# Personalized Saliency in Task-Oriented Semantic Communications: Image
Transmission and Performance Analysis

Jiawen Kang, Hongyang Du, Zonghang Li, Zehui Xiong, Shiyao Ma, Dusit Niyato,
_Fellow, IEEE_ , Yuan Li  Jiawen Kang is with Automation of School, Guangdong
University of Technology, China. (Email: kavinkang@gdut.edu.cn). Hongyang Du
and Dusit Niyato are with School of Computer Science and Engineering, Nanyang
Technological University, Singapore. Zonghang Li is with School of Information
and Communication Engineering, University of Electronic Science and Technology
of China, Chengdu, China. (Email: zhli@std.uestc.edu.cn). Zehui Xiong is with
Pillar of Information Systems Technology and Design, Singapore University of
Technology and Design, Singapore. Shiyao Ma is with College of Information and
Communication Engineering, Dalian Minzu University. Yuan Li is with Shangdong
University, China.

###### Abstract

Semantic communication, as a promising technology, has emerged to break
through the Shannon limit, which is envisioned as the key enabler and
fundamental paradigm for future 6G networks and applications, e.g., smart
healthcare. In this paper, we focus on UAV image-sensing-driven task-oriented
semantic communications scenarios. The majority of existing work has focused
on designing advanced algorithms for high-performance semantic communication.
However, the challenges, such as energy-hungry and efficiency-limited image
retrieval manner, and semantic encoding without considering user personality,
have not been explored yet. These challenges have hindered the widespread
adoption of semantic communication. To address the above challenges, at the
semantic level, we first design an energy-efficient task-oriented semantic
communication framework with a triple-based scene graph for image information.
We then design a new personalized semantic encoder based on user interests to
meet the requirements of personalized saliency. Moreover, at the communication
level, we study the effects of dynamic wireless fading channel on semantic
transmission mathematically and thus design an optimal multi-user resource
allocation scheme by using game theory. Numerical results based on real-world
datasets clearly indicate that the proposed framework and schemes
significantly enhance the personalization and anti-interference performance of
semantic communication, and are also efficient to improve the communication
quality of semantic communication services.

###### Index Terms:

Semantic communication, personalized saliency, resource allocation, unmanned
aerial vehicle.

##  I Introduction

###  I-A Background and Motivations

The fast-growing 6G communication technology is enabling the transition from
serving people and things to supporting the “Internet of Everything” [1, 2,
3]. Specifically, 6G communication technology serves intelligent production
and life through intelligent interconnection and collaborative symbiosis of
human-machine-object, and actively promotes the construction of an inclusive
and intelligent human society [4, 5, 6]. In the 6G era, however, the
traditional point-to-point information transmission communication system, that
relies on the resource optimization of physical-layer dimension and the stable
transmission protocol at the network layer, cannot meet the increasing
requirements of complex, diverse, and intelligent information transmission
needs, e.g., supporting virtual reality, holographic projection and Metaverse
applications [7, 8]. Therefore, it is essential to design a new communication
paradigm for efficient information transmission thus meeting the demands of
future communication.

Fortunately, semantic communication [9], as a new architecture that can
integrate user needs and information semantic features into the communication
process, is expected to become a new communication paradigm for the Internet
of Everything in the future [10, 11, 12]. Different from the traditional
communication architectures, the semantic communication system aims to
fundamentally solve the problems of cross-system, cross-protocol, cross-
network, and cross-human-machine information transmission redundancy in
traditional information-transmission based communication protocols. The
ultimate goal of the semantic communication system is to efficiently transmit
content-aware and semantic-related information in a task-oriented manner, and
make the grand vision of “Internet of Everything” come true. In this context,
to better serve the two core technical standards of semantics and validity in
6G networks, the Task-Oriented Semantic Communication Systems (TOSC) was
designed with two parts: semantic reconstruction and goal execution [13]

For semantic reconstruction, a semantic feature extractor is applied to
extract the semantic features behind the data to be transmitted and
reconstruct the semantic information at the receiver. For example, Zhu et al.
in [14] proposed an adaptive transformer to encode the semantic information
and decode it at the receiver. For task-oriented applications, semantic
communication aims to extract semantic information related to the decision
goal of the receiver. Prior work generally focuses on image recognition
scenarios and develops image classification-oriented semantic communication
for improving recognition accuracy rather than image semantic reconstruction
[15, 16]. Since Unmanned Aerial Vehicle (UAV) sensing has been widely applied
in various industries with 6G, in this paper, we focus on investigating UAV
sensing-driven task-oriented semantic communication systems.

Particularly, UAV-sensing-driven task-oriented semantic communication aims to
provide users with cross-regional intelligent services with the help of UAV’s
image retrieval, image recognition, image transmission, and image coding
features. UAV-sensing-driven Task-oriented Semantic Communication (UTSC)
generally serves a multi-demand, complex cross-modal intelligent task with
multiple users. The UTSC is particularly suitable for emerging intelligent
scenarios in daily life [9, 6] and industry [17] (e.g., smart agriculture
[18]). The service mode of UTSC is realized by collecting task demands from
users and using UAV sensing equipment to collect image data, and returning
demand feedback to users through cloud servers in the form of semantic
information. For example, in smart agriculture, different farmers (i.e.,
users) require UAVs to accomplish different tasks (e.g., monitoring and
shooting). In this case, it is challenging for UAVs to accomplish the task
goals of all users simultaneously. Furthermore, due to resource limitations
and power supply problems, UAVs cannot hover in the air for a long time to
complete the personalized user demands in turn. Therefore, there exists
following unique challenges when designing USTC systems:

  * •

Energy-hungry and efficiency-limited image retrieval: Traditional
communication manners generally send all the captured images to the users,
while many of the images are not interesting/needed by the users. Therefore,
such inefficient communication manners may cause large waste of communication
resources of UAVs and consume unnecessary UAV energy. A straightforward
solution is to use keyword subscriptions, namely, UAVs push images of interest
to users by extracting scene graphs of sensing images that match the
subscription words provided by users. However, this solution cannot execute
well in the traditional communication manners under the scenarios of limited
UAV energy or poor wireless channel. It is because that image packet drop and
re-transmission bring large delay. Thus the inefficiency of wireless
transmission makes it difficult to realize real-time push according to keyword
subscriptions. To this end, it is urgently necessary to design an efficient
and energy-efficient semantic-based real-time subscription method to improve
subscription accuracy and wireless resource utilization.

  * •

Semantic encoding without personality: Existing work ignores the personalized
needs of semantic communication for encoding retrieval results and does not
set user preferences for the importance of semantically encoded values. In the
face of large-scale semantic communication, due to the limited bandwidth
resources between UAVs and users, semantic coding is prone to signal fading
during transmission, resulting in the drop of important coding values (i.e.,
important information for users). Therefore, we need to design a personalized
semantic coding value weight setting scheme, and design different resource
allocation schemes for users with different interests to ensure that important
information about user preferences can be efficiently conveyed.

  * •

Without insights between wireless fading channel and semantic communication:
The semantic triplet drop probability is defined as the probability that the
number of error bits in the triplet exceeds the error correction capability.
However, existing works rarely consider the drop of encoded information caused
by the physical environment during information transmission. A common approach
is to use neural networks to model the wireless channel, which cannot help the
system design with mathematical analysis [19]. The problems about the multi-
path effect, shadow effect, and co-channel interference for wireless
transmission environment affect the communication quality and increase the
semantic triplets drop problem during transmission. Thereby, it is essential
to study the joint optimization problem of the wireless fading channel and
semantic triplet drop probability, and also design a resource optimization
scheme.

###  I-B Solutions and Contributions

To address the above challenges, in this paper, we propose an energy-efficient
task-oriented semantic communication framework for 6G-enabled UAV image
sensing scenarios. More specifically, in this framework, image information is
modeled as a triple-based scene graph to provide users with images that meet
their preference requirements in an efficient retrieval manner. On this basis,
we further execute the triplets by weight-encoding and use a personalized
attention-based mechanism to implement differential weight encoding of
triplets for important information according to user preferences. Moreover,
for the UAV power allocation issues, we further consider the dynamic wireless
fading effects on the semantic information transmission, and thus
mathematically analyze the triplet drop probability. Based on the theoretical
analysis results, we formulate a game theory model and design a multi-user
resource allocation scheme to achieve efficient resource utilization and
maximize the resource utility of UAVs.

The key contributions are summarized as follows:

  * •

Unlike traditional UAV-sensing communications that require all images to be
transmitted, we propose an energy-efficient semantic communication-based
framework that enables UAV only to transfer the selected interested images of
the users, which is achieved by matching the user’s query text with the
semantic information of all images.

  * •

We design a novel personalized semantic encoder with the help of the user’s
subjective interest. After obtaining the semantic information, i.e., triples,
from the image, the triplets of more interest to the user are given higher
weights, thus ensuring the correct reception.

  * •

We analyze the performance of semantic triplets transmission mathematically.
We derive the exact expression for the semantic triplet drop probability by
considering the generalized fading channel model. From the derived
expressions, we obtain insights into the wireless channel environment on the
impact of semantic communication.

  * •

Considering the resource limitation of UAVs and the requirements to send
semantic information to multiple users, we propose a multi-user resource
allocation scheme based on game theory, whose utility function of the
retrieval task is used as the optimization objective for better resource
utilization.

The remainder of this paper is organized as follows. We first summarize the
related work about Semantic Communication in Sec. II. We then introduce our
system model in Sec. III. Then, we present the proposed semantic triplets
transmission method from the communication level in Sec. IV. Next, we
elaborate on the proposed semantic communication framework in Sec. V.
Subsequently, we conduct a series of case studies and analyze the simulation
results in Sec. VI. Finally, we conclude this paper in Sec. VII. We summarize
the mathematical symbols and explanations in Table I.

TABLE I: Summary of Main Symbols. Symbol |  Explanation
---|---
$m_{f}$ |  The fading parameter for the $k_{\rm th}$ user in Fisher-Snedecor $\mathcal{F}$ fading model.
$m_{s}$ |  The shadowing parameter for the $k_{\rm th}$ user in Fisher-Snedecor $\mathcal{F}$ fading model.
${\bar{z}}$ |  The average value of $\mathcal{F}$ random variables (RVs), i.e., $z$, for the $k_{\rm th}$ user in Fisher-Snedecor $\mathcal{F}$ fading model.
$\bm{a}^{T}$ |  Transpose of vector $\bm{a}$.
$\Gamma\\!\left(\cdot\right)$ |  Gamma function [20, eq. (8.310.1)].
$\Gamma\\!\left({\cdot,\cdot}\right)$ |  Upper incomplete Gamma function [20, eq. (8.350.2)].
${B\\!\left({\cdot,\cdot}\right)}$ |  Beta function [20, eq. (8.384.1)].
$F\left({\cdot,\cdot;\cdot;\cdot}\right)$ |  Gauss hypergeometric function [20, eq. (9.111)], which is also known as ${}_{2}{F_{1}}\left({\cdot,\cdot;\cdot;\cdot}\right)$.
$G\,\begin{subarray}{c}m,n\\\ p,q\end{subarray}(\cdot)$ |  Meijer’s $G$-function [20, eq. (9.301)].
$H_{\cdot\cdot}^{\cdot\cdot}\left({\cdot\left|\cdot\right.}\right)$ |  Multivariate Fox’s $H$-function [21, eq. (A-1)].
$G\,\begin{subarray}{c}\cdot,\cdot:\cdot,\cdot:\cdot,\cdot\\\ \cdot,\cdot:\cdot,\cdot:\cdot,\cdot\end{subarray}(\cdot)$ |  Bivariate Meijer’s $G$-function [22, eq. (1)].
$N_{T}$ |  The number of antennas in the UAV
$x$ |  The input image.
$K$ |  The number of users.
$k$ |  The identity of user.
$q^{k}$ |  The personal query text of user $k$.
$\mathcal{T}$ |  The Triplet Detection (TD) function.
$\mathcal{P}$ |  The Personalized Saliency Prediction (PSP) function.
$\mathcal{C}$ |  The crop function, used to crop a sub-image from $x$ according to the box coordinates.
$\tau$ |  The set of (subject-relation-object) triplets.
$\tau_{\mathrm{recv}}^{k}$ |  The triplets received by user $k$.
$H_{\mathrm{sub}},H_{\mathrm{obj}}$ |  The attention heatmaps of subject and object entities.
$B_{\mathrm{sub}},B_{\mathrm{obj}}$ |  The box coordinates of subject and object entities.
$p^{k}$ |  The personalized triplet priority of user $k$.
$S^{k}$ |  The personalized saliency heatmap of user $k$.
$\alpha$ |  The coefficient for fusing attention heatmap and saliency heatmap.
$F^{k}_{\mathrm{sub}},F^{k}_{\mathrm{obj}}$ |  The fused attention heatmaps of subject and object entities of user $k$.
$\tilde{F}^{k}_{\mathrm{sub}},\tilde{F}^{k}_{\mathrm{obj}}$ |  The sub-heatmaps of subject and object entities of user $k$, cropped from $F^{k}_{\mathrm{sub}},F^{k}_{\mathrm{obj}}$.
$s$ |  The match score between the triplets received and the personal query.

##  II Related Work

###  II-A Semantic Communication

Semantic communication is a new communication paradigm, and it can transmit
more information when the external environment is the same [23]. The sender
sends the semantic information extracted from the original information (such
as images, text, and video) to the receiver in a semantic communication system
and the receiver recovers the original information from the semantic
information. By transmitting the semantic information, the semantic
communication system can eliminate the unnecessary information from the
original information to reduce communication overhead. The research on
semantic communication is roughly divided into four parts: how to optimize
semantic encoding, how to complete the goal-orient communications, how to
protect semantic information privacy, and how to analyze the systems’
performance.

Semantic Encoding Optimization: Semantic encoding is crucial for the semantic
communication system because it determines the efficiency and effectiveness of
information transmission. Xie et al. [19] proposed a DeepSC framework that is
based on a Transformer for text transmission tasks, DeepSC can extract the
semantic information from the original text under the interference of noise.
Xie et al. [17] further considered the more realistic situation that designing
a lightweight deep learning semantic communication system makes the model
easier to deploy on IoT devices. The above work only focused on text-based
semantic communication. Besides, images-based semantic communication has been
proposed. Bourtsoulatze [24] proposed a semantic communication system that
utilizes joint source and channel coding techniques to reduce communication
overhead for image transmission tasks. Although the above work [19, 17, 24]
proposed the semantic communication system to reduce the communication
overhead, they only considered the transmission on single-domain, such as
text-to-text or image-to-image. It is unrealistic in the real world.
Therefore, we consider the transmission of multi-domain and multimodal in this
paper. We design the framework in which the sender extracts the triplets with
semantic information from the original images, and then the sender sends the
triplets to the receiver. It can further reduce the communication overhead and
be more practical.

Task-oriented Communications: The task-oriented communication is also
important for the semantic communication system because it transmits different
semantic information according to different needs. That is to say, task-
oriented communication systems do not need to transmit data directly under
corresponding circumstances. To this end, Farshbafan et al. [25] proposed a
task-oriented semantic communication framework, which can transmit different
semantic information in the different goals of the system. However, reference
[25] only considered a single sender and receiver at the same time. Xie at el.
[13] proposed a task-oriented multi-user semantic communication system, the
framework utilized different encoders and decoders to solve the multi-task and
multi-user problems. Although the above work [25, 13] proposed the task-
oriented communication system to complete the corresponding goal, they ignored
the individual differences in different users, i.e., other receivers will have
different needs in the real world. Therefore, we consider the personalized
saliency in our framework to adapt to different users’ goals.

Secure Semantic Encoding: Since semantic information can reflect the real data
distribution of users to a certain extent and is also vulnerable to privacy
leakage in communication, we need to protect the semantic information
transmitted by users. For example, Chen et al. [26] proposed a federated
learning framework in semantic communication systems, which can protect the
privacy of the system. Yang et al. [27] proposed a federated learning-based
semantic communication framework to cope with the computing and communication
overhead under protecting the privacy of the system. The above work
illustrates that federated learning can be applied to wireless communication
systems to protect the devices’ data privacy. Therefore, Tong et al. [28]
designed a wav2vec-based autoencoder federated semantic communication
framework, and it can significantly reduce transmission error and heavy
communication overhead. Due to the low efficiency of the current semantic
communication system, we focus on how to extract semantic information
effectively and effectively adapt to different goals.

Semantic Communications Performance Analysis: In a wireless semantic
communication system, the transmission performance of the system is negatively
affected by multipath fading, that is, interference between different signals.
Therefore, it is crucial to accurately model fading channels to better
understand the performance impact of fading channels on semantic communication
systems. Previous work focused on the performance analysis of wireless
communication systems. For example, Yoo et al. [29] proposed the $\mathcal{F}$
distribution as fading model to analyze the performance of the semantic
communication systems. Based on this, reference [30] further explored a
comprehensive performance analysis of the $\mathcal{F}$ composite fading
channels in conventional wireless communication systems. Due to the rise of
semantic communications, some researchers currently turned attention to
studying the impact of fading channels on the performance of wireless semantic
communication systems. Xie et al. [31] and Weng et al. [32] explored the
performance of their framework over Rayleigh and Rician channels in semantic
communication systems. However, reference [31, 32] only explored the
communication performance in Rayleigh and Rician fading channels that are the
traditional multipath fading models. Due to the Fisher-Snedecor $\mathcal{F}$
fading channel is a commonly used fading channel model in wireless
communication systems, and it can cover the situation of classical fading
channel analysis through changing parameters. Therefore, in this paper, we
analyze the performance of our model by considering Fisher-Snedecor
$\mathcal{F}$ channel model in wireless semantic communication and obtain
insights into the wireless channel environment on the impact of semantic
communication.

###  II-B Personalized Saliency

Personalized saliency means that different observers have different regions of
interest in the same image. In recent years, personalized saliency has
received a lot of attention in the computer vision community. Xu et al. [33]
proposed a CNN-based and personal information framework to predict a
personalized saliency map. However, personalized information and images always
change in the real world. Dodge et al. [34] proposed a framework that combines
the global scene information from all categories and the extracted local
information to predict the saliency map. However, many categories are
unknowable. Mahdi et al. [35] utilized three CNN-based models to obtain the
bottom-up and top-down deep features to predict a personalized saliency map.
However, due to the storage capacity and the computing resources, it may be
difficult to utilize this framework for extracting complex features when the
number of users increases. Berkovsky et al. [36] proposed a framework for
predicting personalized saliency based on eye tracking data and the framework
needs to capture physiological responses, such as brain signals. However,
there exist massive users in semantic communication systems and it is
difficult to capture signals between multiple users, so the framework is
difficult to adapt to multi-user situations. Moroto et al. [37] proposed the
framework to extract personalized saliency maps (PSMs) through Gaussian
process regression. However, considering the limitation of storage capacity,
the receivers, i.e., UAVs, are difficult to store the PSMs for all users.
Therefore, we convert PSMs into triples to further reduce memory overhead in
this paper. The above work may be unsuitable for semantic communication
systems, especially for UAV scenarios. Therefore, we consider the situation of
a multi-user semantic communication system and propose personalized saliency-
based semantic communication.

In summary, we propose a personalized saliency-based task-oriented semantic
communication system to cope with the above problems in this paper. Firstly,
we predict the saliency heatmap of the user through the customized information
and the image captured by the UAV. Meanwhile, UAV executes triplet detection
[38] to generate an attention heatmap from the image captured by the UAV.
Secondly, UAV executes the attention fusion step to obtain the fused attention
for each user and obtains the personalized triplet from the fused attention.
The above steps complete the purpose of personalized saliency. Thirdly, UAV
allocates multi-user power through triplet priority estimation and transmits
the triplets by power allocated. Finally, the user obtains the match score
between the received triplets and personal query and decides whether to
download the image based on the matching score. The last steps complete the
purpose of goal-orient semantic communication.

##  III System Model

Figure 1: An illustration of the proposed task-oriented SemCom system model.

In this section, we first describe our proposed task-oriented SemCom system
and then describe the metrics used to evaluate the effectiveness of the
proposed design.

###  III-A Task-oriented SemCom Design

When users hire a UAV for image acquisition, in many cases, not all the images
taken by the UAV are what the user needs. Therefore, a retrieval task needs to
be performed on all the images, i.e., the users input the text of the scene
they want and get the corresponding images. However, considering that the
energy of the UAV is limited and that one UAV may need to serve multiple
users, performing all the users’ retrieval tasks in the UAV will affect the
quality of images and the UAV’s endurance. Moreover, sending all the images to
users and retrieving images on the user side also involve unnecessary energy
consumption, i.e., users need to download some images that are not of
interest.

The development of semantic communication has given us a solution to solve the
above problems. As shown in Fig. 1, instead of transmitting all the images
back to users after the photography task, the UAV transmits the semantic
features (text format) of the images to users. The transmission of semantic
features of images in text format requires few channel resources and is
convenient for users to store. The users determine a query text according to
their interests, match the images in the received semantic features, and then
download the original image from the UAV. In the rest of this paper, we focus
on the extraction and transmission of semantic information.

###  III-B Optimization Problems Analysis

The UAV extracts the triplets that represent the corresponding image
information from the captured images. If ${{n_{i}}}$ triplets can be extracted
from the $i_{\rm th}$ image, we have
${{\bm{\tau}}_{i}}=\left\\{{{\tau_{i,1}},\ldots,{\tau_{i,{n_{i}}}}}\right\\}$,
where ${{\bm{\tau}}_{i}}$ denotes the set of triplets from the $i_{\rm th}$
image. In Phase 1, the UAV transmits the triplets to the users. Note that
users are not necessarily located close to each other, and the different
interests of users will make them have different query texts. Therefore, we
consider the TDMA scheme in Phase 1. In each time slot, i.e., $T_{1}$, the UAV
uses all the antennas to serve one user and designs the beamforming vector
accordingly. Let us consider an energy-constrained scenario, which means that

$\sum\limits_{j\in{\cal K}}{{P_{j}}T_{1}}<{W_{A}},$ (1)

where $\cal K$ is the users selected in this round, ${P_{j}}$ is the transmit
power for the $j_{\rm th}$ user and $W_{A}$ is the total energy. Thus, we need
to solve two optimization problems:

  * •

P1-power allocation among users: One user per time slot is served. Because the
total energy of the UAV is limited, we need to determine how many resources
each user can occupy, in the form of transmit power.

  * •

P2-power allocation among one user’s triplets: After determining the available
power for each user, we also need to determine the power that should be
allocated to each triplet.

Let $s_{k}$ denote the match score between the triplets received and the
personal query of the $k_{\rm th}$ user,

${s_{k}}=\frac{{{N_{{\mathop{\rm in}\nolimits},k}}}}{{{N_{\rm rec}}}},$ (2)

which represents the proportion of the number of interested images of the
$k_{\rm th}$ user obtained by matching, i.e., ${{N_{{\mathop{\rm
in}\nolimits},k}}}$, to the total number of images captured by UAV, i.e.,
${{N_{\rm rec}}}$.

Let $\tilde{s}_{k}$ denote the optimal match score,

${\tilde{s}_{k}}=\frac{{{N_{{\mathop{\rm truth}\nolimits},k}}}}{{{N_{\rm
rec}}}},$ (3)

which represents the proportion of the number of interested images of the
$k_{\rm th}$ user in truth (without considering the impact of triplets drop
that may be caused by wireless transmission), i.e., ${{N_{\rm truth}}}$, to
${{N_{\rm rec}}}$. Then, we can use $\frac{s_{k}}{\tilde{s}_{k}}$ to represent
the effectiveness of semantic communication.

If P1 can be solved, we derive the power resources available to each user.
Then, P2 for each user can be solved with the help of the personalized weights
for the triplets. The solution for P2 is discussed in Section V. Now we focus
on P1. We consider the power allocation problem among users as cooperative
bargaining. Thus, with the help of NBS, we need to maximize
$\prod\limits_{k=1}^{K}{\frac{{{s_{k}}}}{{{{\tilde{s}}_{k}}}}}$. Because
${\tilde{s}}_{k}$ represents the ground-of-truth which is only decided by the
query text, the optimization problem can be transformed into

$\mathop{\max}\limits_{{P_{k}}\left({k=1,\ldots,K}\right)}\prod\limits_{k=1}^{K}{{s_{k}}}.$
(4)

For a given query text of the $k_{\rm th}$ user, the $s_{k}$ is mainly
affected by the number of received triplets. Due to the random nature of the
wireless communication environment, the transmitted triplets may not be
decoded correctly because of excessive error codes. Therefore, the higher
transmit power should be allocated to the more important triplets, i.e., the
triplets that are of more interest to the user, to guarantee error-free
transmission.

###  III-C SINR Analysis

We consider a set of ${\cal K}=1,\ldots,K$ user, where each user has their own
preference. One UAV performs the photography task and needs to transmit the
semantic features of the image to $K$ users. To obtain considerable array
gains and improve the channel quality, we consider the UAV is equipped with
$N_{T}$ antennas. The UAV is hovering above the ground $K$ users. The
horizontal coordinate of the $k_{\rm th}$ ground device is assumed to be
${u_{{k}}}=\left({{x_{{k}}},{y_{{k}}},0}\right)$,
${k}=\left({1,\ldots,K}\right)$, while the UAV is hovering at a fixed altitude
$z_{u}$ with the coordinate ${u_{\rm u}}=\left({{x_{\rm u}},{y_{\rm
u}},{z_{\rm u}}}\right)$. Thus, the distance between the $k_{\rm th}$ user and
the UAV can be expressed as ${D_{{\rm
u}{k}}}=\sqrt{{{\left\|{{u_{{k}}}-{u_{\rm{u}}}}\right\|}^{2}}}$. Let
$\alpha_{k}$ denote the path loss exponents of the UAV-$k_{\rm th}$ user link.

We denote the channel vector from the UAV to the $k_{\rm th}$ user as
${\bm{h}}_{k}\in{\mathbb{C}}^{1\times K}$. By adopting the linear beamforming,
the data symbol $t_{k}$ intended for user $k$ is multiplied with the
beamformer ${\bm{w}}_{k}\in{\mathbb{C}}^{K\times 1}$. $N_{Ik}$ paths of
interferes are assumed to be present at the $k_{\rm th}$ user, where $I$ means
the abbreviation of interference, which is used to distinguish symbols. Each
of the $j_{\rm th}$ user interfering signals has an average transmit power
$P_{Ik}$. ${t_{I,k,j}}$ is the $j_{\rm th}$ interfering symbol. Accordingly,
because TDMA is used, the received signal at the $k_{\rm th}$ user is given
by111Note that the large scale fading of the interference signal is considered
in the mean value of $h_{I,k,j}$.

${\color[rgb]{0,0,0}{r_{k}}}=\sqrt{{P_{k}}{D_{{\rm
u}{k}}^{-\alpha_{k}}}}{{\bf{h}}_{k}}{{\bf{w}}_{k}}{x_{k}}+{{P_{Ik}}}\sum\limits_{j=1}^{{N_{Ik}}}{\sqrt{{h}_{I,k,j}}{\color[rgb]{0,0,0}{{t_{I,k,j}}}}}+{n_{k}},$
(5)

where $n_{k}\in{\cal{CN}}\left({0,{\sigma^{2}}}\right)$ is the noise, $P_{k}$
is the transmit power for the $k_{\rm th}$ user. The SINR at the $k_{\rm th}$
user can be expressed as

${\gamma_{k}}=\frac{{{P_{k}}D_{{\rm{u}}k}^{-{\alpha_{k}}}{{\left\|{{{\bf{h}}_{k}}{{\bf{w}}_{k}}}\right\|}^{2}}}}{{{\sigma^{2}}+{P_{Ik}}\sum\limits_{j=1}^{{N_{Ik}}}{h_{I,k,j}^{2}}}}.$
(6)

With the help of maximum ratio transmission [39], the optimal beamforming
vector can be expressed as
${{\bf{w}}_{k}}=\frac{{{{\bf{h}}_{k}}^{T}_{1}}}{{\left\|{{{\bf{h}}_{k}}}\right\|}}$.
Thus, we have
${\left\|{{{\bf{h}}_{k}}{{\bf{w}}_{k}}}\right\|^{2}}=\sum\limits_{j=1}^{{N_{T}}}{h_{k,j}^{2}}$.

###  III-D Channel Model

The small scale fading of UAV-$k_{\rm th}$ user link is modeled as the Fisher-
Snedecor $\mathcal{F}$ fading distribution. The Fisher-Snedecor $\mathcal{F}$
composite fading model assumes that small-scale variations follow the
Nakagami-$m$ distribution and shadowing follows the inverse Nakagami-$m$
distribution. Channel measurements at 5.8 GHz have demonstrated that the
Fisher-Snedecor $\mathcal{F}$ fading model fits experimental results better
than the KG fading model both in line-of-sight and non-LOS scenarios [29].

Thus, ${\left\|{{{\bf{h}}_{k}}{{\bf{w}}_{k}}}\right\|^{2}}$ follows the
distribution of sum of $N_{T}$ Fisher-Snedecor $\mathcal{F}$ RVs [40].
However, the PDF and CDF of
${\left\|{{{\bf{h}}_{k}}{{\bf{w}}_{k}}}\right\|^{2}}$ is in terms of
Multivariate Fox’s $H$-function [21, eq. (A-1)], which is hard to provide
insights. Considering that the Fisher-Snedecor $\mathcal{F}$ RV is defined as
the ratio of two Gamma RVs and the sum of Gamma RVs still follows the Gamma
distribution, we can use the single Fisher-Snedecor $\mathcal{F}$ distribution
to approximate the distribution of the sum of Fisher-Snedecor $\mathcal{F}$
RVs [40].

Let
$Z\triangleq{\left\|{{{\bf{h}}_{k}}{{\bf{w}}_{k}}}\right\|^{2}}\sim\mathcal{F}\left({{m_{fk}},{m_{sk}},\bar{z}_{k}}\right)$,
the PDF and CDF of $Z$ are given as [41, eq. (6)] and [41, eq. (12)],
respectively.

We consider the interference signals follow the Rayleigh distribution, i.e.,
${h_{I,k,j}}\sim{\rm Rayleigh}\left({\eta_{k}}\right)$. Let
$Y\triangleq\sum\limits_{j=1}^{{N_{Ik}}}{h_{I,k,j}^{2}}$. Because the sum of
$N_{Ik}$ i.i.d. Rayleigh-fading signals have a Nakagami-$m$ distributed signal
amplitude with $m=N_{Ik}$, the PDF and CDF expressions of
$\lVert\mathbf{h}_{k}\rVert^{2}$ can be written as [42].

$f_{Y}\left(y\right)=\frac{{{y^{N_{Ik}-1}}}}{{\eta_{k}^{N_{Ik}}{\Gamma\\!\left({{N_{Ik}}}\right)}}}\exp\\!\left({-\frac{y}{{{\eta_{k}}}}}\right),$
(7)

and

$F_{Y}\left(y\right)=\frac{{\Gamma\\!\left({{N_{Ik}},\frac{y}{{{\eta_{k}}}}}\right)}}{{\Gamma\\!\left({N_{Ik}}\right)}},$
(8)

where ${{\eta_{k}}}={{{\mathbb{E}}\left[h_{k}^{2}\right]}}$, and
${\mathbb{E}}\left[\cdot\right]$ denotes expectation. We then derive the PDF
and CDF of the SINR,
${\gamma_{k}}=\frac{{{P_{k}}D_{{\rm{u}}k}^{{\alpha_{k}}}Z}}{{{\sigma^{2}}+{P_{Ik}}Y}}$.

######  Theorem 1.

The PDF and CDF of the SINR,
${\gamma_{k}}=\frac{{{P_{k}}D_{{\rm{u}}k}^{{\alpha_{k}}}Z}}{{{\sigma^{2}}+{P_{Ik}}Y}}$,
can be derived as (1) and (1), respectively, shown at the bottom of the next
page, where
${\Lambda_{k}}\triangleq\frac{{{P_{k}}D_{{\rm{u}}k}^{-{\alpha_{k}}}\left({{m_{sk}}-1}\right){{\bar{z}}_{k}}}}{{{m_{fk}}}}$,
${\Theta_{1}}=\left({1-{N_{Ik}}:\left\\{{-1,-1,0}\right\\}}\right)$, and
${\Theta_{2}}=\left({1-{m_{fk}}-{m_{sk}}:\left\\{{0,-1,-1}\right\\}}\right)$.

$\displaystyle{f_{{\gamma_{k}}}}\left(\gamma\right)$
$\displaystyle=\frac{{{\Lambda_{k}}^{{m_{sk}}}{{\left({{\sigma^{2}}}\right)}^{{N_{Ik}}+{m_{fk}}}}{\gamma^{{m_{fk}}-1}}}}{{{{\left({{P_{Ik}}{\eta_{k}}}\right)}^{{N_{Ik}}}}{{\left({{\Lambda_{k}}+\gamma{\sigma^{2}}}\right)}^{{m_{fk}}+{m_{sk}}}}{\Gamma\\!\left({{N_{Ik}}}\right)}\Gamma\\!\left({{m_{sk}}}\right)\Gamma\\!\left({{m_{fk}}}\right)}}$
$\displaystyle\times
G_{0,0:0,2:1,2}^{1,0:2,0:1,1}\left({\left.{\begin{array}[]{*{20}{c}}{{N_{Ik}}}\\\
-\end{array}}\right|\left.{\begin{array}[]{*{20}{c}}-\\\
{{m_{sk}}-{N_{Ik}},0}\end{array}}\right|\begin{array}[]{*{20}{c}}{1-{m_{fk}}-{m_{sk}}}\\\
{0,1-{m_{sk}}}\end{array}\left|{\frac{{{\sigma^{2}}}}{{{P_{Ik}}{\eta_{k}}}},\frac{{-{\Lambda_{k}}}}{{{\Lambda_{k}}+\gamma{\sigma^{2}}}}}\right.}\right)$
(15)

$\displaystyle{F_{{\gamma_{k}}}}\left(\gamma\right){\rm{=}}\frac{{{\Lambda_{k}}^{-{m_{fk}}}{{\left({{\sigma^{2}}}\right)}^{{N_{Ik}}+{m_{fk}}}}{\gamma^{{m_{fk}}}}}}{{{{\left({{P_{Ik}}{\eta_{k}}}\right)}^{{N_{Ik}}}}{\Gamma\\!\left({{N_{Ik}}}\right)}\Gamma\\!\left({{m_{sk}}}\right)\Gamma\\!\left({{m_{fk}}}\right)}}$
$\displaystyle\times\\!\\!H_{2,0:2.0;2,0;2,1}^{0,2:0,2;0,1;1,1}\\!\\!\\!\left(\\!\\!\\!\\!{\left.{\begin{array}[]{*{20}{c}}{{{{{P_{Ik}}{\eta_{k}}}}}{\sigma^{-2}}}\\\
{-1}\\\
{{\sigma^{-2}}{\Lambda_{k}}\gamma^{-1}}\end{array}}\\!\\!\right|\\!\\!\\!\begin{array}[]{*{20}{c}}{{{\Theta_{1}},{\Theta_{2}}}}\\\
-\end{array}\left[{\begin{array}[]{*{20}{c}}{\left({1-{m_{sk}}+{N_{Ik}},1}\right)\left({1,1}\right)}\\\
-\end{array}}\right]\left[{\begin{array}[]{*{20}{c}}{\left({1,1}\right)\left({{m_{sk}},1}\right)}\\\
-\end{array}}\right]\left[{\begin{array}[]{*{20}{c}}{\left({1,1}\right)\left({1+{m_{fk}},1}\right)}\\\
{\left({{m_{sk}},1}\right)}\end{array}}\right]}\right)$ (27)

###### Proof:

Please refer to Appendix A. ∎

###  III-E Approximation Analysis

Although the previously derived PDF and CDF are obtained in closed-form, it is
hard to bring valuable insights if we derive performance expressions with the
help of (1) and (1). Therefore, in the following, we derive the accurate
approximate CDF by presenting an approximate solution to a complex
mathematical integral equation. Moreover, we analyze the approximate CDF in
the high-SNDR regime and verify our derived results by numerical analysis.

####  III-E1 Accurate Approximation

Let us consider the integration as follows:

$I_{A}=\int_{a}^{\infty}{{x^{b}}{{\left({x-a}\right)}^{c}}\exp\\!\left({\frac{{x-a}}{d}}\right){F}\left({\alpha,\beta,\varepsilon;\rho
x}\right){\rm{d}}x}.$ (11)

Note that $I_{A}$ has not been studied in any mathematical integral theory
book or website such as [20, 43]. It is difficult, if not impossible, to
obtain the closed solution of $I_{A}$. Here we derive the accurate approximate
solution of $I_{A}$ in the Lemma 1.

######  Lemma 1.

An accurate approximation of $I_{A}$ when $\rho$ is small can be expressed as

${I_{A}}=\exp\\!\left({\frac{a}{d}}\right)\\!\\!\frac{{\Gamma\\!\left(\varepsilon\right){d^{b+c+1}}}}{{\Gamma\\!\left(\alpha\right)\Gamma\\!\left(\beta\right)}}G_{3,2}^{1,3}\left(\\!\\!{d\rho\left|\\!\\!{\begin{array}[]{*{20}{c}}{1\\!-\\!\beta,-b-c,1\\!-\\!\alpha}\\\
{1\\!-\\!\varepsilon}\end{array}}\right.}\\!\\!\\!\right).$ (12)

###### Proof:

Please refer to Appendix B. ∎

With the help of Lemma 1, we can re-derive the CDF of $\gamma_{k}$ as

######  Theorem 2.

An accurate CDF of $\gamma_{k}$ can be obtained as

$\displaystyle{F_{{\gamma_{k}}}}\left(\gamma\right)$
$\displaystyle=\frac{1}{{\Gamma\\!\left({{N_{Ik}}}\right)\Gamma\\!\left({{m_{sk}}}\right)\Gamma\\!\left({{m_{fk}}}\right)}}\exp\\!\left({\frac{{{\sigma^{2}}}}{{{P_{Ik}}{\eta_{k}}}}}\right)$
$\displaystyle\times
G_{3,2}^{1,3}\left({\frac{{\gamma{P_{Ik}}{\eta_{k}}}}{{{\Lambda_{k}}}}\left|{\begin{array}[]{*{20}{c}}{1-{m_{sk}},1-{N_{Ik}},1}\\\
{{m_{fk}},0}\end{array}}\right.}\right).$ (15)

####  III-E2 High-SNDR approximation

In the following, we analyze asymptotic CDF in the high-SNDR regime.

######  Theorem 3.

The CDF of $\gamma_{k}$ can be approximated in the high transmit power regime
as

$\displaystyle{F_{{\gamma_{k}}}}\left(\gamma\right)=$
$\displaystyle\frac{{\Gamma\\!\left({{m_{fk}}+{m_{sk}}}\right)\Gamma\\!\left({{N_{Ik}}+{m_{fk}}}\right)}}{{\Gamma\\!\left({{N_{Ik}}}\right)\Gamma\\!\left({{m_{sk}}}\right)\Gamma\\!\left({{m_{fk}}+1}\right)}}$
$\displaystyle\times\exp\\!\left({\frac{{{\sigma^{2}}}}{{{P_{Ik}}{\eta_{k}}}}}\right){\left({\frac{{\gamma{P_{Ik}}{\eta_{k}}}}{{{\Lambda_{k}}}}}\right)^{{m_{fk}}}}.$
(16)

####  III-E3 Verification and Insights

We use the OP to verify the derived CDF expression, (1), and two approximate
expressions, (12) and (3). The outage probability (OP) is defined as the
probability that the SINR falls below a given outage threshold, i.e., $OP_{\rm
k}={\mathbb{P}}(\gamma_{k}<\gamma_{\rm th})=F_{\gamma_{k}}(\gamma_{\rm th})$.
As shown in Fig. 2, we study the OP versus the transmit power, with $D_{\rm
uk}=1.5$ ${\rm m}$, $\alpha_{k}=2$, $m_{sk}=5$, $m_{fk}=2.6$, $\bar{z}_{k}=-1$
${\rm dB}$, $\sigma^{2}=1$ ${\rm W}$, $\eta_{k}=0.4$, $P_{Ik}=5$ ${\rm W}$,
$N_{Ik}=3$, and different values of $m_{fk}$. We can observe that the accurate
approximate expression (12) matches almost exactly with the closed-form
analytic expression (1). In the high-SINR regime, e.g., when $P_{k}$ is larger
than $25$ ${\rm dBW}$, the values obtained from the high-SINR approximate
expression (3) are close to that obtained from analytic expression.
Furthermore, from (3), we can observe that the multi-path fading parameter
$m_{fk}$, instead of the shadowing parameter $m_{sk}$, determines the slope of
the OP with decreasing transmit power. In Fig. 2, it is shown that the larger
the $m_{fk}$ is, the more rapidly the OP decreases with the increase of
transmit power.

Figure 2: The outage probability versus the transmit power, with different
multi-path fading parameter $m_{fk}$.

##  IV Communication Level: Triplet Drop Probability

We encode the semantic information of the image into triplets. Due to the
instability of wireless transmission, the receiver cannot guarantee the
perfect receiving of the semantic triplets transmitted by the UAV. Therefore,
we analyze the impact of the wireless environment on the semantic triplets
transmission. Suppose a triplet is encoded with bit length $D_{T}$, and that
the use of bit error correction codes allows for at most $D_{E}$ error bits.

###  IV-A Bit Error Probability

Under a variety of modulation formats, the BEP, $E_{k}$, can be expressed as
[44, eq. (13)]

$E_{k}=\int_{0}^{\infty}\frac{{\Gamma\\!\left({{\color[rgb]{0,0,0}{\lambda}_{2}},{\color[rgb]{0,0,0}{\lambda}_{1}}\gamma}\right)}}{{2\Gamma\\!\left({{\color[rgb]{0,0,0}{\lambda}_{2}}}\right)}}{f_{\gamma_{k}}\left(\gamma\right){\rm{d}}\gamma},$
(17)

where
${{{\Gamma\\!\left({{\color[rgb]{0,0,0}{\lambda}_{2}},{\color[rgb]{0,0,0}{\lambda}_{1}}\gamma}\right)}}/{{2\Gamma\\!\left({{\color[rgb]{0,0,0}{\lambda}_{2}}}\right)}}}$is
the conditional bit error probability, ${\color[rgb]{0,0,0}{\lambda}_{1}}$ and
${\color[rgb]{0,0,0}{\lambda}_{2}}$ are modulation-specific parameters which
have different values under different modulation and detection schemes [44].

######  Theorem 4.

The BEP of the $k_{\rm th}$ user can be derived as

$\displaystyle{E_{k}}=\frac{{{\Gamma^{-1}}\left({{m_{sk}}}\right){\Gamma^{-1}}\left({{m_{fk}}}\right)}}{{2\Gamma\\!\left({{\color[rgb]{0,0,0}{\lambda}_{2}}}\right)\Gamma\\!\left({{N_{Ik}}}\right)}}\exp\\!\left({\frac{{{\sigma^{2}}}}{{{P_{I,k}}{\eta_{k}}}}}\right)$
$\displaystyle\times
G_{4,2}^{1,4}\left({\frac{{{P_{I,k}}{\eta_{k}}}}{{{\color[rgb]{0,0,0}{\lambda}_{1}}{\Lambda_{k}}}}\left|{\begin{array}[]{*{20}{c}}{1-{m_{sk}},1-{N_{Ik}},1,1-{\color[rgb]{0,0,0}{\lambda}_{2}}}\\\
{{m_{fk}},0}\end{array}}\right.}\right).$ (20)

###### Proof:

Please refer to appendix D. ∎

###  IV-B Triplet Drop Probability

We consider that the BEP of $k_{\rm th}$ user is $E_{k}$. The TDP $P_{k}$ can
be expressed as

$P_{k}=\sum\limits_{j=D_{E}+1}^{D_{T}}{{E_{k}}^{j}{{\left({1-{E_{k}}}\right)}^{{D_{T}}-j}}},$
(21)

which can be calculated with the help of (17).

##  V Semantic Level: Personalized Saliency Fused Semantic Communication
Framework

Figure 3: An overview of the Personalized Saliency Fused Semantic
Communication Framework (PerSF-SemCom).

In applications such as real-time sensing of UAV aerial photography, the
autonomous patrol UAV cruises along the specified trajectory and transmits
aerial pictures back to users (e.g., monitoring centers and photographers). In
such a wireless communication environment with fading channels, transmitting
all aerial images to all users is expensive, which is impractical in reality
and limits the application of UAV aerial photography subscription. In this
work, we propose that users have the right to specify which type of pictures
they prefer, then the UAV only needs to transmit a small number of specific
images to each user. For example, user A only needs to download pictures of
“man wearing a jacket”, and user B prefers pictures of “bus on the street.”
These texts are called personal queries, based on which the user decides
whether to download an image from the UAV. Does the problem come from how do
personal users know they need a given picture without downloading the original
picture? This paper addresses this problem by proposing a Personalized
Saliency Fused Semantic Communication framework (PerSF-SemCom), which
leverages a Triplet Detector to infer a fixed-size set of (subject-relation-
object) triplets for each picture, and transmits these tiny-size triplets to
users for triplet matching, in which only the matching images need to be
downloaded. Besides, to prevent the triplets concerned by personalized users
from being lost in the harsh wireless competitive environment, we quantify the
priority of triplets and propose a transmission power allocation strategy,
under which triplets with higher priority have more transmission power and
therefore have a lower probability of being dropped.

###  V-A OA-SemCom: A Fully Objective Approach

As shown in Figure 3, the architecture mainly contains Triplet Detection (TD),
Personalized Saliency Prediction (PSP), Attention Fusion (AF), Triplet
Priority Estimation (TPE), and Power Allocation (PA) on the UAV, and a Triplet
Search (TS) module on the user terminal. Whenever the UAV captures a picture
$x$, TD $\mathcal{T}(x)$ infers a fixed-size set of (subject-relation-object)
triplets, i.e., the semantic information, $\tau$, from $x$, and respectively
the attention heatmaps $H_{\mathrm{sub}},H_{\mathrm{obj}}$ and box coordinates
$B_{\mathrm{sub}},B_{\mathrm{obj}}$ of their subject and object entities.
Specifically, the pretrained RelTR [38] model is used as the kernel of the TD
module, which builds an encoder-decoder architecture like Transformer [45],
where the encoder infers the visual feature context that is then used by the
decoder for triplet inference. However, the TD module can also be implemented
using any other pretrained scene graph generation technique. For example, two-
stage approaches employ Fast/Faster R-CNN [46][47] to extract object features,
and then apply scene graph generation [48][49] for graph inference. The
alternative is one-stage approaches such as FCSGG [50] and the RelTR we use,
which predict objects and their relations concurrently, in an end-to-end
fashion, and are thus more lightweight and faster. Regardless of which
technique is used to implement TD, the general formula $\mathcal{T}(x)$ for TD
obeys

$H_{\mathrm{sub}},H_{\mathrm{obj}},B_{\mathrm{sub}},B_{\mathrm{obj}},\tau\leftarrow\mathcal{T}(x),$
(22)

where $H_{\mathrm{sub}},H_{\mathrm{obj}}$ are objective attention heatmaps of
subjects and objects, $B_{\mathrm{sub}},B_{\mathrm{obj}}$ are bounding boxes
of subjects and objects, respectively, and $\tau$ is the prediction set of
(subject-relation-object) triplets.

After this step, a naive idea would be to transmit the triplet set $\tau$ to
all users to match their personal queries $q^{k}(\forall k\in[1,K])$. This
naive approach (named Naive-SemCom) faces the problem of key triplets being
dropped due to intense competition among multiple users for scarce wireless
channel resources. For example, the user $k$ has the personal query
$q^{k}=\it{man\ wearing\ jacket}$, but unfortunately, the packet of the key
triplet $\it{man\ wearing\ jacket}$ is dropped in the wireless channel, then
the current image will fail to match the personal query. The reason is that
the wireless channel treats packets of all triplets as equally important,
making the key triplets drop with equal probability as other triplets.

To this end, we propose prioritizing triplets for each user and allocating
more transmission power to triplets with higher priority to ensure that key
triplets are successfully delivered to the user terminal. To achieve this, one
challenge should be addressed, that is, how to prioritize triplets and
identify the key triplets for personalized users? As a benchmark, we can use
the product of maximum values of the subject and object attention heatmaps
$H_{\mathrm{sub}},H_{\mathrm{obj}}$ to obtain the triplet priority $p$ in an
objective view, namely,
$p=\max(\mathcal{C}(H_{\mathrm{sub}},B_{\mathrm{sub}}))\otimes\max(\mathcal{C}(H_{\mathrm{obj}},B_{\mathrm{obj}}))$,
where $\mathcal{C}(H_{\mathrm{sub}},B_{\mathrm{sub}})$ is a cropping function
that crops the attention sub-image from $H_{\mathrm{sub}}$ according to the
box coordinates $B_{\mathrm{sub}}$. Note that the cropping function
$\mathcal{C}$ and $\max$ in this section are channel-wise operations, and
“$\otimes$” is an element-wise multiplier. We refer to this benchmarking
approach as Objective Attention-Based Semantic Communication (OA-SemCom),
which, as the name suggests, only considers the objective global attention of
the image itself, and its triplet priority is common to all users. However,
users have personalized saliency, and their triplets should be prioritized
differently than others, as are key triplets, but OA-SemCom fails to capture
the personalization in subjective saliency among different users.

###  V-B PerSF-SemCom: Achieve Personalization Through Fused Saliency

To address the above issues, we develop a PerSF-SemCom framework that
integrates objective visual attention from RelTR and subjective visual
attention from a personalized saliency prediction module, namely PSP, to
assist the UAV in personalized priority estimation for each user. In our
implementation, the PSP module $\mathcal{P}(x,k)$ leverages a pretrained fully
convolutional encoder-decoder network structure[51] to predict personal
saliency heatmap $S^{k}$ for user $k$,

$S^{k}\leftarrow\mathcal{P}(x,k).$ (23)

These heatmaps show the things that different users are most interested in
when looking at the same image: the users’ subjective saliency distribution.
For example, some users may only follow persons, while others also follow
cars.

The encoder uses VGG16 [52] without pooling layers as the backbone, followed
by an ASPP module to capture multi-scale visual information, and then the
decoder restores the original image resolution by stacking convolution and up-
sampling layers. Since how to achieve personalization in PSP is not the focus
of this study, for simplicity, we use a plain but effective method to achieve
personalization, which is to train user saliency models separately on
different user datasets to obtain personalized behaviors. Please note that
similar to the TD module, the PSP module is also a replaceable plugin that can
be replaced with other pretrained personalized saliency models, depending on
the researcher’s preference. For instance, treat each user’s prediction task
separately and use a multi-task model to train a personalized saliency model
for each user [33], or train a meta-learning model that can quickly adapt to
new personalized tasks [53].

Then in Figure 3, we take a person $k$ as an example to illustrate how to fuse
objective attention and subjective saliency. In the AF module, the attention
heatmaps $H_{\mathrm{sub}},H_{\mathrm{obj}}$ and the saliency heatmap $S^{k}$
are first normalized, and then fused by weighted sum, where $\alpha\in[0,1]$
is the fusion coefficient, “$\oplus$” is the broadcast add operator, and
$\mathrm{norm}$ is a global normalizer,

$\displaystyle F^{k}_{\mathrm{sub}}$
$\displaystyle=\alpha\cdot\mathrm{norm}(S^{k})\oplus(1-\alpha)\cdot\mathrm{norm}(H_{\mathrm{sub}}),$
(24) $\displaystyle F^{k}_{\mathrm{obj}}$
$\displaystyle=\alpha\cdot\mathrm{norm}(S^{k})\oplus(1-\alpha)\cdot\mathrm{norm}(H_{\mathrm{obj}}).$
(25)

In order to accurately locate the attention heatmaps of the subject and object
entities, the fused attention heatmaps
$F^{k}_{\mathrm{sub}},F^{k}_{\mathrm{obj}}$ should be cropped according to the
box coordinates $B_{\mathrm{sub}},B_{\mathrm{obj}}$ to obtain the sub-heatmaps
$\tilde{F}^{k}_{\mathrm{sub}},\tilde{F}^{k}_{\mathrm{obj}}$ of the subject and
object entities. These sub-heatmaps are then fed into the TPE module for
priority estimation, where their maxima are multiplied and used as the triplet
priorities $p^{k}$,

$\displaystyle\tilde{F}^{k}_{\mathrm{sub}}=\mathcal{C}(F^{k}_{\mathrm{sub}},B_{\mathrm{sub}}),$
(26)
$\displaystyle\tilde{F}^{k}_{\mathrm{obj}}=\mathcal{C}(F^{k}_{\mathrm{obj}},B_{\mathrm{obj}}),$
(27) $\displaystyle
p^{k}=\max(\tilde{F}^{k}_{\mathrm{sub}})\otimes\max(\tilde{F}^{k}_{\mathrm{obj}}).$
(28)

Finally, the PA module allocates transmission power for triplets according to
personalized priorities $p^{k}$. The key triplets with higher priority will be
allocated more transmission power, which makes them less likely to be dropped
while traversing the wireless channel.

On the receiver side (i.e., the user terminal $k$), the TS module uses the
received triplets $\tau_{\mathrm{recv}}^{k}$ to match the personal query
$q^{k}$ and calculate a match score $s$. Here, we recommend two types of TS
modules: Accurate Mode (TS-AM) and Fuzzy Mode (TS-FM). TS-AM aims to find the
same received triplet as the personal query, and it returns a match score of 1
if found and 0 otherwise. TS-AM is preferred if the user’s personal query is
forced to meet the (subject-relation-object) format. However, if the personal
query is free text, TS-FM could be better because it can return a match score
at the semantic level (e.g., HEM[54]). Once a matching score $s$ is obtained,
the user can decide whether to download the current image $x$. In our
implementation, we use TS-AM by default because semantic sentence matching is
not the focus of this work, and only images with matching scores $s=1$ will be
downloaded. We summarize the pseudo code of the proposed PerSF-SemCom in
Algorithm 1.

Algorithm 1 PerSF-SemCom (Main)

1:Captured image $x$ on UAV, user identity $k$.

2:Match score $s$, downloaded image $x$ on user $k$.

3:procedure UAV-Send($x,k$)

4: TD detects triplets $\tau$ and their attention heatmaps
$H_{\mathrm{sub}},H_{\mathrm{obj}}$ and box coordinates
$B_{\mathrm{sub}},B_{\mathrm{obj}}$:
$H_{\mathrm{sub}},H_{\mathrm{obj}},B_{\mathrm{sub}},B_{\mathrm{obj}},\tau\leftarrow\mathcal{T}(x);$

5: PSP predicts the personalized saliency heatmap $S^{k}$ for user $k$:
$S^{k}\leftarrow\mathcal{P}(x,k)$;

6: AF fuses the objective attention $H_{\mathrm{sub}},H_{\mathrm{obj}}$ and
the subjective saliency $S^{k}$ by Eqs. (24)-(25);

7: TPE calculates the priority $p^{k}$ of triplets $\tau$ using the fused
attention heatmaps $F^{k}_{\mathrm{sub}},F^{k}_{\mathrm{obj}}$ by Eqs.
(26)-(28);

8: PA allocates transmission power to triplets $\tau$ according to their
priority $p^{k}$ using RCGA[55];

9: UAV sends triplets $\tau$ to user $k$’s terminal;

10:procedure User-Receive($\tau_{\mathrm{recv}}^{k}$)

11: TS calculates the match score $s$ between received triplets
$\tau_{\mathrm{recv}}^{k}$ and personal query $q^{k}$ via TS-AM/FM;

12: if $s$ is greater than a user-specified threshold then User $k$ downloads
current image $x$; return Match score $s$ and downloaded image $x$;

##  VI Numerical Results

###  VI-A Environment Setup

The experimental platform is built on a generic Ubuntu 18.04 system with
Intel(R) Xeon(R) E5-2678 CPU and 4 Geforce RTX 2080 TI GPUs. The RelTR model
is adopted as the core of the TD module, which has been pretrained on the
Visual Genome (VG) dataset [56], and has a top-50 recall rate of 25.2 on the
scene graph detection metric, with the corresponding mean value being
8.5222The pretrained model is available at: https://github.com/yrcong/RelTR.
The VG dataset contains 108k images with 150 objects and 50 relationship
categories. For the PSP module, we use the saliency prediction model in
literature [51] pretrained on 3 visual attention datasets, respectively,
including SALICON [57], MIT1003 [58] and DUT-OMRON [59], to simulate the
visual saliency discrepancy of 3 users333The pretrained model is available at:
https://github.com/alexanderkroner/saliency. The reason this works is that
researchers collect these datasets from different perspectives, which can be
regarded as real-world experiences and environments of different persons, thus
presenting independent personalities. The validation dataset used in our
experiments is real-world video frames downloaded from YouTube444The video is
available at: https://www.youtube.com/watch?v=RPZ3xWy70IE. We framed this
video at an interval of 5 frames and obtained a dataset of 59 images, which we
named “STREET”. In Figure 4, we visualize a portion of the STREET dataset.
Each user’s personal queries and their experience datasets are summarized in
Table III.

Figure 4: A partial overview of our STREET dataset.

If not otherwise specified, the parameters of the small-scale fading model and
the system parameters such as power and transmission distance are shown in
Table II following common parameter settings in the literature [60, 61].

TABLE II: Channel Configuration Parameters for 3 users. User ID | 1 | 2 | 3
---|---|---|---
Fading parameter $m_{f}$ | 2 | 2 | 5
Shadowing parameter $m_{s}$ | 2 | 4 | 2
Signal amplitude decrease $\bar{z}$ $({\rm dB})$ | -3
Distance $D_{\mathrm{u}k}$ $({\rm m})$ | 10
Number of antennas $N_{T}$ | 3
Paths of interferes $N_{I,k}$ | 2
Interference power $P_{I,k,j}$ $({\rm W})$ | 2
$\eta_{k}$ $({\rm dB})$ | -3
Noise $n_{k}$ $({\rm W})$ | 1
$\tau_{1}$ | 1
$\tau_{2}$ | 0.5
Path loss exponent $\alpha_{k}$ | 2

Two benchmark approaches are used for performance comparison, that is, Naive-
SemCom and OA-SemCom. Naive-SemCom aims to allocate transmit power when
transmitting to each user equally, and the triplets of each user are also
allocated with equal power. In other words, Naive-SemCom has no awareness of
the importance of semantic triples. Instead, OA-SemCom quantifies the priority
of triplets and uses these priorities to schedule transmit power for each user
and triplet. However, OA-SemCom only considers the objective attention
obtained by TD but ignores the user’s subjective attention and personality. To
address this issue, our PerSF-SemCom is proposed, and PSP, AF modules are
introduced to fuse the objective and subjective attention. We set the fusion
coefficient $\alpha=0.2$ and the transmit power $P=3000$ by default and
calculated the average of each user’s match score on all images as the user’s
score. Each experiment was repeated 5 times, and the average results are
shown.

TABLE III: users’ identities, experience datasets and personal queries. Identity | Dataset | Personal Queries
---|---|---
User 1 | SALICON | woman has hair
User 2 | MIT1003 | sign on building
User 3 | DUT-OMRON | woman wearing shirt

###  VI-B Results and Analysis

Effectiveness of PerSF-SemCom over $\alpha$ and $P$. We first show the
effectiveness of the proposed PerSF-SemCom. To find the optimal
hyperparameters, we increase the fusion coefficient $\alpha$ from 0 to 1 and
the total transmits power $P$ from 1kW to 3kW. The utility value (i.e., the
product of all user scores) curves are shown in Figure 5. Please note that OA-
SemCom corresponds to our PerSF-SemCom with $\alpha=1.0$. Benefiting from the
introduction of subjective attention, PerSF-SemCom outperforms Naive-SemCom in
most cases, for example, when $\alpha\in[0,0.6]$ and
$P\in[1\mathrm{kW},\mathrm{3kW}]$. The curves of PerSF-SemCom first increase
to the optimal and then rapidly degrade. The optimal utility value usually
occurs when $\alpha$ is between 0.1 and 0.2; that is, the objective attention
should contribute 10%-20% to the fused attention, while the subjective
attention contributes 80%-90%. After this, the PerSF-SemCom performance
gradually deteriorated with the withdrawal of subjective attention, especially
when $\alpha=1.0$, PerSF-SemCom degenerates to OA-SemCom, which performs even
worse than Naive-SemCom. The above results show that the introduction of
appropriate subjective attention can significantly enhance semantic
communication’s personalization and anti-interference ability and demonstrates
the effectiveness of the proposed PerSF-SemCom. In subsequent experiments, we
use the recommended $\alpha=0.2$ as the default setting.

Figure 5: The value curves of utility function over different fusion
coefficient $\alpha$ and transmit power $P$.

The effects of transmit power $P$. To explore the optimality gap over
different transmit powers $P$, we increase $P$ from 1kW to 3kW and illustrate
the gap between PerSF-SemCom and the theoretical optimal in Figure 6. The top
dashed lines represent the theoretical upper bounds of each user’s score. They
use infinite transmit power, so no triplet packets get dropped. Users have
different upper bounds because of their personality divergence. As expected,
the optimality gap of PerSF-SemCom becomes smaller as the transmit power $P$
increases because higher transmit power effectively reduces the probability of
packet loss. Compared with Naive-SemCom, when $P=3\mathrm{kW}$, PerSF-SemCom
reduces the optimality gap by 54%, 57%, 37% on the three users, respectively,
which shows a significant improvement in the accuracy of the UAV aerial
imagery subscription service. However, OA-SemCom, which only considers
objective attention, widens the optimality gap by 26%, 57%, and 86%. These
results prove the necessity to incorporate personal attention.

Figure 6: The score curves for each user over different total transmit power
$P$.

The effects of power allocation. Intuitively, users with poor channel
conditions should be allocated more transmission power. In this experiment,
the channel condition ranking of users 1-3 is user 1 $<$ user 3 $<$ user 2. We
use the Real-Coded Genetic Algorithm (RCGA)[55] to solve the NBS problem and
allocate power among users, and then proportionally distribute power among
triplets according to priority. RCGA uses the population size of 50, the
mutation probability of 0.001, and the maximum iteration of 20. Given the
transmit power $P=3\mathrm{kW}$ and 3 users, we traverse all possible settings
of full power allocation (i.e., the sum of the proportions of the power
allocated to each user is 1) and visualize their utility function surface in
Figure 7. RCGA found the best power allocation per user to be (40.6%, 18.4%,
40.0%), with the score (0.46, 0.12, 0.33) per user and the utility value
0.0175, which outperforms Naive-SemCom with the power allocation (33.3%,
33.3%, 33.3%), the scores (0.36, 0.09, 0.29) and the utility value 0.0091. The
resulting power allocation strategy also supports our intuitive idea that more
power should be allocated to users with poor channel conditions rather than
simply evenly allocated.

Figure 7: The utility function surface under different power allocations.

The effects of small-scale channel conditions $m_{sk},m_{fk}$. Given the
transmission power of user $k$ is 1kW, we investigate the effect of different
values of multi-path fading parameter $m_{fk}$ and shading parameter $m_{sk}$
on the utility function values. As shown in Fig. 8, when the values of both
$m_{fk}$ and $m_{sk}$ are large, which means the multipath effect is weak and
there is less shading, the value of the utility function is large. A more
interesting insight is that an increase in $m_{fk}$ leads to a faster increase
in the utility function value compared to the same increase in $m_{sk}$. This
suggests that, at the wireless channel level, the goal-oriented semantic
communication system that we studied in this paper is more affected by the BER
increase due to the multi-path effect, instead of shadowing.

Figure 8: Utility function values under different multi-path fading parameter
$m_{fk}$ and shadow fading parameter $m_{sk}$. Figure 9: Utility function
values under different transmission distance $D_{\rm uk}$ and interference
power $P_{Ik}$.

The effects of large-scale channel conditions $D_{\mathrm{u},k},P_{Ik}$. Given
the transmission power of user $k$ is 1kW, we investigate the effect of
transmission distance and interference power on the value of the utility
function. In Fig. 9, we can observe that, when the interference power is
small, i.e., $P_{Ik}<1$ ${\rm W}$, the increase in the transmission distance
does not result in a significant decrease in the value of the utility
function. However, in the high interference regime, e.g., when $P_{Ik}>10$
${\rm W}$, every 5 ${\rm m}$ increase in transmission distance results in an
about $58\%$ decrease in the value of the utility function. Therefore, when
there is substantial interference in the environment, we need to reduce the
transmission distance by adjusting the trajectory of the UAV to ensure the
quality of the semantic communication services.

Figure 10: Comparison of total transferred bytes of images.

The effects of reducing communication overhead. Considering a vanilla approach
that the UAV sends a total of 59 images to 3 subscribers, each image is 1.27MB
in size and the total bytes transferred is 224.8MB. As an improvement, PerSF-
SemCom selectively sends fewer images (64 in total) to specified subscribers,
before that 873 triplets were sent with a negligible additional communication
cost of 10.24KB. Then, the UAV only needs to send 81.29MB in size, which
reduces the communication cost by 64% and thus saves the power consumption
during transmission.

##  VII Conclusions

In this paper, we have focused on the semantic communication personalization
and resource allocation optimization issues for personalized saliency-based
task-oriented semantic communication in UAV image sensing scenarios. We have
first presented an energy-efficient task-oriented semantic communication
framework with an efficient image retrieval manner based on a triple-based
scene graph. To ensure personalized semantic communication, we have designed a
personalized attention-based mechanism to realize differential weight encoding
of triplets for important information according to user preferences.
Furthermore, we have analyzed mathematically the effects of wireless fading
channels on semantic communication and proposed a game-based model for a
multi-user resource allocation scheme to achieve efficient utilization of UAV
resources. We evaluate performance of the proposed framework and schemes on
real-world datasets. The numerical results have confirmed that the proposed
framework and schemes can realize personalized semantic communication and
significantly enhance the UAV resource utilization.

##  Appendix A Proof of Lemma 1

###  A-A Proof of PDF

Let $X\triangleq{\sigma^{2}}+{P_{Ik}}Y$ and
$U\triangleq{P_{k}}D_{{\rm{u}}k}^{-{\alpha_{k}}}Z$. Thus, we have
${\gamma_{k}}=\frac{U}{X}$. The PDF of ${\gamma_{k}}$ can be expressed as

${f_{{\gamma_{k}}}}\left(\gamma\right)=\int_{0}^{\infty}{x{f_{U}}\left({\gamma
x}\right){f_{X}}\left(x\right){\rm{d}}x}.$ (A-1)

Substituting (7) and [41, eq. (6)] into (A-1), we have

${f_{{\gamma_{k}}}}\\!\left(\gamma\right)\\!=\\!\frac{{{m_{fk}}^{{m_{fk}}}{{\left({{m_{sk}}1}\right)}^{{m_{sk}}}}{{\bar{z}}_{k}}^{{m_{sk}}}{\gamma^{{m_{fk}}1}}}}{{{{\left({{P_{Ik}}{\eta_{k}}}\right)}^{{N_{Ik}}}}\Gamma\\!\left(K\right){{\left({{P_{k}}D_{{\rm{u}}k}^{{\alpha_{k}}}}\right)}^{{m_{fk}}}}B\\!\left({{m_{fk}},{m_{sk}}}\right)}}I_{1},$
(A-2)

where

$I_{1}=\int_{{\sigma^{2}}}^{\infty}{\frac{{{x^{{m_{fk}}}}{{\left({x{\sigma^{2}}}\right)}^{{N_{Ik}}1}}\exp\\!\left({\frac{{x{\sigma^{2}}}}{{{P_{Ik}}{\eta_{k}}}}}\right)}}{{{{\left({\frac{{{m_{fk}}\gamma
x}}{{{P_{k}}D_{{\rm{u}}k}^{{\alpha_{k}}}}}+\left({{m_{sk}}1}\right){{\bar{z}}_{k}}}\right)}^{{m_{fk}}+{m_{sk}}}}}}{\rm{d}}x}.$
(A-3)

With the help of [20, eq. (9.301)] and [43, eq. (01.03.26.0004.01)], we can
express the $exp(\cdot)$ function in terms of the Mellin-Barnes integral form
as

$\displaystyle\exp\\!\left({-\frac{{x-{\sigma^{2}}}}{{{P_{Ik}}{\eta_{k}}}}}\right)=G_{0,1}^{1,0}\left({\left.{\frac{{x-{\sigma^{2}}}}{{{P_{Ik}}{\eta_{k}}}}}\right|0}\right)$
$\displaystyle=\frac{1}{{2\pi i}}\int_{{{\cal
L}_{1}}}{\Gamma\\!\left({-{s_{1}}}\right)}{\left({\frac{{x-{\sigma^{2}}}}{{{P_{Ik}}{\eta_{k}}}}}\right)^{{s_{1}}}}{\rm{d}}{s_{1}}.$
(A-4)

Substituting (A-A) into $I_{1}$, we obtain that

$\displaystyle{I_{1}}=\frac{1}{{2\pi i}}\int_{{{\cal
L}_{1}}}{\Gamma\\!\left({-{s_{1}}}\right)}{\left({\frac{1}{{{P_{Ik}}{\eta_{k}}}}}\right)^{{s_{1}}}}$
$\displaystyle\times\\!\\!\int_{0}^{\infty}\\!\\!\\!{\frac{{{x^{{s_{1}}+{N_{Ik}}-1}}{{\left({x\\!+\\!{\sigma^{2}}}\right)}^{{m_{fk}}}}}{\rm{d}}x{\rm{d}}{s_{1}}}{{{{\left(\\!{\frac{{{m_{fk}}\gamma
x}}{{{P_{k}}D_{{\rm{u}}k}^{-{\alpha_{k}}}}}\\!+\\!\frac{{{m_{fk}}\gamma{\sigma^{2}}}}{{{P_{k}}D_{{\rm{u}}k}^{-{\alpha_{k}}}}}\\!+\\!\left(\\!{{m_{sk}}\\!-\\!1}\\!\right){{\bar{z}}_{k}}}\\!\right)}^{{m_{fk}}+{m_{sk}}}}}}}.$
(A-5)

Let
${\Lambda_{k}}\triangleq\frac{{{P_{k}}D_{{\rm{u}}k}^{-{\alpha_{k}}}\left({{m_{sk}}-1}\right){{\bar{z}}_{k}}}}{{{m_{fk}}}}$.
With the help of [20, eq. (3.197.1)], the integration part in $I_{1}$ can be
solved. Thus, we can re-write $I_{1}$ as

$\displaystyle{I_{1}}=\frac{1}{{2\pi
i}}{\left({\frac{{{P_{k}}D_{{\rm{u}}k}^{-{\alpha_{k}}}}}{{{m_{fk}}\gamma}}}\right)^{{m_{fk}}+{m_{sk}}}}\int_{\cal
L}{\Gamma\\!\left({-{s_{1}}}\right)}$
$\displaystyle\times\\!{\left({\frac{1}{{{P_{Ik}}{\eta_{k}}}}}\right)^{{s_{1}}}}{\left({\frac{{{P_{k}}D_{{\rm{u}}k}^{-{\alpha_{k}}}\left({{m_{sk}}-1}\right){{\bar{z}}_{k}}}}{{{m_{fk}}\gamma}}+{\sigma^{2}}}\right)^{-{m_{fk}}-{m_{sk}}}}$
$\displaystyle\times\\!{\sigma^{2{s_{1}}+2{N_{Ik}}+2{m_{fk}}}}B\\!\left({{s_{1}}\\!+\\!{N_{Ik}},{m_{sk}}-{s_{1}}-{N_{Ik}}}\right)$
$\displaystyle\times\\!F\\!\left(\\!{{m_{fk}}\\!+\\!{m_{sk}},{s_{1}}\\!+\\!{N_{Ik}};{m_{sk}};1\\!-\\!\frac{{{\sigma^{2}}}}{{\frac{{{\Lambda_{k}}}}{\gamma}+{\sigma^{2}}}}}\\!\right){\rm{d}}{s_{1}}.$
(A-6)

Using [20, eq. (9.113)] and [20, eq. (8.384.1)], we can further express
$I_{1}$ as

$\displaystyle{I_{1}}={\left({\frac{1}{{2\pi
i}}}\right)^{\rm{2}}}{\left({\frac{{{P_{k}}D_{{\rm{u}}k}^{-{\alpha_{k}}}}}{{{m_{fk}}\left({{\Lambda_{k}}+\gamma{\sigma^{2}}}\right)}}}\right)^{{m_{fk}}+{m_{sk}}}}\frac{{{{\left({{\sigma^{2}}}\right)}^{{N_{Ik}}+{m_{fk}}}}}}{{\Gamma\\!\left({{m_{fk}}+{m_{sk}}}\right)}}$
$\displaystyle\times\\!\int_{{{\cal L}_{1}}}{\int_{{{\cal
L}_{2}}}{\frac{{\Gamma\\!\left({{m_{sk}}\\!-\\!{s_{1}}\\!-\\!{N_{Ik}}}\right)\Gamma\\!\left({-{s_{1}}}\right)\Gamma\\!\left({{m_{fk}}\\!+\\!{m_{sk}}\\!+\\!{s_{2}}}\right)}}{{\Gamma\\!\left({{m_{sk}}\\!+\\!{s_{2}}}\right){\Gamma^{-1}}\left({-{s_{2}}}\right){\Gamma^{-1}}\left({{s_{1}}\\!+\\!{N_{Ik}}\\!+\\!{s_{2}}}\right)}}}}$
$\displaystyle\times\\!{\left({\frac{{{\sigma^{2}}}}{{{P_{Ik}}{\eta_{k}}}}}\right)^{{s_{1}}}}{\left({\frac{{-{\Lambda_{k}}}}{{{\Lambda_{k}}+\gamma{\sigma^{2}}}}}\right)^{{s_{2}}}}{\rm{d}}{s_{2}}{\rm{d}}{s_{1}}.$
(A-7)

Therefore, substituting $I_{1}$ into (A-2), using the definition of Bivariate
Meijer’s $G$-function [22, eq. (1)], we can derive (1) to complete the proof.

###  A-B Proof of CDF

According to the definition of CDF, we have

${F_{{\gamma_{k}}}}\left(\gamma\right)=\int_{0}^{\gamma}{{f_{{\gamma_{k}}}}\left(x\right){\rm{d}}x}.$
(A-8)

Combining (1) with (A-8), we have

$\displaystyle{F_{{\gamma_{k}}}}\left(\gamma\right)=\frac{{{m_{fk}}^{{m_{fk}}}{{\left({{m_{sk}}-1}\right)}^{{m_{sk}}}}{{\bar{z}}_{k}}^{{m_{sk}}}}}{{{{\left({{P_{Ik}}{\eta_{k}}}\right)}^{{N_{Ik}}}}{\Gamma\\!\left({{N_{Ik}}}\right)}{{\left({{P_{k}}D_{{\rm{u}}k}^{-{\alpha_{k}}}}\right)}^{{m_{fk}}}}B\\!\left({{m_{fk}},{m_{sk}}}\right)}}$
$\displaystyle\times{\left({\frac{1}{{2\pi
i}}}\right)^{\rm{2}}}{\left({\frac{{{P_{k}}D_{{\rm{u}}k}^{-{\alpha_{k}}}}}{{{m_{fk}}}}}\right)^{{m_{fk}}+{m_{sk}}}}\frac{{{{\left({{\sigma^{2}}}\right)}^{{N_{Ik}}+{m_{fk}}}}}}{{\Gamma\\!\left({{m_{fk}}+{m_{sk}}}\right)}}$
$\displaystyle\times\int_{{{\cal L}_{1}}}{\int_{{{\cal
L}_{2}}}{\frac{{\Gamma\\!\left({{m_{sk}}-{s_{1}}-{N_{Ik}}}\right)\Gamma\\!\left({-{s_{1}}}\right)\Gamma\\!\left({{m_{fk}}+{m_{sk}}+{s_{2}}}\right)}}{{\Gamma\\!\left({{m_{sk}}+{s_{2}}}\right){\Gamma^{-1}}\left({-{s_{2}}}\right){\Gamma^{-1}}\left({{s_{1}}+{N_{Ik}}+{s_{2}}}\right)}}}}$
$\displaystyle\times{I_{\rm{2}}}{\left({\frac{{{\sigma^{2}}}}{{{P_{Ik}}{\eta_{k}}}}}\right)^{{s_{1}}}}{\left({-{\Lambda_{k}}}\right)^{{s_{2}}}}{\rm{d}}{s_{2}}{\rm{d}}{s_{1}},$
(A-9)

where the $I_{2}$ can be expressed as

${I_{\rm{2}}}{\rm{=}}\int_{0}^{\gamma}{\frac{{{x^{{m_{fk}}-1}}}}{{{{\left({{\Lambda_{k}}+x{\sigma^{2}}}\right)}^{{m_{fk}}+{m_{sk}}+{s_{2}}}}}}{\rm{d}}x}.$
(A-10)

With the help of, we can solve $I_{2}$ as

$\displaystyle{I_{\rm{2}}}$
$\displaystyle=\frac{{{\gamma^{{m_{fk}}}}}}{{{\Lambda_{k}}^{{m_{fk}}+{m_{sk}}+{s_{2}}}{m_{fk}}}}$
$\displaystyle\times
F\left({{m_{fk}}+{m_{sk}}+{s_{2}},{m_{fk}};1+{m_{fk}};-\frac{{{\sigma^{2}}}}{{{\Lambda_{k}}}}\gamma}\right).$
(A-11)

According to the integral expression of the hyper-geometric function [20, eq.
(9.113)], we can substitute $I_{2}$ into (A-B) and obtain (1), which completes
the proof.

##  Appendix B Proof of Lemma 1

Let $t\triangleq x\rho$. We can re-write $I_{A}$ as

$\displaystyle{I_{A}}={\rho^{-b-c-1}}\exp\\!\left({\frac{a}{d}}\right)$
$\displaystyle\times\int_{\rho a}^{\infty}{{t^{b}}{{\left({t-\rho
a}\right)}^{c}}\exp\\!\left({-\frac{t}{{\rho
d}}}\right)F\left({\alpha,\beta,\varepsilon;-t}\right){\rm{d}}t}.$ (B-1)

Because $\rho$ is small, we can further express $I_{A}$ as

$\displaystyle{I_{A}}$
$\displaystyle\approx{\rho^{-b-c-1}}\exp\\!\left({\frac{a}{d}}\right)$
$\displaystyle\times\int_{0}^{\infty}{{t^{b+c}}\exp\\!\left({-\frac{t}{{\rho
d}}}\right)F\left({\alpha,\beta,\varepsilon;-t}\right){\rm{d}}t}.$ (B-2)

With the help of [20, eq. (9.113)], we obtain

$\displaystyle{I_{A}}$
$\displaystyle={\rho^{-b-c-1}}\exp\\!\left({\frac{a}{d}}\right)\frac{{\Gamma\\!\left(\varepsilon\right)}}{{\Gamma\\!\left(\alpha\right)\Gamma\\!\left(\beta\right)}}\frac{1}{{2\pi
i}}$ $\displaystyle\times\int_{{{\cal
L}_{1}}}{\frac{{\Gamma\\!\left({{s_{1}}+\alpha}\right)\Gamma\\!\left({{s_{1}}+\beta}\right)\Gamma\\!\left({-{s_{1}}}\right)}}{{\Gamma\\!\left({{s_{1}}+\varepsilon}\right)}}}{I_{3}}{\rm{d}}{s_{1}},$
(B-3)

where

${I_{3}}=\int_{0}^{\infty}{{t^{{s_{1}}+b+c}}\exp\\!\left({-\frac{t}{{\rho
d}}}\right){\rm{d}}t}.$ (B-4)

By using [20, eq. (3.351.3)] and [20, eq. (8.339.1)], $I_{3}$ can be solved as

${I_{3}}={\left({d\rho}\right)^{b+c+{s_{1}}+1}}\Gamma\\!\left({1+b+c+{s_{1}}}\right).$
(B-5)

Substituting $I_{3}$ into (B), we have

$\displaystyle{I_{A}}=\exp\\!\left({\frac{a}{d}}\right)\frac{{\Gamma\\!\left(\varepsilon\right){d^{b+c+1}}}}{{\Gamma\\!\left(\alpha\right)\Gamma\\!\left(\beta\right)}}\frac{1}{{2\pi
i}}$ $\displaystyle\times\int_{{{\cal
L}_{1}}}{\frac{{\Gamma\\!\left({{s_{1}}+\alpha}\right)\Gamma\\!\left({{s_{1}}+\beta}\right)\Gamma\\!\left({-{s_{1}}}\right)}}{{{\Gamma^{-1}}\left({1+b+c+{s_{1}}}\right)\Gamma\\!\left({{s_{1}}+\varepsilon}\right)}}}{\left({d\rho}\right)^{{s_{1}}}}{\rm{d}}{s_{1}}.$
(B-6)

According to the definition of Meijer’s $G$-function [20, eq. (9.301)], we can
re-write $I_{A}$ as (12) to complete the proof.

##  Appendix C Proof of Theorem 2

Using the definition of CDF, we have

${F_{{\gamma_{k}}}}\left(\gamma\right)=\int_{0}^{\infty}{{F_{U}}\left({\gamma
x}\right){f_{X}}\left(x\right){\rm{d}}x},$ (C-1)

where

$\displaystyle{F_{U}}\left(u\right)$
$\displaystyle=\Pr\left({U<u}\right)=\Pr\left({Z<\frac{u}{{{P_{k}}D_{{\rm{u}}k}^{-{\alpha_{k}}}}}}\right)$
$\displaystyle={F_{Z}}\left({\frac{u}{{{P_{k}}D_{{\rm{u}}k}^{-{\alpha_{k}}}}}}\right).$
(C-2)

Thus, the CDF of $\gamma_{k}$ can be expressed as

$\displaystyle{F_{{\gamma_{k}}}}\left(\gamma\right)=\frac{1}{{{m_{fk}}B\\!\left({{m_{fk}},{m_{sk}}}\right)}}{\left({\frac{\gamma}{{{\Lambda_{k}}}}}\right)^{{m_{fk}}}}\frac{1}{{{{\left({{P_{Ik}}{\eta_{k}}}\right)}^{{N_{Ik}}}}{\Gamma\\!\left({{N_{Ik}}}\right)}}}$
$\displaystyle\times\int_{{\sigma^{2}}}^{\infty}{{x^{{m_{fk}}}}{{\left({x-{\sigma^{2}}}\right)}^{{N_{I,k}}-1}}\exp\\!\left({-\frac{{x-{\sigma^{2}}}}{{{P_{Ik}}{\eta_{k}}}}}\right)}$
$\displaystyle\times
F\left({{m_{fk}},{m_{fk}}+{m_{sk}},{m_{fk}}+1;-\frac{{\gamma
x}}{{{\Lambda_{k}}}}}\right){\rm{d}}x.$ (C-3)

The integration part in (C) can be solved with the help of Lemma 1. Then,
after some algebraic manipulations, we have

$\displaystyle{F_{{\gamma_{k}}}}\left(\gamma\right)=\frac{1}{{\Gamma\\!\left({{N_{Ik}}}\right)\Gamma\\!\left({{m_{sk}}}\right)\Gamma\\!\left({{m_{fk}}}\right)}}\exp\\!\left({\frac{{{\sigma^{2}}}}{{{P_{Ik}}{\eta_{k}}}}}\right)$
$\displaystyle\times\frac{1}{{2\pi i}}\int_{\cal
L}{\frac{{\Gamma\\!\left({{s_{2}}}\right)\Gamma\\!\left({{s_{2}}+{m_{sk}}}\right)\Gamma\\!\left({{N_{Ik}}+{s_{2}}}\right)}}{{\Gamma\\!\left({{s_{2}}+1}\right){\Gamma^{-1}}\left({-{s_{2}}+{m_{fk}}}\right)}}{{\left({\frac{{\gamma{P_{Ik}}{\eta_{k}}}}{{{\Lambda_{k}}}}}\right)}^{{s_{2}}}}{\rm{d}}{s_{2}}}.$
(C-4)

Using [20, eq. (9.301)], we can derive the CDF of $\gamma_{k}$ as (1), which
completes the proof.

##  Appendix D Proof of Theorem 4

Using the definition of Gamma function [20, eq. (8.350)], we can express
$E_{k}$ as

${E_{k}}=\frac{{{\color[rgb]{0,0,0}{\lambda}_{1}}^{{\color[rgb]{0,0,0}{\lambda}_{2}}}}}{{2\Gamma\\!\left({{\color[rgb]{0,0,0}{\lambda}_{2}}}\right)}}\int_{0}^{\infty}{{x^{{\color[rgb]{0,0,0}{\lambda}_{2}}-1}}{e^{-{\color[rgb]{0,0,0}{\lambda}_{1}}x}}{F_{{\gamma_{k}}}}\left(x\right){\rm{d}}x}.$
(D-1)

By substituting (C) into (D-1), we obtain

$\displaystyle{E_{k}}=\frac{{{\color[rgb]{0,0,0}{\lambda}_{1}}^{{\color[rgb]{0,0,0}{\lambda}_{2}}}{\Gamma^{-1}}\left({{m_{sk}}}\right){\Gamma^{-1}}\left({{m_{fk}}}\right)}}{{2\Gamma\\!\left({{\color[rgb]{0,0,0}{\lambda}_{2}}}\right)\Gamma\\!\left({{N_{Ik}}}\right)}}\exp\\!\left({\frac{{{\sigma^{2}}}}{{{P_{I,k}}{\eta_{k}}}}}\right)\frac{1}{{2\pi
i}}$ $\displaystyle\times\int_{\cal
L}{\frac{{\Gamma\\!\left({{s_{2}}}\right)\Gamma\\!\left({{s_{2}}+{m_{sk}}}\right)\Gamma\\!\left({{N_{Ik}}+{s_{2}}}\right)}}{{\Gamma\\!\left({{s_{2}}+1}\right){\Gamma^{-1}}\left({-{s_{2}}+{m_{fk}}}\right)}}{{\left({\frac{{{P_{I,k}}{\eta_{k}}}}{{{\Lambda_{k}}}}}\right)}^{{s_{2}}}}{I_{4}}{\rm{d}}{s_{2}}},$
(D-2)

where

${I_{4}}{\rm{=}}\int_{0}^{\infty}{{x^{{s_{2}}+{\color[rgb]{0,0,0}{\lambda}_{2}}-1}}{e^{-{\color[rgb]{0,0,0}{\lambda}_{1}}x}}{\rm{d}}x}.$
(D-3)

Using [20, eq. (3.351.3)], we can solve $I_{4}$ as

${I_{4}}={\color[rgb]{0,0,0}{\lambda}_{1}}^{-{s_{2}}-{\color[rgb]{0,0,0}{\lambda}_{2}}}\Gamma\\!\left({{s_{2}}+{\color[rgb]{0,0,0}{\lambda}_{2}}}\right).$
(D-4)

Combining $I_{4}$ and (D), we derive $E_{k}$ as (4) to complete the proof.

## References

  * [1] S. Dang, O. Amin, B. Shihada, and M.-S. Alouini, “What should 6g be?” _Nat. Electron._ , vol. 3, no. 1, pp. 20–29, 2020.
  * [2] Y. Liu, X. Yuan, Z. Xiong, J. Kang, X. Wang, and D. Niyato, “Federated learning for 6g communications: Challenges, methods, and future directions,” _China Commun._ , vol. 17, no. 9, pp. 105–118, Sept. 2020.
  * [3] M. Giordani, M. Polese, M. Mezzavilla, S. Rangan, and M. Zorzi, “Toward 6g networks: Use cases and technologies,” _IEEE Commun. Mag._ , vol. 58, no. 3, pp. 55–61, 2020.
  * [4] X. You, C.-X. Wang, J. Huang, X. Gao, Z. Zhang, M. Wang, Y. Huang, C. Zhang, Y. Jiang, J. Wang _et al._ , “Towards 6g wireless communication networks: Vision, enabling technologies, and new paradigm shifts,” _Science China Information Sciences_ , vol. 64, no. 1, pp. 1–74, 2021.
  * [5] L. Zhang, Y.-C. Liang, and D. Niyato, “6g visions: Mobile ultra-broadband, super internet-of-things, and artificial intelligence,” _China Commun._ , vol. 16, no. 8, pp. 1–14, Aug 2019.
  * [6] W. Yang, H. Du, Z. Liew, W. Y. B. Lim, Z. Xiong, D. Niyato, X. Chi, X. S. Shen, and C. Miao, “Semantic communications for 6G future internet: Fundamentals, applications, and challenges,” _arXiv preprint arXiv:2207.00427_ , 2022.
  * [7] W. Saad, M. Bennis, and M. Chen, “A vision of 6G wireless systems: Applications, trends, technologies, and open research problems,” _IEEE Netw._ , vol. 34, no. 3, pp. 134–142, Mar. 2019.
  * [8] M. Xu, W. C. Ng, W. Y. B. Lim, J. Kang, Z. Xiong, D. Niyato, Q. Yang, X. S. Shen, and C. Miao, “A full dive into realizing the edge-enabled metaverse: Visions, enabling technologies, and challenges,” _arXiv preprint arXiv:2203.05471_ , 2022.
  * [9] P. Zhang, W. Xu, H. Gao, K. Niu, X. Xu, X. Qin, C. Yuan, Z. Qin, H. Zhao, J. Wei _et al._ , “Toward wisdom-evolutionary and primitive-concise 6g: A new paradigm of semantic communication networks,” _Engineering_ , vol. 8, pp. 60–73, 2022.
  * [10] E. C. Strinati and S. Barbarossa, “6g networks: Beyond shannon towards semantic and goal-oriented communications,” _Computer Netw._ , vol. 190, p. 107930, 2021.
  * [11] Q. Lan, D. Wen, Z. Zhang, Q. Zeng, X. Chen, P. Popovski, and K. Huang, “What is semantic communication? a view on conveying meaning in the era of machine intelligence,” _J. Commun. Netw._ , vol. 6, no. 4, pp. 336–371, 2021.
  * [12] G. Shi, Y. Xiao, Y. Li, and X. Xie, “From semantic communication to semantic-aware networking: Model, architecture, and open problems,” _IEEE Commun. Mag._ , vol. 59, no. 8, pp. 44–50, Aug. 2021.
  * [13] H. Xie, Z. Qin, and G. Y. Li, “Task-oriented multi-user semantic communications for vqa task,” _IEEE Wireless Commun. Lett._ , 2021.
  * [14] Q. Zhou, R. Li, Z. Zhao, C. Peng, and H. Zhang, “Semantic communication with adaptive universal transformer,” _IEEE Wireless Commun. Lett._ , 2021.
  * [15] X. Kang, B. Song, J. Guo, Z. Qin, and F. R. Yu, “Task-oriented image transmission for scene classification in unmanned aerial systems,” _arXiv preprint arXiv:2112.10948_ , 2021.
  * [16] O. Ayan, P. Kutsevol, H. Y. Özkan, and W. Kellerer, “Task-oriented scheduling for networked control systems: An age of information-aware implementation on software-defined radios,” _arXiv preprint arXiv:2202.09189_ , 2022.
  * [17] H. Xie and Z. Qin, “A lite distributed semantic communication system for internet of things,” _IEEE J. Sel. Areas Commun._ , vol. 39, no. 1, pp. 142–153, Jan. 2020.
  * [18] O. Friha, M. A. Ferrag, L. Shu, L. A. Maglaras, and X. Wang, “Internet of things for the future of smart agriculture: A comprehensive survey of emerging technologies.” _IEEE CAA J. Autom. Sinica_ , vol. 8, no. 4, pp. 718–752, Apr. 2021.
  * [19] H. Xie, Z. Qin, G. Y. Li, and B.-H. Juang, “Deep learning enabled semantic communication systems,” _IEEE Trans. Signal Process._ , vol. 69, pp. 2663–2675, 2021.
  * [20] I. S. Gradshteyn and I. M. Ryzhik, _Table of Integrals, Series, and Products_ , 7th ed. Academic Press, 2007\.
  * [21] A. M. Mathai, R. K. Saxena, and H. J. Haubold, _The $H$-function: Theory and Applications_. Springer Science & Business Media, 2009.
  * [22] B. L. Sharma and R. F. A. Abiodun, “Generating function for generalized function of two variables,” _Proc. American Mathematical Society_ , vol. 46, no. 1, pp. 69–72, Oct. 1974.
  * [23] Z. Qin, X. Tao, J. Lu, and G. Y. Li, “Semantic communications: Principles and challenges,” _arXiv preprint arXiv:2201.01389_ , 2021.
  * [24] E. Bourtsoulatze, D. B. Kurka, and D. Gündüz, “Deep joint source-channel coding for wireless image transmission,” _IEEE Trans. Cogn. Develop. Syst._ , vol. 5, no. 3, pp. 567–579, 2019.
  * [25] M. K. Farshbafan, W. Saad, and M. Debbah, “Common language for goal-oriented semantic communications: A curriculum learning framework,” _arXiv preprint arXiv:2111.08051_ , 2021.
  * [26] M. Chen, Z. Yang, W. Saad, C. Yin, H. V. Poor, and S. Cui, “A joint learning and communications framework for federated learning over wireless networks,” _IEEE Trans. Wireless Commun._ , vol. 20, no. 1, pp. 269–283, Jan. 2020.
  * [27] Z. Yang, M. Chen, W. Saad, C. S. Hong, and M. Shikh-Bahaei, “Energy efficient federated learning over wireless communication networks,” _IEEE Trans. Wireless Commun._ , vol. 20, no. 3, pp. 1935–1949, Mar. 2020.
  * [28] H. Tong, Z. Yang, S. Wang, Y. Hu, W. Saad, and C. Yin, “Federated learning based audio semantic communication over wireless networks,” in _Proc. of GLOBECOM_. IEEE, 2021.
  * [29] S. K. Yoo, S. L. Cotton, P. C. Sofotasios, M. Matthaiou, M. Valkama, and G. K. Karagiannidis, “The Fisher–snedecor $\mathcal{F}$ distribution: A simple and accurate composite fading model,” _IEEE Commun. Lett._ , vol. 21, no. 7, pp. 1661–1664, Jul. 2017.
  * [30] S. K. Yoo, P. C. Sofotasios, S. L. Cotton, S. Muhaidat, F. J. Lopez-Martinez, J. M. Romero-Jerez, and G. K. Karagiannidis, “A comprehensive analysis of the achievable channel capacity in $\mathcal{F}$ composite fading channels,” _IEEE Access_ , vol. 7, pp. 34 078–34 094, 2019.
  * [31] H. Xie and Z. Qin, “A lite distributed semantic communication system for internet of things,” _IEEE J. Sel. Areas Commun._ , vol. 39, no. 1, pp. 142–153, 2021.
  * [32] Z. Weng and Z. Qin, “Semantic communication systems for speech transmission,” _IEEE J. Sel. Areas Commun._ , vol. 39, no. 8, pp. 2434–2444, 2021.
  * [33] Y. Xu, S. Gao, J. Wu, N. Li, and J. Yu, “Personalized saliency and its prediction,” _IEEE Trans. Pattern Anal. Mach. Intell._ , vol. 41, no. 12, pp. 2975–2989, Dec. 2018.
  * [34] S. F. Dodge and L. J. Karam, “Visual saliency prediction using a mixture of deep neural networks,” _IEEE Trans. Image Process._ , vol. 27, no. 8, pp. 4080–4090, Aug 2018.
  * [35] A. Mahdi, J. Qin, and G. Crosby, “Deepfeat: A bottom-up and top-down saliency model based on deep features of convolutional neural networks,” _IEEE Trans. Cogn. Develop. Syst._ , vol. 12, no. 1, pp. 54–63, 2019.
  * [36] S. Berkovsky, R. Taib, I. Koprinska, E. Wang, Y. Zeng, J. Li, and S. Kleitman, “Detecting personality traits using eye-tracking data,” in _Proc. CHI Conf. Hum. Factors Comput. Syst._ , 2019, pp. 1–12.
  * [37] Y. Moroto, K. Maeda, T. Ogawa, and M. Haseyama, “Few-shot personalized saliency prediction using person similarity based on collaborative multi-output gaussian process regression,” in _Proc. of ICIP_. IEEE, 2021, pp. 1469–1473.
  * [38] Y. Cong, M. Y. Yang, and B. Rosenhahn, “Reltr: Relation transformer for scene graph generation,” _arXiv preprint arXiv:2201.11460_ , 2022.
  * [39] T. K. Lo, “Maximum ratio transmission,” in _IEEE Int. Conf. Commun. (Cat. No. 99CH36311)_ , vol. 2, 1999, pp. 1310–1314.
  * [40] H. Du, J. Zhang, J. Cheng, and B. Ai, “Sum of Fisher-snedecor $\mathcal{F}$ random variables and its applications,” _IEEE Open J. Commun. Soc._ , vol. 1, pp. 342–356, Mar. 2020.
  * [41] S. K. Yoo, P. C. Sofotasios, S. L. Cotton, S. Muhaidat, F. J. Lopez-Martinez, J. M. Romero-Jerez, and G. K. Karagiannidis, “A comprehensive analysis of the achievable channel capacity in $\mathcal{F}$ composite fading channels,” _IEEE Access_ , vol. 7, pp. 34 078–34 094, 2019.
  * [42] M. Nakagami, “The m-distribution—a general formula of intensity distribution of rapid fading,” in _Stat. methods Radio Wave Propag._ Elsevier, 1960, pp. 3–36.
  * [43] Wolfram, “The wolfram functions site,” http://functions.wolfram.com.
  * [44] J. Zhang, W. Zeng, X. Li, Q. Sun, and K. P. Peppas, “New results on the fluctuating two-ray model with arbitrary fading parameters and its applications,” _IEEE Trans. Veh. Technol._ , vol. 67, no. 3, pp. 2766–2770, Mar. 2017.
  * [45] A. Vaswani, N. Shazeer, N. Parmar, J. Uszkoreit, L. Jones, A. N. Gomez, Ł. Kaiser, and I. Polosukhin, “Attention is all you need,” _Advances in neural information processing systems_ , vol. 30, 2017.
  * [46] R. Girshick, “Fast r-cnn,” in _Proceedings of the IEEE international conference on computer vision_ , 2015, pp. 1440–1448.
  * [47] S. Ren, K. He, R. Girshick, and J. Sun, “Faster r-cnn: Towards real-time object detection with region proposal networks,” _Advances in neural information processing systems_ , vol. 28, 2015.
  * [48] D. Xu, Y. Zhu, C. B. Choy, and L. Fei-Fei, “Scene graph generation by iterative message passing,” in _Proceedings of the IEEE conference on computer vision and pattern recognition_ , 2017, pp. 5410–5419.
  * [49] R. Zellers, M. Yatskar, S. Thomson, and Y. Choi, “Neural motifs: Scene graph parsing with global context,” in _Proceedings of the IEEE conference on computer vision and pattern recognition_ , 2018, pp. 5831–5840.
  * [50] H. Liu, N. Yan, M. Mortazavi, and B. Bhanu, “Fully convolutional scene graph generation,” in _Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition_ , 2021, pp. 11 546–11 556.
  * [51] A. Kroner, M. Senden, K. Driessens, and R. Goebel, “Contextual encoder–decoder network for visual saliency prediction,” _Neural Netw._ , vol. 129, pp. 261–270, 2020.
  * [52] K. Simonyan and A. Zisserman, “Very deep convolutional networks for large-scale image recognition,” _International Conference on Learning Representations (ICLR)_ , 2015.
  * [53] X. Luo, Z. Liu, W. Wei, L. Ye, T. Zhang, L. Xu, and J. Wang, “Few-shot personalized saliency prediction using meta-learning,” _Image and Vision Computing_ , p. 104491, 2022.
  * [54] W. Lu, X. Zhang, H. Lu, and F. Li, “Deep hierarchical encoding model for sentence semantic matching,” _J. Vis. Commun. Image Represent._ , vol. 71, p. 102794, 2020.
  * [55] F. Herrera, M. Lozano, and J. L. Verdegay, “Tackling real-coded genetic algorithms: Operators and tools for behavioural analysis,” _Artif. Intell. Rev._ , vol. 12, no. 4, pp. 265–319, 1998.
  * [56] R. Krishna, Y. Zhu, O. Groth, J. Johnson, K. Hata, J. Kravitz, S. Chen, Y. Kalantidis, L.-J. Li, D. A. Shamma _et al._ , “Visual genome: Connecting language and vision using crowdsourced dense image annotations,” _International journal of computer vision_ , vol. 123, no. 1, pp. 32–73, 2017\.
  * [57] M. Jiang, S. Huang, J. Duan, and Q. Zhao, “Salicon: Saliency in context,” in _IEEE Conf. Comput. Vis. Pattern Recognit._ , June 2015.
  * [58] T. Judd, K. Ehinger, F. Durand, and A. Torralba, “Learning to predict where humans look,” in _IEEE Int. Conf. Comput. Vis._ , 2009.
  * [59] C. Yang, L. Zhang, H. Lu, X. Ruan, and M.-H. Yang, “Saliency detection via graph-based manifold ranking,” in _IEEE Conf. Comput. Vis. Pattern Recognit._ , 2013, pp. 3166–3173.
  * [60] P. Zhang, J. Zhang, K. P. Peppas, D. W. K. Ng, and B. Ai, “Dual-hop relaying communications over Fisher-snedecor $\mathcal{F}$-fading channels,” _IEEE Trans. Commun._ , vol. 68, no. 5, pp. 2695–2710, May 2020.
  * [61] H. Du, J. Zhang, K. P. Peppas, H. Zhao, B. Ai, and X. Zhang, “On the distribution of the ratio of products of Fisher-snedecor $\mathcal{F}$ random variables and its applications,” _IEEE Trans. Veh. Technol._ , vol. 69, no. 2, pp. 1855–1866, Feb. 2019.