# Multiple Access in the Era of Distributed Computing and Edge Intelligence

Nikos G. Evgenidis, Nikos A. Mitsiou, , Vasiliki I. Koutsioumpa,
Sotiris A. Tegos, , Panagiotis D. Diamantoulakis, ,
and George K. Karagiannidis The authors are with the Department of Electrical
and Computer Engineering, Aristotle University of Thessaloniki, 54124
Thessaloniki, Greece (e-mails<EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS>geokarag@auth.gr).G. K. Karagiannidis is also with the Artificial Intelligence
& Cyber Systems Research Center, Lebanese American University (LAU).

###### Abstract

This paper focuses on the latest research and innovations in fundamental next-
generation multiple access (NGMA) techniques and the coexistence with other
key technologies for the sixth generation (6G) of wireless networks. In more
detail, we first examine multi-access edge computing (MEC), which is critical
to meeting the growing demand for data processing and computational capacity
at the edge of the network, as well as network slicing. We then explore over-
the-air (OTA) computing, which is considered to be an approach that provides
fast and efficient computation of various functions. We also explore semantic
communications, identified as an effective way to improve communication
systems by focusing on the exchange of meaningful information, thus minimizing
unnecessary data and increasing efficiency. The interrelationship between
machine learning (ML) and multiple access technologies is also reviewed, with
an emphasis on federated learning, federated distillation, split learning,
reinforcement learning, and the development of ML-based multiple access
protocols. Finally, the concept of digital twinning and its role in network
management is discussed, highlighting how virtual replication of physical
networks can lead to improvements in network efficiency and reliability.

###### Index Terms:

Next-generation multiple access, multi-access edge computing, over-the-air
computing, semantic communications, machine learning, digital twinning

##  I Introduction

The next generation of wireless communication networks is expected to provide
intelligence, limitless connectivity and full synchronization of the physical
and digital worlds, paving the way for the development of novel applications
both indoors and outdoors. Specifically, the key performance indicators (KPIs)
expectations of academia and industry are converging toward an ever-increasing
deployment of machine-type nodes in 2D/3D service areas (10 Gbps/m3), and the
need for even higher reliability ($10^{-9}$ frame error rate), lower latency
(0.1 msec), higher data rates (1 Tbps), higher energy efficiency (1 pJ/bit).

However, except achieving higher data rates, lower latency, and more connected
devices, future wireless networks can be seen as a distributed computing
platform and, thus, purely communication metrics are not sufficient to
describe their performance. In more detail, using wireless networks as a
flexible and scalable computing platform radically changes the design and
optimization of multiple access schemes, since the aim is to efficiently
process the users’ data, either independently at any of the available
processing units of by performing calculations using as input the datasets of
multiple users. In addition, due to the complex nature of future wireless
networks, they are expected to integrate native artificial intelligence (AI),
which will facilitate the optimal use of communication and distributed
computing resources, as well as the provision of services that are based on
distributed artificial intelligence.

###  I-A Background on multiple access

To meet the stringent requirements of next-generation wireless networks, a key
challenge is the development of advanced multiple access schemes, known as
next-generation multiple access (NGMA). NGMA aims to efficiently and
intelligently connect numerous users and devices using available wireless
resources. Historically, multiple access schemes have played a critical role
in wireless communications. These schemes are broadly divided into two types:
orthogonal and non-orthogonal transmission strategies [1].

Orthogonal strategies, which include frequency division multiple access (FDMA)
in 1G, time division multiple access (TDMA) in 2G, code division multiple
access (CDMA) in 3G, and orthogonal frequency division multiple access (OFDMA)
in 4G, allocate different frequency, time, or code resources to each user.
These schemes are simple and reduce interference, making them popular in
practical systems. However, as the number of wireless devices increases and
spectrum availability remains limited, these strategies become less efficient.
They have low spectral efficiency and can only support a limited number of
users due to rigid resource allocation.

In contrast, non-orthogonal transmission strategies, which have attracted
significant research interest, allow multiple users to share the same resource
blocks. This approach requires additional techniques at the transmitter and
receiver level to manage the resulting interference. These techniques include
superposition coding, rate splitting [2, 3, 4], successive interference
cancellation (SIC), and message passing. Despite increasing complexity at the
transmitter and receiver, non-orthogonal strategies offer significant
advantages. They support massive connectivity, achieve high spectral and
energy efficiency, and ensure user fairness [5].

NGMA can also be categorized into multi-tool NGMA, multi-concept NGMA, and
multi-functional NGMA, each of which focuses on different aspects of wireless
communication [6]. Multi-tool NGMA emphasizes the dynamic allocation of
available resource blocks using either orthogonal multiple access (OMA) or
non-orthogonal multiple access (NOMA). This approach focuses on the efficient
use of different types of resource blocks to optimize network performance,
with OMA and NOMA offering different resource allocation strategies. On the
other hand, multi-concept NGMA aims to enhance network capabilities by
integrating NGMA with other advanced transmission concepts, including but not
limited to technologies such as cell-free massive multiple-input multiple-
output (MIMO), reconfigurable intelligent surfaces (RISs), full-duplex
relaying, millimeter-wave (mmWave) communications, and heterogeneous networks.
By combining NGMA with these cutting-edge technologies, multi-concept NGMA can
create synergistic effects that lead to significant improvements in network
performance and the ability to serve a large number of users simultaneously.
In addition, multi-functional NGMA focuses on designing wireless signals to
support multiple functions. This involves the joint design of signal waveforms
and signal processing techniques. For example, this approach is particularly
relevant in applications such as integrated sensing and communication (ISAC).
In ISAC, the superposition of communication and sensing signals represents a
form of non-orthogonal resource sharing that is consistent with the principles
of NOMA. This multi-functional approach in NGMA allows for the simultaneous
handling of different wireless communication tasks, such as sensing,
localization, and data transmission, within the same spectral resources.

Multiple access in wireless networks can also be divided into contention-free
(CF) and contention-based (CB) categories, each with different resource
allocation methods. CF multiple access uses a coordinated approach where
network resources are allocated in a planned and orderly manner. This method
is particularly favored in enhanced mobile broadband (eMBB) applications where
high spectral efficiency is the primary goal. The structured nature of CF
allows optimal use of the spectrum, making it suitable for high data rate
applications such as streaming video and large file transfers in eMBB
scenarios. On the other hand, CB multiple access uses an opportunistic
resource allocation strategy. This approach is more flexible because it allows
devices to access network resources as they become available, creating a kind
of competition among devices for resources. This method is particularly
advantageous in massive machine-type communications (mMTC), a domain
characterized by a large number of devices, such as in internet of things
(IoT) networks. In mMTC, the sporadic and unpredictable activity patterns of
devices make centralized coordination less practical. The opportunistic nature
of CB helps to efficiently manage the sporadic data transmissions typical of
IoT environments, where devices may only need to transmit small amounts of
data infrequently. Considering these aspects, OMA schemes are predominantly
used in current eMBB applications due to their efficiency in handling high
data rates and their ability to maximize spectral utilization. In contrast,
for mMTC applications, where the key challenge is managing a large number of
intermittently active devices, random access schemes are emerging as the
preferred solution. Random access approaches provide the flexibility and
scalability needed to meet the unique requirements of mMTC environments, such
as those found in large-scale IoT networks. These schemes allow a large number
of devices to access the network in an uncoordinated manner, which is ideal
for handling the irregular traffic patterns typical of mMTC scenarios [7, 8,
9, 10, 11].

In the context of random access, grant-based random access and grant-free
random access are two approaches to wireless communications, each with its own
set of characteristics and applications. In grant-based random access, the
base station (BS) plays a central role in scheduling and authorizing users
through a four-message handshake process. This method ensures reliable data
transmission by maintaining synchronization and proper resource allocation.
The structured approach of grant-based random access is advantageous in
scenarios where reliable transmission is critical, despite the associated
higher signaling overhead and potential for increased latency in high-traffic
environments. Grant-free random access provides a more streamlined process
that uses a two-step random access procedure. In this approach, active users
transmit preambles and data directly to the BS without waiting for prior
authorization. This reduces latency and control-signaling overhead, making
grant-free random access suitable for scenarios where speed and efficiency are
priorities. While this can lead to increased signal processing complexity at
the receiver, grant-free random access provides a balance between efficiency
and simplicity in many use cases. Unsourced random access is another approach
designed to further streamline the process for scenarios requiring massive
connectivity [12, 13]. In unsourced random access, all potential users share a
common codebook, and the BS decodes a list of messages rather than identifying
individual active users. This eliminates the need for preambles, reducing
overhead and minimizing collision frequency. Unsourced random access is
particularly advantageous in NGMA scenarios such as mMTC, where the focus is
on accommodating a large number of users with sporadic and short traffic. In
this context, fast uplink grant has also been proposed and used, which
requires a one-way handshake and allows only devices that have received an
uplink grant to transmit data, resulting in reduced access delay and
collisions [14, 15].

The field of NGMA is in its early stages, and there is still a lot of room for
research in a number of important areas. One key area is the development of
new multiple access schemes. Techniques such as NOMA and space division
multiple access (SDMA) are being explored. These new schemes aim to improve on
traditional methods by offering higher bandwidth efficiency and better
connectivity, which are critical for the evolving demands of wireless
networks. Another important area of research is the development of new
techniques that can enhance NGMA systems. This includes exploring the
potential of RISs, which can adaptively modify electromagnetic waves for
better signal transmission. In addition, advances in random access protocols
and more sophisticated modulation and channel coding schemes are being
investigated to improve network performance and reliability. Finally, advanced
machine learning (ML) tools and big data analytics are becoming more prominent
in NGMA research, promising to address complex challenges in NGMA by enabling
more intelligent and adaptive network solutions. Through the use of ML and big
data, researchers can develop systems that are better equipped to handle the
diverse and dynamic nature of future wireless communication needs. Overall,
the combination of new multiple access schemes, innovative techniques, and the
application of ML and big data is essential for the progress and success of
NGMA.

TABLE I: NGMA in the context of integrated communication and computing:
Objectives and enablers.

Objective | Integrated resource communication efficiency (IRCE) | Integrated resource distributed computing efficiency (IRDCE)
---|---|---
Definition |  Level of achieving a communication objective per number of communication and computing resources |  Level of achieving a computing objective per number of communication and computing resources
Enablers | ML-aided multiple access protocol design | Higher IRCE
Waveform design | Over-the-air computing
Semantic communications | Multi-access edge computing
Proactive resource allocation | Federated learning, federated distillation, and split learning
Network slicing
Machine learning algorithms (e.g., deep reinforcement learning)
Digital twinning

###  I-B Contribution

In this paper, we provide a comprehensive overview of NGMA in the context of
communication and computation. In this direction, as it is briefly shown in
Table I, we identify the main enablers for achieving two different objectives,
hereinafter termed as integrated resource communication efficiency (IRCE) and
integrated resource distributed computing efficiency (IRDCE). Although both
IRCE and IRDCE consider the efficient use of communication and computing
resources, the respective key performance indicators are substantially
different. More specifically, IRCE focuses on achieving the required
communication quality of service, which can be expressed as a function of
spectral/energy efficiency, latency, reliability and connectivity. On the
other hand, IRDCE focuses on achieving a computing objective, e.g., maximizing
number of bits of bits that are processed either locally or at the edge or
minimizing the mean square error of a certain calculation on the sources’
data.

We first provide an overview of multi-access edge computing (MEC), which is
essential to address the increasing demand for data and computing power at the
edge of the network, while also exploring network slicing. We then discuss
over-the-air (OTA) computing as a scheme that shows promise for calculating a
range of functions quickly and efficiently, proving particularly beneficial
for real-time computing needs. Next, we analyze semantic communication as a
promising approach to make communication systems more efficient by focusing on
transmitting meaningful data, reducing redundancy, and thus increasing
communication efficiency. The mutual relationship between ML and multiple
access is also discussed, emphasizing in federated learning (FL), federated
distillation (FD), split learning (SL), reinforcement learning (RL), as well
as ML-aided multiple access protocol design. Finally, we analyze digital
twinning and its application to network management, providing insight into how
virtual modeling of physical networks can improve network efficiency and
reliability.

###  I-C Structure

The rest of the paper is organized as follows. In Section II, MEC in NGMA is
discussed, while Section III analyzes the concept of OTA. Section IV discusses
semantic communication and joint computing and communication for distributed
ML applications is analyzed in Section V. Next, in Section VI, digital twin-
aided multiple access is examined. Finally, concluding remarks are provided in
Section VII.

##  II Multi-access edge computing

Next-generation wireless communications and the vision of IoT have led to a
significant shift in mobile computing. The conventional centralized mobile
cloud computing model cannot satisfy the strict delay requirements of emerging
mobile applications due to the long distances to the end users and the
backhaul bandwidth limitation, which, together with the limited battery
lifetime as well as computational and storage resources of mobile end devices,
have recently paved the way for the integration of the MEC, also known as
mobile edge computing [16, 17, 18]. The primary feature of MEC is to bring
mobile computing, network control and storage in close proximity to wireless
end devices [19, 20]. The MEC servers can be small-scale data centers co-
located with BSs, wireless access points or cellular backhaul units [21].
Bringing intelligence closer to the end users offers several advantages. In
addition to providing high-bandwidth, low-latency communications, proximity,
location and mobility awareness, and real-time visibility into radio network
information, MEC can enable a variety of IoT and delay-sensitive applications
and services. It can provide real-time information on user location and
behavior to improve quality of service (QoS) and user quality of experience
(QoE), while reducing backhaul traffic and supporting wireless power transfer
[22] to mobile devices.

The fundamental feature of MEC that allows the realization of the
aforementioned applications is computational offloading, i.e. the distribution
of computational tasks from the computationally limited end devices to the
better performing MEC servers. This attribute of MEC can offer an efficient
way to prolong battery life by limiting power consumption caused by extensive
computational processing, while enabling end devices to successfully support
various applications, even if they would be extremely challenging to perform
at their end from a computational point of view. Although the end devices may
have insufficient resources for the timely execution of a computationally
intensive task on their own, offloading can accelerate the required
computation time by taking advantage of highly computational performing
servers to perform the most intensive parts of computing. Depending on the
computational load of a task, offloading can be divided in two categories:

  * •

Binary offloading: A computationally intensive or relatively simple task
cannot be partitioned and is offloaded to the MEC server or processed locally
on the mobile device.

  * •

Partial offloading: A computational task is partitioned into two parts, one
for local execution and one for MEC offloading.

A mobile end user’s task can be represented by a tuple
$\mathcal{A}=\\{L,\;X,\;T_{\max}\\}$, where $L$ is the task input data size in
bits, $X$ is the computational workload/intensity in CPU cycles per bit, and
$T_{\max}$ is the required completion time in seconds. Let us consider
$\theta\in[0,1]$ be the task offloading factor, e.g., the fraction of
offloaded data to the total data, and $1-\theta$ is the amount of the locally
processed task. Thus, the local computation latency can be derived as

$T_{\mathrm{c}}=\frac{(1-\theta)LX}{f},$ (1)

where $f$ denotes the frequency of the CPU cycles. Furthermore, the time
required to transmit the offloaded amount of task to the MEC server is given
by

$T_{\mathrm{t}}=\frac{\theta L}{R},$ (2)

where $R$ is the transmission rate and can be calculated according to the
multiple access protocol being used. Although MEC servers have large
computational capabilities compared to their computational load, their
computational power is not unlimited, thus it is necessary to account for the
MEC server execution time in the general design of MEC systems. To this end,
the offloaded task execution time in the MEC server can be written as

$T_{\mathrm{s}}=\frac{\theta LX}{f_{\mathrm{s}}},$ (3)

where $f_{s}$ is the CPU-cycle frequency of the MEC server. Therefore, the
total latency of task offloading is the sum of the transmission latency and
MEC execution latency given by

$T_{\mathrm{of}}=T_{\mathrm{t}}+T_{\mathrm{s}}=\frac{\theta L}{R}+\frac{\theta
LX}{f_{\mathrm{s}}}.$ (4)

Taking into account that the transmission between a user and the MEC server
can occur in parallel with the local computation, an end user can perform
offloading and task processing simultaneously. Therefore, the total latency in
the case of partial offloading is computed as
$T_{\mathrm{total}}=\max\\{T_{\mathrm{c}},\,T_{\mathrm{of}}\\}$. It should be
noted that the case of binary offloading is denoted by an offloading factor
equal to 0 or 1. Specifically, $\theta=1$ corresponds to full offloading with
a total latency equal to (4), while $\theta=0$ represents the case where no
offloading is performed, e.g. the task is executed locally, and the total
latency is given by (1). In any case, the total system latency should not
exceed the threshold $T_{\max}$, thus $T_{\mathrm{total}}\leq T_{\max}$.

As previously mentioned, mobile devices are energy constrained, so the energy
consumption for local computation and offloading to MEC is another critical
measure of mobile computing efficiency. The energy consumption of local task
computation can be expressed as

$E_{\mathrm{c}}=\kappa_{\mathrm{c}}(1-\theta)LXf^{2},$ (5)

where $\kappa_{\mathrm{c}}$ is a constant related to the hardware
architecture. In the case of offloading, the energy consumption for
transmitting a task to the edge server is given by

$E_{\mathrm{t}}=pT_{\mathrm{t}}=p\frac{\theta L}{R},$ (6)

where $p$ is the transmission power. The energy consumption for the MEC
execution can be written as

$E_{\mathrm{s}}=\kappa_{\mathrm{s}}\theta LXf_{\mathrm{s}}^{2},$ (7)

but is usually omitted, as we are more interested in the energy consumption of
end devices.

In addition, the time and energy required by the MEC server to send the
computed tasks to the edge users are not considered, since the size of the
tasks is typically very small and the capabilities of the server are large.

###  II-A Cross-layer design in MEC

In the context of MEC, edge computing refers to the delivery of computing
resources to end users in close proximity to and at the edge of the radio
access network (RAN). Consequently, MEC demonstrates the ability to
decentralize computing resources from a centralized cloud to the network edge
to serve a large number of users. However, scalability concerns and server
congestion may arise, especially as the workload intensity of end users
gradually escalates [23, 24]. Additionally, in practical scenarios, the
offloaded tasks cannot be immediately executed on the MEC server due to its
limited computational capabilities [25, 26]. The computational tasks generated
by mobile end users create a data queue that encompasses dynamic and
stochastic processes such as traffic arrivals, packet service, and waiting in
each user’s or server’s buffer. The queuing dynamics of computational tasks
can have a significant impact on user offloading decisions and the overall
performance of MEC. To make effective offloading decisions in MEC, end users
need to understand the queuing dynamics of their upper-layer tasks in addition
to their communication and computation dynamics to facilitate cross-layer
optimization. The most typical procedure followed is the application of a
threshold-based task offloading policy, while the data packets’ arrival time
is generally modelled by a Poisson process to capture the dynamic of data
bursts in networks.

A MEC system consisting of a MEC server and a mobile device with energy
harvesting components is presented in [27]. Considering the adequacy of energy
resources, the computational tasks can be executed by the local CPU to reduce
the transmission delay, or by the MEC server to reduce the energy consumption,
or can be dropped. Both local and remote execution delay include queuing
delay. The wireless channel status affects the offloading, and an appropriate
wireless channel environment must be selected to save power consumption.
Offloading tasks to the MEC server can reduce the intensive computation
workload of the end device while increasing the transmission delay. Therefore,
a trade-off between energy consumption and execution delay should be
considered.

Another offloading decision based on users’ channel gains is described in a
multi-user and single-server MEC scenario where multiple users share the
limited spectrum and interfere with each other [26]. Good communication
conditions, i.e., a user’s channel gain exceeds a threshold, indicate task
offloading to the network edge for remote execution, otherwise the task is
pushed into a queue buffer. A user’s offloading decision is influenced by the
others’, and its offloading decision threshold can be adjusted in order to
optimize the expected successful offloading rate. A higher threshold can
reduce the probability of task offloading and thus lose the benefits of edge
computing, while a lower threshold can lead to a higher probability of task
offloading, which increases the intensity of physical-layer channel contention
and wireless interference.

In a MEC network consisting of a finite number of active MEC servers, as
demonstrated in [23], the continuous increase in the number of incoming data
packets can exceed the servers’ service capacity, leading to overloaded MEC
servers and a system out of steady state. A threshold value is used to
indicate server capacity overflow. Since no waiting queues are formed, server
bursts occur and can lead to service outages for some complex delay-sensitive
tasks due to overloading of MEC resources. To overcome this issue, the ability
to dynamically offload the workload to cloud computing servers is provided,
and minimizing the waiting time before offloading to the cloud services is of
great importance.

Since workload arrivals are often uneven among the MEC-equipped small-scale
BSs (SBSs), computation offloading between peer SBSs can be enabled to harness
underutilized, otherwise wasted computational resources to improve the overall
system efficiency [28]. Peer offloading relies on the cooperative behavior of
SBSs in sharing their computational resources as well as their energy costs,
but can also cause additional delay due to network congestion.

A MEC system with a limited computation buffer at the edge server has been
studied in [29]. Saturation of the computation buffer causes the task
transmission to be paused until additional capacity is available in the
computation buffer, while saturation of the transmission buffer results in
local computation. However, with a high task arrival rate, the latency
requirements of all tasks that cannot enter the transmit buffer may not be
satisfied, and more communication and computation resources must be allocated.
The total delay of a task consists of the waiting time for transmission, the
transmission time, the waiting time for computation, and the computation time.
The transmit process is linked to the state of the computation buffer.
Therefore, the transmission and computation processes are coupled when
analyzing the random delay characteristics.

###  II-B Multiple access protocols

In a network with multiple end users or multiple MEC servers, data
transmission to a MEC server for remote execution can be performed under
several access schemes. The transmission rate plays a crucial role in the task
offloading latency and energy consumption, as described by (2) and (6), and
depends on the utilized multiple access protocol. Therefore, in addition to
the efficient utilization of the computation and communication resources, the
appropriate selection of the multiple access scheme is crucial for the
efficient use of MEC. The multiple access protocols can be used for both
uplink and downlink transmissions. An uplink MEC transmission is referred to
as a network with multiple end user wanting to offload their tasks to a single
MEC server, while the downlink MEC transmission is considered as a user with
multiple tasks being offloaded to multiple MEC servers simultaneously.

####  II-B1 OMA

In OMA, e.g., TDMA, FDMA, users belonging to the same cell are allocated to
different resource blocks and do not interfere with each other [30]. For the
TDMA system, time is divided into slots and the duration of each time slot is
selected to meet the latency requirements of the users. For the OFDMA system,
the total bandwidth is divided into multiple orthogonal subchannels, and each
subchannel can be assigned to at most one user.

A resource allocation strategy is proposed in [31] for a multi-user single-
server MEC network. The offloading transmission is based on TDMA and OFDMA to
achieve high energy efficiency and low latency of task offloading. In the
multi-server MEC network topologies presented in [32, 33], multiple
optimization objectives are accounted simultaneously, e.g., minimizing the
total time and energy overhead of the MEC system and the user subscription
cost. The power and computing resource allocation of the users is achieved, as
well as the task offloading decision is derived. The above works are under the
assumption of perfect CSI. However, in practical wireless communication
networks, obtaining accurate CSI is challenging, mainly due to the feedback
delay or error in channel estimation. A multi-user MEC-enabled network for IoT
and Internet of Vehicles (IoV) under imperfect CSI was studied in [34, 35],
respectively, where different frequency blocks are assigned to end users. The
proposed algorithms provide advantages in terms of weighted sum of energy
consumption, satisfying delay requirements, and reducing system overhead.

####  II-B2 NOMA

NOMA is considered a key enabler for current and next-generation networks. The
key idea of NOMA is the use of superposition coding and interference
cancellation techniques. Compared to conventional OMA, NOMA can allow multiple
users to share the same time or frequency resources and has the potential to
achieve higher spectral efficiency, lower latency, massive connectivity, and
relaxed channel feedback [36, 37, 38]. These advantages are mainly due to the
fact that in NOMA, users with bad channel conditions do not exclusively occupy
the resource blocks. The combination of MEC and NOMA can improve user
satisfaction and network performance by leveraging NOMA’s spectral efficiency
and latency reduction benefits with MEC’s end-user, operator, and overall
network efficiency benefits. In addition, the flexible scheduling, grant-free
access and increasing number of users provided by NOMA, as well as the
empowerment of services running at the edge, can lead to low-latency and
energy-efficient communications [36], distributed computation and
reinforcement of services and applications supported by next-generation
networks. It is worth noting that NOMA and MEC can be dynamically integrated
with other wireless technologies, such as MIMO, massive MIMO, mmWave
communications, etc., to further increase connectivity, spectral efficiency,
energy efficiency, and computing capacity.

According to [39], NOMA-based MEC is superior to its OMA counterpart when
server grouping with strong channel conditions is applied in downlink
transmission, and when user grouping with diverse channel conditions is
applied in uplink transmission. Under the assumption of imperfect CSI, a
multi-user multi-BS MEC network was investigated in [40] and an energy-
efficient resource allocation when users utilize the NOMA protocol was
performed, while in [41] the offloading outage probability, energy consumption
and throughput were investigated for a NOMA-based multi-user and single-server
MEC network. The proposed schemes outperform the orthogonal counterparts.
However, imperfect CSI degrades the system performance compared to perfect
CSI.

####  II-B3 Hybrid NOMA

Integrating NOMA into MEC promises to minimize energy consumption and mitigate
significant delays. However, studies have demonstrated that employing NOMA
alone may not necessarily enhance performance of MEC computing systems,
particularly when users have different latency requirements. Therefore, a
hybrid NOMA-OMA scheme has been proposed [42, 43, 44, 30]. In this hybrid NOMA
scheme, both users can transmit their messages to the MEC server utilizing the
NOMA protocol in the first phase of transmission, and in the second phase,
only one of the users can transmit the rest of its task using the OMA
protocol. In pure NOMA, both users offload their tasks in the first phase,
while in OMA, the first phase is accessed by only one user.

Pure NOMA can outperform hybrid NOMA when there is sufficient energy for MEC
offloading, while hybrid NOMA always outperforms pure NOMA in terms of
minimizing energy consumption [42]. MEC based on hybrid NOMA was shown to
outperform its OMA counterpart when users have demanding latency requirements
for their task offloading, while OMA-based MEC is preferred when a user’s task
is delay tolerant [43]. The NOMA-based MEC scheme is not preferred for either
situation. A generalized MEC offloading strategy based on hybrid NOMA was
proposed in [44] for a MEC network with more than two users, and a multi-
objective optimization problem was formulated to minimize the energy
consumption of offloading. In [30], it was concluded that the use of dynamic
user scheduling and time-sharing during the initial transmission phase can
significantly reduce latency, especially when energy consumption is kept
relatively low. A partial offloading scenario with controllable CPU-clock
speed was also considered, which is interesting because it involves optimizing
both communication and computational resources. Increasing the CPU speed of
the local processor implies a reduction in latency without significantly
increasing transmission power consumption and potential interference. However,
it also results in higher local power consumption. Therefore, the coordinated
optimization of advanced communication protocols and computing resources holds
the potential for significant improvements in terms of latency reduction and
energy consumption.

####  II-B4 RSMA

In recent years, RSMA has been investigated as a multiple access strategy for
upcoming wireless communications, focusing on aspects such as non-orthogonal
transmission, interference management, and rate maximization. Compared to
uplink NOMA with SIC processing, the adoption of uplink RSMA offers the
advantage of attaining the full capacity region of multiple access channel
(MAC) [45]. However, the optimal SIC decoding order and the transmit power
allocation need to be determined by exhaustive search to realize the full
capacity region of uplink MAC using RSMA [46, 47]. This requirement restricts
the indiscriminate use of uplink RSMA in latency-critical MEC applications.
Effectively applying RSMA to uplink MACs necessitates efficient interference
management and low-complexity SIC processing.

Therefore, an RSMA-aided MEC scheme was introduced in [48] to enhance the
successful computation probability and reduce offloading latency within a MEC
system consisting of a single MEC server and multiple randomly distributed
users. Each user pair is assigned to different orthogonal time/frequency
resource blocks based on distance and employs two-user uplink RSMA,
eliminating interuser interference within each pair. To facilitate
simultaneous offloading of paired users to the MEC server, cognitive radio
(CR)-inspired rate splitting is employed, which exhibits superior performance
compared to its NOMA counterpart. In [49], a single-server MEC network was
studied, focusing on air user offload tasks using the RSMA protocol, and a
joint optimization problem involving offload decisions, transmission rates,
uplink power control, and decoding order was formulated. In addition, [50]
explored an RSMA-based multi-server MEC system where users are assigned to
separate frequency bands and downlink RSMA principles are applied to
facilitate a single user’s concurrent offloading of computation tasks to
multiple MEC servers. The joint optimization of computational task assignment,
radio and computational resource allocation to minimize the sum of the maximum
delays experienced by users was examined.

####  II-B5 Hybrid RSMA-TDMA

Although the use of pure RSMA in MEC systems has not been widely investigated,
a hybrid RSMA-TDMA scheme for a two-user MEC network was introduced in [51].
The offloading phase is divided into two stages. First, a CR-inspired RSMA
strategy is used for users to offload their computational tasks to the MEC
server. Subsequently, only a single user has the ability to offload during the
second phase. The objective is to minimize the offloading delay, and the power
allocation is optimized under energy and power constraints. The hybrid RSMA-
TDMA scheme demonstrates superiority over its hybrid NOMA-TDMA and TDMA
counterparts.

####  II-B6 Grant-free random access

In IoT applications where devices have sporadic or bursty data to transmit and
may not need to access the network constantly, grant-free random access is a
suitable multiple access protocol. In traditional communication systems,
devices typically have to contend for access to the network, and once granted
access, they can transmit their data. However, in grant-free random access,
devices can directly transmit their data without prior coordination, leading
to access delay and signal overhead reduction and making them more flexible
and scalable than traditional grant-based protocols.

In [52], the slotted ALOHA protocol was used for the wireless powered devices
(WPDs) to access the medium for binary offloading tasks to a MEC server. This
protocol allows the WPDs to contend for the available slots to transmit their
data to the MEC server, enabling efficient and low-complexity access for the
devices. Additionally, the use of grant-free random access with adaptive rate
as the multiple access protocol for offloading tasks to the edge server has
been proposed in [53]. This approach offers lower implementation costs and
improved efficiency for task offloading, while the average delay and resource
allocation strategy are also analyzed.

###  II-C MEC with network slicing

In next-generation wireless communications, network slicing has emerged as a
key technology that facilitates the delivery of customized services that
require high flexibility and scalability. Through network slicing, a physical
network can be partitioned into multiple logical networks, enabling the
simultaneous support of on-demand customized services for different
application scenarios on a shared physical network [16, 18, 54]. In addition,
network resources can be dynamically and efficiently allocated to logical
network slices according to QoS requirements. Network slicing integrates cloud
and network resources, including utilities such as storage, big data
processing, RAN access, and bandwidth, collectively referred to as general MEC
utilities [55].

Combining network slicing with MEC addresses specific requirements such as
edge analytics and scalability [56]. This integration is proven valuable for
latency-critical services such as the industrial Internet, healthcare, and
autonomous driving, where MEC and network slicing help reduce latency and
prioritize traffic. Network slicing is also of supreme need for three generic
use cases in next-generation wireless networks, including eMBB, ultra reliable
and low-latency communication (URLLC), and mMTC. As mentioned in [55], for
high-capacity mobile broadband network slices, MEC increases core network and
mobile backhaul capacity through content caching at the edge and traffic
offloading. In the context of automotive network slices with stringent latency
and scalability requirements, the capabilities of MEC are tailored to service
needs. For massive IoT services that require scalability to handle large
volumes of IoT data, MEC provides storage and computation capabilities that
support network slice scalability.

The effectiveness of network slicing in a NOMA-enabled MEC network was
investigated in [57]. A network slicing technique was introduced to categorize
users based on their service requirements and to efficiently allocate compute
and radio resources. This access scheme showed significant advantages over OMA
and NOMA without network slicing in terms of latency, energy efficiency, and
spectral efficiency.

###  II-D Future directions

Current communication protocols such as OFDM, used as the physical-layer
modulation scheme in 5G mobile systems, exhibit near-capacity performance over
channels with minimal Doppler effect. However, as we transition to the more
dynamic and mobile environments of 5G and beyond deployments, characterized by
time-varying multipath fading due to mobility, OFDM encounters significant
performance challenges. Furthermore, NOMA, particularly under real-world
conditions with imperfect impairments, has demonstrated degraded performance,
which may not justify its use compared to OMA protocols in many use cases [58,
59, 60, 61]. Addressing these challenges and advancing beyond current
limitations is crucial for meeting the KPIs of future MEC networks. An
important approach in this direction is ML-based multiple access schemes
design, which will be discussed in section V-E. Another interesting research
direction is the design of new waveforms for medium access control. One such
promising paradigm is orthogonal time frequency space (OTFS).

Unlike traditional modulation, OTFS operates in a 2D time-frequency space,
spreading signals over multiple dimensions and encoding information in the
delay-Doppler domain. This representation as a 2D matrix of signal delay and
Doppler shift offers advantages such as high spectral efficiency, robustness
to channel variations, low latency, and accurate channel estimation. OTFS is
well suited for applications such as autonomous vehicles, cellular networks,
and satellite communications, since it is resilient to fading, multipath
effects, and Doppler shifts [62]. However, implementing OTFS can pose
challenges in terms of the required transceiver complexity, which may be
beyond the capabilities of low-power devices [63, 64].

To address these challenges, orthogonal time sequency multiplexing (OTSM) has
been also proposed. Unlike OTFS, which operates in the delay-Doppler domain,
OTSM multiplexes information symbols in the delay-sequency domain, where
sequency represents the number of zero crossings per unit time interval. OTSM
achieves this by transforming information symbols from the delay-sequency
domain to the delay-time domain using the inverse Walsh-Hadamard transform
(WHT) along the sequency domain. This transformation allows channel delay
spread and Doppler spread to cause intersymbol interference along the delay
and sequency dimensions, respectively, while remaining separable at the
receiver, similar to OTFS. Notably, this separability is not achieved by OFDM,
where channel delay spread and Doppler spread jointly cause interference along
the frequency dimension, leading to orthogonality issues between OFDM
subcarriers. OTSM stands out for its low-complexity transceiver design, which
relies only on WHT, and its efficient detection, comparable to traditional
baseline OFDM schemes. Additionally, OTSM demonstrates strong performance in
high-mobility channels, making it suitable for very low-power wireless devices
such as sensors and IoT devices [63, 64].

Nevertheless, OTSM has received comparatively less attention than OTFS.
Additionally, [65] introduced unitary-precoded single-carrier (USC) modulation
as a family of waveforms that multiplex information symbols on time-domain
unitary basis functions spanning the entire time and frequency plane. Notably,
OTFS and OTSM, based on discrete Fourier transform and WHT, respectively, fall
within the general framework of USC waveforms. Future research on USC and OTSM
can focus on further analysis of channel representation, low complexity
channel estimation and detection in the delay-sequency domain. Also, reducing
the peak-to-average-ratio (PAPR) of USC waveforms has yet to be thoroughly
analyzed, while, adaptive modulation for USC is also crucial to support eMBB
application in high-mobility scenarios. Furthermore, current OTSM research
focuses mainly on single-user communication, which cannot adequately capture
the KPIs of future multi-acess wireless networks. Although [66] took a first
step towards multi-user scenarios, many open questions remain. The study of
multi-antenna OTSM is essential for its integration into future networks.
Beamforming techniques can enhance spatial multiplexing and mitigate
interference in multi-user communication scenarios. Another promising
direction is to evaluate the scalability of OTSM for mMTC, serving numerous
devices with sporadic traffic patterns simultaneously.

##  III Over-the-air computing

###  III-A Preliminaries

In the next-generation communication systems, new applications are expected to
be utilized, highlighting the need for new multiple access schemes that are
appropriate for each case. A particular example of such applications is
computing based on data aggregation from multiple devices. Although the
computation itself is currently done with great efficiency in fusion centers,
i.e., in the processing units of the BSs, the massive connectivity of devices
that is expected will pose a great challenge to real-time computing, as
traditional multiple access schemes will not be able to handle the amount of
incoming data. For example, TDMA will result in high latency when data
aggregation is required because the fusion center (FC) can only perform
computation when data is available from all devices. Similarly, FDMA
techniques, while preferable in terms of latency, are inefficient in terms of
bandwidth allocation. On the other hand, NOMA techniques would also be quite
difficult to implement, both because of the more sophisticated hardware
required and the large number of devices that would need to be connected.

With this in mind, a multiple access scheme that has received a lot of
attention lately is OTA computing. Unlike traditional schemes, OTA computing
is designed for simultaneous transmission from all devices. In addition, it is
designed to reduce the amount of data processing itself, which is usually not
possible with transmission alone. Therefore, OTA computing is considered an
efficient wireless data aggregation technique, which makes it an attractive
option for many IoT applications. As shown in the seminal works [67, 68, 69],
OTA computing can be used to calculate the value of a wide variety of
functions by utilizing the superposition property of a MAC. Assuming that
there are $K$ devices in the system, the functions that can be calculated
using this technique are called nomographic and are characterized by the
following decomposition rule:

$f(x_{1},x_{2},\cdots,x_{K})=\psi\left(\sum_{k=1}^{K}\phi_{k}(x_{k})\right),$
(8)

where $f:\mathbb{R}^{K}\rightarrow\mathbb{R}$ denotes the multivariate target
function of OTA computing and $\psi:\mathbb{R}\rightarrow\mathbb{R}$ and
$\phi_{k}:\mathbb{R}\rightarrow\mathbb{R},\forall k\in\\{1,\cdots,K\\}$ are
suitable post- and pre-processing univariate functions, respectively. As
proven in [70, 71], any multivariate function can be written in this form.
Since many goal-driven applications require the computation of such general
functions, e.g., the average temperature of an area can be calculated by
superimposing the transmitted signals and a post-processing dividing factor,
the use of OTA is intertwined with the computation of a function of interest
for some specific goal.

One of the distinguishing characteristics of OTA computing, unlike other
traditional multiple access systems such as NOMA, is that it does not require
the extraction of each user’s information through sophisticated techniques
such as SIC, but is based on the superposition principle resulting from the
simultaneous transmission of all devices. This allows OTA computing not only
to approximate any real multivariate function, but also to drastically reduce
the calculation time of its target function. However, studies have proved that
from an information-theoretic point of view, OTA computing’s potential is
maximized when analog transmission is used [72] instead of the highly utilized
digital transmission used by current communication systems. This means that
instead of conventional performance metrics, like bit error rate, the focus is
on minimizing the mean squared error (MSE) between the ideal and actual
received signal at the receiver point. Although, as in analog communications,
no error correction can be performed, it is important to note that digital
transmission itself would suffer from a computational point of view, since the
required quantization for a large number of devices will result in distortion
between the ideal function to be calculated and the received one. For
simplicity and without loss of generality, it is assumed here that the desired
function to be calculated is the arithmetic mean of the transmitted data,
i.e., the ideal and received signals are given, respectively, as

$y=a\left(\sum_{k=1}^{K}x_{k}b_{k}h_{k}+n\right)\hskip 2.84526pt\text{ and
}\hskip 2.84526ptr=\sum_{k=1}^{K}x_{k},$ (9)

where $h_{k}$ are the channels of the corresponding devices, $b_{k},\ \forall
k\in\\{1,\cdots,K\\}$ are the pre-processing power factors at the
transmitters, $a$ is the post-processing receiver gain factor and $n$ denotes
the AWGN present at the receiver with noise power $\sigma^{2}$. For practical
reasons, the transmitter power factors are also constrained up to a maximum
power $P$, i.e., $|b_{k}|\leq\sqrt{P},\forall k\in\\{1,\cdots,K\\}$. Thus,
assuming that the transmitted signals have zero mean and unit variance, the
MSE between the received signal and the desired target function is given as

$\mathrm{MSE}=\mathbb{E}[|y-r|^{2}]=\sum_{k=1}^{K}\left|ab_{k}h_{k}-1\right|^{2}+\sigma^{2}a^{2},$
(10)

where the expectation is taken with respect to the transmitted signals and
noise.

Figure 1: Model of an OTA computing system consisting of $K$ transmitting
devices and $1$ fusion centre.

###  III-B State-of-the-art and other technologies

To this end, many research works have emphasized on finding optimal power
transmission schemes to minimize (10) mainly under perfect knowledge of the
system environment, i.e., the channel conditions. In [73, 74], the optimal
power allocation was found under individual power constraints at each user,
yielding a policy that utilizes maximum power transmission for the weakest
channel devices and inverse channel transmission for the rest of them. As
proven, defining the number of devices that utilize maximum power as

$i^{*}=\underset{1\leq i\leq K}{\mathrm{argmax}}\\{a_{i}\\},$ (11)

where the receiver gain factor is given as

$a_{i}=\frac{\sqrt{P}\sum_{k=1}^{i}|h_{k}|}{\sigma^{2}+P\sum_{k=1}^{i}|h_{k}|^{2}},$
(12)

the MSE in (10) can be rewritten as

$\mathrm{MSE}=\sum_{k=1}^{i^{*}}\left|ab_{k}h_{k}-1\right|^{2}+\sigma^{2}a^{2},$
(13)

from which the MSE performance is directly evaluated. The same problem was
investigated in [75] for a global power constraint over all OTA computing
users. Furthermore, a great deal of analysis has been made on the assumption
of MIMO users for an OTA computing system. More specifically, in [76], a joint
hybrid beamforming of a MIMO OTA computing system was analyzed to minimize the
MSE in an effective way in terms of resources management. In [77], an energy
efficiency maximization was studied to minimize the consumption of power at
the transmitting devices considering a minimum MSE threshold constraint.
Moreover, in [78], a multiple target function scenario for parallel
simultaneous computing through MIMO utilization was studied. Furthermore, in
[79], a zero-forcing beamforming transmit scheme was proposed along with a
selection combining implementation at the receiver side and the performance of
the system was measured by an MSE outage metric. Finally, in [80], MIMO was
considered as a means to enable multiple functionalities such as integrated
sensing, communication, and computing through OTA computing and various
algorithms that support the coexistence of these functionalities were
examined.

In addition to the fundamental optimization problems and their generalizations
through MIMO, OTA computing has also been investigated in conjunction with
other emerging technologies. Among others, RISs have been investigated as a
means to implement OTA computing with higher performance gains [81]. The main
idea behind RIS integration with OTA computing is that it can provide coverage
for devices that would otherwise not be able to participate in the system for
computing while also improving the channel conditions of all devices through
the additional multipath available for exploitation. Closely related to this
is the use of unmanned aerial vehicles (UAVs) as a means of enabling OTA
computing systems if the channel conditions between the devices and a ground-
located FC pose severe performance degradation, for example due to extremely
high fading resulting from multiple obstacles. With this in mind, in [82], a
UAV trajectory optimization problem was studied to minimize the MSE and, in
[83], a similar scenario was considered under channel state information (CSI)
imperfect knowledge and the UAV acting as an FC itself.

###  III-C OTA computing and ML

In addition to the optimization problems and collaboration with other
technologies described above, the ability of OTA computing to reduce
processing time during computing has made it an attractive option for
distributed learning techniques, such as FL [84, 85]. In this scenario, OTA
computing assists in updating the global parameters of deep neural networks
(DNNs), where local terminals are responsible for updating the parameters of
local DNNs and the FC is responsible for updating the global parameters, which
are then passed back to the local terminals for another training round. OTA
computing can provide a timely update at the FC, thus reducing the overall
training time. It also is important to highlight the fact that although there
is a gap between the desired calculation and the received signal, it has been
shown that the utilization of OTA computing leads to convergence of training
[86], which is the task of interest. Furthermore, it is worth noting that a
digital version of over-the-air that performs FL with one-bit quantized
gradients, called OBDA, was proposed in [87] and its performance along with
its convergence capability was studied for various scenarios, including pure
AWGN channel, fading channel with perfect CSI and fading channel with
imperfect CSI. Since successful training is the goal of FL, the convergence of
FL through the OTA computing implementation showcased in [87, 86] is extremely
important.

###  III-D Practical implementation and challenges

Perhaps the biggest drawback of OTA computing is its use of analog
transmission. Although this is optimal in terms of MSE performance, modern
communication systems are intertwined with digital transmission and are thus
unable to support a practical implementation of OTA computing in its current
form. With this in mind, it is crucial that future research focuses on finding
ways to adapt OTA computing in digital systems. This opens up a new area of
research for OTA computing, since even fundamental principles need to be
studied, such as which type of pulses are preferable to use and how the
performance is affected by interpulse interference. In this front, a ML model
called ChannelComp [88] that tries to find appropriate signals to be
transmitted for a digital implementation of OTA computing has been proposed as
a possible solution, however, further research is needed to provide insights
about the performance of this DNN for a greater number of devices and
different target functions.

One of the major advantages of OTA computing over other multiple access
schemes is its ability to enable massive connectivity. However, because of
this feature, any imperfections on a single-user basis can potentially cause
large impairments due to the large number of connected devices in the OTA
computing system, which will lead to incremental performance degradation. In
general, these imperfections can be products of electronic impairments or
natural phenomena such as the presence of noise. To address this practical
problem, it is necessary to study the effect of imperfections in OTA computing
and to find new optimal policies that can mitigate their effects. For example,
as shown in [89], imperfect CSI knowledge requires a different optimization
problem to be formulated, as the direct application of the technique proposed
in [73] results in

$\displaystyle\mathrm{MSE}=$
$\displaystyle\underbrace{\sum_{k=1}^{i^{*}}\left|\left(a\sqrt{P}\frac{{h_{k}^{\prime}}^{H}}{|h_{k}^{\prime}|}h_{k}-1\right)\right|^{2}}_{\text{Full
Power Terms}}+\sigma^{2}|a|^{2}$ (14)
$\displaystyle+\underbrace{\sum_{k=i^{*}+1}^{K}\left|\left(\frac{h_{k}}{h_{k}^{\prime}}-1\right)\right|^{2}}_{\text{Inverse
Channel Terms}}.$

In [89], a thorough analysis of the performance of OTA computing under
imperfect CSI knowledge was investigated and an optimal power allocation
policy was proposed to improve it. As shown in (14), these imperfections will
cause performance degradation and thus need to be addressed to mitigate their
effects. Similar studies on other types of imperfections, such as signal
misalignment or phase noise, also need to be investigated in order to create a
general OTA computing system model that can be adapted to practical operating
conditions. In addition to studying the performance of these scenarios, the
scope of future studies should also include the study of resource utilization.
This is extremely important because from a practical point of view, certain
performance improvements may be plausible, e.g., by re-estimating the channels
for more accurate CSI, but at the cost of valuable resources of the OTA
computing devices [89]. The use of appropriate utility functions, such as the
retransmission policy cost (RPC) [89], which jointly consider MSE and
resources, can be useful in this direction. RPC is defined as

$\zeta(k)=\mathcal{C}(k)^{m_{1}}\left(\frac{\mathbb{E}[\mathrm{MSE}_{k}]}{K}\right)^{m_{2}},$
(15)

where $\mathcal{C}(k)$ denotes the resource cost required for $k$
retransmissions, $\frac{\mathbb{E}[\mathrm{MSE}_{k}]}{K}$ symbolizes the MSE
for $k$ retransmissions, and the primary concern over available resources is
considered to be the selected cost. Furthermore, the parameters
$\\{{m_{1}},\,{m_{2}}\\}\in\mathbb{R}^{2}$ are considered as weights for the
selected cost and the MSE, respectively. The parameters can be chosen in
different ways to prioritize either the resource cost for retransmissions or
the maximum error tolerance. By definition, RPC can be modified, i.e.,
different costs can be considered, and its weight parameters can be
appropriately adjusted whenever new channel information becomes available to
better capture the current state and needs of the system, making it an
interesting utility function to consider in practical OTA computing designs.
Similar utility functions can be studied to address MSE performance in
combination with other valuable resources of the system depending on the state
of the latter.

As this discussion indicates, it is of paramount importance to generalize
existing OTA computing resource allocation policies to more practical
situations. To achieve this, we need to consider generalizations related to
the availability of the resources themselves, apart from system models that
encapsulate realistic operational parameters. For example, the most commonly
studied models in the literature are based on power constraints that are
identical for all devices, as described in the presented system model, or take
all devices into account, i.e., $\sum_{k=1}^{K}|b_{k}|^{2}\leq P_{tot}$, where
$P_{tot}$ is an overall power constraint of all devices. Note, however, that
in many cases such constraints may not be accurate, especially when energy
efficiency is also of interest. In such cases, it may be more realistic to
allocate resources according to their current availability, e.g., a battery-
powered device may need to adjust its transmit power levels to extend its
lifetime. These factors also need to be taken into account to provide more
accurate performance simulations of OTA computing systems for operational use.

###  III-E Future directions

As explained so far, OTA computing is a scheme that can be used in MAC, but
until now we have assumed that the number of devices participating in such a
system is known and fixed. However, in many scenarios, a device may want to
communicate or join a system randomly, which is common in practice to achieve
greater energy efficiency by not wasting resources unnecessarily. For example,
we can consider a scenario where a device is inactive and thus does not
transmit data, but when it is active it needs to transmit its current state.
In these cases, the number of devices in the system is not fixed, but varies
randomly, which would change the optimal power allocation policy of (10).
Thus, the study of OTA computing in random access environments would be of
great interest, especially considering the fact that, unlike other random
access channels, interference is actually useful in OTA computing since
superposition is desired.

Another interesting topic to study in OTA computing systems is security. In
one-to-one communication, a single device transmits its data to a BS, so any
eavesdropper can receive the signal from that device and try to decipher
information about its data. To address this, different layers are used to
handle information at different levels and certain protocols can act as a
protection by encrypting the original data of the device. On the other hand,
in OTA computing systems, data information can still be intercepted by
eavesdroppers, but the case differs from the one-to-one scenario in two
fundamental ways. First, the pre-processing function of each device already
acts as a protection on the original data, but most importantly, the
superposition of all signals from the OTA computing devices does not allow the
extraction of individual data information from the devices. Even in digital
form, OTA computing could prove vulnerable to eavesdroppers due to the large
number of devices it can support, as extremely sophisticated hardware would be
required to even attempt to process individual device data. With this in mind,
OTA computing could be an interesting way to make computing not only more
timely, but also more secure than other techniques.

Because of its great potential for computing, another intriguing topic that
could take on substance is multi-function computing. Since OTA computing is
very resource-efficient compared to other multiple access protocols such as
TDMA and FDMA, it would be interesting to combine OTA computing with one of
these protocols to enable parallel computation of multiple target functions.
For example, FDMA techniques could be used to compute different functions from
different subcarriers. Although this concept seems easy to study, since
orthogonality in time or frequency could be used, in practice orthogonality is
rarely achieved. For this reason, multi-function computation would require the
study of imperfections that would cause interference between the different
functions to be computed. Since this type of parallel computing through OTA
computing could greatly reduce the amount of traffic and free up valuable
resources for other network applications, multi-function computing could be
another direction for future studies.

##  IV Semantic communications

In next-generation communication systems, one of the main goals will be to
achieve extremely high data rates to handle the amount of data trafficking
along the networks [90]. The most common way to increase data rate is usually
to increase bandwidth, which increases the capacity of digital communication
systems. However, this comes at the cost of reducing available bandwidth
resources from other applications that need to be processed by the network. In
addition, to increase the bandwidth allocated to an application, it is
necessary to support larger carrier frequencies, i.e., to move to higher
frequencies. As a result, devices must be equipped with the hardware to
support this transition. For example, larger carrier frequencies require
smaller antenna sizes and more sophisticated electronics for oscillators,
which can be challenging for widespread commercial use. While there are ways
to overcome these challenges, at least when not many device changes are
required, this view fails to capture the characteristics of the data being
transmitted that can be exploited to improve network efficiency and
performance.

Many applications in next-generation networks will be more interested in the
correct inference for a task based on the received data than in the error-
free, accurate reception of the data itself. Taking advantage of the rise of
AI, it is possible to consider inference as the goal of communication by
implementing DNNs that are trained to provide appropriate representations of
the original data that can be correctly interpreted by the receiver, even if
they differ from the original data. Semantic communications can change the way
communication is achieved by taking into account the disparity between the
underlying meaning of transmitted and received messages as explained above.
Shannon and Weaver, in their seminal work [91], distinguished three levels of
communication, the first of which, level A, addresses the technical problem of
how accurately information is transmitted and is the one that has driven
communication to date. Taking into account the meaning of the transferred
data, two more levels are identified, level B, which is the semantic problem
and is related to the amount of information a message can convey, and level C,
which is the effectiveness problem. By incorporating underlying semantic
information into the conventional communication paradigm, semantic
communication aims to improve data exchange [91]. To take advantage of the
semantics of messages, information is shared a priori among all network
participants in the form of knowledge bases that contain semantic
relationships of the data to be transmitted. In this way, semantic
communications can also increase reliability, since an error at the bit level
does not always translate into an error at the semantic level. In addition,
semantic communications can reduce the amount of redundant information related
to the task at hand by transmitting only the necessary information and thus
not overloading the network with unneeded data. Although the concept of
semantic communications is quite old, it has recently come back into the
limelight due to recent advances in the field of DNNs, such as natural
language processing and image processing, which allow it to take shape. These
developments enable the recognition of contextual relationships within text
and images. These relationships are then used to extract semantic information
from new data to be transferred. Another powerful tool that has enabled the
use of semantic communication is the joint source-channel coding (JSCC)
scheme, which provides robustness against channel fading conditions and
semantic noise. The use of JSCC schemes both reduces the amount of information
to be transmitted and achieves better performance. Thus, current AI techniques
provide realistic ways to implement semantics-aware systems.

Apart from the use cases enabled by DNNs themselves, the study of multiple
access schemes in the context of semantic communications is of great interest.
In contrast to conventional techniques, in semantic communications, multiple
access must be incorporated into the training process of the semantic
receivers to achieve reliable performance. While in orthogonal multiple access
schemes, such as TDMA or FDMA, semantic communications could be adopted and
used as they currently are in schemes such as NOMA, where users also act as
interference to each other, the training must take them into account, thus
differentiating the semantic transceiver from its originally proposed design.
For this reason, multiple access is of great interest to integrate semantic
communication in next generation systems.

Regarding the modeling and formulation of semantic communications, some
general concepts based on information theory exist [92, 93], however most of
the relevant literature focuses on their applications. The most characteristic
of them are related to the extraction of information from images, speech, and
text. Due to the different inference tasks that are performed as a result of
the different types of data, we distinguish them as the basic application
cases that semantic communications have focused on so far. Although in
principle the concept behind this type of communication is the same for each
case, different DNN architectures and performance metrics are required to suit
the data characteristics of each category.

###  IV-A Semantic communications for text inference

Text data is frequently responded to in many everyday applications and is thus
the focus of many works. Due to the fact that the conveyed meaning of the
original data rather than the exact data itself is of primary interest, it is
challenging to find appropriate performance metrics to measure the likelihood
of the received and original data. For text transmission, two different
metrics have emerged as the most representative for performance evaluation.
One of them is the bilingual evaluation understudy (BLEU) score. The BLEU
score evaluates the performance of semantic systems by counting the number of
different $m$-grams between sentences, where an $m$-gram is any part of a
sentence consisting of $m$ consecutive words. Recently, the most commonly used
performance metric has been sentence similarity, which describes the
similarity between the original transmitted data and the reconstructed data at
the receiver, since it is more suitable for detecting semantic features along
whole sentences, in contrast to BLEU. Given a set of $J$ sentences
$\mathcal{S}=\\{S_{1},\cdots,S_{j},\cdots,S_{J}\\}$, the sentence similarity
is defined as

$M_{j}=\frac{\mathbf{B}(S_{j})\mathbf{B}(S_{j}^{\prime})^{T}}{\|\mathbf{B}(S_{j})\|\|\mathbf{B}(S_{j}^{\prime})^{T}\|},$
(16)

where $(\cdot)^{T}$ denotes the transpose operator of a vector, and
$\mathbf{B}(\cdot)$ denotes the bidirectional encoder representations from
transformers (BERT) for each sentence $S_{j}$, which is a vector form
representation of the original sentence after its processing by a source-
channel encoder and measures the similarity between the transmitted and
reconstructed sentence after reception. As observed by (16), some DNN encoding
architecture is needed to generate an equivalent vector form of the original
data, the most common of which is DeepSC [94], which aims at reducing the data
information to be transmitted while maximizing the mutual information through
end-to-end training.

Figure 2: Example of semantic network with a DeepSC implemented tranceiver.

Given a sentence $S_{j}$, we denote $S_{j}^{\prime}$ its equivalent semantic
form, i.e., the output of the semantic encoder part of DeepSC when the input
is the given sentence $S_{j}$. To make the transmitted data resilient to the
effects of AWGN and fading, DeepSC encodes $S_{j}^{\prime}$ through the
channel encoder into a vector $\mathbf{X_{j}}=[x_{1},\cdots,x_{kO_{j}}]$,
where $\mathbf{X_{j}}$ consists of the encoded symbols that will be
transmitted, $O_{j}$ symbolizes the word number in the $j$-th sentence and $k$
is the number of outputs of the DNN for each word. Since the generated symbols
can take arbitrary values, it is clear that DeepSC utilizes discrete-time
analog transmission (DTAT), which means that the maximum achievable data rate
for it is $C=W$, where $W$ is the allocated bandwidth. Consequently, for $k$
DNN outputs, the number of semantic symbols per sentence is equal to $kO_{j}$
and the corresponding delay when semantic transmission is utilized is given as

$D_{l}=\frac{k\sum_{j=1}^{J}{O_{j}}}{{C}}.$ (17)

It is straightforward to observe that due to the different number of symbols
and capacity of DeepSC, the delay will be different from the one we would get
if we had used traditional Shannon communication. From (17) we can deduce that
DeepSC can reduce the delay by appropriately choosing $k$ to meet the desired
similarity levels of an application, but cannot achieve the delay reduction of
the Shannon paradigm since its rate is fixed.

To make DeepSC more suitable for practical applications, in [95], a
quantization technique on the constructed unstructured constellation resulting
from DeepSC was proposed. A different approach based on knowledge bases and
digital transmission instead of end-to-end DNN architectures like DeepSC was
also studied in [96], where for energy efficiency reasons, energy harvesting
was proposed and the similarity maximization of the system was studied. A
variation of sentence similarity, called semantic accuracy, has also been
studied in [97] where energy efficiency is of interest and no energy
harvesting is performed.

Regarding multiple access, a NOMA-based system utilizing DeepSC was considered
in [98] and in [99] a QoE maximization problem was investigated. Furthermore,
in [100], the design and use of a DeepSC-like DNN were examined when two users
must be served simultaneously. To account for this, the training loss function
in this scenario was modified from the original DeepSC to account for both
users. Finally, in [101] a hybrid system consisting of both digital and
semantic transmission was studied as a means to combine the advantages of both
techniques. For this purpose an OFDMA technique was considered and delay
minimization was studied in combination with sentence similarity constraints.

###  IV-B Semantic communications for image inference

Regarding image transmission, the main goal of semantic transmission is the
accurate reconstruction of the transmitted image at the receiver side. As in
text transmission, the most studied approach for semantic image transmission
is through a DNN implementation version of DeepSC, called DeepJSCC, which maps
image pixels directly to the channel inputs to be transmitted [102]. Given a
sequence of symbols $\mathbf{t}$ representing the original image data and the
reconstructed data denoted as $\mathbf{\hat{t}}$, the goal of DeepJSCC is to
minimize the distance between the two sequences, which means that the training
loss function used is the MSE. To evaluate the performance of image
reconstruction, the most appropriate metric is the peak signal-to-noise ratio
(SNR), defined as

$\mathrm{PSNR}=10\log_{10}\left(\frac{\max{\\{\mathbf{t}\\}}^{2}}{||\mathbf{t}-\mathbf{\hat{t}}||^{2}}\right),$
(18)

which gives a measure of the quality of the reconstructed image, with higher
peak SNR indicating higher accuracy.

Based on DeepJSCC, there have been several works that aim to improve the
performance of the originally proposed model while making it more practical
from a usage point of view. In particular, in [103], a version of DeepJSCC was
proposed that quantizes its channel inputs in order to adapt it to existing
digital communication systems, and it was shown to have significant
performance gains over conventional image transmission techniques.
Furthermore, in [104] a peak-to-average power ratio (PAPR) efficient
implementation for an OFDM scheme using semantic communications was
considered. Apart from these, learned perceptual image patch similarities
(LPIPS) have recently been investigated as a means to improve the semantic
extraction part of the DNN architecture. In this direction, in [105] the
perceptual understanding of the reconstructed image data has been studied by
optimizing the MSE and LPIPS. In this direction, a collaborative way between
conventional and semantic communications was proposed, where the original
image data is partially transmitted using conventional source and channel
coding techniques and partially using DeepJSCC, while the receiver combines
both streams to improve its perceptual similarity between the original and
reconstructed data. Similar in concept, but with higher complexity and
accuracy, multiple views of the same image are transmitted and a combination
of them is used at the receiver end to maximize the peak SNR.

###  IV-C Semantic communications for speech inference

With respect to speech signals, the primary concern of semantic communications
is the correct understanding of a speech-transmitted signal by humans. Similar
to the text case, a DNN implementation is needed to extract information about
the semantics of speech and to perform source-channel coding for robustness
against channel fading and noise. As such, an architecture similar to DeepSC,
called DeepSC-S, has been proposed for this task [106, 107]. If we consider a
speech sample sequence $\mathbf{s}$ as the original speech data and
$\mathbf{\hat{s}}$ as the output of the speech decoder at the receiver side,
the goal of DeepSC-S is to minimize the difference between the original and
the reconstructed speech sample sequences. Therefore, DeepSC-C is trained with
MSE as the most appropriate loss function. Since the task at hand is the
reconstruction of the original speech signals, the performance metric used for
such cases is the signal-to-distortion ratio (SDR), which measures the
distance between $\mathbf{s}$ and $\mathbf{\hat{s}}$ and is defined as

$\mathrm{SDR}=10\log_{10}\left(\frac{||\mathbf{s}||^{2}}{||\mathbf{s}-\mathbf{\hat{s}}||^{2}}\right).$
(19)

It is easy to observe that the lower the MSE between $\mathbf{s}$ and
$\mathbf{\hat{s}}$ is, the larger the SDR will be and consequently better
quality at the receiver is achieved. Apart from SDR a useful metric for speech
quality recommended by ITU-T is the perceptual evaluation of speech distortion
(PESQ), which aims to measure the listening experience of the retrieved speech
signals. As such, DeepSC-S has been tested under both performance metrics and
shown to outperform traditional communication schemes for both of them.

A slightly different task that can be of interest when speech signals are
involved is speech recognition. In this scenario, text is also of great
importance because the received signals are transformed into text data to be
compared with the original data. For this purpose, another DNN architecture
similar to DeepSC-S was proposed [108], namely DeepSC-SR, which is responsible
for transforming the original speech signals into text transcriptions and then
performing source-channel coding for communication efficiency. As such, the
performance metrics associated with speech recognition are the character error
rate (CER) and the word error rate (WER), which measure the difference between
the original and retrieved text transcriptions. If we consider a text
transcription $\mathbf{t}$, CER and WER are defined as

$\mathrm{CER}=\frac{S_{C}+D_{C}+I_{C}}{N_{C}}\text{ and
}\mathrm{WER}=\frac{S_{W}+D_{W}+I_{W}}{N_{W}},$ (20)

where $S_{(\cdot)}$, $D_{(\cdot)}$, $I_{(\cdot)}$ represent the number of
character/word substations, deletions, insertions, respectively, and
$N_{(\cdot)}$ is the number of characters/words in $\mathbf{t}$, respectively.

###  IV-D Semantic communications and multiple access

As discussed, semantic communications can revolutionize the way current
communication systems operate by allowing semantic extraction of information
and reducing the amount of redundant transmitted data. However, semantic
communications have not been extensively studied in multiple access scenarios.
Due to the nature of the semantic transceivers proposed so far, i.e., through
DNN implementations for encoding, decoding, and information extraction,
semantic communications face additional difficulties compared to their
conventional counterparts when considering multiple access. In this context,
in [100], the authors proposed a semantic transceiver design that can support
multiple users and also operate for different tasks at the same time, such as
text and image transmission. The opposite scenario of a one-to-many broadcast
channel was also studied in [100] and a semantic transceiver was proposed to
optimize the performance for all users in the network.

Another challenge that semantic communications must overcome is related to the
multimodal nature of the tasks that it can support. Since the semantic
transceivers for different tasks each require different DNN architectures and
training processes, a device cannot use one transceiver for multiple tasks.
With this in mind, in [100], a semantic transceiver was designed that can work
for different tasks simultaneously. Simulation results showed that such
implementations still offer better performance compared to conventional
transmission schemes, especially under low SNR, thus highlighting the
usefulness of integrating semantic communications in next-generation
communication systems.

Despite these major challenges, it is clear that semantic communications are a
possible way to provide services for next-generation applications. However,
one must consider the practicality of radically changing the existing
infrastructure to support them, as well as the fact that they may not always
be optimal when traditional KPIs such as delay time are considered apart from
the ability of semantic communications to successfully reconstruct the
original information. Thus, in [101], a multicarrier system was studied that
aims to minimize its transmission delay under strict sentence similarity
constraints when both semantic and conventional transmission are possible. As
shown, due to the limitations of semantic transceivers to achieve every
similarity level, conventional transmission schemes may sometimes be
mandatory, while in high SNR values, where Shannon’s capacity formula offers a
large gain over the fixed data rate of DTAT, conventional schemes are again
preferable for transmission.

###  IV-E Future directions

It is evident that in order to integrate semantic communications into next-
generation communication systems, further studies are needed to improve the
currently proposed transceiver designs, along with the introduction of
multiple access as a fundamental feature in them. To improve the performance
of semantic transceivers, it is imperative to consider significant
communication KPIs as part of the system. In this sense, a possible direction
to explore would be to incorporate application-required KPIs into the training
process of designs such as DeepSC to provide joint optimal solutions both for
data reconstruction and for meeting application requirements. In this
direction, online learning can also be considered as an attractive option to
further improve transceiver performance by using the current on-the-fly
characteristics of the network to adapt the performance to the new traffic and
desired network parameters.

Perhaps one of the most interesting and practical topics for further research
is multiple access for semantic communications. One direction that could be
exploited is the implementation of special multiple access protocols that
support the use of semantic transceivers. The multimodal nature of the
different tasks that can be performed could provide another degree of freedom
for multiple access. For example, in next-generation systems, the network
controller could allow a mix of conventional multiple access protocols, such
as TDMA and NOMA for each time slot, where users participating in NOMA could
transmit heterogeneous data to take advantage of transceivers that can decode
data for different tasks.

##  V ML & multiple access: A mutual relationship

The field of ML has experienced a significant shift from the dominant “big
data” strategy, where substantial amounts of data are collected and managed in
a central cloud, to a “small data” approach [109]. In this approach, a
collective of agents or devices process their data at the edge of a mobile
network. This framework is particularly relevant in scenarios where data is
distributed among devices, such as in edge computing configurations or IoT
applications. The main incentive for adopting distributed ML is the increasing
congestion of wireless channels due to the overwhelming amount of data, which
discourages agents from sharing their datasets with ML servers [110].

Consequently, the inherent difficulties associated with wireless networks,
such as constrained bandwidth, fluctuating latency, and potential
communication breakdowns, pose significant challenges to the smooth
integration of ML algorithms. Therefore, in the field of distributed learning,
the primary goal of communication shifts from rate maximization to
accelerating the training of ML models using distributed data. The convergence
of an ML model now depends on both the selected training algorithm and the
utilized multiple access protocol, supporting distributed wireless training of
the ML model [111]. This facilitates the creation of coherent computation-
communication strategies, where the training algorithm is adapted to the
communication process of the agents, taking into account factors such as their
data volume, the network topology, and the communication pattern of the agents
[112]. In the following, we present some promising distributed ML frameworks
and discuss existing multiple access protocols as well as potential avenues
for future research.

###  V-A Federated learning

Consider the set $\mathcal{N}$ containing all devices that will participate in
the FL procedure, with the number of devices equal to $N$. We assume that the
$i$-th participating device has its own dataset $\mathcal{D}_{i}$ of $D_{i}$
training samples, where each training sample $k$ consists of an input vector
$\boldsymbol{x}_{i,k}$ and a target vector $\boldsymbol{y}_{i,k}$. The
training goal of the FL procedure is given by

$\underset{\boldsymbol{w}}{\text{min}}\quad\sum_{i\in\mathcal{N}}\frac{d_{i}}{D_{i}}\sum_{k\in\mathcal{D}_{i}}f\left(\boldsymbol{w},\boldsymbol{x}_{i,k},\boldsymbol{y}_{i,k}\right),$
(21)

where $\boldsymbol{w}$ are the training parameters of the ML model that the
devices should jointly construct, $f(\cdot)$ is the loss function that
describes the ML task of all devices, and $d_{i}$ is a scaling parameter with
$\sum_{i}d_{i}=1$. The goal of the FL procedure is to find the vector
$\boldsymbol{w}$ that minimizes the loss function of the entire dataset, as
given in (21) [113].

However, the convergence of the FL model cannot be studied independently of
the wireless conditions and the capabilities of the devices [114, 115].
Specifically, we define the convergence time of the FL as

$T=(T_{\mathrm{L}}+T_{\mathrm{T}})N_{\mathrm{T}},$ (22)

where $T_{\mathrm{L}}$ is the local ML computation latency at each device,
$T_{\mathrm{T}}$ is the maximum ML model transmission latency, and
$N_{\mathrm{T}}$ is the number of learning steps [116]. Furthermore, the
energy consumption of each device is given by

$E=(E_{\mathrm{L}}+E_{\mathrm{T}})N_{\mathrm{T}},$ (23)

where $E_{\mathrm{L}}$ is the energy consumed by each device during a round of
local training, and $E_{\mathrm{T}}$ is the energy consumed during a round of
communication [117].

We note that the convergence time of the FL is strongly influenced by the
available energy per device and the available bandwidth. It is a common
assumption that all devices can upload their local updates during each
iteration, while the use of sequential polling with multiple access channels
may allow the upload of more local updates at the expense of more bandwidth.
However, in practical scenarios, certain users (e.g., mobile phones) may be
busy with other tasks or in a sleep state. Consequently, even if they are
instructed to upload, they may not be able to access local updates, resulting
in channel waste. In addition, from (22) and (23), it is observed that a
unified computing and communication design is crucial to reduce FL latency,
while also considering FL energy consumption [118, 119, 120, 121, 122]. Thus,
multiple access for FL must encompass the balance between loss function
convergence, time and energy consumption, and effective management of
communication resources [123]. FL convergence analysis is a critical step in
the development of multiple access protocols for FL. The results of FL
convergence analysis illustrate the impact of wireless factors on key learning
metrics, thus helping to optimize wireless resource allocation and determine
other wireless system parameters [115, 109, 112]. For convergence analysis, it
is essential to examine how wireless factors and multiple access protocols
affect the convergence of realistic FL with non-convex local ML models and
loss functions. For example, let us consider the result of [124]. The authors
of [124] mention that the upper bound of performance is influenced by the
quantization error. This indicates that increasing the number of quantization
bits reduces the quantization error. However, it was also shown that this
approach leads to larger sizes of the local model parameters, potentially
causing increased transmission latency. Considering this trade-off between
model accuracy and fast convergence, the authors proposed a joint computation
and communication design to optimize the OMA protocol used in the FL process
and the quantization levels per round. It is noted that wireless fading
significantly affects the chosen quantization levels, highlighting the
importance of integrated communication and computation design for FL and ML
applications.

###  V-B Federated distillation

While FL is known for its communication efficiency, it still necessitates the
transmission of large models over the air. DNN architectures usually consist
of a substantial number of model parameters, making the exchange of such
models costly and impeding frequent communication, particularly in
environments with limited wireless resources. Conversely, FD only transmits
the outputs of the DNN models, which have significantly smaller dimensions
compared to the model sizes [125]. For instance, in a classification task,
each device conducts local iterations while retaining the average model
output. These local average outputs are periodically uploaded to the parameter
server, which aggregates and averages the local average outputs across devices
per class. The resulting global average outputs are then downloaded by each
device. To incorporate the downloaded global knowledge into local models, each
device undergoes local iterations with its own loss function, in addition to a
regularizer that assesses the discrepancy between its prediction output for a
training sample and the global average output for the corresponding class of
the sample. The communication delay of a device executing FD is detailed in
[126],

$T_{\mathrm{L}}=\frac{\mathrm{dim}(\boldsymbol{y})Db}{R},$ (24)

where $R$ is the transmission rate, $\mathrm{dim}(\boldsymbol{y})$ is the
dimension of the DNN’s output, $D$ is the batch size, and $b$ is the number of
bits used to represent a float number. Compared to FL, which transmits all the
parameters of the DNN, the transmission delay caused by transmitting the
outputs of the DNN is generally lower, thus the FD has a lower communication
overhead [125, 127, 128, 126, 129, 130, 131].

Nevertheless, in [125] it was observed that the performance of FD is slightly
worse than that of FL. Thus, there is a trade-off between communication
overhead and ML accuracy that is worth investigating. In this context, hybrid
FD has been proposed in [131], which combines the concepts of FD and FL to
provide a high-accuracy scheme with low communication complexity. However, the
convergence analysis of FD has not been widely explored, and most results on
FD are based on empirical observations. This limitation can hinder the
understanding of the performance of FD under fading conditions and energy
consumption constraints. Nevertheless, the joint multiple access and
computation design of FD can be studied using the JSCC prism. JSCC does not
require a theoretical analysis of FD convergence, yet it can provide an
appropriate physical-layer modulation based on fading and the statistics of
the information to be transmitted per communication round.

###  V-C Split learning

SL is another recently emerged collaborative training framework for
distributed learning, which is capable of training an ML model between a
device and an edge server by splitting the ML model into a device-side model
and a server-side model at a cut layer [132]. The procedure for SL is as
follows: First, the device executes the device-side model with local data and
sends intermediate output associated with the cut layer, called smashed data,
to the edge server. Subsequently, the edge server executes the server-side
model, completing the forward propagation process [132, 133]. Second, the edge
server updates the server-side model and sends the gradient of smashed data
associated with the cut layer back to the device. The device then updates the
device-side model, completing the backward propagation process. This completes
the SL process for a device. The updated device-side model is then transferred
to the next device, and the process is repeated until all devices are trained.
In SL, small-sized device-side models, smashed data, and gradients of smashed
data are exchanged between devices and the edge server, resulting in reduced
communication overhead compared to uploading the entire AI model in FL [134,
135, 136]. Due to its superior efficiency, SL is potentially suitable for
resource-constrained IoT devices [137]. However, when multiple devices
participate in SL, all devices interact with the edge server sequentially,
resulting in significant training latency, especially when the number of
devices is large. The latency of SL is thus strongly influenced by the chosen
cut layer and the wireless communication latency [138, 139].

Split learning (SL) is a recently developed collaborative training approach
for distributed learning that facilitates the training of a ML model between a
device and an edge server by dividing the ML model into a device-side model
and a server-side model at a designated cut layer [132]. The SL process
unfolds as follows: Initially, the device utilizes the device-side model using
local data and transmits the intermediate output related to the cut layer, to
the edge server. Subsequently, the edge server uses the server-side model,
completing the forward propagation of the DNN model [132, 133]. Next, the edge
server updates the server-side model and sends the gradient associated with
the cut layer back to the device. The device then updates the device-side
model to conclude the backward propagation process, marking the completion of
the SL process for a device. The updated device-side model is subsequently
passed on to the next device, and this cycle repeats until all devices have
been trained. In SL, the exchange of small-sized device-side models, smashed
data, and gradients of smashed data between devices and the edge server
reduces communication overhead compared to uploading the entire AI model in FL
[134, 135, 136]. Given its efficiency, SL holds promise for resource-
constrained IoT devices [137]. However, in scenarios where diverse devices
wish to participate in SL, all devices communicate with the edge server
sequentially, leading to considerable training latency, particularly in cases
with a large number of devices. The latency of SL is thus heavily influenced
by the selected cut layer and the latency associated with wireless
communication [138, 139].

As a consequence, an interesting trade-off between FL and SL arises, which
facilitates the study of joint computation and communication. Let us assume
$N$ clients/devices, with an ML model of $K$ parameters, where $D$ is the size
of the dataset, $q$ is the size of the smashed layer, $\eta$ is the fraction
of model parameters (weights) with the client, and thus $1-\eta$ is the
fraction of parameters with the server. Therefore, the communication
efficiency, computed as the ratio of the data transfers of FL and SL, is given
by [132]

$\rho=\frac{2ND}{2pq+\eta ND}.$ (25)

Thus, SL is better for communication efficiency when $\rho>1$, while FL is
better when $\rho<1$. By rearranging the terms and expressing them as an
equality, and dividing the numerator and denominator by $ND$, we get the
equation of a rectangular hyperbola as $N=\frac{2pq}{(2-\eta)D}$ in the case
of client weight sharing, and $N=\frac{pq}{D}$ in the case of no client weight
sharing with alternating epochs. This hyperbola separates the areas where one
technique performs better than the other. From this example, it is obvious
that if both ML methods use the same multiple access protocols, choosing FL or
SL based on the equation (25) can speed up the training latency of the global
ML model.

However, it is interesting to explore whether SL and consequently FL might
have different optimal joint computation and communication protocols, given
their different training procedures. In such a scenario, (25) may need to be
modified. For example, in [137], an SL scheme called cluster-based parallel SL
(CPSL) is designed to reduce training latency by following a “first-parallel-
then-sequential” approach. CPSL involves partitioning devices into clusters,
training device-side models in parallel in each cluster, and then aggregating
them. Then, CPSL trains the entire AI model sequentially across clusters,
thereby parallelizing the training process and reducing the training latency
of SL. A joint computation-communication design is provided by implementing a
resource management algorithm to minimize the training latency of CPSL, taking
into account device heterogeneity and network dynamics in wireless networks.
This is achieved by stochastically optimizing cut layer selection, device
clustering, and radio spectrum allocation. While CPSL is shown to outperform
an FL benchmark, a detailed comparison between CPSL and an optimally designed
FL is still lacking. Furthermore, the interplay between FD and SL has not
received much attention. It is also worth noting that the effect of fading and
noise on the convergence of SL is unknown. The convergence analysis of SL has
not yet been explored, and consequently, a comprehensive analysis of the
wireless medium on SL has not been performed. This is critical for real-time
IoT applications, where the low-power data transmission of IoT devices is
prone to communication errors.

###  V-D Reinforcement learning over wireless networks

RL allows wireless devices to predict strategies, such as resource management
schemes, via trial and error with their underlying wireless environment. RL
provides efficient solutions to a wide variety of optimization problems,
ranging from Markov decision processes and games to intractable non-convex
optimization problems [140, 141, 111]. Importantly, RL does not require
precise modeling of the environment. RL agents can autonomously learn implicit
knowledge about network dynamics from raw, high-dimensional observations
through interaction with the environment. In multi-agent RL paradigms, agents
may need to share various RL information with each other. This could include
sharing rewards, RL model parameters, actions, and states among agents.
Different collaborative RL algorithms may involve sharing different types of
RL information.

Consequently, in wireless networks, the convergence of multi-agent RL depends
not only on RL parameters such as the size of the ML model, but also on other
factors such as the limited number of resource blocks, the imperfect
transmission of RL parameters, and limited transmit power and computational
capabilities of devices [142, 143]. In particular, the number of resource
blocks determines how many devices can execute the multi-agent RL algorithm.
At the same time, fading channels can introduce errors in the RL process. In
addition, limited transmit power and computational capabilities significantly
affect the time required for RL model updates and RL parameter transmission.
Hence, significant hurdles in deploying multi-agent RL across wireless
networks are present across several domains. These encompass optimizing
resource block allocation and device scheduling for transmitting RL
parameters, ensuring reliable and energy-efficient transmission of RL
parameters, jointly optimizing RL training methods and wireless resource
allocation to minimize RL convergence time, and devising coding and decoding
methods.[144, 141].

###  V-E ML-aided multiple access protocol design

Recent advances in deep RL (DRL) have generated enthusiasm in the network
research community, leading to the exploration of DRL applications in various
protocol optimization tasks, including congestion control and multiple access
protocol design. The integration of DRL techniques offers the potential to
minimize the manual effort required to tune protocol parameters. With numerous
ways for a user to communicate with a BS using a given protocol, the
application of DRL ensures that wireless networks are not limited to human-
designed protocols [145]. The upcoming challenge in protocol learning is to
enable users and BSs to explore the full range of potential protocols.
Communication protocols serve as languages used by network nodes. Therefore,
before a user equipment (UE) exchanges data with a BS, it must negotiate the
terms and parameters of the transmission. This negotiation involves signaling
messages across all layers of the protocol stack. The challenge arises because
for two radios to coordinate effectively, they must find a state in which they
can interpret each other’s messages. Recent research suggests that addressing
this common signaling discovery problem in the context of DRL initially
involves training the nodes with supervised learning [146]. This provides
radios with an initial communication protocol, which they can subsequently
refine through trial and error.

Essentially, the successful effectiveness of communication between a user and
the BS, encompasses various network metrics such as access delay, data rate,
and energy efficiency, depends on two key concepts. First, the utilized
channel access scheme, which is the method employed by multiple radios to
share a communication channel, such as a wireless medium. The channel access
scheme is implemented and constrained by the physical layer, with examples
including FDMA and TDMA. Second, the multiple access protocol, which
encompasses the combination of a channel access policy and signaling used in
conjunction with a channel access scheme. Channel access policies, such as
listen before talk (LBT) and dynamic scheduling, define how radios access the
channel. Signaling serves as the vocabulary and rules, described by the
structure of protocol data units, subheaders, etc., that guide radios in
coordination. The channel access policy determines when data is sent through
the user-plane pipe, while the signaling rules dictate when and what is sent
through the control-plane pipe. It is important to note that the end-to-end
communication delay of a data transmission is affected by both the signaling
overhead and the data rate. Therefore, the joint optimization of control
signaling and channel access policies is critical to to enhancing current
communication protocols to meet the diverse communication objectives of future
networks [147, 148].

Figure 3: RL-aided multiple access protocol design.

Consider the illustration in Fig. 3, where a multiple access protocol design
employing deep learning and RL attempts to identify the most effective
multiple access protocol from the existing options. Within the DRL framework,
it is crucial to define the communication objective that is aligned with
specific use cases and device categories across different scenarios. This
definition shapes the reward function, a critical component in the
optimization process. For instance, in scenarios where IoT devices prioritize
maximizing throughput while minimizing energy consumption, the objective
function aims for successfully transmitted bits divided by consumed energy per
bit. Notably, previous works such as [146, 149, 150] utilized the average
throughput of the link as the reward function, focusing on maximizing the
information data rate. In the DRL agent’s state-action representation, a
vector captures the building blocks, and a history of average link throughput
values (for a fixed link) serves as input. The building blocks include various
elements such as ACK/NACK usage, back-off mechanisms, listen before talk
(LBT), physical layer parameters (e.g., data rate), and the uplink signaling
action space (USAS). The USAS, which features larger vocabularies, provides
more control information to the channel access policy, providing a richer
context to the radio nodes. While this may result in increased signaling
overhead, it enables the implementation of more sophisticated channel access
algorithms. The size of the signaling vocabulary becomes a crucial hyper-
parameter, striking a balance between channel access performance and signaling
cost. This delicate equilibrium is exemplified in [148], where the DRL agent
adapts to low network load situations by eliminating control packets (e.g.,
ACK), thereby increasing channel throughput. Conversely, in high-traffic
scenarios, the agent opts for protective measures such as ACK, request to
sendRTS, clear to send (CTS), smaller frame sizes, and lower bit rates to
effectively manage collisions.

Future work could focus on training multiple access protocol learners in
networks with a reduced number of UEs and lower traffic volume before
deploying them in larger networks. Investigating the mirroring problem of
training a BS to learn an expert UE signaling can provide insights into the
challenges of protocol learning. The ultimate objective is to jointly train
UEs and the BS to evolve an entirely new multiple access protocol. This
involves learning not only the signaling and channel access policies, but also
the signaling vocabulary. Research in [146] suggests that this is challenging
when all agents (i.e., UEs and the BS) start with no prior protocol knowledge.
Therefore, one potential approach is scheduled training alternating between
supervised and unsupervised learning to facilitate the emergence of entirely
new protocols. Additionally, exploring multiple access protocol design for
random access schemes in mMTC traffic is an intriguing research direction
[151].

###  V-F State-of-the-art multiple access protocols

####  V-F1 OMA

OMA protocols, which include techniques such as TDMA and FDMA, play a critical
role in distributed ML by facilitating efficient communication between all
devices and a central node, if present. In scenarios where devices need to
communicate with the central server in a synchronized manner, taking turns to
transmit updates, TDMA proves beneficial. TDMA allocates different time slots
to each device, preventing interference and ensuring that each device has a
dedicated time to transmit its data. On the other hand, FDMA allows devices to
transmit their ML model updates on separate frequency bands. This approach
prevents interference and allows simultaneous communication. This is
especially useful when devices have different available frequency bands, and
it can also parallelize the ML training process. In addition, OMA protocols
have fewer synchronization issues compared to interference-based protocols
such as OTA computing. This is crucial in distributed ML to ensure that all
updates from the devices are received and processed in a coordinated manner.
For these reasons, the optimization of communication for distributed ML,
utilizing OMA transmissions, has been extensively explored in recent
literature [152, 153, 154, 155, 156, 157, 117, 116, 124, 125, 127, 128, 126,
129, 130, 131].

####  V-F2 Interference-based protocols

Computional capabilities, data sizes, and transmission requirements often vary
among different devices. Multiple access protocols designed for interference
mitigation enable non-orthogonal resource sharing, allowing multiple devices
with different requirements and channel conditions to communicate
simultaneously [158, 155]. In this context, NOMA with its non-orthogonal
channel access can improve spectral efficiency in distributed ML scenarios
[159, 160]. Devices can share the same time and frequency resources, allowing
more efficient communication of ML models, which is particularly relevant when
dealing with a large number of devices. Compared to OMA protocols, NOMA can
reduce communication delays, thereby accelerating ML training [161, 162, 163].
In addition to NOMA, RSMA has found application in distributed ML [164, 165,
166, 167]. The uplink communication between devices and the central node
typically serves as the latency bottleneck for these ML schemes. RSMA involves
splitting each agent’s data rate into two parts: a common part shared by all
users and a private part exclusive to each user. This allows multiple devices
to simultaneously transmit their private information while sharing a common
message, contributing to increased spectral efficiency. As a result, RSMA has
been shown to reduce the training time of distributed ML models compared to
NOMA and OMA [164, 165, 166, 167]. RSMA is also easier to implement in the
uplink and is compatible with multiple antennas. Furthermore, the concept of
OTA computing has been used to reduce communication delays during the training
of distributed ML models, which significantly improves the spectral efficiency
of communication during ML training.

###  V-G Future directions

####  V-G1 Contention-based protocols

Contention-based protocols are particularly beneficial in scenarios where
devices can dynamically join or leave the distributed ML process, as they help
manage communication efficiently with low communication overhead. In addition,
these protocols address partial participation by allowing devices to transmit
their updates to the central server whenever they are ready, without requiring
prior coordination. This requires that the ML training algorithm take partial
participation into account during training, and convergence analysis is
essential to assess the impact of random access and collisions on the training
process. Furthermore, contention-based protocols are valuable for modeling
asynchronous communication, where devices transmit their updates
independently. This is practical in distributed ML scenarios, as devices may
have different computational speeds, data sizes, and transmission
capabilities. These protocols are also effective in conserving communication
resources in sparse networks, where the number of active devices transmitting
at any given time is small. For example, random access can be used in
scenarios involving low-power IoT devices at the edge, where network sparsity
can be observed. Indeed, in [168, 169, 170, 171], random access was shown to
efficiently handle such conditions.

The convergence analysis of FL, FD, SL or distributed RL under random access
has not been sufficiently studied, despite the use of state-of-the-art random
access protocols. There is an opportunity to propose new random access
protocols by appropriately designing their back-off mechanisms, taking into
account the computational capabilities of the devices. In addition,
incorporating priority mechanisms to manage devices with different priorities
in transmitting their updates is an interesting avenue. These priorities can
be either delay-based or information-based, assessing the importance of the
update from a particular device for the convergence speed of the ML scheme.
Furthermore, interference mitigation protocols such as CDMA can be used to
reduce the number of collisions without increasing the communication overhead.
However, it is important to note that contention-based protocols, including
random access, do not guarantee communication delay. This aspect should be
carefully considered, especially when investigating these protocols for delay-
intolerant ML applications. It is worth noting that random-access protocols as
enablers have not been extensively studied in the context of SL, FD, or
distributed RL, while they have received minimal attention in the context of
FL.

####  V-G2 Adaptive modulation

While there has been considerable research on improving the communication
efficiency and learning performance of wireless FL, the impact of modulation
selection on learning performance remains largely unexplored, with exceptions
found in [172, 173]. In addition to channel conditions, local processing power
and data importance also influence modulation selection. Furthermore,
modulation selection has an impact on both learning latency and convergence
rate due to transmission rate and symbol error rate (SER). High-order
modulation schemes can yield a large SER and a high transmission rate,
potentially reducing learning latency at the expense of a slower convergence
rate [172, 173]. Conversely, a small modulation order may improve the
convergence rate but increase the learning latency. Despite these
considerations, adaptive modulation has not received significant attention for
ML applications. The joint design of computation and adaptive modulation for
future ML applications is critical to the integration of distributed ML
applications in future wireless networks.

####  V-G3 Multiple access protocols under communication errors

The majority of works on distributed ML typically assume a perfect
communication channel between the devices and the central node. In these
scenarios, the communication data rate is often modeled using the Shannon
capacity formula. However, the real-world implications of unreliable
communication on learning performance cannot be underestimated, as SER impacts
both communication and convergence outcomes [174]. It is imperative to
investigate strategies for enhancing the learning performance of distributed
ML systems operating within unreliable channels. For instance, [175] examined
the impact of packet error rate on FL performance, leading to the formulation
of an optimization problem for user scheduling and resource allocation. In a
more practical context involving imperfect CSI, the Lyapunov optimization
framework was utilized to address joint scheduling and resource allocation
concerns in [176]. Additionally, [177] introduced a scheduling scheme tailored
for imperfect CSI with the objective of achieving a specific training
accuracy, albeit at the expense of devices unable to maintain a predefined
transmission rate to expedite convergence time. While these studies offer
valuable insights, further research is warranted to explore the ramifications
of fading and imperfect knowledge of the communication environment,
particularly concerning FD, SL, and multi-agent RL.

##  VI Digital twinning

In the context of next-generation multiple access, digital twins play a
critical role. Multiple access schemes are essential in communications to
allow many users or devices to share the same communication channel. As
networks become more complex, especially in the beyond-5G era, managing and
optimizing these networks becomes more challenging. Digital twinning is
valuable in this area because it can simulate complex network scenarios. This
capability is important for testing and improving multiple access strategies
in a controlled, virtual environment. It helps to understand how different
devices and users interact within a network and to predict the impact of
changes in one part of the system on the entire network. By mirroring the
network in a virtual space, digital twinning gives operators insight into
where the network is underperforming, where it might fail and where there are
opportunities to make it more efficient. Digital twinning also supports
advanced network management concepts such as network slicing and dynamic
resource allocation in multi-access networks. With a real-time digital version
of the physical network, operators can more effectively allocate resources
based on current and predicted demand. This approach increases network
efficiency and reliability.

Besides their utilization in applications related to communications, digital
twins are considered effective in other use cases. For example, they can be
applied in smart factory and industry 4.0, where the goal is to reduce
production costs, increase efficiency, and provide companies with an
increasingly flexible approach to production. Another use case is smart
infrastructure and smart cities, where infrastructure management through
digital twinning aims to minimize construction and maintenance costs while
ensuring safety and lifetime [178].

###  VI-A Proactive resource allocation

In the context of next-generation multiple access, digital twinning
revolutionizes resource allocation by effectively allocating network resources
based on current and predicted network demand. Digital twins help make this
allocation both efficient and proactive with their real-time data analysis and
predictive modeling capabilities.

Digital twins incorporate various parameters such as user density, traffic
patterns, and resource utilization to create a dynamic model of the network
that accurately reflects its current state. This model is constantly updated
with real-time data to provide an up-to-date representation of the state of
the network. However, digital twins not only reflect the current state of the
network, but also use predictive analysis to forecast future network
conditions. By analyzing trends and patterns in data usage, device
connectivity and service demand, network operators can anticipate where
resources will be needed most before demand actually occurs.

This foresight enables automated adjustments to resource allocation. For
example, to prevent congestion or service degradation, the digital twin can
proactively reroute resources to a particular network zone if it predicts high
demand in that area. Conversely, during periods of low demand, resources can
be reduced to save energy and lower operating costs. This level of automation
in resource management is critical to maintaining network efficiency and
reliability.

In addition, digital twins allow operators to simulate different scenarios and
plan resource allocation strategies accordingly. They can model the impact of
various events, such as a large public gathering or the introduction of a new
high-bandwidth service, and create robust resource allocation plans that can
efficiently handle such scenarios. This capability is critical to ensuring
that the network is prepared for a wide range of potential situations.

The primary objective of proactive resource allocation through digital
twinning is to improve the user experience. By ensuring that network resources
are optimally distributed and available exactly where and when they are
needed, digital twins help maintain high quality of service, reduce latency
and prevent outages. They also provide a feedback loop that continuously
monitors the results of resource allocation decisions, allowing the network to
adapt to changing demands and usage patterns. To this end, digital twinning
can be utilized to provide proactive resource allocation in various scenarios,
such as open RAN (O-RAN) [179], smart grids [180], wireless power transfer
[181], among others.

###  VI-B Digital twinning in MEC

Many works on digital twinning for wireless communication focus on designing
digital twins for MEC servers [182, 183, 184, 185, 186, 187, 188], where the
MEC digital twin is used to extract optimal network orchestration in real
time. For example, in [183, 184, 185], algorithms based on DRL were
investigated for training the digital twin of the MEC network to make offload
decisions, edge and resource allocation, increase energy efficiency, and
reduce migration costs. Moreover, [186, 187] used the digital twin of a MEC
system to minimize the end-to-end latency by also taking into account the
deviations between the two twins. Furthermore, digital twinning has also been
proposed for use in the internet of vehicles [189, 190] to enable efficient
resource allocation policies of vehicles and real-time traffic prediction.
However, an important issue is that the digital twin may not always accurately
reflect that of its real-world counterpart, since the latter may be subject to
rapid changes along with the evolution of time. Therefore, it is necessary to
synchronize the digital twin with its physical counterpart to ensure that its
state is accurate. To address this challenge, a dynamic hierarchical framework
has been designed in [191], where a cluster of IoT devices is used to sense
and collect status information of physical objects to support the update of
the digital twin.

###  VI-C Multiple access for digital twinning

Selecting an appropriate access scheme is critical when designing the wireless
interface for digital twinning to enable communication between the digital
twin and physical entities. In this direction, several schemes can be used to
achieve wireless access, such as OFDMA, TDMA, CDMA, and NOMA [192].

OFDMA, which uses orthogonal resource blocks for communication, is
characterized by low complexity in receiver design. However, it tends to have
low spectral efficiency and can only accommodate a limited number of users.
NOMA, on the other hand, allows all users to use the entire available
bandwidth simultaneously, with decoding at the receiver based on received
power levels. This method has high spectral efficiency, supports high
connection density, and improves user fairness. However, the trade-off is
increased complexity at the receiver and sensitivity to channel uncertainty.

CDMA is known for providing better coverage and operating efficiently at low
transmit power levels. Despite these advantages, it faces challenges,
especially in the asynchronous wideband CDMA variant, which is associated with
high complexity. In addition, channel equalization in CDMA tends to be more
complex than in TDMA, and there is a need for guard time between adjacent
channels to prevent interference.

On the other hand, TDMA generally has less complex channel equalization
requirements than CDMA and does not require a frequency guard band. However,
it does require guard bands between adjacent channels to minimize crosstalk
and has a high synchronization overhead, which can be a drawback in certain
network configurations.

To this end, it should be noted that energy efficiency is also a critical
factor in the air interface design for digital twinning. The choice of access
scheme has a significant impact on the energy consumption of the network,
which affects both the cost of ownership and the environmental footprint of
the system.

##  VII Conclusion

In this work, the role of NGMA in communication and computation has been
explored, focusing on two main objectives: IRCE and IRDCE. Although both
objectives aim to use communication and computing resources more effectively,
they measure success differently. IRCE focuses on meeting communication
quality requirements, including factors such as efficiency, speed, reliability
and connectivity. IRDCE, on the other hand, looks at achieving computing
goals, such as processing more data either locally or at the edge of the
network, or reducing errors in data analysis.

We first examined MEC, which is key to meeting the growing need for data
processing and computing power close to the user, and also discussed network
slicing. We then explored OTA computing, which is promising for the rapid
processing of various functions, particularly useful for immediate computing
needs. We also discussed semantic communications, which aims to make
communication systems more efficient by focusing on sending meaningful
information and reducing unnecessary data. We also looked at how ML interacts
with multiple access technologies, highlighting the importance of FL, FD, SL,
RL, and ML-based protocol design for multiple access. Finally, we discussed
digital twinning and its use in network management, showing how creating
virtual models of physical networks can help make networks more efficient and
reliable.

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