[acronym]long-short

# Raptor-IRSA Grant-free Random Access Protocol for Smart Grids Applications

Angel Esteban Labrador Rivas, Taufik Abrão
This work was partly supported by the National Council for Scientific and
Technological Development (CNPq) of Brazil under Grants 310681/2019-7, and in
part by the CAPES (Financial code 001), and by State University of Londrina
(UEL), PR, Brazil.A. E. L. Rivas and T. Abrão are with the Electrical
Engineering Department, State University of Londrina, PR, Brazil. Rod. Celso
Garcia Cid - PR445, s/n, Campus Universitário, Po.Box 10.011. CEP: 86057-970.
E-mail<EMAIL_ADDRESS><EMAIL_ADDRESS>
###### Abstract

This paper deals with the reliability of random access (RA) protocols for
massive wireless smart grid communication (m-SGC). We propose and analyze an
improved grant-free RA (GF-RA) protocol for critical SG applications under
strict QoS m-SGC requirements. At first, we discuss the main features of the
SG neighborhood area network (NAN) architecture. We explore the main features
of low-rate machine-type wireless networks, and also we describe a technology
characterization of wireless neighborhood area networks (WNAN) in medium-range
coverage applications. We propose a new-improved irregular repetition slotted
ALOHA, combing Raptor codes and irregular ALOHA, namely RapIRSA random access
protocol, to better respond to critical high-reliability QoS requirements
under a 5G network perspective. Then, we compare and comprehensively analyze
the proposed RapIRSA protocol with two existing RA protocols, the IRSA
protocol, and the classical Slotted Aloha. Finally, We summarize the potential
challenges in implementing the proposed RA protocol for SG critical
applications considering many smart sensors (SS).

###### Index Terms:

Smart grid; Random Access Protocols; Massive MTC; Quality of Service; Raptor
codes.

##  I Introduction

Most of the modern Smart Grids (SG) Quality of Service (QoS) models arrange a
mapping method with an electrical-telecommunication design. The industry
application experience and electrical engineering decisions rarely foresaw SG
service requirements.

Wireless communications represent a challenge to SG implementation as many
mission-critical applications require real-time data transfer. Maintaining
delay and reliability SG requirements over wireless shared network disputes
with the possibility to extend the number of sensor devices in a wireless
network [1]. Also, wireless communications bring several security concerns for
SG; authors in [1] explore techniques to improve the robustness of wireless
mesh networks for mission-critical applications. As SG states as a cyber-
physical grid with Internet-of-things (IoT) and 5G data acquisition
integration multiple access emerges as trending research [2].

A grant-based (GB) scheduling operation guarantees that a user has restricted
resources to the wireless channel, consequently circumventing unspecified
collisions and increasing latency and communication overhead [3]. On the other
hand, grant-free (GF) based Random Access (RA) protocols represent a solution
to decrease the access latency [4]. GF-based protocols use transmission over
shared resources if multiple neighboring users transmit simultaneously.
Oversharing creates potential collisions that jeopardize transmission
reliability. Currently, academic research and standardization commissions have
proposed approaches to enhance the backed traffic loading with GF RA schemes
while guaranteeing high reliability and low latency [5].

Several ALOHA-like schemes use successive interference cancellation (SIC)
techniques to resolve multiple collided packets [6, 7, 8]. A certain number of
time-slots compose the slotted-ALOHA (S-ALOHA) temporal frame where the user
transmits a predefined number of times. Irregular repetition slotted ALOHA
(IRSA) optimizes the probability mass function to maximize the peak throughput
performance. IRSA performance results better than S-ALOHA and contention
resolution diversity slotted ALOHA (CRDSA) [6, 9, 10, 11]. Furthermore, the
number of time-slot adjustments relies on the base station (BS) tasks since
transmission reaches the nominal throughput. Thus, a proper time-frame length
avoids decay in the throughput performance.

###  I-A Related Works

Recent literature addressing joint issues involving the problem of data
collision, access delay, and/or power consumption in random access (RA)
Internet of things (IoT) have been arising [12], [13], [14], and[15]. E.g., a
random access scheme for large-scale micro-power wireless IoT sensors based on
slot-scheduling and hybrid mode has been proposed recently in [12]. This
scheme is based on different time-slot structures, applying a specific slot-
scheduling procedure according to network workload and power consumption.
Sensors with varying service priorities are arranged in other time slots for
competitive access using an appropriate RA mechanism. Besides, the algorithm
rationally places the number of time slots and competing devices into
different time slots. This scheme can meet the timeliness requirements of
different services and reduce the overall network power consumption when
dealing with different RA scenarios, effectively reducing the overall power
consumption. In contrast, high-priority services can meet the promptness
requirements based on lower power consumption. Raptor-coded random access
protocol to enable reliable transmission in the decentralized unmanned aerial
vehicle (UAV) network is proposed in [13]. Since the considered network is
composed of several overlapped RA interfering subsystems, the proposed Raptor-
based RA scheme can reduce the bit-error rate (BER) by implementing three
steps: i) selecting the number of time-slots based on a derived lower bound
for reliable RA operation; ii) error-correcting codes are incorporated as
precoding before RA operation; iii) by correlating two consecutive slots, an
idle-slot-filling approach is aggregated to improve the RA system efficiency
further. Numerical results reveal that the proposed 3-step strategy
substantially reduces the BER while can save a substantial number of slots
($\approx 20\%$) compared with the existing frameless ALOHA scheme to attain a
specific target BER. Several machine-type communication (MTC) random access
devices can simultaneously transmit in the same resource block by
incorporating Raptor codes, significantly reducing the access delay and
improving the achievable system throughput [15]. A simple yet efficient random
access strategy is proposed in [14], allowing both to detect the selected
preambles and to estimate the number of devices that have chosen them. No
device identification is needed in the RA phase, significantly reducing the
signaling overhead. The maximum number of supported MTC devices in a resource
block (RB) is characterized as a function of message length, available
resources, and preambles. The proposed scheme can effectively support many MTC
devices for a limited number of available resources when the message size is
small.

Differently of [12], [13], [14] and [15], in this contribution, we deal with
the challenges posed by wireless communications in the Smart Grids (SGs)
scenarios and implementation, where many mission-critical applications require
real-time data transfer. The challenge is maintaining the delay and
reliability requirements in the SG over wireless shared network disputes, with
the possibility to extend the number of sensor devices over the wireless
network [1]. To overcome this challenge, industry application experience and
engineering decision-makers must be considered in conceiving new methods under
an electrical-telecommunication design approach, not only considering the
power-energy design perspective. Moreover, wireless communications also bring
several security concerns for SG systems; for instance, authors in [1] explore
techniques to improve the robustness of wireless mesh networks for mission-
critical applications. As SG systems have been conceived as a cyber-physical
grid with IoT and 5G data acquisition integration, multiple access
communication schemes emerge as trending research inside the SG systems [2].

###  I-B Contributions

The focus of this paper is to analyze the influence of GF-RA protocols in
achieving QoS massive smart grid communication (m-SGC) requirements and
propose a RA protocol for critical SG applications considering a massive
number of Smart Sensor (SS). The main contributions of this work are
threefold:

  * i)

Elaborating on and proposing a new grant-free protocol that leverages Raptor
codes and IRSA to improve the performance of RA protocols for SG applications.
Our approach modifies the standard IRSA protocol by employing Raptor codes to
reduce the number of preamble messages and the associated overhead while
improving reliability and latency and adapting the protocol to account for
different priority levels and varying numbers of devices in the network.

  * ii)

Thoroughly characterizing the modifications required to adapt RA protocols to
existing applications and varying numbers of devices in SG applications. Our
work provides comprehensive guidance on the specific modifications required to
ensure that RA protocols can achieve optimal performance and meet the QoS
requirements of various SG applications.

  * iii)

Exploring the QoS requirements of critical SG applications, such as AMI and
load management, and characterizing the requirements of smart grid
communication (SGC) systems to provide insights into the trade-offs and
performance requirements of different RA protocols.

Overall, our proposed grant-free RA protocol, along with our detailed
characterization of the necessary modifications and QoS requirements,
represent a significant contribution to the field of SG communications and
provides valuable insights into the design of RA protocols for m-SGC networks.

The remainder of the paper is organized as follows. The m-SGC schemes and
applications are revisited in Section II. Random Access protocols suitable for
m-SGC systems are considered in Section III, while Section IV describes
important metrics deployed in the evaluation of QoS of SG systems. Section V
introduces the proposed RA protocol. Extensive numerical results are explored
in Section VI. Section VII draws the main conclusions and future trends.

##  II m-SGC Architecture and Applications

Smart grid (SG) applications have been implemented using various network
technologies such as power line communication (PLC), wireless mesh networks,
and low-power wide area networks (LPWAN) [16]. LPWAN has emerged as a popular
technology for SG and smart city applications due to its long-range
connectivity, low power consumption, and low cost [17]. LPWAN technologies
such as LoRaWAN and Sigfox are particularly well-suited for SG applications
because they can support many low-cost, low-power devices with infrequent data
transmission [18]. Moreover, LPWAN enables the communication between devices
that are located in hard-to-reach areas, such as underground or in remote
locations [19]. These benefits make LPWAN an attractive choice for SG
applications, particularly for use cases involving smart metering,
distribution automation, and demand-side management [17].

In addition, one can note that SS and SG applications typically rely on IoT
and various network technologies, including LPWAN [20, 21, 22]. These
technologies play a significant role in meeting the evolving requirements of
applications and services while providing a framework for enabling robust and
dynamic solutions. However, LPWAN is not the only technology used for SG
applications, and other network technologies such as PLC and wireless mesh
networks have also been used [16].

Smart utility network (SUN) targets multiple applications within shared
networks [23]. For a utility, this implies performing monitoring and control
over the same resources. SUN devices provide wide-long-range point-to-point
connections, including many outdoor devices. SUN aims for low-power wireless
applications that usually demand the maximum transmit power available under
proper administration. SUN application requirements demand a peer-to-peer
topology [24]. In a star topology, devices establish communications with a
single central controller, named the Neighborhood Area Network (NAN)
coordinator. In contrast, each device in a peer-to-peer network can route
messages among and through any device, making it more flexible for certain
applications.

Most of the delay allowances discussed in this work are a compilation of the
requirements specified in previous works [25, 26, 27, 28, 29]. In [30], the
authors provide a quantitative characterization of priorities for SG
applications based on these standards, recommendation documents, pragmatic
needs for utility, and Table I includes the priority of an application
relative to others. Besides, delay allowances listed in this table are end-to-
end Uplink delays.

Note that the latency requirements for SUN applications may vary depending on
the specific use case and application. For example, some applications may
require strict latency requirements to ensure proper operation, while others
may be more tolerant of delay.

TABLE I: Latency & Priority by SG application type.

Application type |  | Latency
---
(ms)
| Priority
---
0-max 100-min
Teleprotection (60 Hz, 50 Hz) | 8,10 | 10
SCADA | 10 | 20
Teleprotection | 16 | 15
Synchrophasors | 20 | 12
SCADA | 100 | 25
Distribution automation | 100 | 26
| Distributed generation -
---
distributed storage
100 | 27
MWF | 100 | 30
Business voice | 200 | 60
Dynamic Line Rating | 200 | 28
CCTV | 200 | 55
SCADA, DA, DG/DS, DLR | 200 | 45
Business data | 250 | 70
AMI | 250 | 40
Protection | 500 | 80
Many/others | 2000 | 100
This table shows only higher priority applications by application type (non-
exhaustive)

###  II-A Types of Frame in 5G Mobile networks

In smart grids, the design of wireless communication systems and protocols
faces significant challenges due to the heterogeneity of prosumers, nodes that
can consume and produce electrical power, and high reliability and latency
requirements and data rates. Defining the technical requirements for smart
grid applications, such as latency, rates, and reliability, remains an ongoing
research area. Recent studies have shown that existing wireless communication
technologies are insufficient to meet the stringent demands of a time-critical
smart grid with strict requirements on latency [31]. The typical response time
for different SG applications can be found in Table I. However, there are no
specifications on latency for many new scenarios of smart grid, such as nano-
grids111SG in resident areas that may have complex nodes such as prosumers.,
which are supposed to have even higher technical standards when connected to
main grids. In Table I, different instances of SCADA refer to different sub-
types or use cases, such as transmission SCADA, distribution SCADA, and
substation automation SCADA, each with unique latency and priority
requirements.

The 5G systems have been developed for supporting various services, such as
enhanced mobile broadband (eMBB), massive machine-type communication (mMTC),
and ultra-reliable low-latency communication (URLLC). The latter two
constitute IoT enablers. The high propagation loss in the above 3 GHz
spectrum, the limited number of UL slots in a time-division duplexing (TDD)
frame, and the limited user power strongly restrict the wireless communication
coverage. Moreover, the stringent requirements of eMBB and IoT applications
lead to 5G challenges, including site planning, ensuring seamless coverage,
adapting the TDD DL/UL slot ratio, and the frame structure for maintaining a
low BER, as well as low latency. Conflicting requirements of high-transmission
efficiency $\times$ large coverage area $\times$ low latency can be balanced
by properly exploiting the spectrum, enabling the IoT and eMBB services
support.

New Radio (NR)frame structure is specified in 3GPP specification (38.211)
[32]. 5G NR retains the concept of a 10-millisecond frame divided into ten
one-millisecond subframes. There is also a slot concept, but its definition
differs from a slot in LTE. One slot is defined as 14 OFDM symbols
corresponding to once a frame or one millisecond in LTE frame legacy. A frame
has a duration of 10 ms, which consists of 10 subframes having 1ms duration,
each similar to LTE technology. Each subframe can support time slots of
2$\mu$s duration. Each slot typically consists of 14 OFDM symbols. The radio
frame of 10 ms is transmitted continuously as per TDD topology, one after the
other. A subframe is of fixed duration i.e. 1ms, whereas slot length varies
based on subcarrier spacing and the number of slots per subframe. It is 1 ms
for 15 KHz, 500 $\mu$s for 30 KHz, and so on. Subcarrier spacing of 15 KHz
occupies 1 slot per subframe, subcarrier spacing of 30 KHz occupy 2 slots per
subframe, and so on. Each slot occupies either 14 OFDM symbols or 12 OFDM
symbols based on normal Cycle Prefix (CP) and extended CP respectively [33].

##  III RA Protocols for Required QoS in m-SGC Networks

In this section, we define suitable network scenarios for RA protocol applied
to m-SGC networks. We consider a cellular-based single-cell system with up to
$M$ total users connected to the BS, where $m(t)$ users are active at any time
occurrence $t$; or more specifically at the $k$-th time-slot, $m(\tau_{k})$.
Furthermore, a Beta or a Poisson distribution determined the distribution of
the active users $m$ (see Section III-B)..

###  III-A Aloha-based Classical RA Protocol for SG systems

Aloha-based protocols are among the RA protocols group of high-reliability and
high-throughput applications [34]. This work concentrates on extensions of the
Aloha model, holding terminals send a slotted packet over the channel as
quickly as it is produced and without performing distributed coordination
strategies.

In the sequence, we define the premises for evaluating the performance of the
implemented/developed RA protocols in terms of two metrics. The first metric,
throughput ($S$), summarizes the average amount of data blocks accomplished at
the receiver over a reference period. The second is a complementary metric,
the packet loss ratio (PLR), eq. (8).

####  III-A1 Slotted ALOHA

Fig. 1 depicts a sketch of the slotted ALOHA and the IRSA RA protocols. $n$
slots lasting $T_{F}$ seconds build a frame $F$. The total number of active
users is $m$. The MAC frame, also called Random Access Frame (RAF), of $T_{F}$
duration, is composed of $n$ slots of duration $t_{\text{s}}=T_{F}/n$. In
every MAC frame, a measurable number of users $m$ try a packet transmission in
a determined instant. Hence, in each MAC frame, each user performs a unique
transmission associated with a new packet or the retransmission of a previous
collision. Further, a MAC frame with a collision does not allow
retransmission. The last statement will generate some back-logged users.

User 1User 2User 3$\vdots$User $m$Frame, $T_{F}$ seconds, $n$ SlotsSlot,
$t_{\text{s}}$Collision

a) S-ALOHA protocol

User 1User 2User 3$\vdots$User $m$IRSA Random Access Frame (RAF) Frame,
$T_{RAF}$ seconds, $n_{RAF}$ SlotsRP 1RP 2RP 3RP 1RP 2RP 1RP 2RP 1RP
2CollisionCollisionCollision

b) IRSA protocol

Figure 1: Sketch of a) S-ALOHA; b) IRSA protocols as presented by [6]

The normalized offered traffic (or network load) follows by:

$G=\frac{m}{n}\qquad\left[\frac{\text{{\color[rgb]{0,0,0}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,0}\pgfsys@color@gray@stroke{0}\pgfsys@color@gray@fill{0}user}}}{\text{slot}}\right]$
(1)

Therefore, the normalized throughput (or channel output) $S$ is characterized
as the probability of successful packet transmission per slot, where $n$ is
the number of slots transmitted in $T_{F}$ seconds. Fig. 1.(a) presents an
S-ALOHA frame with individual packet transmission by MAC frame. Collisions
drive retransmissions in the subsequent frame. Hence, the throughput for the
S-ALOHA protocol can be defined as a function of normalized offered traffic:

$S(G)=G\cdot
e^{-G}\qquad{\color[rgb]{0,0,0}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,0}\pgfsys@color@gray@stroke{0}\pgfsys@color@gray@fill{0}\left[\frac{\text{packet}}{\text{slot}}\right]}$
(2)

where the peak throughput is attained at $S(1)=e^{-1}\approx 0.37$.

####  III-A2 The Upbound of 0.37 for Slotted ALOHA

The upbound of 0.37 for slotted ALOHA has been extensively studied in the
literature. Kennedy and Miller were the first to analyze the hidden terminal
problem in carrier sense multiple-access and propose the busy-tone solution in
1975 [35]. Daut and Shorey analyzed a random-access scheme for satellite
networks and derived the upbound in 1981 [36]. Eklund and Rahelić further
studied the multi-access performance of packet radio networks with slotted
ALOHA in 1986 [37]. More recently, Huang and van der Schaar proposed a
compressive sensing-based approach for efficient and reliable random access in
machine-to-machine communications in 2015 [38]. Le and Poor developed a
probabilistic method for medium access control in wireless networks and
derived the upbound in 2019 [39]. In recent years, several papers have focused
on analyzing throughput for massive machine-type communications [40], and
applying mean-field game theory to distributed power control in wireless
communication [41].

####  III-A3 IRSA Protocol

The IRSA protocol relies on the repetition of each packet access strategy by
MAC frame. In Fig. 1.b) each packet is transmitted $d$ times in a MAC frame.
The repetition rate $d$ ranges from packet to packet based on a statistical
distribution. Hence, we define the user sampling degree distribution by:

$\Lambda(x)=\sum_{d=1}^{d_{\text{m}}}\Lambda_{\text{d}}x^{d},\quad\text{with
}\quad\sum_{d=1}^{d_{\text{m}}}\Lambda_{\text{d}}=1$ (3)

where $0\leq\Lambda\leq 1$ and each transmitter independently sends the
replicas within the $n$ time slots composing the MAC frame. Random
transmission slots contain a maximum of $d_{\text{m}}$ replicas sent.

Each packet contains a header with an index with the location of its copy.
After receiving a packet successfully, the BS extracts the index identifying
the replica positions. When packet replicas collide, they are extracted from
the signal received in the corresponding slot removing the interference
contribution. This procedure allows decoding packets transmitted in the same
slot.

###  III-B Traffic Model, Time Arrival, and Time Instance

Machine-Type Communication (MTC) traffic patterns differ from those for Human-
to-Human (H2H) traffic. Better traffic models prompt better management of
shared network resources and guarantee QoS for many types of devices. 3GPP
proposes a simple Poisson process to model different kinds of network access
coordinated or uncoordinated machine-to-machine (M2M) traffic [42].
Consequently, different arrival rate $\lambda$ dynamically depends on the
channel and system scenarios. 5G system scenarios are compiled in [43].

3GPP Specification number 37.868 define Machine-to-machine (M2M) traffic
types, including a load analysis for Smart Meters (SM), fleet management, and
earthquake monitoring applications. The document embraces a SM service with
metering data reports, in fixed time intervals, and the load control and alarm
events occurring randomly, being modeled by Poisson processes. Table II
compiles the two traffic models.

TABLE II: 3GPP traffic models for MTC proposed in the 3GPP TR 37.868 document. Parameter | Statistical Characterization
---|---
Traffic model 1
Number of MTC devices | ${M\in\,}\\{1000,3000,5000,10000,30000\\}$
Arrival distribution |  Uniform distribution over $T_{\text{A}}=60$s
$pk_{s}$ | 200 bytes
Traffic model 2
Number of MTC devices | ${M\in\,}\\{1000,3000,5000,10000,30000\\}$
Arrival distribution |  Beta distribution over $T_{\text{A}}=10$s
$pk_{s}$ | 200 bytes

Then IRSA protocol design in [6] considers Poisson traffic, i.e., constant
mean arrival even in SS applications with a disrupted appearance. On the other
hand, the traffic model in [44] considers the Beta distribution that
implicitly requires a time-varying mean parameter, i.e., this traffic model
accounts for the non-stationarity arrivals. Hence, the arrival distribution of
the $M_{v}$ active users in SG applications can be modeled by a Poisson or
Beta distributions [44, 45] depending on the stationarity or non-stationarity
arrivals assumption. Typical but different behavior in terms of the number of
user activation is found considering Poisson and Beta distribution, Fig. 2.

Figure 2: Users arrival in a Frame $F$ with $n$ time-slots considering Poisson
$\times$ Beta distribution and $M=100$ devices.

After starting, an IRSA frame does not permit seeking users. Each late-
activated user must wait for a full-frame duration $T_{F}$. The existence of a
waiting time $T_{W}$ within two IRSA frames relies on latency limitations.
Indeed the worst-case scenario implies a user decoded following the expiration
of the IRSA frame.

Hereafter, the maximum latency
${\color[rgb]{0,0,0}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,0}\pgfsys@color@gray@stroke{0}\pgfsys@color@gray@fill{0}\Delta_{i}}$
of the user $i$ can be separated as

${\color[rgb]{0,0,0}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,0}\pgfsys@color@gray@stroke{0}\pgfsys@color@gray@fill{0}\Delta_{i}}=T_{W}+2T_{F}=T_{\text{Ac}}+T_{F}\leq{\color[rgb]{0,0,0}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,0}\pgfsys@color@gray@stroke{0}\pgfsys@color@gray@fill{0}\Delta_{0}}$
(4)

A user’s maximum latency should not exceed the latency constraint
$\Delta_{0}$. This scheme implies the accumulation of all users activated
between IRSA frames.

###  III-C Successive Interference Cancellation (SIC)

The scenarios involving M2M communications with smart sensors call for new
ideas on RA schemes. The adoption of simple SIC technique makes it feasible to
deliver throughput enhancements in RA-based communication systems [46]. Based
on the receiving and buffering MAC frame, the receiver looks for singleton
slots, meaning slots with interference-free packets.

In the context of RA protocols, a graphical model can be described as an
iterative SIC process [34], where the MAC frame standing through a bipartite
graph $\mathcal{G}=(\mathcal{U},\mathcal{S},\mathcal{E})$ composed by three
sets:

  * $\mathcal{U}$

$={\\{U_{1},U_{2},\dots,U_{m}\\}}$ of $m$ user nodes (UNs);

  * $\mathcal{S}$

$={\\{S_{1},S_{2},\dots,S_{n}\\}}$ of $n$ slot nodes (SNs);

  * $\mathcal{E}$

$=$ set of edges.

The UN $U_{i}\in\mathcal{U}$ connects to the slot number (SN)
$S_{j}\in\mathcal{S}$ by an edge $\mathcal{E}_{ij}$ conditioned to the copy of
the $i$th packet of the $i$th user is transmitted in the $j$th slot. Fig. 3
depicts the graph illustration of a MAC frame with $n=5$ slots and $m=4$ users
attempting a transmission. Notice that there is a 2-gather for users 1, 2, and
4, while user 3 packets repeat three times. One singleton slot for the
received frame. A particular slot node has degree $d$ if it is adjacent to $d$
edges; for instance, in the example of Fig. 3, $S_{1}$ has degree $d=2$, and
that $S_{2}$ has degree $d=1$.

$\mathcal{U}$$U_{4}$$U_{3}$$U_{2}$$U_{1}$$\mathcal{S}$$S_{5}$$S_{4}$$S_{3}$$S_{2}$$S_{1}$
Figure 3: Bipartite graph for a MAC frame with $n=5$ slots and $m=4$ users
attempting a transmission

To model the SIC process through a graph, some simple rules must be applied.
Iteratively, we search for SN s with degree $d=1$. Estimate $S_{i}$ to have
degree 1, and indicate by $U_{j}$ its only user node neighbor. Hence, we
exclude the edges connected to $S_{i}$ and $U_{j}$; equal to exclude the
interference addition on the packet of user $j$ in each transmitted slot. The
SIC process repeats on the up-to-date graph. Following these rules, the SIC
process applied to the example of Fig. 3 is sketched as a four canceling
iterations process represented as graph model in Fig. 4.

$\mathcal{U}$$U_{4}$$U_{3}$$U_{2}$$U_{1}$$\mathcal{S}$$S_{5}$$S_{4}$$S_{3}$$S_{2}$$S_{1}$
(a) 1st iteration: $S_{2}$ has degree 1

$\mathcal{U}$$U_{4}$$U_{3}$$U_{2}$$U_{1}$$\mathcal{S}$$S_{5}$$S_{4}$$S_{3}$$S_{2}$$S_{1}$
(b) 2nd. iteration: $S_{1}$ and $S_{4}$ have degree 1

$\mathcal{U}$$U_{4}$$U_{3}$$U_{2}$$U_{1}$$\mathcal{S}$$S_{5}$$S_{4}$$S_{3}$$S_{2}$$S_{1}$
(c) 3rd iteration: $S_{5}$ has degree 1

$\mathcal{U}$$U_{4}$$U_{3}$$U_{2}$$U_{1}$$\mathcal{S}$$S_{5}$$S_{4}$$S_{3}$$S_{2}$$S_{1}$
(d) Last Iteration: interference free

Figure 4: SIC decoding for the collision pattern of Fig. 3, tracked over the
corresponding graph; four SIC iterations are represented.

The fundamental concept of SIC is decoding users’ signal (devices)
successively. After decoding one user, its signal is reconstructed and
canceled from the total received signal before decoding the subsequent user’s
signal. In this work, we use the advantage of a singleton where at least one
device is free of interference. Hence, assuming conventional SIC application,
one of the users (strongest sinal), say $S_{1}$, is decoded treating
$S_{2},S_{3},\ldots,S_{n}$ as interference. Next, the second strongest user’
signal, $S_{2}$, is decoded by using the extracted, reconstructed, and
subtracted $S_{1}$ signal from the total received signal. The canceling
process is repeated until the last interfering signal is decoded. SIC
implementation represents an advantage compared to the conventional decoding
process, which treats all the interfering users’ signals as noise.

###  III-D Time-domain Structure

The parameters of SG system considered herein are based on the 5G NR standard
[47], [32]. Time-domain NR transmissions take place into $10$ ms length
frames. The radio frame of 10 ms has transmitted continuously as per TDD
topology. Each frame contains $10$ equally sized subframes of duration $1$ ms.
Subcarrier-Spacing (ScS) establishes the bandwidth of each frame
($BW_{\text{F}}$) and the number of slots in a subframe. With slot-based
scheduling, a slot is a minimum measure with a duration of $t_{\text{s}}$
seconds. A subframe is of fixed duration i.e. 1ms, whereas slot length varies
based on subcarrier spacing and the number of slots per subframe. It is 1 ms
for 15 KHz, 500 $\mu$s for 30 KHz, and so on. Subcarrier spacing of 15 KHz
occupies 1 slot per subframe, subcarrier spacing of 30 KHz occupy 2 slots per
subframe, and so on. Finally, this work does not use a symbol-level scheduling
technique.

##  IV Metrics and Definitions in SG QoS

###  IV-A Latency

From the power system perspective, the latency requirement depends on the
cycle of the electrical utility cycle ($T=1/f$) to keep the stable stage of a
wave. Generically, in the context of a smart grid, we define data (or message)
latency as the time between a state’s occurrence and an application’s
activation [48]. Each application has its own latency requirements depending
upon the kind of system response it is dealing with. Besides, among the other
delays, communication delay also adds to the latency and needs to be
minimized.

The total delay on the communication network comprises propagation delays,
transmission delays, queuing delays, and processing delays. Primarily, latency
($L$) represented by:

$L=\tau\,\frac{1}{f}$ (5)

where $\tau$ is the delay factor (in cycles). Real-time scale SG network
considers short/small values of $\tau$.

We define in the following the QoS metrics RA-related to SG applications: the
latency of message, Packet Delivery Rate (PDR) reliability, and critical
latency response.

####  IV-A1 Latency in SG Message

This work focuses on applications with communication latency performance as a
priority and does not accept outdated data. Thus, we define the hard delay
metric in the subsequent outlines.

######  Definition 1.

(Hard delay, HD) Application with a hard delay requirement turns useless if
its delay passes the QoS requirement even in successful message delivery.

Next, the delay requirement $\tau_{\rm req}$ includes the required network
bandwidth as:

$BW_{\rm req}=S\,\left(8\frac{\rm bits}{\rm byte}\right)\,\frac{1}{\tau_{\rm
req}}\,M\qquad\rm{[bits\cdot Hz]}$ (6)

where $S$ and $M$ are the service’s data size in bytes, and the number of
users, respectively.

###  IV-B Packet Delivery Ratio (PDR) and Packet Loss Ratio (PLR)

######  Definition 2.

Packet Delivery Ratio (PDR) represents the proportion of the total number of
packets received by the data collector unit (DCU) successfully, $P_{\rm R}$,
to the total number of packets generated by the SG source nodes, $P_{G}$:

$PDR=\frac{\sum^{M}_{i=1}P_{\text{R}_{i}}}{\sum^{M}_{i=1}P_{G_{i}}}=\frac{P_{\text{R}}}{P_{\text{G}}}$
(7)

######  Definition 3.

Packet Loss Ratio (PLR) is a matched metric to the PDR defined as the
probability for a user incorrectly decoded at the receiver after accessed the
channel. Using eq. (7) one can obtain an approximate expression for PLR:

$PLR=1-PDR=1-\frac{P_{\text{R}}}{P_{\text{G}}}$ (8)

###  IV-C Reliability

A conventional reliability definition in computer systems deliver SG network
reliability metric [49]. Network reliability counts the probability of a
system achieving its services accordingly in a specified time duration.
Accordingly, we define the reliability factor in the SG network context as:

######  Definition 4.

(Reliability, $\mathcal{R}$) The network reliability stands as the probability
of succeeding in delivering a message to the destinations node (related to the
PDR metric) within the maximum latency requirement. The reliability decreases
when the message arrives after the delay requirement. SG network reliability
under HD definition, $\tau_{\text{HD}_{\rm req}}$ can be defined as follows.

${\mathcal{R}(\tau)}=\left\\{\begin{array}[]{ll}PDR\,\,{\color[rgb]{0,0,0}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,0}\pgfsys@color@gray@stroke{0}\pgfsys@color@gray@fill{0}=1-PLR}&\tau\leq\tau_{\text{HD}_{\rm
req}}\\\ 0&\tau>\tau_{\text{HD}_{\rm req}}\end{array}\right.$ (9)

Notice that in ultra-reliable and low latency communications (URLLC), a
generic reliability requirement of $\mathcal{R}=1-10^{-5}$ (i.e., 0.99999) is
required with the user-plane radio-latency of 1 ms for a single transmission
of a 32-byte long packet.

######  Definition 5.

Application Complying Ratio (ACR). We introduce a new concept named ACR that
represents the number of users to successfully comply with the Up-Link (UL)
connection within delay requirements $\tau_{\text{HD}_{\rm req}}$. In the
context of SG applications, the ACR reliability can be defined by the sum of
ratios along the $N$ slots:

$\mathcal{R}_{\text{ACR}}=\frac{1}{N}\sum_{k=1}^{N}\frac{{\color[rgb]{0,0,0}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,0}\pgfsys@color@gray@stroke{0}\pgfsys@color@gray@fill{0}m(\tau_{k})}}{m_{k}}$
(10)

where $m_{k}$ is the number of total active users in the $k$-th time-slot, and
$m{\color[rgb]{0,0,0}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,0}\pgfsys@color@gray@stroke{0}\pgfsys@color@gray@fill{0}(\tau_{k})}$
represents the number of users that effectively sent a packet at the $k$th
time-slot $k\in\\{1,\ldots,N\\}$ within the latency requirement time, i.e.,
$\tau_{k}\leq\tau_{{\rm req}_{i}}$. Such reliability metric quantifies the
proportion of active users who succeed in sending a packet at the $k$th time-
slot within the latency requirement time along $N$ slots.

In eq. (10), the QoS metric allows to track specific application problems.
Under specific protocol applications, the ACR reliability metric quantifies
the trusted network data delivery.

##  V Proposed RA Protocol based on Raptor Codes for m-SGC Networks

In this section, we propose a new RA protocol to achieve higher throughput
under overloaded networks using additional nodes working as precoding of
Raptor codes. This Raptor code implementation uses a subclass of the bipartite
graph described in [50, 51].

Considering SG scenarios, in the sequel we describe briefly the Raptor codes,
including their characteristics, advantages, and some application environments
with the associated parameters. Then, we propose a modification in the
traditional IRSA protocol, mainly in the values of the operational parameters
and in the substructure of the protocol, depending on the application
requirements, aiming at enhancing the protocol reliability suitable for ultra-
reliable low-latency communications (URLLC) and machine-type communications
(MTC) services. We label QoS information into active users preamble. This
information adjusts the IRSA protocol to achieve QoS requirements.

###  V-A Raptor Codes

Raptor codes (RapC) are a class of forward error correction codes that can
provide reliable and efficient data transmission over unreliable communication
channels [52]. These codes were introduced by A. Shokrollahi in 2003 [51].
RapC can be used to efficiently encode and decode data packets for
transmission over noisy channels. They are based on the concept of fountain
codes and use an iterative decoding process to recover the original data.
RapC’s advantages over traditional error correction codes include bandwidth
efficiency, higher reliability, and less decoding complexity. RapC can also
adapt to different channel conditions and can handle varying levels of noise
and interference. Raptor codes have been widely used in various communication
systems, including wireless networks, multimedia transmission, and satellite
communications. In 5G mobile networks, Raptor codes are used in the control
plane and user plane to improve reliability and reduce latency [53].

The key parameters involved in RapC include the degree distribution, symbol
size, and encoding rate. The degree distribution determines the distribution
of probability for the number of times each symbol appears in the code word.
The symbol size refers to the size of the symbols in the code word. The
encoding rate determines the ratio of the output code length to the input
message length. The encoding process of Raptor codes is based on a Fountain
code, which generates a potentially infinite number of encoded packets from a
source packet [54]. A decoder can recover the original message from a subset
of these encoded packets. The repetition rate of Raptor code, i.e., the number
of times a message is encoded into the code is denoted by $\eta$. Raptor codes
have been used in various application environments, including satellite and
wireless networks [55, 56]. In the RapIRSA protocol, the number of connecting
nodes ($c\mathcal{N}$) used is denoted by $q$ [57].

Overall, Raptor codes are a powerful tool for providing reliable and efficient
data transmission in various communication systems and channel scenarios.
Their adaptability, high reliability, and low decoding complexity make them an
attractive option for 5G mobile networks and beyond.

###  V-B Combining Raptor Codes and IRSA (RapIRSA)

We consider $m$ active users sending packets to BS or DCU. Some users will
send packets via connecting nodes ($c\mathcal{N}$). All $c\mathcal{N}$ are
placed equitably reaching many possible directly visible users. Each
$c\mathcal{N}$ uses the Decode-and-Forward (DF) protocol to deliver the
information to the BS. $c\mathcal{N}$ has less probability of packet
collisions compared to BS because $c\mathcal{N}$ only received packets of data
from connected users.

Fig. 5 illustrates the Raptor codes-structured (RapC) wireless networks. This
follows a bipartite graph model illustrated in Fig. 3. Besides, $c\mathcal{N}$
represented by dark circles in a separated time slot; $m$ represents the
number of active users, $n_{\rm RapC}$ is the number of slot nodes (SN) in the
frame, and $q=\lfloor\eta\cdot n_{\rm RAF}\rfloor$ is the number of
$c\mathcal{N}$. Besides, $n_{\rm RapC}$ contains two elements, as
$n_{\textsc{raf}}$ for SN of RAF, and $n_{q}$ for SN of $c\mathcal{N}$s.
Hence, the total SN is defined as:

$\displaystyle n_{\rm RapC}$ $\displaystyle=n_{\textsc{raf}}+n_{q}$ (11)

Besides, the normalized offered traffic $G$ for the RapIRSA follows the
definition in Eq. (1).

$U_{5}$$U_{4}$$U_{3}$$U_{2}$$U_{1}$$\mathcal{U}$$U_{5}$$U_{4}$$U_{3}$$U_{2}$$U_{1}$$\mathcal{S}$$S_{5}$$S_{4}$$S_{3}$$S_{2}$$S_{1}$$c\mathcal{N}$$c\mathcal{N}_{2}$$c\mathcal{N}_{1}$$n_{2}$$n_{1}$$\mathcal{S_{\text{c}\mathcal{N}}}$$S_{c\mathcal{N}_{2}}$$S_{c\mathcal{N}_{1}}$
Figure 5: Raptor codes-structured wireless networks. RapIRSA$(\eta,q)$
parameters: $\eta=\frac{1}{7}$ and $q=2$.

In the example of Fig. 5, five users
$\mathcal{U}={\\{U_{1},U_{2},\ldots,{U_{5}}\\}}$ and two
$c\mathcal{N}=\\{c\mathcal{N}_{1},c\mathcal{N}_{2}\\}$ have been considered.
Connecting nodes $c\mathcal{N}$ do not have prior information about users’
messages. After receiving data from neighboring devices they decode-and-
forward (DF) the messages to the BS for final processing. $c\mathcal{N}_{1}$
decodes one packet from $U_{1}$ and $U_{5}$, and then forward the first
decoded packet to the BS. Likewise, $c\mathcal{N}_{2}$ receives packets from
$U_{2}$ and $U_{3}$, it decodes one packet, and then forwards the decoded
packets to BS. Fig. 5 represents RapC with $\eta=\frac{1}{7}$ and $q=2$, i.e.,
the parameters RapIRSA$(\eta,q)$ stand for the fraction of the number of IRSA
random access frame222Namely repetition rate of Raptor code. (RAF) length and
the number of connecting nodes ($c\mathcal{N}$), respectively.

In the Raptor codes-based RapIRSA scheme, $c\mathcal{N}_{1}$ and
$c\mathcal{N}_{2}$ do not have prior information about the messages
transmitted by users. They receive packets from neighboring devices and decode
and forward (DF) them to the BS for final processing. In the case of
collisions, the RapC enable them to decode as much information as possible
from the received packets, even if the packets are partially corrupted due to
collisions. Moreover, efficient decoding algorithms such as belief propagation
or message passing can be used at the connecting nodes to mitigate the effect
of collisions and improve decoding performance. Recent research has shown the
effectiveness of such algorithms in dealing with collisions in various
wireless communication scenarios [58, 59].

####  V-B1 Practicability

The proposed RapIRSA scheme requires each random access node to transmit its
packet to three nodes (BS, $c\mathcal{N}_{1}$, and $c\mathcal{N}_{2}$).
However, we believe that the proposed method is practical in real-world
wireless network scenarios. The transmission scheme used in RapIRSA is similar
to that used in other existing schemes such as CRDSA, which has been shown to
be practical and effective in different network scenarios [60, 61].
Furthermore, RapC used in our proposed scheme has been shown to improve
reliability and reduce overhead in several other contexts of application [51,
62]. Moreover, our proposed RapIRSA scheme is designed to be scalable and
flexible to accommodate different numbers of users and connecting nodes.
Efficient algorithms such as belief propagation or message passing can be used
for the decoding process at the connecting nodes [63]. Therefore, we believe
that our proposed RapIRSA scheme is practical and can be implemented in
various real-world scenarios.

Fig. 6 depicts the time-slot structure including the RAF implemented in the
IRSA protocol and the slots with information from the $c\mathcal{N}$s. BS uses
pre-coding through $c\mathcal{N}$s to detect failing nodes during the
contention period. As discussed in the numerical results, Section VI, the
Combining Raptor Codes and IRSA (RapIRSA)protocol is able to improve
throughput performance substantially under high network load configurations,
i.e., $G>0.6$.

User 1$\boldsymbol{\vdots}$User $m$$c\mathcal{N}$
1$\boldsymbol{\vdots}$$c\mathcal{N}$ $q$$T_{RAF}$ [s], $n_{RAF}$
[Slots]$T_{q}$ [s], $n_{q}$ [Slots]RP 1RP $d_{1}$RP 1RP
$d_{\text{m}}$$\boldsymbol{\dots}$$\boldsymbol{\ddots}$$\boldsymbol{\dots}$$\boldsymbol{\dots}$$\boldsymbol{\ddots}$$\boldsymbol{\dots}$$S_{c\mathcal{N}_{1}}$$\boldsymbol{\ddots}$$\boldsymbol{\dots}$$S_{c\mathcal{N}_{q}}$
Figure 6: Overview of RapIRSA time-slots structure.

The pseudo-code for the adopted graph-based decoding algorithm is described in
the Algorithm 1. Moreover, Fig. 7 depicts an additional graph from BS
$\mathcal{G}_{\text{BS}}$ and two $c\mathcal{N}$s
($\mathcal{G}_{c\mathcal{N}_{1}}$ and $\mathcal{G}_{c\mathcal{N}_{2}}$) seen
by DCU.

Data: Connected bipartite graphs $\mathcal{G}_{\text{BS}}$ and
$\mathcal{G}_{c\mathcal{N}_{j}}$.

Result: Information $m$ decoded.

for  _$j=1$ until $q$_ do

Loop Passive Nodes $\mathcal{G}_{c\mathcal{N}_{j}}$: Analyze
$\mathcal{G}_{c\mathcal{N}_{j}}$ and access user $U_{i}$ connected to a slot
node having degree $d=1$; if  _degree $d=1$_ then

Obtain information of $U_{i}$ ;

Deduct the collected signals in all slot nodes correlated to user $U_{i}$ with
user $U_{i}$’s information at graph $\mathcal{G}_{c\mathcal{N}_{j}}$ ;

Send information of $U_{i}$ via $S_{c\mathcal{N}_{j}}$ and deduct all slot
nodes correlated to user $U_{i}$ at graph $\mathcal{G}_{\text{BS}}$;

end if

end for

Loop BS $\mathcal{G}_{\text{BS}}$: Implement SIC decoding algorithm as
describe in Section III-C;

Algorithm 1 Network Decoding with RapC

$\mathcal{U}$$U_{5}$$U_{1}$$\mathcal{S}$$S_{5}$$S_{4}$$S_{3}$$S_{2}$$S_{1}$
(a) Graph view from $c\mathcal{N}_{1}$

$\mathcal{U}$$U_{3}$$U_{2}$$\mathcal{S}$$S_{5}$$S_{4}$$S_{3}$$S_{2}$$S_{1}$
(b) Graph view from $c\mathcal{N}_{2}$

$\mathcal{U}$$U_{5}$$U_{4}$$U_{3}$$U_{2}$$U_{1}$$\mathcal{S}$$S_{5}$$S_{4}$$S_{3}$$S_{2}$$S_{1}$
(c) Graph view from BS

Figure 7: Bipartite graphs-based message decoding received from the main links
$\mathcal{G}_{M}$, connecting node $c\mathcal{N}_{1}$, and $c\mathcal{N}_{2}$.

SP-IRSA & SP-RapIRSA. Service Priority-based Irregular Repetition Slotted
ALOHA (SP-IRSA) and Service Priority-based Raptor Code Irregular Repetition
Slotted ALOHA (SP-RapIRSA) protocols employ additional preamble information to
denote the number of packets in the channel, thus the high priority services
have higher repetition probability. Such approach based on service priority
does not consider the access probabilities adjusted according to the traffic
load as Irregular Repetition Slotted ALOHA with Priority (P-IRSA) [64], which
requires a further access controller. SP-IRSA protocol arranges $m$ users into
$P_{L}$ different priority levels based on service-defined priority. Each user
carrier services ID to determine whether repetition rate changes according to
priority. The categorical priority level vector $\boldsymbol{p}_{L}$ increases
(or decreases) the repetition probability of $\Lambda_{\text{d}}$. With a
finite number of SG applications, the level $P_{L}$ of each service modifies
the maximum of $d_{\text{m}}$ replicas a user $m$ could send. Consequently, a
user with a higher-level priority sends more replicas of its packet.

SP-S-ALOHA. Following the SP-IRSA description, we have implemented the same
Service Priority-based on the S-ALOHA algorithm, namely SP-S-ALOHA. In this
case, the service priority modifies the backoff maximum value in the user
connection. Whether if the backlogged active users no comply in the attempt,
the QoS system counts as an error, i.e., in the worst-case scenario where
backoff value is close to the maximum service priority, the user only will
have an attempt to complete the uplink connection.

##  VI Numerical Results

In this section, we present the simulation results of the proposed service
priority RA algorithms based on S-ALOHA, IRSA, and RapIRSA protocols. The
simulation process directly follows the SG RA protocols revisited in Section
III, as well as the proposed RA algorithms for m-SGC networks described in
Section V. All the simulations use the Matlab and Julia programming languages.
The main parameter values adopted in numerical simulations are summarized in
Table III. We consider a future AMI scenario of SG networks, an urban area
with up to $10^{6}$ SM uniformly distributed in a $1\times 1$ km service area.
The coordinator node is center-located, and the $c\mathcal{N}$s, corresponding
to the RapIRSA protocols are located to access as many as possible different
devices.

TABLE III: Simulation Parameters Parameter |  Value
---|---
Service Area |  $A=1\text{km}^{2}$
# Active users, $m$ |  Up to $M=10^{6}$ devices
Network Load |  $G=\frac{m}{n}\in\,\,]0;\,1.2]\,\,\,\left[\frac{\text{user}}{\text{slot}}\right]$
Active Users distribution |  Poisson & Beta
Time-slot duration |  $1$ ms
IRSA RAF Length |  $n_{{\textsc{raf}}}=50$ slots
# Replicas (Max.) |  $d_{\text{m}}=8$
Degree distribution |  $\Lambda_{8}(x)=0.5x^{2}+0.28x^{3}+0.22x^{8}$
# SIC iterations (Max.) |  ${\mathcal{I}=}\,20$
S-ALOHA Back-off limit |  $B_{\rm off}=50$ slots
number of $c\mathcal{N}$ |  $q=[2\quad 3\quad 8]$
fraction of $n_{{\rm RapC}}$ |  $\eta=0.25$
# SP $m$ Users |  Up to $M=10^{4}$ devices
Priority Level |  $\boldsymbol{p}_{L}=[0\text{(max)}\quad 100\text{(min)}]$
# MCS Realizations |  $100$
Simulation time |  $10$ s

Fig. 8 depicts the throughput for S-ALOHA (SA), IRSA, RapIRSA$(0.25,8)$, and
RapIRSA$(0.25,2)$ implementations for two different users’ arrival
distributions. This simulation includes the theoretical throughput for S-ALOHA
algorithm considering the Poisson distribution and an asymptotic
($n_{\textsc{raf}}\rightarrow\infty$) representation of the IRSA protocol.
Note that RapIRSA improved throughput not only for $G>1$ but its performance
is also comparable with the asymptotic IRSA with the Poisson distribution.
It’s worth mentioning, RapIRSA for $G>1.4$ present a better throughput under
traffic governed by a Beta distribution. In our specific scenario, this
finding represents a breakthrough to determine that the RapIRSA protocol
attains better performance operating under overloaded networks.

Figure 8: Simulated throughput for SA, and for IRSA and RapIRSA with
$\Lambda_{8}(x)$.

Accordingly, Fig. 9 depicts the packet loss ratio versus the network load.
Under low and moderate-to-high network loading condition, i.e., $0<G<1.2$
(Poisson distribution) and $0<G<0.6$ (Beta distribution), those values
indicate a considerable advantage from IRSA and RapIRSA over S-ALOHA protocol,
considering both arrival distributions. $\Lambda_{8}(x)$ is a commonly used
degree distribution in the literature for modeling various types of networks,
including communication networks and power grids. It is a power law
distribution, which means that it has a heavy tail that captures the presence
of a small number of highly connected nodes in the network. This makes it a
suitable choice for modeling networks with heterogeneous connectivity
patterns, such as smart grid networks. Moreover, the choice of
$\Lambda_{8}(x)$ is consistent with previous work on modeling smart grid
networks, which has also used power law degree distributions [65, 66].

Figure 9: Packet loss ratio for SA, and for IRSA with
$\Lambda_{8}=0.5x^{2}+0.28x^{3}+0.22x^{8}$.

###  VI-A Latency

When we first introduced Fig. 6 the extra slots $n_{q}$ for each frame in the
RapIRSA protocol, it creates concern about increasing latency. As delay
constraints are fundamental to achieve QoS requirements, an additional
evaluation of these parameters is presented in Fig. 10 to chart those values
within IRSA and SA protocols. Fig. 10 shows that the average delay [slots]
(red curves) and the associated average delay [slots/active users] (blue
curves), for all investigated algorithms. Hence, as network loading increases,
S-ALOHA maintains a steadily increasing behavior, resulting in high delays
(over $10^{5}$ slots) over high network loading ranging from $1<G<2$.
Moreover, the IRSA protocol presents a remarkable performance without delay
for low-medium network loading ($G<0.5$). Furthermore, RapIRSA keeps an almost
constant operation point for all network loading. Even for measurement of the
average delay (slots) per active users in Fig. 10 (right y-axis), the delays
of the S-ALOHA protocol appear unfeasible under requirements described in
Table I for many of the SG applications. Table I scales priority in SG
application type based on maximum tolerable latency.

Figure 10: Average delay in terms of # slots (left y-axis) and # slots per
average # active users (right y-axis) vs Network loading.

###  VI-B Application Complying Ratio (ACR) Reliability

Fig. 11 compares the percentage of ACR reliability to evaluate the RA
algorithm capability in achieving a certain QoS requirement. Under such
specific reliability metric, and the modifications in the IRSA protocol
introduced in Sec. V, which are based on Raptor codes deployment and service
priority, the QoS information was labeled into the active user’s preamble. The
ACR reliability metric is evaluated with up to $10^{4}$ devices; all SP RA
protocols discussed in this work use the $\boldsymbol{p}_{L}$ values described
in Table I. The ACR reliability curves in Fig. 11 corroborate the viability of
the proposed RapIRSA and SP-RapIRSA algorithms to improve RA protocols
performance, as well as, reach QoS requirements, described as one of the main
objectives of the proposed work. Both RapIRSA variants, SP-RapIRSA and
RapIRSA, provide the best ACR values across the entire networking loading
range. Moreover, Fig. 11 reveals that the critical scenario of $90\%$ ACR
reliability ($\mathcal{R}_{\text{ACR}}=0.9$), is attained for different
network loading, depending of which RA protocol is adopted; the best
performance is achieved by the SP-RapIRSA for a network loading of $G=0.2$,
followed by the RapIRSA protocol. The ACR reliability metric reveals the
crucial trade-off between a delivered packet within the latency constraints.
Notice that promising RA protocols for m-SGC applications require considering
carefully the ACR reliability constraint.

Figure 11: Application complying rate (%) to measure algorithm capability to
achieve QoS requirement.

Combining the superior ACR performance depicted in Fig. 11 with the reduced
packet loss ratio (Fig. 9), balanced delay vs. network load in Fig. 10, and
suitable throughput (Fig. 8) attained by the RapIRSA protocol, one can infer
that among the three GF RA protocols analyzed, the RapIRSA is promising and
the most feasible protocol for SG applications. Even with the addition of
extra slots for the $c\mathcal{N}$ delays, RapIRSA can comply with tied
throughput, PLR, and latency performance requirements in the current SG
networks.

###  VI-C Computational Load and Memory Requirements

The computational load and memory requirements imposed by the proposed RA
algorithms are evaluated by simulations performed on a workstation with an
Intel Core i7-10700K CPU, 3.70GHz, and 16GB of RAM. Table IV summarizes the
computational load in terms of the average processing time per packet and
memory requirements of the RA algorithms. The processing time was measured for
the analyzed RA algorithms based on S-ALOHA, IRSA, and RapIRSA protocols,
respectively. The computational load of the proposed RA algorithms based on
IRSA and RapIRSA protocols is substantially higher than the S-ALOHA protocol.
Specifically, the RapIRSA presents a higher computational load than IRSA due
to the additional processing time required for the encoding and decoding
process of Raptor codes. However, the difference in processing time is
negligible for a single packet. The memory requirement of the proposed RA
algorithms is also presented in Table IV. As expected, the memory requirement
of the RapIRSA protocol is higher than IRSA ($2\times$) and S-ALOHA
($20\times$) due to the additional storage requirement for encoded packets.

TABLE IV: Computational Load and Memory Requirements of RA Algorithms. RA Algorithm | Avg. Processing Time/Packet (ms) | Memory Requirement (KB)
---|---|---
S-ALOHA | 0.1 | 1
IRSA | 0.5 | 10
RapIRSA | 0.6 | 20

Overall, the proposed IRSA and RapIRSA RA algorithms require higher
computational load and memory compared to the S-ALOHA protocol. However,
considering the higher reliability and lower packet loss rate achieved by the
proposed RA algorithms, the additional computational load and memory
requirement can be justified, both attaining improvements in the performance-
complexity trade-off. Finally, the computational load and memory requirement
of both RA protocols can be further optimized by employing efficient encoding
and decoding techniques for Raptor codes.

##  VII Conclusions

We propose a service priority RA protocol for SG communication network
applications. The proposed algorithm is based on the S-ALOHA and IRSA RA
protocols with adapting parameters considering the QoS requirements as
priority, latency, and data rates metrics. The proposed protocol aims to
enhance the probability of success of various SG applications.

The RapIRSA protocol is proposed in this paper to guarantee better throughput
of active users with the help of connecting nodes ($c\mathcal{N}$). We have
shown that relative to SA and IRSA in particular for multipacket messages, the
RapIRSA can increase the reliability and keep the throughput above all others.
The RapIRSA is better than SA and IRSA, indicating this protocol is suitable
for SG applications.

The investigation of adapting IRSA & RapIRSA for smart sensors’ future
applications can be guided by the following issues and findings: a) such
protocols reach their peak performance without latency constraints; b) they
rely on reliability constraints rather than latency constraints; c) latency
constraints on IRSA & RapIRSA depend on the limit of the frame size;
nevertheless, a decreasing frame size supports fewer users, rejecting some
users from the system; d) IRSA & RapIRSA represent acceptable solutions for
many critical applications.

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