Active RIS-NOMA Uplink in URLLC, Jamming Mitigation via Surrogate and Deep Learning

The integration of Non-Orthogonal Multiple Access (NOMA) and Reconfigurable Intelligent Surfaces (RIS) significantly enhances 5G across a variety of technologies such as the Internet of Things (IoT), smart cities, and industrial automation. This work explores an active RIS-assisted NOMA uplink system aimed at mitigating jamming attacks while ensuring the reliability and latency requirements of ultra-reliable low-latency communication (URLLC) applications. We investigate the potential of RIS with active elements that adjust the phase and amplitude of the received signals for robust jamming mitigation. The study incorporates finite blocklength (FBL) and Automatic Repeat Request (ARQ) strategies to handle real-world complex configurations effectively. A thorough examination of various network parameters is conducted, including user transmit powers, active RIS elements amplitude, and the number of RIS elements. The paper utilizes the surrogate optimization technique, particularly the Radial Basis Function (RBF), to address the non-convex optimization problem minimizing the power consumption. The complexity of the optimization problem, involving numerous interacting variables, leads us to develop a deep regression model to predict optimal network configurations, providing a computationally efficient approach as well as reducing the signaling overhead. The findings emphasize the delicate balance required in optimizing network parameters. For instance, increasing the blocklength from 100 to 150 increases the reliability feasibility by 12.19%. The results demonstrate an optimal range for the amplitude value of active RIS elements $(2\lt \beta \lt 15)$ . Exceeding this range results in over-amplification, high latency, and lower reliability, due to the interference related to NOMA cluster users. The deep regression model converges to a weighted mean square error (WMSE) of 10.6 for RIS with 25 elements and 15.8 for larger RIS size, highlighting the effectiveness of the deep regression model and RIS configuration’s importance.

SECTION I. Introduction

5G has emerged to address the exponential growth of mobile users and the integration of recent technologies such as the Internet of Things (IoT), automated vehicles (AVs), industrial automation, and smart cities [1]. However, these technologies require high connectivity, data rate, and minimal latency to operate effectively [2]. For instance, IoT devices require continuous data transfer [3], AVs rely on real-time communication with low latency [4], and augmented reality applications demand high bandwidth to function properly [5]. While 4G technology was an impressive improvement over 3G, it has the maximum data transmission rate of 1 Gbps [6] and faces latency issues with delays of 30 to 50 milliseconds [7]. Furthermore, the limited capacity of 4G makes it inefficient to manage a high density of connected devices which is the case with technologies mentioned before [8]. Thus, 5G with speeds up to 10 Gbps, latency as low as 1 ms, and the capability to support 1000 times denser scenarios is the essential technology to achieve high performance and user satisfaction in advanced network applications [9], [10].

Besides numerous advantages, 5G has some restrictions such as interference management, spectral efficiency, user capacity, and power consumption [11]. Non-Orthogonal Multiple Access (NOMA) addresses interference issue caused by using the same frequency band by dedicating different power levels to each user [12]. This method helps to distinguish the users and eliminate the inter-cell interference and intra-cell interference using Successive Interference Cancelation (SIC) decoding [13]. Through SIC decoding, the receiver decodes the received signals based on instantaneous Channel State Information (CSI) and separates the strong user from the weak user based on a fixed or dynamic ordering [14]. This technique helps to serve multiple users on the same frequency channel and therefore increases user capacity and spectral efficiency of the network [15]. Moreover, NOMA optimizes the power allocation of users in the network which reduces the overall energy consumption which is critical in applications such as IoT with devices with limited battery source [16]. Another 5G characteristic essential for applications such as IoT, AVs, and factory automation is Ultra-Reliable Low Latency Communication (URLLC) [17]. NOMA can provide efficient resource utilization and lower delay which addresses the required reliability and latency demanded by URLLC applications [17].

NOMA-based communication systems are vulnerable to jamming attacks due to the broadcast nature of wireless channels [18], [19]. Jamming attacks can effectively interfere with the performance of the system in situations involving uplink NOMA as in most scenarios, the transmitter is a low-power device with fewer equipment resources [20]. High interference complicates the detection process in uplink NOMA systems, leading to imperfect successive interference cancelation (SIC) and error propagation [21]. Some approaches to mitigate these attacks on uplink NOMA systems are studied in the literature. Reference [22] proposes a joint power allocation and access point positioning to increase communication reliability in the presence of a jammer. Moreover, research on user pairing and optimal power allocation in uplink NOMA is conducted to optimize the effectiveness of NOMA as an interference management technology [23]. The incorporation of a relay node for jamming mitigation in uplink NOMA is discussed in [24]. The paper investigates two relaying protocols along with a retransmission scheme using uplink pairwise NOMA. However, using jamming mitigation methods such as power control and beamforming and employing active relays results in high power consumption [25]. Reconfigurable Intelligent Surfaces (RIS) have recently attracted considerable interest as a potential solution to these challenges. RIS is considered a smart entity which can be programmed to enhance physical layer security (PLS) under different security conditions such as eavesdropping and jamming [26]. On the other side, integrating RIS with NOMA introduces enhancements in network throughput, thereby leading to RIS-assisted NOMA systems as an effective approach to improving the performance of the communication [27]. RIS is a 2D surface including an array of elements with the ability to generate distinct phase shifts on the received signal [28] and alter their electromagnetic properties dynamically to adjust the wireless signal propagation [29]. These surfaces are capable of improving signal-to-noise ratio (SNR), particularly in scenarios where direct transmission experiences considerable degradation due to dynamic channel conditions between the base station and a mobile vehicle [30]. Various research works demonstrate that employing RIS to aid the network performance can lead to a significant improvement in secrecy rate and transmission rate [20], [31], [32], [33]. This makes the RIS a valuable tool to boost the physical layer security of communication systems. Nonetheless, research demonstrates that RIS itself is vulnerable to a variety of security attacks depending on the network architecture [34]. Therefore, there is a need for further research to investigate the optimal network parameters and architectures that can improve the robustness of RIS-assisted networks.

In this work, we analyze a RIS-based uplink NOMA system with active RIS elements in the presence of a jamming attack. We focus on reliability, latency, and power consumption as main performance indicators. Our study considers finite blocklength (FBL) and Automatic Repeat Request (ARQ) strategies to enhance the robustness of communication. The latency requirements are considered to achieve URLLC in the communication system. Subsequently, the effect of network parameters (such as transmit powers, amplitude of RIS, and number of RIS elements) on network metrics (such as reliability, latency, and power consumption) is explored. Finally, a deep regression model is developed to address the challenges of solving the optimization problem using evolutionary algorithms. The main contributions of this work are summarized below:

• Introducing an active RIS-assisted 5G NOMA uplink system to counteract jamming attacks while maintaining the reliability and latency required for URLLC applications.

• Incorporation of FBL and ARQ schemes to ensure a practical design compatible with complex configurations considering the data traffic behavior of the users.

• Formulating and analyzing various network parameters including the transmit powers of users, amplitude of active RIS, and the number of RIS elements and their impact on reliability, latency, and signal-to-jammer-plus-noise ratio (SJNR).

• Employing surrogate optimization, specifically Radial Basis Functions (RBF), to address the non-convex problem of minimizing the power consumption of the network setup while considering the power consumption of active RIS elements.

• Developing a deep regression model to be implemented at RIS to predict the most effective network configuration while reducing the signalling overhead since only received jamming power at gNB needs to be reported.

The remainder of this paper is organized as follows. Section II briefly reviews current literature on jamming mitigation in RIS-based systems. Section III presents the system model and problem formulation. Results are provided in Section IV and finally, Section V concludes the study.

SECTION II. Related Work

Recently, the operation of RIS has drawn attention to enhance the performance and security of different wireless communication schemes and address various challenges in wireless networks, particularly in dynamic environments [35], [36]. Adding intelligent surfaces to the wireless network architecture leads to more deterministic data rates which enhance the reliability and reduce the latency [37]. RIS is a two-dimensional surface divided into elements that apply phase shift on the received signal managed by a controller planted at the base station [38]. RIS elements in the literature are divided into two main groups: passive and active RIS. RIS with passive elements reflects the signal by altering the phase values using low-power electronic devices such as PIN diodes and varactors without requiring an active power source [39]. Passive RIS can be implemented to mitigate the effect of multipath fading and dynamic channel conditions [40]. On the other hand, active RIS can adjust both the amplitude and phase of the signal using power amplifiers [41]. This is mostly beneficial when users move at high speed and signal attenuation is significant [42]. Reference [43] investigates how active RIS can improve throughput and energy efficiency by amplifying the desired signal and requiring less energy compared to passive RIS. Furthermore, incorporating RIS into the communication scheme increases the security of the network. RIS can be used to apply additional noise or a misleading signal towards an illegitimate user or eavesdropper. This is discussed in [44] which explores the enhancement of physical layer security in wireless communications using RIS. The authors propose a joint optimization of transmit beamforming, access point artificial noise injection, and RIS phase shifts to maximize the sum rate of the system while limiting the amount of information that could be leaked to potential eavesdroppers. The physical layer security of single-input multiple-output (SIMO) wireless systems including a passive RIS is discussed in [20]. To optimize the secrecy rate of the connection, a combination of passive beamforming and active jamming is employed to confuse the eavesdropper. The authors validated the proposed method by the outcome of multiple simulations, especially when compared to traditional approaches that do not use RIS. A similar strategy is explored in [45] to mitigate eavesdropping in an IRS-NOMA network with multiple users transmitting simultaneously. Reference [46] presents a novel method of partitioning the elements of RIS to simultaneously enhance the quality of transmission for legitimate users and jam the eavesdropper to improve the secrecy rate. Authors in [47] propose using active RIS to mitigate eavesdropping in an unmanned aerial vehicle (UAV) communication under imperfect CSI. A twin-deep deterministic policy gradient deep reinforcement learning (TDDRL) is employed to solve the joint optimization problem of the active beamforming of the UAV, RIS beamforming matrix, and UAV trajectory. The study shows that incorporating RIS can considerably improve the sum secrecy rate and communication efficiency.

The use of passive RIS to secure transmission in a network under the combination of jamming and eavesdropping attacks is studied in [48]. In the proposed methodology, the base station jointly optimizes transmit beamforming by the base station and reflect beamforming by RIS despite the lack of information regarding the eavesdropper and jammer. The optimization problem, which is non-convex due to incomplete information, is converted to a solvable convex format by applying mathematical techniques such as the auxiliary variable method, the Cauchy-Schwarz inequality, and the General Sign-Definiteness transformation. Reference [49] presents an anti-jamming algorithm based on the Bayesian Stackelberg game. The primary objective of this work is to create a robust design that addresses imperfect channel state information, specifically uncertainties in angular information which is crucial for RIS, to enhance the security of the system against jammer.

Considering the increasing complexity of RIS, especially in dynamic situations, machine learning becomes a key tool for optimizing the capabilities of RIS scenarios. Reference [25] explores the use of passive RIS to maximize the achievable rate of user equipment (UE) using reinforcement learning in a 5G network. The proposed method focuses on optimizing both the power allocation at the base station (BS) and the beamforming at the RIS. Another study leveraging machine learning to enhance the performance of a jammed uplink connection is referenced in [32]. In this work, the authors transform the communication strategy to a Markov Decision Process (MDP) and optimize the phase shifts and transmission energy of a passive RIS using Deep Q-Networks (DQN). The use of DQN helps to deal with high dimensionality arising from managing multiple RIS phase shifts and transmission energy parameters. Reference [50] employs a passive RIS attached to UAV to improve the achievable rate of users while under an intelligent jamming attack. The intelligent jammer in this study refers to a jammer capable of keeping its location and power unknown. To solve the optimization problem, authors follow the same strategy as [32] to deal with the complexity of the optimization problem. The use of Deep Reinforcement Learning (DRL) along with passive RIS to enhance jamming resistance is further investigated in [33]. This novel approach helps to maximize the performance of a downlink multiuser OFDM system without requiring knowledge of channel state information. While DRL is investigated in the aforementioned studies due to its adaptability and dynamic optimization capabilities, its application in scenarios involving active RIS under stringent latency and reliability constraints remains unexplored. DRL can present notable challenges in such scenarios including the need for continuous exploration and frequent policy updates during the jamming mitigation procedure. The Aerial RIS (ARIS) usage for anti-jamming approaches is discussed in [31]. The authors proposed jointly optimizing the ARIS deployment and the phase shifts of RIS passive elements. The location of ARIS is optimized using successive convex approximation and manifold optimization is applied to the reflection beamformer. The results obtained from the simulation validate the impact of adding ARIS on the transmission rate. Reference [51] studies the implementation of multiple RIS in an aerial-ground communication system to optimize SINR with a jammer in the network. Authors employ the relax-and-retract algorithm to optimize the non-convex problem as it is challenging to optimize transmit beamforming at the base station and reflecting beamforming at RIS. Reference [52] discusses using ARIS to mitigate a multi-jammer attack during a public event in the urban environment. The multi-objective optimization problem is formulated to maximize the achievable transmission rate and minimize energy consumption. The authors suggest using reinforcement learning to deal with the mixed-integer non-convex multi-objective problem and dynamic environmental conditions. Thus, the problem is first formulated as an MDP and then is solved using the Deep Deterministic Policy Grant (DDPG) algorithm. However, using ARIS is challenging due to its power and energy constraints, environmental factors, dynamic channel conditions, and security concerns [53], [54].

RIS is proposed by several studies to enhance network security in a NOMA-based communication system. Reference [55] introduces a system in which the RIS elements are divided into two groups; one that improves the quality of received signal for legitimate users in NOMA, and the other group that suppresses potential eavesdroppers through the generation of artificial noise or jamming. This ensures secure communication while maximizing spectrum utilization. While multiple research investigates using RIS to improve the physical layer security in NOMA [45], [55], [56], [57], [58], [59], [60], jamming attack mitigation in the RIS-based NOMA communication remains nearly unexplored. Reference [61] explores the application of RIS technology to assist uplink power-domain NOMA system in mitigating jamming attacks. The authors study a traditional RIS which only reflects the signal and an advanced RIS which attenuates the incoming signal. The proposed model helps to maintain the quality of service while minimizing the total power transmitted by users even in the presence of the jammer.

Active RIS unlike passive RIS can change both the phase and amplitude of the signal which can be particularly advantageous when the network is under a jamming attack. Reference [41] introduces an innovative receiver architecture that combines active and passive RIS to improve the anti-jamming capabilities of MIMO communications. The proposed architecture improves signal integrity by eliminating interference from the jammer and optimizing the manipulation of received electromagnetic waves. The concept of active RIS is also investigated in NOMA by [62], [63], [64], [65] in which authors propose using active RIS to enhance physical layer security. These studies demonstrate that active RIS can be designed to mitigate the eavesdropping attack or perform signal reflection to enhance legitimate communication while also generating jamming signals to prevent eavesdropping.

Based on the thorough literature review above, this work bridges the following identified gaps:

• Integration of active RIS to 5G uplink NOMA to mitigate jamming attacks: State-of-the-art is mostly centred on downlink scenarios and eavesdropping or PLS security attacks.

• Incorporation of FBL and integration of ARQ strategies: State-of-the-art assume infinite block length and simplify the challenges of real-world scenarios

• Alongside URLLC constraints, consideration of user transmit powers, active RIS phase shifts, active RIS amplitude, blocklength and number of retransmissions in optimizing network power performance: State-of-the-art does not consider all of these constraints.

• Consideration of the interference noise produced by active RIS elements and power consumed during the amplification process of active RIS.

• Using deep regression for dynamic optimization of RIS and network settings: Evolutionary algorithms pose several challenges when used in optimization of RIS and network configurations.

SECTION III. Problem Formulation

A. System Model

Consider the scenario of uplink transmission in an RIS-assisted NOMA system including K single-antenna user equipment (UEs) and a single-antenna base station as demonstrated in Fig. 1. Each user in the NOMA cluster is considered to have a packet at each frame with the probability of $\omega$ . Due to obstructions along the direct path, the communication between the UEs and the base station is facilitated through an active RIS equipped with $N=N_{R}N_{C}$ number of elements designed on a 2-D rectangular surface with $N_{R}$ elements in each row and $N_{C}$ elements in each column. Each element is a $A_{n} = d_{W}\times d_{H}, n\in \{1,\ldots , N\}$ rectangle with $d_{W} = \Delta _{h}\lambda$ as the width and $d_{H} = \Delta _{v}\lambda$ as the height, where $\Delta _{h}$ represents the horizontal antenna spacing and $\Delta _{v}$ denotes vertical antenna spacing, and $\lambda ={}\frac {c}{f_{c}}$ is the wavelength with c as the speed of light and $f_{c}$ as the central frequency. Thus, the total area of the RIS is $N\times A_{n}$ . Considering that the elements are indexed row by row, the position of the nth antenna element is as follows [66]: $$\begin{align*} \boldsymbol {u}_{n} = \begin{bmatrix} 0 \\ i_{R}(n)d_{W}\lambda \\ i_{C}(n)d_{H}\lambda \end{bmatrix}, \tag {1}\end{align*}$$ where $i_{R}(n)=mod(n-1,N_{R})$ is the horizontal index of nth antenna element, $i_{C}(n)=\lfloor (n-1)/N_{R}\rfloor$ is the vertical index of nth antenna element. Assume $\phi ^{A}$ the azimuth angle $\phi ^{A} \in (-\pi /2,\pi /2)$ and $\phi ^{E}$ as the elevation angle $\phi ^{E} \in (-\pi /2,0)$ . When a wave vector impinges on an antenna array each antenna element at position $u_{n}$ experiences a phase shift of $\boldsymbol {\zeta }(\phi ^{A},\phi ^{E})^{T}u$ where $\boldsymbol {\zeta }(\phi ^{A},\phi ^{E})\in \mathbb {R}^{3\times 1}$ is a wave vector described by [66]: $$\begin{align*} \boldsymbol {\zeta }\left ({{\phi ^{A},\phi ^{E}}}\right )=\frac {2\pi }{\lambda }\begin{bmatrix}\cos {\phi ^{A}}\cos {\phi ^{E}} \\ \sin {\phi ^{A}}\cos {\phi ^{E}} \\ \sin {\phi ^{E}}\end{bmatrix}. \tag {2}\end{align*}$$ The corresponding array response $a(\phi ^{A},\phi ^{E})\in \mathbb {C}^{N\times 1}$ is based on (3) [67]. $$\begin{equation*} \boldsymbol {a}\left ({{\phi ^{A},\phi ^{E}}}\right ) = \left [{{e^{j\boldsymbol {\zeta }\left ({{\phi ^{A},\phi ^{E}}}\right )^{T}\boldsymbol {u}_{1}},\ldots , e^{j\zeta \left ({{\phi ^{A},\phi ^{E}}}\right )^{T}\boldsymbol {u}_{N}}}}\right ]^{T}. \tag {3}\end{equation*}$$

FIGURE 1.

Uplink RIS-based NOMA system with K UEs under jamming attack.

Let $\boldsymbol {I} \in \mathbb {C}^{N\times 1}$ be the channel vector between the RIS and the base station which can be defined as $$\begin{equation*} \boldsymbol {I} = \sqrt {Ld_{_{RIS-BS}}^{-\delta }} e^{-j\frac {2\pi d_{_{RIS-BS}}}{\lambda }}\times a\left ({{\phi ^{A}_{BS},\phi ^{E}_{BS}}}\right ), \tag {4}\end{equation*}$$ where L is the path gain at the reference distance of $1m$ , $d_{_{RIS-BS}}$ is the distance between RIS and base station, $\delta$ denotes the path loss exponents, $\phi ^{A}_{BS}$ and $\phi ^{E}_{BS}$ represent the azimuth and elevation angles between RIS and base station.

Additionally, $\boldsymbol {G}_{k} \in \mathbb {C}^{N\times 1}$ represents the channel vector between RIS and kth user and is modeled as follows: $$\begin{equation*} \boldsymbol {G}_{k} = \sqrt {Ld_{_{RIS-{UE}_{k}}}^{-\delta }}e^{-j\frac {2\pi d_{_{RIS-{UE}_{k}}}}{\lambda }}\times a\left ({{\phi ^{A}_{k},\phi ^{E}_{k}}}\right ), \tag {5}\end{equation*}$$ with $d_{_{RIS-{UE}_{k}}}$ as the distance between RIS and kth user, $\phi _{k}^{A}$ and $\phi _{k}^{E}$ as the azimuth and elevation angle between kth user and RIS.

Concurrently, a jammer strategically positioned to affect the uplink communication attempts to disrupt the signal by transmitting a jamming signal both directly and via RIS. Assume $h_{j}$ is the direct LoS channel between the jammer and base station which is described below: $$\begin{equation*} h_{j} = \sqrt {Ld_{j}^{-\delta }} e^{-j\frac {2\pi d_{j}}{\lambda }}, \tag {6}\end{equation*}$$ where $d_{j}$ is the distance between the jammer and base station, additionally, the RIS reflects the jamming signal towards the base station, the jamming signal is received by RIS through the channel $\boldsymbol {G}_{j}\in \mathbb {C}^{N\times 1}$ , defined in the following equation: $$\begin{equation*} \boldsymbol {G}_{j} = \sqrt {Ld_{j}^{-\delta }} e^{-j\frac {2\pi d_{j}}{\lambda }}a\left ({{\phi ^{A}_{j},\phi ^{E}_{j}}}\right ), \tag {7}\end{equation*}$$ with $\phi ^{A}_{j}$ and $\phi ^{E}_{j}$ denoting the azimuth and elevation angles between RIS and jammer.

Therefore, the received signal at the base station in the time domain can be defined as [68] $$\begin{align*}& y_{BS} = \sum _{k=1}^{K}\left ({{\boldsymbol {I}^{T} \boldsymbol {\Theta } \boldsymbol {G}_{k}}}\right )~x_{k} + \left ({{h_{j} + \boldsymbol {I}^{T} \boldsymbol {\Theta } \boldsymbol {G}_{j}}}\right )x_{j} + \boldsymbol {I}^{T}\boldsymbol {\Theta } \boldsymbol {\eta } + z, \\& \qquad \qquad \qquad \qquad k\in \{1,\ldots , K\}, \tag {8}\end{align*}$$ where $\boldsymbol {\Theta } \in \mathbb {C}^{N\times 1}$ is the matrix of active beamforming for nth element of RIS, with $\boldsymbol {\Theta }=diag{(\sqrt {\beta _{1}}e^{j\theta _{1}},\ldots , \sqrt {\beta _{N}}e^{j\theta _{N}})}$ , in which $\beta _{n}\in [0,\beta ^{max}], n\in \{1,\ldots , N\}$ denotes the amplitude of RIS beamforming with $\beta ^{max}$ as the maximum amplitude value of the RIS elements and $\theta _{n}\in [0,2\pi],n\in \{1,\ldots , N\}$ represents the RIS phase shifts, $x_{k}$ is the transmitted signal from kth user in the time domain, $x_{j}$ is the transmitted jamming signal in the time domain, and $z\sim \mathcal {CN}(0,\sigma ^{2})$ is the additive white Gaussian noise (AWGN) environmental noise at the base station with $\sigma ^{2}$ as the variance of the environmental noise. The amplification process performed by active RIS elements introduces additional noise to the system [39], [69]. The term $\boldsymbol {I}^{T}\boldsymbol {\Theta }\boldsymbol {\eta }$ in (8) represents the most common type of dynamic noise of active elements of RIS, thermal noise, which is modeled by $\boldsymbol {\eta }\sim \mathcal {CN}(0,\sigma _{\eta }^{2}\mathbb {I}^{N\times 1})$ with $\sigma _{\eta }^{2}$ as the variance of the thermal noise.

In NOMA, the channel gain of each user depends on both the transmission power of the users and the phase shifts at the RIS. Different combinations can affect the order in which signals are decoded at the base station during SIC. To ensure efficient SIC, the system must satisfy a specific condition: the signal received by the base station from $i[th]$ user $(1\leq i \lt K)$ should be stronger than that of $j^{th}$ user $(j \geq i)$ which means that the base station must first decode the signals from user 1 to user $i-1$ in sequence before decoding the signal from user i, i.e., $P_{i}|\boldsymbol {I}^{T}\boldsymbol {\Theta } \boldsymbol {G}_{i}|^{2} \geq P_{j}|\boldsymbol {I}^{T}\boldsymbol {\Theta } \boldsymbol {G}_{j}|^{2}~(j \geq i)$ . Therefore, the SJNR of a typical user- say $k^{th}$ user- at the base station can be formulated as (9), shown at the bottom of the page $$\begin{equation*} \gamma _{k} = \frac {P_{k}|\boldsymbol {I}^{T}\boldsymbol {\Theta } \boldsymbol {G}_{k}|^{2}}{\sum _{k^{\prime }=k+1}^{K} P_{k^{\prime }}|\boldsymbol {I}^{T}\boldsymbol {\Theta } \boldsymbol {G}_{k^{\prime }}|^{2} + P_{j}|h_{j} + \boldsymbol {I}^{T} \boldsymbol {\Theta } \boldsymbol {G}_{j}|^{2} + ||\boldsymbol {I}^{T}\boldsymbol {\Theta } ||^{2}\sigma _{\eta }^{2}+\sigma ^{2}} \tag {9}\end{equation*}$$ . In this equation (9), $P_{k}$ is the power of users and $P_{j}$ represents the power of the jammer. Furthermore, $|.|$ and $||.||$ denote the absolute value of a variable and the norm of a vector, respectively.

In a URLLC system within NOMA, it is important to achieve both high reliability and low latency. This is particularly challenging while considering FBL, where short packets are transmitted to minimize delay, and traditional Shannon capacity is not effective because of the significant decoding block errors [70]. Thus, for a given blocklength of $n_{b}$ and $n_{d}$ number of information bits per data packet, the block error probability [71], [72] of user k is approximated by the following equation: $$\begin{equation*} \epsilon _{k} \approx Q\left ({{ \sqrt {\frac {n_{b}}{v\left ({{\gamma _{k}}}\right )}} \left ({{C\left ({{\gamma _{k}}}\right )-\frac {n_{d}}{n_{b}} }}\right ) }}\right ). \tag {10}\end{equation*}$$ In this equation, Q denotes the Q-function, representing the probability of Gaussian distribution, $C(\gamma _{k}) = \log _{2} (1+\gamma _{k})$ denotes the effective capacity, and $v(\gamma _{k}) = \left ({{1-{}\frac {1}{(1+\gamma _{k})^{2}}}}\right)(\log _{2}e)^{2}$ is the channel dispersion. It can be concluded that shorter blocklengths result in an increase in the error rates because of the limited redundancy and error-correction capabilities. The longer the blocklengths, on the other hand, enhance the error correction but result in higher latency, which is crucial in URLLC scenarios. Therefore, the optimization of blocklength requires a trade-off between minimizing latency and maintaining reliable communication.

To achieve low latency, the system uses short packet transmissions. It also employs ARQ with a limited number of retransmissions $\mathcal {L}$ to improve reliability. Assume $\omega ^{k}_{s}$ denotes the probability that a packet is transmitted successfully from user k, which is dependent on the decoding error of all the previous users as defined in (11). $$\begin{equation*} \omega ^{k}_{s} = \Pi _{k^{\prime }=1}^{k} \left ({{1-\epsilon _{k^{\prime }}}}\right ). \tag {11}\end{equation*}$$ Fig. 2 illustrates the equivalent queuing model, where packets are transmitted from the users to the BS. If a packet error occurs, detected with a probability of $(1-\omega ^{k}_{s})$ for the $k^{th}$ user, the packet is returned to its queue,1 improving the reliability. The packet continues to be retransmitted until it is successfully received or the system reaches its maximum number of retransmissions for that packet.

FIGURE 2.

Packet transmission Queuing model.

By examining the transmission-reception process demonstrated in Fig. 2, we observe that the process can be modeled as a discrete Markov chain when seen at the beginning of time frame instances. This process is represented by the state diagram in Fig. 3. The state variables $(l=0,1,2,\ldots ,)$ represent the number of packets in the queue. The transition between states is determined based on the packet arrival probability, packet error, and successful transmission probabilities. Let ${\mathcal {P}}_{u,v}$ be the transition probability from state u to state v. If there is no packet in the user’s buffer at the beginning of the current frame, the buffer will be empty with the probability of $1-\omega$ at the beginning of the next frame and there is one packet in the buffer with the probability of $\omega$ . Then, $$\begin{align*} {\mathcal {P}}_{0,0}=& 1-\omega , \\ {\mathcal {P}}_{0,1}=& \omega . \tag {12}\end{align*}$$ If there is $l~(l\geq 1)$ packet(s) in the buffer, the probability of having $l+1$ packets in the buffer at the beginning of the next frame equals the probability of arriving a packet during the current frame $(\omega)$ while having an error on the current packet transmission $(1-\omega ^{k}_{s})$ . Therefore, $$\begin{equation*} {\mathcal {P}}_{l,l+1}=\omega \left ({{1-\omega ^{k}_{s}}}\right ), \quad l\geq 1. \tag {13}\end{equation*}$$

FIGURE 3.

Markov chain state diagram for the packet transmission model.

For ${\mathcal {P}}_{l,l-l}~(l\gt 0)$ , no arriving packet is assumed while a successful packet transmission is needed. Hence, $$\begin{equation*} {\mathcal {P}}_{l,l-1}=\left ({{1-\omega }}\right )\omega ^{k}_{s}, \quad l\geq 1. \tag {14}\end{equation*}$$

Finally, $$\begin{align*} {\mathcal {P}}_{l,l}=& 1-{\mathcal {P}}_{l,l-1}-{\mathcal {P}}_{l,l+1}, \\=& \left ({{1-\omega }}\right )\left ({{1-\omega _{s}^{k}}}\right )+ \omega \omega _{s}^{k}, \quad l\geq 1. \tag {15}\end{align*}$$

Having derived the transition probabilities, we can calculate the steady-state probabilities as follows. Let $\pi _{l}^{k}$ denote the steady-state probability of having l packets in the buffer of the kth user. The steady-state probabilities for the states $\pi _{0}^{k}$ and $\pi _{1}^{k}$ are as follows: $$\begin{align*} \pi _{0}^{k}=& \left ({{1-\omega }}\right )\pi _{0}^{k} + \omega ^{k}_{s}\left ({{1-\omega }}\right )\pi _{1}^{k}, \\ \pi _{0}^{k}=& \frac {\omega ^{k}_{s}\left ({{1-\omega }}\right )}{\omega } \pi _{1}^{k}, \\ \pi _{1}^{k}=& \pi _{0}^{k} \omega +\pi _{2}^{k} \left ({{\omega ^{k}_{s}}}\right ) \left ({{1-\omega }}\right )+\pi _{1}^{k}\left ({{\omega \omega ^{k}_{s} + (1-\omega )(1-\omega ^{k}_{s})}}\right ). \tag {16}\end{align*}$$ For a general state of $\pi _{l}^{k}$ , where $l\geq 1$ we have: $$\begin{align*} \pi _{l}^{k} = \pi _{l-1}^{k} \omega + \pi _{l+1}^{k} \left ({{\omega ^{k}_{s}}}\right )\left ({{1-\omega }}\right )+\pi _{l}^{k} \left ({{1-\omega -\omega ^{k}_{s}}}\right ). \tag {17}\end{align*}$$ Equation (17) is simplified as $$\begin{equation*} \pi _{l}^{k}\left ({{\omega +\omega ^{k}_{s}}}\right ) = \pi _{l-1}^{k}\omega +\pi _{l+1}^{k}\omega ^{k}_{s}\left ({{1-\omega }}\right ), l\geq 1. \tag {18}\end{equation*}$$ To solve (18), we assume $\pi _{l}^{k}=\alpha \pi _{l-1}^{k}$ where $0\lt \alpha \lt 1$ . Then, $$\begin{align*} \pi _{l}^{k}=& \alpha \pi _{l-1}^{k}, \\ \pi _{l}^{k}=& \alpha ^{2}\pi _{l-2}^{k}, \\ \pi _{l}^{k}=& \alpha ^{l-1}\pi _{1}^{k}. \tag {19}\end{align*}$$ Substituting (19) into (18), we get: $$\begin{equation*} \pi _{1}^{k}\left ({{\omega +\omega ^{k}_{s}}}\right )\alpha ^{l-1} = \pi _{1}^{k}\omega \alpha ^{l-2} + \pi _{1}^{k}\omega ^{k}_{s}\left ({{1-\omega }}\right )\alpha ^{n}. \tag {20}\end{equation*}$$ Then we derive: $$\begin{equation*} \omega ^{k}_{s}\left ({{1-\omega }}\right )\alpha ^{2} - \left ({{\omega +\omega ^{k}_{s}}}\right )\alpha +\omega =0. \tag {21}\end{equation*}$$ Solving this quadratic equation for $\alpha$ using the quadratic formula results in $\alpha$ derived as: $$\begin{equation*} \alpha = \frac {\omega +\omega ^{k}_{s}\pm \sqrt {4\omega ^{2}\omega ^{k}_{s}+\omega ^{2}-2\omega \omega ^{k}_{s}+{\omega ^{k}_{s}}^{2}}}{2\left ({{1-\omega }}\right )\omega ^{k}_{s}}. \tag {22}\end{equation*}$$ Only $\alpha = {}\frac {\omega +\omega ^{k}_{s}-\sqrt {4\omega ^{2}\omega ^{k}_{s}+\omega ^{2}-2\omega \omega ^{k}_{s}+{\omega ^{k}_{s}}^{2}}}{2(1-\omega)\omega ^{k}_{s}}$ is less than one and is the admissible solution (see Appendix). To find $\pi _{l}^{k}$ , we know that $\sum _{l=0}^{\infty }\pi _{l}^{k}=1$ then $$\begin{align*} \pi _{0}^{k}+\sum _{l=1}^{\infty } \pi _{l}^{k}=& \pi _{0}^{k}+\sum _{l=1}^{\infty }\alpha ^{l-1}\pi _{1}^{k} \\ \pi _{0}^{k}+\sum _{l=1}^{\infty }\alpha & ^{l-1}\pi _{1}^{k}=1. \tag {23}\end{align*}$$ Therefore, $$\begin{equation*} \pi _{0}^{k}+\pi _{1}^{k}\left ({{\frac {1}{1-\alpha }}}\right )=1. \tag {24}\end{equation*}$$ From (24) and (16) it can be concluded that $$\begin{equation*} \pi _{1}^{k} = \frac {\omega \left ({{1-\alpha }}\right )}{\omega +\omega ^{k}_{s}\left ({{1-\alpha }}\right )\left ({{1-\omega }}\right )}. \tag {25}\end{equation*}$$ Thus, considering $\pi _{l}^{k}=\pi _{1}^{k}\alpha ^{l-1}$ , it is derived that $$\begin{equation*} \pi _{l}^{k} = \frac {\alpha ^{l-1}\omega \left ({{1-\alpha }}\right )}{\omega +\omega ^{k}_{s}+\left ({{1-\alpha }}\right )\left ({{1-\omega }}\right )}. \tag {26}\end{equation*}$$

The average delay for each user is defined as the sum of transmission delay and waiting time delay defined in (27). $$\begin{equation*} \overline {\tau }_{k}= T_{f} + T_{f}\sum _{l=0}^{\infty } l \pi _{l}^{k}= T_{f}\left [{{1+\sum _{l=0}^{\infty } l \pi _{l}^{k}}}\right ], \tag {27}\end{equation*}$$ where $T_{f} = T_{h}+T_{p}+T_{A}$ is the frame duration with $T_{h}$ as the header duration, $T_{p}={}\frac {n_{b}}{B}$ is the payload duration where B represents the bandwidth, and $T_{A}$ denotes the duration of the acknowledgement message. Considering (26), the average delay is derived as follows: $$\begin{align*} \overline {\tau }_{k}=& T_{f}\left [{{1+\frac {\omega \left ({{1-\alpha }}\right )}{\omega +\omega ^{k}_{s}+\left ({{1-\alpha }}\right )\left ({{1-\omega }}\right )}\sum _{l=1}^{\infty } l\alpha ^{l-1} }}\right ] \tag {28}\\ \overline {\tau }_{k}=& T_{f}\left [{{1+\frac {\omega }{\omega +\omega ^{k}_{s}\left ({{1-\omega }}\right )\left ({{1-\alpha }}\right )^{2}}}}\right ]. \tag {29}\end{align*}$$

To calculate the reliability of each user, we consider the probability of success for all the previous users discussed in (11) as demonstrated as follows: $$\begin{equation*} Rel_{k} = 1-\left [{{1-\Pi _{k^{\prime }=1}^{k}\left ({{1-\epsilon _{k^{\prime }}}}\right )}}\right ]^{\mathcal {L}}, \tag {30}\end{equation*}$$ where $\mathcal {L}$ denotes the number of retransmissions.

Power consumption in active RIS scenarios is an important factor that must be taken into account. The passive RIS power consumption is mainly due to the switch and control circuit at the reflecting element (RE) [73]. Representing $P_{c}$ as the power consumption of the switch and control circuit at each RE, the power dissipated at the passive RIS is written as, $$\begin{equation*} P_{RIS}^{p}=N P_{c}. \tag {31}\end{equation*}$$

Assuming the active RIS is equipped with N identical active REs, the total power consumption is thus given by [74], $$\begin{equation*} P_{RIS}^{a}=N \left ({{P_{c} + P_{DC}}}\right ) + \zeta P_{out}, \tag {32}\end{equation*}$$ where $\zeta ^{-1}$ and $P_{DC}$ are the RIS amplifier efficiency and the DC power consumption, respectively. Furthermore, $P_{out}$ is the output power of the amplifier which is expressed as, $$\begin{align*} P_{out}=& \sum _{k=1}^{K} P_{k} ||\boldsymbol {\Theta } \boldsymbol {G}_{k}||^{2} + ||\boldsymbol {\Theta } \boldsymbol {G}_{k}||^{2} \sigma ^{2}_{\eta } \\=& \beta \sum _{k=1}^{K} P_{k} ||\boldsymbol {\theta } \boldsymbol {G}_{k}||^{2} + N \beta \sigma ^{2}_{\eta }. \tag {33}\end{align*}$$

As can be seen, active RIS provides the system with the advantage of both constructive signal combinations at the receiver and power amplification. Finally, the total power consumption of transmitting entities in the network is formulated as, $$\begin{equation*} P_{total}= P_{RIS}^{a} + \sum _{k=1}^{K} P_{k}. \tag {34}\end{equation*}$$

A very important note is that the total power budget $P_{RIS}^{a}$ is limited. Hence, from (32) and (33), a trade-off between the number of RIS elements, N, and amplification factor, $\beta$ , can be realized. Specifically, given a power budget, $P_{RIS}^{a}$ , the active RIS can allocate the remaining power to amplify the incident signal using active loads, after accounting for the hardware power consumption of the total N REs. In brief, while increasing the number of RIS elements can significantly enhance the output gain related to signal construction at the receiver, less power budget remains for the amplification of the intended signals.

B. Optimization Problem

The discussed analytical derivations are used to achieve the optimal energy efficiency of the overall system. Since the phase shifts matrix and phase amplitudes reflect the jamming waveform besides legitimate user signals, proper values must be considered for $\theta _{n}$ and $\beta _{n}$ , $n\in \{1,\ldots , N\}$ . The optimization problem focuses on minimizing the total power consumption in a RIS-based NOMA system under the jamming attack. It considers average delay, reliability, active RIS parameters, and finite blocklength as constraints, defined as follows: Power Consumption-Min: $$\begin{align*} \mathop {minimize}_{P_{k}, \theta _{n}, \beta _{n}, n_{b}, \mathcal {L}}& {P_{total} } \tag {35a}\\ {}{} subject~to& {\overline {\tau }_{k}}{\leq \overline {\tau }^{thr},\, \, \, \forall k \in \{1,\ldots , K\} }, \tag {35b}\\& {Rel_{k} }{\geq Rel^{thr}, \, \, \, \forall k \in \{1,\ldots , K\}}, \tag {35c}\\& {\rho \lt 1}{ \,}, \tag {35d}\\& {0 \leq \beta _{n}}{\leq \beta ^{max}}, \, \, \forall n \in \{1,\ldots , N\}, \tag {35e}\\& {P_{RIS}^{a} \leq P_{RIS}^{thr}}, \, \, \forall n \in \{1,\ldots , N\}, \tag {35f}\\& {\theta _{n} \in \{0,2\pi \}}, \,{\forall n \in \{1,\ldots , N\} }, \tag {35g}\\& {\mathcal {L}}{\in \{1,\ldots , {\mathcal {L}}^{max}\} }, \tag {35h}\\& {0\lt P_{k}}{\leq P_{k+1} \, \, \, \forall k \in \{1,\ldots , K-1\} }, \tag {35i}\\& {P_{k}}{\leq P_{max} \, \, \, \forall k \in \{1,\ldots , K\} }, \tag {35j}\\& {n_{b}}{\in \mathbb {N}.} \tag {35k}\end{align*}$$ where Constraint (35k) ensures the required latency for the URLLC communication, Constraint (35k) is related to the required reliability of URLLC connection,2 Constraint (35k) amplifies or absorbs the signal received by the active RIS, Constraints (35k), (35k), and (35k) define the range of the phase shifts, number of retransmissions, and maximum value of UE power respectively, Constraint (35k) establishes the SIC decoding order, Constraint (35k) makes sure the blocklength is a positive integer, in constraint (35k), $\rho _{k}$ is the server utilization in the queuing model which ensures that the $k^{th}$ user’s queue is stable and it is obtained as (36). $$\begin{equation*} \rho _{k} = 1-\pi _{0}^{k}= 1-\frac {\alpha ^{\prime }}{\omega +\alpha ^{\prime }}, \tag {36}\end{equation*}$$ where $\alpha ^{\prime }$ is defined as $\alpha ^{\prime } = \omega ^{k}_{s}(1-\omega)(1-\alpha)$ . For a stable queue resulting in finite buffer size at the users, $\rho _{k}$ must be less than 1. Otherwise, the transmission process is not stable and the packet waiting time is such that the average packet latency is not fulfilled.

C. DL-Based RIS Optimizer

Although the objective function in problem Power Consumption-Min is convex, the constraints (35k) and (35k) are not convex. As a result, problem (35k) is a non-convex mixed-integer nonlinear programming (MINLP) problem which is NP-hard. Evolutionary algorithms such as genetic algorithms are time-consuming to reach a solution and may fail to converge within the URLLC constraints. In this section, we propose a deep-learning regression model to efficiently solve the Power Consumption-Min problem. The deep regression model can handle high-dimensional, non-linear optimization problems effectively [76]. Meanwhile, compared to other machine learning algorithms, it does not require extensive online training which results in an intensive computation load. An advantage of this deep-learning approach is that the model can be processed locally within the RIS, minimizing the need for extensive signaling. Meanwhile, this approach significantly reduces the overall computation time.3

A comprehensive dataset is required to train the deep learning model effectively. The dataset should consist of different scenario settings that reflect the behaviour of the network under different conditions. Different locations are generated for each user by changing the distance between users and RIS and users’ azimuth angles. Furthermore, different jamming power levels are assigned to the jammer to cover a wide range of possible jamming attack scenarios. These various scenario setups are recorded in $\boldsymbol {\chi }\in \mathbb {R}^{\Upsilon \times (2K+1)}$ where $\Upsilon$ is the total number of observations and $2K+1$ is the number of azimuth angles and distances of all the users and the power of jammer. A typical observation—say $\upsilon ^{th}$ observation—is constructed as: $$\begin{equation*} \boldsymbol {\chi }^{\upsilon } = \left [{{P_{j}^{\upsilon }, \phi ^{A,\upsilon }_{1},\ldots , \phi ^{A,\upsilon }_{K}, d_{_{RIS-UE_{1}}},\ldots , d_{_{RIS-UE_{K}}} }}\right ]. \tag {37}\end{equation*}$$ Each observation $\upsilon$ in $\boldsymbol {\chi }$ goes through surrogate algorithm optimization to achieve a target optimal solution. Surrogate optimization is used to solve complex, high-dimensional problems such as antenna design that are computationally costly [77]. There are various types of surrogate models including Gaussian processes (Kriging), polynomial Response Surface Model (RSM), and RBF [78]. The poor surrogate model can directly impact the performance of the optimization process [79]. Since RBF has been proven more effective for highly nonlinear problems [80]. RBF enables smoother approximations which results in faster convergence. Here we use RBF for our optimization problem solver. Assume data points of $(\boldsymbol {\chi }^{\upsilon }_{\xi },{\mathcal {F}}_{\xi })$ for each observation of $\upsilon = 1,\ldots , \Upsilon$ for $\xi =1,\ldots , \Xi$ , with $\Xi$ radially symmetric functions, the predicted function $\mathcal {F}^{*}(\boldsymbol {\chi }^{\upsilon })$ is constructed as [81]: $$\begin{equation*} \mathcal {F}^{*}\left ({{\boldsymbol {\chi }^{\upsilon }}}\right ) = \sum _{{\xi }=1}^{\Xi }\mu _{\xi }\psi \left ({{||\boldsymbol {\chi }^{\upsilon }-c_{\xi }||}}\right )+\varepsilon _{\xi }, \tag {38}\end{equation*}$$ where $\mu _{\xi }$ are the coefficients determined by solving the system, $c_{\xi }$ represents the $\xi$ th of $\Xi$ basis functions, $\varepsilon _{\xi } \sim \mathcal {N}(0,\sigma ^{2}_{RBF})$ denotes the estimation error, and $\psi (r)$ (with r as the Euclidean distance between prediction values and basis function centres) is the RBF which is commonly a Gaussian as below: $$\begin{equation*} \psi (r) = \exp {\frac {-r^{2}}{2\vartheta ^{2}}}, \tag {39}\end{equation*}$$ with $\vartheta$ as a width control value of the Gaussian function.

The deep-regression model used for training is a supervised learning model. Thus, the dataset $\boldsymbol {\chi }$ is paired with the correspondent target matrix $\boldsymbol {\mathcal {Z}}\in \mathbb {R}^{\Upsilon \times (2N+K+2)}$ , where $\boldsymbol {\mathcal {Z}}^{\upsilon }$ is the output of optimization problem for each scenario of $\upsilon =1,\ldots , \Upsilon$ which can be defined as $\boldsymbol {\mathcal {Z}}^{\upsilon }=\mathcal {F}^{*}(\boldsymbol {\chi }^{\upsilon })$ , and $(2N+K+2)$ is the set of optimal solutions. The target dataset corresponding to $\upsilon$ th observation is constructed as: $$\begin{align*} \boldsymbol {\mathcal {Z}}^{\upsilon } = \left [{{\theta _{1},\ldots , \theta _{N}^{\upsilon }, \beta _{1}^{\upsilon },\ldots , \beta _{N}^{\upsilon }, P_{1}^{\upsilon },\ldots , P_{K}^{\upsilon }, n_{b}^{\upsilon }, {\mathcal {L}}^{\upsilon }}}\right ]. \tag {40}\end{align*}$$ For a given paired set of input dataset and target dataset of $(\boldsymbol {\chi }, \boldsymbol {\mathcal {Z}}) = \{(\boldsymbol {\chi }^{1}, \boldsymbol {\mathcal {Z}}^{1}),(\boldsymbol {\chi }^{2}, \boldsymbol {\mathcal {Z}}^{2}),\ldots , (\boldsymbol {\chi }^{\Upsilon }, \boldsymbol {\mathcal {Z}}^{\Upsilon })\}$ it is assumed that a function $f~:~ \mathbb {R}^{\Upsilon \times (2K+1)}\rightarrow \mathbb {R}^{\Upsilon \times (2N+K+2)}$ exists such that $\hat {\boldsymbol {\mathcal {Z}}}=f(\boldsymbol {\chi })$ , where $\hat {\boldsymbol {\mathcal {Z}}}$ represents the predicted target values. The input layer goes through $\iota$ number of hidden layers with weights $W^{(\iota)}$ and biases $B^{(\iota)}$ and passes through the activation function of $g(.)$ as follows: $$\begin{equation*} H^{\iota } = g\left ({{W^{(\iota -1)}H^{(\iota -1)}+B^{(\iota )}}}\right ), \tag {41}\end{equation*}$$ where $H^{0}$ is the input layer, $W^{(\iota -1)}$ are the weights connecting layer $\iota -1$ to layer $\iota$ , $B^{(\iota)}$ is the bias for layer $\iota$ . Finally, the output layer produces the predicted target solution.

The empirical error represents the difference between the predicted target $(\hat {\boldsymbol {\mathcal {Z}}})$ and the actual target. It is formulated as: $$\begin{equation*} E = \frac {1}{\Upsilon } \sum _{\upsilon =1}^{\Upsilon } \left ({{\mathcal {F}^{*}(\chi ^{\upsilon })-\hat {\boldsymbol {\mathcal {Z}}}^{\upsilon }}}\right ) \odot \left ({{\mathcal {F}^{*}(\chi ^{\upsilon })-\hat {\boldsymbol {\mathcal {Z}}}^{\upsilon }}}\right ) \mathcal {W}, \tag {42}\end{equation*}$$ with $\mathcal {W}\in \mathbb {R}^{(2N+K+2)\times 1}$ as the weight corresponding to the model, and $\odot$ denotes Hadamard product.

The weight and bias values of hidden layers in (41) are updated according to the empirical error [82] as follows: $$\begin{align*} W^{\left ({{\iota }}\right )} \leftarrow W^{\left ({{\iota }}\right )}-\Gamma \frac {\partial E}{\partial W^{\left ({{\iota }}\right )}}, \tag {43}\\ B^{\left ({{\iota }}\right )} \leftarrow B^{\left ({{\iota }}\right )}-\Gamma \frac {\partial E}{\partial B^{\left ({{\iota }}\right )}}, \tag {44}\end{align*}$$ with $\Gamma$ representing the learning rate.

The Weighted Mean Squared Error (WMSE) optimization model adapted from [83] is as follows:

WMSE-Min: $$\begin{align*} \mathop {minimize}& {E } \tag {45a}\\ {subject~to}& {\sum _{j=1}^{2N+K+2} {\mathcal {W}}_{j}}{= 1} \tag {45b}\\& {{\mathcal {W}}_{j} }~{\geq 0.} \tag {45c}\end{align*}$$

The equation WMSE-Min minimizes the WMSE during the training of the deep regression model. Constraint (45c) is a normalization constraint that ensures that the sum of the weights in the deep regression model is equal to 1. Constraint (45c) ensures that all the weight values are non-negative.

The model aims to predict discrete variables of $n_{b}$ and $\mathcal {L}$ which are inherently integers. However, the deep regression model produces continuous outputs. To address this situation, we categorize the possible values of $n_{b}$ and $\mathcal {L}$ into a total of $\mathcal {K}$ distinct classes, denoted as $(n_{b},{\mathcal {L}})^{{\kappa }}$ , $\kappa \in \{1,\ldots , \mathcal {K}\}$ . Furthermore, a separate deep regression model is trained for each class along with the input dataset $\chi$ . In the online testing phase, when unseen data is presented, all the well-trained deep regression modules are fed with their corresponding inputs. Each model produces an output which then are evaluated by an evaluation module to ensure the best final decision is made. Fig. 4 illustrates the online testing process. It demonstrates the process of feeding the input data and $(n_{b},{\mathcal {L}})^{ {\kappa }}$ classes to the separate deep regression models. The final decision is made by selecting the best output among the models.

FIGURE 4.

The blockdiagram of the deep regression optimizer.

After training the deep regression model, the model is tested to evaluate the proposed model under different network setups.

SECTION IV. Numerical Results

In this section, the results from the simulation implemented using MATLAB are presented and discussed to validate the effectiveness of the proposed algorithm. The simulation environment includes two UEs $(K=2)$ sending 5G signals with power levels changing between $0\ mW$ and $100\ mW$ to the base station using a RIS with varying number of elements from $N=9$ to $N=900$ [84]. The environmental noise and dynamic interference from active elements are $\sigma _{\eta }^{2}=\sigma ^{2}=-100\ dBm$ [69]. The amplitude of all active RIS elements is considered as $\beta$ . The power consumed by electronic components of RIS, DC power consumption, and the RIS amplifier efficiency are set as $P_{c}=-10\ dBm$ , $P_{DC}=-5\ dBm$ , and $\zeta ^{-1}=0.8$ , respectively [74]. The RIS is located in (0,0) based on the Cartesian coordinate system and the distribution of base station, users, jammer, and other environment parameters are provided in Table 1 [85].

TABLE 1 Description of Notations

Fig. 5 demonstrates the SJNR values for two users in the system as a function of different power-level combinations. Fig. 5(a) shows the SJNR for the first user, which degrades with the second user’s growing power, suggesting strong interference from the second transmitting user. The SJNR of the second user is illustrated in Fig. 5(b). It can be seen that by increasing the power of the second user the SJNR increases linearly as expected due to perfect SIC assumption.

FIGURE 5.

SJNR values of user 1 and user 2 with different power combinations, $N=64$ . (a) Near user SJNR (b) Far user SJNR.

The impact of the blocklength on the reliability is illustrated in Fig. 6. As the blocklength increases from 100 to 150 in Fig. 6(a) and Fig. 6(b), respectively, the number of data points which meet the URLLC reliability increases by 12.19%. This is due to the reduced error probability which increases the power level combinations with high reliability. With a larger blocklength value, more symbols are available to encode the information, which results in improved error correction capabilities and more robust signal representation.

FIGURE 6.

The reliability of the second user under different blocklength values, $N=64$ , $\mathcal {L}=10$ , and $\beta =100$ . (a) Reliability of the second user while the blocklength is fixed on 100 (b) Far user Reliability, $n_{b}=150$ .

A. Optimizing the Power Consumption

The optimization problem Power Consumption-Min is solved using a surrogate optimization for RIS with the maximum number of function evaluations of 500 (the optimization model converges successfully after 500 function evaluations thus a higher number of evaluations adds unnecessary computation cost) and constraint tolerance of $10^{-10}$ to ensure the satisfaction of constraints. The surrogate model is employed to minimize the objective function defined as $f(x) = P_{total}$ . The number of RIS elements can be changed from 9 to 900 elements. This section analyzes the genetic algorithm for an RIS with 64 elements. The effect of the number of elements will be discussed later in Section IV-B. The total power consumption of active RIS should not exceed the threshold of $P_{RIS}^{thr} = 20\ dBm$ [74] to avoid excessive energy consumption and potential thermal issues. The maximum transmission power allowed for UEs is $P_{max} = 100\ mW$ compatible with the transmit power range for power class 3 corresponding to mmWave in [86]. Active RIS includes elements capable of amplifying the signal, thus, the RIS amplitude value $(\beta)$ can vary from 0 up to a maximum value of $\beta _{max} = 100$ . The choice of $\beta _{max} = 100$ is specifically made to ensure convergence of the optimization algorithm especially when the number of RIS elements is a small value (for instance $N=9$ ). The maximum number of retransmissions for uplink 5G is adapted from the 3GPP standard and is set to ${\mathcal {L}}^{max}=10$ to ensure meeting the Quality of Service (QoS) requirements and network efficiency [87]. To guarantee the URLLC connection reliability, a threshold value of $Rel^{thr}=1-10^{-5}$ (i.e., 99.999%) is considered for all the connections in the system [88], [89]. Meanwhile, the required user plane latency for URLLC communication and 32 bytes of the data frame is $1 ms$ based on the standard and the threshold $\overline {\tau }^{thr} = 1 ms$ is defined to meet the latency requirements of the system [89], [90]. Table 3 summarizes the parameters used in the optimization algorithm.

TABLE 2 Simulation Configuration

TABLE 3 Surrogate Model Setting

Fig. 7 demonstrates the convergence behaviour of the surrogate optimization model over 400 function evaluations. The plot represents the evolution of the objective function values as the number of function evaluations increases. Orange circles are related to infeasible best points which represent the best objective function values that are considered infeasible. The points demonstrate the best solutions that do not satisfy the constraints. Orange crosses represent the points corresponding to the incumbent solutions that are infeasible. Orange triangles are infeasible solutions sampled randomly to explore the solution space broadly. These infeasible points give insight into the complexity of the feasible region and trade-offs between the parameters of the model and constraints. Orange dots denote infeasible solutions achieved through adaptive sampling methods focusing on more promising regions of the solution space near the feasibility borders. Best solutions are demonstrated using blue circles indicating the best feasible solutions found during the optimization process. These points meet all the constraints and have the lowest power consumption values.

FIGURE 7.

The convergence behaviour of the surrogate optimization model.

Yellow crosses show incumbent feasible solutions, which are the best solution points at the current stage of the optimization. Green triangles represent feasible solutions achieved through random sampling to ensure a broad search in the solution space. Finally, purple dots are feasible adaptive samples generated based on previous sampling results.

Based on this figure, at the beginning of the optimization, the model explores many infeasible solutions. As the process advances, the feasible solutions converge towards a more stable objective function value of 10.4746. After 100 functions evaluation, the model reaches a stable state in the solution space. Based on the proposed optimum values by the surrogate algorithm, the system can bypass the jammer and reach the URLLC reliability $(Rel_{1} = 1.0000, Rel_{2}=1.0000)$ and latency $(\overline {\tau }_{1}=0.9216\times 10^{-3}\ s, \overline {\tau }_{1}=0.9267\times 10^{-3}\ s)$ requirements by utilizing $n_{b} = 132$ blocklength, maximum retransmission of $\mathcal {L}=2$ , and RIS amplitude of $\beta =11.4072$ while $UE_{1}$ and $UE_{2}$ transmit $P_{1}=0.0285$ and $P_{2}=0.0025\ W$ powers, respectively. It should be noted that the optimal values can be changed based on the locations of UEs and jammer and the power of the jammer.

B. Performance Analysis

The impact of varying amplitude settings for the RIS elements on system performance is explored in this section. We focus particularly on the performance of the second user due to its sensitivity to the decoding error of the first user. Fig. 8(a) shows the relationship between average delay and different RIS amplitude values for different power settings of $P_{1}$ and $P_{2}$ corresponding to the first and second UE, respectively. It is observed that for all considered power combinations, while the RIS amplitude $\beta \leq 1$ , the average delay is significantly large. However, it decreases with a sharp slope as the $\beta$ increases to 2 and then slightly increases again as $\beta$ continues to rise. Notably, these power settings fail to meet the URLLC delay requirement. Fig. 8(b) presents the effect of different RIS amplitude values on the reliability of the second user under different power configurations. The results indicate an improvement in the system reliability as the RIS amplitude increases to 2. Nevertheless, further increasing the amplitude results in a decline in reliability. Meanwhile, certain power settings such as when the transmission power of the first UE is set to 48 mW and the transmission power of the second UE is set to 36, do not achieve the URLLC requirement even with increasing the amplitude.

FIGURE 8.

Reliability and latency of the far user versus $\beta$ for different power combinations, $N=64$ . $P_{1}$ represents the transmit power of UE 1 and $P_{2}$ is the transmit power of UE 2. (a) The average latency of the far user vs $\beta$ . (b) Far user reliability vs $\beta$ .

In the next set of experiments, the transmission power of the second user is set to $P_{2} = 4 mW$ while the power of the first user increases. Fig. 9(a) illustrates that the average delay decreases to below $1 ms$ as the RIS amplitude increases to a value of 2. Any further increase in the amplitude results in a rise in the average delay with a higher rate of growth for higher $P_{1}$ levels. The reliability of the second user with the mentioned power settings is presented in Fig. 9(b). Here, the reliability peaks at 1 as the amplitude reaches 1.5, and this maximum reliability is maintained as the amplitude goes up further to $\beta =15$ . However, when $\beta$ is increased from 15 to 100, there is a significant reduction in reliability. These observations suggest that rising RIS amplitude beyond a certain threshold does not lead to better system performance. In fact, high $\beta$ can amplify the power of the jamming signal sensed by the base station, affecting system performance.

FIGURE 9.

Network metrics of the far user versus $\beta$ for different power configurations for UE1, $P_{2} = 4 mW$ , $N=64$ . $P_{1}$ represents the transmit power of UE 1 and $P_{2}$ is the transmit power of UE 2. (a) Average latency of UE2 vs $\beta$ (b) Reliability of UE2 vs $\beta$ .

Fig. 10 illustrates the impact of different numbers of RIS elements on the network performance while RIS phase shifts and other network variables are set to optimal values from the surrogate algorithm $P_{1}=79 mW$ , $P_{2}=39 mW$ , $n_{b}=150$ , $\mathcal {L}=10$ . The average delay is presented in Fig. 10(a). The figure shows that as the number of RIS elements increases, there is a general trend that the system achieves $1 ms$ URLLC average delay with lower values of $\beta$ . On the other hand, Fig. 10(b) displays the reliability of the system under a similar configuration. It is observed that for the lower number of RIS elements higher amplitude is required to achieve URLLC-defined reliability. These results suggest that increasing the number of RIS elements improves the performance of the system with optimal RIS amplitude adjustments.

FIGURE 10.

Network metrics versus RIS amplitude in response to different numbers of RIS elements $(N)$ . (a) Average delay of the second user (far user). (b) Reliability of the second user (far user).

C. Deep Regression Performance

The performance of the deep regression model as a problem solver is discussed in this section. To generate a data set for the DL entity training, varying power of jammer from $P_{j}=0.1\times 10^{-3}\ W$ to $P_{j}=10\times 10^{-3}\ W$ in increments of $5\times 10^{-3}\ W$ are used to reflect different jamming effects. Each UE is distanced from $d_{_{RIS-UE_{k}}}=5\ m$ to $d_{_{RIS-UE_{k}}}=50\ m$ with step size of $5\ m$ with azimuth angles between $\phi _{k}^{A}=0$ and $\phi _{k}^{A}={}\frac {\pi }{2}$ with step size of ${}\frac {\pi }{16}$ . 60% of the generated dataset is used for training, 20% is used for validation and another 20% is used to test the model. The parameters of the deep regression model are provided in Table 4.

TABLE 4 Deep Regression Model Setting

In training, the goal is to minimize weighted MSE as indicated in (42). Fig. 11 shows how WMSE decreases in the training process among different iterations for different RIS sizes, N. As observed, the lower the number of RIS elements, the lower the WMSE. This is due to the fact that increasing N leads to a larger deep regression model with a high number of outputs. Consequently, the training process involves more variables, which typically results in a higher WMSE. That is why the WMSE increases from 10.6 for $N=25$ to 12.2 for $N=64$ and then, to 14.9 and 15.8 for $N=100$ and $N=196$ , respectively.

FIGURE 11.

Deep regression model convergence under different RIS sizes.

The training process takes 1326 seconds (approximately 22 minutes for N=64) on a PC equipped with a 13th Gen Intel(R) Core(TM) i7-3700 CPU at 2.10 GHz and 32.0 GB of RAM. However, since the training is performed offline, this duration is not critical. Once trained, the model can be efficiently fine-tuned using transfer learning, which requires minimal time and can be done periodically as needed.

After training and validating, the DL entity undergoes test data. 20% of the whole data set is assigned for test data. One way to justify the performance of the proposed DL solver is to compare the distribution of the predicted values with the optimum values. Fig. 12 shows the histogram of the RIS elements phase for both the optimal values derived from solving the optimization problem and for the predicted values given by the DL solver. The results demonstrate a strong goodness of fit between the two.

FIGURE 12.

Distribution of the results corresponding to RIS phase shift (test data set) (a) Optimum distribution. (b) Predicted distribution.

The distribution for the other parameters, transmit power of UEs and amplification factor $(\beta)$ can be seen in Figs. 13, 14, and 15, all showcasing a good agreement between the predicted and optimal solutions. Comparing Figs. 13 and 14 one can realize that the distribution of the transmit power for the first UE (near user) is weighted toward higher values than that for the second UE (far user), which justifies the power constraint is met in the solutions.

FIGURE 13.

Distribution of the results corresponding to transmit power of the first user (test data set) (a) Optimum distribution. (b) Predicted distribution.

FIGURE 14.

Distribution of the results corresponding to transmit power of the second user (test data set) (a) Optimum distribution. (b) Predicted distribution.

FIGURE 15.

Distribution of the results corresponding to amplification factor (test data set) (a) Optimum distribution. (b) Predicted distribution.

SECTION V. Conclusion

This work explores the integration of RIS into the 5G NOMA system with FBL and ARQ to mitigate the effects of jamming attacks on network metrics including power consumption, average delay, and reliability. Our results demonstrate that active RIS configured with optimal system parameters can significantly bypass the jammer, enhancing the reliability and latency of the network. The observations suggest that optimal configurations of RIS elements and their amplitudes are required to achieve the desired URLLC communication with a noticeable trade-off between system reliability and latency as the network settings change. Therefore, proposing a deep regression-based design which predicts optimal network configurations offers a computationally efficient solution to the complex MINLP optimization problem. Future research includes exploring more advanced machine learning algorithms to further optimize network configurations dynamically based on real-time data. Models such as reinforcement learning or federated learning are possible options to adaptively optimize RIS configurations in response to dynamic network conditions. However, these models can introduce limitations under URLLC conditions and in real-time applications. Thus, developing hybrid approaches can be investigated further to enhance network performance while meeting latency and reliability requirements. Potential applications include mission-critical domains such as autonomous vehicles and industrial automation, where low latency and high reliability are essential.

To prove $\alpha = {}\frac {\omega +\omega ^{k}_{s}-\sqrt {4\omega ^{2}\omega ^{k}_{s}+\omega ^{2}-2\omega \omega ^{k}_{s}+{\omega ^{k}_{s}}^{2}}}{2(1-\omega)\omega ^{k}_{s}} \leq 1$ , we know that $\omega$ is a probability metric and hence $\omega \leq 1$ . Therefore, by multiplying both sides to $\omega$ , we obtain $$\begin{equation*} \omega ^{2} \leq \omega \tag {46}\end{equation*}$$

Since $\omega _{s}^{k}$ is also a probability metric, (46) can be expanded as, $$\begin{equation*} \left ({{\omega _{s}^{k}}}\right )^{2} \omega ^{2}\leq \left ({{\omega _{s}^{k}}}\right )^{2} \omega \implies 4\left ({{\omega _{s}^{k}}}\right )^{2}\omega ^{2} - 4\left ({{\omega _{s}^{k}}}\right )^{2}\omega \leq 0 \quad \tag {47}\end{equation*}$$ By adding some terms to both sides to reconstruct $\alpha$ , (48) is given. $$\begin{align*}& 4\omega _{s}^{k}\omega ^{2} + \omega ^{2} -2 \omega _{s}^{k} \omega + \left ({{\omega _{s}^{k}}}\right )^{2} \geq \\& \omega ^{2} + \left ({{\omega _{s}^{k}}}\right )^{2}+ 4 \omega ^{2} \left ({{\omega _{s}^{k}}}\right )^{2} -2 \omega \omega _{s}^{k}+ 4\omega _{s}^{k}\omega ^{2} -4\left ({{\omega _{s}^{k}}}\right )^{2} \omega \tag {48}\end{align*}$$ Finally, by doing some mathematical calculations, (49) is obtained as, $$\begin{align*}& 4\omega ^{2}\omega ^{k}_{s}+\omega ^{2}-2\omega \omega ^{k}_{s}+{\omega ^{k}_{s}}^{2} \leq \left ({{\omega -\omega _{s}^{k} +2 \omega \omega _{s}^{k} }}\right )^{2} \\& \implies \sqrt {4\omega ^{2}\omega ^{k}_{s}+\omega ^{2}-2\omega \omega ^{k}_{s}+{\omega ^{k}_{s}}^{2}} \leq \omega -\omega _{s}^{k} +2 \omega \omega _{s}^{k} \\& \implies \frac {\omega +\omega ^{k}_{s}-\sqrt {4\omega ^{2}\omega ^{k}_{s}+\omega ^{2}-2\omega \omega ^{k}_{s}+{\omega ^{k}_{s}}^{2}}}{2\left ({{1-\omega }}\right )\omega ^{k}_{s}} \leq 1 \tag {49}\end{align*}$$ which proves the clause.