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A Deep Learning-Based Approach for Cell Outage Compensation in NOMA Networks

January 2022
IEEE Open Journal of Vehicular Technology 3(DEC-TR-301):1-1

January 2022
3(DEC-TR-301):1-1

DOI:10.1109/OJVT.2022.3164685

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CC BY 4.0

Authors:

Elaheh Vaezpour

Iran Telecommunication Research Center

Layla Majzoobi

University of Tehran

Mohammad Akbari

University of Ottawa

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Cell outage compensation enables a network to react to a catastrophic cell failure quickly and serve users in the outage zone uninterruptedly. Utilizing the promising benefits of non-orthogonal multiple access (NOMA) for improving the throughput of cell edge users, we propose a newly NOMA-based cell outage compensation scheme. In this scheme, the compensation is formulated as a mixed integer non-linear program (MINLP) where outage zone users are associated to neighboring cells and their power are allocated with the objective of maximizing spectral efficiency, subject to maintaining the quality of service for the rest of the users. Owing to the importance of immediate management of cell outage and handling the computational complexity, we develop a low-complexity suboptimal solution for this problem in which the user association scheme is determined by a newly heuristic algorithm, and power allocation is set by applying an innovative deep neural network (DNN). The complexity of our proposed method is in the order of polynomial basis, which is much less than the exponential complexity of finding an optimal solution. Simulation results demonstrate that the proposed method approaches the optimal solution. Moreover, the developed scheme greatly improves fairness and increases the number of served users.

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Journal of Vehicular Technology

>OJVT-2022-03-0025 <1

A Deep Learning-Based Approach for Cell Outage Compensation in

NOMA Networks

Elaheh Vaezpour, Layla Majzoobi, Mohammad Akbari, Saeedeh Parsaeefard, Halim Yanikomeroglu, Fellow, IEEE

Cell outage compensation enables a network to react to a catastrophic cell failure quickly and serve users in the outage zone

uninterruptedly. Utilizing the promising beneﬁts of non-orthogonal multiple access (NOMA) for improving the throughput of cell

edge users, we propose a newly NOMA-based cell outage compensation scheme. In this scheme, the compensation is formulated

as a mixed integer non-linear program (MINLP) where outage zone users are associated to neighboring cells and their power

are allocated with the objective of maximizing spectral efﬁciency, subject to maintaining the quality of service for the rest of the

users. Owing to the importance of immediate management of cell outage and handling the computational complexity, we develop

a low-complexity suboptimal solution for this problem in which the user association scheme is determined by a newly heuristic

algorithm, and power allocation is set by applying an innovative deep neural network (DNN). The complexity of our proposed

method is in the order of polynomial basis, which is much less than the exponential complexity of ﬁnding an optimal solution.

Simulation results demonstrate that the proposed method approaches the optimal solution. Moreover, the developed scheme greatly

improves fairness and increases the number of served users.

Index Terms—Cell Outage Compensation, Deep Neural Network (DNN), Nonorthogonal Multiple Access (NOMA), Self-healing.

I. INTRODUCTION

GROWING demand for very high speed and low latency

wireless services is making cellular networks denser and

more complex. The planning and management of networks

with a huge number of elements and parameters is one of

the biggest challenges that cellular network operators face.

Owing in part to this, inefﬁciencies in manual solutions has

lead self-organizing networks (SONs) to become an essential

part of the management of wireless cellular networks [1]. SON

technology aims to reduce capital and operational expenditures

by minimizing human intervention in a network by means

of various functionalities, including self-conﬁguration, self-

optimization, and self-healing [2]. Cell outage management is

one of the most important use cases of self-healing. It applies

to BSs that can no longer serve users in its zone, which leads to

a coverage hole in the network [3]. In cell outage management,

compensation refers to the parameter adjustment of the cells

surrounding the outage zone, which is intended to minimize

the impact of the outage on the network.

Recently, non-orthogonal multiple access (NOMA) has been

proposed in 5G networks to improve the throughput of cell-

edge users [4] and the spectral efﬁciency (SE) of networks by

supporting more users than the number of available orthogonal

resources [5]. Due to NOMA’s ability to boost performance

for cell edge users, it can be a good candidate in cell outage

compensation. In this scenario, users in the outage zone (failed

Elaheh Vaezpour is with Communication Department, ICT Research Insti-

tute, Tehran, Iran (e-mail: e.vaezpour@itrc.ac.ir).

Layla Majzoobi is Research Assistant at Communication Department, ICT

Research Institute, Tehran, Iran (e-mail: l.majzoobi@itrc.ac.ir).

Mohammad Akbari is with Communication Department, ICT Research

Institute, Tehran, Iran (e-mail: m.akbari@itrc.ac.ir).

Saeedeh Parsaeefard is with the Department of Electrical and Com-

puter Engineering, University of Toronto, Toronto, Canada (email: saei-

deh.fard@utoronto.ca).

Halim Yanikomeroglu is with the Department of Systems and

Computer Engineering, Carleton University, Ottawa, Canada (email:

halim@sce.carleton.ca)

users) are indeed the cell edge users of the surrounding cells

taking part in the compensation process. To fully utilize the

beneﬁt of the proposed NOMA-based compensation scheme,

we model the compensation process as a mixed integer non-

linear program (MINLP) where there are two key problems:

(1) optimally assigning failed users to neighboring cells; and

(2) allocating power in order to maximize the sum of the failed

users’ SE while maintaining quality of service (QoS) for users

in neighboring cells. To the best of our knowledge, this is

the ﬁrst work that attempts to mathematically model the joint

problem of failed user association and power allocation in a

NOMA-based cell outage compensation scheme. This problem

is computationally difﬁcult to solve [6]. We decompose the

original problem into two sub-problems that we solve sequen-

tially (i.e., user association and then power allocation), and

we propose effective low complexity solutions for each sub-

problem.

A. Related Work

Several proposals for cell outage compensation frameworks

can be found in the literature. Here, we brieﬂy review some

of the most important existing works in this area.

The authors in [7] studied the effectiveness of different pa-

rameter adjustments, such as reference signal power, antenna

tilt, and scheduling parameters in cell outage compensation. In

[8], a guideline to improve compensation process is provided.

In [9]–[11], orthogonal frequency-division multiple access

(OFDMA)-based compensation methods were proposed where

the total bandwidth of each cell was split into two parts: a part

used to transmit data for normal users (normal bandwidth),

and a part used to serve users in an outage zone (healing

bandwidth). The proposed algorithm in [10] utilized coop-

erative beamforming in the healing channel and formulated

the compensation process as an optimization problem. The

objective was to ﬁnd an optimal subchannel assignment and

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Journal of Vehicular Technology

>OJVT-2022-03-0025 <2

power allocation scheme to maximize the weighted sum-rate

of users in the network. In [11], a low-complexity resource

allocation algorithm based on an optimization approach was

proposed for cell outage compensation. The aim was to

maximize sum-rate in the network while providing all users

with a minimum rate requirement. In [9], compensation was

modeled as a utility maximization problem and a distributed

algorithm was proposed to solve it. However, the authors

did not consider the performance degradation for users in

the neighboring cells due to the compensation nor did they

consider bandwidth splitting. The use of Unmanned Aerial

Vehicles (UAV) for compensation of cell outage is studied in

[12]. In [13], an actor critic (AC) based reinforcement learning

(RL) cell outage compensation algorithm was proposed to

tune power and antenna tilt of the neighboring cells. A deep

RL-based approach for outage compensation was proposed

in [14] where association of users in the outage zone to

neighboring cells was done through a K-means clustering

algorithm; and for compensation the antenna downtilt and

user power was determined by a Deep Q-learning method.

In [15] a cell outage compensation mechanism based on an

improved particle swarm algorithm (IPSO) is proposed. In

this work, IPSO is adopted based on adaptive weights to

comprehensively adjust the downtilt, horizontal azimuth, and

user power allocation of the neighboring base station to ensure

the QoS requirement of the users. In [16], a cell outage

compensation mechanism using a network cooperation scheme

in a heterogeneous network with densely deployed Femto Base

Stations (FBSs) is proposed. The proposed scheme utilizes the

Coordinated Multi-Point (CoMP) transmission and reception

with joint processing technique where the main objective is to

guarantee service to UEs even in cases where their primary

FBSs or their backhauls fail. In spite of all the above efforts,

cell outage compensation in NOMA-based networks has been

overlooked and needs to be studied. Therefore, we do so by

considering the problem of joint power allocation and user

association.

The problem of power allocation in a NOMA-based system

can be solved by traditional optimization-based numerical

approaches. In [17], power allocation in uplink and downlink

were cast as convex optimization problems, and closed-form

solutions were proposed for them. An imperfect NOMA

scheme suffering from receiver sensitivity and interference

residue from non-ideal decoding was analyzed in [18], where

the objective of resource allocation optimization problem

captured a trade-off between maximum throughput and pro-

portional fairness, and an iterative algorithm was developed to

solve it. However, these optimization-oriented methods need

to be performed repeatedly whenever network characteristics

(such as a change in propagation scenarios) vary over time.

Therefore, they incur considerable online computational cost

and high overhead that impair their real-time development.

Meta-heuristic algorithms such as genetic algorithms [19]

and particle swarm optimization [20] have also been used to

deal with the power allocation problem in NOMA systems.

However, they have the same drawbacks as the optimization-

based numerical approaches mentioned above.

Taking these limitations into account, learning-based ap-

proaches have recently been proposed. One popular such

approach used to deal with the problem of unknown varying

environments is RL [21]. In [13] and [14], RL-based methods

were proposed for power allocation in an outage compensation

scenario. Yet one drawback of RL-based approaches is that

they try to ﬁnd the optimal solution by interacting with the

environment through trial and error and may require a long

time to converge. This makes them less attractive in practical

implementations of cell outage compensation scenarios where

the network needs to react quickly to the catastrophic failure

and provide users with service. Unsupervised learning algo-

rithms do not leverage the data that can be achieved ofﬂine dur-

ing the operation of a network. To utilize the data that can be

obtained ofﬂine and achieve much lower online computational

complexity, we propose a supervised deep neural network

(DNN) for the cell outage compensation problem. DNNs have

been shown to be a promising approach for approximating the

optimal policy for different resource allocation problems in

wireless networks, such as user association [22], power control

[23]–[25], subchannel assignment [26], and beamforming [27].

Although several works have focused on DNN-based resource

allocation in wireless networks, none have investigated its

potential in dealing with the problem of cell outage compen-

sation, which is addressed in this paper.

B. Contributions and Paper Organization

The key contributions of this work can be summarized as

follows:

•A NOMA-based cell outage compensation scheme is

proposed.

•The proposed scheme manages the cell outage with the

least required changes in the users connections, which

in turn imposes minimum signaling overhead on the

network.

•A new formulation for joint failed user association and

power allocation is presented as an optimization problem.

•For the NP-hard joint failed user association and power

allocation problem, a newly and efﬁcient two-step se-

quential approach is proposed. The computational com-

plexity of this approach is in the order of polynomial

basis. Our proposed approach follows the concept of

learning to optimize where we use deep neural networks

(DNN) to provide the best map for the power allocation

step of our algorithm.

The rest of the paper is organized as follows: The system

model and problem formulation are introduced in Section II

and III, respectively. The proposed solution methodology is

presented in Section IV and Section V. In Section VI, we will

explain how our proposed method can be extended to MIMO

case. Section VII demonstrates the evaluation of the proposed

scheme, and conclusions are drawn in Section VIII.

II. SY ST EM MO DE L

Consider a two-tier cellular network architecture, where

control and data planes are separated [28] and [29]. The

control plane, constructed of macro cells, handles user con-

nectivity and signaling procedures, including synchronization,

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Journal of Vehicular Technology

>OJVT-2022-03-0025 <3

broadcast, multicast, paging, and RRC functionalities. The

data plane consists of small cells and provides the connectivity

facilities with high data rates for end-users. In this context, the

two layers operate in different sub-bands, which prevents co-

channel interference between the data plane and control plane

cells. In this paper, we focus on the management of the data

plane, where a single input single output downlink NOMA-

based network is considered. It is assumed that the neighboring

cells transmit on different sub-bands, and therefore, the co-

channel interference between them is negligible. Each base

station (BS) operates in power-domain NOMA where users

are divided into multiple clusters. Users in each cluster share

the same time-frequency resources, which are orthogonal to

the resources allocated to the other clusters. We assume that

perfect channel-state information (CSI) is available at the

transmitter.

Power domain NOMA allows assigning one transmission

channel to multiple user in a cluster, and exploits the channel

gain difference between them for the purpose of multiplexing

[30]. It superposes users signal in the power domain at the

transmitter. The superposition is performed such that each

NOMA receiver can successfully decode the desired signal

by applying a particular successive interference cancellation

(SIC) technique at the corresponding receiver [4]. A base

station transmits the superposed signal to users with different

powers allocated to each user. For simplicity of explanation,

let us consider a two-user downlink scenario. The base station

transmit a signal xito user i, where i= 1,2with power pi.

The transmitted signal is

x=pP1x1+pP2x2.

The received signal at user iis

yi=hix+wi,

where hiis the channel coefﬁcient between the base station

and user i.wiis the Gaussian noise, and its power density is

Ni. Prior to decoding the desired signal, the receiver cancels

the strong interference signals of the users with lower channel

gains than the considered receiver. The signals for users with

higher channel gains is considered as inter-user interferences.

Hence, the corresponding SINR depends on the power allo-

cated to a user and sum of the powers allocated to those having

higher channel gains. Assuming that h1> h2, the SINR in the

two-user case would be

σ1=P1h1

, σ2=P2h2

N2+P1h2

The power allocation mechanism in NOMA is performed

in such way that higher transmission power is allocated to

users with lower channel gain and vice versa. Therefore, the

strongest interference that a user senses is due to the high

powers allocated to users with weaker channel gains which

is removed by using a proper SIC technique. To successfully

decode the desired signal, a minimum difference is required

between a user’s signal and non-decoded inter-user interfer-

ence.

We consider a cell outage scenario in which one of the BSs

experiences outage during normal network operations and can

Fig. 1. Illustration of the network model where the outage BS and its users

are depicted in red.

no longer serve the users in its coverage area. Our objective

is to compensate for the failure of this BS via serving its

users by some or all of its neighboring cells. The neighboring

cells participating in the compensation process are called

compensating cells. We assume that users in the outage zone

can receive the pilot of compensating cells [10] meaning that

they can estimate compensating cells channel gains and send

the measurements to the OAM unit which manages outage

compensation procedure. At the time of failure, the outage

BS was serving a set Ufof Ufusers (failed users), and cell

nof compensating set Nwas serving a set Unof Unusers

(connected users). The BS n∈ N groups its Unusers into a

set Lnof LnNOMA clusters and serves them using a set of

orthogonal subcarriers. It is assumed that all active users in

the network are provided with the same portion of available

bandwidth. Figure 1 demonstrates the network model. In this

ﬁgure, the outage BS and its users are depicted in red. As

we can see, this BS has three neighbors each of which serves

a number of connected users in a NOMA-based system. We

assume that the cell outage compensation process is managed

by a central unit called ”network operation and management”

(OAM).

When a BS experiences outage, the network enters the

compensation state. In this state, the objective is to serve

users in the coverage zone of the outage BS by its com-

pensating cells while minimizing the impact on the normal

operation of connected users. To achieve objective, we aim

to efﬁciently assign failed users to clusters of compensating

cells and allocate power to all users while serving connected

users without interruption and preserving their minimum QoS

requirements. The compensation process can be cast as an

optimization problem, which is described in the next section.

Remark 1. In order to minimize the inﬂuence of the com-

pensation process on the network, we assume that connected

user association schemes are the same before and after the cell

outage.

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>OJVT-2022-03-0025 <4

III. PROB LE M FOR MU LATI ON

In this section, we formulate the joint failed user association

and power allocation problem with the objective of maximiz-

ing the sum of SE of the failed users subject to maintaining

the QoS of other connected users in the system.

Let us deﬁne binary parameter βu,ℓ,n as the connected user

clustering parameter for all n∈ N :

βu,ℓ,n =(1,if u∈ Unis assigned to cluster ℓ∈ Ln,

0,otherwise.(1)

As mentioned in Remark 1, βu,ℓ,n parameters do not change

after cell outage compensation. Without loss of generality, we

assume that connected users in each compensating cell are

sorted according to the descending order of their channel gain

as hc

1,n ≥hc

2,n ≥ · · · ≥ hc

Un,n, where superscript cdenotes

the connected users of compensating cell n. Similarly, let sort

the failed users according to their channel gains in descending

order as hf

1,n ≥hf

2,n ≥ · · · ≥ hf

Uf,n, where hf

i,n represents

the ith largest channel gain among failed users with respect

to the nth compensating cell. Since users in the outage zone

are typically further from the compensating BS than their

connected users, they experience weaker channel gain than

their connected users, and we have

1,n ≥ · · · ≥ hc

Un,n ≥hf

1,n ≥ · · · ≥ hf

Uf,n,∀n∈ N .(2)

Taking into account that the SIC decoding algorithm resolves

interference from users with weaker channel gain [17], the

minimum SE requirement of connected users can be written

as follows for all u∈ Unand n∈ N :

C1 :X

ℓ∈Ln

βu,ℓ,n log21+ pc

u,ℓ,nhc

u,n

u−1

k=1

βk,ℓ,npc

k,ℓ,n +σ2≥smin

where pc

u,ℓ,n is the power allocated to connected user u∈ Un

if it belongs to cluster ℓ∈ Ln,σ2is the noise power, and smin

is the minimum SE requirement of user u.

Let αu,ℓ,n be a binary variable indicating if failed user u∈

Ufis associated with cluster ℓ∈ Ln, for all n∈ N :

αu,ℓ,n =(1,if u∈ Ufis assigned to cluster ℓ∈ Ln,

0,otherwise.(3)

In order to reduce the computational complexity and SIC

decoding delay at the receivers [5] and [31], each cluster

in the compensating cells is allowed to serve at most one

failed user from the outage zone. As a consequence, we have

Uf≤Pn∈N Ln, and

C2 :X

u∈Uf

αu,ℓ,n ≤1,∀n∈ N ,∀ℓ∈ Ln.

It should be noted that applying techniques such as load

balancing results in uniform distribution of users among

neighboring cells. In this way, we can assume that the number

of users in the failed cell and in each of compensating cells are

almost the same, i.e., Uf≈Un,∀n∈ N . Considering NOMA

clusters of qusers, we have Ln=Un/q ≈Uf/q. Assuming

N≥q, we have NLn≥Uf, which means that the number

of failed users is not greater than the total number of clusters

in the compensating cells. Due to the practical size of NOMA

clusters and the number of available compensating cells (which

can be considered equal to the number of neighbors of the

failed cell), N≥qis a practical assumption, and hence

Constraint C2 is reasonable. In addition, in cases where

N < q, we need an admission control policy. However, this

is beyond the scope of this paper and will be left for future

work.

We also assume that each failed user is allowed to be

associated with exactly one NOMA cluster in the network,

which means that

C3 :X

n∈N X

ℓ∈Ln

αu,ℓ,n = 1,∀u∈ Uf.

In order to successfully apply the SIC algorithm to both

connected and failed users, the following conditions need to

be satisﬁed [17]:

C4 :αu,ℓ,npf

u,ℓ,n −X

k∈Un

βk,ℓ,npc

k,ℓ,nHu−1,ℓ,n ≥

ptol −(1 −αu,ℓ,n)B, ∀n∈ N ,∀ℓ∈ Ln,∀u∈ Uf

C5 :βu,ℓ,npc

u,ℓ,n −

u−1

k=1

βk,ℓ,npc

k,ℓ,nHu−1,ℓ,n ≥

ptol −(1 −βu,ℓ,n)B, ∀n∈ N ,∀ℓ∈ Ln,2≤u≤Un,

where pf

u,ℓ,n is the power allocated to failed user u∈ Uf

if it belongs to cluster ℓ∈ Ln, and ptol is the minimum

power difference required to distinguish between the signal to

be decoded and the remaining non-decoded message signals.

Bis a sufﬁciently large number that is used to ensure that

these constraints are non-binding when αu,ℓ,n = 0 and/or

βu,ℓ,n = 0. For all n∈ N ,Hu−1,ℓ,n is the minimum channel

gain of the users in cluster ℓ∈ Ln, which is greater than the

channel gain of user u, and can be determined as

Hu−1,ℓ,n =





min

1≤k≤u−1{hc

k,nβk,ℓ,n |βk,ℓ,n = 1},if u∈ U n, u = 1,

min

1≤k≤Un{hc

k,nβk,ℓ,n |βk,ℓ,n = 1},if u∈ U f.

(4)

From a practical point of view, we need to put a limit of pmax

on the available power at each BS n∈ N as follows:

C6 :X

ℓ∈LnX

u∈Uf

αu,ℓ,npf

u,ℓ,n +X

ℓ∈LnX

u∈Un

βu,ℓ,npc

u,ℓ,n ≤pmax.

In the compensation process, the objective function is maxi-

mizing sum of SE of the failed users. From (2), since channel

gain of failed users is weaker than the channel gain of

connected users, failed users cannot cancel interference from

connected users. Hence, the achievable SE of a failed user

u∈ Ufis

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Journal of Vehicular Technology

>OJVT-2022-03-0025 <5

n∈N X

ℓ∈Ln

αu,ℓ,n log21 + pf

u,ℓ,nhf

u,n

k=1

βk,ℓ,npc

k,ℓ,n +σ2.(5)

Considering conditions C1 -C6, the joint user association and

power allocation optimization problem in the outage scenario

with the objective of maximizing sum of SE of the failed users

can be formulated as Problem 1.

Problem 1. Given the channel gains of failed and connected

users in the network and clustering parameter βu,ℓ,n for all n∈

N,ℓ∈ Lnand u∈ Un, the joint user association and power

allocation optimization problem in the outage compensation

scenario is formulated as follows:

max

A,Pf,PcX

u∈UfX

n∈N X

ℓ∈Ln

αu,ℓ,nSu,ℓ,n ,

subject to:

C1 −C6 ,

C7 :pf

u,ℓ,n ≥0,∀n∈ N ,∀ℓ∈ Ln,∀u∈ Uf,

C8 :pc

u,ℓ,n ≥0,∀n∈ N ,∀ℓ∈ Ln,∀u∈ Un,

C9 :αu,ℓ,n ∈ {0,1},∀n∈ N ,∀ℓ∈ Ln,∀u∈ Uf,

where

Su,ℓ,n = log21 + pf

u,ℓ,nhf

u,n

k=1

βu,ℓ,npc

k,ℓ,n +σ2,

and A,Pfand Pcare sets whose elements are αu,ℓ,n,pf

u,ℓ,n

and pc

u,ℓ,n, respectively. Constraints C7 and C8 guarantee the

nonnegativity of power allocated to all users, and constraint

C9 deﬁnes variable αu,ℓ,n as a binary one.

As we can see, Problem 1 is a MINLP, which is an NP-hard

combinatorial problem [6]. Accordingly, ﬁnding the optimal

solution for user association and power allocation requires

an exhaustive search that incurs exponential computational

complexity. In the following, we propose an efﬁcient low-

complexity solution for this problem.

IV. THE PROPOSED SOLUTION

In this section, we propose a two-step low-complexity

sequential solution for Problem 1. In the ﬁrst step, we heuris-

tically ﬁnd a suboptimal user association scheme, and in the

second step, the optimal power allocation is found for the user

association scheme from the ﬁrst step.

A. User Association

Here, we present our heuristic suboptimal failed user asso-

ciation algorithm. In our proposed algorithm, the goal is to

assign failed users to the clusters that can provide them with

higher SE. Hence, we need to estimate the amount of power

each cluster can allocate to failed users while still fulﬁlling the

QoS requirements of connected users. To do so, we need to

know the clustering and power allocation policy of connected

users in the compensating cell before the cell outage event.

Therefore, we ﬁrst describe this policy and then present our

failed user association algorithm.

1) Power allocation and user association before the outage

We assume that prior to the outage users at BS nare

clustered on the basis of the downlink clustering algorithm

proposed in [17]. The aim of the algorithm is to put users

with high channel gain in different clusters and pair them with

those whose channel gain is low. In addition, we assume that

at BS n∈ N , optimal power allocation is done to maximize

the sum of SE of its users while considering their minimum

SE requirement as follows:

max

P′c

u∈UnX

ℓ∈Ln

βu,ℓ,nS

′c

u,ℓ,n,

subject to:

C1 : X

ℓ∈Ln

βu,ℓ,nS

′c

u,ℓ,n ≥smin

u,∀u∈ Un,

C2 : βu,ℓ,np

′c

u,ℓ,n −

u−1

k=1

βk,ℓ,np

′c

k,ℓ,nHc

u−1,ℓ,n ≥

ptol −(1 −βu,ℓ,n)M, 2≤u≤Un,∀ℓ∈ Ln,

C3 : X

ℓ∈LnX

u∈Un

βu,ℓ,np

′c

u,ℓ,n ≤pmax,

C4 : p

′c

u,ℓ,n ≥0,∀u∈ Un,∀ℓ∈ Ln,

(6)

where p′c

u,ℓ,n is the power that BS nallocates to user uwhich

belongs to cluster ℓ∈ Lnat the time of failure, P′c

nis a set

whose elements are p′c

u,ℓ,n, and

S′c

u,ℓ,n = log21 + p′c

u,ℓ,nhc

u,n

u−1

k=1

βk,ℓ,np′c

k,ℓ,n +σ2.

Constraint C1 guarantees the minimum SE requirement for the

users. Constraint C2 denotes the necessary power constraint

for efﬁcient SIC decoding in a NOMA cluster. Constraint C3

is total power constraint of each BS, and constraint C4 ensures

nonnegativity of power allocated to each user.

2) Failed user association algorithm

According to Problem 1, after the outage, all clusters

allocate all of their power to the failed users except what is

required to satisfy the SIC decoding and the minimum SE

requirement of connected users. Knowing the amount of power

required by connected users of each cluster, we can determine

how large the SE of a failed user would be if it connected to

that cluster.We can then assign each failed user to the cluster

that offers the highest SE.

As Problem 1 indicates, the minimum power that needs

to be allocated to the user with the highest channel gain in

cluster ℓ∈ Ln, which is denoted as umℓin the sequel, can be

determined on the basis of its QoS requirement as follows:

umℓ,ℓ,n =σ2

umℓ,n 2smin

umℓ−1,∀n∈ N ,∀ℓ∈ Ln.(7)

The amount of power that needs to be allocated to other

connected users in each cluster can be approximated according

to the following Proposition. In this proposition, following

the literature in this context, we apply asymptotic analysis in

inference-limited case.

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Proposition 1. Consider Problem 1 and Subsection IV-A1.

We assume that the noise power σ2is negligible compared to

the interference term, and ptol << 1. The amount of power

that needs to be allocated to connected users after the outage

event, i.e., solution of Problem 1, can be approximated as

u,ℓ,n ≈δℓ,np′c

u,ℓ,n,∀n∈ N ,∀ℓ∈ Ln,∀u∈ U n,(8)

where p′c

u,ℓ,n is the solution of the problem in (6), and

δℓ,n =pc

umℓ,ℓ,n

p′c

umℓ,ℓ,n

,∀n∈ N ,∀ℓ∈ Ln,(9)

where pc

umℓ,ℓ,n can be calculated from (7).

Proof. Due to the assumption of negligibility of noise variance

σ2compared to the interference term, prior to the outage the

SE of connected user ucan be approximated as

S′c

u,ℓ,n ≈log21 + p′c

u,ℓ,nhc

u,n

u−1

k=1

βk,ℓ,np′c

k,ℓ,n ,

∀n∈ N ,∀ℓ∈ Ln, u ∈ U n, u =umℓ.

(10)

In the compensation step, let pc

u,ℓ,n =δℓ,np′c

u,ℓ,n. Then, the

SE of user ucan be approximated as

u,ℓ,n ≈log21 + δℓ,np

′c

u,ℓ,nhc

u,n

u−1

k=1

βk,ℓ,nδℓ,n p′c

k,ℓ,n 

(a)

′c

u,ℓ,n,∀n∈ N ,∀ℓ∈ Ln, u ∈ U n, u =umℓ,

(11)

where (a)follows from (10). Note that according to (2), after

the outage, connected users can resolve interference from the

failed users, and we do not need to consider the interference

from failed users in (11).

According to (11), reducing the power of all users in cluster

ℓ∈ Lnby factor δℓ,n in the compensation step does not

change their SE. The assumption of ptol << 1implies that

this power allocation policy also meets the SIC decoding

power constraints in C5. Consequently, (8) is an appropriate

approximation for the ﬁrst step of of the solution to Problem

1, which completes the proof.

Now from (8), we can propose an efﬁcient scheme for the

association of failed users to the clusters of compensating cells

according to the following steps:

•Determine the amount of power each cluster can allocate

to a failed user: According to Proposition 1, the amount

of power that cluster ℓ∈ Lncan allocate to a failed user

can be calculated as

∆ℓ,n = (1−δℓ,n)X

u∈Un

βu,ℓ,np′c

u,ℓ,n,∀n∈ N ,∀ℓ∈ Ln.

(12)

•Determine the SE of each failed user if it is associated

with cluster ℓ∈ Ln: According to (8) and (12), the SE

of user u∈ Ufif it connects to cluster ℓ∈ Lnis

Algorithm 1 : Heuristic user association algorithm

Initialization: αu,ℓ,n = 0,∀u∈ Uf, n ∈ N , ℓ ∈ Ln.

for all n∈ N , ℓ ∈ Ln, u ∈ Ufdo

Calculate Sf

u,ℓ,n using (13);

for all i= 1,2, . . . , U fdo

Determine (u∗

i, ℓ∗

i, n∗

i)according to (14);

αu∗

i,ℓ∗

i,n∗

i= 1;

Update Sf

u,ℓ,n using (15)-(16);

u,ℓ,n = log21 + ∆ℓ,nhf

u,n

k=1

βu,ℓ,nδℓ,n p′c

k,ℓ,n +σ2,

∀n∈ N ,∀ℓ∈ Ln,∀u∈Uf.

(13)

•Determine the efﬁcient failed user association scheme:

To maximize the sum of SE of the failed users, the

user association scheme can be determined according to

u,ℓ,n values in an iterative manner. At iteration i, triple

(u∗

i, ℓ∗

i, n∗

i)is determined as follows:

(u∗

i, ℓ∗

i, n∗

i) = argmax

n,ℓ,u

{Sf

u,ℓ,n}.(14)

User u∗

i∈ Ufwill be associated with cluster ℓ∗

iof BS

n∗

i. According to C2 and C3 in Problem 1, since each

cluster can at most serve one failed user, and also each

user can be served just by one cluster, cluster ℓ∗

iand user

u∗

ishould be removed from the candidate list in the next

iterations. To do so, we can update the set {Sf

u,ℓ,n}at

iteration ias follows:

u∗

i,ℓ,n = 0,∀n∈ N ,∀ℓ∈ Ln,(15)

u,ℓ∗

i,n∗

i= 0,∀u∈ Uf.(16)

Due to the fact that there are Uffailed users in the

network, user association scheme can be determined in

Ufiterations.

This failed user association algorithm is outlined in Algo-

rithm 1.

B. Power Allocation

As discussed above, BSs operate on different frequencies

and do not interfere with each other. Thus, given the user

association scheme, i.e., A, the power allocation problem can

be solved separately for the BSs that serve at least one failed

user. BSs that do not serve any failed users continue to operate

as before. Therefore, the power allocation problem for each

BS ncan be written as Problem 2.

Problem 2. Given the user association scheme, i.e., A, and

clustering parameter βu,ℓ,n for all ℓ∈ Lnand u∈ Un, the

power allocation problem for each BS nis formulated as

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>OJVT-2022-03-0025 <7

follows:

max

Pf,PcX

u∈UfX

ℓ∈Ln

αu,ℓ,n log21 + pf

u,ℓ,nhf

u,n

k=1

βk,ℓ,npc

k,ℓ,n +σ2,

subject to:

C1 :X

ℓ∈Ln

βu,ℓ,n log21 + pc

u,ℓ,nhc

u,n

u−1

k=1

βu,ℓ,npc

k,ℓ,n +σ2≥smin

∀u∈ Un,

C2 :αu,ℓ,npf

u,ℓ,n −X

k∈Un

βk,ℓ,npc

k,ℓ,nHu−1,n ≥

ptol −(1 −αu,ℓ,n)B, ∀u∈ Uf,∀ℓ∈ Ln,

C3 :βu,ℓ,npc

u,ℓ,n −

u−1

k=1

βk,ℓ,npc

k,ℓ,nHu−1,ℓ,n ≥

ptol −(1 −βu,ℓ,n)B, ∀u∈ Un,∀ℓ∈ Ln,

C4 :X

ℓ∈LnX

u∈Uf

αu,ℓ,npf

u,ℓ,n +X

ℓ∈LnX

u∈Un

βu,ℓ,npc

u,ℓ,n ≤pmax,

C5 :pf

u,ℓ,n ≥0,∀u∈ Uf,

C6 :pc

u,ℓ,n ≥0,∀u∈ Un.

Constraints C2,C3 , and C4 are afﬁne. The SE function

of variables pf

u,ℓ,n and pc

k,ℓ,n in the objective function and

constraint C1 are concave functions. Since the proof procedure

of the concavity of this function is similar to that in [32,

Lemma 1], it is omitted for the sake of brevity. Therefore,

Problem 2 is a convex optimization problem. Mathematical-

based methods inevitably rely on network parameters and need

to be performed for every system realization. This makes them

a computational burden and limits their implementation in

real time. Traditional iterative methods, such as the waterﬁll-

ing algorithm, also suffer from computational complexity in

practical implementation [24]. We propose exploiting DNN

to approximate this problem and utilize it to predict the

power allocation scheme with much lower online complexity

than optimization-oriented methods. We adopt a feedforward

fully connected DNN, which can exhibit a universal function

approximation property [33], [34].

A feedforward fully connected DNN is composed of an

input layer, multiple hidden layers, and one output layer of

neurons. The general structure of this DNN is depicted in

Figure 2. An input vector of D0dimension is fed to the

network through D0number of neurons in the input layer.

Then, it passes the hidden layers, where each hidden layer m

has Dmneurons. Finally, the output vector with dimension

DMis achieved from the output layer Mwith DMneurons.

Each neuron iin layer ktakes inputs from the previous layer

k−1and returns an output zi,k which is derived by the

following equation:

zi,k =fi,k(

Dk−1

j=1

wj,k−1zj,k−1+bi,k ),(17)

where fi,k is the activation function of neuron iin layer k,

wj,k−1denotes the weight of the output of neuron jin the

previous layer k−1, and bi,k denotes the bias term. The input

to the activation function is the weighted sum of all the outputs

Input

Layer

Hidden

Layers

Output

Layer

,1jk

z

1, 1k

z

1,1

z

,1jk

w

1,1

w

D

, , 1 , 1 ,

()

i k j k j k i k

f w z b











,ik

1, 1k

w

Fig. 2. Illustration of a feedforward fully connected DNN.

from the previous layer plus a bias term.

In the training process, weights and biases are updated

iteratively using a supervised procedure that aims to minimize

the error between the predicted and target values of the output

layer. The loss function which calculates the error can be

any suitable measure of the distance between the predicted

and target values. Once the training process converges and

the weights and biases are conﬁgured, DNN can be used to

predict the output for the inputs that have not been used in

the training process. In fact, the DNN learns the mapping

between the input and the output. In the sequel, we describe

the detailed architecture and techniques of our proposed DNN-

based method for Problem 2.

1) DNN architecture

The power allocation problem, i.e., Problem 2, can be

considered as an unknown mapping Mfrom the channel gains

between a BS and its users (both connected and failed users)

to the optimal power allocation for the failed and connected

users in that BS, i.e.,

M:H= [hu′,ℓ′]7→ P∗= [p∗

u′,ℓ′](18)

where superscript ∗indicates the optimal values of the corre-

sponding variable. hu′,ℓ′is equal to the channel gain of user

u′assigned to cluster ℓ′∈ Lnof BS n.p∗

u′,ℓ′is the optimal

power allocated to user u′assigned to cluster ℓ′∈ Lnof BS

In order to emulate this mapping, the DNN is trained by a

training set that includes KSpairs of the input and the target

output, i.e., {Hs,P∗

s}KS

s=1.

As discussed above, the DNN is composed of an input layer,

multiple hidden layers, and one output layer. In our proposed

DNN, activation functions fi,k of the neurons in each layer are

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>OJVT-2022-03-0025 <8

BS1

Cluster 1 Cluster 2



BS1

Cluster 1 Cluster 2

Cluster 1

Cluster 2

1,1

3,1

2,1

4,1

1,1

2,1

Cluster 1

Cluster 2

1,1,1

3,2,1

2,1,1

4,2,1

1,1,1

2,2,1

'

Cluster 1

Cluster 2

2,1

4,1

1,1

3,1

1,1

2,1

Cluster 1

Cluster 2

2,1,1

4,2,1

1,1,1

3,2,1

1,1,1

2,2,1

Fig. 3. Row permutation for both the input and output of the DNN.

assumed to be ReLU which is deﬁned as follows:

fi,k(X) = (X, if X > 0,

0,otherwise.(19)

2) Dataset generation

To build a dataset, we ﬁrst position BSs in the network.

Then, users are randomly distributed in the network area.

Assuming that one BS experiences failure, failed users are

assigned to the compensating cells based on Algorithm 1.

Then, Problem 2 is solved by an off-the-shelf interior point

method solver for every cell that serves at least one failed

user. This procedure is repeated until we have a large enough

dataset, which is then divided into training, test, and validation

datasets. We assume that we have KSpairs of {Hs,P∗

s}in

our training dataset, and the rest are divided between test and

validation datasets.

3) Data preprocessing

For better performance in the training phase, a preprocessing

step is required to prepare the input and output data. We ﬁrst

express the channel gain values in logarithmic units to avoid

numerical problems. We also notice that switching the columns

and rows of the input (i.e., H) does not affect the output

when its columns are also switched accordingly. Therefore,

we can produce new samples and augment the training data.

For example, consider a base station with four connected

users and two failed users assigned to two NOMA clusters,

as shown in Figure 3. If the ﬁrst and second rows of the

matrix Hare permutated (producing matrix H′), then the same

rows of the power allocation matrix Pare also permutated

accordingly (producing matrix P′). The same property exists

for column permutation as shown in Figure 4. The ﬁrst and

second columns of the matrix Hare switched, and the same

columns of the power allocation matrix are also switched. As

a result, a new sample is generated without the need to solve

the optimization problem.

4) Training procedure

First, weights and biases of each neuron in the DNN is

randomly initialized. Let us denote the matrices of weights

and biases of the whole DNN by Wand B, respectively. In

each iteration of the training process, a sample Hsfrom the

training set is fed forward as input to the DNN, and predicted

output ˆ

pu′,ℓ′is obtained. To calculate the error between the

desired values and predicted values, we use the mean square

BS1

Cluster 1 Cluster 2



BS1

Cluster 1 Cluster 2

Cluster 1

Cluster 2

1,1

3,1

2,1

4,1

1,1

2,1

Cluster 1

Cluster 2

1,1,1

3,2,1

2,1,1

4,2,1

1,1,1

2,2,1

'

Cluster 2

Cluster 1

3,1

1,1

4,1

2,1

1,1

Cluster 2

Cluster 1

3,2,1

1,1,1

4,2,1

2,1,1

2,2,1

1,1,1

Fig. 4. Column permutation for both the input and output of the DNN.

error (MSE) function, which is a widely used loss function in

regression problems [35]. MSE is the average of squares of

error between the predicted and optimal power values.

The error is then backpropagated through the DNN to grad-

ually adjust the weights and biases. We use ADAM optimizer

with Nesterov momentum [36], which is a fast and powerful

learning algorithm to update weights and biases according to

the error.

In this paper, we consider batch learning. In batch learning,

ksamples are randomly chosen at each iteration, and the mean

of the kcorresponding gradients is utilized in the updating

procedure of weights and biases. When all samples in the

entire dataset is passed through the DNN one time, an epoch

is elapsed. If the batch size is k,KS

knumber of parameter

updates are performed during an epoch.

5) Testing procedure

To evaluate the performance and assess the predictive power

and generalization of the DNN, we need a test dataset. The

channel gains of the test dataset are passed through the

network and predicted power values are obtained which are

then compared against optimal power values.

Remark 2. Our proposed algorithm can be extended to the

case of multi-cell outage experience in a straightforward

manner. After the user assignment procedure, the proposed

DNN approach for solving Problem 2 can be applied for any

compensating cell with at least one failed user regardless of

the number of failed cells.

V. PROPOSED SOLUTION IN PRESEN CE O F CO -CH AN NE L

IN TE RF ER EN CE

In this section, for more practicality, we assume that neigh-

boring cells can operate on the same subchannel and cause

co-channel interference to one another. Let us denote by B

the set of available subchannels. In addition, let ζb,l,n be

the subchannel allocation parameter which equals to one if

subchannel b∈ B is allocated to the cluster ℓ∈ Lnof BS

n∈ N . We follow the approach of [37] in taking the co-

channel interference into account which is a commonly used

approach in the literature. Our objective is to perform user

association and power allocation in a way that can sustain the

highest possible co-channel interference level. In this regard,

a constraint is added to the problem limit the co-channel

interference on each UE in a NOMA cluster to a maximum

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Journal of Vehicular Technology

>OJVT-2022-03-0025 <9

threshold. Then, we try to maximize the worst-case spectral

efﬁciency of the failed users assuming that the co-channel

interference constraint holds with equality. Please note that

clusters in the same BS operate on different subchannels and

do not cause interference to each other.

Problem 1 in presence of co-channel interference is refor-

mulated as follows.

Problem 3. Given the channel gains of failed and connected

users in the network, clustering parameter βu,ℓ,n, and sub-

channel allocation parameter ζb,l,n for all ∀b∈ B,n∈ N ,

ℓ∈ Lnand u∈ Un, the joint user association and power

allocation optimization problem in the outage compensation

scenario considering co-channel interference is formulated as

follows:

max

A,Pf,PcX

u∈UfX

n∈N X

ℓ∈Ln

αu,ℓ,nSu,ℓ,n ,

subject to:

C1 : log21 + pc

u,ℓ,nhc

u,n

u−1

k=1

βk,ℓ,npc

k,ℓ,n +|Dn| × Imax +σ2≥smin

∀u∈ Un, n ∈ N ,

C2 −C9 ,

C10 :

ζb,l′,n′ζb,l,n 

X

u∈Uf

αu,ℓ,npf

u,ℓ,n +X

u∈Un

βu,ℓ,npc

u,ℓ,n

×αu′,ℓ,n′hf

u,n

≤ζb,l′,n′ζb,l,nImax ,

∀b∈ B,∀n∈ N ,∀n′∈ Dn,∀ℓ∈ Ln,∀ℓ′∈ Ln′

,∀u′∈ Uf,

C11 :

ζb,l′,n′ζb,l,n 

X

u∈Uf

αu,ℓ,npf

u,ℓ,n +X

u∈Un

βu,ℓ,npc

u,ℓ,n

×βu′,ℓ,n′hc

u,n

≤ζb,l′,n′ζb,l,nImax ,

∀b∈ B,∀n∈ N ,∀n′∈ Dn,∀ℓ∈ Ln,∀ℓ′∈ Ln′

,∀u′∈ Uc,

where Dnis the set of neighboring cells of BS n, and Imax

is the maximum co-channel interference that can be tolerated

by failed and connected users in other neighboring cells, and

Su,ℓ,n = log21+ pf

u,ℓ,nhf

u,n

k=1

βu,ℓ,npc

k,ℓ,n +|Dn| × Imax +σ2.

Constraints C10 and C11 imply that the co-channel interfer-

ence that one BS can generate for the failed and connected

users in the neighboring cells is limited to Imax. Constraints

C10 and C11 is active only if two clusters in a BS and its

neighboring cell use the same subchannel.

In presence of co-channel interference, the user association

algorithm is similar to the one described in Subsection IV-A2,

with the difference that in this case, in approximation of the

power budget of each cluster which can be allocated to the

failed users, we need to consider the co-channel interference

effect. Similar to Section IV-A1, we assume that prior to the

outage event, BS n∈ N optimal power allocation is done to

maximize the sum of SE of its users while considering their

minimum SE requirement as described in problem (6). In co-

channel interference scenario we have:

max

P′c

u∈UnX

ℓ∈Ln

βu,ℓ,nS

′c

u,ℓ,n,

subject to:

C1 : X

ℓ∈Ln

βu,ℓ,nS

′c

u,ℓ,n ≥smin

u,∀u∈ Un,

C2 : βu,ℓ,np

′c

u,ℓ,n −

u−1

k=1

βk,ℓ,np

′c

k,ℓ,nHc

u−1,ℓ,n ≥

ptol −(1 −βu,ℓ,n)M, 2≤u≤Un,∀ℓ∈ Ln,

C3 : X

ℓ∈LnX

u∈Un

βu,ℓ,np

′c

u,ℓ,n ≤pmax,

C4 : p

′c

u,ℓ,n ≥0,∀u∈ Un,∀ℓ∈ Ln,

C5 : :ζb,l′,n′ζb,l,n X

u∈Un

βu,ℓ,npc

u,ℓ,n!×αu′,ℓ,n′hf

u,n

≤ζb,l′,n′ζb,l,nImax ,

∀b∈ B,∀n∈ N ,∀n′∈ Dn,∀ℓ∈ Ln,∀ℓ′∈ Ln′

,∀u′∈ Uf

C6 : :ζb,l′,n′ζb,l,n X

u∈Un

βu,ℓ,npc

u,ℓ,n!×βu′,ℓ,n′hc

u,n

≤ζb,l′,n′ζb,l,nImax ,

∀b∈ B,∀n∈ N ,∀n′∈ Dn,∀ℓ∈ Ln,∀ℓ′∈ Ln′

,∀u′∈ Uc,

(20)

where p′c

u,ℓ,n is the power that BS nallocates to user uwhich

belongs to cluster ℓ∈ Lnat the time of failure, P′c

nis a set

whose elements are p′c

u,ℓ,n, and

S′c

u,ℓ,n = log21+ p′c

u,ℓ,nhc

u,n

u−1

k=1

βk,ℓ,np′c

k,ℓ,n +σ2+|Dn| × Imax .

Assume that Iℓ,n ={iℓ,n

1, iℓ,n

2, . . . , iℓ,n

q}is the set of con-

nected user indices in cluster ℓof BS nin a way that

iℓ,n

1,n ≥hc

iℓ,n

2,n ≥. . . , hc

iℓ,n

q,n. From the constraint C1 in

Problem 3, it can be seen that the minimum amount of power

that needs to be allocated to the user whose index is iℓ,n

1, can

be determined on the basis of its QoS requirement as follows:

iℓ,n

1,ℓ,n =σ2+|Dn| × Imax

iℓ,n

1,n 2

smin

iℓ,n

1−1,

∀n∈ N ,∀ℓ∈ Ln.

(21)

For the other connected users in cluster ℓof BS n, the required

amount of power can be determined according to the following

proposition:

Proposition 2. Consider Problem 3 and (20). With assumption

that ptol << 1, the amount of power that needs to be allocated

to connected users after the outage event can be approximated

as follows:

iℓ,n

k,ℓ,n ≈

hiℓ,n

k,n Pk−1

j=1 pc

iℓ,n

j,ℓ,n +σ2+|Dn| × Imax

hiℓ,n

k,n Pk−1

j=1 p′c

iℓ,n

j,ℓ,n +σ2+|Dn| × Imax p′c

iℓ,n

k,ℓ,n,

∀k≥2, n ∈ N , ℓ ∈ Ln,

(22)

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>OJVT-2022-03-0025 <10

where pc

iℓ,n

1,ℓ,n can be calculated from (21).

Proof. If the power of connected users are determined based

on (22), the SE of connected users will be as follows:

iℓ,n

k,ℓ,n = log21 +

ikℓ,n,n pc

iℓ,n

k,ℓ,n

ikℓ,n,n

k−1

j=1

k,ℓ,n +σ2+|Dn| × Imax 

= log21 +

ikℓ,n,n p

′c

iℓ,n

k,ℓ,n

hiℓ,n

k,n Pk−1

j=1 p′c

iℓ,n

j,ℓ,n +σ2+|Dn| × Imax 

′c

ikℓ,n ,ℓ,n

(23)

Since SE requirement for connected users is the same before

and after the outage event, from (23) we can conclude that

the power allocation according to (22) satisﬁes the QoS

requirement of the connected users.

Based on power allocation in (21), we have

iℓ,n

k,ℓ,n −

k−1

j=1

iℓ,n

j,ℓ,n

hiℓ,n

k,n Pk−1

j=1 pc

iℓ,n

j,ℓ,n +σ2+|Dn| × Imax

hiℓ,n

k,n Pk−1

j=1 p′c

iℓ,n

j,ℓ,n +σ2+|Dn| × Imax p

′c

iℓ,n

k,ℓ,n

−

k−1

j=1

iℓ,n

j,ℓ,n

(a)

≥

hiℓ,n

k,n Pk−1

j=1 pc

iℓ,n

j,ℓ,n +σ2+|Dn| × Imax

hiℓ,n

k,n Pk−1

j=1 p′c

iℓ,n

j,ℓ,n +σ2+|Dn| × Imax

k−1

j=1

′c

iℓ,n

j,ℓ,n

−

k−1

j=1

iℓ,n

j,ℓ,n

(σ2+|Dn| × Imax)(Pk−1

j=1 p

′c

iℓ,n

j,ℓ,n −Pk−1

j=1 pc

iℓ,n

j,ℓ,n)

hiℓ,n

k,n Pk−1

j=1 p′c

iℓ,n

j,ℓ,n +σ2+|Dn| × Imax

≥0,

(24)

where (a)follows from C2 in (20). with the assumption of

ptol << 1, from (24) we can conclude that power approxima-

tion as (22) meets constraint C2 in (V). Finally, due to the

fact that co-channel interference threshold is the same before

and after the outage, the power approximation in (22) does not

deviate co-channel interference constraint which completes the

proof.

Having the required power of connected users at hand, we

can determine the amount of power each cluster can allocate

to a failed user as follows:

∆ℓ,n =X

u∈Un

βu,ℓ,np′c

u,ℓ,n −X

u∈Un

βu,ℓ,npc

u,ℓ,n,

∀n∈ N ,∀n∈ N , ℓ ∈ Ln,

(25)

where pc

u,ℓ,n are calculated based on (21) and (22). Now from

(25), we can propose an efﬁcient scheme for the association of

failed users to the clusters of compensating cells as described

Algorithm 2 : Heuristic user association algorithm in presence

of co-channel interference

Initialization: αu,ℓ,n = 0,∀u∈ Uf, n ∈ N , ℓ ∈ Ln.

for all n∈ N , ℓ ∈ Ln, u ∈ Ufdo

Calculate Sf

u,ℓ,n using (26);

for all i= 1,2, . . . , U fdo

Determine (u∗

i, ℓ∗

i, n∗

i)according to (14);

αu∗

i,ℓ∗

i,n∗

i= 1;

Update Sf

u,ℓ,n using (15)-(16);

in Algorithm 2 where

u,ℓ,n = log21 + ∆ℓ,nhf

u,n

k=1

βu,ℓ,nδℓ,n p′c

k,ℓ,n +|Dn| × Imax +σ2,

∀n∈ N ,∀ℓ∈ Ln,∀u∈Uf.

(26)

Given the user association scheme, i.e., A, and the fact that

constraints C10 and C11 are linear, Problem 3 remains convex.

We follow the same procedures as in Subsections IV.B.1-5

to build and train our DNN. The only difference is that the

input to the DNN not only consists of channel gains between

a BS and its users, but also the channel gains between a

BS and users in the neighboring cells that operates in the

same subchannel. Therefore, the new input layer has more

number of neurons compared to the case where co-channel

interference does not exist. To reduce the number of neurons in

the input layer, we leverage the fact that when the co-channel

interference that a BS generates on the neighboring user with

the highest channel gain is lower than the threshold, the co-

channel interference it generates on other neighboring users in

the same subchannel also satisﬁes the constraint.

VI. EX TE ND TO MULTI -ANT EN NA CASE

The multiple antennas at the transmitter (and/or receiver)

side provide additional degrees of freedom for performance

improvement [38]. Hence, the application of MIMO in NOMA

is of great interest and is well-discussed in the literature [39],

[40]. The main goal of this paper is proposing a method for cell

outage compensation in NOMA scheme. Thus, without loss of

generality and for simplicity, we considered SISO-NOMA. To

complete the argument, in this section, we explain how in three

steps our proposed scheme can be extended to MIMO-NOMA

case.

1) Model Adaptation

First, let discuss how the problem formulation will change in

MIMO-NOMA case. Consider the same network architecture

as depicted in Figure 1 with the base stations, each of which is

equipped with NTxantennas at the transmitter side. The users

are also equipped with MRxantennas at the receiver side.

Adopting the proposed framework in [41], we assume that

each BS serves each of its clusters with one of its antennas.

Therefore, the maximum number of clusters in each BS would

be NTx. It should be noted that, with this assumption, we have

no change at transmitter side on BS. However, we need to

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adapt the receive model at the users’ side to MIMO. Let yu,n

denote the received signal at the uth user connected to BS n.

It can be expressed as

yu,n =Hu,nPnsn+zu,(27)

where Hu,n ∈CMRx×NTxand Pn∈CNTx×NTxare the

channel matrix between user uand BS nand the precoder

matrix of BS n, respectively; sn∈CNTx×1with the following

deﬁnition is the transmitted vector containing the intended

symbols of all clusters, and zu∈CMRx×1is the noise vector,

sn=vec (ml)Tx

l=1 , ml=

u=1

pl,u ×sl,u,

∀n∈ N ,∀l∈ Ln,

(28)

where mlis the aggregated transmitted signal to users in

cluster l,pl,u is the power allocated to users uof cluster

l, and, sl,u is the transmitted symbol to uth user of cluster

lwith normalized power. As it can be seen from (27), each

user receives a combination of all transmitted signals by MRx

antennas. It is well-known in literature that the Maximal-

Ratio Combining (MRC) with appropriate design of precoder

matrix Pnand its corresponding detector at the receiver side is

optimal [38]. Using (27), (28) and mathematically rephrasing

our analysis above, we will have the extended version of the

problem formulation in MIMO case.

2) Compensation in MIMO-NOMA case

In the second step, we will show that how our proposed

solution will be applicable to the cell outage compensation

problem in MIMO-NOMA scenario. The proposed user as-

sociation algorithm is based on the answer to this question

that how large the SE of a failed user would be if it is

served by a candidate compensatory cell, knowing the extra

amount of power of each cell while being able to fulﬁll the

QoS requirements of its connected users. We have the similar

arguments for the user association algorithm in MIMO case

with no changes. For the NN-based power allocation method,

in MIMO-NOMA case, the input variables of the NN of cell n

would be the channel matrices and the precoder matrix Hu,n

and Pn,∀u∈ Un,∀n∈ N , respectively, and the output is the

power allocation coefﬁcients pl,u,∀l∈ Ln,∀u∈ Un.

3) Model Training

The third step toward developing the proposed scheme for

MIMO-NOMA is the training process of the neural network.

For this purpose, we adopt the two-step training method

proposed in [41]. In this method, the network is initially

trained based on an AWGN channel and using water-ﬁlling

algorithm and then it is regarded as a basic model that can be

trained for representing another channel type using transfer

learning [42]. In the secondary phase and in order to adapt to

new environment samples, an online learning policy for power

allocation is proposed.

Using the three steps explained above, our proposed method

for cell compensation in SISO-NOMA and its corresponding

analysis can be extended to MIMO-NOMA case.

VII. PER FO RM AN CE EVALUATIO N

In this section, we ﬁrst present the complexity analysis

of our proposed method and that of the mathematical-based

approach. Then, the simulation results are provided in the next

subsection.

A. Complexity Analysis

Here, we analyze the computational complexity of the

proposed suboptimal approach for Problem 1 and compare it

with that of the mathematical-based solution method. To obtain

the global optimal solution, we need to examine all possible

user association schemes and solve the corresponding convex

optimization problem (Problem 2) for all BSs that serve at

least one failed user. Let Lbe the total number of clusters

in the compensating cells, i.e., L=Pn∈N Ln. The number

of possible association schemes is P(L, U f)where P(x, y)

is the number of ypermutations of xobjects. Problem 2 is

convex and can be solved using the interior point method.

The worst-case complexity of the interior point method for

this problem is O((Uf+Pn∈N Un)3)[43]. Therefore, the

overall complexity of ﬁnding the global optimal solution is

O(P(L, U f)(Uf+Pn∈N Un)3). It should be noted that the

optimization-based method is completely performed in real

time and only suffers from online complexity. As mentioned

above, this makes the method inapplicable for cell outage

compensation, which is inherently time sensitive.

Our proposed method includes two sequential steps: user

association and DNN-based power allocation. The proposed

failed user association algorithm consists of computing and

sorting L×Ufnumbers. Hence, its order of complexity is

O(L×Uflog(L×Uf)). The computational complexity of the

DNN-based solution method can be divided into the following

two stages:

1) Ofﬂine complexity

Ofﬂine computational complexity involves generating the

labeled dataset and training the DNN. Generating each la-

beled sample of the dataset requires solving Problem 2 for

a realization of the channel gains with worst-case complexity

O((Uf+Pn∈N Un)3). Assuming that we have KSnumber

of samples in the dataset, the overall complexity of this step

is O(KS(Uf+P

n∈N

Un)3).

2) Online complexity

Assume that the DNN has Mlayers (including hidden and

output layers), each layer mhaving Dmnumber of neurons.

Given any input, the output of the DNN can be obtained

by calculating PM

m=1 Dm−1Dmnumber of multiplications,

m=1 Dmnumber of summations, and PM

m=1 Dmnumber

of calculations of activation functions. In the online step, the

DNN architecture is ﬁxed and the number of calculations is

constant. Therefore, the complexity of DNN is O(1). Since the

DNN needs to be performed for Nnumber of compensating

cells, the overall complexity of this step is O(N).

To summarize, the optimization-based method has worst-

case exponential complexity, while the complexity of our

proposed method is in the order of polynomial basis. It should

also be pointed out that ofﬂine computational complexity can

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TABLE I

SIM ULATI ON PAR AM ETE RS

Parameter Value

pmax 46.02 dBm

ptol -101.4 dBm [17]

σ2-150 dBm

smin

u4 bit/sec/Hz

Path loss model 38 + 30log10 ddB [44]

be afforded, while real-time developments have constrained

resources.

B. Simulation Results

In this subsection, we evaluate the performance of the

proposed solution through simulations. We consider a network

consisting of one BS, which experiences failure, and its

compensating cells. The cells radius is 120 m. Users are

randomly and uniformly placed in each cell where the distance

between each user and BS is at least 20 m. The path loss at

a distance dm from the BS is modeled as 38 + 30log10(d)

dB [44]. The simulation setup parameters are summarized in

Table I. For the DNN-based power control, we use a DNN

with one input layer, three hidden layers, and one output

layer. Each hidden layer has 200 neurons. Input to the DNN

are the channel coefﬁcients of users (connected and failed)

in one BS. The output of the network is the power that has

been assigned to each user and its size is the same as the

input. The proposed DNN is implemented in Python 3.2.2

using Keras library [45] with tensorﬂow [46] as back-end. We

perform cross-validation to ﬁnd the best hyperparameters for

the training process. Unless otherwise noted, the parameters

selected for our DNN are shown in Table II.

To generate the dataset, we use an off-the-shelf solver for

Problem 2 in MATLAB. Moreover, we exploit the permutation

invariance property of the input data in order to augment the

training dataset and reduce the time of generating the labeled

dataset.

For the sake of brevity, we use the following abbreviations

to refer to the different approaches:

•LC NOC refers to the proposed method, which is a

low complexity algorithm for the NOMA-based outage

compensation. This is fully discussed in Section IV.

•OPT NOC corresponds to the global optimal solution of

Problem 1.

•DNN PA refers to the proposed DNN for the power

allocation problem discussed in Subsection IV-B.

•OPT PA refers to the optimal solution of power alloca-

tion Problem 2.

•No OC corresponds to the case where no compensation

technique is used after the cell outage.

1) Effect of the batch size and learning rate

In this experiment, we illustrate the effect of batch size and

learning rate on the mean square error of DNN PA for the

validation dataset. As we can see from Figure 5, smaller batch

sizes achieve better stability and generalization performance,

TABLE II

PARA MET ER S OF DN N PA

Parameter Value

Batch Size 128

Learning Rate 0.0005

Decay Rate 0.9

Number of samples in whole dataset 130,000

Percentage of whole samples in training set 70%

Percentage of whole samples in validation set 15%

Percentage of whole samples in test set 15%

0 50 100 150 200 250 300

Epochs

0.005

0.01

0.015

0.02

0.025

0.03

MSE (Validation Dataset)

Batch Size = 1024

Batch Size = 512

Batch Size = 256

Batch Size = 128

Batch Size = 64

Batch Size = 32

230 240 250 260 270 280 290 300

10-5

Fig. 5. Effect of the batch size on the mean square error.

leading to lower MSE for the validation dataset. However,

smaller batch sizes incur a greater computational cost since the

optimization should be performed for more iterations during

an epoch. We choose a batch size of 128 for our DNN to

address this trade-off. For this batch size, we vary the learning

rate to evaluate its effect on convergence. As Figure 6 shows,

large learning rates result in divergent behavior and small

learning rates require more steps to converge. In fact, when

the learning rate is small, weights and biases are updated

accordingly and the loss decreases at a shallow rate. However,

increasing the learning rate may cause the learning to jump

over the minimum. For our DNN, a learning rate of 0.0005 is

selected to address this trade-off.

2) Performance evaluation of our proposed method

In this experiment, we investigate the average SE of failed

users in the solution of LC NOC and compare the results

with those of OPT NOC. Since solving Problem 1 is very

time consuming, we limit the number of compensating cells

to N= 2 and N= 3 in this experiment, each of which

serves Un= 4 connected users. The average SE of failed

users is reported in Figure 7. As we can see, the average SE

of LC NOC is very close to that of the optimal solution. This

suggests that our assumptions in the proposed algorithms are

not restrictive and that the DNN is well trained to allocate

near optimal power to compensating BSs.

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0 50 100 150 200 250 300

Epochs

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

MSE (Validation Dataset)

Learning Rate = 0.01

Learning Rate = 0.005

Learning Rate = 0.001

Learning Rate = 0.0005

Learning Rate = 0.0001

250 260 270 280 290 300

310-5

Fig. 6. Effect of the learning rate on the mean square error.

(a)

2 3

0.5

1.5

2.5

Average SE of Failed Users (bps/Hz)

LC_NOC

OPT_NOC

(b)

2 3

0.5

1.5

2.5

Average SE of Failed Users (bps/Hz)

LC_NOC

OPT_NOC

Fig. 7. Average SE of the failed users of LC NOC method compared to the

OPT NOC method, (a): Uf= 3, (b): Uf= 4.

3) Fairness evaluation of our proposed method

In this experiment, LC NOC is compared to No OC. We

vary the number of failed users and present values of the Jain’s

fairness (JF) index and average SE of all users, including both

connected and failed users in Figure 8. Jain’s fairness index

is deﬁned as follows [47]:

JF =

n∈N P

u∈Un

SEc

u,n +P

n∈N P

u∈Uf

SEf

u,n)2

(Uf+P

n∈N

Un)P

n∈N P

u∈Un

(SEc

u,n)2+P

n∈N P

u∈Uf

(SEf

u,n)2,

where SEc

u,nand SEf

u,n are the achieved SE of connected user

uand failed user uif it is served by BS n, respectively. If user

uis not served by any BS, its corresponding achieved SE is

zero. As Figure 8(a) shows, LC NOC provides much higher

fairness. Besides, using LC NOC, a greater number of users in

the network are served. As expected, Figure 8(b) shows that

the average SE of LC NOC is lower due to the fact that a

portion of resources of compensating cells is now allocated to

the failed users with less channel gain. However, we observe

that the reduction in average SE is at most 5%.

6 7 8 9 10 11 12

Number of Failed Users

0.7

0.75

0.8

0.85

0.9

0.95

Jain's Fairness Index

N=3 (LC_NOC)

N=3 (No_OC)

N=6 (LC_NOC)

N=6 (No_OC)

(a)

6 7 8 9 10 11 12

Number of Failed Users

3.3

3.4

3.5

3.6

3.7

3.8

3.9

4.1

4.2

Average SE of All Users (bps/Hz)

N=3 (LC_NOC)

N=3 (No_OC)

N=6 (LC_NOC)

N=6 (No_OC)

(b)

Fig. 8. Comparison of the LC NOC method to the No OC method, (a)

Fairness vs. the number of failed users, (b) Average SE vs. the number of

failed users.

4) Effect of the number of failed users

In this experiment, we evaluate the effect of Ufand Non

the average SE of failed users. We also compare the results of

DNN PA with OPT PA. Figure 9 shows that the average SE

of failed users decreases with the increase in the number of

failed users. This is due to the fact that when the number of

failed users is large, the remaining resources are shared among

a higher number of failed users after providing all connected

users with their minimum data rate requirement. Comparing

the results between our method and the optimal one shows

that DNN PA can approach the average SE in proximity of

the optimization-based method.

It should be noted that in case of a large number of failed

users, an appropriate admission control policy is required with

a view to maximizing the number of users served in the

network. Admission control is beyond the scope of this paper.

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6 7 8 9 10 11 12

Number of Failed Users

1.2

1.4

1.6

1.8

2.2

2.4

2.6

Average SE of Failed Users (bps/Hz)

N=3 (OPT_PA)

N=3 (DNN_PA)

N=6 (OPT_PA)

N=6 (DNN_PA)

Fig. 9. Effect of the number of failed users on the average SE of failed users

as a function of number of compensating base stations (N).

5) Constraint satisfaction of the DNN-based method

In this subsection, we conduct an experiment to investigate

the satisfaction of the constraints in Problem 2 with DNN PA.

We test the model on the unseen test dataset with 8,600

samples and evaluate the results. Constraints C1,C2, and C4

are satisﬁed for all users.

For constraint C3, we calculate the relative error between

the achieved SE of each connected user and its minimum

SE requirement, i.e., smin

u. The results are depicted in Figure

10, which shows that a relative error of less than 0.01 for

98.9 percent of users whose achieved SE deviate from their

minimum requirement.

It should be noted that these constraints prevent the

optimization-based methods from having a closed-form solu-

tion and result in a long execution time. On the other hand,

the DNN-based method greatly reduces the online complexity,

as discussed in Section VII-A, with very little constraint

violation. It is also worth noting that there are some methods

for improving the DNN in this area, such as penalizing the

constraint violation in the loss function during the training of

neural network or implementing a cascading DNN with more

than one neural network. However, an investigation of these

methods will be left for future work.

6) Average runtime performance

In this experiment, we compared the average runtime of

LC NOC and that of OPT NOC. We conducted our simula-

tions on a computer with a 2.60 GHz Intel Core i7 CPU and 16

GB of RAM. We assumed that Unwas 12 for each n∈ N and

N= 3. Tables III and IV show the average ofﬂine and online

runtime required for each of these methods, respectively. To

calculate online runtime for OPT NOC, we ﬁrst computed the

average runtime of Problem 2, and then multiplied it by the

number of possible associations.

As mentioned above, LC NOC needs ofﬂine dataset gener-

ation and DNN training. In general, DNN-based algorithms

suffer from resource constraints in the ofﬂine phase of im-

plementation. However, since powerful processors can be

utilized for ofﬂine procedure, the runtime of this phase is not

0 0.00001 0.0001 0.001 0.01 0.1 >0.1

Relative Error

Percentage of Samples

DNN_PA

Fig. 10. Distribution of deviation from constraint C3.

TABLE III

ONL INE RU NT IME

UfLC NOC OPT NOC

Heuristic Algorithm DNN

12 0.016255 s 0.015625 ms 2.5 ×1015 s

8 0.013926 s 0.015625 ms 1.4 ×1010 s

4 0.011790 s 0.015625 ms 5.9 ×105s

TABLE IV

OFFLI NE RUN TI ME

LC NOC OPT NOC

Dataset Generation Neural Network Training

28.62 hours 14.45 min 0

challenging. Table III shows that LC NOC works efﬁciently

in real time even when the size of the network increases, while

the runtime of OPT NOC increases exponentially in relation

to the size of the network. Therefore, proposing algorithms

with high performances (close to the optimal solutions) and

short runtime is of essential for real scenarios. The above

simulations demonstrate that the online DNN runtime is short.

Since DNN complexity is O(N)and Nis assumed to be ﬁxed

in this experiment, the runtime remains constant.

7) Fairness evaluation in the presence of co-channel inter-

ference

We conducted an experiment to evaluate our proposed

solution in presence of co-channel interference discussed in

Subsection V. For DNN, we use the same architecture as

discussed in Subsection VII-B except for the input layer. A

dataset containing 100,000 samples is generated using an off-

the-shelf solver for Problem 3 (given the user association

matrix) in MATLAB. After data preprocessing, the DNN is

trained with batch learning method and is tested using the test

dataset.

We vary the number of failed users and evaluate its effect

on Jain’s fairness index. In this experiment, the algorithm

presented in Subsection V is compared against the case where

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6 7 8 9 10 11 12

Number of Failed Users

0.18

0.2

0.22

0.24

0.26

Jain's Fairness Index

N=3 (LC_NOC)

N=3 (No_OC)

Fig. 11. Jain’s fairness index evaluation in presence of co-channel interfer-

ence.

no compensation technique is used after outage. As can be

seen from Figure 11, the trend is the same as Figure 8(a), and

our algorithm shows higher fairness. However, the average

SE is lower due to the co-channel interference which can be

improved with an efﬁcient channel allocation algorithm. The

problem of channel allocation is beyond the scope of this paper

and is left to future work.

VIII. CON CL US IO N

In this work, we proposed a newly scheme for cell outage

compensation in NOMA-based systems. The scheme aims

to serve users in the outage zone by surrounding cells in a

way that maximize the SE of failed users while providing

connected users with a predeﬁned level of QoS. We formulated

the compensation process as a joint failed user association

and power allocation problem that was NP-hard. An inno-

vative, low complexity, suboptimal solution was proposed,

where we associated the users in the outage cell with a

heuristic algorithm and allocated their transmit power through

a DNN-based approach. The proposed algorithm was shown

to signiﬁcantly improve the computational complexity, i.e.,

polynomial order with respect to the exponential complexity of

ﬁnding an optimal solution. Simulation results demonstrated

that the performance of the proposed algorithm approached the

optimal solution. The next steps in this research could involve

investigating the effect of other medium access procedures

including but not limited to admission control policy on

the performance of the network in cell outage compensation

processes.

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Elaheh Vaezpour received the Ph.D., M.Sc., and

B.Sc. degrees in computer engineering from Amirk-

abir University of Technology (Tehran Polytechnic)

in 2017, 2011, and 2008, respectively. She was a

Visiting Scholar with the University of California,

Irvine (UCI), USA and also the Newcastle Uni-

versity, Newcastle, Australia in 2016 and 2007,

respectively. She is currently an Assistant Profes-

sor with Iran Telecommunication Research Center,

Tehran, Iran. Her current research interests include

radio resource allocation in wireless networks and

applications of optimization theory and machine learning in system designs.

Layla Majzoobi received the B.S and M.S. de-

grees in electrical engineering from the Amirkabir

University of Technology, Tehran, Iran in 2006 and

2009, respectively, and the Ph.D degree from the

University of Tehran, Tehran, Iran, in 2019. She has

been Research Assistant at the Iran Telecommuni-

cation Research Center, Tehran, Iran, from 2018.

Her current research interests include large scale

distributed optimization, machine learning, and 5G

and 6G networks.

Mohammad Akbari received his B.Sc. in Electrical

Engineering in 2008 from Tabriz University, Tabriz,

Iran and the M.Sc. and Ph.D. degrees both from

Iran University of Science and Technology (IUST),

Tehran, Iran in 2010 and 2016 respectively. During

2010-2017, he was a senior system designer at

Afratab R&D group, Tehran, Iran. In 2017, he joined

as a research assistant professor to the Department

of Communication Technology, ICT Research In-

stitute (ITRC), Tehran, Iran. His current research

interests span topics in telecommunication system

and networks including Self-Organizing Networks, 5G and 6G Networks and

application of Machine Learning techniques in wireless communication.

Saeedeh Parsaeefard (IEEE Senior Member) is

currently a research scientist and visiting faculty

member in University of Toronto. Her research has a

special focus on applying optimization theory, game

theory, and machine learning tools for better under-

standing and analyzing interactions of heterogonous,

non-cooperative, distributed multi-agent systems in

uncertain environments; and in particular wireless

networks (5G and 6G), and IoT, IIoT, and URRLC

applications. She has more than 50 journal and

conference papers all in the best venue of IEEE

transactions and comsoc ﬂag conferences. Her research has been cited more

than 1000 times with h-index of 16 and i10-index of 27. She is a co-author of

two books in wireless network virtualization and robust resource allocation in

future wireless networks, published by Springer. She received the Ph.D. degree

in electrical and computer engineering from Tarbiat Modares University in

2012. From November 2010 to October 2011, she was a visiting Ph.D. student

with the University of California, Los Angeles, Los Angeles, CA, USA. She

was a Postdoctoral Research Fellow with the Department of Electrical and

Computer Engineering, McGill University, Montreal, QC, Canada from 2013

to 2015. She received the IEEE Senior Membership and IEEE Women in

Engineering awards (in region 8) in 2018.

This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/

Journal of Vehicular Technology

>OJVT-2022-03-0025 <17

Dr. Halim Yanikomeroglu is a Professor in the

Department of Systems and Computer Engineering

at Carleton University, Ottawa, Canada. His primary

research domain is wireless communications and

networks. His research group has made contributions

to 4G and 5G wireless technologies. In recent years,

his work has focused on non-terrestrial networks

including UAVs as users and base stations, high

altitude platform stations, and dense satellite net-

works. His collaboration with industry has resulted

in 39 granted patents. He is a Fellow of IEEE,

EIC (Engineering Institute of Canada), and CAE (Canadian Academy of

Engineering), and a Distinguished Speaker for both IEEE Communications

Society and IEEE Vehicular Technology Society. He is currently serving as

the Chair of the IEEE WCNC (Wireless Communications and Networking

Conference) Steering Committee.

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Sep 2023

Sudeep Tanwar

This study's goal is to provide an early analysis of deep learning (DL) for signal identification in wireless systems that use non-orthogonal multiple access (NOMA). The successive interference cancellation (SIC) approach is frequently used at the receiver in NOMA systems when several users are decoded successively. Without explicitly calculating channels, a DL-based NOMA receiver can decode messages for several users at once. To estimate the multiuser uplink channel (CE) and recognize the initial broadcast signal in this study, it is recommended that a deep neural network with bi-directional long short-term memory (Bi-LSTM) be utilized. The suggested Bi-LSTM model, in contrast to conventional CE techniques, may immediately retrieve transmission signals impacted by channel distortion. During the offline training phase, the Bi-LTSM model is trained using simulation data based on channel statistics. The trained model is then applied to retrieve the transmitted symbols in the stage of online deployment. According to the findings, the DL method could outperform a maximum probability detector that considers interference effects when inter-symbol interference is substantial.

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Non-Orthogonal Multiple Access (NOMA) has become a promising evolution with the emergence of fifth-generation (5G) and Beyond-5G (B5G) rollouts. The potentials of NOMA are to increase the number of users, the system's capacity, massive connectivity, and enhance the spectrum and energy efficiency in future communication scenarios. However, the practical deployment of NOMA is hindered by the inflexibility caused by the offline design paradigm and non-unified signal processing approaches of different NOMA schemes. The recent innovations and breakthroughs in deep learning (DL) methods have paved the way to adequately address these challenges. The DL-based NOMA can break these fundamental limits of conventional NOMA in several aspects, including throughput, bit-error-rate (BER), low latency, task scheduling, resource allocation, user pairing and other better performance characteristics. This article aims to provide firsthand knowledge of the prominence of NOMA and DL and surveys several DL-enabled NOMA systems. This study emphasizes Successive Interference Cancellation (SIC), Channel State Information (CSI), impulse noise (IN), channel estimation, power allocation, resource allocation, user fairness and transceiver design, and a few other parameters as key performance indicators of NOMA systems. In addition, we outline the integration of DL-based NOMA with several emerging technologies such as intelligent reflecting surfaces (IRS), mobile edge computing (MEC), simultaneous wireless and information power transfer (SWIPT), Orthogonal Frequency Division Multiplexing (OFDM), and multiple-input and multiple-output (MIMO). This study also highlights diverse, significant technical hindrances in DL-based NOMA systems. Finally, we identify some future research directions to shed light on paramount developments needed in existing systems as a probable to invigorate further contributions for DL-based NOMA system.

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In this paper, we propose a long short-term memory-based deep learning (DL) architecture for signal detection in uplink and downlink rate-splitting multiple access systems with multi-carrier modulation, over Nakagami-m fading and generalized Gaussian noise (GGN). The proposed DL detector completely eliminates the need for the use of successive interference cancellation (SIC), which suffers from disadvantages such as error propagation. In an orthogonal frequency division multiplexing setting, we show that the proposed DL detector outperforms the standard SIC receivers such as the least squares detector and the minimum mean-squared error receiver, and attains the performance of the optimal maximum likelihood detector, in terms of the symbol error rate (SER). Furthermore, we study the effects of the shaping parameter of GGN, hyperparameters of the DL network such as batch size and learning rate on the SER performance.

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Abstract In this paper, a system for LTE Cell Outage Compensation (COC) based on hybrid Genetic Algorithms (GA) and Artificial Neural Networks (ANN) has been proposed. COC aims to minimize the impact of cell outage which leads to decrease in operator revenue and/or the customer satisfaction. The proposed system adopts an optimization module to search for an optimal setting of a set of LTE operational parameters to achieve a targeted set of key performance indicators. The optimization process always leads to good enough solutions, but it also requires a huge number of trials. So, in the proposed system, a huge set of outage scenarios is collected along with their optimal argument settings that are acquired by the optimization module and they are used to train an artificial neural network (ANN) module, which acts as an expert that can optimally act on the different situations in real‐time mode. Simulation environment is set to evaluate different LTE measures and Key Performance Indicators (KPIs) on different outage scenarios. Simulation results proved the capability and robustness of the proposed system to minimize the number of users experiencing outage. Simulation results also show that the proposed system achieves optimal parameter settings without violating the overall system performance and with minimal processing time, while introducing significant impact on the performance of LTE.

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Abstract: The ambitious high data-rate applications in the envisioned future beyond fifth-generation (B5G) wireless networks require new solutions, including the advent of more advanced architectures than the ones already used in 5G networks, and the coalition of different communications schemes and technologies to enable these applications requirements. Among the candidate communications schemes for future wireless networks are non-orthogonal multiple access (NOMA) schemes that allow serving more than one user in the same resource block by multiplexing users in other domains than frequency or time. In this way, NOMA schemes tend to offer several advantages over orthogonal multiple access (OMA) schemes such as improved user fairness and spectral efficiency, higher cell-edge throughput, massive connectivity support, and low transmission latency. With these merits, NOMA-enabled transmission schemes are being increasingly looked at as promising multiple access schemes for future wireless networks. When the power domain is used to multiplex the users, it is referred to as the power domain NOMA (PD-NOMA). In this paper, we survey the integration of PD-NOMA with the enabling communications schemes and technologies that are expected to meet the various requirements of B5G networks. In particular, this paper surveys the different rate optimization scenarios studied in the literature when PD-NOMA is combined with one or more of the candidate schemes and technologies for B5G networks including multiple-input-single-output (MISO), multiple-input-multiple-output (MIMO), massive-MIMO (mMIMO), advanced antenna architectures, higher frequency millimeter-wave (mmWave) and terahertz (THz) communications, advanced coordinated multi-point (CoMP) transmission and reception schemes, cooperative communications, cognitive radio (CR), visible light communications (VLC), unmanned aerial vehicle (UAV) assisted communications and others. The considered system models, the optimization methods utilized to maximize the achievable rates, and the main lessons learnt on the optimization and the performance of these NOMA-enabled schemes and technologies are discussed in detail along with the future research directions for these combined schemes. Moreover, the role of machine learning in optimizing these NOMA-enabled technologies is addressed.

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May 2020

The increasing demands for massive connectivity, low latency, and high reliability of future communication networks require new techniques. Multiple-input-multiple-output non-orthogonal multiple access (MIMO-NOMA), which incorporates the NOMA concept into MIMO, is an appealing technology to enhance system throughput and energy efficiency. However, rapidly changing channel conditions and extremely complex spatial structure degrade the system performance and hinder its application. Thus, to tackle these limitations, in this paper, we propose a deep learning-based MIMO-NOMA framework for maximizing the sum data rate and energy efficiency. To be specific, we design an effective communication deep neural network (CDNN) in which several convolutional layers and multiple hidden layers are included. Thanks to the impressive representation ability of the deep learning technique, the CDNN framework addresses the power allocation problem for achieving higher data rate and energy efficiency of MIMO-NOMA with the aid of training algorithms. Additionally, simulation results corroborate that the proposed CDNN framework is a good candidate to enhance the performance of MIMO-NOMA in term of power allocation, and extensive simulations show that it realizes larger sum data rate and energy efficiency compared with conventional strategies.

Distributed User Clustering and Resource Allocation for Imperfect NOMA in Heterogeneous Networks

Article

Full-text available

Jul 2019

In this paper, we propose a distributed cluster formation (CF) and resource allocation (RA) framework for non-ideal non-orthogonal multiple access (NOMA) schemes in heterogeneous networks. The imperfection of the underlying NOMA scheme is due to the receiver sensitivity and interference residue from non-ideal successive interference cancellation (SIC), which is generally characterized by a fractional error factor (FEF). Our analytical findings first show that several factors have a significant impact on the achievable NOMA gain. Then, we investigate fundamental limits on NOMA cluster size as a function of FEF levels, cluster bandwidth, and quality of service (QoS) demands of user equipments (UEs). Thereafter, a clustering algorithm is developed by taking feasible cluster size and channel gain disparity of UEs into account. Finally, we develop a distributed α-fair RA framework where α governs the trade-off between maximum throughput and proportional fairness objectives. Based on the derived closed-form optimal power levels, the proposed distributed solution iteratively updates bandwidths, clusters, and UEs’ transmission powers. Numerical results demonstrate that proposed solutions deliver a higher spectral and energy efficiency than traditionally adopted basic NOMA cluster size of two. We also show that an imperfect NOMA cannot always provide better performance than orthogonal multiple access under certain conditions. Finally, our numerical investigations reveal that NOMA gain is maximized under downlink/uplink decoupled (DUDe) UE association.

A Cell Outage Compensation Mechanism Based on IPSO for 5G Ultra-dense Small Cell Networks

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A Decade Survey of Transfer Learning (2010–2020)

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Oct 2020

Transfer learning (TL) has been successfully applied to many real-world problems that traditional machine learning (ML) cannot handle, such as image processing, speech recognition, and natural language processing (NLP). Commonly, TL tends to address three main problems of traditional machine learning: (1) insufficient labeled data, (2) incompatible computation power, and (3) distribution mismatch. In general, TL can be organized into four categories: transductive learning, inductive learning, unsupervised learning, and negative learning. Furthermore, each category can be organized into four learning types: learning on instances, learning on features, learning on parameters, and learning on relations. This article presents a comprehensive survey on TL. In addition, this article presents the state of the art, current trends, applications, and open challenges.

A CoMP-based Outage Compensation Solution For Heterogeneous Femtocell Networks

Article

Dec 2019
COMPUT NETW

In wireless cellular networks, self-healing is one of the three functionalities for self-organizing networks, and it has four major components: fault detection, fault diagnosis, fault response and fault recovery. In this paper, we propose a cell outage compensation mechanism (fault response scheme) using a network cooperation scheme in a heterogeneous network environment with densely deployed Femto Base Stations (FBSs). The network cooperation scheme for FBSs uses the Coordinated Multi-Point (CoMP) transmission and reception with joint processing technique where the main purpose of cooperation among FBSs is to guarantee service to UEs even in cases where their primary FBSs or their backhauls fail. The objective of our proposed mechanism is to maximize the total users’ throughput taking into consideration the spectrum and power constraints. Therefore, different clustering methods are studied and analyzed to improve the performance of the network cooperation scheme. Simulation results show that our proposed network cooperation scheme using CoMP can improve the Femto User Equipment (FUE) throughput by more than 30% compared to a non-cooperation solution for self-healing, and CoMP schemes with spectral clustering and k-means clustering algorithms can improve FUE throughput by up to 50%. Moreover, the proposed CoMP operation schemes prevent service rate from dramatic drop when FBSs fail.

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Article

Dec 2019

A deep neural network (DNN) based power control method that aims at solving the non-convex optimization problem of maximizing the sum rate of a fading multi-user interference channel is proposed. Towards this end, we first present PCNet, which is a multi-layer fully connected neural network that is specifically designed for the power control problem. A key challenge in training a DNN for the power control problem is the lack of ground truth, i.e., the optimal power allocation is unknown. To address this issue, PCNet leverages the unsupervised learning strategy and directly maximizes the sum rate in the training phase. We then present PCNet+, which enhances the generalization capacity of PCNet by incorporating noise power as an input to the network. Observing that a single PCNet(+) does not universally outperform the existing solutions, we further propose ePCNet(+), a network ensemble with multiple PCNets(+) trained independently. Simulation results show that for the standard symmetric K-user Gaussian interference channel, the proposed methods can outperform state-of-the-art power control solutions under a variety of system configurations. Furthermore, the performance improvement of ePCNet comes with a reduced computational complexity.

Deep Neural Network for Resource Management in NOMA Networks

Article

Nov 2019

Resource management plays a crucial role in improving sum rate of non-orthogonal multiple access (NOMA) networks. However, the traditional resource management methods have considerable complexity, creating a huge challenge in computational efficiency. To handle this challenge, a resource management method is proposed based on a deep neural network (DNN). The key advantage of the method is that the DNN can perform in almost real-time resource allocation because it requires a very simple operation. In this paper, the resource management problem of the NOMA system adopting successive interference cancellation (SIC) technology in the receivers is studied, including the power allocation stage and the user scheduling stage. For power allocation stage, the generic fullyconnected DNN is trained to approximate the power allocation of interior point method (IPM), which not only greatly improves the computational efficiency but also increases the sum rate of the system. Based on the allocated power, the user scheduling algorithm is performed to further increase the system sum rate. Finally, simulation results verify some performances of the proposed algorithms.

A Deep Reinforcement Learning based Mechanism for Cell Outage Compensation in Massive IoT Environments

Conference Paper

Jun 2019

Deep Learning for Radio Resource Allocation in Multi-Cell Networks

Article

Apr 2019

The increased complexity and heterogeneity of emerging 5G and B5G wireless networks will require a paradigm shift from traditional resource allocation mechanisms. Deep learning (DL) is a powerful tool where a multi-layer neural network can be trained to model a resource management algorithm using network data.Therefore, resource allocation decisions can be obtained without intensive online computations which would be required otherwise for the solution of resource allocation problems. In this context, this article focuses on the application of DL to obtain solutions for the radio resource allocation problems in multi-cell networks. Starting with a brief overview of a DNN as a DL model, relevant DNN architectures and the data training procedure, we provide an overview of existing state-of-the-art applying DL in the context of radio resource allocation. A qualitative comparison is provided in terms of their objectives, inputs/outputs, learning and data training methods. Then, we present a supervised DL model to solve the sub-band and power allocation problem in a multi-cell network. Using the data generated by a genetic algorithm, we first train the model and then test the accuracy of the proposed model in predicting the resource allocation solutions. Simulation results show that the trained DL model is able to provide the desired optimal solution 86.3 percent of the time.

A Deep Learning-Based Approach for Cell Outage Compensation in NOMA Networks

Abstract

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