# Statistical QoS Provisioning Architecture for 6G Satellite-Terrestrial
Integrated Networks

Jingqing Wang, Wenchi Cheng, Wei Zhang, Hui Liang
This work was supported by the Key Area Research and Development Program of
Guangdong Province under Grant 2020B0101110003, in part by the National
Natural Science Foundation of China under Grant 62341132, the National Key
Research and Development Program of China under Grant 2021YFC3002102, the Key
Research and Development Plan of Shaanxi Province under Grant 2022ZDLGY05-09,
and the Natural Science Basic Research Program of Shaanxi under Grant 2024JC-
YBQN-0642. Jingqing Wang and Wenchi Cheng are with Xidian University, Xi’an,
710071, China (e-mails<EMAIL_ADDRESS>wccheng@xidian.edu.cn). Wei
Zhang is with the School of Electrical Engineering and Telecommunications, The
University of New South Wales, Sydney, Australia (e-mail:
w.zhang@unsw.edu.au).

###### Abstract

The emergence of massive ultra-reliable and low latency communications
(mURLLC) as a category of age/time/reliability-sensitive service over 6G
wireless networks has received considerable research attention, which has
presented unprecedented challenges. As one of the key enablers for 6G,
satellite-terrestrial integrated networks have been developed to offer more
expansive connectivity and comprehensive 3D coverage in space-aerial-
terrestrial domains for supporting 6G mission-critical mURLLC applications
while fulfilling diverse and rigorous quality-of-service (QoS) requirements.
In the context of these mURLLC-driven satellite services, data freshness
assumes paramount importance, as outdated data may engender unpredictable or
catastrophic outcomes. To effectively measure data freshness in satellite-
terrestrial integrated communications, age of information (AoI) has recently
surfaced as the new dimension of QoS metrics to support time-sensitive
applications. It is crucial to design new analytical models that ensure
stringent and diverse QoS metrics bounded by different key parameters,
including AoI, delay, and reliability, over 6G satellite-terrestrial
integrated networks. However, due to the complicated and dynamic nature of
satellite-terrestrial integrated network environments, the research on
efficiently defining the new statistical QoS provisioning schemes while taking
into account varying degrees of freedom has still been in their infancy. To
remedy these deficiencies, in this paper we develop statistical QoS
provisioning schemes over 6G satellite-terrestrial integrated networks in the
finite blocklength regime. Particularly, we firstly introduce and review key
technologies for supporting mURLLC. Secondly, we formulate a number of novel
fundamental statistical-QoS metrics in the finite blocklength regime. Finally,
we conduct a set of simulations to validate and evaluate our developed
statistical QoS provisioning schemes over satellite-terrestrial integrated
networks.

###### Index Terms:

Statistical QoS provisioning, mURLLC, peak AoI, satellite-terrestrial
integrated networks, QoS exponents, HARQ, finite blocklength coding.

##  I Introduction

With 5G wireless networks being deployed globally, researchers are actively
conceptualizing future 6G mobile wireless networks[1] for supporting
overwhelmingly unparalleled modern wireless applications with increasingly
rigorous and diverse technical performance requirements, such as stringent
end-to-end delay, ultra-high reliability, unparalleled data rate, among
others. One of the key focuses of 6G development is the design of systems to
enable massive Ultra-Reliable Low-Latency Communications (mURLLC)[2],
requiring diverse quality-of-services (QoS) guarantees to ensure their timely
and reliable delivery. However, the crucial obstacle presented by expansive
connectivity and comprehensive coverage imposes a pivotal challenge in
supporting 6G mission-critical mURLLC applications. To enable comprehensive 3D
coverage for various 6G services using space-aerial-terrestrial integration,
satellite communication systems have been developed as a potential alternative
for terrestrial communication systems to offer global coverage and seamless
connectivity, while guaranteeing stringent QoS benchmarks requisite. On the
other hand, conventional terrestrial networks still play an important role in
providing low-cost and high-speed wireless services considering densely
populated areas. Therefore, integrating satellite and terrestrial networks can
leverage the advantages of both systems, enabling ubiquitous network service.

Since end-to-end satellite communication can effectively provide seamless
coverage and lower latency in comparison to terrestrial networks, particularly
in remote rural areas and isolated deserts, satellite-terrestrial integrated
networks present significant potential in facilitating various emerging time-
sensitive applications, such as intelligent traffic, environment monitoring,
and disaster relief. In the context of these real-time applications, ensuring
a variety of stringent QoS benchmarks becomes of paramount importance, as
outdated and unreliable data may engender unpredictable or catastrophic
outcomes. Nevertheless, the complicated and dynamically evolving nature of
satellite-terrestrial integrated network environments inevitably engenders
system performance requirements, thus, in turn, would significantly impact QoS
assurances in terms of data freshness, delay, and reliability. In light of the
aforementioned challenges, it is imperative to develop potential diverse QoS
measurement and control strategies, guaranteeing the stringent mURLLC
requirements over 6G satellite-terrestrial integrated networks.

As a result, providing distinct levels of QoS measurement with specific data
freshness/delay/reliability constraints for diverse categories of
age/time/error-sensitive wireless multimedia data constitutes a pivotal
element within the framework of 6G satellite-terrestrial integrated networks.
Traditionally, researchers have established delay-bound QoS provisioning for
supporting real-time wireless services. The inherently unstable nature of
wireless fading channels and the intricate, diverse, and ever-changing
structures of 6G satellite-terrestrial integrated networks make it challenging
to uphold the conventional deterministic QoS criteria for upcoming
age/time/error-sensitive multimedia data transmission. Towards this end, the
statistical QoS provisioning theory has been developed as a potent strategy
for defining and implementing QoS guarantees. The authors of Ref. [3] have
defined and characterized the novel statistical QoS metrics in terms of delay
and error-bounded QoS exponents.

Nevertheless, the ever-increasing amount of age, delay, and error sensitive
multimedia traffic necessitates 6G networks to meet increasingly complex and
demanding QoS requirements. More specifically, in scenarios involving space
communication, it becomes essential to effectively measure and manage the data
freshness for guaranteeing mURLLC services. To effectively measure/control
data freshness, age of information (AoI)[4]-[5] has recently surfaced as a
novel QoS metric that quantifies the freshness of information at the
receiver’s end for accurately reflecting data packets’ update speed in short-
pack-based status update systems, particularly for satellite applications[3].
It represents the time elapsed since the most recently received update was
generated at the source and provides insights into how “up-to-date” the
information, irrespective of the transmission delays incurred along the
communication path. Due to the limited number of information bits in satellite
status updates and the need for prompt delivery to remote destinations, long
codewords impose significant demands on receiver’s storage and computational
resources, thereby diminishing the system’s timeliness. Thus, small-packet
communications, such as finite blocklength coding (FBC)[6]-[7], play a crucial
role in measuring/controlling the AoI metric across satellite-terrestrial
integrated networks.

Despite the diligent efforts from both academia and industry for guaranteeing
stringent QoS requirements of mURLLC services via satellite-terrestrial
integrated networks, most previous studies have focused on investigating QoS
metrics in terms of the delay-bound violating probability, without considering
the non-vanishing decoding error probability and the AoI violation
probability. It is crucial to design and model satellite-terrestrial
integrated wireless network architectures while taking into account stringent
and diverse age/delay/error-rate bounded QoS guarantees by defining more
fundamental statistical QoS performance metrics and characterizing their
analytical relationships, such as delay-bound-violation probability, decoding
error probability, and AoI violation probability, in the finite blocklength
regime. However, due to the lack of comprehensive grasp of QoS-driven
fundamental performance-limits and modeling analyses over satellite-
terrestrial integrated networks, how to efficiently identify and define novel
FBC-based QoS metrics bounded by AoI, delay, and error-rate as well as the
associated relationships, including diverse QoS-exponent functions, is still a
challenging task.

To address these challenges, in this paper we develop a series of fundamental
statistical QoS metrics and their modeling/controlling techniques for mURLLC
over 6G satellite-terrestrial integrated networks. Firstly, for supporting
mURLLC, we introduce and review key techniques and potential solutions within
the purview of standards development entities. Secondly, we develop a set of
new statistical QoS metrics and controlling functions. Finally, a set of
simulations is performed to verify, assess, and examine the effectiveness of
the proposed statistical QoS provisioning schemes over satellite-terrestrial
integrated 6G wireless networks.

The rest of this paper is structured as follows. Section II reviews the most
recent advancements and potential solutions. Section III develops a set of new
and fundamental statistical QoS metrics. Section IV validates and evaluates
our developed modeling techniques and controlling schemes. The paper concludes
with Section V.

##  II QoS Provisioning for 6G Satellite-Terrestrial Integrated Networks:
Challenges and Open Issues

Figure 1: The system model for the satellite-terrestrial integrated wireless
networks using fast HARQ protocol in the finite blocklength regime

Consider the scenario of delivering downlink Telemetry (TM) status updates
over satellite-terrestrial integrated wireless networks. Fig. 1 shows
satellite-terrestrial integrated system architecture model for remote TM
status update transmissions, which consists of $K_{\text{G}}$ ground base
stations (GBSs). Specifically, we focus on the satellite’s responsibility to
monitor dynamic physical processes by transmitting remote status updates. The
satellites capture these status messages as needed and subsequently transmits
the updates to GBSs while guaranteeing stringent and diverse QoS constraints
for mURLLC. The distinctive characteristics of satellite communications
introduce many new challenges when attempting to adapt terrestrial 5G NR
technologies for these contexts.

Researchers have addressed the incorporation of QoS provisioning over
satellite-terrestrial integrated architecture through analyzing relevant QoS
mechanisms in different layers and evaluating the corresponding influence.
However, there are still numerous unresolved issues crucial for ensuring QoS
guarantees over satellite-terrestrial integrated wireless networks. These
encompassed concerns related to bandwidth allocation and enhancements of the
transmitting protocols tailored for satellite communications. Due to space
limitations, we focus on part of the most critical aspects for the satellite-
terrestrial integrated architecture when taking into account the large delays
and reliability issues, many other factors will need a proper analysis and
characterisation to fully implement 6G satellite-terrestrial integrated
networks, as, for instance, the downlink status update transmissions in LEO
scenarios.

###  II-A The Preliminary Analyses for Delay-Bounded QoS in Satellite-
Terrestrial Integrated Wireless Networks

The implementation of statistical delay-bounded QoS guarantees has allowed for
the investigation of queuing behaviors that are influenced by the fluctuations
of both arrival and service processes over time. To meet statistical tail-
latency requirements, we present the delay-bounded QoS provisioning, which
characterizes the probability of processing queue length surpassing a
specified threshold.

Definition 1: The delay-bounded delay-QoS exponent: By using the large
deviations principle (LDP), under sufficient conditions, the queueing process
approaches a random variable $Q(\infty)$ in distribution such that

$-\lim_{Q_{\text{th}}\rightarrow\infty}\frac{\log\left(\text{Pr}\left\\{Q(\infty)>Q_{\text{th}}\right\\}\right)}{Q_{\text{th}}}=\theta_{\text{delay}}$
(1)

where $Q_{\text{th}}$ represents the overflow threshold for the queueing
systems and $\theta_{\text{delay}}$ $(\theta_{\text{delay}}>0)$ is defined as
the delay-QoS exponent of queuing delay, which measures the exponential decay
rate of the delay-bounded QoS violation probabilities.

The delay-bounded QoS exponent serves as an indicator of the level of
stringency with bounded delay as the threshold advances. Specifically, a
sufficiently small delay-bounded QoS exponent enables the satellite-
terrestrial integrated system to accommodate an arbitrarily prolonged delay,
whereas a sufficiently large delay-bounded QoS exponent renders the system
intolerant of any delay. For a given designated delay threshold, the delay
violation probability characterizes the tail behaviors of the queueing delay,
which is a crucial factor in determining the fundamental performance-limits of
statistical delay-bounded QoS.

However, the existing research works mainly focus on characterizing system
performances without considering stringent end-to-end delay and reliability
requirements for mURLLC. It is crucial to design and model satellite-
terrestrial integrated wireless network architectures while taking into
account diverse QoS requirements by identifying and defining more fundamental
statistical QoS performance metrics and characterizing their analytical
relationships, such as various QoS-exponent functions, in the finite
blocklength regime. Moreover, many existing publications delve into the
typical challenges that arise during the implementation of satellite networks,
regardless of their specific integration with terrestrial infrastructures. In
our examination of the specific satellite-terrestrial integrated scenario, the
investigations of end-to-end QoS provisionings with statistical delay and
error-rate constraints, are still in their infancy. This can be attributed to
both insufficient research efforts on the mURLLC-oriented 6G network protocol
designs and lack of the comprehensive understanding on various QoS-driven
fundamental performance-limits and their modeling analyses.

###  II-B Protocol Adaptations for Satellite-Terrestrial Integrated Wireless
Networks

Researchers have investigated the modification of protocols to enhance the
suitability and operational efficacy for satellite communications. The HARQ
protocols have been developed to allow receivers to exploit small data packets
from previous HARQ transmissions to improve the probability of successful
decoding for a specific data packet. As shown in Fig. 1, employing the FBC
technique enables encoding the status update packet into a small codeword
consisting of $n$ channel uses for reducing access latency and decoding
complexity. Each finite-blocklength codeword with length $n$ is divided into
$L$ sub-codewords of $\widehat{n}$ symbols, and the sub-codewords are
transmitted successively during consecutive time slots. The system capacity
relies on various factors, such as the blocklength $\widehat{n}$,
retransmission round $l$, and transmitting packet size. Note that when the
number of HARQ retransmissions increases, the amount of redundancy is
introduced, leading to a decreased system capacity. This decrease in coding
rate results in a corresponding reduction in the decoding error portability,
thereby enhancing the reliability of wireless communication systems.
Nevertheless, in scenarios characterized by extended round-trip times (RTTs)
and the stop-and-wait protocol, communication throughput may be compromised as
transmissions will stall when all HARQ processes await feedback. Accordingly,
HARQ protocols can introduce significant delays due to the need for
retransmissions and multiple decoding attempts, resulting in the degradation
of QoS provisioning.

To mitigate these challenges stemming from extended delays, it becomes
essential to explore avenues for enhancing the management of HARQ protocol.
Therefore, we need to carefully design the proposed satellite-terrestrial
integrated schemes to ensure overall age, delay, and reliability based QoS
requirements. A common solution to such an issue involves the provision of
support for a substantial number of parallel HARQ processes in order to be
compatible and to offer the desired peak data rate over satellite link. While
awaiting an ACK/NACK, multiple HARQ processes operate concurrently to enhance
throughput by enabling other processes to engage in simultaneous work on other
packets while a process remains in waiting state for an ACK/NACK. HARQ
protocol plays a pivotal role in determining the number of parallel HARQ
processes and required retransmissions, thereby influencing the end-to-end
delay, buffer size, and payload capacity of the satellite. The research on
comprehensively analyzing the delay components contained in the end-to-end
delay while implementing HARQ has still been in their infancy. Thus, simply
expanding the number of parallel HARQ processes is considered undesirable.

Towards this end, 3GPP has embarked on research efforts focusing on the above-
mentioned concerns, while further endeavors are required to enhance the
initial conceptual solution. Potential designs including dynamic HARQ
deactivation, ACK-free HARQ, and adaptive HARQ feedback mechanisms should be
contemplated. Strategies for judicious reuse of the same HARQ process prior to
the completion of a full RTT should also be employed to prevent stalling.
Moreover, examining the deactivation of HARQ feedback represents an additional
facet to explore for a comprehensive understanding of potential advantages and
drawbacks for the proposed satellite-terrestrial integrated schemes.

In particular, researchers have proposed the fast HARQ protocol[8] as a
potential design for guaranteeing statistical QoS, which eliminates some HARQ
feedback signals and successive message decoding by estimating the number of
HARQ retransmission rounds, as shown in Fig. 1. In Phase 1, upon receiving the
initial sub-codeword of a status update, the satellite proceeds with the
estimation of the necessary number of HARQ retransmission rounds $l_{0}$ for
ensuring successful decoding at the receiver. The decoder remains inactive
during $l_{0}$ transmission attempts. Correspondingly, the transmitter
determines the retransmission round and transmission rate. In Phase 2, i.e.,
round $l=l_{0},\dots,L$, the satellite decodes the sub-codewords received and
returns an ACK/NACK to the transmitter, thus saving decoding and feedback
delays through the use of the fast HARQ protocol.

###  II-C The End-to-End Delay-Bounded QoS Metrics Using HARQ

Due to the elevated altitudes involved, the extended end-to-end delay,
including queuing delay, transmission delay, processing delay, and propagation
delay, exerts a pronounced influence on various facets of the radio interface.
The end-to-end delay is intricately linked to both the one-time access delay
and the HARQ retransmissions. In light of statistical QoS theory, it is
possible to approximately characterize the behavior of remote tails in
relation to the delay violation probability while implementing the HARQ
protocol. However, varying numbers of HARQ retransmissions contribute to
distinct compositions of delay, affecting the queuing delay value, the count
of processing delays, and propagation delays.

Figure 2: The end-to-end delay versus the blocklength using HARQ in the finite
blocklength regime.

To support mURLLC services, we need to investigate the end-to-end delay-
bounded QoS metrics through using HARQ protocols and analyze the number of
required HARQ retransmission rounds and their corresponding impact on
statistical delay-bounded QoS provisioning schemes to improve the performance
of satellite-terrestrial integrated wireless communication system.
Specifically, the tradeoff relationship among queuing delay, transmission
delay, and the number of HARQ retransmissions (including the propagation
delays) within the intricate and dynamic contexts of satellite-terrestrial
integrated wireless network environments need to be elucidated in the finite
blocklength. This forms the basis for the development of the end-to-end delay-
bounded QoS metrics.

Previous research has studied the tradeoff relationship between the queuing
delay and transmission delay in the terrestrial system[9]. Within the finite
blocklength regime, reducing the blocklength in 5G NR leads to an increase in
queuing delay and the number of retransmissions[10]. On the other hand, the
transmission delay exhibits a gradual decrease as the blocklength diminishes.
This implies that, as the blocklength decreases, there exist a tradeoff
relationship among the transmission delay, queuing delay, and the number of
HARQ retransmissions, as shown in Fig. 2. Optimal tradeoff is achieved when
these three components reach an optimal balance, resulting in the minimum end-
to-end delay. Fig. 2 shows that when setting a large number of HARQ
retransmissions $L$, there is an observable increase in the end-to-end delay.
This observation suggests that the HARQ protocol has the potential to extend
the propagation delay, necessitating the application of a fast HARQ protocol
as a potential remedy. However, within the intricate and dynamic contexts of
satellite-terrestrial integrated wireless network environments, how to apply
statistical QoS theory to characterize the relationship between the end-to-end
delay-bounded QoS metrics and the number of necessary HARQ retransmissions and
find the optimal tradeoff point remain an open and challenging problem.

Figure 3: The statistical QoS provisioning metrics for the controlling
functions over satellite-terrestrial integrated networks.

##  III Statistical QoS Control Metrics Over Satellite-Terrestrial Integrated
Networks in the Finite Blocklength Regime

One critical aspect to consider for designing satellite-terrestrial integrated
wireless services is the efficient guarantee of low-tail requirements for
age/time/reliability-sensitive data transmissions, which play a crucial role
in the fundamental performance analysis and provide practical engineering
guidance for designing, analyzing, and evaluating diverse statistical QoS
provisioning schemes. As illustrated in Fig. 3, to measure, analyze, and
effectively manage the stochastic behaviors during the data transmissions via
satellite, our investigation is focused on analyzing the essential analytical
modeling metrics, especially the tail behaviors of the delay-bounded bounded
QoS metric, peak-AoI bounded QoS metric, and the error-rate bounded QoS
metric. Diverse statistical QoS metrics can provide valuable insights into the
worst-case scenario performances for our proposed schemes. However, the
analysis of tail behaviors, i.e., the peak AoI violation probability, presents
several challenges. For instance, meeting the demanding requirements for
mURLLC services, such as stringent data freshness, latency, and reliability,
becomes increasingly challenging as complexity increases. Moreover, suboptimal
tail behaviors can have a negative impact on user experience, particularly as
degrees of parallelism intensify. As a result, our proposed modeling schemes
prioritize facilitating QoS provisioning for low-tail cases. This emphasis is
directed towards evaluating the violation probability, ensuring efficient
support for the specific requirements associated with low-tail considerations
for age-sensitive data transmissions, rather than solely assessing average
performance metrics. However, traditional statistical QoS theory only
investigates low-tail metrics in terms of queueing delay, without analyzing
tail behaviors for AoI and error-rate. The reduction of violation probability
that AoI of status updates exceeds a given age constraint is of great
significance for guaranteeing the data freshness in our proposed systems.
Consequently, in this section, we develop a set of new fundamental
statistical-QoS controlling metrics to characterize the violation
probabilities with regard to peak AoI through using HARQ-IR, which can
severely impact network performance for the developed satellite-terrestrial
integrated schemes using FBC.

Statistical delay-bounded QoS provisioning has been proposed in the previous
section as an effective approach to ensure the probability guarantee for
violating service constraints rather than average performance metrics.
However, traditional statistical QoS theory only investigates low-tail metrics
in terms of queueing delay, without analyzing tail behaviors for AoI and
error-rate. Towards this end, to statistically measure/control delay, peak
AoI, and error-rate associated with mURLLC, we develop the statistical delay,
peak AoI, and error-rate bounded QoS provisioning framework, as depicted in
Fig. 4. The probabilities of such violating service constraints are considered
to be essential QoS metrics, which play a crucial role in the fundamental
performance analysis and provide practical engineering guidance for designing,
analyzing, and evaluating novel statistical QoS provisioning schemes.

Figure 4: The framework of statistical diverse QoS provisioning for downlink
satellite-terrestrial integrated networks.

###  III-A The Peak-AoI Bounded QoS Metrics Using HARQ

####  III-A1 The AoI Metric Modeling in the Finite Blocklength Regime

The TM status updates are transmitted from the satellite to GBSs via a
wireless link susceptible to errors, with the objective of facilitating timely
and reliable data processing and analysis. To quantify and manage the
timeliness of status update packets, we employ the AoI metric as a new
fundamental QoS measure to indicate the recency of received data. The service
time for each TM status update consists of the queuing delay, transmission
delay, and propagation delays by implementing HARQ. The transmission delay is
decided by the coding redundancy, while the propagation delay is dependent on
the HARQ retransmission rounds and satellite communication distance. The AoI
metric increases linearly in the absence of any new arrival updates, and upon
receiving a successful update, it is reset to a lower value.

The total AoI over a period indicates the average delay of the updated data,
representing the freshness of the sensory information. By regarding the AoI as
the crucial QoS metric, the challenge of pursuing obscured data freshness in
satellite communications can be approached as a mathematical problem that can
be solved through the implementation of optimization methods. However,
previous research mainly focuses on analyzing the average AoI to guarantee
data freshness. The average AoI provides a limited understanding of the
latency by only characterizing the typical average latency of the satellite
communication system, without considering the system’s worst-case performance,
which essentially serves as the primary impediment in ensuring mURLLC
services. Towards this end, we proposed to investigate the peak AoI as a
potential solution to address the bottleneck issues in time-sensitive
applications while using HARQ.

####  III-A2 The Peak-AoI Bounded QoS Exponent

To support the peak-AoI bounded QoS provisioning, we propose to conduct a
characterization of the probability of peak AoI violation, which can be
determined by the probability that the peak AoI exceeds the designated peak
AoI threshold. Accordingly, the peak AoI violation probability, denoted as
$p^{\text{AoI}}$, can be determined by the probability that the peak AoI
exceeds the designated peak AoI threshold, i.e.,

$\displaystyle
p^{\text{AoI}}\triangleq\text{Pr}\left\\{P^{\text{AoI}}>\frac{A_{\text{th}}}{n}\right\\}$
(2)

where $A_{\text{th}}$ is the peak AoI violation threshold in channel uses
through using FBC. Then, we proceed to characterize the peak AoI violation
probability through using the peak-AoI bounded QoS exponent, which is defined
as follows.

Definition 2: The peak-AoI bounded QoS exponent: By using the LDP, under
sufficient conditions, the probability that peak AoI violation probability
$P_{\text{AoI}}$ exceeds a certain threshold $A_{\text{th}}$ decays
exponentially fast as the threshold $A_{\text{th}}$ increases, i.e.,

$\displaystyle\text{Pr}\left\\{P^{\text{AoI}}>\frac{A_{\text{th}}}{n}\right\\}\approx
e^{-\frac{A_{\text{th}}}{n}\theta_{\text{AoI}}}$ (3)

where $\theta_{\text{AoI}}>0$ is the peak-AoI bounded QoS exponent, which
quantifies the rate of exponential decay of the violation probability in terms
of the peak AoI violation probability within the framework of our proposed
modeling schemes when considering the end-to-end QoS provisionings including
queuing delay, transmission delay, and propagation delays by implementing
HARQ. Note that the peak-AoI bounded QoS exponent is an indicator of the level
of stringency associated with statistical peak-AoI bounded QoS provisioning as
the threshold increases, which describes the relationship between the peak AoI
threshold and the probability of peak AoI exceeding that threshold.

For a given designated peak AoI threshold, the peak AoI violation probability
characterizes tail behaviors for the peak AoI, which can be used to compare
with the delay and error-rate violation probabilities. Accordingly, a
sufficiently small peak-AoI bounded QoS exponent enables the satellite-
terrestrial integrated system to accommodate an arbitrarily large peak AoI,
whereas a sufficiently large peak-AoI bounded QoS exponent renders the system
intolerant of any peak AoI. Towards this end, to guarantee stringent mURLLC
requirements, it is essential to consider the peak AoI violation probability
as a new dimension of the QoS metric, which enables the analysis, management,
and assessment of the data freshness and alleviate the tail behaviors of the
peak AoI.

###  III-B The Error-Rate Bounded QoS Metrics Using HARQ in the Finite
Blocklength Regime

In analyzing the reliability issues, we investigate the statistical QoS
requirement that describes the tail behavior of the probability of the
decoding error with an increasing blocklength over satellite-terrestrial
integrated networks when using HARQ. In the realm of small-packet
communications, the tradeoff between reliability and throughput has
conventionally been studied by characterizing the error-rate bounded QoS
exponent. Consequently, it is imperative to investigate the correlations
between the error-rate bounded QoS exponent and the decoding error probability
as a means of characterizing error-rate bounded QoS metric over satellite-
terrestrial integrated wireless networks.

Definition 3: The error-rate bounded QoS exponent: Based on the LDP, the
error-rate bounded QoS exponent, denoted by $\theta_{\text{error}}$,
quantifies the rate of exponential decay of the QoS violation probability in
terms of the decoding error probability $\epsilon(\mu)$, within the framework
of our proposed modeling schemes for satellite-terrestrial integration, which
is defined as follows:

$\theta_{\text{error}}\triangleq\lim\limits_{\widehat{n}\rightarrow\infty}-\frac{1}{\widehat{n}}\log(\epsilon(\mu)).$
(4)

Our proposal centers on the modeling and assessment of fundamental
performance, with a particular emphasis on various facets related to the
error-rate bounded QoS exponent. This exponent delineates the rate at which
the decoding error probability exponentially decays as the codeword
blocklength tends to infinity, i.e.,

$\epsilon(u)\leq\exp(-n\theta_{\text{error}}).$ (5)

The error-rate-bounded QoS exponent exhibits a consistent trend of decrement
as the blocklength increases. The error-rate bounded QoS exponent plays a
critical role in establishing the fundamental performance boundaries for
statistical QoS provisioning. In addition, the error-rate-bounded QoS exponent
is determined by the channel capacity, the coding rate, and the channel
dispersion.

However, how to analytically derive the closed-form expression of the error-
rate bounded QoS exponent over satellite-terrestrial integrated wireless
networks remains an open and challenging problem. One potential solution is to
apply the LDP and Laplace transform for characterizing the asymptotic
behaviors of remote tails regarding the decoding error probability.

Correspondingly, by using FBC, there exists a tradeoff between the peak AoI
violation probability and the delay violation probability. Specifically, the
Mellin transform of the service time intends to decrease monotonically, while
the Mellin transform of the service process aims to increase monotonically as
the decoding error probability function approaches zero.

##  IV Performance Evaluations

Figure 5: The peak AoI vs. the number of GBSs for our proposed satellite-
terrestrial integrated networks.

We present a series of numerical results to verify and assess the
effectiveness of our proposed statistical QoS provisioning schemes over
satellite-terrestrial integrated 6G mobile wireless networks. Before the
simulation, it is necessary to determine the relationship between channel use
(cu) and second. Assuming that 2PSK modulation is employed and the
transmission rate of the satellites is 1 Mbit/s, then we obtain 1 cu =
$10^{-6}$ s. We assume that the nearby GBSs are located within a finite
annular area centered around the destination node with an inner radius,
denoted by $R_{\text{in}}$, and an outer radius, denoted by $R_{\text{out}}$,
beyond which the interference is assumed to be negligible due to pathloss.
Throughout our simulations, we set the outer radius $R_{\text{out}}=10$ Km,
inner radius $R_{\text{in}}=2$ km, the antenna gain at satellite to be $20$
dBi, and the transmit power at the satellite$\in[10,50]$ dBm.

Fig. 5 depicts the peak AoI violation probability against the blocklength for
the developed satellite-terrestrial integrated networks (STIN) as compared
with the pure satellite networks (PSN). Fig. 5 indicates that the peak AoI
violation probability exhibits an increasing trend concerning the blocklength.
In addition, Fig. 5 shows that the proposed STIN achieves better peak AoI
performance when compared to the PSN since the peak AoI in terrestrial systems
is relatively lower than that of the PSN. Fig. 5 also illustrates that as the
peak-AoI bounded QoS exponent $\theta_{\text{AoI}}$ increases, there is a
corresponding reduction in the peak AoI. This indicates that a smaller peak-
AoI bounded QoS exponent $\theta_{\text{AoI}}$ establishes an upper bound,
while a large peak-AoI bounded QoS exponent sets a lower bound on the peak AoI
violation probability.

Fig. 6 depicts the error-rate bounded QoS exponent against the blocklength for
the developed performance modeling formulations. The graph in Fig. 6
demonstrates that as the blocklength approaches infinity, the error-rate
bounded QoS exponent also decays exponentially, providing further confirmation
of the definition of the error-rate bounded QoS exponent
$\theta_{\text{error}}$. Fig. 6 also illustrates that when setting a large
number of HARQ retransmissions $L$, there is an observable increase in the
error-rate bounded QoS exponent. This suggests that the decoding error
probability experiences a rapid decline as $L$ increases, indicating an
augmented level of reliability.

Figure 6: The error-rate bounded QoS exponent $\theta_{\text{error}}$ vs. the
blocklength.

##  V Conclusions

We have proposed satellite-terrestrial integrated 6G mobile wireless networks
architectures and developed a set of fundamental QoS metrics and their
controlling techniques for statistical QoS provisioning in the finite
blocklength regime. Firstly, we have reviewed key techniques and potential
solutions within the purview of 3GPP considering HARQ and AMC. Secondly, using
the HARQ protocol, a collection of novel fundamental statistical-QoS metrics,
including the peak-AoI bounded QoS exponent, delay-bounded QoS exponent, and
error-rate bounded QoS exponent are developed within the framework of FBC.
Finally, a series of simulations have been conducted to verify, assess, and
examine our established statistical QoS provisioning schemes for satellite-
terrestrial integrated 6G mobile wireless networks.

Conflict of interest statement. None declared.

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|  Jingqing Wang (Member, IEEE) received the B.S. degree from Northwestern
Polytechnical University, Xi’an, China, in Electronics and Information
Engineering and the Ph.D. degree from Texas A&M University, College Station,
TX, USA, in Computer Engineering in 2022. She is currently a Jingying
assistant professor with Xidian University. She has published more than 60
international journal and conference papers in IEEE JOURNAL ON SELECTED AREAS
IN COMMUNICATIONS, IEEE magazines, IEEE TRANSACTIONS, IEEE INFOCOM, GLOBECOM,
WCNC, and ICC. She won the Best Paper Award from the IEEE GLOBECOM in 2020 and
2014, respectively. Her current research interests focus on next generation
mobile wireless network technologies, statistical QoS provisioning, 6G URLLC,
information-theoretic analyses of FBC, emerging machine learning techniques.
---|---
|  Wenchi Cheng (Senior Member, IEEE) received the B.S. and Ph.D. degrees in
telecommunication engineering from Xidian University, Xian, China, in 2008 and
2013, respectively. He was a Visiting Scholar with the Department of
Electrical and Computer Engineering, Texas A&M University, College Station,
TX, USA, from 2010 to 2011. He is currently a Full Professor with Xidian
University. His current research interests include B5G/6G wireless networks,
emergency wireless communications, and orbital-angular-momentum-based wireless
communications. He has published more than 100 international journal and
conference papers in IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, IEEE
magazines, IEEE TRANSACTIONS, IEEE INFOCOM, GLOBECOM, and ICC. He received the
IEEE ComSoc Asia-Pacific Outstanding Young Researcher Award in 2021, the URSI
Young Scientist Award in 2019, the Young Elite Scientist Award of CAST, and
four IEEE journal/conference best papers. He has served or serving as the
Wireless Communications Symposium Co-Chair for IEEE ICC 2022 and IEEE GLOBECOM
2020, the Publicity Chair for IEEE ICC 2019, the Next Generation Networks
Symposium Chair for IEEE ICCC 2019, and the Workshop Chair for IEEE ICC
2019/IEEE GLOBECOM 2019/INFOCOM 2020 Workshop on Intelligent Wireless
Emergency Communications Networks. He has served or serving as an Associate
Editor for IEEE SYSTEMS JOURNAL, IEEE COMMUNICATIONS LETTERS, and IEEE
WIRELESS COMMUNICATIONS LETTERS.
---|---
|  Wei Zhang (Fellow, IEEE) received the Ph.D. degree from The Chinese
University of Hong Kong in 2005. He is currently a Professor at the School of
Electrical Engineering and Telecommunications, University of New South Wales,
Sydney, Australia. His current research interests include UAV communications,
5G, and beyond. He has served as a member in various ComSoc boards/standing
committees, including Journals Board, Technical Committee Recertification
Committee, Finance Standing Committee, Information Technology Committee, and
Steering Committee for IEEE TRANSACTIONS ON GREEN COMMUNICATIONS AND
NETWORKING and IEEE NETWORKING LETTERS. He received six best paper awards from
the IEEE conferences and ComSoc technical committees. He is currently serving
as an Area Editor for the IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS and the
Editor-in-Chief of Journal of Communications and Information Networks.
Previously, he has served as an Editor for IEEE TRANSACTIONS ON
COMMUNICATIONS, IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, IEEE
TRANSACTIONS ON COGNITIVE COMMUNICATIONS AND NETWORKING, and IEEE JOURNAL ON
SELECTED AREAS IN COMMUNICATIONS COGNITIVE RADIO SERIES. Within the IEEE
ComSoc, he has taken many leadership positions, including the Member-at-Large
on the Board of Governors from 2018 to 2020, the Chair of the Wireless
Communications Technical Committee from 2019 to 2020, the Vice Director of the
Asia Pacific Board from 2016 to 2021, the Editor-in-Chief of the IEEE WIRELESS
COMMUNICATIONS LETTERS from 2016 to 2019, the Technical Program Committee
Chair of APCC 2017 and ICCC 2019, and the Award Committee Chair of the Asia
Pacific Board and the Technical Committee on Cognitive Networks. He was an
IEEE ComSoc Distinguished Lecturer from 2016 to 2017. He is the Vice President
of the IEEE Communications Society.
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