Enhanced Distributed Resource Selection and Power Control for High Frequency NR V2X Sidelink

The 3GPP has standardized the 5G New Radio (NR) sidelink (SL) technology that enables direct device-to-device communications. SL will be key in realizing several high-speed, low-latency vehicle-to-everything (V2X) applications, such as automated driving. To meet these applications’ high data rate requirements, operating SL at mmWave and sub-THz frequencies will be essential. However, the current SL design primarily caters to sub-6 GHz frequencies and does not consider the directionality of transmissions at high frequencies. For Mode 2 of SL, where SL UEs perform sensing-based autonomous resource selection, this results in hidden node interference due to the transmit (Tx) UE’s inability to sense transmissions not aligned with the primary direction of communication. We propose paired transmission and sensing of sidelink control information (SCI), whereby SL Tx UEs transmit and receive SCI in an additional paired direction directly opposite to the primary direction. This helps eliminate hidden node interference while reducing the number of exposed nodes. Simulations in NR V2X highway deployments show that the paired scheme improves the average packet reception ratio (PRR) by 27% over the state-of-the-art at the highest traffic loads. We also propose enhanced transmit power control strategies to minimize interference between concurrent SL transmissions. This enables better resource reuse and further improves performance, with our combined solution achieving at least 95% average PRR in all scenarios. Finally, we present a stochastic geometry-based analytical model for a single-lane highway V2X network and validate it against simulation results. Our model provides insights into the reliability and capacity of high-frequency SL networks.

the first version of D2D communication in Release-12 for proximity services. Later in Release-14, 3GPP standardized vehicle-to-everything (V2X) based on the 4G Long-Term Evolution (LTE) air interface. This underwent further feature enhancements in Release-15. V2X communications based on the 5G New Radio (NR) air interface was first standardized in 3GPP Release-16. A major development in NR V2X is the introduction of the NR sidelink (SL) to support enhanced V2X use cases. SL communication is the direct communication between devices without data passing through the base stations. NR V2X use cases and requirements have been detailed by the 3GPP in [3] and [4], respectively. These specifications became the basis for the NR SL work done in Release-16. The use cases can be broadly categorized into the following groups [3], [5]: 1) Vehicle Platooning: A ''platoon'' is a group of vehicles, which is dynamically formed and can travel together with small inter-vehicle distances. 2) Advanced Driving: This includes applications like semi-automated and fully-automated driving where vehicles can share local sensor data, as well as driving intentions, through the NR SL interface. 3) Extended Sensors: Sharing of raw/processed sensor data between vehicles, roadside units and pedestrians. 4) Remote Driving: Enabling remote (tele-operated) driving through a V2X application.
Several applications derived from the above use cases have very high data rate and low latency requirements [4], [6]. Thus, millimeter wave (mmWave) and sub-THz frequency bands are ideal candidates for supporting the NR SL due to the large spectrum available in these bands. While NR SL supports both Frequency Range 1 (FR1), i.e., sub-6 GHz spectrum, and FR2 (up to 52.6 GHz with an extension to 71 GHz considered in Release-17), the SL procedures developed so far are primarily for communication in the FR1 bands. 1 They will not be suitable for high frequencies, i.e., FR2 and beyond, where highly directional transmission/reception is used to overcome the high propagation losses. Several enhancements are needed to make SL feasible for high-frequency carriers.
This paper focuses on the user equipment (UE) autonomous resource allocation aspect of NR SL in the context of directional SL systems at high frequencies. In the UE autonomous mode, also known as Mode 2, SL transmitter (Tx) UEs select resources for their transmissions without any help from the 5G NR base station, i.e., the gNodeB (gNB). To do so, SL Tx UEs continuously sense ongoing transmissions by receiving and decoding the SL control 1 3GPP Release-18 will start considering some aspects of SL operation over FR2 licensed spectrum [7], [8]. The initial discussions in 3GPP Rel-18 are on determining the evaluation methodology to study SL over FR2 bands and the beam management aspects. Detailed SL resource allocation for FR 2 operation may not be handled in this release. Omni scheme -TX 1 acts as an exposed node for TX 2, (b): directional scheme -TX 1 is a hidden node for TX 2, arrows show direction of data transmission. information (SCI) 2 sent by other UEs in the network. The Tx UE then excludes any prior reservations made by other UEs, as indicated in their SCIs, to avoid potential collisions of its future transmissions with ongoing SL transmissions. More details on NR SL Mode 2 3 are provided in Section II.
Legacy SL Mode 2 resource allocation involves omnidirectional transmission and reception (sensing) of SCI by the SL Tx UE. This is referred to as the omni scheme in this paper. While the omni scheme is used in FR1 bands, it is impractical for SL systems at mmWave/sub-THz frequencies for two reasons. Firstly, it will have zero antenna/beamforming gain and, therefore, cannot compensate for high propagation losses at high frequencies. Secondly, suppose a potential SL Tx UE uses omnidirectional sensing for resource allocation. In that case, it will detect SL transmissions from all directions, including those that would not result in any data channel interference 4 at its target receiver (Rx) UE. This is known as an exposed node issue (Fig. 1a).
Conversely, if SCI transmission/reception is performed only in the intended direction of communication, referred to as the directional scheme in this paper, we may run into hidden node problems. These are situations where an ongoing directional SL transmission between neighboring SL UEs is not aligned to the sensing direction of the SL Tx UE but may cause interference at its Rx UE (Fig. 1b). These issues, collectively termed as directional deafness, cause significant performance degradation.
In our previous work in [1], we pointed out these directional deafness issues and proposed a joint control transmission/reception strategy for directional SL networks, referred to as the paired scheme. In this scheme, SCI transmission and reception at the SL Tx UEs is done in the intended direction of transmission (primary direction) as well as the direction opposite to it (paired direction). In Sec. IV, we present a detailed analysis of the benefits of the proposed 2 Each SL transmission comprises control information followed by data. More precisely, SCI includes first-stage and second-stage control information. In Mode 2, the first stage SCI enables channel sensing and resource allocation. 3 From now on, we will refer to NR SL Mode 2 simply as SL Mode 2. 4 Data channel transmissions at high carrier frequencies are assumed to be directional, i.e., only in the direction of the intended receiver. paired scheme. The main contributions of our previous paper [1] were as follows: • We analyzed the omni scheme and demonstrated that this would be impractical at high frequencies due to high propagation losses and exposed node issues. We further showed that the directional scheme is also not a viable option due to directional deafness issues.
• We proposed a novel composite control transmission/reception strategy for directional SL systems. This is referred to as the paired scheme, and it helps the SL Tx UEs detect critical hidden node interference while avoiding many exposed node issues, as explained in greater detail in section IV-B. We further provide new details on its design and implementation, not included in our previous work (Sec. IV-C).
• We developed a MATLAB-based system level simulator which is inspired by 3GPP's system simulation setup [9]. Our results validate the gains for the proposed paired scheme over the omni and directional schemes in terms of key performance indicators such as the packet reception ratio (PRR). We reproduce the details of our simulation setup and those results in section VII-A2. Simulation-based studies have been used widely in the literature to evaluate SL Mode 2. However, in order to obtain quick, realistic insights on Mode 2 performance, it is important to have an analytical model of the resource allocation procedure. In section V, we develop the first stochastic geometry-based analytical model for a SL ad-hoc (purely D2D) network at high carrier frequencies with the SL UEs operating in Mode 2, i.e., distributed, UE-autonomous resource allocation. Our model incorporates the wireless channel characteristics of mmWave frequency bands, the proposed paired solution for the SL control channel, as well as a path loss compensation-based power control scheme that conforms with the current 3GPP SL design.
A careful analysis of our analytical and simulation studies led us to consider the problem of transmit power control for SL networks at mmWave frequencies. Given the distributed nature of SL Mode 2, pairs of SL Tx-Rx UEs must select their own transmit (Tx) power. To maximize system-wide performance, the Tx power control of a SL Tx UE must consider (i) the interference experienced at its intended SL Rx UE and (ii) the interference the SL Tx UE itself may cause to other ongoing transmissions in the network. Interference estimation is challenging in Mode 2 as we cannot assume any central coordination via the 5G NR gNB. We also do not have any explicit cooperation among different SL Tx-Rx pairs in the network. In Mode 2, the SCI acts as an implicit information exchange mechanism between the SL Tx UEs to estimate the resource reservations of their neighboring transmissions. Our work shows how the SCI can also be leveraged for interference estimation and transmit power control. If available, the SL Tx UE may also use feedback from its own Rx UE for interference estimation and cancellation. In section VI, we design several transmit power control strategies that help improve the overall system performance by enabling more efficient resource reuse. Through system-level simulations, we also show that the proposed power control designs have the most significant positive impact on users that are worst affected by interference in the SL network.
The main novel contributions of this paper are as follows: • We develop a stochastic geometry-based analytical model of a single-lane highway vehicular ad-hoc network with directional SL unicast transmissions at mmWave frequencies. We incorporate Mode 2 resource allocation with paired SCI transmission/reception, and path loss compensation-based power control, to obtain some key insights into the performance of our system.
• We propose distributed transmit power control strategies for directional SL networks incorporating practical interference estimation and compensation techniques.
• We use the MATLAB-based system-level simulator developed for our work in [1] to i) validate the results of our analytical model against simulation results, and ii) evaluate the performance of the proposed transmit power control schemes and show that they significantly improve the PRR of directional SL systems in NR V2X highway scenarios.

FIGURE 2.
Outline of our work on SL communications at high frequencies, Pink boxes -where we make novel contributions and enhancements, Blue boxes -as per current 3GPP NR SL design (The Tx and Rx vehicles act as SL Tx and Rx UEs respectively).
The key components of our work have been highlighted in Fig. 2, clearly distinguishing between the components where we make novel contributions to the current standard and protocols and the components that are modeled exactly as per the current design of 3GPP's NR SL. The rest of the paper is organized as follows. We provide a brief introduction of the NR SL resource allocation procedures in Section II. In Section III, we discuss the related work in the literature. Section IV presents an analysis of different transmission/reception schemes for directional SL, including a detailed description of the proposed paired scheme. Our stochastic geometry based analysis of the single-lane highway directional SL ad-hoc network is presented in section V. The design of transmit power control for directional SL networks is covered in Section VI. In Section VII, we describe our system-level simulation setup and the corresponding results. We summarize the conclusions and future research directions in Section VIII.

II. NR SL MODE 2 RESOURCE ALLOCATION
A. PHY LAYER STRUCTURE OF NR SL NR SL uses an orthogonal frequency division multiplexing (OFDM) waveform with a cyclic prefix for its transmissions. In the time domain, a single SL radio frame has a duration of 10 ms. The SL frame is divided into 10 subframes, each of duration 1 ms. The minimum unit of resource allocation for the SL in time domain is a slot. The flexible numerology feature of NR allows the use of different OFDM subcarrier spacings (SCS) ({15, 30, 60, 120}kHz). The duration of a single slot is decided based on the SCS value used. For FR2 frequencies, SCS of 60 or 120 kHz can be used, corresponding to a slot duration of 0.25 ms and 0.125 ms, respectively.
A physical resource block (PRB) consists of 12 contiguous subcarriers in the frequency domain. The minimum unit of resource allocation in SL is a subchannel consisting of 10,12,15,20,25,50,75 or 100 consecutive PRBs. In NR V2X, only a certain pre-configured set of time slots and PRBs, called the SL resource pool, can be used for SL.
A single SL slot consists of 14 OFDM symbols, with the first symbol reserved for automatic gain control (AGC) and the last symbol acting as a guard symbol. A SL transport block (TB) within a slot can span multiple subchannels. For the first subchannel allocated to a TB, two or three OFDM symbols are reserved for the physical SL control channel (PSCCH), which is used to transmit the first stage of the SCI. For a slot with no HARQ feedback transmissions, the remaining symbols will carry the second stage of SCI and SL data over the physical SL shared channel (PSSCH). Fig. 3 illustrates the typical structure of an NR SL slot with a two-symbol SCI configuration. PSCCH is not transmitted in other subchannels of a TB (i.e., second onwards), and the unused symbols in these subchannels are utilized for PSSCH transmission (as shown in Fig. 3b)). SCI is sent in two stages by a SL Tx UE. The first stage of the SCI contains information about the resources reserved by the SL Tx UE for transmission of the current TB, retransmission of the same TB, and the resource reserved for the next TB in case periodic resource allocation is used. It also includes the Quality of Service (QoS) priority 5 of the packet, as specified by higher layers. The first stage SCI (SCI 1) is carried over the PSCCH. All SL UEs in the network that operate in the same SL resource pool and can receive the first stage of SCI are able to decode it. They use this information to sense ongoing transmissions and avoid selecting the slots and subchannels already reserved by other SL Tx UEs. The second stage of SCI (SCI 2), which is carried over PSSCH along with the data payload, contains additional control information needed to decode the data part of the TB. 6 Fig . 4 shows an ongoing SL transmission between Tx1 and Rx1, while Tx2 is sensing the channel before selecting a resource for its transmission to its intended receiver, Rx2. Rx1 can receive and decode the entire TB, while other nearby SL UEs (e.g., Tx2) can only decode SCI 1. SCI 1 includes information about the resources reserved by Tx1, and its resource reservation interval (RRI), i.e., the transmission periodicity. A reserved resource refers to a set of contiguous subchannels in the frequency domain. If Tx2 receives an SCI (specifically, SCI 1) from Tx1 in time slot x, indicating that Tx1 uses resource S with an RRI of y, then it knows that Tx1 will also occupy the same resource in time slots x + y, x + 2y, and so on.

B. SL RESOURCE ALLOCATION
3GPP Release-16 has standardized two designs for SL resource allocation [5], [10]. For the SL UEs in-coverage of an NR cell, SL resource allocation can be done by the gNB, known as Mode 1 resource allocation. This paper focuses on Mode 2 where SL UEs perform autonomous resource allocation based upon sensing the reservations of other UEs.
Mode 2 Resource Allocation Procedure: In Mode 2, SL Tx UEs autonomously select their resources from a resource pool. SL UEs have pre-configured resource pools which can be updated by the network when the UEs are in coverage. 5 In this paper, for simplicity, we assume that all transmissions have the same QoS priorities. 6 Henceforth, we shall refer to the first stage SCI simply as SCI.
A Mode 2 SL Tx UE can either perform dynamic or semi-persistent resource allocation. The semi-persistent scheme can be used to select and reserve resources for the transmission of several TBs (and their retransmissions). These resources are a set of time-frequency resources that a SL Tx UE reserves for its future transmission(s) by notifying neighboring UEs using the SCI. The simplified Mode 2 procedure can be defined as a two-step process [5], [10]: Step 1 -(Resource Identification): A SL Tx UE decides a suitable time window to transmit a packet depending upon its delay budget, called the resource selection window. It then uses sensing information obtained in the last W sense ms (called sensing window with duration W sense = 100 ms or 1100 ms). An SCI must be received with reference signal received power (RSRP) higher than a configured threshold. The RSRP threshold depends upon the QoS priorities of the detected and the intended transmissions. If the SCIs received during the sensing window indicate reservation of future slots and subchannels inside the selection window, the SL Tx UE excludes these resources from the set of candidate resources for resource selection in Step 2. At the end of this step, if the identified candidate resources are less than X % of the total resources in the selection window, the RSRP threshold is increased by 3 dB, and the SL Tx UE repeats Step 1. The possible values of X are 20, 35 or 50 [11]. In the rest of this paper, we assume X = 20.
Step 2 -(Resource Selection): Among the identified candidate resources in Step 1, the SL Tx UE will choose a resource randomly for its next packet transmission. This resource is a fixed set of subchannels in a time slot within the selection window. Random selection in Step 2 leads to interference randomization and avoids scenarios with multiple neighboring UEs repeatedly selecting the same set of SL resources.
Once a resource is reserved, the SL Tx UE uses it for its next RRC consecutive transmissions in periodic time slots, where the period is referred to as the resource reservation interval (RRI). RRC is the resource re-selection counter. Once a reservation expires, i.e., the resource counter goes to 0, the SL Tx UE can perform a new resource selection procedure with probability p change or keep the same resources for another RRC transmissions with probability 1 − p change .
Before actual transmission, a SL Tx UE will perform a re-evaluation procedure (similar to the Mode 2 procedure) to confirm the validity of its pre-selected resources and reallocate resources in case previous ones are not valid. The detailed procedure for SL Mode 2 is given in [10]. Fig. 5 shows the sensing and selection windows for a SL Tx UE performing the Mode 2 resource allocation procedure. Here, the new packet to be transmitted arrives at slot n, T 2 is the packet delay budget, T proc,0 and T 1 are the processing delays needed to perform sensing and resource selection, and T 0 − T proc,0 is the size of the sensing window (in slots).
SL Mode 2 in Release-16 assumed continuous sensing. While this is feasible for NR V2X vehicular UEs that do not have power limitations, the same would not be the case for smartphones or other user devices that may use SL for a diverse set of applications in the future [12]. 3GPP Release-17 introduced partial sensing based resource selection to alleviate this issue. Random selection, i.e., resource selection without sensing is also an option for saving UE power. In addition to this, Release-17 also standardized inter-UE coordination, where a SL Tx UE can assist other SL UEs in their resource selection process. These enhancements to resource allocation mainly targeted toward power savings and UE coordination are not considered in this paper. However, our proposed solutions for SL at high carrier frequencies will apply to all variants of Mode 2 resource allocation (i.e., with or without Release-17 enhancements).

III. RELATED WORK
The early research on D2D communications in cellular networks leading up to its introduction in 3GPP Release 12 is comprehensively summarized in [2]. D2D was initially introduced as a solution for extending cellular network coverage and providing basic proximity services. However, the emergence of new applications, such as the Internet of Things (IoT), augmented and virtual reality (AR/VR), and V2X, have diversified the set of use cases for D2D technology. Among these, V2X has emerged as the primary use case for cellular D2D communications in recent years [13], leading to the development of the 5G NR V2X standard, which utilizes SL as the D2D communication interface [5]. Our work focuses on enhancing SL operation at high carrier frequencies such as mmWave/sub-THz by proposing novel distributed resource allocation and power control strategies for SL Mode 2. This section will provide an overview of existing literature related to the problems addressed by our work later in this paper.
A. SENSING-BASED CHANNEL ACCESS AT HIGH FREQUENCIES SL Mode 2 resource allocation relies on sensing the wireless channel to detect ongoing transmissions. The SL UEs must decode the SCI of ongoing transmissions. After decoding received SCIs, a SL Tx UE can precisely determine the frequency domain subchannels and the time domain slots reserved by other SL UEs. This is conceptually similar to sensing-based channel access commonly used in wireless technologies operating in unlicensed frequency bands (e.g., WiFi). The problem of channel access in unlicensed mmWave bands has been addressed by several papers [14], [15], [16], [17], [18], [19]. The ''listen-before-talk'' (LBT) [14], [20] sensing procedure used for unlicensed channel access involves a short duration energy-based sensing procedure. A Tx device can access the channel for its next packet if the energy it detects during sensing is below a certain threshold. It is therefore of interest to look into the literature on unlicensed systems operating at mmWave/THz frequencies to understand the limitations of sensing-based channel access protocols.
Exposed and hidden node issues are a major concern for unlicensed systems with directional transmissions, e.g., 802.11ad and NR-unlicensed (NR-U). They are well known and studied in this context for a long time [21], [22]. More recently, substantial work has been done on improving channel access procedures for directional mmWave systems in unlicensed bands [14], [15], [16], [17], [18], [19]. Some of these works propose central coordination by the WiFi access point (AP) or the gNB, and/or some form of cooperation between the users accessing the channel [17], [18], [19]. While this may be feasible for SL UEs in coverage of a gNB, in this paper, we only consider Mode 2 resource allocation, which is more prevalent in out-of-coverage UEs.
Rx side sensing for LBT is proposed in [15]. Although additional Rx assistance may be beneficial for sensing-based channel access, the information exchange between the Tx and Rx incurs overheads, and may also lead to increased latency. In this work, we consider Tx-only sensing and the resource allocation does not use any Rx feedback. Paired sensing at the Tx is proposed in [14] for NR-U systems in unlicensed mmWave bands. While this may reduce the impact of hidden nodes, it operates within the realms of energy-based sensing and is not applicable to NR SL, where we need to decode the received SCI to obtain information about the usage of SL time-frequency resources.
In this work, we propose a channel access solution for SL in licensed mmWave/sub-THz bands with a new SL transmission/reception structure wherein SL UEs both transmit and receive SCI in paired directions. Thus, we explore another degree of freedom available for SL systems, which is the direction of SCI transmission and reception. This has not been explored in the above-cited literature on unlicensed mmWave communications, primarily because there is no segregation of control and data channel transmissions in unlicensed wireless systems, and the sensing is purely based on energy detection.
Due to similarities in the general system behavior, it is instructive to look at how autonomous channel sensing is analyzed in the cellular D2D literature. Shang et al. in [23] analyze 3D spectrum sharing between unmanned aerial vehicles (UAVs) and D2D networks, where the UAVs perform spectrum sensing in the 3D space to contend for channel access. In [24], the authors introduce a multi-armed bandit problem to solve for an optimal distributed auction-based channel allocation in an LTE D2D network. Li et al. propose elderly health monitoring using a wireless D2D network in [25], where they propose an autonomous sensing-delivering-gathering system for collecting lifelog data. While all these references make valuable contributions to autonomous sensing-based channel access in ad-hoc and D2D networks, none of them explicitly model the sensing-based autonomous resource selection protocol of either C-V2X or NR V2X SL. They also do not consider directional transmissions at high carrier frequencies.
The authors in [26] propose a SL, full duplex, grant-free transmission procedure for the C-V2X SL and show that it performs better than the 3GPP-compliant semi-persistent sensing scheme. However, mmWave/sub-THz band operation was not considered, which requires additional enhancements to adapt to the directional nature of transmissions at these frequencies. To the best of our knowledge, ours is the first work to incorporate the crucial advancements made in NR V2X SL, along with our proposed resource allocation and transmit power control strategies, for enhanced FR2 operation.
More recently, several simulation-based studies have evaluated the impact of parameters like numerology, modulation and coding scheme (MCS), resource retention probability, etc., on the performance of SL Mode 2 [27], [28], [29]. These studies have only looked at NR SL systems at sub-6 GHz frequencies, whereas our focus in this paper is on directional SL at higher frequencies. Finally, an ns-3 simulator for NR V2X at mmWave frequencies was introduced in [30]. This model uses a Time Division Multiple Access (TDMA) scheme with a pre-configured scheduling pattern for resource allocation at the MAC layer. This is fundamentally different from the Mode 2 sensing-based resource allocation defined in 3GPP Release-16, which is what we use in our simulations.

B. ANALYTICAL MODELING OF SL NETWORKS WITH UE AUTONOMOUS RESOURCE ALLOCATION
LTE C-V2X (Cellular-V2X) was the predecessor to the 5G NR V2X standard. The UE autonomous resource allocation mode of C-V2X is known as Mode 4. In recent years, there have been several efforts to analyze the C-V2X Mode 4 MAC layer protocol [31], [32], [33], [34]. In [31], the authors present the average packet delivery ratio as a function of the distance between transmitter and receiver and investigate different types of packet transmission errors in C-V2X Mode 4. A multi-dimensional Markov model was proposed in [32] to evaluate the MAC layer performance of C-V2X Mode 4, providing insights on the average delay, the collision probability, and the channel utilization in Mode 4. Most of this work either obtained the channel access collision probability by simplifying the MAC or by neglecting the influence of hidden nodes. The work in [34] develops an expected value analysis of the channel access collision probability for a C-V2X Mode 4 network in a highway deployment scenario, taking into account the effect of sensing range of the vehicular UEs and the presence of hidden node terminals. The NR V2X SL specifications have made significant advances from the legacy C-V2X systems, as explained in detail in section II, therefore a fresh analytical model is needed.
A stochastic geometry-based approach was first considered in [35] for modeling the packet reception probability and throughput of a linear vehicular ad-hoc network. While we make use of the basic system model and analysis approach developed in this work, we move away from the simple ALOHA-like MAC layer resource selection used by the authors. Instead, we design a separate model for the control channel sensing-based resource allocation, which captures the dynamics of Mode 2 resource allocation used in today's 5G NR SL design. Moreover, our analysis considers communication at mmWave frequencies, for which we use a different fading distribution than the Rayleigh fading assumption used in [35]. We also take into account the directionality of transmissions at high carrier frequencies and work with a path loss compensation-based power control scheme, instead of the constant transmit power assumption used in [35].
We are the first to approach the problem of analyzing vehicular SL ad-hoc networks operating at mmWave frequencies. All of the previous related work [31], [32], [33], [34], [35], [36] considered sub-6GHz LTE operation, with omnidirectional data and control channel transmissions, and omnidirectional sensing.

C. TRANSMIT POWER CONTROL STRATEGIES FOR SL COMMUNICATIONS
The current 3GPP design of NR SL considers SL path loss compensation for transmit power control of SL devices in out-of-coverage scenarios [5], [10]. We extend this approach by proposing novel interference estimation techniques that can be used to adapt the transmit power of SL Tx UEs. While interference-aware power control has been studied in previous works for wireless ad-hoc networks and distributed cellular D2D networks [37], [38], [39], it has not yet been standardized for 3GPP's NR SL due to the challenge of estimating interference for a SL device's transmissions without causing significant overhead. In Section VI, we address this challenge by leveraging the SCI information already available at a Mode 2 SL Tx UE performing sensing for resource selection. Previously, [40] and [41] proposed sensing-based power adaptation for C-V2X Mode 4 communication. Power control for C-V2X mode 4 was also considered in [42] and [43]. While these approaches inspire some of our power control design, the schemes proposed in our work also take into account the directional nature of communication at high frequencies. Our power control strategies are designed to complement our proposed paired scheme for SL Mode 2 resource allocation in directional SL networks. We aim to improve the overall system performance using a combination of our novel control channel transmission/reception strategies and our distributed transmit power control design.

IV. PROPOSED TRANSMISSION/RECEPTION STRATEGIES FOR DIRECTIONAL SL RESOURCE ALLOCATION
This section highlights the critical issues in the omni and directional schemes for SL Mode 2 resource selection. We then introduce the proposed paired scheme to resolve hidden node issues while minimizing potentially exposed node scenarios. As we operate at high frequencies, directional beamforming is used for both SL transmission and reception. We assume a simple ''cone plus circle'' antenna model commonly used in the mmWave literature [44], [45] where the antenna pattern is a step function with a constant mainlobe gain over the beamwidth and a constant side-lobe gain otherwise. 7

A. DRAWBACKS OF CURRENT TRANSMISSION/RECEPTION TECHNIQUES
In Fig. 6, we show four examples of SL deployment scenarios. All data transmissions are assumed to be highly directional.
In each example, we have two pairs of SL UEs: Tx1-Rx1 and Tx2-Rx2. The Tx1-Rx1 link is an ongoing NR SL transmission. We assume that Tx2 is a SL Tx UE that wants to start a new directional transmission to its corresponding Rx UE, i.e., Rx2. We use these scenarios to highlight drawbacks of the aforementioned omni and directional schemes. Further, we will explain how our proposal of paired SCI transmission and paired sensing can resolve these cases, as an illustration of its general effectiveness for directional SL systems. • Exposed node issues for the omni scheme: In scenario (a) of Fig. 6, there is no interference between the two SL transmissions, as their directions are not aligned. But, if Tx1 sends its SCI omnidirectionally, and Tx2 performs omnidirectional sensing, Tx2 perceives the Tx1-Rx1 transmission as interference. Consequently, it will exclude resources reserved by Tx1 from its selection window, which may lead to a scenario where Tx2 cannot find enough resources for its own transmission. Furthermore, omnidirectional transmission/reception of SCI will be impractical at high frequencies due to high propagation losses. This will cause decoding failures of the SCI at the intended Rxs.
• Paired sensing can resolve some hidden node issues: In scenario (b) of Fig. 6, the Tx1-Rx1 link acts as a hidden node if Tx2 performs directional sensing, i.e., only in the direction towards Rx2. A straightforward solution to resolve this is for Tx2 to also perform sensing in the paired direction, which is at a 180 • angle w.r.t. to the Tx2-Rx2 link. This is what we call paired sensing.
• Paired sensing alone can not resolve all hidden nodes: Scenario (c) in Fig. 6 shows another case where two SL transmissions are aligned. The difference from scenario (b) is that the sensing UE (Tx2) is located behind the Tx1-Rx1 link. Hence, irrespective of the type of sensing used at Tx2, it will never sense the directional SCI transmissions of Tx1. Such cases can be resolved if Tx1 transmits its SCI in two directions, one in the direction of transmission, i.e., towards Rx1, and another in the opposite direction. This is what we call paired SCI transmission. Finally, in Fig. 6(d), a new Tx2-Rx2 transmission can interfere with Tx1-Rx1. Tx2 should ideally exclude resources reserved by Tx1, but this will only be possible if Tx1 uses paired SCI transmissions. From the above analysis, we would also like to note that hidden node problems in highly directional SL systems occur only when two (or more) interfering transmissions are aligned in 2D space, i.e., they are collinear. This becomes particularly significant in NR V2X SL, where vehicles communicating on the roads can result in collinear transmissions. For instance, a highway with a single lane and all vehicles communicating within the same lane presents a worst-case scenario, as all SL transmissions are then collinear.

B. PROPOSAL OF PAIRED SENSING AND PAIRED SCI TRANSMISSION
The proposed scheme, referred to as the paired scheme, comprises a joint transmit/receive strategy. In this scheme, when a SL Tx UE transmits, the SCI is transmitted in the intended direction of transmission (primary direction) as well as the direction opposite to it (paired direction). The sensing of SCI for resource allocation is neither omnidirectional (as in omni scheme) nor only in the intended direction of transmission (as in directional scheme). A SL Tx UE doing autonomous resource allocation performs SCI sensing in the (i) primary direction, and (ii) paired direction simultaneously.
The SCI transmission in primary and paired directions may be realized simultaneously if the UE is equipped with multiple antenna panels and necessary hardware. They may use the same PSCCH/PSSCH structure as in legacy SL design. In a design with a single antenna panel (less hardware), the two SCI transmissions can be done in a TDMA manner. For a TDMA based structure, we propose three different multiplexing patterns for a SL slot, as shown in Fig. 7.
In the first design ( Fig. 7a), paired SCI (SCI in the paired direction) transmission follows primary SCI (SCI in the primary direction), which is followed by the data. This is backward compatible from the perspective of sensing done by legacy SL UEs, which can only decode primary SCI sent in the first two symbols of a slot. However, it requires two beam switch events within a slot (primary to paired to primary). It also introduces a gap between primary SCI and data, which may have negative implications on channel estimation quality. The second design (Fig. 7b), reverses the order of transmission of primary and paired SCI, thus eliminating one beam switch event and the gap between primary SCI and data.
The drawback of this design is its lack of backward compatibility. The third design (Fig. 7c) proposes the transmission of paired SCI at the end of the slot. This maintains backward compatibility for legacy SL UEs and also requires only one beam switch event.
Recall from Sec. II-A that the PSCCH is only sent over the first subchannel of a SL TB which can comprise multiple subchannels in the frequency domain (Fig. 3). Hence in a TDMA based structure for paired SCI transmission, the overhead of the two extra paired SCI symbols (Fig. 7) is only applicable to the first subchannel of a multi-subchannel TB.
For the simulations in this paper, we assume that SL UEs are equipped with multiple antenna panels and can perform simultaneous transmission/reception in primary/paired directions. A detailed study with lower capability devices requiring the use of TDMA-based primary/paired operation is left to future work. Non-ideal beamforming may cause performance losses in practice, but we ignore those effects for simplicity and focus on the directional deafness issues in this work. In NR V2X, vehicles are typically assumed to have enough battery power, so increased UE power consumption from using the paired scheme is not a major concern. However, for a wider range of applications, such as AR/VR and industrial IoT, we aim to consider the impact of non-ideal beamforming and power consumption in the future.

C. DIRECTIONALITY INDICATION IN THE PAIRED SCHEME AND OPTIMAL SENSING RESPONSE OF MODE 2 SL TX UEs
As explained earlier, in a directional SL system at mmWave/sub-THz frequencies, the interfering transmissions of concern are only from collinear devices that are aligned with a SL Tx UE's own transmission direction. For a SL Tx UE, the main purpose of sensing is to determine the resources reserved by ongoing transmissions and to avoid any potential collisions. This includes all SL transmissions that can cause potential interference to the sensing Tx UE's transmission, or that may be harmed by interference if the sensing Tx UE starts a new transmission of its own over the same resource.
At this point, we would like to define key terminology related to the paired scheme, that would be useful in following the discussion in the rest of the paper: • Primary direction: For a SL Tx UE, this is the direction of its intended SL Rx UE (receiver).
• Paired direction: For a SL Tx UE, this is the directly opposite direction w.r.t. its intended SL Rx UE (receiver). In other words, this direction is at a 180 • angle from its primary direction.
• Primary SCI: This is the SCI transmitted by a SL Tx UE in its primary direction.
• Paired SCI: The SCI transmitted by a SL Tx UE in its paired direction. We assume that a SL Tx UE performing sensing can determine whether any SCI received from other SL Tx UEs is a primary SCI or a paired SCI. In a setting where the primary and paired SCIs are transmitted in a TDMA manner, this is easy to determine based on the OFDM symbol locations at which an SCI is received. When primary/paired SCI transmissions are done simultaneously, we would need an extra bit of information in the SCI that could indicate whether it is a primary or a paired SCI. A second assumption here is that while doing paired sensing, a SL Tx UE can distinguish between the set of SCIs received from its primary direction and the set of SCIs received in its paired direction. Thus, any SCI received in the primary detection does not interfere with any SCI received in the paired direction, and vice-versa. Now, from the perspective of a SL Tx UE that performs sensing for resource allocation, we can define the following scenarios for the SCI received from ongoing SL transmissions in the network: • Case A: Primary SCI received in its primary direction • Case B: Primary SCI received in its paired direction • Case C: Paired SCI received in its primary direction • Case D: Paired SCI received in its paired direction The above-listed cases have also been depicted in Fig. 8. In each case, we have two pairs of SL UEs: Tx1-Rx1 and Tx2-Rx2. The Tx2-Rx2 link is an ongoing NR SL transmission. We assume that Tx1 is a SL Tx UE that wants to start a new directional transmission to its corresponding Rx UE, i.e., Rx1 (depicted by the directional beam from Tx1 to Rx1 in Fig. 8). For both Tx1 and Tx2, the primary and paired directions are shown using solid and dotted arrows respectively. Here, we discuss how the aforementioned scenarios in Fig. 8 should be dealt with by a SL Tx UE performing sensing for its Mode 2 resource allocation: • Case A: Ignore the received SCI. This is because the actual data transmission directions of the two Tx-Rx pairs are not aligned, thus they will not cause any significant data channel interference to each other. Note that this is true, irrespective of the location of Rx2.
• Case B: This SCI should be taken into account while performing Mode 2 resource allocation. The SL Tx UE performing sensing should exclude from its own selection window the resources already reserved by the sender of this SCI. In both cases B(i) and B(ii) shown in Fig. 8, the Tx2-Rx2 transmission will interfere with a new transmission started by Tx1. In case B(i), a new Tx1-Rx1 transmission will not interfere with the ongoing Tx2-Rx2 link but in case B(ii), where Rx2 is located ahead of Tx1, a new Tx1-Rx1 transmission can also interfere with the ongoing Tx2-Rx2 link.
• Case C: The received SCI should be treated similarly as in Case B. In case C(ii), the Tx1-Rx1 link will be interfered by Tx2, if both Tx1 and Tx2 use the same resource. In case C(i), Tx2 is located ahead of Rx1. Hence, in this case, the Tx1-Rx1 link has no potential interference from Tx2-Rx2. At the same time, we must note that a new Tx1-Rx1 transmission can interfere with the already ongoing Tx2-Rx2 transmission.
• Case D: Ignore the received SCI. Same as Case A, here the transmission directions are not aligned, which means there will be no actual data channel interference between the two links, i.e., Tx1-Rx1 and Tx2-Rx2. From the discussion above, we conclude that a SL Tx UE performing paired sensing should consider only those received SCIs that falls under the scenarios described by Case B or Case C. In addition to the directionality, the RSRP of the received SCI must be greater or equal to the pre-configured RSRP threshold for resource allocation, for it to be considered in Step 1 of the Mode procedure.

1) PAIRED SCHEME IN ACTION IN V2X HIGHWAY DEPLOYMENTS
So far, our discussion on Mode 2 resource allocation for high-frequency SL has been general in nature. In Fig. 9, we provide a visual illustration of our target deployment scenario and system model. Fig. 9 shows how the paired scheme resolves hidden and exposed node issues for directional SL in a 5G NR V2X highway scenario. It shows the case of two pairs of vehicles in a single lane of a highway. The Tx1-to-Rx1 transmission acts as a hidden node for the Tx2to-Rx2 transmission. The use of an additional paired beam for channel sensing helps the Tx2 vehicle to gain additional ''visibility'' into the ongoing transmissions in the V2X network. In this case, the paired scheme resolves the hidden node issue by making Tx1 visible to Tx2. However, the use of paired scheme can create a new exposed node situation where the vehicle Tx2 can act as an exposed node for the Tx1-Rx1 link. The use of an extra bit for directionality indication, as described in Sec. IV-C, helps us in resolving these new exposed node situations. The paired scheme is a Tx-only enhancement; hence it does not introduce any new handshaking protocol or similar control information exchange mechanism. The SL Mode 2 protocol with the paired scheme is still a fully distributed UE-autonomous procedure where the SL Tx UE does not need to communicate with the gNB or the Rx UE for resource scheduling.

V. ANALYSIS OF DIRECTIONAL SIDELINK MODE 2 SYSTEM
In the previous section, we discussed in detail our proposed paired sensing and SCI transmission procedure for the NR V2X SL at high carrier frequencies. To obtain quick and intuitive insights on the working of this procedure, it is useful to have a mathematical model which can show how key system parameters can affect some key performance metrics. We now propose a simple analytical model for the NR V2X SL, and use it to compute the probability of successful packet reception for various traffic densities.

A. LINEAR VANET MODEL WITH NAKAGAMI-M FADING CHANNELS
We consider an infinite linear vehicular ad-hoc network (VANET) as a representation of our single-lane highway vehicular network. We assume, for simplicity, that there is only one channel for which the vehicles are competing in each time slot. 8 We model this as a one-dimensional Poisson point process (PPP), = {X i }, where X i denotes the locations of the transmitter vehicles, with uniform density λ [35]. We assume [35] that each vehicle represented in transmits to a receiver (not represented in ) within a distance R from it. We assume that the vehicles are all moving at the same speed on the highway, i.e., their relative locations do not change over time. A simple ALOHA transmission protocol was assumed in [35] where each Tx vehicle transmits on a given slot with probability p independent of other Tx vehicles in the network. This protocol does not involve any channel sensing based resource selection, and hence will not be suitable for a SL Mode 2 based mmWave vehicular network. NR V2X SL networks have evolved significantly from ALOHA-based VANETs. In this work, we model the following new capabilities: • Periodic transmissions -vehicles transmit periodically, therefore in a time slot not all vehicles will transmit.
• Sensing procedures -vehicles sense transmissions from other vehicles and decide on whether to transmit depending on whether the channel is busy or not.
• Directional data channel transmissions -vehicles transmit data in either the East:West or West:East direction.
• Paired SCI transmission/reception -The analytical model incorporates the paired scheme proposed in Sec. IV-B.
• Appropriate channel model for NR FR2 frequencies: The authors in [35] consider a Rayleigh fading channel model, which is unsuitable for NR FR2 frequencies.
We therefore consider the Nakagami-m fading channel which is commonly used in stochastic geometry literature [45]. We define the following events for a typical Tx vehicle employing paired SCI transmission and reception in the single-lane highway: • E 1 : the event that a vehicle has a packet to transmit at a given time slot • E 2 : the event that a vehicle decides to transmit at a given time slot, based on the sensing information it has collected • E 3 : the event that a vehicle transmits in a given direction (either East:West or West:East) We now model the periodic nature of SL transmissions. Let T slot denote the OFDM slot time, and T period denote the periodicity of each vehicle's transmissions. A vehicle transmits once in every time period (T period ), 9 for a duration of 8 The extension of the analysis to multiple frequency domain subchannels is left for future work. A simple approach would be to independently analyze each subchannel and average the results of our single-channel model. We can use the subchannel bandwidth and V2X UE traffic requirements to determine the density of vehicles per subchannel. 9 This is an approximation for simplicity. As explained in Sec. II-B, the SL Tx UE may change resources after its RRC counter expires. This will temporarily break the periodic nature of transmission. one-time slot T slot . Therefore, based on the above definitions of events, we now define the probability p 1 that a vehicle has a packet to transmit at any time instant as p 1 ≜ P(E 1 ) = T slot T period . Each Tx vehicle performs UE autonomous (Mode 2) resource allocation, whereby it senses and decodes the SCI of other ongoing SL transmissions. Based on this sensing, the Tx vehicle then decides to transmit if it finds that the channel is free in a given slot and in the direction of its intended transmission. Therefore, based on the above definitions of events, we now define the probability p 2 that at any time slot, a vehicle transmits given that it has a packet in its transmission queue as p 2 = P(E 2 |E 1 ).
To model directional transmissions, we define q as the probability that a vehicle transmits in a a particular direction. Therefore, based on the above definition of events, we can write q = p(E 3 ).
Note that the event E 3 is independent of the other two events, E 1 and E 2 . We now write the following equation to model the autonomous sensing procedure in directional SL networks.
P(a vehicle transmits in a particular direction at any given time slot) We define ′ i as a PPP comprising the set of transmitters that can potentially interfere with the ith transmitter. Possible interferers must i) be scheduled to transmit in the same slot, ii) transmit in the same direction, and iii) decide to transmit after decoding the SCI of other transmitters. Therefore, we can consider ′ i as a homogeneous thinned PPP of , with uniform density λ ′ ≜ λqp 1 p 2 .
Consider the ith receiver to be at the origin. Denote d i = |X i | as the Tx-Rx distance for the ith Tx-Rx pair. We assume that the Tx-Rx distance between a SL Tx UE and its intended SL Rx UE is uniformly distributed between (d min , R), i.e., d i ∼ U(d min , R), with d min = 7m as the minimum possible distance (center-to-center) between two vehicles. This aligns well with our simulation setup and is in line with 3GPP recommendations for NR V2X evaluation [9]. The signal-to-interference-plus-noise ratio (SINR) for the ith Tx-Rx pair can be written as: where P Tx,i is the transmit power for the ith transmitter, F is a random fading coefficient for the channel, l(r) = (Ar) −β is the attenuation function with β = 2 [5] as the path-loss exponent, and A = (10 −0.1 * (32.4+20 * log f c ) ) −1/β , where f c is the carrier frequency (obtained by comparing l(r) with path loss expressions in [5]), W denotes additive white external Gaussian noise (including thermal noise at the receiver), and We analyze a simplified version of the distance-based power control schemes discussed later in Section VI. For analytical tractability, we assume that the power control only focuses on compensating the path loss incurred from the transmitter to the receiver. Therefore, we have P Tx, i = P Tx /l(d i ) ⇒ P Tx, i × l(d i ) = P Tx . For successful detection of the transmitted signal, we require that the following condition holds where T is a predetermined SINR threshold given an appropriate modulation and coding scheme (MCS). 10 We choose the Nakagami-m channel model [45], i.e., F is assumed to be a normalized gamma random variable with parameter m, whose probability distribution function (pdf) is expressed as We can appropriately tune the parameter m to control the relative strength of line-of-sight (LoS) and non-LoS (NLoS) components of the Nakagami-m fading channel (the LoS component increases with m). We take advantage of the following lemma which helps us perform an analytically tractable analysis.
Alzer's Lemma [46]: Consider a normalized gamma random variable h, with parameter m. The complementary cumulative distribution function (CCDF), P(h > γ ), is tightly upper-bounded as where η ≜ m(m!) −1/m and equality holds when m = 1. With a sufficient vehicle density and moderate-to-high traffic load, we observed in our simulations that our network is interference-limited. In light traffic conditions, with no interference, the Tx signal power is sufficient to ensure high signal quality and overcome receiver-side noise. Hence, we set W = 0 in our analysis to neglect the effect of noise.
The SL Tx-Rx transmission is not interfered by vehicles that are ''behind'' the receiver. Therefore, keeping the receiver at the origin, we only need to consider the interferers on one side. Using equations (3)-(5), we can write the probability of successful transmission for the ith Tx-Rx pair as follows: where L I ′ i (·) denotes the Laplace functional for the PPP ′ i with the interferers on one side of the receiver as derived in Appendix A. We now state the following theorem: 10 Link adaptation using 5G NR MCS adaptation is not considered here for simplicity of analysis.
Theorem 1: The average probability of successful reception for the single-lane vehicular ad-hoc network with directional SL transmissions, as a function of λ ′ = λqp 1 p 2 , and T is: Proof: Refer to Appendix A. □ Here, d j ∼ U(d min , R), i.e., the distance between the jth Tx-Rx pair is uniformly distributed between (d min , R).
While the above result gives us an analytical expression for the system-level data packet reception probability, we have not yet computed p 2 , the sensing adjustment factor in our model. We do this next using a model of the control channel of our directional SL vehicular network.

B. SCI DETECTION AND COMPUTATION OF p 2
In the control channel, the vehicles transmit sidelink control information (SCI), and also continuously sense the SCI transmitted by other vehicles. All SL Tx vehicles use the paired scheme proposed in section IV. The use of the paired scheme entails the following assumptions: • For each SL data packet that a Tx vehicle transmits, it also transmits the SCI associated with that transmission in the same slot. The SCI is transmitted in both the primary and paired directions of the Tx vehicle.
• Whenever a SL Tx vehicle performs sensing, it does so in both its primary and paired directions. The sensing in both directions is performed in an independent fashion, i.e., any SCI received in the primary detection does not interfere with any SCI received in the paired direction, and vice-versa. The ith SL Tx vehicle performs sensing and detects SCI from all other Tx vehicles in the network. Consider this Tx UE to be at the origin. We define ′′ i as a PPP comprising the set of transmitters that can potentially cause interference in the control channel with the ith sensing Tx vehicle. Similar to the data channel, we can assume ′′ i to be a homogeneous PPP with uniform density λ ′′ . Note that because we use the paired scheme, we do not include the ''directionality factor'' q in the control channel analysis. Hence, instead of λ ′ = λqp 1 p 2 used earlier, here we use the thinning probability λ ′′ = λp 1 p 2 .
Assuming the same power control mechanism as the data channel, we can write down the signal-to-interference-plusnoise ratio (SINR) for the SCI of the jth interfering transmitter at the ith sensing Tx vehicle located at the origin, i.e., X i = 0, where the terms P Tx,j , F, l(|X j |)) and W are defined identically as earlier for the data channel in Eq. (2), and I ′′ i ≜ {X j }∈ ′′ i P Tx,j × F × l(|X j |) denotes the control channel interference at the ith sensing Tx vehicle. As explained in Sec. V-A, we again set W = 0. The probability of successful decoding of SCI of a typical interfering transmitter (with Tx-Rx distance d ∼ U (d min , R)) at a distance r from the ith sensing Tx vehicle is where L I ′′ i (·) denotes the Laplace functional for the PPP ′′ i for interferers on one side of the receiver for the primary as well as paired directions, as derived in Appendix B.
If a vehicle has data to transmit in a particular slot (with probability p 1 , as defined earlier), it will sense the SCI of other vehicles and determine whether or not the channel is busy. It will transmit with a probability p 2 , defined as the probability that the channel is ''free'', i.e., every other vehicle either does not transmit in the same slot in the same direction (with probability 1 − qp 1 p 2 ), or otherwise, if they transmit (with probability qp 1 p 2 ) their SCI fails to be decoded. Hence, the probability of transmission of a vehicle after decoding the SCI from other transmitting vehicles in that slot is derived as where p SCI i (r, λ ′′ , T ) is given by the following theorem: Theorem 2: The average probability of successful detection of SCI at a distance r for the single-lane vehicular ad-hoc network with directional SL transmissions, as a function of λ ′′ = λp 1 p 2 , and T is given by: Proof: Refer to Appendix B. □ VOLUME 11, 2023

C. THROUGHPUT ANALYSIS
In the previous discussion, we assumed a binary detection model, i.e., the reception is successful if the received SINR is above a threshold, else it is a failure. We now consider that at any value of SINR, transmission would be possible with a bit-rate τ , depending on the SINR value itself [35]. Assuming near-perfect adaptive coding, we consider the rate to approach the maximum given by Shannon's law for the additive white Gaussian noise (AWGN) channel. Assuming unit bandwidth, we compute the instantaneous throughput (bit-rate) at which for the ith Tx-Rx pair, the Rx vehicle receives information from the Tx vehicle at x i as where SINR i is the received SINR for the ith Tx-Rx pair.
Using standard probability theory, the mean throughput is with p(λ ′ , T = 2 t − 1) denoting the average probability of successful reception for a Tx-Rx pair for a VANET with effective vehicular density λ ′ given an SINR threshold T . From the discussion in Section V, λ ′ ≜ λqp 1 p 2 . For a Nakagami-m fading channel, p(λ ′ , T ) is given by Theorem 1.
Substituting 2 t − 1 = v β , and assuming an interferencedominated regime (W ≈ 0), we solve (13) to get Similar to the authors in [35], we propose a metric called the mean density of transport, d trans , defined as the average number of bits that are successfully transported per unit of time per unit length of the network. Using Campbell's theorem, we can write the expression for d trans (in bits/s/Hz/m) as Therefore, the above quantity d trans (λ ′ , t ′ ) is a measure of the average throughput of successfully received information for the single-lane vehicular ad-hoc network.
In Section VII, we compare our proposed analytical model in this section with an equivalent simulation using realistic 3GPP NR V2X traffic models and demonstrate its validity. We additionally show how the analytical model can be used to obtain insights on the capacity of the NR V2X network.

VI. ENHANCED POWER CONTROL SCHEMES FOR DIRECTIONAL SL MODE 2 SYSTEMS
In this section, we address the issue of distributed transmit power control for directional sidelink networks at high carrier frequencies. First, we provide an overview of the SL power control mechanism specified in 3GPP Release-16. Next, we introduce our ideas for interference estimation-based power control, followed by a detailed description of our proposed practical Tx power control strategies that utilize the existing SL control and feedback information to implement those ideas effectively.

A. SL POWER CONTROL IN 3GPP RELEASE-16
In the latest 3GPP standards for sidelink communication, there is no closed loop power control; only open loop power control is supported. Sidelink power control can be based on the estimation of the downlink (DL) path loss (between the gNB and SL Tx UE) or sidelink (SL) path loss (between the SL Tx and SL Rx UE). A SL Tx UE can be configured to use the DL path loss or SL path loss or both to compute its transmit power to a given SL Rx UE [5].
Power control can be based on the DL path loss when the SL Tx UE is in network coverage. This allows for mitigating the interference at the gNB (for uplink reception). However, this work does not consider any DL path loss compensation based power control for the SL Tx UEs, which aligns with our assumption that the network only consists of unicast SL transmissions between SL Tx-Rx pairs, and the SL Tx UEs operate in Mode 2 (i.e., out of coverage).
For unicast transmissions between pairs of SL Tx-Rx UEs, compensating the path loss in the link between the SL Tx UE and its intended Rx UE, is of more interest. This is termed as SL path loss (PL SL ) based power control, and can be used to compensate the attenuation due to large-scale path loss in the sidelink wireless channel. SL path loss-based power control can be used when the SL Tx UE is in or out of coverage and can be enabled or disabled via (pre-)configuration. For this power control scheme, the Tx UE requires an estimate of the SL path loss that can be obtained from feedback of the Rx UE. Based on PSSCH DMRS transmitted by the Tx UE, the Rx UE can obtain an average RSRP over several RSRP measurements in order to mitigate fluctuations in the received power. The Rx UE cannot derive the SL path loss based on the RSRP measurements since the transmit power of the PSSCH DMRS is not indicated to the Rx UE. Thus, the Rx UE feeds back the average RSRP to the Tx UE using higher layer signaling. The Tx UE may use the fed back average RSRP along with the average transmit power of the PSSCH DMRS to derive the sidelink path loss PL SL (in dB) as follows: For a LoS link at high carrier frequencies (mmWave/ sub-THz), SL path loss based power control can work well to mitigate the effects of the wireless channel between a SL Tx UE and its intended SL Rx UE. However, in a network with multiple ongoing SL Tx-Rx transmissions, interference is a key contributor to signal quality degradation. If the power control only compensates the SL path loss, it is oblivious to the potential interference levels that a SL transmission will face, and thus the SL Rx UE may not be able to decode a packet when there is significant interference on the overlapping SL sub-channels (despite path loss compensation). Unlike the Tx-Rx path loss, it is much more difficult for a SL Tx UE to get an estimate of the interference levels experienced by its intended receiver. This is because the interference at the receiver depends on the current transmit power levels and resource selection of the other SL Tx UEs in the network.
In SL Mode 2, channel sensing is used to estimate the resources already reserved by other SL Tx UEs in the network. While this helps the sensing Tx UE to avoid potential collisions, the Tx UE cannot observe the exact interference levels as seen on the Rx side. This is a fundamental limitation of Tx only sensing, which is why we advocate for a novel transmit power control scheme on top of our already proposed paired control transmission/reception scheme for SL Mode 2 systems at mmWave/sub-THz frequencies.

B. KEY IDEAS AND POWER CONTROL ALGORITHMS
As a baseline for comparison, we use a coarse distance-based path loss compensation scheme for transmit power control at the SL Tx UEs. A SL Tx UE is assumed to have distance estimation to its intended Rx UE which it can compute through measurements supported by NR SL. Knowing the distance, each SL Tx UE chooses the minimum power that results in an SNR equivalent to the data decoding threshold (10 dB). A fixed interference margin of 5 dB 11 is added to account for neighboring transmissions that are not known a priori. This is referred to as the Baseline scheme in the rest of the paper. While this scheme aligns well with the SL power control procedures in 3GPP's Release 16, we believe there is major scope for performance improvement, especially in directional SL systems at high frequencies with Mode 2 (UE autonomous and distributed) resource allocation.
In a SL network with Mode 2 resource allocation, the resource selections of all the Tx UEs keep changing over time. Hence, for a SL Tx UE, the interference levels experienced by its transmissions or potential future transmissions over the SL time-frequency resources are constantly changing. A Tx power level determined by path loss compensation-based power control and a fixed interference margin may not be a reliable choice. If there is minimal interference to a SL Tx UE's transmissions, it should use a low interference margin, thus reducing power consumption to the minimum necessary. This will improve the system's energy efficiency and also reduce the probability of this SL Tx UE causing interference to other SL Tx-RX pairs in the same network. On the other hand, if a SL Tx UE's transmissions experience heavy interference, it should have the flexibility to increase its interference margin, transmitting at a higher power to maintain a successful link to its intended receiver. The maximum allowed Tx power for SL TX UEs in NR V2X highway networks is 26 dBm [9]. 11 The 5dB value was selected through simulations after careful tuning to maximize system performance (for the case of a fixed interference margin) To adapt to a highly dynamic environment, SL Tx UEs must continuously adjust their transmit power levels based on the interference they are experiencing at any given time. Monitoring and quantifying the interference experienced at the receiver is a significant challenge in a distributed SL network. We cannot assume centralized coordination by a gNB or explicit cooperation between the different SL Tx-Rx pairs in our vehicular ad-hoc network. This eliminates the option of a centralized power optimization scheme that can utilize system-wide information.
The next best case for a SL Tx UE would be if it could receive some help from its intended receiver, i.e., the SL Rx UE. The interference is best known at the receiver side. Thus, for our first power control strategy, we assume that a ''genie'' can measure the exact interference levels at each SL Rx UE of the network and sends this information to their respective Tx UEs without delay. Any Tx-Rx control feedback signaling will involve overhead and delay in a practical implementation. However, we use this genie-assisted Rx infobased power control as a reference for comparison.
Algorithm 1 contains the details of this power control scheme. The genie measures the SINR of each packet that was received in error (data decoding failure) at the SL Rx UE. The genie also knows P rx , the receive signal power of the SL transmission and the noise power, P noise . With this, we can calculate the actual interference power experienced by this SL packet if packet . We store this value for each packet received in error in the last 10 ms, in an array (IM est ). This gives us an account of the interference levels experienced by those SL packets that suffered a decoding failure in a recent time window (by default, 10 ms). We use the maximum entry of IM est for our update to the interference margin of the SL Tx UE. This is to ensure that the SL Tx UE is able to maintain a transmit power level which is enough to counter the worst channel conditions it encounters in real-time. The update rule is an exponentially weighted moving average (EWMA) using the previous value (IM) and max(IM est ). Recall that this algorithm is running in a distributed manner at all SL Tx UEs in the vehicular network. With the steps explained so far, we observed in our simulations that all SL Tx UEs gradually increased their Tx power levels to counter the interference they were experiencing, and eventually, the average system transmit power approaches the maximum power limit. The second part of algorithm 1 was designed to keep this behavior in check. Here, our genie looks at the number of SL transmissions of the SL Tx UE that were received in error (num err ). If this number is observed to be at 0 for a continuous time interval of 10 ms, this indicates that the given SL Tx-Rx pair is not facing significant interference from its neighboring transmissions. This gives us an opportunity to reduce the transmit power of this SL Tx UE, which may help in reducing the interference to other ongoing transmissions.
Next, we consider Tx-only power control, where we do not allow any coordination between the SL Tx and Rx UEs. Fig. 10 illustrates the key design goals for any such power  Remove any entry of IM est with ts older than 10 ms After every 1 ms, if there was no packet error event at in the last 1 ms then num err + + else num err = 0 if num err == 10 then control scheme. We show three different cases in a V2X highway single-lane deployment where the vehicle labeled as TX has to perform transmit power control for its directional SL transmission to its intended RX. If there is no other SL V2X UE using the same time-frequency resource, TX can operate at a low power level, enough to communicate with the RX, e.g., 5 dBm. In the second case, we have another Tx UE, TX 1 using the same resource, which causes interference.
To overcome this, TX has to increase its transmit power (e.g., to 10 dBm) to ensure a high SINR for its transmission to RX. In the final scenario shown in Fig. 10, we have another set of vehicles, TX2 and RX2, using the same SL resources. Now, the vehicle TX must find a good balance between improving the SINR for its own transmission and not causing excessive interference to other ongoing transmissions that are ''ahead'' of it in the same direction. Thus, TX could reduce its power level slightly, e.g., to 7.5 dBm, to meet both these requirements. The first Tx-side power control approach we propose relies on the ACK/NACK feedback from the receiver. HARQ ACK/NACK info can be fed back through the physical sidelink feedback channel (PSFCH) [5]. This information enables a Tx UE to measure the fraction of packets that were received and decoded successfully at its intended Rx UE, and the remaining fraction that were received in error (due to data or control decoding failures). This metric is correlated with the interference experienced at the receiver because our 5G NR V2X highway network with SL Tx-Rx pairs is an interference-limited system. We use the knowledge of ACK/NACK feedback to continuously adapt the interference margin used by the SL Tx UEs. We call this scheme ''Tx-only power control based on ACK feedback'' and Algorithm 2 embodies its detailed implementation. The SL Tx UE increases its interference margin by a step of 0.25 dB whenever it experiences a packet error (i.e., collision). The interference margin is reduced by 1 dB whenever the SL Tx UE does not experience any packet error for a continuous interval of 10 ms. Finally, we propose a Tx-only power control scheme without receiver-side feedback. We do this by taking advantage of the sensing-based resource allocation mechanism, whereby a sensing UE needs to decode the SCIs of ongoing SL transmissions in the network. While the primary purpose of this procedure is to avoid collisions during resource allocation, we use the measurement of the received power of SCIs sensed by the SL Tx UE to estimate potential interference levels at its intended Rx UE. We call this scheme ''Tx-only power control based on sensing information'' and Algorithm 3 contains its detailed implementation. For a packet, to be transmitted over slot number s, we look at the total received power of the SCIs received in the slot s − RRI, where RRI is the resource reservation interval used by all the Tx UEs in the network. We only look at the received power of ''primary SCIs received in the paired direction'' received in slot s−RRI. This is denoted as P SCI,s-RRI (primary, paired), and corresponds to Case B of Fig. 8 discussed in Sec. IV-C. We do not take ''paired SCIs received in the primary direction'' into account for this power control. This is because it is not possible to distinguish between Case C(i) and C(ii) of Fig. 8 without additional information. Moreover, we observed in our simulations, that the interference scenario of Case C(ii) is less common, as the maximum distance between a SL Tx UE and its intended Rx UE is limited, thereby limiting the chances of an interfering Tx UE being in between them.
As we already know, the SL Tx UE can estimate the path loss in the wireless channel between itself and its intended Rx UE. In Algorithm 3, we add this path loss to the measured SCI power (P IF ) to get an estimate of the potential interference at the Rx UE (P IF,RX ). This is then used in calculating the estimated SINR of a potential new transmission of the SL Tx UE over the same periodic slot. The interference margin is then adjusted based on the difference between the estimated SINR and the target SINR threshold for data detection in our network (10dB, by default). if UE has a packet to transmit in slot s then P IF = P SCI,s-RRI (primary, paired) P IF,RX = P IF + PL P RX = P TX + G TX + G RX − PL SINR estimated = P RX − 10 * log 10 (10 0.1 * P noise + 10 0.1 * P IF, RX ) if SINR estimated < SINR Th,data then Transmit power control can also be seen as an enabler of efficient resource reuse, e.g., when a SL Tx UE lowers its Tx power, it gives the opportunity to some more UEs (that are a sufficient distance away) to reuse the same resources. However, doing this in a distributed setting is the key challenge addressed by our proposed power control schemes. We would like to reiterate that the proposed Tx power control schemes are Tx-side only enhancements, i.e., they do not introduce any additional handshaking protocol or similar control information exchange mechanism between the Tx UE and the gNB, the intended Rx UE, or other SL Tx UEs. Hence, we continue operating in a fully-distributed, UE autonomous mode of operation.

VII. PERFORMANCE EVALUATION
In this section, we first use system level simulations to evaluate the performance of the proposed paired scheme for SL Mode 2 resource selection in different deployment scenarios and compare it with omni and directional schemes. After that, we validate the performance of analytical models presented in Section V against the results generated from system level simulations for the paired scheme. Finally, we present the performance of different power control mechanisms discussed in Section VI.

A. PERFORMANCE OF THE PAIRED SCHEME 1) SIMULATION SETUP
We now describe our simulation setup in detail. The key configurations and parameter settings have also been summarized in Table 1 for easier reference. We simulate unicast SL communication wherein SL UEs communicate in pairs, with one UE acting as Tx and the other as an Rx. The NR V2X Highway (Single-Lane) deployment scenario is considered. This is a special case of the NR V2X Highway scenarios recommended by 3GPP in TR 37.885 [9]. We simulate a single-lane of a highway road of length 8 km with 200 SL vehicular UEs (100 Tx-Rx pairs). We follow the guidelines specified by the 3GPP in [9] for the vehicle positions and inter-vehicle distances. For a Tx UE, the corresponding Rx UE is chosen randomly from the vehicles located within a distance of 150 m. We assume that the vehicles are all moving at the same speed on the highway, i.e., their relative locations do not change over time.
The carrier frequency of the simulated system is 28 GHz and a slot time of 0.25 ms (SCS = 60 kHz). In the frequency domain, we consider a maximum of 10 subchannels available for the SL and the subchannel size is 10 PRBs. We use a periodic traffic model, where a new packet arrives at each UE every T period ms. In our simulations, we present results for T period = {5, 4, 3, 2, 1}ms. The packet size at each Tx UE VOLUME 11, 2023 is uniformly distributed between 1 to 10 subchannels. In a single run of the simulation, the packet size of a given Tx UE remains constant.
We ensure that our parameter settings for Mode 2 resource allocation are in line with 3GPP specifications. The resource reservation interval (RRI) is assumed to be the same as the packet arrival period, i.e., T period ms, where T period = {5, 4, 3, 2, 1}. The packet delay budget (PDB) is fixed at 10 ms. The lengths of the sensing and selection window in Mode 2 are 100 ms and 10 ms, respectively. The processing time at the UE for identifying candidate resources and selecting a new resource is assumed to be negligible. All SL UEs have the same priority. The RRC is set randomly within the interval [5 * C, 15 * C], where C = 100/max(20ms, RRI) [47]. The probability of changing resources (p change ) is set to 0.8.
Directional transmission and reception of data (PSSCH) is assumed with a directional antenna of beamwidth 30 • at both the Tx and Rx UEs. For directional sensing and directional transmission of SCI (PSCCH), the beamwidth is 30 • . Directional antenna gain (main lobe) is assumed to be equal to 5dB for both the Tx and Rx UEs. In the case of omnidirectional transmission and reception, no antenna gain is assumed.
The paper assumes data transmission/reception using a single stream, with no MIMO spatial multiplexing (SM) techniques employed. The primary focus is resolving the directional deafness problem in SL Mode 2 systems to enhance SL transmission reliability. We expect to meet the QoS requirements with the high bandwidth available at high carrier frequencies even without MIMO SM techniques. However, incorporating MIMO SM techniques into the paired scheme is an interesting area and is deferred to future work.
HARQ retransmissions are not considered. For each packet, we consider three possible outcomes. If a packet is received successfully, that counts as a success. If a packet's data (PSSCH) decoding fails, that counts as a decoding failure. If the SCI of the transmitted packet could not be decoded at its intended Rx UE, this counts as a control failure.
Packet detection and decoding is based on the received SINR. For the data channel, the SINR threshold for successful data reception is 10 dB [48]. For the control channel, we consider a 5 dB SINR threshold for decoding the received SCI [48]. The same 5 dB threshold is applied while considering the set of received SCIs for the resource allocation procedure. These thresholds will vary if MCS adaptation is performed. However, we only consider a single threshold-based decoding criterion. This simplifies our network analysis while still allowing us to study the relative impact of the proposed paired solution as compared to the omni/ directional schemes. A more rigorous analysis considering link-level aspects is left for future studies.
A pure line-of-sight (LoS) channel model with 3GPP's path loss model for the highway NR V2X scenario [9] is used for the highway deployment scenario in our simulations. All SL Tx UEs use the coarse distance-based power control mechanism described in Section VI-B, with a fixed FIGURE 11. Performance comparison of the directional, omni, and paired schemes, in the highway deployment scenario in terms of (a) performance of the 10-th percentile of UEs, and (b) average system performance.
interference margin of 5 dB, and minimum and maximum Tx power levels of 5 dBm and 26 dBm respectively.

2) RESULTS -PAIRED SCHEME
In this section, we compare the performance of the proposed paired scheme with omni and directional scheme for UE autonomous resource allocation in directional SL systems. Simulation results are averaged across 100 distributions of SL UEs for both the deployment scenarios.
First, we focus on the performance of the SL Mode 2 UEs that experience the highest interference and consequently have the worst performance. This is analogous to the analysis of cell-edge user performance in cellular wireless communication systems, where the goal is to study the impact of a new solution on the users worst affected by interference. Fig. 11a shows the average packet reception ratio (PRR) of the 10 worst performing SL Tx-Rx pairs in the highway deployment scenario (10-th percentile). PRR is the fraction of packets received successfully without decoding errors (success). In Fig. 11a, we can observe the improvement in PRR when using the paired scheme. At a packet arrival period of 1 ms, when the system is heavily loaded, the PRR of the paired, directional and omni schemes is 0.56, 0.34, and 0.02, respectively. Thus, the paired scheme increases the PRR by 64% relative to the directional scheme, which has the second-best performance. Fig. 11b, shows the average PRR for all SL Tx-Rx pairs in the highway scenario. At the 1 ms packet arrival period, the PRR of the paired, directional and omni schemes is 0.89, 0.70, and 0.27, respectively. Here, the paired scheme increases the PRR by 27% w.r.t. the directional scheme. Hence, the paired scheme improves the system performance on average and can significantly improve the quality of service for the SL Tx-Rx pairs that are worst affected by interference.
In Fig. 12, we examine the performance of the directional and paired schemes for the 10-th percentile users in the highway deployment. For both schemes, we plot the ratio of packet control failure and packet decoding failure events, w.r.t. the total number of packets transmitted. The frequency of occurrence of these two events reduces significantly when using the proposed solution, e.g., at a packet arrival period of 2 ms, the paired scheme offers a reduction of 83.04% and 45.95% in control and decoding failures. Even at the highest traffic load, when the network is most congested (packet arrival period of 1 ms), we observe a reduction of 73.62% and 9.75% in control and decoding failures, respectively. This agrees with our analysis in Section IV, where we showed how the paired scheme can prevent hidden node interference. The paired scheme does an overall better job of avoiding the selection of resources already reserved by another Tx UE, which reduces the chances of data/control decoding failures.
We can also clearly observe from Figs. 11a and 11b that the omni scheme has the worst PRR in all scenarios which degrades with increasing traffic intensity. As the intensity increases, a higher number of packets suffer control failures. This is because omnidirectional SCI transmission and reception experiences high propagation losses at higher frequencies, as discussed in Section IV. Furthermore, the omni scheme also suffers from exposed node problems, especially in more general deployments such as a 2D square grid [1]. Consequently, the SINR of the SCI received by the target Rx UE drops significantly due to interference from the SCIs sent by other exposed nodes in the network.
Hereafter, we assume all SL Tx UEs use the paired scheme while performing SL Mode 2 resource allocation. This applies to both analytical and simulation results.

B. ANALYTICAL MODEL VERIFICATION AND NETWORK CAPACITY
In Section V, we derived an analytical expression for the average probability of successful reception for our single-lane vehicular ad-hoc network with directional SL transmissions (Eq. 7, with p 2 derived in Eq. 10). To validate this result, we simulate a single-lane of a highway road of length 4 km with 100 SL vehicular UEs (50 Tx-Rx pairs) and a single frequency-domain subchannel available for SL transmissions. The SL packet size is fixed to 1 subchannel. We consider equal probabilities of vehicles transmitting in East: West and West: East directions, i.e., q = 0.5 for both directions. The rest of the assumptions on the carrier frequency, slot time, traffic model, directional antenna model, path loss model, and packet decoding criteria remain the same as in Sec. VII-A2. Path loss compensation power control using Tx-Rx distance information is used for both our analysis and the simulation.   13a shows the probability of successful reception predicted by our analytical model, as well as the predictions from the legacy ALOHA VANET model proposed in [35]. It also shows the average PRR across 100 simulations, an empirical measure of the probability of successful reception obtained from simulations. In the simulation result in Fig. 13, we use a Ricean fading channel with K = 7, which is consistent with 3GPP recommendations for Line-of-Sight (LoS) channels at high frequencies [49]. For the corresponding analysis, we adopt an equivalent Nakagami-m fading channel model, as discussed in Section V, with m = 4, as the relationship between m and K can be expressed as m ≈ (K +1) 2 (2K +1) [50]. 12 As shown in Fig. 13, our stochastic geometry-based model aligns well with simulation results, except for the period of highest traffic intensity (1 ms packet arrival). This is a significant improvement over the ALOHA VANET model in [35]. Our model incorporates the key features of directional SL networks, including periodic transmissions, sensing-based channel access, directional transmissions, and the paired scheme. However, it is not an exact representation of 3GPP's SL Mode 2 due to several simplifying assumptions used for analytical tractability. For example, we do not consider the iterative RSRP threshold increase procedure in Mode 2, as described in Sec. II. The model performs well in light-to-moderate traffic conditions, but further refinement may be necessary for high traffic loads. Nevertheless, our model provides useful insights into the network and the impact of system parameters on key performance indicators.
In Fig. 13b, we plot the variation of the mean density of transport, d trans , whose analytical expression for Nakagami-m fading is obtained in (15), with the packet arrival period, T period for Tx vehicle density λ = 0.01 m −1 , 400 Tx-Rx pairs and slot time T slot = 0.25 ms. Note that p 1 = T slot T period and m = 4, as discussed in the previous paragraph. For the plots using Rayleigh fading, we take m = 1 [50]. For both the Nakagami and Rayleigh fading models, we observe that the analytical result is very close to the simulations for packet arrival periods between 5 ms (light traffic) to 1 ms (heavy traffic). Packet arrival periods of 0.5 and 0.25 ms represent scenarios where each SL Tx UE will have a new packet to send every 2 and 1 time slots, respectively. Our analytical results diverge from the simulations at these points, and this can be attributed to the explanation given in the previous paragraph for this behavior. However, these scenarios represent worst-case traffic loads for an NR V2X system and may not be the desired operating point for most practical use cases [9].
From Fig. 13b, we also observe that with increasing traffic intensity (or decreasing packet arrival period), the transport density increases steadily until it hits a maximum and starts to fall. The maximum indicates the capacity of the system, i.e., the highest traffic load it can support. This demonstrates the fundamentally unstable nature of our sensing algorithm, similar to what is observed in persistent CSMA [51], wherein it cannot sustain traffic intensities higher than a certain threshold when the interference leads to increased decoding failures. We note here that we have not modeled the sidelink congestion control mechanisms employed in 3GPP [5] in this analysis, which may help address this traffic management issue. Stabilizing this algorithm for higher traffic loads and analyzing it more accurately with congestion control protocols is left for future work.

C. IMPACT OF POWER CONTROL MECHANISM
We now show the effectiveness of our proposed power control solutions in improving the system's performance. The following power control schemes were simulated: The aforementioned distributed transmit power control schemes were all simulated in a network where the SL Tx UEs use the Mode 2 resource allocation algorithm. The details of the Baseline scheme and the proposed power control designs (Algorithms 1, 2 and 3) were described in Sec. VI. For more details of the two additional baseline schemes, you may refer to Appendix D.
In addition to these, we also simulate an upper bound for distributed resource allocation, which we refer to as the RAUB scheme. The design of the RAUB scheme is described in detail in Appendix C. Note that the power control scheme in Algorithm 1 is itself an upper bound on transmit power control since it assumes perfect knowledge of the interference at the Rx UE of each SL Tx-Rx pair. We refer to this as an upper bound on power control or PCUB. When we use the PCUB and RAUB schemes together, the resulting simulation generates the results labeled as upper bound in Fig. 14. This combined upper bound (PCUB + RAUB) gives us an upper bound on the joint distributed resource allocation and power control problem for our SL Mode 2 network. In [1], we showed that this is a distributed, mixed-integer non-convex problem, making it extremely difficult to find an optimal analytical solution. The simulated upper bound curve in Fig. 14a and Fig. 14b is thus used as a benchmark for comparison against our proposed solutions.
From Fig. 14a, we can observe that the enhanced power control schemes proposed in Section VI can significantly outperform the baseline scheme, especially at the highest traffic intensity. The result shows the system-level average PRR obtained using our simulation setup described earlier in Sec. VII-A1. We use the NR V2X highway single-lane scenario with 100 vehicles (50 Tx-Rx pairs). The genieassisted power control scheme (Algorithm 1) has the best performance, which is expected as we assumed perfect knowledge of the Rx-side interference and zero-delay feedback to the Tx UE. At the same time, we can see that the performance of the more practical power control designs in Algorithms 2 and 3 are quite close to the genie-assisted scheme. At the highest traffic intensity point, i.e., packet arrival period of 1 ms, we achieve an average PRR of 0.969, 0.959, 0.963 using the power control schemes of Algorithms 1, 2 and 3 respectively. The Baseline scheme achieved a PRR of 0.908 for the same conditions. Thus, our Tx-only power control solutions help achieve above 95% average system reliability (PRR) in the highest traffic load conditions, a significant upgrade over the current 3GPP standard approach (Baseline). While the two additional heuristic approaches, i.e., Min power boost and Max power allocation, improve over the Baseline scheme, they cannot match the performance offered by our proposed solutions.
The impact of the proposed power control designs is further demonstrated when we focus on the performance of the worst-performing users in our simulation. Fig. 14b shows the average PRR of the 10 worst performing SL Tx-Rx pairs in the highway deployment scenario (20-th percentile). At the highest traffic intensity point, i.e., packet arrival period of 1 ms, we achieve an average PRR among these users of 0.892, 0.872, 0.876 using the power control schemes of Algorithms 1, 2 and 3 respectively. The Baseline scheme achieved a PRR of 0.693 for the same conditions. The proposed interference-estimation-based power controls thus improve the PRR by around 26 − 28% relative to the path loss compensation-based Baseline scheme. This demonstrates that the biggest positive impact of the proposed power control strategy is on the performance of the SL users (vehicles) that are worst affected by interference in a congested V2X highway network. Our results demonstrate the need to consider the power control solutions discussed in Section VI for future SL networks.
Finally, we also observe from Fig. 14a and Fig. 14b that the proposed solutions are closely matching the performance of the upper bound curve described earlier, except for a 2% drop at the point of highest traffic intensity, i.e., the packet arrival period of 1 ms. As described in Appendix C, the genie-assisted upper bound uses information of future resource reservations, which will never be available in a practical, distributed system. Thus, it is natural to expect a larger performance gap between the upper bound and the proposed scheme when the system is heavily loaded (highest traffic intensity point with a packet arrival periodicity of 1 ms). However, the combination of the paired scheme and the transmit power control algorithms designed in Sec. VI-B can achieve near-optimal performance.

D. PAIRED SCHEME IN MULTI-LANE HIGHWAY DEPLOYMENTS
The analysis and evaluation so far have focused on single-lane highway V2X deployments. We now show that our proposed solutions have the potential to extend to a generalized multi-lane highway scenario. We present simulation results for multi-lane highway scenarios in Fig.15, where 15a depicts a two-lane highway, and 15b shows a three-lane highway, with 100 vehicles deployed in each lane. The lane width is 4 meters, and the road length is 4 km. The Tx-Rx vehicle pairing process follows the guidelines in [9], where the ratio of same-lane to cross-lane pairings is approximately 50% and 35% for the two-lane and three-lane cases, respectively. The rest of the settings are the same as our single-lane highway simulations. The paired scheme offers significant improvements over the omni and directional schemes. Our proposed transmit-only power control schemes, i.e., Algorithms 2 and 3, improve system-level performance, particularly at the highest traffic loads. Hence, we conclude that our distributed resource allocation and power control solutions are scalable to generalized multi-lane highway deployments. 13 The intuition behind why the paired scheme generalizes to the multi-lane setting was discussed in Sec. IV-A, where we pointed out that the most critical hidden node interference in highly directional SL systems occurs when two (or more) interfering transmissions are closely aligned in 2D space, i.e., are almost collinear. A single-lane highway with all vehicles communicating in the same lane presents a worst-case scenario w.r.t. hidden node issues. The paired scheme can resolve most of these issues by creating ''visibility'' in the paired direction for a Mode 2 SL Tx UE. The same holds in a multilane highway, even though there are cross-lane transmissions, and interference from SL UEs (vehicles) in nearby lanes may occur. Variants of the paired scheme, such as using a wider paired beam or multiple paired beams [14], may improve performance. Additional investigation and analysis of the multi-lane scenario is left for future work.

VIII. CONCLUSION AND FUTURE WORK
This paper looked at UE autonomous resource allocation for directional SL systems. First, we proposed paired sensing and SCI transmissions to address directional deafness issues that may result in hidden node and exposed node problems. We then developed a novel stochastic geometry-based analytical model for a linear vehicular SL ad-hoc network that captures the essential characteristics of sensing-based resource allocation (SL Mode 2) and provides key insights into the performance and reliability of NR V2X communication systems at mmWave/sub-THz frequencies. Finally, we design novel adaptive and distributed transmit power control schemes for SL Mode 2 UEs. These strategies consider the interference from neighboring SL transmissions at the SL Rx UE. They do this by either explicitly using Rx-side feedback or estimating the Rx-side interference at the Tx UE itself, by using SCI information captured during sensing. MATLAB system-level simulations demonstrated the performance gains achieved by the paired scheme relative to the omni and directional schemes for Mode 2 resource allocation. We propose a stochastic-geometry-based analytical model for the single-lane highway network and validate it through comparison with simulations. Our enhanced power control schemes significantly improved the system-level and worstcase performance of directional NR V2X SL.
As part of our future work in this area, we would like to incorporate Rx-side feedback for sensing-based resource allocation. While this may improve performance, a more careful cost vs. benefit analysis of such solutions is needed. As the proposed paired scheme needs either additional 13 There exists some literature on general multi-lane highway scenarios, involving lanes that may intersect in oblique/perpendicular angles [52], [53] or considering additional complexities in the system model such as cellular relay V2V [54] or multi-hop [55]. However, our current results focus on the simple, realistic case of parallel highway lanes with single-hop transmissions, which can be modelled adequately with parallel single-lane VANETs. Analysis of complex system models is deferred to future work. hardware support for simultaneous SCI transmission or the use of TDMA, a detailed analysis of energy efficiency and throughput can provide more insights. A more in-depth analysis of the performance of our proposed solutions in multi-lane highway deployments would be useful. This work can be expanded to include broadcast and multicast messages relevant for vehicular platoons and V2X basic safety message exchange. For our simulations and the analytical model, we would also like to incorporate additional features like the mobility of SL users and aperiodic SL traffic. Game-theoretic or machine-learning (ML) solutions can be considered for optimal power control in a distributed setting.

APPENDIX A
We only need to consider the interferers on the side of the receiver facing the transmitter. Assume the ith receiver to be at the origin, i.e., Y i = 0 and d j = |X j − Y j | be the distance between the jth Tx-Rx pair, i.e., l(|X j −Y j |) = (Ad j ) −β . Recall that the fading coefficient is a normalized Gamma random variable with parameter m, i.e., F ∼ Gamma(m, 1/m). Using Eq. (4), the Laplace functional of the interference is computed as follows Substituting the result in (16) into (6), we get the result in (7).

APPENDIX B
For the control channel, we need to consider the interferers on both sides of the receiver, since all vehicles transmit and receive sidelink control information (SCI) in transmitting as well as paired direction. At the same time, as we use the proposed paired scheme, we make the assumption that the sensing done by a SL Tx UE in primary and paired directions are independent of each other. Hence, the interference to a SCI received in primary(paired) direction will only come from other SCIs received in the primary(paired) direction. Assume the ith receiver to be at the origin, i.e., Y i = 0 and d j = |X j − Y j | be the distance between the jth Tx-Rx pair, i.e., l(|X j − Y j |) = (Ad j ) −β . Recall that the fading coefficient is a normalized Gamma random variable with parameter m, i.e., F ∼ Gamma(m, 1/m). Using Eq. (4), the Laplace functional of the interference is computed as Substituting the result in (17) into (9), we get the result in (11).

APPENDIX C -DESIGN OF THE UPPER BOUND
To properly benchmark the performance of our proposed power control and resource allocation algorithms, we propose two kinds of approaches that are guaranteed to be an upper bound on our algorithms, namely, a power control upper bound (PCUB) and a resource allocation upper bound (RAUB). We elaborate the design of these bounds as follows: Design of the PCUB: The PCUB is obtained by executing Algorithm 1. It acts as an upper bound since it assumes perfect knowledge of the interference at the Rx UE of each SL Tx-Rx pair. We have already explained the detailed working of this algorithm in Sec. VI.
Design of the RAUB: Mode 2 of NR SL is a distributed, UEautonomous resource allocation scheme. However, we know that a centralized resource allocation controlled by the NR gNB (i.e., Mode 1) will always outperform Mode 2 because, in a centralized setting, the base station has much more information available to it as compared to the distributed SL Tx UEs performing sensing in Mode 2. In particular, a centralized resource scheduler like the gNB will have the following key features: 1) The gNB knows all future resource reservations made for SL users inside its coverage area and can use this information to prevent collisions. 2) There is no half-duplex sensing constraint, unlike SL Mode 2. In the design of Mode 2 in 3GPP Release 17, it is assumed that SL devices have only half-duplex transceivers. We will soon explain how this can be a drawback; however, we note for now that in the centralized setting, i.e., Mode 1, this constraint does not exist. This is because there is no sensing-based channel access in Mode 1. The gNB knows all the resource allocations inside its coverage area and can use this information to prevent collisions among SL transmissions.
3) The gNB has location information for all the SL UEs and can utilize this information for reusing resources among SL Tx-Rx pairs far from each other.
For designing the RAUB, we assume the existence of a ''genie'' that provides additional information or capability to all the Mode 2 SL Tx UEs at no cost. The genie's extra information fills the gap between Mode 2 (distributed) and Mode 1 (centralized) by emulating three key features listed above, as follows: • Knowledge of future resource reservations: In Mode 2, the SL Tx UE looks at the recent history of SCIs received during sensing to make its resource selection decision. Two Tx UEs who make a new reservation around the same time can select the same resource because they have no prior knowledge of each other's new reservations. This leads to the problem of persistent packet collisions [56]. We assume that our genie will provide all Tx UEs with information about the resources reserved by other Tx UEs in the future. We implement this by extending the sensing window into the future (up to the end of the selection window). This means that any upcoming new reservations made by neighboring Tx UEs can be used while performing Step 1(resource exclusion) of Mode 2, thereby avoiding collisions.
• Full-duplex sensing capability: The lack of full-duplex (FD) capability constrains the sensing-based Mode 2 procedure. This is because a SL Tx UE cannot perform sensing over the time slots it was transmitting. To avoid any potential collisions due to the half-duplex constraint, 3GPP specifies that the Tx UE has to exclude from its resource selection any future time slots that are periodic with its last reservation [5]. FD sensing can be helpful in heavy interference situations, as it opens up the option of using the same periodic reservation again instead of choosing a new resource when restricted by half-duplex sensing. This was shown to improve SL Mode 2 performance by Campolo et al. [57]. Therefore, we assume our genie can provide the SL Tx UEs with full-duplex sensing information.
• Location information: This is implicitly accounted for in sensing-based Mode 2 resource allocation, because the SL Tx UEs use the RSRP level of received SCIs to make their resource selection decisions. For example, an SCI received from a user far away from a sensing UE will be received with a low RSRP. The resource reservations made by such far-away users are more likely to be ignored by the sensing UE, since they are not strong interferers. Hence, the design of Mode 2 facilitates location-based resource reuse.
To summarize the above discussion, the genie augments the SL Tx UE with additional information that helps it make better resource allocation decisions. The genie-assisted RAUB scheme emulates a centralized resource scheduler and is an upper bound for the 3GPP's distributed, sensingbased Mode 2 resource allocation. When we use the PCUB and RAUB schemes together, the resulting scheme is a joint upper bound on resource allocation and power control (PCUB+RAUB). In Sec. VII-C, we compared the performance of our proposed power control solutions against this joint upper bound, labeled as upper bound in Fig. 14.

APPENDIX D ADDITIONAL POWER CONTROL BASELINES FOR COMPARISON
• Min Power Boost: This is the baseline scheme but with the minimum Tx power level set to 10 dBm. In the baseline scheme, the Tx-Rx pairs with short Tx-Rx distances end up transmitting at very low powers. In our interference-heavy network, we observed that these UEs were the worst affected by interference from other SL Tx-Rx pairs that use higher Tx power because their Tx-Rx distance is higher. The idea behind this scheme is to provide a power boost to short-range SL Tx-Rx pairs so that they can counteract the effects of interference. This scheme comes with no additional cost and improves over our baseline. We use this as another reference for comparison for our proposed Tx power control strategies.
• Max power allocation: All UEs have the same Tx power level, which is set to the maximum permissible Tx power of SL vehicular UEs, i.e., 26 dBm. This considers a selfish network with all vehicular UEs trying to maximize their own SINR without caring about other UEs in the network. We observe that this scheme does well in low traffic load conditions, however, with higher traffic loads, the performance gets degraded severly.

ACKNOWLEDGMENT
An earlier version of this paper was presented in part at the 2022 IEEE Vehicular UMER SALIM received the M.S. degree in electrical engineering with a specialization in communication theory and signal processing from EURECOM, France, and the Ph.D. degree in electrical engineering with a specialization in communication theory and signal processing from Supelec, France. He is currently a 6G Consultant with InterDigital Communications Inc. Earlier, he was with TCL Communications as a 5G Systems Architect and a 3GPP RAN1 Delegate for 5G standardization activity. Before joining TCL, he was with Intel Mobile Communications in the group of algorithm design, where he worked on many novel baseband algorithms for improved reception and interference cancellation. Many of these algorithms are currently part of high-end smartphones and tablets. His main research interests include signal processing techniques for multi-cell multiuser MIMO systems, novel and practical CSI feedback design techniques and analysis, information-theoretic analysis of cognitive radio, and multiuser information theory in general. He