# Integrated Access and Backhaul (IAB) in Low Altitude Platforms

Reza Ghasemi Alavicheh , S. Mohammad Razavizadeh , and Halim Yanikomeroglu
Reza Ghasemi Alavicheh and S. M. Razavizadeh are with the School of Electrical
Engineering, Iran University of Science and Technology (IUST), Tehran, Iran
(emails<EMAIL_ADDRESS>and smrazavi@iust.ac.ir). H.
Yanikomeroglu is with the Non-Terrestrial Networks (NTN) Lab, Department of
System and Computer Engineering (SCE), Carleton University, Ottawa, Canada
(email: halim@sce.carleton.ca).
CORRESPONDING AUTHOR: S. Mohammad Razavizadeh 0009-0002-3620-5481
0000-0002-1732-4779 0000-0003-4776-9354

###### Abstract

In this paper, we explore the problem of utilizing Integrated Access and
Backhaul (IAB) technology in Non-Terrestrial Networks (NTN), with a particular
focus on aerial access networks. We consider an Uncrewed Aerial Vehicle
(UAV)-based wireless network comprised of two layers of UAVs: (a) a lower
layer consisting a number of flying users and a UAV Base Station (BS) that
provides coverage for terrestrial users and, (b) an upper layer designated to
provide both wireless access for flying users and backhaul connectivity for
UAV BS. By adopting IAB technology, the backhaul and access links
collaboratively share their resources, enabling aerial backhauling and the
utilization of the same infrastructure and frequency resources for access
links. A sum-rate maximization problem is formulated by considering aerial
backhaul constraints to optimally allocate the frequency spectrum between
aerial and terrestrial networks. We decompose the resulting non-convex
optimization problem into two sub-problems of beamforming and spectrum
allocation and then propose efficient solutions for each. Numerical results in
different scenarios yield insightful findings about the effectiveness of using
the IAB technique in aerial networks.

###### Index Terms:

6G, Integrated Access and Backhaul (IAB), Low Altitude Platform (LAP),
Wireless Backhaul, Hybrid Beamforming, Successive Convex Approximation (SCA),
Uncrewed Aerial Vehicle (UAV), Unmanned Aerial Vehicle

##  I Introduction

We are witnessing a significant increase in the demands for wireless services
and applications, leading to more densely populated networks of users and Base
Stations (BS). For instance, BS density has increased from
$5~{}\rm{BSs}/\rm{km}^{2}$ in 3G to over $50~{}\rm{BSs}/\rm{km}^{2}$ in 5G,
and the deployment plans are shifting from Macro Base Stations (MBS) to Small
Base Stations (SBS) to manage the massive traffic loads [1]. This growth will
place immense stress on the Radio Access Network (RAN) and especially the
backhaul links. Employing fiber optic backhaul for each SBS is both
economically and geographically impractical. Therefore, new generations of
wireless networks like 6G require cost-effective wireless backhaul solutions
for practicality, scalability, and reduced hardware [2].

Integrated Access and Backhaul (IAB), first proposed in 3GPP Release 15 [3] is
a promising wireless backhauling technique that addresses the challenges of
dense mobile networks through self-backhauling, combining access and backhaul
link resources in the BS. It uses a chain architecture, where multiple SBSs
are ultimately connected to a macro BS. Traditional wireless backhaul in
microwave frequency bands is unsuccessful due to insufficient spectrum
availability to meet the ever-evolving capacity demands. In contrast,
millimeter-Wave (mmWave) bands offer a cost-effective solution for high-speed
data transmission, making them ideal for wireless backhaul. However, the
mmWave bands suffer from high path-loss and range restrictions. The IAB
technique addresses these challenges with the help of this multi-hop
capability and shared utilization of both access and backhaul resources [4].
Although the IAB technique is well-understood as a potential solution for the
backhaul limitations in dense terrestrial networks [5], [6], and [7] its usage
in Aerial Networks (ANs) is still under exploration and requires further
research and evaluation to provide better coverage for ANs [8]. In general,
when studying the IAB technique and UAV-based networks together, two
approaches can be adopted. In the first approach, UAVs are used to help and
improve the performance of the IAB technique in providing the required
backhaul for terrestrial networks (UAV-assisted IAB) [9], [10], [11], [12],
[13], [14], [15]. The second approach that (to the best of our knowledge) has
not been explored in the literature is utilizing the IAB technique to address
the backhaul challenges to the UAV-based ANs (IAB-assisted UAV). Regarding the
first approach, the problem of mitigating interference between access and
backhaul links in the UAV-assisted IAB networks has been studied in some
papers. Using terrestrial BSs for backhaul and exploiting UAVs’ 3D mobility
for interference management and power optimization was studied in [9], [11].
Some of the papers investigate the optimal placement of UAV-IAB nodes and
proposed solutions such as adaptive deployment  [12] and joint path selection
and resource allocation [13]. Moreover, some works compare the performance of
UAV-assisted IAB networks with fully ground-based networks in terms of energy
efficiency [14], [15]. Another aspect considered is the uplink access of users
and imperfect fronthaul of UAV-aided IAB in a cell-free network, which can be
optimized by adjusting UAV power and 3D placement [16]. However, most of these
works fail to address the challenge of limited aerial access and backhaul
coverage caused by down-tilt antennas of terrestrial BSs, as noted in [17].

As discussed above, in the realm of aerial wireless backhaul, the concept of
IAB-assisted UAV networks remains relatively unexplored. In this paper, we aim
to fill this gap by proposing a novel framework for IAB-assisted UAV networks.
The primary objective is to alleviate the backhaul bottleneck commonly
encountered in UAV networks, which also has the potential to worsen and become
critical in future wireless networks that rely more on non-terrestrial
networks [18]. This is achieved by leveraging aerial IAB-nodes and eliminating
reliance on terrestrial BSs. While our proposed framework does consider both
aerial and terrestrial network coverage as a result of its innovative
architecture, and addresses interference issues through the application of a
hybrid beamforming method, the main objective is to evaluate our proposed
network’s performance in terms of network sum-rate. This evaluation is carried
out using analytical methods and examined with simulation results. Our
considered Uncrewed Aerial Systems (UAS) or aerial wireless network model
employs a multi-tier aerial architecture, comprising two tiers of UAV BSs. In
the lower tier, there is a UAV BS that provides coverage for terrestrial
users. This UAV acts as a so-called IAB-node for the IAB technique and
receives aerial backhaul connectivity service from a so-called IAB-donor in
the upper layer. It is designated to provide aerial access for some flying
users or aerial User Equipment (UE) as well as backhaul connectivity for UAV
BS. In addition, in the upper layer, the IAB-donor UAV node is assumed to be
potentially part of a Vertical Heterogeneous Network (VHetNet) and connected
to High Altitude Platform Stations (HAPS) or satellites for its backhaul
provisioning. These aerial and terrestrial networks share the same frequency
spectrum resources, and we aim to optimize the allocation of the spectrum
between them, with the goal of achieving sum-rate maximization. To address the
non-convex and complex optimization problem, we propose an efficient solution
that decomposes the main problem into two sub-problems. We spatially separate
the aerial access and backhaul links by proposing a hybrid beamforming scheme
within this Multiple-Input Single-Output (MISO) multi-user system.
Subsequently, we derive a closed-form solution for the spectrum allocation
problem. In conclusion, we compare the results obtained from our approach with
an equivalent non-IAB scenario. Our findings underscore the superior
performance of the IAB approach for aerial wireless backhauling, particularly
in terms of sum-rate and energy efficiency, making it suitable for catering to
both aerial and terrestrial users.

The paper is structured in the following way: We begin by presenting the
system and channel models in Sec. II. Then, in Sec. III, we discuss the
problem formulation and present the optimization problems, which include
hybrid beamforming design, spectrum allocation, and evaluation of bandwidth
impact on thermal noise. Finally, we present the numerical results in Sec. IV,
followed by the conclusion in Sec. V.
Notation Conventions: Symbol ${\mathbb{C}^{m\times n}}$ denotes a complex
space with dimensions $\mathrm{m}$ by $\mathrm{n}$. Scalar values, vectors,
and matrices are respectively represented by $\mathrm{a}$, a, and A. Transpose
and Hermitian transpose of a matrix are indicated by $\textbf{A}^{T}$ and
$\textbf{A}^{H}$. Symbol $\textbf{I}_{K}$ signifies an identity matrix of size
$K\times K$. $\textbf{[A]}_{i,j}$ denotes the element in the $i$th row and
$j$th column of matrix A. The symbols $\mathrm{Tr}\hskip 1.0pt[.]$,
$\mathrm{log(.)}$, and $\mathbb{E}\hskip 1.0pt[.]$ represents the trace,
logarithm, and expected value operations, respectively. A diagonal matrix is
represented by $\mathrm{diag}\hskip 1.0pt[.]$ Symbols ${\lvert.\rvert}$ and
${\lVert.\rVert}_{F}$ respectively denote absolute value and the Frobenius
norm.

###  I-A IAB Workflow

Each node in IAB architecture consists of two components. In an IAB-node,
these components are the IAB-node Distributed Unit (IAB-node-DU) and the IAB-
node Mobile Termination (IAB-node-MT). In an IAB-donor, the components are the
IAB-donor Centralized Unit (IAB-donor-CU) and IAB-donor-DU. The MT part is
responsible for establishing the radio connection, including various backhaul
link layers with the IAB-donor. The CU primarily handles the control plane and
the user plane functionalities for the backhaul. The DU is responsible for
providing New Radio (NR) functions to a UE or the MT part of another IAB-node.
To better integrity with the traditional network model, based on [19], the MT
part of each node acts like a UE, and the DU part functions like the DU of a
gNB. A new protocol in IAB, called Backhaul Adaptation Protocol (BAP), is
responsible for forwarding Internet protocol (IP)-based packets between an
IAB-node or IAB-donor over the backhaul link. The BAP header includes a unique
identifier that specifies the connection’s destination IAB-node and the path
(if there are multiple nodes ahead) through the BAP address and BAP path ID.
The BAP header must ensure that the sent packets reach their final
destination, distinguishing IAB backhaul features from the traditional model.
The lower layer protocols, including physical (PHY), Medium Access Control
(MAC), and Radio Link Control (RLC), and the upper layer protocols, including
Packet Data Convergence Protocol (PDCP), Radio Resource Control (RRC), and
Service Data Adaptation Protocol (SDAP), are performed in the DU and CU,
respectively. The process of adding an IAB-node to the network is designed by
3GPP to be similar to the traditional method of adding a gNB to the network,
which is carried out in three stages [20], [21].

Initialization and Synchronization: The IAB-node-MT initiates a connection to
the IAB-donor similar to a regular UE, acting in the lower layer of the system
model. This initialization and synchronization process involves the IAB-node-
MT scanning the frequency band for Synchronization Signal Blocks (SSBs) and
performing a random access procedure. Following this, an RRC connection is
established with the IAB-donor-CU and authentication with the Core Network is
completed.

Backhaul Link Establishment: Next, the backhaul link is established. This
involves configuring a new Backhaul RLC channel. The BAP address for the IAB-
node is configured, and the default BAP Routing ID for the upstream direction
is set. Additionally, the BAP sublayer is updated to support routing between
the new IAB-node and the IAB-donor-DU, ensuring efficient data flow.

IAB-node Configuration: Finally, the DU part of the new IAB-node is
configured, and an F1 link is established between the IAB-donor-CU and the
IAB-node-DU. Once setup is complete, the new IAB-node begins serving UEs.

Initializationand SynchronizationNetwork ConnectionFrequency Band
ScanningRandom Access and RRC SetupBackhaul LinkEstablishmentBH RLC Channel
ConfigurationBAP Sublayer UpdateIAB NodeConfigurationDU ConfigurationService
Activation Figure 1: Three stages of IAB Workflow.

##  II System Model

The proposed model can be incorporated into a broader Non-Terrestrial Network
(NTN) scenario, which includes satellites, HAPS, and additional UAVs, for
instances such as urban emergency coverage [22] and situations like natural
disasters or other emergency events in urban areas where terrestrial
communication infrastructure may be compromised. The proposed system model
leverages an upper-layer of aerial nodes (e.g. UAV) to provide backhaul
connectivity to a lower-layer of aerial base stations serving both aerial and
terrestrial users. During natural disasters or emergencies when terrestrial
networks may fail, maintaining this aerial backhaul connectivity becomes
critical to ensure data can still be forwarded between the upper aerial layer
and terrestrial users served by the lower-layer IAB-node. Data for terrestrial
users must be forwarded through the aerial backhaul link from the upper-layer
network (IAB-donor) to the lower-layer aerial base station (IAB-node), as the
IAB-node doesn’t have a direct connection to the core network. The flexibility
of the IAB approach to dynamically allocate bandwidth and resources between
aerial and terrestrial links (as opposed to static allocation in non-IAB) can
help alleviate the backhaul bottleneck when more capacity is needed. Each IAB-
node is equipped with a uniform planar array (UPA) with total $N=N_{x}\times
N_{y}$ array elements. Each antenna array is divided into multiple sub-arrays,
in which some are assigned to the aerial access links and others to the aerial
backhaul link in the IAB-donor node. The LoS aerial channel between an aerial
user and the IAB-donor and also the LoS backhaul channel are denoted by
${\mathbf{h}}_{a,j}\in\mathbb{C}^{N\times 1}$. Also, the channel between a
terrestrial user and the IAB-node is represented by
${\mathbf{h}}_{t,i}\in\mathbb{C}^{N\times 1}$. IAB-donor and IAB-node are
associated with a fixed number of users from $J-1$ and $I$, respectively, as
shown in Fig. 2. The network comprises a total of $J$ aerial-to-aerial links,
with $J-1$ links dedicated to aerial users and one link serving as the
backhaul for the IAB-node. Additionally, there are $I$ aerial-to-terrestrial
links.

Figure 2: Aerial Integrated Access and Backhaul (IAB) enabled system model
serving two sets of aerial and terrestrial users.

Since we were considering a mmWave scenario, we used the Saleh-Valenzuela
channel model [23], [24], [25] that can be expressed as follows for aerial and
terrestrial connections:

TABLE I: The Definitions of The Symbols

Symbol | Definition
---|---
$N$ | Total number of array elements in the uniform planar array (UPA)
$N_{x}\times N_{y}$ | Dimensions of the UPA
${\mathbf{h}}_{a,j}$ | Channel between an aerial user or IAB-node and the IAB-donor
${\mathbf{h}}_{t,i}$ | Channel between a terrestrial user and the IAB-node
$J$ | Number of aerial-to-aerial links
$I$ | Number of aerial-to-terrestrial links
$\gamma_{0}$ | Channel power gain or reference path loss
$d_{0}$ | Reference distance
$n_{LoS}$ | Path loss exponent
$d_{j}$ | Euclidean distance between an aerial user and the IAB-donor
$d_{i}$ | Euclidean distance between a terrestrial user and the IAB-node
$\theta,\phi$ | Azimuth and elevation angles representing the array’s Angle of Departure (AoD)
$\mathbf{a}(\theta,\phi)$ | Array steering vector
$r$ | Antenna element spacing, expressed in half-wavelength
$\lambda$ | Wavelength
$\mathbf{F}_{a}^{RF},\mathbf{F}_{t}^{RF}$ | Analog beamformers for aerial and terrestrial links
$\mathbf{F}_{a}^{BB},\mathbf{F}_{t}^{BB}$ | Digital beamformers for aerial and terrestrial links
$\Lambda$ | Frobenius norm between $\mathbf{F}^{zf}$ and $\mathbf{F}^{RF}\mathbf{F}^{BB}$
$N_{RF}$ | Number of Radio Frequency (RF) chains
$p_{j},p_{i}$ | Transmission power for aerial and terrestrial users
$s_{a,j},s_{t,i}$ | Transmitted symbols for aerial and terrestrial users
$P_{1},P_{2}$ | Total available power at IAB-donor and IAB-node
$n_{a},n_{t}$ | Thermal noise for aerial and terrestrial links
$P_{n}$ | Thermal noise power spectral density
$\mathbf{P}_{t},\mathbf{P}_{a}$ | Diagonal power allocation matrix for terrestrial and aerial users
$\mathbf{I}_{a},\mathbf{I}_{t}$ | Intra-tier interference terms for aerial and terrestrial links
$w$ | Total available bandwidth
$\mu_{a},\mu_{t}$ | Bandwidth coefficients for aerial and terrestrial links
$R_{a,j},R_{t,i}$ | Received Spectral Efficiency (SE) for aerial and terrestrial links
$\mathfrak{R}_{a},\mathfrak{R}_{t}$ | Sum-SE of aerial and terrestrial users
$\sigma_{a}^{2},\sigma_{t}^{2}$ | Thermal noise power for aerial and terrestrial links
$\mathfrak{R}$ | Total sum-rate of the network
$\zeta$ | Bottleneck rate of aerial backhaul link

$\displaystyle\mathbf{h}_{{a,j}}$
$\displaystyle=\sqrt{\frac{\gamma_{0}}{{d_{j}}^{n_{LoS}}}}\mathbf{a}\left(\theta_{j}^{{a}},\phi_{j}^{{a}}\right),$
(1a) $\displaystyle\mathbf{h}_{{t},{i}}$
$\displaystyle=\sqrt{\frac{\gamma_{0}}{{d_{i}}^{n_{LoS}}}}\mathbf{a}\left(\theta_{i}^{{t}},\phi_{i}^{{t}}\right).$
(1b)

The channel matrix, containing all the channel vectors of each set of users,
can be expressed as:

$\displaystyle\mathbf{H}_{{a}}$
$\displaystyle=[\mathbf{h}_{{a,1}}\vdots\dots\vdots\mathbf{h}_{a,J}]^{T},\hskip
14.22636pt\mathbf{H}_{a}\in\mathbb{C}^{J\times N},$ (2a)
$\displaystyle\mathbf{H}_{{t}}$
$\displaystyle=[\mathbf{h}_{{t,1}}\vdots\dots\vdots\mathbf{h}_{t,I}]^{T},\hskip
18.49411pt\mathbf{H}_{t}\in\mathbb{C}^{I\times N}.$ (2b)

According to (1a) and (1b), $\gamma_{0}=-20\log_{10}(f)-32.45$ [dB] represents
the channel power gain or reference path loss with $d_{0}=1$ m as a reference
distance [26]. The constant $n$ denotes the path loss exponent and its value
typically falls within the range of $2-4$. Fig. 3 illustrates a 3D simulation
environment representing the proposed system model. The positions of the nodes
are denoted by their Cartesian coordinates $(x,y,z)$, while their heights are
represented by $h$. The Euclidean distances separating the nodes are
represented by $d$. Specifically, the heights of the IAB-donor and IAB-node
are denoted as $h_{\text{uav}}$ and $h_{\text{cuav}}$, respectively. The
aerial users are positioned at a height of $h_{j}=h_{\text{auav}}$, whereas
the terrestrial users are considered to be at ground level, with a height of
$h_{i}=0$. The distances $d_{j}$ and $d_{i}$ represent the separation between
an aerial user and the IAB-donor or between a terrestrial user and the IAB-
node, as described below:

$\displaystyle{d}_{j}$
$\displaystyle=\sqrt{({x}_{j}-{x}_{0})^{2}+({y}_{j}-{y}_{0})^{2}+({h}_{j}-{h}_{uav})^{2}},$
(3a) $\displaystyle{d}_{i}$
$\displaystyle=\sqrt{({x}_{i}-{x}_{0})^{2}+({y}_{i}-{y}_{0})^{2}+({h}_{i}-{h}_{cuav})^{2}}.$
(3b)

In the azimuth and elevation directions, $\phi$ and $\theta$ respectively
represent the array’s Angle of Departure (AoD). The array steering vector for
both the aerial and terrestrial networks can be expressed as

$\displaystyle\mathbf{a}\left(\theta,\phi\right)$
$\displaystyle=[1,e^{j\frac{2\pi}{\lambda}r\sin{(\theta)}[(n_{x}-1)\cos{(\phi)}+(n_{y}-1)\sin{(\phi)}]},\cdots,$
$\displaystyle\hskip
28.45274pte^{j\frac{2\pi}{\lambda}r\sin{(\theta)}[(N_{x}-1)\cos{(\phi)}+(N_{y}-1)\sin{(\phi)}]}]^{T}.$
(4)

Figure 3: In a $2.25~{}\textrm{km}^{2}$ area, both aerial and terrestrial UEs
are randomly distributed according to a normal distribution. They satisfy a
minimum specified distance from each other, as detailed in [27], and are
within defined sub-regions. All aerial UEs are located at the same altitude.

The parameter $r$ in (II) represents the antenna element spacing, expressed in
half-wavelength. The downlink transmission of a hybrid analog-digital
beamforming scheme is considered, where the analog and digital beamformers are
denoted ${\mathbf{F}_{a}}^{RF}$, ${\mathbf{F}_{t}}^{RF}\in\mathbb{C}^{N\times
N_{RF}}$ for both aerial and terrestrial links and
${\mathbf{F}}_{a}^{BB}\in\mathbb{C}^{N_{RF}\times J}$ for aerial access and
backhaul links and ${\mathbf{F}}_{t}^{BB}\in\mathbb{C}^{N_{RF}\times I}$ for
terrestrial access links in a Multiple Input Single Output (MISO) scenario
[28], [29]. $N_{RF}$ is the number of Radio Frequency (RF) chains that we
consider to be equal to the number of users in each group. Digital or Base
Band (BB) beamformers can be represented as follows:

$\displaystyle\mathbf{F}_{a}^{BB}$ $\displaystyle=[\mathbf{f}_{1}^{BB}\
\dots\mathbf{f}_{J}^{BB}],$ (5a) $\displaystyle\mathbf{F}_{t}^{BB}$
$\displaystyle=[\mathbf{f}_{1}^{BB}\dots\mathbf{f}_{I}^{BB}].$ (5b)

By considering the Frequency Division Multiplexing (FDM) configuration,
frequency resources are allocated to aerial and terrestrial access links. This
allotment results in only intra-tier interference occurring solely between the
aerial access and backhaul links, as well as the terrestrial access links.
Also, hybrid analog-digital beamforming is employed to shape the radiation
pattern of subarrays, direct energy to the desired direction, and minimize
interference between links. This approach facilitates the establishment of
multiple connections simultaneously. The received signals at the $j^{th}$
aerial (access or backhaul) link can be expressed as:

$\displaystyle y_{a,j}=\sqrt{p_{j}}$ $\displaystyle\hskip
2.84526pt\mathbf{h}_{a,j}^{H}\mathbf{F}_{a}^{RF}\mathbf{f}_{a,j}^{BB}s_{a,j}$
(6) $\displaystyle+\sum_{k=1/j}^{J}\sqrt{p_{k}}\hskip
2.84526pt\mathbf{h}_{a,j}^{H}\mathbf{F}_{a}^{RF}\mathbf{f}_{a,k}^{BB}s_{a,k}+n_{a},$

and the received access signal at $i^{th}$ terrestrial user as:

$\displaystyle y_{t,i}=\sqrt{p_{i}}$ $\displaystyle\hskip
2.84526pt\mathbf{h}_{t,i}^{H}\mathbf{F}_{t}^{RF}\mathbf{f}_{t,i}^{BB}s_{t,i}$
(7) $\displaystyle+\sum_{k=1/i}^{I}\sqrt{p_{k}}\hskip
2.84526pt\mathbf{h}_{t,i}^{H}\mathbf{F}_{t}^{RF}\mathbf{f}_{t,k}^{BB}s_{t,k}+n_{t}.$

In these equations, the second term represents the interference among access
links of users and the third term accounts for temperature noise. The
transmitting power for each set is represented by a diagonal matrix for
terrestrial links $\mathbf{P}_{t}=$ diag($p_{1}$, … ,$p_{I}$) and for aerial
links $\mathbf{P}_{a}=$ diag($p_{1}$, … ,$p_{J}$) consisting of power assigned
to each link as $p_{i}=\frac{P_{2}}{I}$, $p_{j}=\frac{P^{\prime}_{1}}{J-1}$
and $P^{\prime}_{1}$ is the remaining power of IAB-donor after allocating the
required power to the backhaul when IAB-node is detected among aerial users.
Eq. (6) and (7) can be represented as a matrix scheme containing total signals
for each group of users. In the below equations, interference terms are shown
by $\mathbf{I}_{a},\mathbf{I}_{t}$ and include all intra-tier interference
between aerial links and terrestrial links and the transmitted symbols are
${\mathbf{s}}_{a}\in\mathbb{C}^{J\times 1}$ and
${\mathbf{s}}_{t}\in\mathbb{C}^{I\times 1}$ and
$\mathbb{E}[{|\mathbf{s}}_{a}|^{2}]=1$,
$\mathbb{E}[{|\mathbf{s}}_{t}|^{2}]=1$,

$\displaystyle\mathbf{y}_{{a}}$
$\displaystyle=\mathbf{H}_{{a}}\mathbf{F}_{{a}}\mathbf{s}_{{a}}+\mathbf{I}_{{a}}+\mathbf{n}_{{a}},$
(8) $\displaystyle\mathbf{y}_{{t}}$
$\displaystyle=\mathbf{H}_{{t}}\mathbf{F}_{{t}}\mathbf{s}_{{t}}+\mathbf{I}_{{t}}+\mathbf{n}_{{t}}.$
(9)

There is a total available bandwidth of $w$, and we aim to utilize this
bandwidth efficiently to provide both aerial and terrestrial services. The
bandwidth allocated to aerial (access and backhaul) links and terrestrial
access links represented as $\mu_{a}$ and $\mu_{t}$, referred to as bandwidth
coefficients, and they must satisfy the following conditions:

$\displaystyle 0\leq\mu_{a}\leq 1,$ (10a) $\displaystyle 0\leq\mu_{t}\leq 1,$
(10b) $\displaystyle\mu_{t}+\mu_{a}=1.$ (10c)

Received Spectral Efficiency (SE) at aerial and terrestrial links can be
written as (11a) and (11b)

$\displaystyle R_{a,j}$
$\displaystyle=\log_{2}\left(1+\frac{{p_{j}}\left|\mathbf{h}_{a,j}^{H}\mathbf{F}_{a}^{RF}\mathbf{f}_{a,j}^{BB}\right|^{2}}{\sum_{k=1/j}^{J}{p_{k}}\left|\mathbf{h}_{a,j}^{H}\mathbf{F}_{a}^{RF}\mathbf{f}_{a,k}^{BB}\right|^{2}+\sigma_{a}^{2}}\right),$
(11a) $\displaystyle R_{t,i}$
$\displaystyle=\log_{2}\left(1+\frac{{p_{i}}\left|\mathbf{h}_{t,i}^{H}\mathbf{F}_{t}^{RF}\mathbf{f}_{t,i}^{BB}\right|^{2}}{\sum_{k=1/i}^{I}{p_{k}}\left|\mathbf{h}_{t,i}^{H}\mathbf{F}_{t}^{RF}\mathbf{f}_{t,k}^{BB}\right|^{2}+\sigma_{t}^{2}}\right).$
(11b)

In these equations, $\sigma_{a}^{2}$ and $\sigma_{t}^{2}$ represent the
thermal noise power for aerial and terrestrial links, respectively.

##  III Problem Formulation

Our objective is to maximize the total sum-rate of the network, which entails
maximizing the sum-rate for both the aerial and terrestrial groups of users.
The sum-rate can be expressed as:

$\displaystyle\mathfrak{R}$
$\displaystyle=\left(\mu_{a}\right)w\sum_{j=1}^{J-1}R_{a,j}+\zeta,$ (12a)
$\displaystyle\zeta$
$\displaystyle=\min\left\\{\left(\mu_{a}\right)wR_{a,b},\left(\mu_{t}\right)w\sum_{i=1}^{I}R_{t,i}\right\\}.$
(12b)

Eq. (12a) consists of two terms: The first term represents the sum-rate of
aerial users, while the second term represents the sum-rate of terrestrial
users. In (12b), aerial backhaul rate denoted as $R_{a,b}$, acts as a
bottleneck and limits the rate of terrestrial users. This effect stems from
the fact that in the proposed architecture, the data to terrestrial users gets
forwarded through the aerial backhaul link from the upper-layer network (IAB-
donor) to the lower-layer aerial base station (IAB-node). So the capacity of
this aerial backhaul link can limit the overall communication rate for
terrestrial users. As the backhaul constraint is related to the value of the
bandwidth coefficient, it is important to take into account its effects on the
bandwidth coefficient range. We initially accounted for the backhaul
limitation through the minimum operation in the objective function (12b).
However, to make the backhaul constraint and its effect on bandwidth
coefficients more explicit, it is introduced as a separate constraint further
in equation (23e), and these constraints are investigated in Sec. III-B. With
the objective function $\mathfrak{R}$, the problem of maximizing the sum-rate,
considering bandwidth allocation, hybrid beamforming, and power limitations of
flying BSs, can be formulated as follows in (13a). $\mathbf{F}_{a}$ and
$\mathbf{F}_{t}$ are hybrid beamforming matrices, constraints (13g) and (13h)
define the total power limitation and $\mathrm{P_{1}}$ and $\mathrm{P_{2}}$
indicate the available power at each UAV BS (IAB-donor and IAB-node). Given
that phase shifters in analog beamformers only change the phase of signals,
each element of the analog matrix should have a constant absolute value in
constraints (13e) and (13f). The height and intra-distance of UAV-IABs are
expressed as $\mathrm{h_{uav}}$ and $\mathrm{d_{uav}}$ and are considered to
be unchanging and assuming the same priority for all users. Due to the
complexity and non-convexity of the optimization problem, caused by (13e) and
(13f), we aim to separate the design of hybrid beamforming from the
optimization of bandwidth coefficients, this decoupling is achieved by
assuming fixed bandwidth coefficients, allowing us to independently maximize
the SE in the first and second terms of the objective function

$\displaystyle\max_{\begin{subarray}{c}\mu_{a},\mu_{t},\mathbf{F}_{a}^{RF},\mathbf{F}_{t}^{RF},\\\
\mathbf{F}_{a}^{BB},\mathbf{F}_{t}^{BB}\end{subarray}}$ $\displaystyle\hskip
2.84526pt\mathfrak{R}(\mu_{a},\mu_{t},\mathbf{F}_{a}^{RF},\mathbf{F}_{t}^{RF},\mathbf{F}_{a}^{BB},\mathbf{F}_{t}^{BB})$
(13a) s.t. $\displaystyle\quad 0\leq\mu_{a}\leq 1,$ (13b) $\displaystyle\quad
0\leq\mu_{t}\leq 1,$ (13c) $\displaystyle\quad\mu_{t}+\mu_{a}=1,$ (13d)
$\displaystyle\quad\left|\left[\mathbf{F}_{a}^{RF}\right]_{l,l^{\prime}}\right|=1\hskip
6.0pt\forall l,l^{\prime},$ (13e)
$\displaystyle\quad\left|\left[\mathbf{F}_{t}^{RF}\right]_{l,l^{\prime}}\right|=1\hskip
6.0pt\forall l,l^{\prime},$ (13f)
$\displaystyle\quad\operatorname{Tr}(\mathbf{{F_{a}}^{H}{F_{a}}})\leq\mathrm{P_{1}},$
(13g)
$\displaystyle\quad\operatorname{Tr}(\mathbf{{F_{t}}^{H}{F_{t}}})\leq\mathrm{P_{2}}.$
(13h)

The problem for hybrid beamforming design can be rewritten as follows:

$\displaystyle\max_{\begin{subarray}{c}\mathbf{F}_{a}^{RF},\mathbf{F}_{a}^{BB}\end{subarray}}$
$\displaystyle\sum_{j=1}^{J}\log_{2}\left(1+\frac{{p_{j}}\left|\mathbf{h}_{a,j}^{H}\mathbf{F}_{a}^{RF}\mathbf{f}_{a,j}^{BB}\right|^{2}}{\sum_{k=1/j}^{J}{p_{k}}\left|\mathbf{h}_{a,k}^{H}\mathbf{F}_{a}^{RF}\mathbf{f}_{a,k}^{BB}\right|^{2}+\sigma_{a}^{2}}\right)$
(14a) s.t.
$\displaystyle\quad\left|\left[\mathbf{F}_{a}^{RF}\right]_{l,l^{\prime}}\right|=1\hskip
14.22636pt\forall l,l^{\prime},$ (14b)
$\displaystyle\quad\operatorname{Tr}(\mathbf{F}_{a}^{H}\mathbf{F}_{a})\leq\mathrm{P_{1}},$
(14c)
$\displaystyle\max_{\begin{subarray}{c}\mathbf{F}_{t}^{RF},\mathbf{F}_{t}^{BB}\end{subarray}}$
$\displaystyle\sum_{i=1}^{I}\log_{2}\left(1+\frac{{p_{i}}\left|\mathbf{h}_{t,i}^{H}\mathbf{F}_{t}^{RF}\mathbf{f}_{t,i}^{BB}\right|^{2}}{\sum_{k=1/i}^{I}{p_{k}}\left|\mathbf{h}_{t,k}^{H}\mathbf{F}_{t}^{RF}\mathbf{f}_{t,k}^{BB}\right|^{2}+\sigma_{t}^{2}}\right)$
(15a) s.t.
$\displaystyle\quad\left|\left[\mathbf{F}_{t}^{RF}\right]_{l,l^{\prime}}\right|=1\hskip
14.22636pt\forall l,l^{\prime},$ (15b)
$\displaystyle\quad\operatorname{Tr}(\mathbf{F}_{t}^{H}\mathbf{F}_{t})\leq\mathrm{P_{2}}.$
(15c)

According to (14a) and (15a), two non-convex optimization problems are
challenging to solve. As an alternative approach, we can assume that the zero-
forcing fully digital beamformer as described in (17) is the upper bound
performance for our problems, and we can design our hybrid beamforming
compared to zero-forcing beamforming. Before solving alternative problems, the
total available power $P_{1}$ and $P_{2}$ was equally shared among users. In
both aerial and terrestrial user sets, problems (14a) and (15a) can be
expressed as follows:

$\displaystyle\max_{\begin{subarray}{c}\mathbf{F}^{RF},\mathbf{F}^{BB}\end{subarray}}$
$\displaystyle\quad R(\mathbf{F}^{RF},\mathbf{F}^{BB})$ (16a) s.t.
$\displaystyle\quad\left|\left[\mathbf{F}^{RF}\right]_{l,l^{\prime}}\right|=1\hskip
14.22636pt\forall l,l^{\prime},$ (16b)
$\displaystyle\quad\operatorname{Tr}(\mathbf{F}^{H}\mathbf{F})\leq\mathrm{P_{d}}.$
(16c)

###  III-A Problem of Hybrid Precoders

An upper bound performance can be obtained using a zero-forcing beamforming
technique [28], as shown in the following:

$\displaystyle\mathbf{F}^{zf}=\mathbf{H}^{H}(\mathbf{H}\mathbf{H}^{H})^{-1}.$
(17)

Eq. (16a) can be adapted to use either terrestrial or aerial channels, along
with their respective power allocation matrices. We aim to design hybrid
digital and analog precoders that are as close as possible to the zero-forcing
precoder, denoted as
$\Lambda={\lVert\mathbf{F}^{zf}-\mathbf{F}^{RF}\mathbf{F}^{BB}\rVert}_{F}$.
Therefore, it is possible to formulate this problem as follows:

$\displaystyle\min_{\begin{subarray}{c}\mathbf{F}^{RF},\mathbf{F}^{BB}\end{subarray}}$
$\displaystyle\quad{\lVert\mathbf{F}^{zf}-\mathbf{F}^{RF}\mathbf{F}^{BB}\rVert}_{F}$
(18a) s.t.
$\displaystyle\quad\left|\left[\mathbf{F}^{RF}\right]_{l,l^{\prime}}\right|=1\hskip
14.22636pt\forall l,l^{\prime}.$ (18b)

The elements of the analog beamformer matrix are generated using an
exponential function
$[\mathbf{F}^{RF}]_{l,l^{\prime}}=e^{j{\theta}_{l,l{\prime}}},\hskip
5.69054pt\forall l,l^{\prime}$ with unit absolute values, $l$ and $l^{\prime}$
represent the row and column of the analog beamforming matrix; we optimize the
digital beamforming matrix and the phases of the analog beamformer matrix in
two separate convex optimization problems by keeping one of the optimization
variables fixed and iteratively optimizing the other until the objective
function meets a predefined criterion. With the use of a fixed digital
beamformer, we can express the problem (16a) in the following manner:

$\displaystyle\min_{\begin{subarray}{c}\mathbf{F}^{RF}\end{subarray}}$
$\displaystyle\quad{\lVert\mathbf{F}^{zf}-\mathbf{F}^{RF}\mathbf{F}^{BB}\rVert}_{F}.$
(19)

Initially, the unit value constraint of the RF precoder is temporarily
ignored, and the RF precoder matrix is computed without this constraint.
Subsequently, its elements are normalized as expressed in (21), then fix the
analog beamformer turns optimization (16a) into an unconstrained and convex
problem, as shown below:

$\displaystyle\min_{\begin{subarray}{c}\mathbf{F}^{BB}\end{subarray}}$
$\displaystyle\quad{\lVert\mathbf{F}^{zf}-\mathbf{F}^{RF}\mathbf{F}^{BB}\rVert}_{F},$
(20)

Input : Initial $\mathbf{F}^{BB}$ and $\mathbf{F}^{RF}$ by SVD of
$\mathbf{F}^{ZF}$ in (22a) and (22b) and update $\mathbf{F}^{RF}$ using (21).
$\ell=J$ for aerial and $\ell=I$ for terrestrial set.

Output : $\mathbf{F}^{BB},\mathbf{F}^{RF},\mathbf{F}_{hyb}$.

1

2for  _$k=1...K$_ do

3

4 Fix $\mathbf{F}^{BB}$;

5
$\mathbf{F}^{RF}\leftarrow\rm{arg~{}min}{\lVert\mathbf{F}^{zf}-\mathbf{F}^{RF}\mathbf{F}^{BB}\rVert}_{F}$;

6 Update $\mathbf{F}^{RF}$ using (21);

7

8 Fix $\mathbf{F}^{RF}$;

9
$\mathbf{F}^{BB}\leftarrow\rm{arg~{}min}{\lVert\mathbf{F}^{zf}-\mathbf{F}^{RF}\mathbf{F}^{BB}\rVert}_{F}$;

10 if  _${g}_{k}-{g}_{k+1}\leq\text{criterion}$ or max iter. happens_ then

11 $\mathbf{P}=\rm{diag}(p_{1},...,p_{\ell}$);

12

13
$\mathbf{F}_{hyb}\leftarrow\frac{\mathbf{F}_{RF}\mathbf{F}_{BB}}{{\lVert{\mathbf{F}_{RF}\mathbf{F}_{BB}\rVert}_{F}}}\mathbf{P}^{\frac{1}{2}}$;

14 break;

15 else

16 continue;

17 end if

18

19 end for

Algorithm 1 Hybrid Beamforming for Aerial and Terrestrial Networks

The transition from (19) to (20), in conjunction with Algorithm 1, involves a
two-stage iterative optimization for hybrid beamforming design. In (19), the
objective is to minimize the Frobenius norm
${\lVert\mathbf{F}^{zf}-\mathbf{F}^{RF}\mathbf{F}^{BB}\rVert}_{F}$ with
respect to the analog precoder $\mathbf{F}^{RF}$ while keeping the digital
precoder $\mathbf{F}^{BB}$ fixed. This problem is initially solved without the
unit norm constraint on $\mathbf{F}^{RF}$. Once $\mathbf{F}^{RF}$ is
optimized, its elements are normalized as described by (21) to ensure that
each element has a unit magnitude. Algorithm 1 shows the iterative procedure
for solving this optimization problem. Steps 2 and 3 fix $\mathbf{F}^{BB}$ and
update $\mathbf{F}^{RF}$. After updating $\mathbf{F}^{RF}$ in step 4, its
elements are normalized. Subsequently, steps 5 and 6 fix $\mathbf{F}^{RF}$ and
optimize $\mathbf{F}^{BB}$ by solving (21), which aims to minimize
${\lVert\mathbf{F}^{zf}-\mathbf{F}^{RF}\mathbf{F}^{BB}\rVert}_{F}$ with
respect to $\mathbf{F}^{BB}$. This procedure continues until convergence, as
controlled by the criterion in step 7. Consequently problem (16a) can be
addressed iteratively. The convergence speed can be affected by the initial
value of Algorithm 1. Appropriate initialization can lead to enhanced and
quicker convergence.

$\displaystyle\mathbf{F}^{RF}=\begin{bmatrix}\frac{{F}^{RF}_{1,1}}{|{F}^{RF}_{1,1}|}&\frac{{F}^{RF}_{1,2}}{|{F}^{RF}_{1,2}|}&\cdots&\frac{{F}^{RF}_{1,N_{RF}}}{|{F}^{RF}_{1,N_{RF}}|}\\\
\frac{{F}^{RF}_{2,1}}{|{F}^{RF}_{2,1}|}&\frac{{F}^{RF}_{2,2}}{|{F}^{RF}_{2,1}|}&\cdots&\frac{{F}^{RF}_{2,N_{RF}}}{|{F}^{RF}_{2,N_{RF}}|}\\\
\vdots&\vdots&\ddots&\vdots\\\
\frac{{F}^{RF}_{N,1}}{|{F}^{RF}_{N,1}|}&\frac{{F}^{RF}_{N,2}}{|{F}^{RF}_{N,2}|}&\cdots&\frac{{F}^{RF}_{N,N_{RF}}}{|{F}^{RF}_{N,N_{RF}}|}\\\
\end{bmatrix}.$ (21)

In (22a) and (22b), $\mathbf{\Sigma}$, $\mathbf{U}$, and $\mathbf{V}$ are
matrices obtained from the Singular Value Decomposition (SVD) of the zero-
forcing beamformer $\mathbf{F}^{zf}$, and the SVD is given by
$\mathbf{F}^{zf}=\mathbf{U}\mathbf{\Sigma}\mathbf{V}^{H}$. $\mathbf{\Sigma}$
is a diagonal matrix containing the singular values of $\mathbf{F}^{zf}$.
$\mathbf{U}$ and $\mathbf{V}$ are unitary matrices representing the left and
right singular vectors of $\mathbf{F}^{zf}$, respectively. The initial values
of Algorithm 1 are determined by selecting the first $N_{RF}=m$ largest
singular values from $\mathbf{\Sigma}$, along with the corresponding first
$N_{RF}$ columns of $\mathbf{U}$ and $\mathbf{V}$. This selection assumes that
$N_{RF}$ equals the number of users, as shown below:

$\displaystyle\mathbf{F}^{RF}_{m}$ $\displaystyle=\mathbf{U}_{m},$ (22a)
$\displaystyle\mathbf{F}^{BB}_{m}$
$\displaystyle=\mathbf{\Sigma}_{m}\mathbf{V}_{m}^{H}.$ (22b)

Utilizing this matrix approximation enhances the quality and speed of
algorithm convergence. To iteratively solve (20) and (19), any solver (e.g.,
the MATLAB Optimization toolbox, CVX) can be employed, with the steps
illustrated in Algorithm 1. The convergence of the overall iterations between
the zero-forcing fully digital beamformer and the hybrid beamformer, which
consists of both analog and digital precoders is depicted in Fig. 4.

###  III-B Problem of Spectrum Allocation

Once the hybrid beamforming matrix is determined, the optimization becomes
solely dependent on bandwidth coefficients and backhaul bottleneck
constraints. This simplifies the problem in (13a) as (23a). The optimization
problem can be reformulated by substituting $\mu_{t}$ with $1-\mu_{a}$ and the
objective expressed as
$\left(\mu_{a}w\right)\sum_{j=1}^{J-1}R_{a,j}+{\left(1-\mu_{a}\right)w\sum_{i=1}^{I}R_{t,i}}=\left(\mu_{a}w\right)(\sum_{j=1}^{J-1}R_{a,j}-\sum_{i=1}^{I}R_{t,i})+{w\sum_{i=1}^{I}R_{t,i}}$.
It is possible to omit the last term in this equation from the optimization
problem, and constraint (23e) can be reformulated accordingly:

$\displaystyle\max_{\begin{subarray}{c}\mu_{a},\mu_{t}\end{subarray}}$
$\displaystyle\quad\left(\mu_{a}\right)w\sum_{j=1}^{J-1}R_{a,j}+{\left(\mu_{t}\right)w\sum_{i=1}^{I}R_{t,i}}$
(23a) s.t. $\displaystyle\quad 0\leq\mu_{a}\leq 1,$ (23b) $\displaystyle\quad
0\leq\mu_{t}\leq 1,$ (23c) $\displaystyle\quad\mu_{a}+\mu_{t}=1,$ (23d)
$\displaystyle\quad\mu_{t}\sum_{i=1}^{I}{R_{t,i}}\leq\mu_{a}\mathrm{R_{a,b}}.$
(23e)

Thus, (23a) can be represented as follows:

$\displaystyle\max_{\begin{subarray}{c}\mu_{a}\end{subarray}}$
$\displaystyle\quad\left(\mu_{a}w\right)(\sum_{j=1}^{J-1}R_{a,j}-\sum_{i=1}^{I}R_{t,i})$
(24a) s.t. $\displaystyle\quad 0\leq\mu_{a}\leq 1,$ (24b)
$\displaystyle\quad\mu_{a}\geq\frac{\mathrm{\sum_{i=1}^{I}R_{t,i}}}{R_{a,b}+\sum_{i=1}^{I}{R_{t,i}}}.$
(24c)

Backhaul constraint (23e) directly represents how the aerial backhaul link
limits the rate of terrestrial users. By substituting $\mu_{t}=1-\mu_{a}$, a
lower bound for $\mu_{a}$ can be derived as (24c). This lower bound, combined
with the upper bound in (24b), ensures that both aerial and terrestrial links
always receive a non-zero bandwidth allocation. On the other hand the closed-
form solution in (25c), shows that $\mu_{a}$ always takes the form of a
fraction less than one. Problem (24a) has a concave linear objective, and the
only variable is the bandwidth coefficient. If the sum-SE of aerial users
becomes greater than the sum-SE of terrestrial users in (24c), a positive
value will be obtained for the concave objective, and the maximization will be
satisfied if the bandwidth coefficient reaches its maximum value while
adhering to the constraints. Furthermore, suppose the sum-SE of terrestrial
users becomes larger than the sum-SE of aerial users. In this case, the
objective takes a negative value, and the bandwidth coefficient must be as
small as possible while satisfying the constraints (24b) and (24c) to maximize
the objective function. Consequently, a closed-form expression can be derived
as follows:

$\displaystyle\hskip 40.0pt\mathfrak{R}_{t}=$
$\displaystyle\sum_{i=1}^{I}R_{t,i},\hskip
10.0pt\mathfrak{R}_{a}=\sum_{j=1}^{J}R_{a,j},$ (25a)
$\displaystyle{\mu_{a}}^{*}$
$\displaystyle=\frac{\textrm{max}(\frac{\mathfrak{R}_{t}(\mathfrak{R}_{a}-\mathfrak{R}_{t})}{\mathfrak{R}_{t}+R_{b}},\mathfrak{R}_{a}-\mathfrak{R}_{t})}{\mathfrak{R}_{a}-\mathfrak{R}_{t}},$
(25b) $\displaystyle=\frac{\mathfrak{R}_{t}}{\mathfrak{R}_{t}+R_{b}}.$ (25c)

Because of the equal power allocation in both the IAB-donor and IAB-node,
along with the additional power required for the backhaul link, the SE of
aerial users will be lower than that of terrestrial users, as shown in Fig. 6.
Thus, when the number of aerial and terrestrial users is assumed to be the
same, (25b) can be expressed as (25c).

###  III-C Non-IAB Scenario

To comprehensively evaluate our proposed IAB-assisted UAV network, we
performed a comparative analysis against a non-IAB scenario. In the non-IAB
scenario, UAVs operate without IAB technology, leading to separate access and
backhaul links. This separation requires dedicated resources, such as
frequency spectrum, antennas, and hardware, making it impossible to share
resources between the links. Consequently, the non-IAB scenario assumes a
fixed bandwidth allocation for both access and backhaul links. In this
context, the bandwidth coefficient remains fixed, regardless of the varying
traffic demands of aerial or terrestrial users. Therefore, in non-IAB mode,
the bandwidth coefficient is not considered an optimization variable in (13a).
Instead, only the hybrid beamforming matrices need to be optimized in (14a)
and (15a) using Algorithm 1 to maximize the sum-rate for both aerial and
terrestrial users. Numerical results demonstrate that the total sum-rate of
the network in the non-IAB mode is lower than that in the IAB mode. Unlike the
IAB mode, the non-IAB scenario cannot optimally utilize available resources in
other links. Consequently, if a traffic overload occurs in the backhaul or
access links, UAVs are unable to meet the requirements of terrestrial networks
due to the lack of shared resources.

###  III-D The Impact of Bandwidth on Thermal Noise

This section analyzes how bandwidth affects thermal noise in our mmWave system
model. When we consider the thermal noise properties more accurately, the
Johnson-Nyquist formula allows us to express $\sigma^{2}$, which is the noise
power in watts, as a function of bandwidth like $\sigma^{2}(\mu w)=\mu
wP_{n}$, where $w$ is bandwidth (in Hz), and $P_{n}$ is noise power spectral
density (in W$/$Hz). To reformulate the optimization problem (23a) while
taking into account the impact of noise-BW, we obtain the following problem:

$\displaystyle\max_{\begin{subarray}{c}\mu_{a}\end{subarray}}$
$\displaystyle\quad\left(\mu_{a}\right)w\sum_{j=1}^{J-1}R_{a,j}(\mu_{a})+{\left(1-\mu_{a}\right)w\sum_{i=1}^{I}R_{t,i}(1-\mu_{a})}$
(26a) s.t. $\displaystyle\quad 0\leq\mu_{a}\leq 1,$ (26b)
$\displaystyle\quad(1-\mu_{a})\sum_{i=1}^{I}{R_{t,i}}(1-\mu_{a})\leq\mu_{a}\mathrm{R_{a,b}}(\mu_{a}).$
(26c)

We can express the rates as follows for aerial users:

$\displaystyle R_{a,j}(\mu_{a})$
$\displaystyle=\log_{2}\left(1+\frac{\left|{g}_{a,j}\right|^{2}}{{\mathfrak{I}}_{a,j}+\mu_{a}wP_{n}}\right),$
(27)

and for terrestrial users:

$\displaystyle R_{t,i}(\mu_{a})$
$\displaystyle=\log_{2}\left(1+\frac{\left|{g}_{t,i}\right|^{2}}{{\mathfrak{I}}_{t,i}+(1-\mu_{a})wP_{n}}\right),$
(28)

and for the backhaul link:

$\displaystyle R_{a,b}(\mu_{a})$
$\displaystyle=\log_{2}\left(1+\frac{\left|{g}_{b}\right|^{2}}{{\mathfrak{I}}_{a,b}+(\mu_{a})wP_{n}}\right).$
(29)

Input :
$\mathbf{h}_{a,j},\mathbf{h}_{t,i},\mathbf{h}_{a,b},\mathbf{F}^{RF},\mathbf{F}^{BB}$
and $P_{n}$

Output : $\mu_{a},\mu_{t}$

Initial : $\mu^{m}_{a}$

1 Approximate objective and constraints by (31) and (31);

2 while  _$|\mu^{m-1}_{a}-\mu^{m}_{a}|\geq\epsilon$_ do

3
$\mu^{*}_{a}=arg~{}\max\left(\mu_{a}\right)w\sum_{j=1}^{J-1}\hat{R}_{a,j}(\mu_{a})+{\left(1-\mu_{a}\right)w\sum_{i=1}^{I}\hat{R}_{t,i}(1-\mu_{a})}$;

4 s.t. (33b) and (33c);

5 $\mu^{m-1}_{a}\leftarrow\mu^{m}_{a}$;

6 $\mu^{m}_{a}\leftarrow\mu^{*}_{a}$;

7 end while

Algorithm 2 Successive Convex Approximation (SCA) algorithm for problem (33a)

This problem is non-convex because the second derivative of the objective
depends on channel coefficients, which may be convex or concave depending on
channel coefficient values. $\left|{g}_{a,j}\right|^{2}$,
$\left|{g}_{t,i}\right|^{2}$ and $\left|{g}_{b}\right|^{2}$ represent the
received power at aerial UEs, terrestrial UEs and backhaul node respectively,
whereas $\mathfrak{I}_{a,j}$, $\mathfrak{I}_{t,i}$ and $\mathfrak{I}_{a,b}$
denote the interference power. We try to rewrite this problem and then use an
SCA-based algorithm to cope with this non-convexity. We can reformulate (27),
(28) and (29) as follows:

$\displaystyle R_{a,j}(\mu_{a})$
$\displaystyle=\log_{2}\left(\frac{{\tilde{g}}_{a,j}+\mu_{a}wP_{n}}{{\mathfrak{I}}_{a,j}+\mu_{a}wP_{n}}\right)$
(30a)
$\displaystyle=\log_{2}\left(\tilde{g}_{a,j}+\mu_{a}wP_{n}\right)-\log_{2}\left({{\mathfrak{I}}_{a,j}+\mu_{a}wP_{n}}\right),$
$\displaystyle R_{t,i}(\mu_{a})$
$\displaystyle=\log_{2}\left(\frac{{\tilde{g}}_{t,i}+(1-\mu_{a})wP_{n}}{{\mathfrak{I}}_{t,i}+(1-\mu_{a})wP_{n}}\right)$
(30b) $\displaystyle=\log_{2}\left(\tilde{g}_{t,i}+(1-\mu_{a})wP_{n}\right)$
$\displaystyle\quad\quad-\log_{2}\left({{\mathfrak{I}}_{t,i}+(1-\mu_{a})wP_{n}}\right),$
$\displaystyle R_{a,b}(\mu_{a})$
$\displaystyle=\log_{2}\left(\frac{{\tilde{g}}_{a,b}+\mu_{a}wP_{n}}{{\mathfrak{I}}_{a,b}+\mu_{a}wP_{n}}\right)$
(30c)
$\displaystyle=\log_{2}\left(\tilde{g}_{a,b}+\mu_{a}wP_{n}\right)-\log_{2}\left({{\mathfrak{I}}_{a,b}+\mu_{a}wP_{n}}\right).$

An approximation of aerial rates can be found using a first-order Taylor
series as follows:

$\displaystyle\log_{2}\left(\tilde{g}_{a,j}+\mu_{a}wP_{n}\right)\approx$ (31a)
$\displaystyle\log_{2}\left(\tilde{g}_{a,j}+\mu^{m}_{a}wP_{n}\right)+\frac{wP_{n}(\mu_{a}-\mu^{m}_{a})}{ln(2)(\tilde{g}_{a,j}+\mu^{m}_{a}wP_{n})}=L_{1}(\mu_{a}),$
$\displaystyle\log_{2}\left(\mathfrak{I}_{a,j}+\mu_{a}wP_{n}\right)\approx$
(31b)
$\displaystyle\log_{2}\left(\mathfrak{I}_{a,j}+\mu^{m}_{a}wP_{n}\right)+\frac{wP_{n}(\mu_{a}-\mu^{m}_{a})}{ln(2)(\mathfrak{I}_{a,j}+\mu^{m}_{a}wP_{n})}=L_{2}(\mu_{a}),$

and then:

$\displaystyle R_{a,j}(\mu_{a})\approx
L_{1}(\mu_{a})-L_{2}(\mu_{a})=\hat{R}_{a,j}.$ (32a)

In (31) and (31), $\mu^{m}_{a}$ represents the value of $\mu_{a}$ in the
${m}^{th}$ iteration of the SCA algorithm. Additionally, we have these
approximations for terrestrial and backhaul links denoted as $\hat{R}_{t,i}$
and $\hat{R}_{a,b}$. Therefore, problem (26a) can be expressed as follows:

$\displaystyle\max_{\begin{subarray}{c}\mu_{a}\end{subarray}}$
$\displaystyle\quad\left(\mu_{a}\right)w\sum_{j=1}^{J-1}\hat{R}_{a,j}(\mu_{a})+{\left(1-\mu_{a}\right)w\sum_{i=1}^{I}\hat{R}_{t,i}(1-\mu_{a})}$
(33a) s.t. $\displaystyle\quad 0\leq\mu_{a}\leq 1,$ (33b)
$\displaystyle\quad(1-\mu_{a})\sum_{i=1}^{I}{\hat{R}_{t,i}}(1-\mu_{a})\leq\mu_{a}\mathrm{\hat{R}_{a,b}}(\mu_{a}).$
(33c)

The SE can be represented as a linear function of the bandwidth coefficient
$\mu_{a}$. The resulting quadratic problem can be solved using Algorithm 2
[30], [31].

##  IV Simulation Results

This section provides a numerical analysis. The parameters utilized in the
simulation are listed in Table II. First, the convergence of the proposed
algorithms is demonstrated and validated. Subsequently, the proposed hybrid
beamforming method is compared with other hybrid beamforming and fully digital
methods. The superiority of the theoretical analysis in terms of sum-rate
maximization is compared with the traditional non-IAB scenario. The closed-
form solution is presented as a function of power and the number of antennas
through various simulations. Additionally, the proposed method is analyzed in
terms of energy efficiency. A contour plot illustrating the simultaneous
variation in both power and bandwidth and its effect on the network’s sum-rate
is provided, and the results are compared with the non-IAB scenario.

TABLE II: Simulation parameters Parameter | Notation | Value
---|---|---
Frequency | $f_{c}$ |  $28~{}$GHz
IAB-donor height | $\mathrm{h_{uav}}$ |  $150~{}$m
IAB-node height | $\mathrm{h_{cuav}}$ |  $70~{}$m
Aerial UEs height | $\mathrm{h_{auav}}$ |  $100~{}$m
Aerial links | $J$ | $4$
Terrestrial links | $I$ | $3$
Bandwidth | $w$ |  $500~{}$MHz
PSD of thermal noise | $\mathrm{P_{n}}$ |  $-170~{}$dBm$/$Hz [32]
RF chains power | $\mathrm{P}_{RF}$ |  $250~{}$mW [33]
Phase shifters power | $\mathrm{P}_{PS}$ |  $1~{}$mW [33]
Path loss exponent | $n$ | $2$
Reference path loss | $\gamma_{0}$ |  $-61.39$ dB
RF chains | $N_{RF}$ | 3
Antenna elements | $N$ | $64$
Antenna dimensions | $N_{x}\times N_{y}$ | $8\times 8$

###  IV-A Algorithms Convergence and Analysis of Proposed Hybrid Beamforming
Technique

Algorithm 1 and Algorithm 2 are separate and independent algorithms in our
proposed solution. Algorithm 1 focuses on the hybrid beamforming design
problem, while Algorithm 2, discussed in Sec. III, addresses the successive
convex approximation for the bandwidth allocation problem under the bandwidth-
dependent thermal noise assumptions. Without assuming the bandwidth-dependent
thermal noise effect, we use the derived closed-form solution in (25c) to find
the bandwidth allocation coefficient instead of Algorithm 2 and these two
algorithms are not part of a joint iterative process.

Figure 4: Convergence of hybrid beamforming (HBF) Algorithm 1 based on the
different initialization methods. Figure 5: Convergence of Successive Convex
Approximation (SCA) Algorithm 2.

Fig. 4 illustrates the convergence of the hybrid beamforming algorithm, which
is achieved after $23$ iterations. With the SVD-initialization performed in
the proposed Algorithm 1, the convergence speed is notably faster than that of
the random-initialization algorithm, as referenced in [28]. The number of
iterations required can be limited, or the algorithm’s stopping condition may
be based on the value of the objective function. In the conducted simulation,
Algorithm 1 stops upon reaching a specific target value ($\Lambda\leq 0.1$).
However, should there be changes in the channel conditions, the algorithm must
be rerun to determine the hybrid beamforming matrices, comprising both analog
and digital precoders. Fig. 5 shows the convergence of the SCA Algorithm 2
used to solve the optimization problem (33a) considering the impact of
bandwidth on thermal noise. The y-axis represents the value of the aerial BW
coefficient $\mu_{a}$. The plot demonstrates that after approximately 4
iterations, the difference between the values of $\mu_{a}$ in consecutive
iterations becomes smaller than the predefined criterion $\epsilon=0.001$.
This convergence criterion is used as the stopping condition for the SCA
algorithm.

Figure 6: Sum Spectral Efficiency (SE) comparison of the proposed hybrid
beamforming (HBF) technique against different beamforming methods for aerial
UEs (top) and terrestrial UEs (bottom), considering variable transmit power at
the IAB-donor and IAB-node with a fixed number of UEs ($I=3,J=4$).

In Fig. 6, we compare our proposed Hybrid Beamforming (HBF) with Maximum Ratio
Transmission (MRT)-matching HBF (based on [28]) and fully digital beamforming
(zero-forcing) methods. As shown, our proposed HBF performs 41.32% better on
average than MRT-matching in terms of achieved sum-SE, in addition to having a
faster convergence speed as previously discussed. Equal power allocation is
assumed for both the IAB-node and IAB-donor and the power of the backhaul link
is also equal to the power required by terrestrial users. Consequently, the SE
of aerial users is expected to be lower than that of terrestrial users, as
seen in Fig. 6. However, hybrid beamforming is less effective than fully
digital beamforming, which is particularly evident in the MISO scenario where
hybrid beamforming underperforms compared to the MIMO scenario. Additionally,
the hybrid beamforming configuration has fewer RF chains than fully digital
beamforming, where the number of RF chains equals the number of sub-arrays
elements. For hybrid beamforming, three RF chains are used, whereas fully
digital beamforming requires 64 RF chains. Hence, the fully digital approach
leads to significant issues in energy consumption and hardware size,
especially in UAVs with limited hardware and energy storage. Therefore, the
39.4% drop in SE for terrestrial users and the 48.2% drop for aerial users due
to hybrid beamforming in the MISO scenario is reasonable from an energy
standpoint.

Figure 7: Sum-rate comparison of proposed IAB mode with dynamic bandwidth
allocation (blue curve), considering bandwidth-dependent thermal noise (black
curve), and non-IAB scenario with fixed bandwidth (green curve). This
comparison considers variable power for the IAB-donor and IAB-nodes, with a
constant number of UE ($I=3,J=4$).

###  IV-B Outperformance Analysis of the Proposed IAB-assisted UAV Network

Fig. 7 presents a comparison of the sum-rate performance achieved under
various network scenarios. The closed-form formula curve represents the
theoretical maximum sum-rate obtained by solving the optimization problem
(24a) using the derived closed-form solution in (25c). This solution optimally
allocates the bandwidth between aerial and terrestrial links to maximize the
overall sum-rate. To validate the accuracy of the closed-form expression, we
benchmark it against the Genetic Algorithm (GA) curve, which depicts the sum-
rate achieved by numerically solving (23a) using a genetic algorithm. As
evident from Fig. 9, the closed-form solution closely matches the GA
benchmark, confirming its validity. Furthermore, we investigate the
performance of a traditional non-IAB network scenario, represented by the non-
IAB scenario or fixed bandwidth allocation curve. In this case, as explained
in Sec. III-C it is impossible to dynamically optimize bandwidth and its
allocation between aerial and terrestrial links is fixed and equally divided,
set at 0.5. Notably, the sum-rate in this non-IAB scenario exhibits a
significant drop compared to the optimized IAB scenarios, highlighting the
performance gains achieved through the proposed IAB-assisted UAV network
framework and optimized bandwidth allocation. Additionally, we analyze the
impact of considering the bandwidth-dependent thermal noise on the system
performance. The SCA curve illustrates the sum-rate achieved when solving the
optimization problem (33a) using the SCA Algorithm 2. This approach accounts
for the dependence of thermal noise power on the allocated bandwidth,
providing a more realistic representation of our proposed framework. As
expected, incorporating the bandwidth effect on noise leads to a further
reduction in the achievable sum-rate compared to the scenario without
considering this factor.

Figure 8: Contour plots of network sum-rate versus available bandwidth and
transmit power for IAB mode (top) and non-IAB scenario (bottom).

Fig. 8 demonstrates contour diagrams that illustrate the variation of the
network’s total sum-rate concerning the available bandwidth and the total
available power ($P_{1}$ and $P_{2}$) at the IAB-donor and IAB-node,
respectively. The two contour diagrams depict the sum-rate performance in the
IAB mode (top figure) and the non-IAB mode (bottom figure). Each contour line
represents a specific sum-rate value in Gbps. In the IAB mode (top figure),
the sum-rate contours are more densely packed, indicating a higher rate of
change in the sum-rate as the available bandwidth and power vary. This
behavior suggests that the IAB mode can effectively leverage the available
resources to achieve higher sum-rates. For instance, to attain a sum-rate of
$25~{}$Gbps, the IAB mode requires approximately $500~{}$MHz of bandwidth and
an available power of $-12~{}$dBW, as indicated by the corresponding contour
line. On the other hand, in the non-IAB mode (bottom figure), the contour
lines are more widely spaced, indicating a slower rate of change in the sum-
rate with respect to the available bandwidth and power. This behavior suggests
that the non-IAB mode is less efficient in utilizing the available resources.
To achieve the same sum-rate of $25~{}$Gbps in the non-IAB mode, a higher
bandwidth of approximately $650~{}$MHz is required, even with an available
power of $-12~{}$dBW.

Figure 9: Comparison between the proposed closed-form solution and the genetic
algorithm with a constant number of UE ($I=3,J=4$)  Figure 10: Sum Energy
Efficiency (Sum-EE) comparison of proposed IAB mode with dynamic bandwidth
allocation (blue curve), considering bandwidth-dependent thermal noise (black
curve), and non-IAB scenario with fixed bandwidth (green curve). This
comparison considers variable power for the IAB-donor and IAB-nodes, with a
constant number of UE ($I=3,J=4$), the number of transmit antennas $N=64$, and
the assumed number of RF chains is $N_{RF}=3$.

This comparison between the two contour diagrams highlights the superior
performance of the proposed IAB mode over the non-IAB mode in terms of sum-
rate and resource utilization. The IAB mode can achieve higher sum-rates while
consuming less resources, making it more efficient and suitable for aerial
wireless backhaul scenarios. Furthermore, the contour diagrams provide
valuable insights into the trade-offs between bandwidth and power in achieving
desired sum-rate targets. For instance, in the IAB mode, if the available
bandwidth is limited, a higher available power can compensate to some extent
and still achieve a reasonable sum-rate. Conversely, if the available power is
constrained, increasing the bandwidth allocation can help maintain the desired
sum-rate performance. Fig. 10 illustrates the variation of Sum-Energy
Efficiency (Sum-EE) to the total available transmit power at the IAB-donor and
IAB-node. The Sum-EE is calculated as the ratio of the total network sum-rate
to the total power consumption, considering the transmit power and power
consumption of Radio Frequency (RF) chains and phase shifters. As the figure
shows, the Sum-EE initially increases with an increment in the available
transmit power for all three scenarios. This behavior is expected, as higher
transmit power generally leads to improved signal-to-noise ratios and higher
achievable data rates, thereby increasing the Sum-EE. However, beyond a
certain power threshold (approximately $-3~{}$dBW), the Sum-EE starts to
decrease for all scenarios. This decrease in Sum-EE at higher power levels can
be attributed to the sum-rate saturation effect. Notably, the proposed IAB
mode outperforms the non-IAB scenario in terms of Sum-EE across the entire
range of transmit power values considered. This superior performance can be
related to the efficient utilization of available resources and ability to the
optimal allocation of bandwidth between aerial and terrestrial links in the
IAB mode. By dynamically adjusting the bandwidth allocation, the IAB mode can
effectively adapt to varying traffic demands, ultimately achieving higher sum-
rates and better energy efficiency. Fig. 11 illustrates the variation of the
bandwidth allocation coefficient ($\mu_{a}$) as a function of the available
power budget at the IAB-donor and IAB-node. The graph depicts the trend of
$\mu_{a}$, which represents the fraction of the total bandwidth allocated to
aerial links, including both access links for aerial users and the backhaul
link.

Figure 11: Variation of the optimal bandwidth allocation coefficient
($\mu_{a}$) as a function of the total power budget at the IAB-donor and IAB-
node, considering both the closed-form solution and the scenario accounting
for bandwidth-dependent thermal noise. Figure 12: Illustration of backhaul
bottleneck constraint satisfaction with sum-rates of backhaul link,
terrestrial users, and aerial users. Figure 13:  Analysis of the proposed IAB-
assisted UAV framework versus number of transmit antennas (N) in terms of:
sum-rate, bandwidth allocation coefficient ($\mu_{a}$), sum energy efficiency
(Sum-EE), and Sum-EE vs sum spectral efficiency (Sum-SE) trade-off for IAB and
non-IAB scenarios. It is assumed that $P_{tr}=0$ dBW and $N_{RF}=3$ and a
constant number of UE ($I=3,J=4$).

As observed in the figure, in both scenarios of considering the bandwidth-
dependent thermal noise solved by the SCA algorithm or using the closed-form
solution, the value of $\mu_{a}$ is optimized as the available power changes.
Its trend can be attributed to the SE formulation of aerial and terrestrial
links, as expressed in (30a) and (30b) for bandwidth-dependent thermal noise,
and in (11a) and (11b) for the closed-form solution. As discussed in Fig. 6,
the SE of aerial links is lower compared to terrestrial links, necessitating a
higher bandwidth allocation to aerial links (higher $\mu_{a}$) to compensate
for the lower SE. However, as the available power increases, the SE of aerial
links improves, allowing for an optimized bandwidth allocation to aerial links
while still maintaining the required data rates. The $\mu_{a}$ is optimized
subject to the backhaul bottleneck constraint, as defined in equation (23e).
This constraint ensures that the sum-rate of terrestrial users does not exceed
the rate of the aerial backhaul link, which acts as a bottleneck. As the
traffic load of terrestrial users grows, the bandwidth coefficient for aerial
links ($\mu_{a}$) must be adjusted to accommodate the increasing backhaul
requirements, ensuring that the backhaul link can support the aggregate data
rate demanded by terrestrial users. Furthermore, the graph demonstrates that
the value of $\mu_{a}$ converges to a specific value as the available power
increases. This convergence point corresponds to the scenario where the SE of
aerial links becomes sufficiently high, and the bandwidth allocation is
primarily governed by the backhaul bottleneck constraint rather than the
individual link SEs. The bar chart in Fig. 12 illustrates the satisfaction of
the backhaul bottleneck constraint (24c), ensuring that the total rate
received by terrestrial users does not exceed the received rate at the IAB-
node, which acts as the bottleneck link.

This constraint is a crucial aspect of the proposed IAB-assisted UAV network
framework, as it ensures that the backhaul link can support the total data-
rate demanded by terrestrial users. This bar chart presents network sum-rate
($R$) plus three distinct bars ($R_{bh}$, $R_{t}$, and $R_{a}$), each
representing a different rate category. The first bar depicts the rate of the
backhaul link, which serves as the bottleneck for the terrestrial users’ rate.
This bar has an equal height to the second bar, representing the sum-rate of
terrestrial users. This equality demonstrates that the proposed optimization
framework successfully allocates the bandwidth between aerial and terrestrial
links, such that the backhaul rate precisely matches the total sum-rate
received by terrestrial users. By adhering to the backhaul bottleneck
constraint, the proposed framework ensures that the terrestrial network’s
performance is not limited by the backhaul capacity. This constraint is
particularly important in scenarios where the traffic load generated by
terrestrial users is high, as it guarantees that the backhaul link can
accommodate the required rates without becoming a performance bottleneck.
Furthermore, it provides insights into the bandwidth allocation strategy
adopted by the proposed framework. The higher sum-rate of aerial users, the
third bar, compared to terrestrial users, suggests that a larger portion of
the available bandwidth is allocated to aerial links, including the backhaul
link. This allocation is necessary to accommodate the additional traffic load
generated by terrestrial users, as well as the resource requirements of the
backhaul link itself. By following the aerial backhaul bottleneck constraint
and optimizing the bandwidth allocation, the proposed IAB framework ensures
efficient resource utilization and maximizes the overall network sum-rate,
while simultaneously providing reliable backhaul connectivity for terrestrial
users.

Fig. 13 illustrates the variation of different performance metrics, including
the bandwidth allocation coefficient ($\mu_{a}$), the network’s total sum-
rate, and the sum-EE, as a function of the number of transmit antennas ($N$)
employed at the IAB-donor and IAB-node. EE is computed using the formula
$EE=\frac{Rate}{P_{t}}$, where $P_{t}=P_{tr}+N_{RF}P_{RF}+N_{PS}P_{PS}$, as in
[33] and [34].

The top-left subplot depicts the network’s total sum-rate as a function of the
number of transmit antennas. As expected, the sum-rate increases with an
increasing number of antennas for both the IAB and non-IAB scenarios. However,
the proposed IAB-assisted UAV network consistently outperforms the non-IAB
scenario across the entire range of antenna numbers considered. This superior
performance can be attributed to the efficient utilization of available
resources and the ability to optimally allocate the bandwidth between aerial
and terrestrial links in the IAB mode which is not possible in non-IAB
scenario.

The top-right subplot shows the variation of optimized $\mu_{a}$ with respect
to the number of transmit antennas. It is important to note that the bandwidth
allocation is optimized subject to the aerial backhaul bottleneck constraint,
ensuring that the summation rate demanded by terrestrial users does not exceed
the capacity of the aerial backhaul link. The bottom-left subplot illustrates
the variation of the Sum-EE with respect to the number of transmit antennas.
The Sum-EE is calculated as the ratio of the total network sum-rate to the
total power consumption, which includes the transmit power as well as the
power consumption of RF chains and phase shifters. Similar to the sum-rate
behavior, the Sum-EE increases with an increasing number of antennas for both
scenarios, and the proposed IAB mode exhibits better energy efficiency
compared to the non-IAB scenario. The bottom-right subplot illustrates the
sum-EE vs. sum-SE plot. It is evident that in all ranges of sum-SE, the Sum-EE
in IAB mode performs better than the non-IAB scenario

Overall, the results presented in Fig. 13 highlight the notable performance
gains achieved by the proposed IAB-assisted UAV network framework in terms of
sum-rate and energy efficiency. By leveraging the IAB technique and optimizing
the bandwidth allocation between aerial and terrestrial links, the proposed
framework can effectively utilize the available resources and adapt to varying
traffic demands, leading to improved network performance. These findings
underscore the suitability of the proposed IAB-assisted UAV network for future
wireless communication systems that rely heavily on non-terrestrial networks.

##  V Conclusion

In this paper, we proposed an IAB-assisted UAV model for providing
simultaneous aerial backhauling and access to terrestrial and aerial users. We
employ the hybrid beamforming technique to mitigate interference between the
aerial user’s access links and the backhaul link, which share the same
frequency band. Furthermore, we conduct a comprehensive analysis to optimize
bandwidth allocation between aerial and terrestrial users, ultimately leading
to a higher overall network sum-rate. Additionally, we investigate the impact
of bandwidth on thermal noise and its influence on network performance. In
summary, while optical fiber is well-suited for terrestrial communications,
the wireless UAV-based communication scenario benefits from mmWave utilization
and the IAB multi-hop architecture, significantly improving network
performance. In future work, it is crucial to explore the integration of
terrestrial and non-terrestrial networks in more realistic scenarios based on
aerial mobile-IAB. This integration can account for factors such as imperfect
channel conditions, UE mobility, and the effects of higher altitudes.
Leveraging machine learning approaches can help address the challenges posed
by this complex system model.

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