# Adaptive RRI Selection Algorithms for Improved Cooperative Awareness in
Decentralized NR-V2X

Avik Dayal1, Vijay K. Shah2, Harpreet S. Dhillon3, and Jeffrey H. Reed3
1 Johns Hopkins University Applied Physics Laboratory, Laurel, MD 20723, USA
2 Cybersecurity Engineering Department, George Mason University, VA, USA
3Wireless@VT, Bradley Department of ECE, Virginia Tech, VA, USA
<EMAIL_ADDRESS>{hdhillon<EMAIL_ADDRESS>and<EMAIL_ADDRESS>An
earlier version of this paper was presented in part at the 2021 IFIP
Networking Conference [1]. A preliminary version of this work appears as a
chapter in Avik Dayal’s Ph.D. Thesis [2].This research is supported by the
Office of Naval Research (ONR) under MURI Grant N00014-19-1-2621.

(June 2020)

###### Abstract

Decentralized vehicle-to-everything (V2X) networks (i.e., C-V2X Mode-4 and
NR-V2X Mode-2) utilize sensing-based semi-persistent scheduling (SPS) where
vehicles sense and reserve suitable radio resources for Basic Safety Message
(BSM) transmissions at prespecified periodic intervals termed as Resource
Reservation Interval (RRI). Vehicles rely on these received periodic BSMs to
localize nearby (transmitting) vehicles and infrastructure, referred to as
cooperative awareness. Cooperative awareness enables line of sight and non-
line of sight localization, extending a vehicle’s sensing and perception
range. In this work, we first show that under high vehicle density scenarios,
existing SPS (with prespecified RRIs) suffer from poor cooperative awareness,
quantified as tracking error. Tracking error is defined as the difference
between a vehicle’s true and estimated location as measured by its neighbors.
To address the issues of static RRI SPS and improve cooperative awareness, we
propose two novel RRI selection algorithms – namely, Channel-aware RRI (Ch-
RRI) selection and Age of Information (AoI)-aware RRI (AoI-RRI) selection. Ch-
RRI dynamically selects an RRI based on channel resource availability
depending upon the (sparse or dense) vehicle densities, whereas AoI-RRI
utilizes a novel information freshness metric, called Age of Information (AoI)
to select a suitable RRI. Both adaptive RRI algorithms use SPS for selecting
transmission opportunities for timely BSM transmissions at the chosen RRI.
System-level simulations demonstrate that both proposed schemes outperform the
SPS with fixed RRI in terms of improved cooperative awareness. Furthermore,
AoI-RRI SPS outperforms Ch-RRI SPS in high densities, whereas Ch-RRI SPS is
slightly better than AoI-RRI SPS in low densities.

###### Index Terms:

NR-V2X, NR-V2X Mode-2, Age-of-Information, Dynamic Spectrum Access, Radio
Resource Management

##  I Introduction

Modern vehicles have been equipped with a plethora of sensors to assist with
autonomous capabilities [3]. The drawback is that most sensors, including
cameras, radars, and LIDAR, are limited to line of sight (LOS) visibility and
are constrained in their scope [4]. This LOS constraint is a major motivation
for the development of Vehicle-to-Everything (V2X) communications. V2X
communications enables both LOS and NLOS exchange of sensor data with
neighboring vehicles, thereby increasing the range of a vehicle’s awareness of
surrounding vehicles and infrastructure [5].

The Third Generation Partnership Project (3GPP) Release 16 has introduced a
V2X communications technology that uses the 5G New Radio (NR) air interface,
referred to as 5G NR-V2X. NR-V2X includes enhancements to the 3GPP’s previous
cellular V2X communications technology (C-V2X) based on the Long-Term
Evolution (LTE) standard. NR-V2X offers two modes of operation, termed Mode-1
and Mode-2, that use sidelink communications, which is direct communication
between users or vehicles without data passing through the gNodeB [6]. NR-V2X
Mode-1 employs a centralized scheduling approach, where a gNodeB schedules and
assigns sidelink radio resources for two or more vehicles to communicate and
exchange data directly. NR-V2X Mode-2 assumes communications to occur outside
the coverage of an gNodeB; therefore, every vehicle uses a sensing-based semi-
persistent scheduling (SPS) protocol to sense and reserve sidelink radio
resources. SPS was introduced as part of the Release 14 C-V2X Mode-4 standard,
the predecessor to NR-V2X Mode-2 [7]. Since cellular connectivity can not be
assumed ubiquitous, NR-V2X Mode-2 is considered as the baseline mode for
NR-V2X.

In NR-V2X Mode-2 SPS, vehicles sense and select suitable (available) radio
resources to transmit packets at predefined fixed time intervals, termed,
Resource Reservation Interval (RRI). Equivalently, RRI is defined as the
inter-transmission time interval between two consecutive transmissions. In the
Release 14 C-V2X standard, RRIs equal to or below $100$ ms were restricted to
$20$ ms, $50$ ms, or $100$ ms [8]. Release 16 NR-V2X Mode-2 provides more
flexibility by allowing any integer RRI between $1$ and $99$ ms for any RRIs
below $100$ ms [9].

The primary use case for NR-V2X Mode-2 SPS is the dissemination of basic
safety messages (BSMs), which carry time-sensitive state information such as a
transmitting vehicle’s speed, heading, and location [10]. Receiving vehicles
can use these BSMs for cooperative awareness, including the localization and
trajectory prediction of neighboring vehicles and infrastructure. Cooperative
awareness can enable safety-critical applications such as forward collision
warnings [11], blind spot/lane change warnings [12], and is likely one of the
key requirements for autonomous driving [13]. One metric that can quantify
cooperative awareness performance is tracking error, the difference between a
vehicle’s actual and estimate location (via most recent BSM) by its
neighboring vehicles. Tracking error, as opposed to conventional communication
metrics such as packet delivery ratio (PDR) and throughput, captures the
impact of multiple lost or outdated BSMs on a vehicle’s awareness and is thus
a more appropriate performance measure for this application.

Since BSMs carry time-sensitive information, outdated BSMs (due to large RRIs)
and/or lost BSMs (due to channel congestion) negatively impact the performance
of cooperative awareness applications, mainly due to erroneous localization of
neighboring vehicles. Therefore, it is critical that the state information in
each vehicles transmission be fresh, as stale information can compromise the
aggregate awareness of the vehicular network. The freshness of information at
receiving vehicles can be measured using Age-of-Information (AoI). AoI is the
time elapsed since new state information has been generated and is a promising
metric to measure the freshness of system state information. Results in [14]
have found that AoI has a strong correlation with tracking error in vehicular
networks, which motivates further study of AoI.

In this work, we explore the deficiencies of the NR-V2X Mode-2 SPS using
static RRIs in terms of tracking error and propose algorithms that choose
adaptive RRIs to improve the overall cooperative awareness performance of
NR-V2X Mode-2. We show in this paper that SPS with static RRIs (e.g. $50$ and
$100$ ms) has cooperative awareness limitations in NR-V2X networks. Consider
these scenarios: (i) high vehicle density scenarios – the NR-V2X network
performance suffers from congestion with a large number of lost packets,
leading to an increased tracking error, and (ii) low vehicle density – the
spectrum resources would be under-utilized in time. The tracking error
performance in low density scenarios can improve with a smaller RRI, which
ensures frequent location updates without fear of channel congestion. We
introduce two adaptive RRI algorithms, termed Channel-aware RRI (Ch-RRI)
selection and AoI-aware RRI (AoI-RRI) selection. Ch-RRI uses channel occupancy
measurements to find the smallest RRI possible without increasing congestion.
Motivated by the benefits of reducing AoI, we propose AoI-RRI, an AoI-aware
RRI selection algorithm for NR-V2X Mode-2 that uses the average AoI observed
by neighboring vehicles to select an optimal RRI.

In this work, we make following key contributions:

  * •

We show that NR-V2X Mode-2 SPS with static RRIs suffers severely from under-
and over-provisioning of radio resources (depending upon the vehicle
densities). This in turn negatively impacts the timely successful delivery of
BSMs and compromises the cooperative awareness of NR-V2X Mode-2 SPS.

  * •

To address the limitations of SPS with static RRIs, we propose Ch-RRI SPS,
which is SPS powered by a channel aware RRI selection algorithm. The Ch-RRI
algorithm uses channel occupancy measurements and chooses the minimum possible
RRI spacing between transmissions without increasing packet loss due to
congestion. Ch-RRI SPS uses this RRI spacing to select radio resources for BSM
transmissions.

  * •

In a similar vein to Ch-RRI SPS, we develop AoI-RRI SPS, SPS powered by a AoI
aware RRI selection algorithm. The AoI-RRI algorithm uses neighborhood age and
channel resource measurements to choose an age optimal RRI iteratively.

  * •

Experiments developed on our NR-V2X simulator show that when compared to
NR-V2X Mode-2 SPS with $20$ ms, $50$ ms, and $100$ ms RRI, the proposed Ch-RRI
and AoI-RRI SPS demonstrate a substantial reduction of tracking error. Ch-RRI
as compared to AoI-RRI shows a lower AoI and tracking error in low density
highway scenarios, and is faster in converging to a local minimum AoI.
However, the average AoI and tracking error of AoI-RRI is lower at higher
densities.

The organization of this paper is as follows: Section II discusses related
works. Section III discusses cooperative awareness, the tracking error metric,
and the NR-V2X Mode-2 standard. In Section IV we illustrate the limitations of
traditional fixed RRI SPS and present the algorithmic details of Ch-RRI SPS.
Section V provides a brief description of AoI, and discusses the details of
AoI-RRI SPS. Finally, Section VI discusses the results and provides an outlook
for future work, followed by concluding remarks in Section VII.

##  II State-of-the-art

There has been a surge of research in the area of simulating and enhancing SPS
for C-V2X Mode-4 [8, 15, 16, 17, 18, 19, 20, 21, 22] and more recently, for
NR-V2X Mode-2 SPS [23, 24, 25, 26]. The research performed in [15] simulated
and provided a baseline for semi-persistent scheduling across various
densities for highway and urban environments. Research in [16], [17], and [7]
varied the probability of reselection, selection window, and RRI in SPS and
measured the impact on the packet delivery ratio (PDR). The authors of [18]
concluded that using short term sensing before resource selection reduced
packet collisions and improved SPS performance. The work in [19] and [27] was
amongst the first to adjust the transmission power and RRI accordingly, to
improve the overall performance of SPS. To address the scheduling overhead of
SPS, [21] has proposed using single shot transmissions as part of SPS for
safety critical messages that have an immediate scheduling need. Although much
of the research for semi-persistent scheduling is simulation driven, [22] has
provided an analytical model for semi-persistent scheduling in vehicular
networks. Recently, the work in [23, 24, 25, 26] has simulated the relatively
new NR-V2X Mode-2 SPS, specifically looking at the impact of the flexible
numerology on SPS. A potential drawback of these works is the focus on
improving the coverage (typically measured through PDR) of C-V2X Mode-4 and
NR-V2X Mode-2, and ignoring the cooperative awareness performance of the
vehicular network.

AoI has recently emerged as a popular metric for quantifying the performance
of scheduling and decentralized radio resource management in vehicular
networks. In particular, there has been a lot of research done in optimizing
the broadcast rate to reduce the AoI in networks that use Dedicated Short
Range Communications (DSRC), a competing V2X technology based on the 802.11p
standard. [28, 29, 30, 31, 32, 33, 34]. Although there are notable differences
between the two standards, changing the broadcast rate can be seen as the
analogous equivalent to using the RRI to minimize the AoI, and merits
discussion. The authors in [28] developed a decentralized algorithm that
iterated the broadcast rate based on AoI measurements for a DSRC network. The
work in [29] proposed a model that uses a vehicular network’s connectivity
graph to show the relationship between the average system AoI and vehicle
density and broadcast intervals. AoI was used to evaluate platooning
applications for convoys of vehicles in [30] and [31]. Furthermore, [33] and
[34] investigated the effect of the backoff window size in CSMA on the AoI.

Although the SPS protocol in C-V2X Mode-4 and NR-V2X Mode-2 is relatively new,
there has been some recent work in applying AoI to SPS. The authors in [20]
analyzed the AoI of Release 14 C-V2X Mode-4 and proposed a piggyback
collaboration method to help decrease half duplex errors, thereby reducing the
AoI. More recently, [35] looked at the effect of RRI spacing on AoI
performance in the NR-V2X Mode-2 standard, and found optimal RRI values across
vehicle densities. Note that although the Release 14 C-V2X Mode-4 SPS is
similar to Release 16 NR-V2X Mode-2 SPS, there are a few key differences
between the two standards. Two differences that are particularly relevant to
this work are the change in ranking of slot resources (discussed in Section
IV) and the inclusion of any integer RRI between 1 and 99 ms111Please refer to
[9] for a detailed discussion on the differences between C-V2X Mode-4 and
NR-V2X Mode-2.. These changes can enable higher transmission rates while
preventing collisions from choosing the same slot resource [24]. While there
have been recent works evaluating the overall performance of Release 16 NR-V2X
SPS, to the best of our knowledge, this is the first work that evaluates the
AoI and cooperative awareness performance for NR-V2X SPS and the first work to
directly use AoI measurements to optimize the RRI for SPS.

##  III Cooperative Awareness and NR-V2X Mode-2

This section discusses cooperative awareness, the tracking error metric, and
the NR-V2X Mode-2 standard for sidelink communications from the physical layer
structure to the semi-persistent scheduling algorithm that vehicles use to
find and reserve suitable transmission opportunities.

###  III-A Cooperative Awareness and Tracking Error

Since cooperative awareness depends on the sharing of time-sensitive
information with other vehicles via BSMs, conventional communication metrics
such as latency, throughput, and packet delivery ratio (PDR) greatly impact a
vehicle’s awareness. However, these metrics alone cannot capture the impact of
multiple lost or outdated BSMs on a vehicle’s awareness, as illustrated by the
following example. Consider a fast moving vehicle travelling at $140$ km/hr
($38.89$ m/s) while transmitting with a high RRI ($100$ ms or more).
Neighboring vehicles receive location packets reliably, but because there is
at least $100$ ms between packets, the localization or tracking error would be
at least $3.89$ m. Likewise, a low RRI ($50$ ms or less) would yield a
tracking error of at least $1.94$ m, though this tracking error could increase
if packets are dropped due to channel congestion. Thus, as the above example
shows, a tracking error metric can provide a better context to the cooperative
awareness performance in vehicular networks.

Illustrated in Fig. 1, tracking error ($e^{track}_{uv}$) in the context of
NR-V2X is defined as the difference in the transmitting vehicle’s (vehicle
$u$) true location, and $u$’s estimated location by neighboring receiving
vehicle $v$. We assume that the receiving vehicle $v$ is transmission range of
$u$ and time $t^{{}^{\prime}}$ is the generation time of the transmission from
$u$ to $v$. The tracking error is calculated as:

$e^{track}_{uv}=\sqrt{(x_{u}^{t}-\hat{x}_{uv})^{2}+(y_{u}^{t}-\hat{y}_{uv})^{2}},$
(1)

where ($x^{t}_{u}$, $y^{t}_{u}$) is $u$’s true current 2-D location at time
$t$ and ($\hat{x}_{uv}$, $\hat{y}_{uv}$) is $u$’s previous location from time
$t^{{}^{\prime}}$ at vehicle $v$ from the last transmission received from $u$.

Figure 1: Illustration of latency induced tracking error in a vehicular
network.

The tracking error has a large impact on the cooperative awareness in
vehicular networks because

  1. 1.

Every transmission has a non-zero propagation delay between transmission and
successful reception and the transmitting vehicle would also likely have moved
during the transmission and reception times.

  2. 2.

The RRI (or inter-packet transmission interval) can cause a large tracking
error, especially at higher speeds.

  3. 3.

Channel congestion could lead to several lost and delayed packets, further
deteriorating tracking error. In the example of a vehicle traveling at $140$
km/hr with a $50$ ms RRI in a congested environment, two consecutive missed
packets could cause a $5.833$ m tracking error.

A lower tracking error at receiving vehicle $v$ implies that $v$ can
accurately position (or localize) $u$. Note from the above discussion that a
lower RRI can decrease the tracking error but can also increase the number of
lost packets due to channel congestion.

###  III-B Physical Layer Structure for the NR-V2X Sidelink

Rel. 16 NR-V2X sidelink is designed to operate in two different frequency
ranges, from $0.410$\- $7.125$ GHz (FR1) and $24.25$\- $52.5$ GHz (FR2) [9].
Though both frequency ranges are supported in Rel. 16, NR-V2X is expected to
operate in the FR1. The NR-V2X sidelink uses cylic prefix orthogonal frequency
modulation (CP-OFDM) and supports multiple subcarrier spacings of $15$, $30$,
and $60$ kHz.

####  III-B1 Resource Structure in Time Domain

In the NR-V2X sidelink, resources in the time domain are made up of frames,
subframes, and slots. Every frame is made up of $10$ subframes, and each frame
time length is typically $10$ ms [6]. Subframes are typically $1$ ms in
length, and broken down into slots. A slot consists of $4$ OFDM symbols, which
means that the length of each slot depends on the chosen subcarrier spacing. A
subcarrier spacing of $15$ kHz corresponds to a slot length of $1$ ms, while a
$60$ kHz subcarrier spacing corresponds to a $0.25$ ms length [36]. For the
purposes of the work, we assume NR-V2X Mode-2 SPS is inter-operable with C-V2X
Mode-4, and take assume a subcarrier spacing of $15$ KHz

####  III-B2 Resource Structure in Frequency Domain

The smallest schedulable unit of frequency are resource blocks (RB). In the 5G
NR standard, a RB is made up of $12$ equally spaced subcarriers. The bandwidth
of each RB depends on the subcarrier spacing value. RBs are combined
sequentially to form subchannels. In NR-V2X, the data packets, or Transport
Blocks, are transmitted on one or more subchannels. In each subframe,
alongside every TB, is a sidelink control information block with modulation
and coding scheme used [7].

###  III-C NR-V2X Mode-2 Semi-persistent Scheduling

Figure 2: Flowchart of SPS Algorithm.

At the MAC layer, the NR-V2X sidelink utilizes semi-persistent scheduling
(SPS) that uses sensing to determine suitable semi-persistent transmission
opportunities, i.e., set of slots, for BSM transmission. Fig. 2 depicts the
SPS algorithm222Please refer to [8] and [9] for a detailed discussion on
NR-V2X and SPS., and is explained below. We use $s_{i}^{j}$ to refer to a
single-slot resource where $i$ is the slot index and $j$ is the subchannel
index of $J$ total subchannels.

  * •

Sensing (Step 1): Each vehicle continuously monitors the slots by measuring
the reference signal received power (RSRP) across all $J$ subchannels; and
stores sensing measurements for a prespecified last $N_{\rm sensing}$ slots,
known as the sensing window. Let slot $s_{n}$ denote the first slot after the
sensing window. Then we can write the sensing window at $s_{n}$ as the
following set of single-slot resources for the $j^{th}$ subchannel:
$\left[s_{n-N_{\rm sensing}}^{j},\dots,s_{n-1}^{j}\right]$.

  * •

Identifying Available Resources (Steps 1-8): Each vehicle initializes a
selection window with a set of consecutive candidate slots (See Step $1$).
$T_{1}\leq 4$ and $T_{2}\leq$ RRI are the start and end slots for the
selection window. The RRI refers to the time interval between two consecutive
BSM transmissions333In NR-V2X Mode-2 SPS, each vehicle selects an RRI at the
time of resource selection, although the standard leaves the selection of RRI
up to the user[9].. Each vehicle utilizes $N_{\rm sensing}$ slots (obtained in
Step $1$) for identifying and subsequently, selecting the available slot
within the selection window for BSM transmission as follows.

    1. 1.

The vehicle sets – (i) the RSRP threshold, $P_{th}$, to a minimum RSRP value,
$P_{min}$ (Steps $2$-$3$) and (ii) initializes set $S_{A}$ as all slots in the
selection window, i.e., $S_{A}=[s_{n+T_{1}},s_{n+T_{1}+1},\cdots,s_{n+T_{2}}]$
(See Step $4$).

    2. 2.

As shown in Step $5$ of Fig. 2, the vehicle excludes all candidate subframes
from set $S_{A}$ if one of the following conditions are met – (i) the vehicle
has not monitored the corresponding candidate subframe in the sensing window
(i.e., $N_{\rm sensing}$) due to the half duplex exclusion criteria and (ii)
the RSRP measurement for corresponding candidate subframe is higher than
$P_{th}$. The RSRP exclusion criteria for the $i^{th}$ subframe (for $j$th
sub-channel) in the selection window can be written as

$RSRP\left(s_{n+T_{1}+i-N_{\rm sensing}}^{j}\right)\geq P_{th}$ (2)

    3. 3.

If the remaining slots in $S_{A}$ is less than $X\%$ of the total available
slots (Step $6$), then $P_{th}$ is increased by $3$ dB (Step $7$), and Steps
$3$ to $5$ are repeated. In NR-V2X Mode-2, X can be set to 20, 35 or 50.

    4. 4.

Each vehicle selects a random slot resource from the resources remaining in
$S_{A}$ for transmission in Step $7$444Note that Release 14 SPS had an
additional selection criteria that selected slot resources with the lowest
sidelink received strength indicator (S-RSSI) measurements. This was removed
in Release 16 to accommodate smaller RRIs [24]. .

  * •

Resource Reselection (Steps 8-10): Each vehicle can reserve the same slot
(selected in Step $7$) for next Resource Counter (RC)555Resource Counter (RC)
is the maximum number of transmissions a certain vehicle is allowed (by
utilizing the selected slot/resource in the current selection window) before
having to reselect a new set of resources. number of subsequent transmissions
with the same transmission interval, i.e., RRI. The RC varies with the RRI to
ensure that the selected slot/resource is in use for at least $0.5$ s and at
most $1.5$ s. This means that for a $20$ ms RRI, $25\leq\textnormal{RC}\leq
75$, for $50$ ms RRI, $10\leq\textnormal{RC}\leq 30$, and for a $100$ ms RRI,
$5\leq\textnormal{RC}\leq 15$.

After RC reaches $0$, the vehicle can either continue utilizing the
preselected resources with a probability $p_{r}$ or reselect new resources for
BSM transmissions with a probability $(1-p_{r})$ (See Steps $8$-$9$).

##  IV Ch-RRI SPS: Semi-persistent Scheduling Using Channel Aware RRI
Selection

In this section, we present the limitations of conventional SPS protocol in
terms of improving cooperative awareness performance of NR-V2X Mode-2,
followed by detailed discussion on how to overcome them through a novel
channel aware RRI selection algorithm (Ch-RRI SPS). The Ch-RRI SPS discussion
first formulates the channel aware RRI selection problem as an Integer Linear
Programming (ILP) problem and then goes into the algorithmic details of the
proposed Ch-RRI SPS protocol.

###  IV-A Limitations of SPS on Cooperative Awareness

Figure 3: NR-V2X example network with three clusters of vehicles.

We present the limitations of SPS through a simple NR-V2X example (See Fig.
3). The example NR-V2X network consists of three clusters666Each vehicle is at
1-hop (i.e., within the transmission range) of every other vehicles belonging
to a certain cluster of vehicle., of vehicles, where clusters $1$, $2$, and
$3$ respectively have $20$, $50$, and $100$ vehicles. We make the following
assumptions for all example NR-V2X scenarios.

  * •

We assume $T_{1}=0$ and $T_{2}=$ RRI, which means, the size of selection
window is equal to the RRI.

  * •

The NR-V2X physical layer consists of $2$ subchannels only. Each BSM
transmission uses both the subchannels and takes 1 ms to transmit. This means
if the selection window is $100$ ms (i.e., RRI = $100$ ms), then at most $100$
distinct vehicles have unique BSM transmission opportunities (assuming no
collision in resource selection).

  * •

Each cluster of vehicles is sufficiently spaced apart from each other so that
there is no inter-cluster interference. This means, for example, no
transmissions from cluster $2$ interfere with any transmissions from cluster
1, and vice-versa.

Under the above assumptions, let us look at the (i) Channel Occupancy
Percentage $C_{occup}^{(i)}$, defined as the percentage of the number of
vehicles transmitting to the total number of available slots transmission
opportunities for the $i^{th}$ cluster, and (ii) Probability of Successful
Reception ($P_{suc})$. For simplicity, let $P_{suc}$ is given by $\frac{1}{N}$
where $N$ is the number of vehicles using the same slot for BSM transmissions.
Note that we only make this $P_{suc}$ assumption here to simplify this
discussion on the limitations of fixed RRI SPS. In simulations and reality,
$P_{suc}$ gets worse as $N$ increases.

Table I depicts the average $C_{occup}^{(i)}$ and $P_{suc}$ observed in the
example ideal NR-V2X network (meaning slot resources are distributed evenly
across all vehicles) under conventional SPS with three different values of
RRIs, i.e., $20$ ms, $50$ ms, and $100$ ms. For instance, the average
$C_{occup}^{(i)}$ for SPS with low RRI = $20$ ms is given by $\frac{\sum
RRI\times(C_{occup}^{(i)}}{\text{total number of vehicles}}$.
$C_{occup}^{(i)}$ for each cluster can be computed as follows: Since RRI is
$20$ ms, there are $20$ transmission opportunities (or slots), (i) in cluster
1, $20$ vehicles attempt to transmit, which implies
$C^{(1)}_{occup}=\frac{20}{20}\times 100=100\%$, (ii) in cluster 2, $50$
vehicles attempt to transmit, which results in
$C^{(2)}_{occup}=\frac{50}{20}\times 100=250\%$, and (iii) in cluster 3, $100$
vehicles attempt to transmit, resulting in $C^{(3)}_{occup}=500\%$. Thus, the
average $C_{occup}$ is $\frac{20\times C^{(1)}_{occup}+50\times
C^{(2)}_{occup}+100\times C^{(3)}_{occup}}{20+50+100}\times 100=379.4\%$. The
average $P_{suc}$ can be computed in the similar fashion, and it turns out to
be $0.35$ in case of SPS with RRI as $20$ ms. On contrary for SPS with high
RRI = $100$ ms the average $C_{occup}$ and $P_{suc}$ are $75.88\%$ and $1$
respectively.

TABLE I: Ideal Channel Occupancy Percentage and Success Probability of Conventional SPS with Fixed RRIs vs Scheduling with Adaptive RRI Metrics | Conventional SPS |  Ch-RRI
---|---|---
|  20 ms |  50 ms |  100 ms |  Adaptive RRI
Channel Occupancy Percentage |  379.4% |  152.94% |  75.88% |  100%
Probability of Successful Reception |  0.35 |  0.7058 |  1 |  1

Note that SPS with low RRI such as, $20$ ms leads to overly congested radio
channels ($379.4\%)$, and thus, large number of dropped BSM packets ($0.35$),
particularly, in clusters $2$ and $3$ with $>20$ vehicles). The lost packets
result in high tracking error, which compromises the awareness of considered
NR-V2X network. Whereas, in case of SPS with high RRI as $100$ ms, the radio
resources are under-utilized ($75\%$), particularly in cluster $1$ and $2$
with $<100$ vehicles. Tracking error performance can be significantly improved
by choosing lower value of RRI as lower value of RRIs will improve timely
delivery of BSMs. From the above discussion, it is evident that SPS with fixed
RRI (irrespective of the chosen value of RRI) is limited in the context of
improving overall cooperative awareness of NR-V2X networks.

To better address the limitations of static RRI SPS, we propose Ch-RRI, an
adaptive RRI selection algorithm where each vehicle chooses its RRI based on
the neighborhood density. Ideally, in the example NR-V2X network depicted in
Fig. 3, Ch-RRI would choose RRI = $20$ ms for a vehicle in cluster $1$ (with
$20$ vehicles). Similarly, Ch-RRI will choose RRI = $50$ ms for cluster $2$
(with $50$ vehicles) and RRI = $100$ ms for cluster $3$ (with $100$ vehicles)
– which will result in $C_{occup}=100\%$ and $P_{s}=1$ (See Table I). It means
that the proposed Ch-RRI strategy with adaptive RRI enables judicious
utilization of the radio resources. This in turn reduces the tracking error
and enhances the cooperative awareness of NR-V2X networks.

###  IV-B Problem Formulation

Notations. At each time instant $t\in T$, let $s(t,P_{th})$ denote the set of
available slots (slots with observed power less than $P_{th}$) in the
neighborhood of any vehicle $v$. RRIv is the $v^{th}$ vehicle’s RRI and
$\mathcal{N}$ is the set of all vehicles in the environment.

Objective function. As shown in Eq. 3, the objective function is to minimize
the resource reservation interval (RRI) (or maximize BSM rate) at each vehicle
$v$ (where $v\in\mathcal{N}$) over the entire time duration $T$.

$\displaystyle\\!\min\sum_{t\in
T}\frac{1}{|\mathcal{N}|}\sum_{v\in\mathcal{N}}\textnormal{RRI}_{v}(t)$ (3)
$\displaystyle\text{subject
to}\sum_{v\in\mathcal{N}}{\textnormal{RRI}_{v}(t)\leq s(t,P_{th})},\forall
v\in\mathcal{N},t\in T$ (4)
$\displaystyle\textnormal{RRI}_{min}\leq\textnormal{RRI}_{v}(t)\leq\textnormal{RRI}_{max},\forall
v\in\mathcal{N},t\in T$ (5)

Constraints. Eq. 4 constrains that the sum total of the RRI interval must be
less than the number of slots available to each vehicle $v$ at time instant
$t$. This constraint ensures that the channel congestion or the outage
probability across all vehicles are not compromised. Eq. 5 restricts the RRI
for each vehicle to be within the range $[$RRI${}_{min},$RRI${}_{max}]$.

Note that solving the aforestated ILP formulation would provide the optimal
solution to Ch-RRI. However, this is impractical in a real-world NR-V2X
setting because of the dynamic nature of the setup (mobility of vehicles) and
lack of global knowledge. Additionally, in order to solve the ILP problem, we
would require the knowledge of available slots at future time instants, which
is impractical to obtain in time varying NR-V2X networks. Therefore, our
proposed Ch-RRI SPS is based on decentralized SPS and estimates the latest
channel occupancy (via sensing window), selecting the suitable value of RRI at
each vehicle in the NR-V2X network based on its local knowledge.

Figure 4: Flowchart of Ch-RRI SPS.

###  IV-C Ch-RRI SPS Description

This subsection discusses in detail the proposed Ch-RRI SPS protocol. As shown
in Fig. 4, Ch-RRI SPS makes significant enhancements to the conventional SPS
algorithm. The green boxes represent the steps of the Ch-RRI algorithm and all
other steps are from the conventional SPS.

  * •

RRI Initialization and Sensing (Steps $1$-$2$): Similar to SPS, Ch-RRI SPS
continuously measures the RSRP and S-RSSI of the previous $N_{\rm sensing}$
slots and stores the sensing measurements in the sensing window (Step $1$). In
Step 2, Ch-RRI initializes the estimated $\widehat{\textnormal{RRI}}$ to
$\textnormal{RRI}_{min}$ and the the RSRP threshold ($P_{th}$) to a minimum
value $P_{min}$. The selection window in Ch-RRI SPS is not initialized before
the resource selection process has started (see Step $2$ in Fig. 2), and as
available resources are identified and the estimated
$\widehat{\textnormal{RRI}}$ is changed, the selection window is updated. As
in SPS, Ch-RRI SPS sets and updates the $P_{th}$ (See Step 3).

  * •

Ch-RRI: Channel-aware RRI Selection (Steps 4-10): Each vehicle utilizes
$N_{\rm sensing}$ slots (obtained in Step 2) for identifying the available
slots and subsequently, selecting the minimum RRI possible in between
transmission while ensuring that there remain resources (or slots) for other
vehicles.

    1. 1.

In Step 4, Ch-RRI updates the estimated $\widehat{\textnormal{RRI}}$ and
initializes the selection window with $T_{1}=1$ and
$T_{2}=\widehat{\textnormal{RRI}}$. $T_{1}$ is fixed to $1$ to maximize slot
resources.

    2. 2.

Each vehicle populates set $S_{A}$ with all slots in the selection window and
$S_{B}$ as an empty set (See Step 5). The candidate slot exclusion criteria is
also borrowed from SPS, except that, $\widehat{RRI}$ is an adjustable
parameter in Ch-RRI.

    3. 3.

If the number remaining slots in $S_{A}$ is less than $20\%$ of the total
available slots (Step $7$), then, Ch-RRI, unlike SPS, first checks whether the
$\widehat{\textnormal{RRI}}<\textnormal{RRI}_{max}$ (Step $8$). If yes,
$\widehat{\textnormal{RRI}}$ is increased by $\Delta$ as shown in Step $9$,
and Steps $4$ \- $7$ are repeated. Once $\widehat{\textnormal{RRI}}$ has
reached $\textnormal{RRI}_{max}$, then $P_{th}$ is increased by $3$ dB in Step
10, and Steps $3$ \- $7$ are repeated.

  * •

Resource Selection (Step $11$) and Resource Reselection (Step $12$) are
similar to SPS. As in SPS, a reselection counter (RC) value is chosen such
that the resource reservation is restricted between $0.5$ and $1.5$ s,
irrespective of chosen $\widehat{\textnormal{RRI}}$. However, in the case of
Ch-RRI SPS, since RC is zero, unlike SPS (see Steps $8$-$9$ in SPS flowchart),
Ch-RRI SPS does not allow re-reservation of slot resources. Both these
modifications are to ensure that Ch-RRI allows each vehicle to adjust its RRI
at the time of resource reselection and account for changing vehicle traffic
conditions.

##  V AoI-RRI: Age of Information Aware RRI Selection Algorithm

In this section, we provide some intuitions on the potential limitations of
Ch-RRI, provide a brief background of Age-of-Information (AoI), and formulate
the problem of AoI minimization in vehicular networks as an ILP problem. We
discuss why the ILP formulation is impractical to solve for a decentralized
network and propose AoI-RRI, a decentralized AoI-aware RRI selection
algorithm.

###  V-A Limitation of Ch-RRI on Cooperative Awareness

Though Ch-RRI is a promising RRI adaptation algorithm and promises to improves
the cooperative awareness as discussed in Section IV, it has certain
limitations as presented in this section.

  * •

Ch-RRI SPS is based on the accurate knowledge of channel occupancy at any
given time, however, given the dynamics of vehicles and channel usage,
obtaining accurate channel availability information at each vehicle is not
possible.

  * •

Ch-RRI SPS attempts to enable each vehicle to transmit at the minimum RRI
while accounting for 100% channel occupancy. However, the optimal trade-off
between channel occupancy and optimal RRI may not be at 100 % channel
occupancy.

Motivated by these limitations, we consider optimizing for a novel information
freshness metric, namely AoI. Since optimizing for AoI guarantees freshness
(and thus the best tracking error in this context), we can better account for
trade-off between the optimal RRI and channel occupancy.

###  V-B Age of Information

The AoI quantifies the freshness of information at any receiving node that was
originally generated and transmitted by the transmitting node[28]. For the
purposes of vehicular networks, AoI is the elapsed time since the last
received location packet was generated at the transmitting vehicle. Let
$t^{g}$ denote the time that the packet containing the most recent location at
sender vehicle $u$ was generated. Assuming a linear cost function for the AoI
evolution, the AoI at the receiving vehicle $v$ assuming the current time is
$t$ is:

$\textnormal{AoI}_{uv}(t)=t-t^{g}.$ (6)

The evolution of the AoI for vehicle $v$ is illustrated in Fig. 5. The
generation, transmission, and reception times of the $i^{th}$ location packet
are denoted by $t^{g}_{i}$, $t^{tx}_{i}$, and $t^{r}_{i}$. Therefore, the
overall delay for a packet = $(t^{r}_{i}-t^{g}_{i})$.

Figure 5: $AoI_{uv}$ is the AoI at vehicle $v$ based on the latest received
transmission from vehicle $u$.

Eq. 6 can be used to find the average AoIuv between vehicle $v$ and
neighboring vehicle $u$. The average AoIuv is found by calculating the area
under AoI${}_{uv}(t)$. The area under AoI${}_{uv}(t)$ is normalized by the
observation time $T_{obs}$ [28]

$\textnormal{AoI}_{uv}=\frac{1}{T_{obs}}\int_{T_{obs}}\textnormal{AoI}_{uv}(t).$
(7)

We represent the set of all vehicles in the environment as $\mathcal{N}$ and
the set of all neighboring vehicles of $v$ as
$\mathcal{N}_{v}\subseteq\mathcal{N}$, where $u\in\mathcal{N}_{v}$. The
average AoI at vehicle $v$ is:

$\textnormal{AoI}_{v}=\frac{1}{|\mathcal{N}_{v}|}\sum_{u\in\mathcal{N}_{v}}\textnormal{AoI}_{uv}.$
(8)

The overall system AoI with $|\mathcal{N}|$ vehicles can be computed as:

$\textnormal{AoI}=\frac{1}{|\mathcal{N}||(\mathcal{N}-1)|}\sum\limits_{v\in\mathcal{N}}\sum\limits_{u\in\mathcal{N}_{v}}\textnormal{AoI}_{uv},$
(9)

where $|\mathcal{N}||(\mathcal{N}-1)|$ are the number of unique pairs of
sender and receivers in the system. Assuming the simple vehicular network in
Fig. 1 with vehicles $u$ and $v$, we can assume that inter-packet reception
interval between receiver $v$ and transmitter $u$ are multiples of the RRI.
Using these assumptions and the fact that the AoI resets to 0 upon successful
reception of location information, the evolution of the AoI at the receiving
vehicle can be written as

$\textnormal{AoI}(t+\textnormal{RRI})=\begin{cases}0,&\text{if}\hskip
2.8903pt\text{a packet is received}\\\
\textnormal{AoI}(t)+\textnormal{RRI},&\text{otherwise}\end{cases}$ (10)

Note that Eq. 10 implies that minimizing the RRI also minimizes the AoI at the
receiving vehicle. However, too many vehicles transmitting with a small RRI
can increase the number of lost packets due to congestion, which also
increases the AoI. Therefore, as in the case of tracking error, there is a
tradeoff between smaller RRIs and improved AoI performance.

###  V-C AoI ILP Problem Formulation

The objective of AoI-RRI is to minimize the overall system AoI based on what
each vehicle observes. As in the Ch-RRI problem formulation, finding an
optimal RRI that minimizes the system AoI can be written as a Integer Linear
Programming (ILP) problem.

Objective function. Eq. 11 is the objective function where each vehicle
chooses a RRI at each vehicle $v$ (where $v\in\mathcal{N}$) such that the AoI
is minimized over the entire time duration $T$.

$\displaystyle\\!\sum_{t\in
T}\frac{1}{|\mathcal{N}|}\sum_{u,v\in\mathcal{N}}\textnormal{AoI}_{uv}(t).$
(11) $\displaystyle\text{subject to
}\textnormal{RRI}_{min}\leq\textnormal{RRI}_{v}(t)\leq\textnormal{RRI}_{max},\forall
v\in\mathcal{N},t\in T$ (12)

Constraints. Eq. 12 restricts the RRI for each vehicle to the range
$[$RRI${}_{min},$RRI${}_{max}]$. Note that there are no capacity constraints
for Eq. 11, and the AoI minimization itself decides the optimal tradeoff.

However, as in the case of Eq. 3, solving Eq. 11 assumes global information at
every vehicle and knowledge of each vehicles channel information and mobility
even at future time instants, which is not realistic. As a result, this ILP is
not practical. Thus we propose AoI-RRI, an algorithm that attempts to
iteratively minimize the NR-V2X system AoI in a decentralized manner,
described in Section V-D

###  V-D AoI-RRI SPS

This section details AoI-RRI SPS, SPS powered by a decentralized AoI-aware RRI
selection algorithm. AoI-RRI finds a RRIv (where
RRI${}_{v}\in[\textnormal{RRI}_{min}$ $\textnormal{RRI}_{max}]$) for vehicle
$v$ by iterating the previously chosen RRI, denoted RRIt-1, such that the
locally measured average AoI is minimized. The algorithm runs in three steps.
First, at the RRI selection time, $v$ uses the sensing window history to
measure the channel congestion in the network. Second, $v$ calculates the time
since the last received packet from every vehicle in the vicinity to estimate
the local average AoI, and adjusts its RRI in order to minimize this last
measured AoI. Finally, $v$ uses the semi-persistent scheduling procedure
presented in Fig. 2 and selects slot resources using the latest selected RRI.
The algorithm details are as follows:

Step 1: Sensing and Channel Congestion Detection. In line 1 of Algorithm $1$,
AoI-RRI uses a channel congestion detection algorithm, further detailed in
Algorithm $2$, to measure and detect whether or not significant channel
congestion has occurred. The channel congestion algorithm returns true if
there is significant congestion detected and like Ch-RRI SPS, uses the
previously chosen $\textnormal{RRI}^{t-1}$ and the RSRP sensing measurements
for the last $N_{\rm sensing}$ slots, i.e. the sensing window, as inputs. In
line $2$ of Algorithm $2$, $v$ calculates the size of the set $S_{\rm total}$,
which is the set of all possible slots resources using RRIt-1. Lines 3-5 of
Algorithm $2$ populate set $S_{\textnormal{avail}}$ with those slots with
linear average RSRP measurements higher than $P_{th}^{t-1}$. If the number of
slots in $S_{\rm avail}$ is less than $20\%$ of the total available slots, it
means that network congestion has increased since the previous resource
reservation, and RRIt-1 or $P_{th}^{t-1}$ must be increased. Using RSRP
measurements can give a robust estimate of the channel congestion without
adding any sensing overhead since the sensing window measurements and RSRP
threshold are taken as a part of the SPS procedure. If the channel congestion
increases, lines $2$-$3$ of Algorithm 1 automatically increase the RRI to
avoid congesting the channel further.

Step 2: AoI Estimation and RRI Adjustment. If the channel has not become
significantly congested, vehicle $v$ uses Eqs. 6 and 8 and computes its local
AoI by calculating and averaging the time since the last received packet from
each neighboring vehicle. The AoI-RRI algorithm iterates upon the last chosen
RRI to minimize the most recent average AoI at each vehicle $v$. AoI-RRI uses
one of the following three actions– (1) DECR \- decrease RRI, (2) INCR \-
increase RRI, and (3) SAME \- maintain the same RRI 777The concept of
utilizing these actions for adjusting the RRI is inspired by the algorithm
presented in [37].. Algorithm $1$ presents the pseudocode for this step.

Lines $4$-$9$ form the core of AoI-RRI where $AoI_{avg}$ for the current and
previous $T_{obs}$ are compared. In lines $4$-$6$ AoI-RRI checks if the local
AoI has increased by a factor of more than $\sigma_{t}$, in which case the AoI
has significantly worsened and AoI-RRI reverses the previously selected
action. If in lines $7$-$9$, $v$ sees that the local AoI has decreased by a
factor of more than $\sigma_{t}$, the previous action selected by the
algorithm is repeated, i.e. the RRI continues to increase or decrease. If
there is no significant change in AoI, AoI-RRI chooses the same RRI as before.
Finally, in $10$-$20$, the new RRI is calculated based on the action selected
in lines $2$-$9$. The new RRI returned is maintained until the end of the
current $T_{obs}$. Further, $\beta$ decides the magnitude by which the RRI
changes if the chosen action was INCR or DECR.

Algorithm 1 AoI-RRI algorithm at vehicle $v$.

Input: RSRP of $N_{\rm sensing}$ slots across $J$ subchannels in sensing
history, $s_{\rm total}=[s^{j}_{1},\cdots,s^{j}_{N_{\rm sensing}}]$, Minimum
Power threshold ($P_{min}$), Maximum Power threshold ($P_{max}$), RRI chosen
during the previous $T_{obs}$, $\textnormal{RRI}^{t-1}$, local average $AoI$
of the previous $T_{obs}$, $AoI_{avg}^{t-1}$, Action chosen during the
previous $T_{obs}$, $\alpha^{t-1})$, Power threshold chosen during the
previous $T_{obs}$, ($P_{th}^{t-1}$)
Output: New $\textnormal{RRI}^{t}$, slot $s_{v}$ for node $v$, and number of
retransmissions $N_{resel}$

1:$[\textnormal{channel}_{\textnormal{flag}}]=\textnormal{channel}_{\rm
cong}(\textnormal{RRI}^{t-1},s_{\rm total},P_{th}^{t-1}$) $\triangleright$
Checks to see if channel is congested

2:if $\textnormal{channel}_{\textnormal{flag}}==$true then

3: $\boldsymbol{\alpha^{t}}=$INCR

4:if $AoI_{avg}^{t}>AoI_{avg}^{t-1}+\sigma_{t}$ then

5: $\boldsymbol{\alpha^{t}}=\textnormal{inverse}(\alpha^{t-1})$
$\triangleright$ Previous action caused AoI to worsen significantly, so
inverse action

6:else if $AoI_{avg}^{t}<AoI_{avg}^{t-1}-\sigma_{t}$ then

7: $\boldsymbol{\alpha^{t}}=(\alpha^{t-1})$ $\triangleright$ Previous action
caused AoI to get better so continue action

8:else

9: $\boldsymbol{\alpha^{t}}=$SAME $\triangleright$ AoI has not significantly
changed from previous value, so maintain same RRI

10:if $\boldsymbol{\alpha^{t}}$ == INCR then

11: if $\textnormal{RRI}^{t-1}\geq\textnormal{RRI}_{max}$ then

12: $\textnormal{RRI}^{t}=\textnormal{ RRI}^{t-1}$$\triangleright$ AoI has
improved but RRI has hit maximum

13: else

14: $\textnormal{RRI}^{t}=\beta\textnormal{ RRI}^{t-1}$

15:else if $\boldsymbol{\alpha^{t}}$ == DECR then

16: if $\textnormal{RRI}^{t-1}\leq\textnormal{RRI}_{min}$ then

17: $\textnormal{RRI}^{t}=\textnormal{ RRI}^{t-1}$ $\triangleright$ AoI has
improve but RRI has hit minimum

18: else

19: $\textnormal{RRI}^{t}=\frac{1}{\beta}\textnormal{ RRI}^{t-1}$

20:else if $\boldsymbol{\alpha^{t}}$ == SAME then

21: $\textnormal{RRI}^{t}=\textnormal{ RRI}^{t-1}$

22:return $P_{th}$, $\textnormal{RRI}^{t}$

Step 3: Semi-persistent Scheduling. Finally, $v$ uses the RRI selected from
Algorithm $1$ to choose a slot for transmission using the SPS procedure
presented in Fig. 2. Note that the $P_{th}$ value that is used to select the
slots is stored as a part of the procedure, and again the next time resources
are selected.

Algorithm 2 Channel Congestion

Input: All slots in sensing history, $s_{total}(1:N_{\rm sensing})$, Power
threshold selected from previous slot selection ($P_{th}^{t-1}$), RRI selected
from previous AoI scheduling instance, RRIt-1
Output: Returns true if the channel is congested as compared to the previous
RRI, and false otherwise

1:procedure $\textnormal{channel}_{\textnormal{cong}}$($s_{total}(1:N_{\rm
sensing})$, $P_{th}^{t-1}$, RRIt-1)

2: $N_{\textnormal{RRI}}=\textnormal{floor}(\frac{N_{\rm
sensing}}{\textnormal{RRI}^{t-1}}-1)$

3:
$S^{j}_{i}=\frac{1}{N_{\textnormal{RRI}}}\sum_{k=0}^{N_{RRI}}s^{j}_{1+i+k\cdot\textnormal{RRI}^{t-1}}$

4:
$S_{\textnormal{total}}=[S^{j}_{0},S^{j}_{1},\dotsc,S^{j}_{\textnormal{RRI}^{t-1}}]$

5: if $S^{j}_{i}<P_{th}^{t-1}$ then

6: $S_{\textnormal{avail}}\leftarrow S^{j}_{i}$

7: if $\frac{|S_{\textnormal{avail}}|}{|S_{\textnormal{total}}|}<0.2$ then

8: return true$\triangleright$ The value of $P_{th}$ has not changed as
compared to the previous slot selection, so the channel is not congested

9: else

10: return false$\triangleright$ The value of $P_{th}$ needs to increase by
$3$ dB as compared to the previous slot selection, so the channel is congested

##  VI Simulation Overview and Results

In this section we cover the simulation settings, performance metrics, and
compare the proposed Ch-RRI SPS and AoI-RRI SPS to static RRI SPS.

###  VI-A Simulation Setting

We modified and enhanced a system-level simulator originally designed to model
C-V2X Mode-4 [38] to model and compare AoI-RRI SPS, Ch-RRI SPS, and NR-V2X
Mode-2 SPS with three different static RRIs. We use the 3GPP highway mobility
models [9] for our simulation results.

In the highway mobility model, vehicles move along a six lane highway, with
three lanes dedicated to each direction. The highway models assume the
velocity of vehicles moving in the positive direction and negative direction
are drawn from truncated Gaussian distributions with means of $v_{avg}$ and
$-v_{avg}$, respectively. The Gaussian distribution mean and variance values
are assumed to be $19.44$ m/s ($70$ km/hr) and $3.0$ m/s, respectively. As
each vehicle in each lane approaches the length of the highway, the warp used
in the model places the vehicle at the opposite end of the highway. All
vehicles remain in the same lane for the duration of the simulation. Each
vehicle’s initial location along the highway follows a Poisson distribution.

For comprehensive analysis, we compare the performance of Ch-RRI SPS and AoI-
RRI SPS against conventional NR-V2X Mode-2 SPS with three different static
RRIs: $20$ ms RRI, $50$ ms RRI, and $100$ ms RRI. The vehicle densities in the
simulation range from $20$ to $160$ veh/km, and initial positions and
velocities do not change across AoI-RRI SPS, Ch-RRI SPS, and NR-V2X SPS. All
simulations used a 10 MHz system bandwidth, $25$ second simulation time, and
results were averaged over $10$ trials. Table II summarizes the default values
of the key simulation parameters for AoI-RRI SPS, Ch-RRI SPS, and NR-V2X SPS
with static RRIs.

TABLE II: Simulation Parameters Parameter | Value
---|---
Vehicle density | {$20$-$160$} veh/km
Road Length/Number of lanes/Lane width |  $2000$ m/ $6$ lanes/ $4$ m
$\beta$ | $1.1$
Reselection time |  $0.5$ -$1.5$ s
Simulation time |  $25$ seconds
Transmission Power |  $23$ dBm
Transmission and Sensing Range |  $300$ meters
Distribution of vehicle speeds |  $N$($19.44$ m/s, $3$ m/s)
AoI-RRI/Ch-RRI RRImax |  $100$ ms
AoI-RRI/Ch-RRI RRImin |  $20$ ms
Packet Size |  $190$ B
MCS Index | $7$
Number of trials | 10
Initial RSRP threshold, $P_{th}$ |  $-90$ dBm

(a) (b)

Figure 6:  (a) Average tracking error and (b) Average system age of
information.

###  VI-B Performance Metrics

This work uses the following three metrics to compare AoI-RRI SPS, Ch-RRI SPS,
and static RRI SPS.

  * •

Tracking Error ($\mathbf{e_{track}}$)\- $e_{track}$ is calculated as the
difference in the transmitting vehicle $u$’s actual location and estimated
location from $u$’s last received transmission at receiver vehicle $v$. (see
Section III-A).

  * •

Age of Information (AoI) \- The difference in the reception time at receiver
vehicle $v$ of vehicle $u$’s last location and the generation time of $u$’s
last location (see Section V-B).

  * •

Packet Delivery Ratio (PDR) \- The likelihood that all neighbors inside the
transmission range of a vehicle successfully receive the transmitted packet.
Formally, the PDR is computed as PDR${}_{u}=\frac{PR_{i}}{PD_{i}}$. $PD_{i}$
is the number of packets sent by vehicle $i$ and $PR_{i}$ is the number of
packets received by neighboring vehicles originally transmitted by vehicle
$i$.

###  VI-C Experimental Results

(a) $20$ veh/km  (b) $60$ veh/km  (c) $120$ veh/km  (d) $160$ veh/km

Figure 7:  RRI distribution during the last 5 seconds of simulations across
vehicle densities for Ch-RRI and AoI-RRI.

(a) $20$ veh/km  (b) $60$ veh/km  (c) $120$ veh/km  (d) $160$ veh/km

Figure 8: Average AoI vs time across vehicle densities for Ch-RRI and AoI-RRI.

(a) $20$ veh/km  (b) $60$ veh/km  (c) $120$ veh/km  (d) $160$ veh/km

Figure 9:  PDR across vehicle densities.

We compare AoI-RRI, Ch-RRI, and static RRI SPS using the aforementioned
tracking error, AoI, and PDR performance metrics. In addition to these
metrics, we also look at the final RRI distributions and average AoI over time
to better understand the operation of AoI-RRI and Ch-RRI.

Average Tracking Error and System AoI. Figs. 6(a) and 6(b) compare the system
tracking error and AoI, respectively, of AoI-RRI SPS and Ch-RRI SPS to $20$
ms, $50$ ms, and $100$ ms static RRI SPS. Fig. 6(a) demonstrates that tracking
error worsens with increasing density, with the $20$ ms RRI SPS tracking error
giving the best static RRI SPS performance. Both tracking error and AoI
increase drastically at higher densities (larger than 100 veh/km). Since there
are insufficient slot resources to support a $20$ ms RRI without two vehicles
in the same vicinity choosing the same slot resource, there are increased
packet losses, leading to worse performance at high densities. The tracking
error for AoI-RRI is smaller than the tracking error of Ch-RRI and all three
static RRIs across large vehicle densities. AoI-RRI outperforms $20$ ms RRI
NR-V2X (the best performing fixed RRI) in terms of AoI by almost $19\%$ and
$16\%$ respectively at $120$ and $160$ veh/km. This indicates that AoI-RRI
finds for each vehicle a RRI that minimizes packet losses and enables timely
cooperative awareness in the network. The AoI improvements found with AoI-RRI
extend to the tracking error. AoI-RRI was also found to have an advantage over
Ch-RRI in high density scenarios as well outperforming Ch-RRI at 120 and 160
veh/km by $9.16\%$ and $10.81\%$, respectively. The tracking error results
show that lower average RRIs aid vehicles in high and low density situations.
Even in high density scenarios, ($160$ vehicles/km), both AoI-RRI and Ch-RRI
outperform the $20$ and $50$ ms RRI.

RRI Distribution. Figs. 7(a)-7(d) show the average RRI distributions for AoI-
RRI and Ch-RRI for selected densities over the last five seconds of the
simulation888We use the last five seconds because by then, every vehicle has
had sufficient time to choose an acceptable RRI and we can analyze steady
state behavior.. Across densities, AoI-RRI shows a larger RRI variance as
compared to the Ch-RRI. This large variance in the RRI distribution for the
AoI-RRI algorithm can be attributed to varying traffic densities and noisy
estimates of the measured AoI which leads vehicles to choose different RRIs
depending on the observed AoI. Although there is a large variance in the RRI
distribution of the AoI-RRI, the AoI-RRI tracking error performance approaches
that of Ch-RRI and $20$ ms SPS for low densities, and outperforms all methods
in high density scenarios. In Ch-RRI, the RRI distribution is comparatively
narrow, and the average chosen RRI is similarly small for low densities ($20$
and $40$ veh/km). This means that there are enough channel resources to
support small RRIs for both Ch-RRI and AoI-RRI. In Fig. 7(d), we see that
while the AoI-RRI RRI distribution skews towards RRImax, many vehicles use
lower RRIs, which contributes to the improved AoI performance.

Average AoI vs Time. Figs. 8(a)-8(d) present the average AoI over simulation
time of AoI-RRI SPS and Ch-RRI SPS. Both AoI-RRI and Ch-RRI algorithms start
with an initial RRI of 50 ms, and only allow for adaptive RRIs to be chosen
after 5 sec. This gives enough time for each algorithm to (i) allow all
vehicles to transmit at least once and (ii) allow each algorithm to gather
channel and AoI measurements. Notice that both AoI-RRI and Ch-RRI start with
an initial value of 120 ms. This is because both algorithms start with
observing the channel for 100 ms (following the NR-V2X Mode-2 SPS standard)
before selecting an initial slot. Once both algorithms start transmitting, the
AoI drops to 70 ms, which is expected for an RRI of 50 ms. In the low density
cases (20 and 40 veh/km), both algorithms drop to average AoI of 40-50 ms.
Note that Ch-RRI slightly outperforms AoI-RRI in lower densities. This is
because Ch-RRI detects an empty channel and automatically transmits at the
lowest possible RRI. Ch-RRI is also able to converge to a steady state value
faster than AoI-RRI, likely because of the noisy nature of the AoI estimates.
When the density increases, AoI-RRI is able to perform better, and is able to
take actions that lead to a lower average AoI.

Packet Delivery Ratio. Fig. 9 compares the AoI-RRI, Ch-RRI, and NR-V2X Mode-2
SPS PDRs across vehicle densities. Among the fixed RRI results, the $100$ ms
RRI performs the best, but correspondingly yield a large tracking error and
AoI. Similarly, $100$ ms RRI NR-V2X gives the worst PDR performance, but gave
the best tracking error and AoI performance, meaning there is a tradeoff
between PDR and RRI, that affects AoI performance. Both AoI-RRI and Ch-RRI
attempt to find the best RRI that optimizes the tracking error and AoI.
Notice that at low densities (20 and 60 veh/km), the PDR of AoI-RRI and Ch-RRI
are similar, as are the average AoI and tracking error. Both AoI-RRI and Ch-
RRI choose similar RRIs and are able to achieve the best tracking error
performance. As the densities increase the RRI distribution of AoI-RRI tends
towards lower RRIs, and the PDR performance is worse than that of Ch-RRI,
which chooses a larger average RRI. This indicates that the AoI-RRI finds that
choosing a slightly lower RRI distribution can minimize the AoI, as the
average age of AoI-RRI is lower than Ch-RRI. However, AoI-RRI does not select
a $20$ ms RRI for all vehicular since the AoI results show there are
diminishing returns for selecting a low RRI, and eventually the increased
congestion and packet collisions will deteriorate AoI and tracking error.

Discussion. Unlike conventional SPS and Ch-RRI, the proposed AoI aware SPS is
able to successfully learn the system AoI and adapt each vehicle’s RRI across
time-varying NR-V2X scenarios. As a result of choosing an optimal RRI, it is
shown that the average tracking error of every vehicle pair is also reduced.
This significantly improves the cooperative awareness of vehicular networks.

##  VII Conclusion

In this work, we proposed two adaptive RRI algorithms to power SPS for
improved cooperative awareness performance of decentralized V2X networks. Ch-
RRI and AoI-RRI choose RRIs based on the availability of channel resources and
measured AoI, respectively, and then use SPS for the selection of suitable BSM
transmission opportunities at those chosen RRIs. Our extensive experiments
based on NR-V2X Mode-2 standard demonstrated that SPS powered by either
algorithm significantly outperforms conventional SPS in terms of the
cooperative awareness performance in all considered NR-V2X scenarios. In the
future, we will explore using nonlinear age functions and designing
reinforcement learning (RL) based scheduling protocols that can learn vehicle
priorities and other contextual factors over time.

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