Contents 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.
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.
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 
\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*}
\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*}
\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*}
Let \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*}
Additionally, \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*}
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 \begin{equation*} h_{j} = \sqrt {Ld_{j}^{-\delta }} e^{-j\frac {2\pi d_{j}}{\lambda }}, \tag {6}\end{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*}
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*}
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 \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 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 \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*}
To achieve low latency, the system uses short packet transmissions. It also employs ARQ with a limited number of retransmissions \begin{equation*} \omega ^{k}_{s} = \Pi _{k^{\prime }=1}^{k} \left ({{1-\epsilon _{k^{\prime }}}}\right ). \tag {11}\end{equation*}
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 \begin{align*} {\mathcal {P}}_{0,0}=& 1-\omega , \\ {\mathcal {P}}_{0,1}=& \omega . \tag {12}\end{align*}
\begin{equation*} {\mathcal {P}}_{l,l+1}=\omega \left ({{1-\omega ^{k}_{s}}}\right ), \quad l\geq 1. \tag {13}\end{equation*}
For \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 \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*}
\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*}
\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*}
\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*}
\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*}
\begin{equation*} \omega ^{k}_{s}\left ({{1-\omega }}\right )\alpha ^{2} - \left ({{\omega +\omega ^{k}_{s}}}\right )\alpha +\omega =0. \tag {21}\end{equation*}
\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*}
\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*}
\begin{equation*} \pi _{0}^{k}+\pi _{1}^{k}\left ({{\frac {1}{1-\alpha }}}\right )=1. \tag {24}\end{equation*}
\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*}
\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*}
\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*}
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 \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*}
\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
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 \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*}
\begin{equation*} \rho _{k} = 1-\pi _{0}^{k}= 1-\frac {\alpha ^{\prime }}{\omega +\alpha ^{\prime }}, \tag {36}\end{equation*}
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 \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*}
\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*}
\begin{equation*} \psi (r) = \exp {\frac {-r^{2}}{2\vartheta ^{2}}}, \tag {39}\end{equation*}
The deep-regression model used for training is a supervised learning model. Thus, the dataset \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*}
\begin{equation*} H^{\iota } = g\left ({{W^{(\iota -1)}H^{(\iota -1)}+B^{(\iota )}}}\right ), \tag {41}\end{equation*}
The empirical error represents the difference between the predicted target \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*}
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*}
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
After training the deep regression model, the model is tested to evaluate the proposed model under different network setups.
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
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.
SJNR values of user 1 and user 2 with different power combinations,
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.
The reliability of the second user under different blocklength values,
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
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.
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
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
Reliability and latency of the far user versus
In the next set of experiments, the transmission power of the second user is set to
Network metrics of the far user versus
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
Network metrics versus RIS amplitude in response to different numbers of RIS elements
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
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
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.
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
Distribution of the results corresponding to transmit power of the first user (test data set) (a) Optimum distribution. (b) Predicted distribution.
Distribution of the results corresponding to transmit power of the second user (test data set) (a) Optimum distribution. (b) Predicted distribution.
Distribution of the results corresponding to amplification factor (test data set) (a) Optimum distribution. (b) Predicted distribution.
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 \begin{equation*} \omega ^{2} \leq \omega \tag {46}\end{equation*}
Since \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*}
\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*}
\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*}