1D-CNN-Based Performance Prediction in IRS-Enabled IoT Networks for 6G Autonomous Vehicle Applications

Abstract

To foster the performance of wireless communication while saving energy, the integration of Intelligent Reflecting Surfaces (IRS) into autonomous vehicle (AV) communication networks is considered a powerful technique. This paper proposes a novel IRS-assisted vehicular communication model that combines Lagrange optimization and Gradient-Based Phase Optimization to determine the optimal transmission power, optimal interference transmission power, and IRS phase shifts. Additionally, the proposed model help increase the Signal-to-Interference-plus-Noise Ratio (SINR) by utilizing IRS, which leads to maximizes energy efficiency and the achievable data rate under a variety of environmental conditions, while guaranteeing that resource limits are satisfied. In order to represent dense vehicular environments, practical constraints for the system model, such as IRS reflection efficiency and interference, have been incorporated from multiple sources, namely, Device-to-Device (D2D), Vehicle-to-Vehicle (V2V), Vehicle-to-Base Station (V2B), and Cellular User Equipment (CUE). A Lagrangian optimization approach has been implemented to determine the required transmission interference power and the best IRS phase designs in order to enhance the system performance. Consequently, a one-dimensional convolutional neural network has been implemented for the optimized data provided by this framework as training input. This deep learning algorithm learns to predict the required optimal IRS settings quickly, allowing for real-time adaptation in dynamic wireless environments. The obtained results from the simulation show that the combined optimization and prediction strategy considerably enhances the system reliability and energy efficiency over baseline techniques. This study lays a solid foundation for implementing IRS-assisted AV networks in real-world settings, hence facilitating the development of next-generation vehicular communication systems that are both performance-driven and energy-efficient.

1. Introduction

With the immense need for very reliable wireless communication that has a lot of throughput and low latency. Sixth-generation (6G) networks are being created to use new technologies that go beyond what current communication systems can do [1]. One of the most well-known techniques that has gotten a lot of attention is non-orthogonal multiple access (NOMA). NOMA helps to improve spectral efficiency by allowing multiple users to transmit data at the same time across the same frequency band, separated by power-domain multiplexing [2]. At the same time, unmanned aerial vehicles (UAVs) have become flexible and scalable communication systems, that can provide wireless coverage on demand in a wide range of settings, from busy cities to remote rural areas [3].

Even though UAV-enabled communications are very useful. They often have problems with non-line-of-sight (NLoS) signals, especially in cities where buildings and other things can block the signal paths [4]. This makes it much harder to connect and lowers the quality of communication while serving mobile ground users. To solve these problems, intelligent reconfigurable surfaces (IRS) have been suggested as a new way to turn passive settings into customizable spaces [5]. An IRS consists of a wide range of inexpensive, programmable reflecting elements. IRS can dynamically alter the phase shifts of incoming signals to change the characteristics of wireless propagation [6].

IRS functions almost passively, using less power than conventional relay systems while yet producing significant improvements in signal strength and coverage [7]. In order to improve channel conditions and enhance energy-efficient communication, IRS may optimize and direct wireless signals toward its dedicated users. This can be achieved by adjusting reflection coefficients in real-time [8]. In general, IRS implementations fall into one of three categories: hybrid, active, or passive. Passive IRS is power-efficient yet has limited performance-enhancing capabilities because it reflects signals without amplification [9]. For signal boosting, Active IRS incorporates powered electronic components. This improves control but increases energy consumption. By mixing passive and active components, hybrid IRS aims to achieve a balance and provide flexible operation that can be adjusted to different communication needs [10].

IRS is essential in the context of Vehicle-to-Everything (V2X) communications. IRS can provide dependable, low-latency connectivity between vehicles and vehicles, pedestrians, and infrastructure, which are the base of intelligent transportation systems [11]. Maintaining reliable V2X connections is a challenge in urban settings due to high mobility and frequent signal blockages [12]. by installing IRS on roadside units, it is feasible to increase signal quality, reduce NLoS impacts, and dynamically rearrange the propagation environment, building facades, or even within automobiles [13]. This strengthens IRS as a key enabler in the development of V2X in 6G networks. IRS supports high-data-rate services like real-time HD map updates and multimedia streaming. In addition, IRS can help in improving safety-critical applications like collision avoidance and autonomous driving coordination [14].

Different works have examined IRS-assisted vehicular networks, most of which focused mainly on either heuristic optimization or machine learning alone, which leads to sub-optimal performance. Furthermore, there are limited efforts have been made to systematically integrate analytical optimization methods. Additionally, despite the improvements in vehicular communication, there is a problem with the existing models when it comes to how to maintain system reliability and data rate or spectral efficiency due to the complexity of the wireless environmental conditions. The previous approaches in the literature focus mainly on how to optimize signal coverage, power consumption, and real-time adaptability [15,16,17]. Additionally, there is a lack of how to control or adapt the wireless propagation environment, which leads to inefficient resource use and a low Signal-to-Interference-plus-Noise Ratio (SINR), which leads to low system reliability and efficiency. To address the identified of researches gap, the proposed model is guided by the following question:

• How can IRS-assisted communication enhance the data transmission efficiency and reliability of autonomous vehicles operating in dynamic environments?

• Can a 1D Convolutional Neural Network (1DCNN) effectively predict the optimal required communication strategy by learning from historical and real-time vehicular data?

• What role does gradient descent optimization play in minimizing the transmission interference power while maximizing the achievable data rate and energy efficiency in IRS-assisted vehicular networks?

• How does the proposed framework compare with existing approaches in terms of energy efficiency and system throughput under similar simulation environments?

To address these limitations, this paper proposed a novel IRS-assisted vehicular communication model that integrates Lagrange optimization and gradient-based phase optimization techniques to determine the optimal transmission power, optimum required interference power, and IRS phase shifts to meet the required system performance for autonomous vehicles (AVs). The main contribution of the paper is as follows:

• A novel IRS-assisted vehicular communication framework is proposed to enhance the communication performance of autonomous vehicle (AV) networks by dynamically adjusting reflection parameters and optimizing the required interference transmission power and the autonomous vehicle transmission power to maximize the energy efficiency and achievable data rate.
• By combining Lagrange optimization with Gradient-Based Phase Optimization, the best autonomous vehicle transmission power, the interference transmission power, and IRS phase shifts, are obtained, while satisfying the required system conditions.
• To enable real-time decision-making in dynamic vehicular environments, a one-dimensional Convolutional Neural Network (1D-CNN) is implemented as a predictive deep learning model to train the optimized parameters to estimate key performance metrics, specifically interference transmission power (PI), Energy Efficiency (EE), and Data Rate (R).
• The proposed model is evaluated through simulation experiments and comparison with previous proposed model which show better performance than previous RS-based methods in terms energy efficiency, and achievable data rate.

The structure of the paper is as follows: Related work in IRS-assisted vehicle communication and associated optimization methods is presented in Section 2. The suggested hybrid proposed model is shown in Section 3, which is also explained in this section how 1D-CNN, gradient-based phase optimization, and Lagrange optimization are integrated. Section 4 offers the performance evaluation of the proposed model. Conclusion of the paper and possible Future directions for further research are covered in Section 5.

2. Related Work

Recently, IRS has gained much attention to enhance the performance of vehicular communication. Additionally, optimization techniques and deep learning approaches have been implemented extensively as promising techniques to address the challenges of the different wireless communications systems [18,19,20,21]. A cooperative IRS-relay network under Nakagami-m fading for intelligent transportation system was proposed in [22]. The aim of this paper was to achieve higher energy efficiency and data rate than a standalone IRS. Additionally, ref. [23] proposed multiple IRSs in 6G IoV networks in order to enhance V2V communication. It maximizes data rate while minimizing power and it implements DCNN to effectively predict system behavior. Furthermore, for addressing signal blockage in urban areas [24] proposed an IRS-assisted NOMA-UAV communications in vehicular networks. This model focused on using a joint optimization of UAV power and IRS beamforming to maximize sum capacity. The results showed improved performance compared with direct IRS communication with vehicles. Moreover, an energy-efficient model for multi-cell NOMA V2I communication with multi-IRS assistance proposed in [25]. The aim of this model was to increase energy efficiency, through optimizing IRS phase shifts, NOMA allocation, and RSU power. This proposed method achieved high energy efficiency compared with some previous benchmark techniques.

In order to enable low-power data communication, ref. [26] introduced an IRS-based V2I BackCom system through backscattering signals generated by vehicles. Also, a different optimization approach was implemented to optimize the collection of information by calculating IRS reflection coefficients and vehicle transmit power. Furthermore, to address excessive energy consumption in V2I networks, ref. [27] combined IRS and BackCom to transmit the information with low power. Two detection techniques are optimized using an alternating algorithm, and by using multiple IRS to send the roadside data using backscatter vehicle signals. Additionally, ref. [28] suggested an edge-enabled digital twin (DT) structure for UAV-assisted IRS vehicular networks to reduce energy consumption. The proposed model implemented the hybrid federated learning (HFL) algorithm and a Markov decision process to jointly optimize IRS phase shifts, power allocation, and offloading decisions. Moreover, ref. [29] shown how combining MIMO and IRS may improve wireless communication. Important advantages were also examined, such as enhanced resource allocation and energy efficiency via sophisticated beamforming and signal processing.

To solve the problem of energy efficiency, latency, and reliability in dynamic vehicle communication, an IRS-enhanced V2X system is proposed [30]. By optimizing communication and computation offloading through intelligent beamforming and spectrum reuse, this proposed model reduced latency and energy consumption. Additionally, in order to improve the signal reliability in order to face the challenge of mobility and dynamic channel circumstances, ref. [31] presented a multi-IRS-assisted SISO system within Open RAN for V2X communications. The aim of this proposed model is to optimize the sum-rate of the network Furthermore, ref. [32] examined the energy efficiency of an IRS-assisted downlink multiuser MISO system through optimizing AP beamforming and IRS phase shifts. The results obtained from the suggested method beats benchmark systems in terms of energy efficiency. Ref. [33] explored the difficulty of multi-resource coordination by introducing a multi-agent DRL-based scheduling method for IRS and UAV-assisted wireless powered edge networks. By modeling the issue as an MDP, the proposed technique achieved better convergence and system energy efficiency, also it improved energy efficiency, charging time, UAV trajectories, and IRS phase changes.

Furthermore, as demonstrated in [34], the IRS plays a significant role in improving 6G-enabled V2X communications, particularly in removing signal obstructions and enhancing latency, coverage, and reliability. IRS-enabled drone-assisted vehicular edge computing for effective resource allocation was highlighted, along with current developments and application examples. In addition, to deal with spectrum shortage and channel unpredictability [35] developed a MARL-based resource allocation technique for V2V networks that uses NOMA. In this proposed model RSUs work together as learning agents under QoS and power restrictions to enhance sub-band scheduling and power allocation. Furthermore, ref. [36] presented a customized MAC protocol (UR-V2X-MAC) for effective resource allocation as well as a UAV-enhanced RIS-assisted V2X communication architecture (UR-V2X) designed for urban 3D IoT traffic. Whereas UAVs acted as coordinators and access points, RISs functioned as passive relays. In this proposed model, RIS phase shifts were optimized and the transmit power was cooperatively allocated using a distributed optimization technique. To improve physical layer security, ref. [37] examined IRS-assisted V2V communication in a MISO IoV system. Based on extended Rayleigh entropy and semidefinite relaxation an alternating optimization technique was used to tackle a secure rate maximization problem under power and IRS phase limitations.

Unlike prior works that have been described previously, the proposed approach allows the integration between Lagrange optimization and gradient descent with 1D-CNN regression.

Table 1. Comparison between the proposed model and different related works.

	Technique or Application	Optimization Method	Deep Learning Model	Evaluation Metrics	Use Case Scenario
[18]	Integration of IoT devices for smart farming to enhance data transmission efficiency	Lagrange optimization techniques applied to determine ideal IoT sensor transmission power	Deep Convolutional Neural Networks (DCNN) combined with mathematical optimization	Energy efficiency and data throughput while ensuring reliable and high-quality data transmission	Smart farming ecosystems focusing on critical parameters such as temperature, humidity, soil moisture, and animal health to improve crop productivity, animal health, and sustainability
[19]	Energy-efficient IoT-based tracking and communication for chronic disease management	Lagrange optimization algorithm for minimizing transmission power and determining optimal distance for emergency signal delivery	1D Convolutional Neural Network (1D-CNN) integrated with energy-efficient sensors and real-time data processing	Mean Squared Error (MSE), Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), and R2 for performance evaluation	Wearable IoT devices transmitting patient health data efficiently to medical centers for emergency response and continuous monitoring
[20]	Internet of Everything (IoE) network performance enhancement through intelligent transmission power control	Multi-objective Lagrange optimization to minimize interference and determine optimal uplink/downlink transmission power	Distributed deep learning model trained on data generated from Lagrange optimization to predict optimal transmission power	Energy Efficiency (EE), System Throughput (S), and interference reduction	Large-scale IoE networks with massive device-to-device, machine-to-machine, and human-to-machine communications
[21]	Adaptive AV2X communication for autonomous vehicles	Lagrange optimization algorithm for optimal inter-vehicle positioning	Distributed deep learning model for predicting ideal inter-vehicle position under varying conditions	Energy efficiency and achievable data rate	Enhancing connectivity in vehicular networks for AV2X to reduce congestion, assist in low-visibility traffic, and improve emergency vehicle alerts
[22]	Cooperative IRS-relay-aided ITS	IRS-assisted relay with Nakagami-m fading channel analysis	Cooperative relay integrated with IRS (passive reflective elements)	EE (bits/joule) and achievable rate under SNR conditions	ITS scenario for energy-efficient communication
[23]	Multi-IRS V2V for IoV	KKT-based framework (to optimize data rate & power)	DNN framework + Monte Carlo simulations	OP (Outage Probability), ASER (Average Symbol Error Rate), EC (Ergodic Capacity)	6G-enabled IoV V2V communication
[24]	IRS-UAV NOMA vehicular links	Taylor + fixed-point & convex methods	NOMA UAV + IRS beamforming	Sum capacity, SINR, convergence	Urban UAV-to-vehicle
[25]	Multi-IRS multi-cell NOMA V2I	BCD + SCA, gradient & interior-point	Multi-IRS with NOMA power allocation	EE, achievable rate	6G for V2I vehicular networks
[26]	IRS + BackCom for V2I data collection	Alternative optimization of IRS coefficients & vehicle power	Multi-IRS backscatter system	Collected data volume	Low-power V2I communications
[27]	IRS + BackCom for V2I beamforming	Alternating optimization of detection matrix, vehicle power & IRS coefficients (PD/ID)	Multi-IRS backscatter with multi-antenna vehicle	Weighted sum-rate, convergence performance	Low-power V2I communications
[28]	Edge-enabled DT UAV with IRS for vehicular networks	MDP-based task offloading; IRS phase-shift, power & offloading optimized via HFL	Hybrid federated learning with multi-agent DT UAVs	Energy efficiency, learning accuracy (vs. MAD2PG, DQN)	UAV-assisted vehicular networks with reduced energy consumption
[29]	MIMO with IRS for wireless communication	Resource allocation & energy efficiency	IRS-assisted MIMO (beamforming, signal manipulation)	Spectral efficiency, coverage, connectivity	MIMO–IRS integration for improved wireless networks
[30]	IRS-enhanced V2X for improved communication & computation offloading	Utility function (latency & energy) minimized via alternating optimization, tabu-search, SDR, penalty methods	Multi-IRS V2X with spectrum reuse & beamforming	Latency, energy consumption, utility function value	IRS-enhanced V2X networks for reliable communication
[31]	Multi-IRS aided SISO communication with passive beamforming	K-means clustering (IRS grouping) + Trellis-search (optimal IRS path)	Multi-hop IRS-assisted SISO system	Achievable sum-rate, throughput gain	RAN-based V2X networks using multi-IRS-assisted communication
[32]	IRS-aided downlink multiuser MISO for energy efficiency	Alternating optimization with SCA (for phase shifts) and MMSE beamforming (power allocation)	IRS-assisted MISO system (AP + IRS)	EE	IRS phase optimization for downlink multiuser MISO networks
[33]	Multi-agent Deep Reinforcement Learning (DRL) for IRS and UAV-assisted wireless powered edge networks	Joint optimization of charging time, IRS phase shifts, UAV association, and UAV trajectories	Multi-agent DRL with value function decomposition	Algorithm convergence and system energy efficiency	Multi-UAV, multi-IRS, and multi-device scheduling in latency-sensitive IoT services
[34]	Intelligent Reflecting Surface (IRS) for 6G-enabled Vehicle-to-Everything (V2X) communications	Energy-efficient signal reconfiguration to enhance wireless coverage and reduce latency	IRS-assisted vehicular edge computing with drones for optimal computation and communication resource allocation.	Signal strength, latency, coverage, positioning accuracy, and physical layer security	IRS-enabled V2X for urban and remote areas
[35]	Multi-Agent Reinforcement Learning (MARL) for resource allocation in vehicular networks (V2V communication)	Joint sub-band scheduling and transmit power allocation under QoS and power constraints to maximize global energy efficiency	MARL framework where RSUs act as cooperative agents using Q-networks for decision-making	Global energy efficiency (sum rate to total RSU power consumption ratio), average energy efficiency, and failure probability	High-mobility vehicular communication with limited spectrum resources, improving throughput and latency by leveraging NOMA-based resource reuse
[36]	UAV-enhanced RIS-assisted V2X (UR-V2X) communication architecture with adapted MAC protocol	Distributed algorithm for transmit power allocation and alternating optimization of RIS phase shift matrix	UR-V2X MAC protocol using UAVs as access points and RIS as passive relays for urban 3D IoT traffic.	System capacity and communication delay	6G-enabled V2X networks in urban environments
Proposed model	IRS-based communication framework for autonomous vehicle (AV) networks	Lagrange optimization and Gradient-descent for predictive resource allocation and IRS phase-shift tuning	Hybrid framework integrating IRS tuning + 1D-CNN for data-driven regression	Energy efficiency, acheivable data rate, $r^2$, MSE, MAE, RMSE	Enhancing AV network performance by jointly optimizing IRS parameters and predicting communication strategies under realistic conditions

highlights the unique characteristics of the proposed model compared to previous research attempts. Despite the models presented in the literature, there is still room to enhance the performance of autonomous vehicle communication under various environmental conditions and limitations. Therefore, the proposed model aims to improve energy efficiency and communication reliability for RIS-assisted autonomous vehicle communication systems using an integrated optimization and learning-based approach. In order to reach this paper’s goal, the proposed approach presents a unique hybrid framework that combines a 1D Convolutional Neural Network (1D-CNN), Gradient Phase Tuning, and Lagrange-based optimization. This paper combines analytical optimization with deep learning-based performance prediction in a novel manner to simultaneously optimize overall system performance in terms of maximizing Energy Efficiency (EE), and achievable Data Rate (R).

3. Materials and Methods

This section presents the proposed IRS-assisted autonomous vehicle communication model, along with the optimization strategies and the deep learning approaches used to improve system performance. The main goal of this proposed model is to optimize and predict important autonomous vehicle communication parameters, such as determining the maximum required transmission power ($P_t$) for autonomous vehicles, the maximum required interference transmission power ($P_I$) and IRS phase shit ($\varphi$) under wireless channel environmental constraints, the methodology combines Lagrange optimization, Gradient-Based Phase Adjustment, and a 1D Convolutional Neural Network (1D-CNN). The energy efficiency (EE) and the achievable data rate (R) are maximized by these ideal characteristics. The system model, mathematical formulation, optimization techniques, and learning architecture are all thoroughly explained in the next subsections.

The proposed approach consists of two integrated phases: (i) Optimization and Analytical Simulation, and (ii) Prediction using 1 DCNN. Figure 1 illustrates how the proposed model operates. First, system parameters must be initialized, including AV transmit power, path loss, required signal-to-interference-plus-noise, transmission distances, and interference transmission distances. To meet the required SINR, the IRS phase shifts are optimized using a gradient descent algorithm. Next, the Lagrange optimization framework is applied to determine the optimum interference power required to maximize energy efficiency and achievable data rate. All the obtained data are used to build the required dataset for the next phase. In the second phase, the generated dataset is preprocessed and fed into a 1D-CNN regression model. The 1 DCNN is learned from the dataset in order to predict $P_I$, EE, and R, and in the future, this study will be extended. The flowchart proposed in Figure 1 depicts the end-to-end integration of these modules, highlighting the synergy between analytical optimization and machine learning for IRS-assisted 6G vehicular networks. Additionally,

Table 2. List of Abbreviations.

Parameter	Definition
$P_t$	Autonomous vehicle transmission power
$P_I$	Interference transmission power
$\varphi$	IRS phase shit
EE	Energy Efficiency
R	Achievable data rate
1 D-CNN	1D Convolutional Neural Network
AV	Autonomous vehicle
SINR	Signal-to-interference-plus-noise
${\mathrm{AV}}_{\mathrm{tx}}$	Transmitted AV
${\mathrm{AV}}_{\mathrm{tx}}$	Receiving AV
IRS	Intelligent Reflecting Surface
CUE	cellular user equipments
D2D	Device-to-device
V2V	Vehicle-to-vehicle
$h_{AVtx-AVrx}$	Direct channel gain from AVtx-AVrx
$h_{r,m}$	The reflected channel gain via the m-th IRS element
${\eta }_m$	The reflection amplitude
x	The transmitted signal
n	The additive white Gaussian noise
${\sigma }^2$	The noise power
I	Interference
$h_{C_{k}A}$	Direct channel gain from CUE-AVrx
$h_{D_{d}A}$	Direct channel gain from Drx-AVrx
$h_{V_{v}A}$	Direct channel gain from Vtx-AVrx
$h_{V_{B}A}$	Direct channel gain from VBtx-AVrx
$P_C$	Interference transmission power of CUE
$P_D$	Interference transmission power of DTx
$P_V$	Interference transmission power of VTx
$P_{max}$	Maximum autonomous vehicle transmission distance
$I_{\max }$	Maximum system required interference
AWGN	Additive white Gaussian noise
NOMA	Non-Orthogonal Multiple Access
V2X	Vehicle-to-everything
${\lambda }_1,{\lambda }_2,{\lambda }_3,{\mu }_1,{\mu }_2$, and ${\mu }_3$	The non-negative Lagrange multiplier
$ϵ$	The learning rate (step size)
$d_{A2A}$	Distance between AVtx-AVrx
$d_{AR}$	Distance between transmitting autonomous vehicle and IRS
$d_{RA}$	Distance between IRS and AVrx
$d_{CA}$	Interference distance CUE and AV
$d_{DA}$	Interference distance DTx and AV
$d_{VA}$	Interference distance VTx and AV
$d_{VBA}$	Interference distance VTx-B and AV
$d_{VA}$	Interference distance VTx and AV
$d_{CA}$	Interference distance CUE and AV
MAE	Mean absolute error
MSE	Mean square error
RMSE	Root mean square error
$r^2$	Coefficient of Determination
$P_o$	Internal circuitry power
6G	Sixth-generation
IoV	Internet of Vehicles
UAV	Unmanned Aerial Vehicle
NLoS	Non-line-of-sight
DT	Digital twin
HFL	Hybrid federated learning
MIMO	Multiple input multiple output
MISO	Multiple input single output
DRL	Deep reinforcement learning
MDP	Markov Decision Process
MARL	Multi-agent reinforcement learning
QoS	Quality-of-service
${\varphi }_m$	IRS phase shift
ReLU	Rectified Linear Unit
PReLU	Parametric Rectified Linear Unit

presents all the symbols used in this paper with their definitions.

Performance evaluation of the proposed model is carried out entirely by simulation under the assumptions of Rayleigh fading channels, fixed interference constraints, and constant ($I_{\max }$). These assumptions are widely implemented in the literature to provide tractable and comparable results in the analysis of wireless communication systems. Rayleigh fading, in particular, serves as a standard statistical channel model to represent rich-scattering environments without line-of-sight, and thus provides a worst-case scenario for evaluating energy efficiency. While real-world channels may include additional effects such as shadowing, path loss variability, and line-of-sight components (e.g., Rician fading), the implementation of Rayleigh fading allows generalization of the paper’s findings to a broad class of urban and dense communication scenarios. Future work will incorporate more realistic channel models and experimental validation to further confirm the applicability of the proposed approach in practical IoT healthcare deployments.

3.1. System Model and Problem Formulation

In the proposed 6G-enabled autonomous vehicle communication system, it is assumed that the network consists of a set of autonomous vehicles equipped with transmitting units (AVtx) and receiving units (AVrx), an Intelligent Reflecting Surface (IRS), a base station (BS), multiple cellular users (CUEs), a group of device-to-device (D2D) users, and a group of vehicle-to-vehicle (V2V) al these share the same frequency spectrum, as illustrated in Figure 2. The supported communication modes include: (i) direct communication between autonomous vehicles (AVtx-AVrx); (ii) IRS-assisted autonomous vehicle communication to enhance signal strength and reliability under different environmental conditions. Due to the spectrum reuse among CUEs, D2D users, and autonomous vehicles, interference may arise at AVrx when any CUE, Dtx, or Vtx transmits concurrently with V2V, D2D pairs or Vtx-BS. The IRS is utilized to dynamically reconfigure the wireless environment by adjusting its phase shifts, thereby improving the received signal quality and mitigating interference. The main objective of the proposed approach is to improve overall autonomous vehicle system performance by jointly optimizing the transmit power and interference transmission power, and IRS reflection coefficients to maximize energy efficiency (EE) and achievable data rate (R), while meeting the required demands of future 6G vehicular.Let the received signal at the autonomous vehicle (AV) be expressed as:

$$y=\left(h_{\mathrm{AVtx}-\mathrm{AVrx}}+\sum _{m=1}^M{\eta }_m{e}^{j{\varphi }_m}{h}_{r,m}\right)x+n$$

(1)

where $h_{AVtx-AVrx}$ is the direct channel gain from AVtx-AVrx, $h_{r,m}$ is the reflected channel gain via the m-th IRS element ${\eta }_m$ represents the reflection amplitude (usually 1 for passive IRS), ${\varphi }_m$ is the phase shift introduced by the m-th IRS element, ${\varphi }_m$ is a continuous variable confined by the interval [0, 2$\pi$). x is the transmitted signal and n is the additive white Gaussian noise. Additionally, The Signal-to-Interference-plus-Noise Ratio (SINR) is given by:

$$\mathrm{SINR}={\displaystyle \frac{P_t{\left|h_{AVtx-AVrx}+{\sum }_{m=1}^M{\eta }_m{e}^{j{\varphi }_m}{h}_{r,m}\right|}^2}{{\sigma }^2+I}},$$

(2)

where $P_t$ is the autonomous vehicle transmit power, ${\sigma }^2$ is the noise power, and I represents all the interfered devices which can be expressed as:

$$I=\sum _{k=1}^K{P}_C{h}_{C_{k}A}+\sum _{d=1}^D{P}_D{h}_{D_{d}A}+\sum _{v=1}^V{P}_V{h}_{V_{v}A}+\sum _{l=1}^L{P}_V{h}_{V_{B}A}$$

(3)

where $h_{C_{k}A}$, $h_{D_{d}A}$, $h_{V_{v}A}$, and $h_{V_{B}A}$ are the direct channel gain from the interfering CUE and receiving autonomous vehicle (CUE-AVrx), the direct channel gain from the interfering transmitter D2D and receiving autonomous vehicle (Drx-AVrx), the direct channel gain from the interfering transmitter V2V and receiving autonomous vehicle (Vtx-AVrx),and the direct channel gain from the interfering transmitter V-BS which communicates with BS and receiving autonomous vehicle (VBtx-AVrx), respectively. $P_C$$P_D$, $P_V$ represent the interference transmission power of CUE, DTX, VTx and VBtx, respectively.

The main objective of the proposed model is to enhance autonomous vehicle system performance using IRS by jointly optimizing the energy efficiency ($EE$) and the achievable data rate (R). This optimization is achieved under constraints related to SINR_min, and maximum autonomous vehicle transmission distance ($P_{max}$), and maximum system required interference ($I_{\max }$) and is defined by the following equations:

$$\begin{array}{cc}\hfill \mathrm{Maximize}& \sum _{n=1}^{N}E{E}_n\hfill \\ \hfill \mathrm{Subject}\mathrm{to}& E{E}_n:=f_1(SINR,P_t,I)\hfill \\ \hfill & \mathrm{with}SINR\ge SIN{R}_{\min },P_t\le P_{\max },I\le I_{\max }\hfill \end{array}$$

(4)

$$\begin{array}{cc}\hfill \mathrm{Maximize}& \sum _{n=1}^N{R}_n\hfill \\ \hfill \mathrm{Subject}\mathrm{to}& R_n:=f_2(SINR,P_t,I)\hfill \\ \hfill & \mathrm{with}SINR\ge SIN{R}_{\min },P_t\le P_{\max },I\le I_{\max }\hfill \end{array}$$

(5)

The proposed model applies Non-Orthogonal Multiple Access (NOMA) to enable efficient sharing of spectrum resources among multiple users, thereby supporting scalable and adaptive communication in IRS-assisted V2X environments [38]. Furthermore, assuming statistically independent channel coefficients, the suggested model dynamically adjusts to shifting vehicle circumstances while operating in a Rayleigh fading channel with additive white Gaussian noise (AWGN) [39]. A scalable, energy-conscious, and predictive IRS-NOMA-V2X communication approach is the end product. The system energy efficiency and achievable data rate are defined by the following expressions:

$$\mathrm{EE}={\displaystyle \frac{R}{P_t+P_o}}={\displaystyle \frac{B·{log}_2\left(1+\frac{P_t{\left|h_{\mathrm{AVtx}-\mathrm{AVrx}}+{\sum }_{m=1}^M{\eta }_m{e}^{j{\varphi }_m}{h}_{r,m}\right|}^2}{{\sigma }^2+{\sum }_{k=1}^K{P}_C{h}_{C_{k}A}+{\sum }_{d=1}^D{P}_D{h}_{D_{d}A}+{\sum }_{v=1}^V{P}_V{h}_{V_{v}A}+{\sum }_{l=1}^L{P}_V{h}_{V_{B}A}}\right)}{P_t+P_o}}$$

(6)

$$\mathrm{R}=B·{log}_2\left(1+{\displaystyle \frac{P_t{\left|h_{\mathrm{AVtx}-\mathrm{AVrx}}+{\sum }_{m=1}^M{\eta }_m{e}^{j{\varphi }_m}{h}_{r,m}\right|}^2}{{\sigma }^2+{\sum }_{k=1}^K{P}_C{h}_{C_{k}A}+{\sum }_{d=1}^D{P}_D{h}_{D_{d}A}+{\sum }_{v=1}^V{P}_V{h}_{V_{v}A}+{\sum }_{l=1}^L{P}_V{h}_{V_{B}A}}}\right)$$

(7)

where $P_o$ represents the internal circuitry power consumption.

The objective is to determine the maximum required autonomous vehicle transmit power $P_t$, the maximum interference transmission power ($P_I$), and IRS phase shifts $\left\{{\varphi }_m\right\}$, while satisfying power and QoS constraints. Consequently, the Lagrangian for the optimization problem represented by Equations (4) and (5) is the following formula:

$$\mathcal{L}(P_t,P_I,\varphi ,{\lambda }_1,{\lambda }_2,{\lambda }_3)=EE-{\lambda }_1({\mathrm{SINR}}_{\min }-\mathrm{SINR})-{\lambda }_2(P_t-P_{max})-{\lambda }_3(I-I_{\max }),$$

(8)

$$\mathcal{L}(P_t,P_I,\varphi ,{\mu }_1,{\mu }_2,{\mu }_3)=R-{\mu }_1({\mathrm{SINR}}_{\min }-\mathrm{SINR})-{\mu }_2(P_t-P_{max})-{\mu }_3(I-I_{\max }),$$

(9)

where ${\lambda }_1,{\lambda }_2,{\lambda }_3,{\mu }_1,{\mu }_2$, and ${\mu }_3$ represent the non-negative Lagrange multipliers. For simplicity it has been assumed that $P_C,P_D,P_V$, and $P_{VB}$ have always the same value, and it has been represented by $P_I$. By taking the derivative of 8 with respect to $P_I$, and $P_I$ the following expressions the value of ${\lambda }_1$, ${\lambda }_2$, and ${\lambda }_3$ can be are obtained as:

$$\begin{array}{cc}\hfill 0=& {\displaystyle \frac{-B·{log}_2\left(1+\frac{P_t{\left|h_{\mathrm{AVtx}-\mathrm{AVrx}}+{\sum }_{m=1}^M{\eta }_m{e}^{j{\varphi }_m}{h}_{r,m}\right|}^2}{{\sigma }^2+{\sum }_{k=1}^K{P}_C{h}_{C_{k}A}+{\sum }_{d=1}^D{P}_D{h}_{D_{d}A}+{\sum }_{v=1}^V{P}_V{h}_{V_{v}A}+{\sum }_{l=1}^L{P}_V{h}_{V_{B}A}}\right)}{{(P_t+P_o)}^2}}\hfill \\ \hfill & +{\displaystyle \frac{1}{P_t+P_o}}·{\displaystyle \frac{B\frac{{\left|h_{\mathrm{AVtx}-\mathrm{AVrx}}+{\sum }_{m=1}^M{\eta }_m{e}^{j{\varphi }_m}{h}_{r,m}\right|}^2}{{\sigma }^2+{\sum }_{k=1}^K{P}_C{h}_{C_{k}A}+{\sum }_{d=1}^D{P}_D{h}_{D_{d}A}+{\sum }_{v=1}^V{P}_V{h}_{V_{v}A}+{\sum }_{l=1}^L{P}_V{h}_{V_{B}A}}}{{\displaystyle 1+\frac{P_t{\left|h_{\mathrm{AVtx}-\mathrm{AVrx}}+{\sum }_{m=1}^M{\eta }_m{e}^{j{\varphi }_m}{h}_{r,m}\right|}^2}{{\sigma }^2+{\sum }_{k=1}^K{P}_C{h}_{C_{k}A}+{\sum }_{d=1}^D{P}_D{h}_{D_{d}A}+{\sum }_{v=1}^V{P}_V{h}_{V_{v}A}+{\sum }_{l=1}^L{P}_V{h}_{V_{B}A}}}}}\hfill \\ \hfill & -{\lambda }_1{\displaystyle \frac{{\left|h_{\mathrm{AVtx}-\mathrm{AVrx}}+{\sum }_{m=1}^M{\eta }_m{e}^{j{\varphi }_m}{h}_{r,m}\right|}^2}{{\sigma }^2+{\sum }_{k=1}^K{P}_C{h}_{C_{k}A}+{\sum }_{d=1}^D{P}_D{h}_{D_{d}A}+{\sum }_{v=1}^V{P}_V{h}_{V_{v}A}+{\sum }_{l=1}^L{P}_V{h}_{V_{B}A}}}-{\lambda }_2\hfill \end{array}$$

(10)

$$\begin{array}{cc}\hfill 0=& {\displaystyle \frac{1}{P_t+P_o}}·{\displaystyle \frac{B\frac{-P_t{\left|h_{\mathrm{AVtx}-\mathrm{AVrx}}+{\sum }_{m=1}^M{\eta }_m{e}^{j{\varphi }_m}{h}_{r,m}\right|}^2\ast ({\sum }_{k=1}^K{h}_{C_{k}A}+{\sum }_{d=1}^D{h}_{D_{d}A}+{\sum }_{v=1}^V{h}_{V_{v}A}+{\sum }_{l=1}^L{h}_{V_{B}A})}{{({\sigma }^2+{\sum }_{k=1}^K{P}_C{h}_{C_{k}A}+{\sum }_{d=1}^D{P}_D{h}_{D_{d}A}+{\sum }_{v=1}^V{P}_V{h}_{V_{v}A}+{\sum }_{l=1}^L{P}_V{h}_{V_{B}A})}^2}}{{\displaystyle 1+\frac{P_t{\left|h_{\mathrm{AVtx}-\mathrm{AVrx}}+{\sum }_{m=1}^M{\eta }_m{e}^{j{\varphi }_m}{h}_{r,m}\right|}^2}{{\sigma }^2+{\sum }_{k=1}^K{P}_C{h}_{C_{k}A}+{\sum }_{d=1}^D{P}_D{h}_{D_{d}A}+{\sum }_{v=1}^V{P}_V{h}_{V_{v}A}+{\sum }_{l=1}^L{P}_V{h}_{V_{B}A}}}}}\hfill \\ \hfill & -{\lambda }_1{\displaystyle \frac{-P_t{\left|h_{\mathrm{AVtx}-\mathrm{AVrx}}+{\sum }_{m=1}^M{\eta }_m{e}^{j{\varphi }_m}{h}_{r,m}\right|}^2\ast ({\sum }_{k=1}^K{h}_{C_{k}A}+{\sum }_{d=1}^D{h}_{D_{d}A}+{\sum }_{v=1}^V{h}_{V_{v}A}+{\sum }_{l=1}^L{h}_{V_{B}A})}{{({\sigma }^2+{\sum }_{k=1}^K{P}_C{h}_{C_{k}A}+{\sum }_{d=1}^D{P}_D{h}_{D_{d}A}+{\sum }_{v=1}^V{P}_V{h}_{V_{v}A}+{\sum }_{l=1}^L{P}_V{h}_{V_{B}A})}^2}}\hfill \\ \hfill & -{\lambda }_3\ast (\sum _{k=1}^K{h}_{C_{k}A}+\sum _{d=1}^D{h}_{D_{d}A}+\sum _{v=1}^V{h}_{V_{v}A}+\sum _{l=1}^L{h}_{V_{B}A})\hfill \end{array}$$

(11)

By taking the derivative of Equation (8) with respect to ${\lambda }_1,{\lambda }_2$, and ${\lambda }_3$, the following expressions are obtained:

$$P_t=P_{\max }$$

(12)

$$P_I={\displaystyle \frac{I_{\max }}{{\sum }_{k=1}^K{P}_C{h}_{C_{k}A}+{\sum }_{d=1}^D{P}_D{h}_{D_{d}A}+{\sum }_{v=1}^V{P}_V{h}_{V_{v}A}+{\sum }_{l=1}^L{P}_V{h}_{V_{B}A}}}$$

(13)

$${\mathrm{SINR}}_{min}={\displaystyle \frac{P_t{\left|h_{\mathrm{AVtx}-\mathrm{AVrx}}+{\sum }_{m=1}^M{\eta }_m{e}^{j{\varphi }_m}{h}_{r,m}\right|}^2}{{\sigma }^2+{\sum }_{k=1}^K{P}_C{h}_{C_{k}A}+{\sum }_{d=1}^D{P}_D{h}_{D_{d}A}+{\sum }_{v=1}^V{P}_V{h}_{V_{v}A}+{\sum }_{l=1}^L{P}_V{h}_{V_{B_l}A}}}$$

(14)

Equation (14) is obtained from the derivative of ${\lambda }_2$, these derivatives relate to the constraints on transmission and interference power and maximum required interference, and solving them leads to necessary conditions for optimality. Nevertheless, the optimal IRS phase shifts ${\varphi }_i$ cannot be determined in closed-form as they are contained within a non-convex function. Rather, we iteratively change the phase shifts in order to maximize EE and R using gradient descent, a numerical optimization approach. This is possible because the phase configuration may be updated by computing (or approximating) the objective’s gradient with respect to ${\varphi }_i$:

$${\varphi }_i^{(t+1)}={\varphi }_i^{\left(t\right)}-ϵ·{\displaystyle \frac{\partial {\mathrm{SINR}}_{min}}{\partial {\varphi }_i}}$$

(15)

where $ϵ$ is the learning rate (step size), and ${\displaystyle \frac{\partial {\mathrm{SINR}}_{min}}{\partial {\varphi }_i}}$ is the gradient of the objective function with respect to the phase shift of the i-th IRS element. With this method, the system may effectively and adaptively converge to a locally optimum IRS configuration, which is consistent with our model’s hybrid learning-optimization architecture. Real-time adaptation in realistic vehicular environments is made possible by the gradient descent algorithm, which enhances the analytical solution of Lagrange optimization.

Similarly, by taking the derivative of Equation (9) with respect to $P_I$, and $P_I$ the following expressions the value of ${\mu }_1$, ${\mu }_2$, and ${\mu }_3$ can be are obtained as:

$$\begin{array}{cc}\hfill 0=& {\displaystyle \frac{B\frac{{\left|h_{\mathrm{AVtx}-\mathrm{AVrx}}+{\sum }_{m=1}^M{\eta }_m{e}^{j{\varphi }_m}{h}_{r,m}\right|}^2}{{\sigma }^2+{\sum }_{k=1}^K{P}_C{h}_{C_{k}A}+{\sum }_{d=1}^D{P}_D{h}_{D_{d}A}+{\sum }_{v=1}^V{P}_V{h}_{V_{v}A}+{\sum }_{l=1}^L{P}_V{h}_{V_{B}A}}}{{\displaystyle 1+\frac{P_t{\left|h_{\mathrm{AVtx}-\mathrm{AVrx}}+{\sum }_{m=1}^M{\eta }_m{e}^{j{\varphi }_m}{h}_{r,m}\right|}^2}{{\sigma }^2+{\sum }_{k=1}^K{P}_C{h}_{C_{k}A}+{\sum }_{d=1}^D{P}_D{h}_{D_{d}A}+{\sum }_{v=1}^V{P}_V{h}_{V_{v}A}+{\sum }_{l=1}^L{P}_V{h}_{V_{B}A}}}}}\hfill \\ \hfill & -{\mu }_1{\displaystyle \frac{{\left|h_{\mathrm{AVtx}-\mathrm{AVrx}}+{\sum }_{m=1}^M{\eta }_m{e}^{j{\varphi }_m}{h}_{r,m}\right|}^2}{{\sigma }^2+{\sum }_{k=1}^K{P}_C{h}_{C_{k}A}+{\sum }_{d=1}^D{P}_D{h}_{D_{d}A}+{\sum }_{v=1}^V{P}_V{h}_{V_{v}A}+{\sum }_{l=1}^L{P}_V{h}_{V_{B}A}}}-{\mu }_2\hfill \end{array}$$

(16)

$$\begin{array}{cc}\hfill 0=& {\displaystyle \frac{B\frac{-P_t{\left|h_{\mathrm{AVtx}-\mathrm{AVrx}}+{\sum }_{m=1}^M{\eta }_m{e}^{j{\varphi }_m}{h}_{r,m}\right|}^2\ast ({\sum }_{k=1}^K{h}_{C_{k}A}+{\sum }_{d=1}^D{h}_{D_{d}A}+{\sum }_{v=1}^V{h}_{V_{v}A}+{\sum }_{l=1}^L{h}_{V_{B}A})}{{({\sigma }^2+{\sum }_{k=1}^K{P}_C{h}_{C_{k}A}+{\sum }_{d=1}^D{P}_D{h}_{D_{d}A}+{\sum }_{v=1}^V{P}_V{h}_{V_{v}A}+{\sum }_{l=1}^L{P}_V{h}_{V_{B}A})}^2}}{{\displaystyle 1+\frac{P_t{\left|h_{\mathrm{AVtx}-\mathrm{AVrx}}+{\sum }_{m=1}^M{\eta }_m{e}^{j{\varphi }_m}{h}_{r,m}\right|}^2}{{\sigma }^2+{\sum }_{k=1}^K{P}_C{h}_{C_{k}A}+{\sum }_{d=1}^D{P}_D{h}_{D_{d}A}+{\sum }_{v=1}^V{P}_V{h}_{V_{v}A}+{\sum }_{l=1}^L{P}_V{h}_{V_{B}A}}}}}\hfill \\ \hfill & -{\mu }_1{\displaystyle \frac{-P_t{\left|h_{\mathrm{AVtx}-\mathrm{AVrx}}+{\sum }_{m=1}^M{\eta }_m{e}^{j{\varphi }_m}{h}_{r,m}\right|}^2\ast ({\sum }_{k=1}^K{h}_{C_{k}A}+{\sum }_{d=1}^D{h}_{D_{d}A}+{\sum }_{v=1}^V{h}_{V_{v}A}+{\sum }_{l=1}^L{h}_{V_{B}A})}{{({\sigma }^2+{\sum }_{k=1}^K{P}_C{h}_{C_{k}A}+{\sum }_{d=1}^D{P}_D{h}_{D_{d}A}+{\sum }_{v=1}^V{P}_V{h}_{V_{v}A}+{\sum }_{l=1}^L{P}_V{h}_{V_{B}A})}^2}}\hfill \\ \hfill & -{\mu }_3\ast (\sum _{k=1}^K{h}_{C_{k}A}+\sum _{d=1}^D{h}_{D_{d}A}+\sum _{v=1}^V{h}_{V_{v}A}+\sum _{l=1}^L{h}_{V_{B}A})\hfill \end{array}$$

(17)

By taking the derivative of Equation (9) with respect to ${\mu }_1,{\mu }_2$, and ${\mu }_3$, the following expressions are obtained:

$$P_t=P_{\max }$$

(18)

$$P_I={\displaystyle \frac{I_{\max }}{{\sum }_{k=1}^K{P}_C{h}_{C_{k}A}+{\sum }_{d=1}^D{P}_D{h}_{D_{d}A}+{\sum }_{v=1}^V{P}_V{h}_{V_{v}A}+{\sum }_{l=1}^L{P}_V{h}_{V_{B}A}}}$$

(19)

$${\mathrm{SINR}}_{min}={\displaystyle \frac{P_t{\left|h_{\mathrm{AVtx}-\mathrm{AVrx}}+{\sum }_{m=1}^M{\eta }_m{e}^{j{\varphi }_m}{h}_{r,m}\right|}^2}{{\sigma }^2+{\sum }_{k=1}^K{P}_C{h}_{C_{k}A}+{\sum }_{d=1}^D{P}_D{h}_{D_{d}A}+{\sum }_{v=1}^V{P}_V{h}_{V_{v}A}+{\sum }_{l=1}^L{P}_V{h}_{V_{B_l}A}}}$$

(20)

As mentioned previously, Equation (20) is obtained from the derivative of ${\mu }_2$, these derivatives relate to the constraints on transmission and interference power and maximum required interference, and solving them leads to necessary conditions for optimality. Nevertheless, the optimal IRS phase shifts ${\varphi }_i$ cannot be determined in closed-form as they are contained within a non-convex function. Rather, we iteratively change the phase shifts in order to maximize EE and R using gradient descent, a numerical optimization approach. This is possible because the phase configuration may be updated by computing (or approximating) the objective’s gradient with respect to ${\varphi }_i$:

$${\varphi }_i^{(t+1)}={\varphi }_i^{\left(t\right)}-ϵ·{\displaystyle \frac{\partial {\mathrm{SINR}}_{min}}{\partial {\varphi }_i}}$$

(21)

where $ϵ$ is the learning rate (step size), and ${\displaystyle \frac{\partial {\mathrm{SINR}}_{min}}{\partial {\varphi }_i}}$ is the gradient of the objective function with respect to the phase shift of the i-th IRS element. With this method, the system may effectively and adaptively converge to a locally optimum IRS configuration, which is consistent with our model’s hybrid learning-optimization architecture. Real-time adaptation in realistic vehicular environments is made possible by the gradient descent algorithm, which enhances the analytical solution of Lagrange optimization.

3.2. Data Generation

The analytical model represented in Section 3.1 is implemented using python in order to generate the required model dataset. The simulation parameters used in the proposed model are shown in

Table 3. Proposed model simulation parameters.

Parameter	Value
$ϵ$	0.05
$\eta$	0.8
B	10 Mbit/s [35]
N	−174 dBm/Hz [35]
$P_o$	0.1 W
$P_{\max }$	17–23 dBm [30]
$I_{\max }$	10−4 [40]
${\mathrm{SINR}}_{\min }$	20 dB
$P{L}_{A2A}$	$128.1+37.6{log}_{10}\left(d_{A2A}\right)$ dB [25]
$\mathrm{Fast}\mathrm{fadng}$	Rayleigh fading [35]

. To enhance autonomous vehicle communication, models deployed on all transmitting devices are trained using a comprehensive dataset. The dataset comprises a total of 42,786 records, each representing a distinct combination of key parameters: the distance between transmitted autonomous vehicle and received autonomous vehicle ($d_{A2A}$), the distance between transmitting autonomous vehicle and IRS ($d_{AR}$), the distance between IRS and receiving autonomous vehicle ($d_{RA}$) and all interference distance which represented by the interference due: the communication between cellular user and the base station ($d_{CA}$), the D2D communication ($d_{DA}$), V2V communication ($d_{VA}$); and communication between vehicle and the base station ($d_{VBA}$), the required signal-to-interference-plus-noise ratio threshold (${\mathrm{SINR}}_{\min }$); the optimum required autonomous vehicle transmission power transmission powers ($P_t$); the optimum required interference transmission power transmission powers ($P_I$); the optimum required IRS phase shift ($\varphi$).

The two important matrix of the proposed model Energy efficiency (EE) and achievable data rate (R) and performance indicators, have linear correlations that may be understood using the Pearson correlation matrix as shown Figure 3. Figure 3 shows that all the distance-related ($d_{A2A}$, $d_{AR}$, $d_{RA}$, $d_{DA}$, $d_{CA}$, $d_{VA}$, and $d_{VBA}$) have strong positive correlation with achievable rate (R), and a moderate positive correlation with energy efficiency EE (around 0.41). This suggests that longer transmission paths, possibly enabled by IRS reflection, contribute significantly to better achievable data rate, while moderately impacting efficiency. The transmission power ($P_t$) is strongly negatively correlated with EE (−0.87), which aligns with expectations that higher power consumption reduces efficiency. Additionally, the interference transmission power ($P_I$), which reflects the system’s optimized power allocation, shows a strong positive correlation with $P_t$ (0.92) and a strong negative correlation with EE (−0.77). The interference constraint $I_{\max }$ has a mild positive relationship with EE (0.18), while $\varphi$, representing the IRS phase shift, ${\mathrm{SINR}}_{\min }$ have near-zero correlations with both EE and R, indicating their minimal direct linear influence in the simulation range. Finally, the moderate positive correlation between EE and R (0.41) underscores that while high throughput often accompanies better energy performance, this is not guaranteed and depends on other interacting variables such as interference and power settings.

3.3. Proposed Deep Learning Model

This section introduces and explains the suggested deep learning model. Before adding the variables to the proposed deep learning model, a normalization step needs to be completed to help in the learning of the model weights. Each variable is normalized using the min-max scaling procedure before being included in the model. The eleven input variables, $d_{A2A}$, $d_{AR}$, $d_{RA}$, $d_{DA}$, $d_{CA}$, $d_{VA}$, $d_{VBA}$, ${\mathrm{SINR}}_{\min }$, $P_t$, $I_{\max }$, and $\varphi$, are used to create the output parameters, $P_I$, EE, and R, from the final dense layer. Thick layers, flattening, and 1D-CNN are the three distinct phases that make up the model, as shown in Figure 4. The normalized input parameters are processed by three 1D-CNN layers, each of which has a size 9 kernel, and 128 filters. The main reason for choosing 1D-CNN over RNN/LSTM is that 1D-CNN provides higher computational efficiency, captures localized temporal patterns relevant to vehicular data, and scales better for real-time applications. These properties align with the requirements of energy-efficient vehicular communication systems, as also validated by prior works. Before deciding on the number of nodes for the dense layers and the number of filters for the 1D-CNN, a grid search was conducted to explore a variety of options. The parameters used for the the proposed 1 DCNN are shown in

Table 4. Proposed deep learning model simulation parameters.

Layer Type	Hyperparameter	Value
Input Layer	Input Shape	(None, 11, 3)
Conv1D	Filters	128
	Kernel Size	9
	Dropout	0.5
	Activation Function	ReLU
BatchNormalization	-	-
Activation	Activation Function	ReLU
Dense	Units	128
	Activation Function	ReLU
Output Layer (Target)	Units	3
Adam
	Learning Rate	0.0001
	Batch Size	16
	Epochs	200
	Loss Function	MAE
	Validation Split	0.2
Random Forest Regressor
	n_estimators	100
	max_depth	10
	random_state	42

. All hidden layers have been activated using the Rectified Linear Unit (ReLU), and the grid search considered the choice of activation function. The regression result is produced by six thick layers that come after the flattening layer. Before choosing the number of nodes for the dense layers and the number of filters for the 1D-CNN, several choices were tested using a grid search. All hidden layers have been activated using the Rectified Linear Unit (ReLU). The grid search also considered the choice of activation functions and experimented with several techniques that may be used to monitor the hidden layers in the suggested model. In order to produce best results, each hidden layer’s output was fed into a parametric rectified linear unit (PReLU) activation.

Additionally, this method shows the importance of preprocessing through normalization to prevent any one variable from unduly affecting the model’s learning process, also to guarantee that all input features are scaled to a consistent range. Furthermore, to identify complex patterns and relationships in the normalized input the 1D-CNN layers are presented to successfully learn spatial hierarchies. It’s also important to note that by adding several thick layers after the CNN stages, the model may enhance predictions through regression. In order to improve the design and strike a balance between compute economy and performance accuracy, grid search is also employed for hyperparameter tuning. By evaluating complex correlations between the eleven input variables, CNN layers and dense layers combine to create a robust architecture that can accurately predict the output parameters. Furthermore, the adaptive moment (Adam) is the optimizer implemented in the proposed deep learning model. The proposed model is evaluated through four metrics, which are Mean Absolute Error (MAE), Mean Squared Error (MSE), Root Mean Squared Error (RMSE), and Coefficient of Determination ($r^2$) which are defined respectively as:

$$\begin{array}{c}\hfill MAE={\displaystyle \frac{{\sum }_{j=1}^n|y_j-x_j|}{n}}\end{array}$$

(22)

$$\begin{array}{c}\hfill MSE={\displaystyle \frac{{\sum }_{j=1}^n{(y_j-x_j)}^2}{n}}\end{array}$$

(23)

$$\begin{array}{c}\hfill RMSE=\sqrt{{\displaystyle \frac{{\sum }_{j=1}^n{(y_j-x_j)}^2}{n}}}\end{array}$$

(24)

$$\begin{array}{c}\hfill r^2=1-{\displaystyle \frac{{\sum }_{i=1}^n{(y_i-{\widehat{y}}_i)}^2}{{\sum }_{i=1}^n{(y_i-\overline{y})}^2}}\end{array}$$

(25)

where n is the total amount of data collected, $y_j$ is the actual data, and $x_j$ is the predicted data. The experiments that were conducted to evaluate, test, and train the proposed model are described in depth in the section that follows.

4. Results

This section presents the performance evaluation of the deep learning proposed model and the optimization proposed technique. Energy efficiency and achievable data rate under various limitations, including maximum transmission power, maximum needed interference, and minimum required SINR, are the two primary criteria used to assess the proposed autonomous vehicle networks. Furthermore, the suggested approach has been contrasted with various benchmarks to demonstrate its efficacy. Figure 5 illustrates the testing and validation of the proposed deep learning model described in Section 3.3. A 20% test set and an 80% train set were created from the datasets. The training and validation mean absolute errors for the necessary $P_I$, EE, and R are displayed in Figure 5a, Figure 5b, and Figure 5c, respectively. The validation and training curves in Figure 5a exhibit a sharp decline in the first few episodes before stabilizing about epoch 50. The two curves stay close together, indicating no indication of overfitting. Good convergence is seen in Figure 5b, where the validation MAE is marginally lower than the training MAE for the majority of epochs. The validation curve also shows a small spike, which is caused by batch level variability and does not signify overfitting. Additionally, Figure 5c is similar to Figure 5b; testing and validation converge and stabilize, there is no overfitting, and a slight spike in data variation occurs at 200 epochs. Lastly, Figure 5d shows that the model is learning well and that low bias, low variance, and well-trained are shown by the tiny difference between validation and training loss.

Figure 6 illustrates the impact of varying the transmission distance between autonomous vehicle and autonomous vehicle under certain environmental channel constraints which are maximum transmission power ($P_{\max }$) equals to 17 dBm and 23 dBm, minimum required signle-to-interference-plus-noise (${\mathrm{SINR}}_{\min }$) equals to 20 dB and maximum interference (${\mathrm{I}}_{\max }$) equals to 10⁻⁴. Also, in this scenario, it has been assumed that the interference distance is always equal to the transmission distance to show how effectively the proposed model performs. The results show that at shorter transmission distances, the required interference power should be low to satisfy the required channel conditions, while when the transmission distance increases, which means an increase in the interference distance, allows an increase in interference power. It is worth mentioning that increases in interference distances lead to a decrease in interference effects on the transmission signal. 1- Additionally, the optimized phase shift of the IRS proposed in this model contributes significantly to enhancing the quality of signal at the receiver, practically in large distances, enabling reliable communication with reduced power consumption also finding the optimum IRS phase shifts will help avoiding interference which enhances system performance. Notably, the results obtained from the proposed analytical model closely match the results obtained from the proposed 1DCNN model, which validates the accuracy and the reliability of the proposed model.

The energy efficiency of the proposed model is evaluated in Figure 7 for the same previously mentioned scenario. In this scenario, it has been assumed that the interference transmission distance is equal to the transmission distance between A2A. Figure 7 shows that increasing the A2A transmission distance leads to an increase in EE, as the proposed model can help to manage interference and power allocation over a longer distance. This behavior is mainly obtained due to the real-time optimization of the IRS phase shifts, which helps dynamically adjust the signal reflection path to ensure lower interference and at the same time, minimize the energy loss. Additionally, this can be attributed to the role of the IRS in enhancing the communication link. While longer distances usually degrade the data rate due to higher path loss, the IRS mitigates these losses by dynamically adjusting the reflection coefficients, improving signal strength, and maintaining a stable link quality. However, it is worth mentioning that increasing transmission power leads to a decrease in EE due to an increase in energy consumption without an increase in data rate under fixed SINR. In addition, increasing transmission power is required to mitigate interference, which further reduces EE. Also, it has been noticed that the results obtained from the analytical and 1DCNN models are approximately matching in values.

Furthermore, for the same scenario, the achievable data rate (R) is evaluated in Figure 8. Figure 8 depicts that the achievable data rate increases with the increase of A2A transmission distance, also it has been noticed that the R curves remain unchanged for both maximum transmission power. This performance may contribute to the system’s power control mechanism, which ensure that the minimum required SINR (${\mathrm{SINR}}_{\min }$) can always be obtained regardless of the value of transmission power. As long as (${\mathrm{SINR}}_{\min }$) can be achieved with lower transmission power, the rate can be constrained by SINR rather than transmission power. Additionally, the dynamic optimization of the IRS phase shifts through adjusting the phase shift based on the required channel environment enhances the effective channel gain and allowing the system to achieve the required SINR with relatively low transmission power. As a result, both scenarios with the two different transmission power yield similar rate performance over the assumed distance range. Furthermore, from Figure 8 it can be noticed that the values of the proposed analytical model are approximately equal to to values predicted by the proposed 1DCNN.

Figure 9 demonstrates the relation between (${\mathrm{SINR}}_{\min }$) and EE under different channel environmental conditions which are two different A2A transmission distances which are 20 and 50 m, two different maximum transmission power 17 and 23 dBm and maximum required interference (${\mathrm{I}}_{\max }$) equals to 10⁻⁴. From Figure 9, it can be mentioned that the performance and values of the analytical and deep learning models are approximately the same. Additionally, Figure 9 indicates that EE remains unchangeable with different values of (${\mathrm{SINR}}_{\min }$), this stability can be explained by the adaptive power allocation strategy, which ensures that (${\mathrm{SINR}}_{\min }$) can be achieved without increase in power. This behavior is obtained due to the capability of the proposed model to optimize the IRS phase shifts, which enhances the effective signal strength at the receiver. At longer distances, the optimized IRS plays a more significant role in maintaining signal quality, thereby compensating for reduced transmission power. Additionally, as mentioned previously, achieving the target SINR at longer transmission distances using minimal transmission power may improve EE. This is due to the fact that EE can be defined as the ratio of R to the transmission power; therefore, maintaining low power while maintaining performance constraints enhances EE.

The achievable data rate is evaluated again for the mentioned scenario as shown in Figure 10. Figure 10 shows the effect of varying (${\mathrm{SINR}}_{\min }$) on the system achievable data rate. It can be demonstrated that the achievable data rate remains constant despite the change of (${\mathrm{SINR}}_{\min }$). This behavior is due to the system stratification once it reaches the required SINR, any further increase leads to only a marginal increase in data rate due to the nature of the Shannon capacity formula. Additionally, it can be shown from Figure 10 that comparing the two different transmission distances together, it can be found that the achievable data rate increases at longer distances. One key factor that contributes to this outcome is the optimization of IRS phase shift, which enhances the effective channel gain by combining the reflected signal at the destination. This optimization allows the system to achieve a higher data rate by compensating for the higher path loss associated with longer distances while still respecting power and interference constraints. In addition, it has been mentioned that the system reinforces the importance of adaptive transmission techniques and IRS-based optimization for achieving the required system performance.

Further to the previous scenario, the energy efficiency (EE) of the proposed is evaluated under varying transmission power levels and two different transmission distances, which are 20 m and 50 m as shown in Figure 11. The evaluation observed in Figure 11 is carried out under a fixed minimum SINR requirement of 20 dB and a maximum required interference (${\mathrm{I}}_{\max }$) equal to 10⁻⁴. The result shows two different trends: first, the higher achievable data rate is reached by the higher transmission distance of 50 m. Second, EE decreases with increasing transmission power. These results can be justified by the following: the higher energy efficiency obtained when the transmission distance is 50 m, which indicates the effectiveness of the proposed IRS-assisted A2A model in optimizing the system performance. On the other hand, the inverse relationship between the energy efficiency and the transmission power is defined by EE, which is the ratio of the achievable data rate to the power consumed by the system. As transmission power increases, leads to a decrease in EE, especially when the achievable data rate has already saturated due to the SINR constraint already satisfied. These results reinforce the importance of adaptive transmission techniques and IRS-based optimization for achieving the required system performance.

Figure 12 depicts the achievable data rate R for the proposed model versus different maximum transmission power under different channel conditions, such as the two different transmission distances: 20 m and 50 m, the minimum SINR requirement of 20 dB and a maximum required interference (${\mathrm{I}}_{\max }$) equal to 10⁻⁴. The results obtained from Figure 12 indicate that the data rate remains unchanged when the maximum transmission power increases. Also, it has been observed that the data rate improves when the transmission distance increases from 20 m to 50 m. This behavior is obtained due to the fact that the system is designed to reach required SINR. Therefore, once the required SINR threshold is achieved, the data rate won’t increase further even if with the increase of the transmission power. This is due to the design of the proposed model which does not utilize the extra power to exceed the SINR target, but it only ensures that the target is met efficiently. Furthermore, the system should restrict power use to avoid exceeding interference levels, which limits raising the data rate, due to the limitation of the maximum necessary interference (${\mathrm{I}}_{\max }$). Furthermore, the efficient use of IRS in system design improves channel conditions and signal quality through constructive interference. If the system effectively handles SINR needs and interference limits through improved IRS phase shift setup and power allocation, this results in a greater attainable rate at longer distances.

To show the effectiveness of the proposed model, the proposed model has been compared with the model proposed [26]. Figure 13 presents the sum-rate performance (in bit/Hz) as a function of the maximum transmission power (${\mathrm{P}}_{\max }$) in dBm, comparing the proposed model and the model proposed in [26], it can be mentioned that both the analytical and 1DCNN proposed models outperform the benchmark across the entire range of (${\mathrm{P}}_{\max }$). This behavior proves that the proposed optimized model helps achieve near-optimal throughput without utilizing the full available transmission power. Additionally, the benchmarks show a linear increase in the sum-rate with increasing (${\mathrm{P}}_{\max }$), which indicates a lack of optimization in resource allocation and control. Furthermore, this shows the ability of the proposed model to maintain high data rates while limiting power consumption, which indicates the intelligence of the proposed model, in terms of adaptive power control, IRS phase optimization, and effective interference management to effectively meet the required SINR constraints. Further raising (${\mathrm{P}}_{\max }$) does not result in performance increases in the optimized models because SINR, not power, limits the system’s capacity. In comparison to conventional, non-optimized systems, this figure highlights the superiority of the suggested frameworks by showcasing their resilience and energy efficiency. It is worth mentioning that [26] focused on maximizing sum capacity through joint UAV transmit power and IRS beamforming optimization, the proposed model targets EE and R. To ensure fairness, it has been assumed that the maximum transmission power, whether it is UAV or AV and channel conditions are identical. Under these general conditions, we compared the results in terms of EE and R to achievable capacity in [26]. This allows for a realistic evaluation of the proposed scheme’s efficiency under similar settings, even though the optimization objectives differ.

The effectiveness of the proposed 1DCNN is presented in

Table 5. Performance evaluation metrics.

Algorithm	Metric	${\mathit{P}}_{\mathit{I}}$	EE	R
	MSE	0.00181	0.00669	0.00587
	RMSE	0.0425	0.0818	0.0766
1 DCNN	MAE	0.0134	0.0402	0.0585
	$r^2$	0.9292	0.9575	0.9460
	MSE	0.00475	0.00716	0.0084889
	RMSE	0.0689	0.0846	0.092135
LSTM	MAE	0.0287	0.05459	0.069078
	$r^2$	0.824833	0.95464	0.92093
	MSE	0.00236	0.00754	0.00794
	RMSE	0.04855	0.0868	0.0891
GRU	MAE	0.02237	0.05893	0.071
	$r^2$	0.9101	0.9523	0.9262

. The results presented in this table show the comparison between 1 DCNN, LSTM and GRU. As it can be mentioned that the proposed 1 DCNN outperforms LSTM and GRU in terms of MSE, RMSE, MAE and $r^2$. This clarifies why the 1 DCNN is chosen. Additionally, the results presented in this table indicate that the proposed 1DCNN model exhibits strong predictive performance across all three output variables: $P_I$, EE, and R. For $P_I$ the values of MSE, RMSE, and MAE highlight that the model performs with high precision and low prediction error in estimating $P_I$. Additionally, it has been mentioned that the value of $r^2$ confirms that the proposed model can successfully captured the majority of the variability in $P_I$ values. Furthermore, Energy Efficiency (EE) had the greatest $r^2$ value (0.957), even though its error metrics were somewhat higher than PI’s. This implies that the model is quite successful in predicting the general trend and variability of EE data, even though the predictions may differ somewhat more in absolute terms. Lastly, the achievable data rate (R) has an $r^2$ of 0.946, the model continues to show good performance in data rate prediction. A little greater variation in individual predictions is shown by the somewhat higher MAE (0.0585), which might be the result of more intricate or irregular patterns in the R. In conclusion, when predicting important communication system performance metrics, the 1DCNN model has strong generalization ability and small error margins. The greatest $r^2$ values for EE and R attest to the applicability of deep learning for simulating time-dependent and nonlinear interactions in wireless communication settings, particularly when IRS and V2X improvements are present.

5. Conclusions

An energy-efficient Internet of Things-based communication model that is tailored for transmitting data in autonomous vehicle communication is presented in this paper. For performance prediction, the system uses a 1D Convolutional Neural Network (1D-CNN) analytical optimization model that incorporates important factors, including data rate (R), energy efficiency (EE), and maximum needed interference transmission power ($P_I$). The outcomes derived from the suggested model show how well it works to achieve high performance even with strict SINR and interference limits. Additionally, it has been noticed that increasing transmission distance leads to better energy efficiency, particularly when A2A communication and appropriate IRS-assisted signal reflection are used. Furthermore, data rate (R) improves dramatically with increasing transmission distance, indicating improved signal durability via the IRS layer, even if it stays constant with increased transmission power. Furthermore, the evaluation metrics show exceptional model performance and validate the 1D-CNN model’s prediction accuracy. Overall, the proposed model provides an intelligent and scalable communication solution for autonomous vehicle networks operating in future 6G settings. Furthermore, the suggested approach improves dependability, reduces power consumption, and ensures efficient data handling. Future work will concentrate on real-time deployment, further optimizing IRS parameters, and expanding the framework to multi-hop and urban mobility. In the future, this study will be extended by deploying the suggested model in a real-world testbed setting with AV communication and 6G-based communication modules to assess its performance under realistic operational situations. This will allow to assess the performance of the suggested approach.