function Glu (p, ) is replaced by the affine
function G˜lu (p, p(it )) to make the objective function concave with respect to the reference point p(it ). Accordingly,
we have a concave utility function at iteration it , that can
be solved efficiently and results in the solution p∗ (it ). At
this point, the original utility function can be expressed as
fp (p∗ (it )) = Flu (p∗ (it )) + Glu (p∗ (it )) + Ωlu (p∗ (it )). Subsequently, the obtained solution is utilized at iteration it +1 such
that G˜lu (p, p(it + 1)) = G˜lu (p, p∗ (it )), in which the optimal
solution will be p∗ (it + 1) and the corresponding utility of
the original problem is fp (p∗ (it + 1)) = Flu (p∗ (it + 1)) +
Glu (p∗ (it + 1)) + Ωlu (p∗ (it + 1)).
By comparing the original utility functions in the two
subsequent iterations, we can find that:


− log2 (N0 + Ibu,UL (p))
fp (p∗ (it ))= Flu (p∗ (it ))+Glu (p∗ (it ))+Ωlu (p∗ (it ))

DL
DL
+ wu fb log2 (N0 + pb hbu + Ibu,DL (p))
= Flu (p∗ (it ))+ G˜lu (p∗ (it ), p(it + 1))+Ωlu (p∗ (it ))

− log2 (N0 + Ibu,DL (p))
≤ Flu (p∗ (it +1))+ G˜lu (p∗ (it +1),p(it +1))+Ωlu(p∗(it +1))

i
≤ Flu (p∗ (it + 1))+Glu (p∗ (it + 1))+Ωlu (p∗ (it + 1))
DL
+ ΩUL
(31)
u (p) + Ωb (p) ,
= fp (p∗ (it + 1)),
concave

convex

concave

convex

X X hz }| { z }| { z }| { z }| {
UL
DL
DL
FUL
=
u (p) + Gu (p) + Fu (p) + Gu (p)
b∈B

u∈Υb
affine

affine

z }| {i z }| { 
DL
+ ΩUL
u (p) + Ωb (p) .

(32)

Finally, we use the convex-concave procedure [33] to convexify the above problem. The convex functions are first substituted by their first order linear approximation at iteration it :
G˜lu (p, p(it )) = Glu (p, p(it )) + ∇Glu (p, p(it ))T (p − p(it )) .
(33)
Algorithm 2 Iterative Power Allocation Algorithm (UDPO)
at time instant t
1:
2:
3:
4:
5:
6:
7:

Initialization: find an initial feasible point, set it = 0.
repeat
calculate G˜lu (p, p(it )), ∀u ∈ Υb from (33).
solve the convex minimization problem using the interior point method.
update iteration: it = it + 1.
until the utility improvement ≤ δ.
Output: optimal power vectors: p = {pUL , {pDL
b }}.

The problem is then solved iteratively, as depicted in Algorithm 2. The feasibility problem [34] is solved to find a feasible
initial starting point. In this problem, the utility function is set
to zero such that if the optimal value is zero, the solution fits
as an initial point that satisfies the problem constraints. In the
subsequent iterations, the initial point is always feasible, as it
is the optimal solution of the previous iteration.

where the first inequality is due to the lower term being
the optimal (maximum) solution to the problem at iteration
it + 1, and the second inequality is due to the convexity of
G˜lu (p, p(it + 1)) ≤ Glu (p). Therefore, Algorithm 2 will generate a sequence of p(it ) that leads to a non-decreasing utility
function, i.e., fp (p∗ (1)) ≤ · · · ≤ fp (p∗ (it )) ≤ fp (p∗ (it + 1)).
Finally, due to the bounded constraints, the utility function is
bounded, and will converge to a solution that is local optimal.
A flowchart of the UAMS and the UDPO problems is
presented in Figure 2. Next, we analyze the complexity of
the proposed scheme in terms of signaling overhead.
C. Complexity Analysis
First, to analyze the complexity of Algorithm 1, we investigate the maximum number of request signals coming from
users’ proposal to an arbitrary SBS in a time instant. Let
Ub ⊆ U be the set of users under the coverage of SBS b.
In the worst case scenario, let all the users have SBS b as
their most preferred SBS. Hence, the SBS will receive requests
from all the users in the first iterations, and it has to accept
at most a single user in HD-OMA operation, a pair of users
in FD-OMA mode, or a maximum of q users in HD-NOMA
mode. The worst case will occur if, at each iteration, the
SBS is only accepting one user for HD-OMA operation and
rejecting the others. In this case, the maximum number of
iterations will be |Ub |, and the total number of proposals is
|Ub | + (|Ub | − 1) + · · · + 1 = |Ub |(|Ub | + 1)/2. Therefore, the
complexity of Algorithm 1 is O(|Ub |2 ).

10

Next we analyze the complexity of Algorithm 2. Since the
power allocation is performed only over the subset of users
that are selected using Algorithm 1, the maximum number of
users from an SBS will be in the HD-NOMA mode, which
is equivalent to the quota q. Then, the maximum number of
users in the network (assuming all SBSs are in operation) will
be q tot = |B|q. Then, an SBS needs to report the channel
between its q users and the other q tot − q users. The total
amount of signaling will be = |B|q(q tot −q) = |B|q(|B|q−q) =
|B|q 2 (|B| − 1) which results in a complexity of O (|B|q)2 .

Users remove rejecting
SBSs from their
preference list

Users propose to the most
preferred SBS in their lists

No

Inter-cell interference learning

Users estimate
experienced during the DL.
[equation (21)]

User level

Matching algorithm
(Algorithm1)

are reported to the SBS.

and
are fed to
the matching algorithm

Yes
Optimal power levels are
reported to the SBSs

SBSs estimate
experienced during the UL.
[equation (20)]

SBS level

SBSs admit most preferred set
of users and reject others

Optimal UL and DL power allocation of the matched users and their SBSs
(Algorithm 2)

A. Simulation setup
We consider an outdoor cellular network where SBSs are
distributed uniformly over the network area and users are distributed uniformly within small cells area. An SBS is located
at the center of each small cell. SBS operate in TDD HD or
in FD. If HD is used, they can operate in NOMA or OMA
to serve multiple users. A packet-level simulator is considered
and each experiment is run for 4000 time subframes, which
are sufficient for the traffic and virtual queues to get stable.
Each result is averaged over 30 different network topologies.
The main simulation parameters are presented in Table II.
Table II
S IMULATION PARAMETERS

SBSs report the channels of
all matched users to the
central controller

Central controller level

All users are
matched or have
empty preference
lists

4) Uncoordinated scheme: in this scheme, users can be
served in either HD or FD and in OMA or NOMA
modes. The proposed matching algorithm, with intercell interference learning, is used for mode selection
and user association. Power is assumed to be fixed for
OMA and is similar to that of baseline 2 for NOMA.
This baseline represents an uncoordinated version of the
proposed scheme.

Figure 2. A flowchart illustrating the sequence, implementation and connections between the proposed learning scheme, matching algorithm and power
allocation scheme.

V. S IMULATION R ESULTS
In this section, we present simulation results and analysis
to evaluate the performance of the proposed framework. For
benchmarking, we consider the following baseline schemes:
1) HD-OMA scheme: users are associated to the nearest
SBS and are allocated orthogonal resources for UL
and DL. Requests are served using a round robin (RR)
scheduler.
2) HD-NOMA only scheme: users are associated to the
nearest SBS and RR scheduler is used to serve UL and
DL queues. If there are multiple users in a scheduling
queue, they are ranked according to their channel gains,
and are served using NOMA if the ratio between their
channel gains is at least 2, otherwise, OMA is used.
Power is allocated to NOMA users based on their
channel ranking, in uniform descending order for UL
NOMA and uniform ascending order for DL NOMA.
SBSs operate either in UL or in DL depending on the
queue length on each link direction.
3) FD-OMA scheme: users are associated to the nearest
SBS and a pair of users is served in FD mode if the
channel gain between them is greater than a certain
threshold, otherwise users are served in HD mode using
RR scheduler.

Parameter
Value
System bandwidth
10 MHz
Duplex modes
TDD HD/ FD
Multiplexing mode
OMA/NOMA
Sub-frame duration
1 ms
Network size
500 × 500 m2
Small cell radius
40m
Max. SBS transmit power
22 dBm
Max. user transmit power
20 dBm
Path loss model
Multi-cell pico scenario [35]
Shadowing standard deviation
4 dB
Penetration loss
0 dB
SI cancellation capability
110 dB
Max. quota of NOMA users q
5
Lyapunov parameters
v parameter
5 × 107
UL
UL
UL power threshold δu
0.5 × Pmax
DL
DL power threshold δbDL
0.9 × Pmax
Learning parameters
SBS learning parameter ν1
0.1
User learning parameter ν2
0.1

B. Performance under different traffic intensity conditions
We start by evaluating the performance of the proposed
scheme under different traffic intensity conditions. An average
of 10 users per SBS are distributed within the small cell area,
DL
= λUL
with a user mean packet arrival rate λtotal
u
u + λu ,
l
and λu = 5 packet/s. Traffic intensity is varied by changing
the mean packet size 1/µlu between 50 kb and 400 kb. In
Figure 3, the packet throughput performance is depicted for
the different schemes. The packet throughput is defined as
the packet size successfully transmitted to the user divided
by the delay encountered to complete its transmission. In
moderate traffic conditions, the packet throughput increases
with increasing traffic intensity, as the packet size increases
and not much queuing delay is encountered. As the traffic
intensity increases, queuing delay increases, correspondingly

11

FD
UL-NOMA
DL-NOMA

0.12
0.1
0.08
0.06
0.04
0.02

50
0
5

10

40

15

20

25

30

35

40

Mean traffic intensity (Mbps)

Figure 4. FD and NOMA mode selection ratios at different traffic intensity
levels, for a network of 10 SBSs and an average of 10 UEs per SBS.
Remaining transmissions are in HD-OMA mode.
Proposed Scheme
HD-OMA
HD-NOMA
FD-OMA
Uncoordinated

20

10
5

10

15

20

25

30

35

40

Mean traffic intensity (Mbps)

Figure 3. Average packet throughput performance for different schemes as
the traffic intensity increases, for a network of 10 SBSs and an average of 10
UEs per SBS.

We continue by investigating the effect of traffic intensity on
SBS mode selection. To that end, Figure 4 provides the ratio of
transmissions carried out in FD or NOMA with respect to all
transmissions in different traffic intensity conditions. Notice
here that, although not explicitly represented, HD-OMA was
the operation mode for the remaining of the transmissions.
The results show an increasing rate of operation in both FD
and NOMA as the traffic intensity increases. The use of FD
varies from about 3% at low traffic conditions to 13% at high
traffic intensity, whereas NOMA operation accounts for up to
10% of the transmissions under high traffic intensity conditions. The rest of transmissions are in HD-OMA mode. These
results clearly indicate that an SBS can benefit more from
scheduling multiple users simultaneously as traffic intensifies.
This is mainly due to the higher request diversity, in which
the chances to have subsets of users that benefit from being
served simultaneously increase.
Next, the impact of traffic intensity on UL/DL user rate
throughput performance is analyzed through Figure 5. A
close up look into Figure 5(a) and Figure 5(b) shows that
results from all baseline schemes fall below HD-OMA for UL
whereas for the DL this scheme is outperformed.
The DL-to-UL interference has a significant impact in the
uncoordinated schemes due to the higher transmitting power of
SBSs and lower pathloss between the SBS and user. In the DL
case, the UL-to-DL interference can be partly avoided within
each cell by the pairing thresholds used in the FD-OMA and
HD-NOMA baselines. As our proposed scheme optimizes the
UL and DL power allocation, it achieves UL and DL gains

of 9% and 23% over the HD scheme, and of about 12% in
both UL and DL over the HD-NOMA and FD-OMA baseline
schemes. Moreover, the coordination gain over the FD-NOMA
matching scheme is even more evident in the UL (12%) as
compared to the DL (7%), which is due to the dominance of
DL-to-UL interference in the uncoordinated scenarios.
4

4

Average user rate throughput (Mbps)

30

Average user rate throughput (Mbps)

Average packet throughput (Mbps)

60

0.14

Mode selection ratio

decreasing the packet throughput. Figure 3 shows that the
proposed scheme outperforms the baseline schemes in packet
throughput performance. At higher traffic intensity condition,
gains of up to 63% and 73% are observed over HD-NOMA and
FD-OMA baseline schemes, respectively. The performance
of the uncoordinated scheme with matching is close to the
proposed scheme at low traffic conditions. However, as the
traffic load increases, the coordination gain reaches up to 31%.

3.5
3
2.5
2
1.5
1
0.5
10

20

30

40

Mean traffic intensity (Mbps)
(a) UL

3.5
3
2.5
2
Proposed Scheme

1.5

HD-OMA
HD-NOMA

1

FD-OMA

0.5
10

Uncoordinated

20

30

40

Mean traffic intensity (Mbps)
(b) DL

Figure 5. Average (a) UL and (b) DL rate throughput performance for
different schemes as the network traffic intensity increases, for a network
of 10 SBSs and an average of 10 UEs per SBS.

To further analyze the data rate throughput performance in
the UL and DL, the cumulative distribution functions (CDFs)
of the UL and DL user rate throughput for light and heavy
traffic intensity cases are provided in Figure 6. As expected, in
the presence of light traffic no significant gains are achieved
with respect to HD scheme performance; Light traffic does
not enable enough diversity for user scheduling purposes.
Accordingly, most of the transmissions are in HD mode,
as was also shown in Figure 4 for the proposed scheme.

12

1

CDF

0.8
0.6
0.4

heavy traffic

Proposed Scheme
HD-OMA
HD-NOMA
FD-OMA
Uncoordinated

70

Average packet throughput (Mbps)

Under heavy traffic conditions, the baseline schemes suffer a
degraded cell-edge throughput in the UL due to the DL-to-UL
interference, as discussed above. Figure 6 also shows that the
proposed scheme power optimization overcomes the cell-edge
throughput degradation and achieves gains of at least 21% and
17% in the UL and DL 10-th percentile throughput.

60

50

40

30

20

0.2

10
4

0
0

1

2

3

4

5

6

7

6

8

8

(a) UL user data throughput (Mbps)
1

Proposed Scheme

CDF

12

14

Figure 7. Average packet throughput performance for different schemes as
the network density increases for an average of 10 UEs per SBS and a mean
traffic intensity of 3 Mbps per user.

light traffic
0.8
0.6

10

Number of SBSs

HD-OMA
HD-NOMA

0.4

FD-OMA

0.2

Uncoordinated

0
0

1

2

3

4

5

6

7

8

increase, making it is less likely to benefit from DL NOMA.
Instead, SBSs schedule DL users either in HD-OMA or FD
modes.

(b) DL user data throughput (Mbps)
0.14

Figure 6. CDFs of UL and DL user throughput at light (20 Mbps) and heavy
(40 Mbps) traffic intensity cases for a network of 10 SBSs and an average
of 10 UEs per SBS.

We proceed by evaluating the performance of our proposed
scheme as the network density increases. Different network
densities will be simulated by introducing an increased number
of SBSs in the system, while intra-cell user density and traffic
influx rates are kept constant. First, we compare the packet
throughput performance against the baseline schemes. Figure 7
shows that, at low network density, all schemes achieve almost
double the packet throughput of the HD baseline scheme.
This is due to multiplexing gain where SBSs are able to
serve more than one user simultaneously and with not much
inter-cell interference to affect the performance. For the same
reason, the uncoordinated scheme performance is close to
the proposed scheme, since coordinating the power to avoid
inter-cell interference is not crucial in this case. On the other
hand, as the network density increases, the coordination gain
increases, reaching up to 55% for 14 SBSs.
Next, we investigate the ratio of selecting FD and NOMA
modes in the proposed schemes as the network density varies.
As Figure 8 shows, as the network density increases, the
selection of DL NOMA decreases. The decrease is due to the
way power is allocated in DL NOMA, where users with less
channel gains (typically cell-edge users) have to be allocated
higher power as compared to users with higher channel gains.
In that case, user with higher channel gains can decode and
cancel others’ data before decoding their own. Therefore, as
the network density increases, inter-cell interference levels

Mode selection ratio

C. Performance under different network densities

0.12

FD
UL-NOMA
DL-NOMA

0.1
0.08
0.06
0.04
0.02
0
4

6

8

10

12

14

Number of SBSs

Figure 8. FD and NOMA mode selection ratios as the network density
increases for an average of 10 UEs per SBS and a mean traffic intensity
of 3 Mbps per user. Remaining transmissions are in HD-OMA mode.

D. Impact of SI cancellation capability
Finally, in this subsection, the effect of the SBS SI cancellation capability on the proposed and baseline schemes is
analyzed. Figure 9 compares the average packet throughput
performance of the different schemes as the SI cancellation
varies from 30 dB to 110 dB, which is the highest reported
capability level. As Figure 9 shows, the degradation in the proposed scheme performance due to having lower SI cancellation
levels is minor compared to the FD-OMA baseline scheme.
As the proposed scheme optimizes the mode selection, it can
operate more frequently in UL NOMA instead of FD to serve

13

UL users, so that the high interference from the SBS DL signal
is avoided.

Average packet throughput (Mbps)

55
50
45
40
35
Proposed Scheme
HD-OMA
HD-NOMA
FD-OMA
Uncoordinated

30
25
20
15
20

40

60

80

100

120

SI cancelation (dB)

Figure 9. Average packet throughput performance for different schemes as the
SBS SI cancellation capability varies, for a network of 10 SBSs, an average
of 10 UEs per SBS, and a mean traffic intensity rate of 3 Mbps per user.

Figure 10 shows the selection ratio of FD and NOMA
modes in the proposed scheme at different SI cancellation
levels. It can be seen that FD mode is selected more frequently
at higher SI cancellation levels, whereas the UL NOMA ratio
decreases correspondingly. The ratio of DL NOMA selection
maintains the same, since SI interference only affects the UL
transmissions.
0.12
FD
UL-NOMA
DL-NOMA

Mode selection ratio

0.1

0.08

0.06

0.04

0.02

0
30

50

70

90

110

SI cancelation (dB)

Figure 10. FD and NOMA mode selection ratios at different SBS SI
cancellation capability levels, for a network of 10 SBSs, an average of 10
UEs per SBS, and a mean traffic intensity rate of 3 Mbps per user. Remaining
transmissions are in HD-OMA mode.

VI. C ONCLUSIONS
In this paper, the problem of mode selection, dynamic
user association, and power optimization has been studied for
IBFD and NOMA operating networks. The problem of timeaveraged UL and DL rate maximization problem under queue

stability constraints has been formulated and solved using
Lyapunov framework. A many-to-one matching algorithm is
proposed that locally select which users to serve and in which
transmission mode to operate. Then, a power optimization
problem of the matched users has been formulated and solved
iteratively. Simulations results show significant gains of up to
63% and 73% in UL and DL packet throughput, and 21%
and 17% in UL and DL cell edge throughput, respectively.
Possible future research directions are to study the problem
in ultra-dense network environments as well as optimizing the
network for latency and reliability requirements.
R EFERENCES
[1] Q. C. Li, H. Niu, A. T. Papathanassiou, and G. Wu, “5G network
capacity: Key elements and technologies,” IEEE Vehicular Technology
Magazine, vol. 9, pp. 71–78, March 2014.
[2] M. Duarte and A. Sabharwal, “Full-duplex wireless communications using off-the-shelf radios: Feasibility and first results,” in 2010 Conference
Record of the Forty Fourth Asilomar Conference on Signals, Systems and
Computers, pp. 1558–1562, Nov 2010.
[3] M. Jain, J. I. Choi, T. Kim, D. Bharadia, S. Seth, K. Srinivasan, P. Levis,
S. Katti, and P. Sinha, “Practical, real-time, full duplex wireless,” in
Proceedings of the 17th Annual International Conference on Mobile
Computing and Networking, MobiCom ’11, (New York, NY, USA),
pp. 301–312, 2011.
[4] H. Thomsen, P. Popovski, E. d. Carvalho, N. K. Pratas, D. M. Kim, and
F. Boccardi, “CoMPflex: CoMP for in-band wireless full duplex,” IEEE
Wireless Communications Letters, vol. 5, pp. 144–147, April 2016.
[5] H. Alves, C. H. M. de Lima, P. H. J. Nardelli, R. D. Souza, and
M. Latva-aho, “On the average spectral efficiency of interferencelimited full-duplex networks,” in 2014 9th International Conference
on Cognitive Radio Oriented Wireless Networks and Communications
(CROWNCOM), pp. 550–554, June 2014.
[6] J. Lee and T. Q. S. Quek, “Hybrid full-/half-duplex system analysis
in heterogeneous wireless networks,” IEEE Transactions on Wireless
Communications, vol. 14, pp. 2883–2895, May 2015.
[7] M. Gatnau, G. Berardinelli, N. H. Mahmood, and P. Mogensen, “Can
full duplex boost throughput and delay of 5G ultra-dense small cell
networks?,” in 2016 IEEE 83st Vehicular Technology Conference (VTC
Spring), pp. 1–5, May 2016.
[8] Y. Saito, Y. Kishiyama, A. Benjebbour, T. Nakamura, A. Li, and
K. Higuchi, “Non-orthogonal multiple access (NOMA) for cellular
future radio access,” in Vehicular Technology Conference (VTC Spring),
2013 IEEE 77th, pp. 1–5, June 2013.
[9] Z. Wei, J. Yuan, D. W. K. Ng, M. Elkashlan, and Z. Ding, “A
survey of downlink non-orthogonal multiple access for 5G wireless
communication networks,” CoRR, vol. abs/1609.01856, 2016.
[10] T. Takeda and K. Higuchi, “Enhanced user fairness using non-orthogonal
access with SIC in cellular uplink,” in Vehicular Technology Conference
(VTC Fall), 2011 IEEE, pp. 1–5, Sept 2011.
[11] S. Goyal, P. Liu, S. Panwar, R. A. DiFazio, R. Yang, J. Li, and E. Bala,
“Improving small cell capacity with common-carrier full duplex radios,”
in 2014 IEEE International Conference on Communications (ICC),
pp. 4987–4993, June 2014.
[12] J. M. B. da Silva, Y. Xu, G. Fodor, and C. Fischione, “Distributed
spectral efficiency maximization in full-duplex cellular networks,” in
2016 IEEE International Conference on Communications Workshops
(ICC), pp. 80–86, May 2016.
[13] P. Tehrani, F. Lahouti, and M. Zorzi, “Resource allocation in OFDMA
networks with half-duplex and imperfect full-duplex users,” CoRR,
vol. abs/1605.01947, 2016.
[14] B. Di, S. Bayat, L. Song, and Y. Li, “Radio resource allocation
for downlink non-orthogonal multiple access (NOMA) networks using
matching theory,” in 2015 IEEE Global Communications Conference
(GLOBECOM), pp. 1–6, Dec 2015.
[15] P. Parida and S. S. Das, “Power allocation in OFDM based NOMA
systems: A DC programming approach,” in 2014 IEEE Globecom
Workshops (GC Wkshps), pp. 1026–1031, Dec 2014.
[16] F. Fang, H. Zhang, J. Cheng, and V. C. M. Leung, “Energy-efficient resource allocation for downlink non-orthogonal multiple access network,”
IEEE Transactions on Communications, vol. 64, pp. 3722–3732, Sept
2016.

14

[17] M. Al-Imari, P. Xiao, M. A. Imran, and R. Tafazolli, “Uplink nonorthogonal multiple access for 5G wireless networks,” in 2014 11th International Symposium on Wireless Communications Systems (ISWCS),
pp. 781–785, Aug 2014.
[18] S. Goyal, P. Liu, and S. Panwar, “User Selection and Power Allocation
in Full Duplex Multi-Cell Networks,” ArXiv e-prints arXiv:1604.08937,
Apr. 2016.
[19] R. Sultan, L. Song, K. G. Seddik, Y. Li, and Z. Han, “Mode selection, user pairing, subcarrier allocation and power control in fullduplex OFDMA HetNets,” in 2015 IEEE International Conference on
Communication Workshop (ICCW), pp. 210–215, June 2015.
[20] B. Di, S. Bayat, L. Song, and Y. Li, “Radio resource allocation for fullduplex OFDMA networks using matching theory,” in Computer Communications Workshops (INFOCOM WKSHPS), 2014 IEEE Conference
on, pp. 197–198, April 2014.
[21] I. Atzeni, M. Kountouris, and G. C. Alexandropoulos, “Performance
evaluation of user scheduling for full-duplex small cells in ultra-dense
networks,” CoRR, vol. abs/1604.05979, 2016.
[22] M. S. Ali, H. Tabassum, and E. Hossain, “Dynamic user clustering
and power allocation for uplink and downlink non-orthogonal multiple
access (NOMA) systems,” IEEE Access, vol. PP, no. 99, pp. 1–1, 2016.
[23] S. Sekander, H. Tabassum, and E. Hossain, “Decoupled uplink-downlink
user association in multi-tier full-duplex cellular networks: A two-sided
matching game,” IEEE Transactions on Mobile Computing, vol. PP,
no. 99, pp. 1–1, 2016.
[24] Y. Sun, D. W. K. Ng, Z. Ding, and R. Schober, “Optimal joint power and
subcarrier allocation for full-duplex multicarrier non-orthogonal multiple access systems,” IEEE Transactions on Communications, vol. 65,
pp. 1077–1091, March 2017.
[25] B. Di, L. Song, and Y. Li, “Sub-channel assignment, power allocation
and user scheduling for non-orthogonal multiple access networks,”
CoRR, vol. abs/1608.08313, 2016.
[26] A. Celik, R. M. Radaydeh, F. S. Al-Qahtani, A. H. A. El-Malek, and
M.-S. Alouini, “Resource allocation and cluster formation for imperfect
NOMA in DL/UL decoupled hetnets,” in IEEE Global Communications
Conference (GLOBECOM), pp. 1–7, Dec 2017.
[27] M. J. Neely, “A Lyapunov optimization approach to repeated stochastic
games,” CoRR, vol. abs/1310.2648, 2013.
[28] M. J. Neely, “Stochastic network optimization with application to
communication and queueing systems,” Synthesis Lectures on Communication Networks, vol. 3, no. 1, pp. 1–211, 2010.
[29] D. Gale and L. S. Shapley, “College admissions and the stability of
marriage,” The American Mathematical Monthly, vol. 69, no. 1, pp. 9–
15, 1962.
[30] A. Roth and M. Sotomayor, “Two-sided matching: A study in gametheoretic modeling and analysis,” Cambridge University Press, Cambridge, 1992.
[31] Y. Gu, W. Saad, M. Bennis, M. Debbah, and Z. Han, “Matching theory
for future wireless networks: fundamentals and applications,” IEEE
Communications Magazine, vol. 53, pp. 52–59, May 2015.
[32] A. L. Yuille and A. Rangarajan, “The Concave-convex Procedure,”
Neural Comput., vol. 15, pp. 915–936, Apr. 2003.
[33] T. Lipp and S. Boyd, “Variations and extension of the convex–concave
procedure,” Optimization and Engineering, vol. 17, no. 2, pp. 263–287,
2016.
[34] S. Boyd and L. Vandenberghe, Convex Optimization. Cambridge
University Press, 2009.
[35] 3GPP, “Further Enhancements to LTE TDD for DL-UL Interference
Management and Traffic Adaptation,” TR 36.828, 3rd Generation Partnership Project (3GPP), June 2012.

Mohammed S. Elbamby received his B.Sc. degree
(honors) in electronics and communications engineering from the Institute of Aviation Engineering
and Technology (IAET), Egypt, in 2010, and his
M.Sc. degree in Communications engineering from
Cairo University, Egypt, in 2013. After receiving
his M.Sc. degree, he joined the Centre for Wireless
Communications (CWC) at the University of Oulu,
where he is working toward his doctoral degree.
His research interests include resource optimization,
UL/DL configuration, fog networking, and caching
in wireless cellular networks. Mohammed S. Elbamby is a recipient of the
Best Student Paper Award from the European Conference on Networks and
Communications (EuCNC’2017).

Mehdi Bennis (Senior Member, IEEE) received his
M.Sc. degree in Electrical Engineering jointly from
the EPFL, Switzerland and the Eurecom Institute,
France in 2002. From 2002 to 2004, he worked as a
research engineer at IMRA-EUROPE investigating
adaptive equalization algorithms for mobile digital
TV. In 2004, he joined the Centre for Wireless
Communications (CWC) at the University of Oulu,
Finland as a research scientist. In 2008, he was a
visiting researcher at the Alcatel-Lucent chair on
flexible radio, SUPELEC. He obtained his Ph.D.
in December 2009 on spectrum sharing for future mobile cellular systems.
Currently Dr. Bennis is an Adjunct Professor at the University of Oulu
and Academy of Finland research fellow. His main research interests are
in radio resource management, heterogeneous networks, game theory and
machine learning in 5G networks and beyond. He has co-authored one book
and published more than 100 research papers in international conferences,
journals and book chapters. He was the recipient of the prestigious 2015
Fred W. Ellersick Prize from the IEEE Communications Society, the 2016
Best Tutorial Prize from the IEEE Communications Society and the 2017
EURASIP Best paper Award for the Journal of Wireless Communications
and Networks. Dr. Bennis serves as an editor for the IEEE Transactions on
Wireless Communication.

Walid Saad (S’07, M’10, SMŠ15) received his
Ph.D degree from the University of Oslo in 2010.
Currently, he is an Associate Professor at the Department of Electrical and Computer Engineering
at Virginia Tech, where he leads the Network Science, Wireless, and Security (NetSciWiS) laboratory, within the Wireless@VT research group. His
research interests include wireless networks, game
theory, cybersecurity, unmanned aerial vehicles, and
cyber-physical systems. Dr. Saad is the recipient of
the NSF CAREER award in 2013, the AFOSR summer faculty fellowship in 2014, and the Young Investigator Award from the
Office of Naval Research (ONR) in 2015. He was the author/co-author of five
conference best paper awards at WiOpt in 2009, ICIMP in 2010, IEEE WCNC
in 2012, IEEE PIMRC in 2015, and IEEE SmartGridComm in 2015. He is the
recipient of the 2015 Fred W. Ellersick Prize from the IEEE Communications
Society. In 2017, Dr. Saad was named College of Engineering Faculty Fellow
at Virginia Tech. From 2015 Ű 2017, Dr. Saad was named the Steven O.
Lane Junior Faculty Fellow at Virginia Tech. He currently serves as an editor
for the IEEE Transactions on Wireless Communications, IEEE Transactions
on Communications, and IEEE Transactions on Information Forensics and
Security.

15

Mérouane Debbah entered the Ecole Normale
Supérieure Paris-Saclay (France) in 1996 where he
received his M.Sc and Ph.D. degrees respectively.
He worked for Motorola Labs (Saclay, France) from
1999-2002 and the Vienna Research Center for
Telecommunications (Vienna, Austria) until 2003.
From 2003 to 2007, he joined the Mobile Communications department of the Institut Eurecom (Sophia
Antipolis, France) as an Assistant Professor. Since
2007, he is a Full Professor at CentraleSupelec (Gifsur-Yvette, France). From 2007 to 2014, he was the
director of the Alcatel-Lucent Chair on Flexible Radio. Since 2014, he is VicePresident of the Huawei France R&D center and director of the Mathematical
and Algorithmic Sciences Lab. His research interests lie in fundamental
mathematics, algorithms, statistics, information & communication sciences
research. He is an Associate Editor in Chief of the journal Random Matrix:
Theory and Applications and was an associate and senior area editor for
IEEE Transactions on Signal Processing respectively in 2011-2013 and 20132014. Mérouane Debbah is a recipient of the ERC grant MORE (Advanced
Mathematical Tools for Complex Network Engineering). He is a IEEE Fellow,
a WWRF Fellow and a member of the academic senate of Paris-Saclay. He
has managed 8 EU projects and more than 24 national and international
projects. He received 17 best paper awards, among which the 2007 IEEE
GLOBECOM best paper award, the Wi-Opt 2009 best paper award, the
2010 Newcom++ best paper award, the WUN CogCom Best Paper 2012 and
2013 Award, the 2014 WCNC best paper award, the 2015 ICC best paper
award, the 2015 IEEE Communications Society Leonard G. Abraham Prize,
the 2015 IEEE Communications Society Fred W. Ellersick Prize, the 2016
IEEE Communications Society Best Tutorial paper award, the 2016 European
Wireless Best Paper Award and the 2017 Eurasip Best Paper Award as well as
the Valuetools 2007, Valuetools 2008, CrownCom2009, Valuetools 2012 and
SAM 2014 best student paper awards. He is the recipient of the Mario Boella
award in 2005, the IEEE Glavieux Prize Award in 2011 and the Qualcomm
Innovation Prize Award in 2012.

Matti Latva-aho received the M.Sc., Lic.Tech. and
Dr. Tech (Hons.) degrees in Electrical Engineering
from the University of Oulu, Finland in 1992, 1996
and 1998, respectively. From 1992 to 1993, he
was a Research Engineer at Nokia Mobile Phones,
Oulu, Finland after which he joined Centre for
Wireless Communications (CWC) at the University
of Oulu. Prof. Latva-aho was Director of CWC
during the years 1998-2006 and Head of Department
for Communication Engineering until August 2014.
Currently he is Professor of Digital Transmission
Techniques at the University of Oulu. He serves as Academy of Finland
Professor in 2017 - 2022. His research interests are related to mobile
broadband communication systems and currently his group focuses on 5G
systems research. Prof. Latva-aho has published 300+ conference or journal
papers in the field of wireless communications. He received Nokia Foundation
Award in 2015 for his achievements in mobile communications research.

