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Blind reconfigurable intelligent surfaceaided fixed nonorthogonal multiple access for intelligent vehicular networks
EURASIP Journal on Wireless Communications and Networking volume 2023, Article number: 83 (2023)
Abstract
In intelligent vehicular networks, vehicles should be able to communicate with their surroundings while traveling. This results in more efficient, safer, and comfortable driving experiences, as well as new commercial prospects in a variety of industries. Connected vehicles and autonomous vehicles expect 100% reliable connectivity without any compromise in quality. However, due to challenges such as difficult channel terrains in urban scenarios and dead zones, the reliability of current vehicletoinfrastructure (V2I) and vehicletovehicle communication systems cannot be guaranteed. The performance of vehicular networks can be considerably enhanced with reconfigurable intelligent surfaces (RIS). Nonorthogonal multiple access (NOMA) allows for massive connectivity with the surroundings. In vehicular networks, the RISassisted NOMA can ensure regulated channel gains, better coverage, throughput, and energy efficiency. In this work, a blind RISassisted fixed NOMA (FNOMA) system is proposed for a downlink V2I scenario. The closedform analytical outage probability and throughput expressions are derived by considering RIS as an intelligent reflector and as a roadside unit. It is observed that the analytical and Monte Carlo simulation results are closely related. In simulations, it has been discovered that RISassisted FNOMA outperforms the traditional NOMA variants in terms of outage and throughput. Even without precise channel knowledge, blind RIS transmission outperforms traditional NOMA variants due to huge array gain. The increase in the number of reflective elements also results in a significant improvement in signaltonoise ratio gains.
1 Introduction
In spite of a worldwide pandemic in 2020, 38,680 persons died in vehicular crashes [1]. By 2030, the World Health Organization hopes to have cut down on vehicularrelated injuries and fatalities by 50% [2]. Vehicular ad hoc network (VANET) has received considerable interest from academic, government, and automotive industries as a critical component of intelligent transportation system (ITS) to improve efficiency and safety of road. To enable safety applications such as lane change warnings, collision avoidance, and harsh braking warnings, data such as the vehicle’s position and speed must be broadcasted to nearby vehicles on frequent intervals [3]. Low latency and high reliability are required for safety applications. Nonsafety applications such as internet access, online games, online payments, and infotainment are also expected to be supported by VANET [4]. Users of infotainment services expect to have a more efficient and enjoyable driving experience. The timely and dependable distribution of this data is critical for a variety of safety applications. In order to get services related to road safety, traffic management, infotainment, and environmental monitoring for autonomous driving, vehicles must maintain a seamless connection with infrastructure units known as roadside units (RSU). Even though VANET is capable of providing all services to its users, ensuring connectivity and signal propagation remains a challenge. The unstable network topologies prevent reliable vehicletoeverything (V2X) communication, which has become a challenging investigation direction.
For connected autonomous vehicle applications, V2X communications must be supported. Because these communications rely on the wireless channel’s signaltonoise ratio (SNR) and fading characteristics, higher frequency bands must be explored to compensate for the spectrum demand in the sub6 GHz band. The millimeter wave (mmWave) is utilized in the new radio (NR) concept, which is supported in thirdgeneration partnership project (3GPP) Release15 is used for cellularV2X communication (CV2X). When there is high path loss and low SNR values, it also imposes some limits on reliability issues. Theoretically, the options proposed by the scientific community to address these challenges are to enhance transmit power and minimize the distance between transmitter and receiver. However, this is not feasible in practice. As a result, softwarecontrolled reconfigurable intelligent surfaces (RIS) are offered as a way to increase V2X communication reliability, and they will be widely adopted in sixthgeneration (6G) networks [5]. Future selfdriving vehicles will require reliable and better quality connectivity between vehicles and between vehicles and infrastructure. The performance of VANET can be considerably enhanced with the RIS [6, 7].
Without the use of a dedicated energy source, a large number of tiny, lowcost passive elements make up RIS, which reflect the incoming signal with a suitable phase shift [8, 9]. RIS functions like mirrors that beamform the incoming signals to the intended users. It has been demonstrated that RIS can improve data rate performance as well as mitigate the Doppler effect of highmobility users [10]. With the help of RIS, the propagation environment can be controlled [11, 12]. The placement of RIS is energy efficient and environmentally friendly. RIS has the compatibility to work with fullduplex relays, nonorthogonal multiple access (NOMA), index modulation (IM), simultaneous wireless information and power transfer (SWIPT), VANET, etc. Due to the above benefits, RIS has become one of the promising technologies of 6G networks [13].
Beamforming, range extension, positioning, and remote sensing are all potential use cases for RIS in VANET communication [14]. Some of the VANET safety applications that leverage the beamforming concept are incident detection, hazardous warning, cooperative collision avoidance, and trajectory alignment. Range extension, support for information interchange in autonomous driving, accurate data, and platooning are all incorporated features. It also covers nonsafety applications including video sharing, traffic information sharing, customized information, locationaware information, and environmental factor detection, in addition to the RIS’s potential use cases stated above.
To improve the spectral efficiency and massive connectivity of RIS, powerdomain NOMA can be integrated with RIS. In NOMA, the signals corresponding to different users are superimposed in power domain so that the spectrum is exploited more efficiently [15,16,17]. The users are explored opportunistically based on the channel conditions [18]. In a VANET, an RSU should be able to accommodate a larger number of vehicles at the same time while meeting their quality of service (QoS) demands. As a result, NOMA’s integration with RIS is important.
A sample scenario for downlink RISassisted V2I is shown in Fig. 1. Because of the blockage, the RSU may deliver very poor services to the vehicles. However, the RIS on the building creates a virtual line of sight (LoS) between the RSU and the vehicles. The array gain and diversity gain benefits are improved by the reflective elements, resulting in improved received signal quality. Figure 2 depicts an example of RISassisted vehicletovehicle (V2V). A source vehicle wants to exchange information with a destination vehicle. However, the vehicle in between may be a blockage or eavesdropper. The RIS in the propagation environment functions as an intelligent reflector (IR), allowing for highquality, seamless communication between source and destination vehicles.
1.1 Related work
RISs have been studied extensively for use in wireless communication, including RISassisted unmanned aerial vehicle (UAV) systems, RISassisted multicast communication, and RISassisted MIMO [19]. However, there have been very few studies on RISassisted vehicular communication. The use of RIS for secure vehicle communications was examined in [20]. The secrecy outage probability of two vehicular scenarios, V2V and V2I, was derived. In V2V, RIS served as a relay node, while in V2I, it served as a receiver. In [7], the expressions for secrecy outage probability was derived by utilizing series expansion and central limit theorem (CLT). The numerical results suggested that RIS could significantly reduce the outage probability for the vehicles in its vicinity. The secrecy outage probability was the function of the number of reflective elements. The performance could be enhanced by increasing the number of RIS elements.
In [21], the authors suggested a QoSdriven spectrum sharing scheme for RISassisted vehicular networks in order to maximize the sum capacity of V2I links utilized for highrate content delivery, while also ensuring the reliability of V2V links utilized for the transmission of safety data. The authors of [22] modeled intervehicle links with Fox’s Hfunction and studied outage probability and effective rate expressions using a passive RISequipped beacon vehicle. The authors of [23] modeled vehicular networks using RIS as an access point (AP). The instantaneous data rate was calculated as a function of the beam width, vehicle speed, and distance.
In [24], the weighted sum capacity of all the users was maximized by jointly designing the beamforming at base station (BS) and phase shift angles at RIS. Through the joint optimization of beamforming at the BS and phase shifts at the RIS, the blockage in the links from the BS/satellite to multiple users was addressed in a hybrid satelliteterrestrial relay network [25]. The total transmit power of the BS and satellite was minimized, while users’ QoS requirements were met. In [26], a physical layer security (PLS) method for cognitive satelliteterrestrial integrated network (STIN) was developed to combat multiple eavesdropper threats. Active RIS was used in this work to alter the amplitude and phase of the signal being received. The proposed method strived to maximize the secrecy rate while meeting the transmit power constraint and the interference threshold. When compared to passive RIS and no RIS systems, active RIS eliminated the impact of double fading and improved security performance. The effectiveness of RISassisted communication systems in improving the security and spectrum efficiency of multiple users was examined in [27].
Because V2X communication involves the exchange of a large volume of data, it causes increased latency and unequal connectivity. When compared to orthogonal multiple access (OMA) approaches, NOMA techniques exhibit better spectrum efficiency and lower latency [28]. Massive connectivity with the same resources is possible with NOMA. In exchange for additional receiver complexity, it also incorporates controllable interference to superpose different vehicle signals. In [18], the closedform outage probability expressions for ordered NOMA (ONOMA) uplink and downlink communication systems were derived using generalized fading channels. The authors studied both statistical and instantaneous channel state information (CSI)based ordering schemes. The performance of celledge users could be improved in cooperative NOMA (CNOMA) [29] and SWIPTCNOMA [30] by compromising the performance of nearby users. In [31], NOMAassisted cooperative relaying was presented for reliable communication. In this scenario, the source and relay transmit a superimposed signal at the first and secondtime slots of the cooperative communication. The exact analytical closedform outage probability expressions were derived considering Rayleigh fading channel and imperfect successive cancellation decoding. The outage probability of the presented scheme was compared with the conventional cooperative relayingassisted NOMA.
In [32], a joint optimization design for NOMAassisted STIN was developed. To maximize the sum rate of STIN, while satisfying the power constraints of each antenna and the QoS needs of satellite and cellular users, a constrained optimization problem was defined. To accommodate more than two users, a unique user clustering was also presented. NOMA and cognitive radio are two potential technologies that can effectively use satellite resources. The effectiveness of NOMAaided STIN, when numerous primary users share the spectrum, was examined in [33]. The outage probability and sum capacity expressions were developed considering the interference limits enforced by multiple primary users. The NOMAaided cognitive satelliteUAV terrestrial network was presented in [34] to improve spectrum efficiency and facilitate exponential user growth. Even with imperfect channel knowledge, the joint power allocation and subchannel assignment algorithm improved the transmission performance of the recommended system. In [35], the authors proposed a novel indexcoded NOMA to increase VANET spectral efficiency. The authors of [36] employed the NOMA technique for decentralized V2V communication, with a focus on channel modeling.
The outage behavior of a STARRISenabled cognitive nonterrestrial UAV with NOMA was studied in [37] under Rician fading and perfect/imperfect successive interference cancellation (SIC) situations. The outage probability expressions for secondary vehicular users were derived by considering primary vehicular users’ as interference. The proposed scheme outperformed both the STARRISOMA and nonSTARRIS schemes. The majority of the existing literature assumed RISIR configuration, in which the channels between the BSRIS and the RISvehicle (user) were known in advance in order to compensate for channel distortions. It is difficult to have ideal channel knowledge of every vehicle in V2X applications. Many of the works assumed RIS between the BS and vehicles. Because it is passive, RIS can only reflect the signal that has been received in the desired direction. As a result, the received signal power at the RIS is very poor, and the benefits that have been conversed about for RIS are not practical. RIS was rarely considered near/at the BS or vehicles in the works.
The blind RISaided FNOMA framework was proposed in [38] with IR and AP configurations for uplink transmission. In [39], the blind RISassisted framework was investigated for ONOMA, where channel gains ascertain the vehicle decoding order. In both [38, 39], an optimization problem for power allocations was formulated to maximize the sum capacity of near and far users. Monte Carlo simulations were employed to validate the theoretical outage expressions. These systems outperformed conventional NOMA by \(\approx\) 30% for 20 dB SNR and 32 reflective elements.
1.2 Contributions
Motivated by the benefits of RISassisted NOMA system for vehicular communication, the performance of blind RISassisted FNOMA for a downlink V2I is considered in the proposed work. The key contributions of this work are emphasized here.

To address the aforementioned issues, blind RIS as an IR (RISIR)assisted FNOMA and RIS as an RSU (RISRSU)assisted FNOMA methods are proposed in this work.

The closedform analytical outage and throughput expressions for RISIRFNOMA and RISRSUFNOMA are derived.

The derived analytical outage probability and throughput expressions are validated through extensive Monte Carlo simulations. There is a tight bound between the analytical and simulation results. This validates the accuracy of derived analytical expressions.

The proposed RISassisted FNOMA and conventional NOMA variants are compared in terms of outage probability and throughput. The blind RISRSUFNOMA is shown to perform comparably to the blind RISIRFNOMA in terms of throughput and outage.
1.3 Organization
The rest of the manuscript is presented in the following order: The analytical closedform outage probability and throughput expressions for the proposed blind RISIRFNOMA and RISRSUFNOMA methods are derived in Sect. 2. Extensive Monte Carlo simulations are used in Sect. 3 to validate the derived analytical expressions. Conclusions summarize the findings and suggest future research.
2 Methods
In this section, two different blind RISassisted FNOMA methods are proposed to reduce outage and increase throughput of both near and far vehicles. The blind configuration of RIS is practical since it does not require prior channel knowledge. In the first proposed method namely blind RISIRFNOMA, FNOMA is combined with a blind RISIR configuration and the RIS is deployed far from the transmitter and receiver in the IR configuration. In the second proposed method, namely blind RISRSUFNOMA, FNOMA is combined with a blind RISRSU configuration. RIS is positioned very close to the RSU. In both methods, passive RIS is used. Passive RIS can only reflect the received signal in the desired direction. Closedform analytical expressions are derived for outage and throughput for both proposed methods.
2.1 Blind RISIRFNOMA
The conceptual diagram of blind RISIRFNOMA for a downlink V2I scenario [20] is shown in Fig. 3. RIS with N reflecting elements is mounted on the wall of a building. RIS can be installed on various surfaces, including building facades, highway polls, advertising panels, vehicle windows, pedestrian clothing, and so on [8]. Even though there is a blockage, the RIS introduces a virtual LoS between RSU and vehicles. As the building with RIS is appropriately far from the RSU and vehicles, RIS serves as a smart reflector. This results in a dualhop channel. It is impractical to have accurate channel information at RIS due to a large number of vehicles and their high mobility. This implies blind transmission, in which the RIS elements introduce no phase shift. Due to the blind RIS configuration, only array gain is achieved based on the number of passive reflecting elements. However, no diversity gain is achieved.
In this proposed method, two vehicles are allotted with an equal number of reflecting elements. Single antenna is used at RSU, near and far vehicles. More power is allocated to the far vehicle than the near vehicle to meet QoS criteria. The order in which the vehicles’ signals are decoded is fixed in FNOMA. The signal from the far vehicle is decoded first, with the signal from the near vehicle treated as interference. The far vehicle’s signal is decoded at the near vehicle, and its impact is removed from the received signal via SIC. The near vehicle’s signal is decoded from the residual signal.
A superpositioncoded signal is generated at BS/RSU. It is given by
where \(\beta _{\mathrm{nv}}\) and \(\beta _{\mathrm{fv}}\) are the fraction of the total transmit power \(P_{s}\) allocated to near and far vehicles, respectively. \(x_{\mathrm{nv}}\) and \(x_{\mathrm{fv}}\) are the transmitted unit energy symbols corresponding to near and far vehicles, respectively. The power is allocated by BS/RSU to near and far vehicles such that the following constraint is met.
The channel between the BS/RSU and the jth RIS element is \(h_{j}=\alpha _{j}e^{i\phi _{j}},\ h_{j}\sim C{\mathcal{N}}\left( 0,1\right)\), where \(\alpha _{j}\) and \({{\phi }}_{j}\) are the magnitude and phase of \(h_{j}\). The channel between jth RIS element and the vehicle is \(g_{j}={\gamma }_{j}e^{i\psi _{j}},g_{j}\sim C{\mathcal{N}} \left( 0,1\right)\), where \({\gamma }_{j}\) and \(\psi _{j}\) are the magnitude and phase of \(g_{j}\). The number of reflecting elements assigned to the near and far vehicles are denoted by \(\left( N_{\mathrm{nv}}\right)\) and \(\left( N_{\mathrm{fv}}\right)\) , respectively. Assuming that they are equal, the received signal at the far vehicle is given by
where \(w_{\mathrm{fv}}\) is the additive white Gaussian noise at the far vehicle, which follows \(C{\mathcal{N}}\left( 0,N_o\right)\), \(N_o\) is the noise variance. In Eq. (3), L is the dualhop channel effect corresponding to a far vehicle. According to the CLT, L follows a complex Gaussian distribution when the number of reflecting elements assigned to the far vehicle is greater than 16, i.e., \(L\sim C{\mathcal{N}}\left( 0,N_{\mathrm{fv}}\right)\) [40]. By substituting (1) in (3), the received signal at far vehicle is rewritten as
In FNOMA, the near vehicle receives less power, while the far vehicle receives more power. The first term in (4) is not dominant over the second term because the cumulative dualhop channel for the far vehicle is weaker and \({\beta }_{\mathrm{nv}}\) is smaller. As a result, the far vehicle’s signal is detected by considering the near vehicle’s signal as interference. The signaltointerference plus noise ratio (SINR) for decoding a signal from a far vehicle while treating a signal from a near vehicle as interference is given by
where \(\rho _{s} =\frac{P_{s}}{N_0}\) is the transmit SNR. The outage occurs at the far vehicle when [18],
where \({\tilde{R}}_{\mathrm{fv}}\) is the desired rate demand of the far vehicle. Substituting (5) in (6), it is rewritten as
Let \(R_{\mathrm{fv}}=2^{{\tilde{R}}_{\mathrm{fv}}}1\) and \({\eta }_{\mathrm{fv}}={\left L\right }^{2}\), (7) is simplified as
The comprehensive derivation of (8) is given in “Appendix 1.” \({\eta }_{\mathrm{fv}}\) follows Chisquare distribution with two degrees of freedom. The corresponding mean of \({\eta }_{\mathrm{fv}}\) is \(E\left\{ {\eta }_{\mathrm{fv}}\right\} ={\delta }^{2}_{\mathrm{fv}}N_{\mathrm{fv}}\), where \({\delta }^{2}_{\mathrm{fv}}\) is the average channel gain of far vehicle. The probability density function (pdf) of \({\eta }_{\mathrm{fv}}\) is given by
The outage probability for the far vehicle is calculated using
Substituting (9), the outage probability for the far vehilce is expressed as
The comprehensive derivation of (11) is given in “Appendix 2.” The received signal at the near vehicle is given by
where \(w_{\mathrm{nv}}\) is the additive white Gaussian noise at the near vehicle, which follows \(C{\mathcal{N}} \left( 0,N_o\right)\). M is the dualhop channel effect corresponding to the near vehicle. According to the CLT, M follows a complex Gaussian distribution when the number of reflecting elements assigned to the near vehicle is greater than 16, i.e., \(M\sim C{\mathcal{N}}\left( 0,N_{\mathrm{nv}}\right)\) [40]. By substituting (1) in (12), the received signal at the near vehicle is rewritten as
The second term in (13) is dominant over the first term, because both the value of M and \({{\beta }}_{\mathrm{fv}}\) are higher. As a result, the signal from the far vehicle is detected first by the near vehicle. The SINR of decoding a signal from a far vehicle at a near vehicle is given by
After eliminating the influence of \({\ x}_{\mathrm{fv}}\) from \(y_{\mathrm{nv}}\) using SIC, the received signal at the near vehicle is given by,
The signal of a near vehicle is detected using (15). The SNR for decoding \(x_{\mathrm{nv}}\) at near vehicle is given by
The decoding of the far vehicle’s signal fails at the near vehicle when [18]
After simplification, (18) is written as,
The comprehensive derivation of (19) is given in “Appendix 3.” The decoding of the near vehicle’s signal fails at the near vehicle when [18],
where \({\tilde{R}}_{\mathrm{nv}}\) is the desired rate demand of the near vehicle. Substituting (16) in (20) gives
After simplification, (21) is written as,
where \(R_{\mathrm{nv}}=2^{{\tilde{R}}_{\mathrm{nv}}}1\). “Appendix 4” illustrates the comprehensive derivation of (22). As a result, the condition for which decoding of a near vehicle’s signal fails at a near vehicle is provided by
\({\eta }_{\mathrm{nv}}\) follows Chisquare distribution with two degrees of freedom. The corresponding mean is \(E\left\{ {\eta }_{\mathrm{nv}}\right\} ={\delta }^{2}_{\mathrm{nv}}N_{\mathrm{nv}}\), where \({\delta }^{2}_{\mathrm{nv}}\) is the average channel gain of near vehicle. The pdf of \({\eta }_{\mathrm{nv}}\) is given by
The outage probability of near vehicle is calculated using
By substituting (24) in (25) and simplifying,
The comprehensive derivation of (26) is given in “Appendix 5.” The throughput of blind RISIRFNOMA is given by [41],
where \(P^o_{\mathrm{nv}}\) and \(P^o_{\mathrm{fv}}\) are given in (26) and (11), respectively.
2.2 Blind RISRSUFNOMA
The conceptual diagram of the blind RISRSUFNOMA system for a downlink V2I scenario is shown in Fig. 4. Enhanced performance is obtained when RIS is deployed in close proximity to the transmitter or receiver units [40, 42]. In Fig. 4, RIS with N reflecting elements is supposed to be near RSU. As a dedicated link is used to connect the RSU and RIS, the RSURIS channel is deterministic, and its fading effect is minimal. As a result, communication between the RISRSU and the vehicles is limited to a single hop. In this section, closedform analytical outage probability and throughput expressions are derived for blind RISRSUFNOMA. The received signal at the far vehicle is given by
In (28), H is the cumulative channel effect corresponding to the far vehicle, and it follows complex Gaussian distribution based on CLT, i.e., \(H\sim C{\mathcal{N}}\left( 0,N_{\mathrm{fv}}\right)\). By substituting (1) in (28), the received signal at the far user is rewritten as
As per the concept of FNOMA, power is allocated for near and far vehicles in RISRSUFNOMA system. The first term in (29) is not dominant over the second term because the cumulative channel for the far vehicle is weaker and \({\beta }_{\mathrm{nv}}\) is smaller. As a result, the far vehicle’s signal is detected by considering the near vehicle’s signal as interference. The SINR for decoding a signal from a far vehicle while treating a signal from a near vehicle as interference is given by
The outage occurs at far vehicle when condition in (6) is met [18]. Let \({\rho }_{\mathrm{fv}}={\left H\right }^{2}\), the condition for the outage of the far vehicle is given by
\({\rho }_{\mathrm{fv}}\) follows Chisquare distribution with two degrees of freedom. The corresponding mean of \({\rho }_{\mathrm{fv}}\) is \(E\left\{ {\rho }_{\mathrm{fv}}\right\} ={\kappa }^{2}_{\mathrm{fv}}N_{\mathrm{fv}}\), where \({\kappa }^{2}_{\mathrm{fv}}\) is the average channel gain of far vehicle. The pdf of \({\rho }_{\mathrm{fv}}\)can be written similar to (9). Using the expression similar to (10), the probability of outage for the far vehicle is obtained as
The received signal at the near vehicle is given by
where G is the cumulative channel effect corresponding to the near vehicle, and it follows complex Gaussian distribution based on CLT, i.e., \(G\sim C{\mathcal{N}}\left( 0,N_{\mathrm{nv}}\right)\). By substituting (1) in (33), the received signal at the near user is rewritten as
The second term in (34) is dominant over the first term, because G and \({{\beta }}_{\mathrm{fv}}\) are higher. As a result, the signal from the far vehicle is detected first by the near vehicle. The SINR of decoding a signal from a far vehicle at a near vehicle is given by
The influence of \({\ x}_{\mathrm{fv}}\) is eliminated from \(y_{\mathrm{nv}}\) using SIC after it has been decoded.
The signal of a nearby vehicle is then detected. The SNR for decoding \(x_{\mathrm{nv}}\) at near vehicle is
The decoding of the far vehicle’s signal fails at the near vehicle when the condition in (17) is met. By substituting (35) in (17), the condition is given by
The decoding of a near vehicle’s signal fails at a near vehicle when the condition in (20) is met. By substituting (37) in (20), the condition is given by
The condition for which decoding of a near vehicle’s signal fails at the near vehicle is provided by
\({\rho }_{\mathrm{nv}}\) follows Chisquare distribution with two degrees of freedom. The corresponding mean is \(E\left\{ {\rho }_{\mathrm{nv}}\right\} ={\kappa }^{2}_{\mathrm{nv}}N_{\mathrm{nv}}\), where \({\kappa }^{2}_{\mathrm{nv}}\) is the average channel gain of near vehicle. The outage probability at near vehicle is obtained as
The throughput of blind RISRSUFNOMA is computed by using (27). Here, \(P^o_{\mathrm{nv}}\) and \(P^o_{\mathrm{fv}}\) are given in (41) and (32), respectively.
3 Results and discussion
In this section, the outage and throughput performances of blind RISIRFNOMA and blind RISRSUFNOMA are validated through simulation results. The simulation setup is given in Table 1. The parameters for the simulation study are chosen based on previous works [18, 29, 30, 38, 39]. The Monte Carlo simulation results are averaged over \({10}^6\) random channel realizations. The outage probability performance of the RISIRFNOMA far vehicle is compared for different numbers of RIS elements in Fig. 5. The simulated outage closely matched closedform analytical curves produced by (11) for greater values of N. \(N=32\), \(N=64\), \(N=128\) and \(N=256\) systems require SNR of \(\approx\) 29 dB, \(\approx\) 26 dB, \(\approx\) 23 dB, and \(\approx\) 20 dB, respectively, to achieve the required outage probability of \({10}^{4}\). The SNR requirement is found to be reduced by \(\approx\) 3 dB when the number of reflecting elements is doubled.
The outage probability performance of RISIRFNOMA near vehicle for various numbers of RIS elements is compared in Fig. 6. The simulated outage resembled the closedform mathematical curves resulting from (26), especially for higher values of N. \(N=32\), \(N=64\), \(N=128\) and \(N=256\) systems require SNR of \(\approx\) 33 dB, \(\approx\) 30 dB, \(\approx\) 27 dB, and \(\approx\) 24 dB, respectively, to achieve a target outage probability of \({10}^{4}\). It has been noted that increasing the number of reflecting elements by twofold lowers the SNR required by \(\approx\) 3 dB. From Figs. 5 and 6, it is observed that the far vehicle’s outage performance is superior to the near vehicle’s because the far vehicle is supplied more power.
In Fig. 7, the throughput (b/s/Hz) performance of blind RISIRFNOMA is compared for different numbers of RIS elements and \({\widetilde{R}}_{\mathrm{nv}}\) = \({\widetilde{R}}_{\mathrm{fv}}\) = 1 b/s/Hz. The throughput curves are plotted based on the expression in (27). The throughput of RISIRFNOMA system is increased by increasing transmit power at RSU. At about \(\approx\) 0 dB, the sum throughput of blind RISIRFNOMA with \(N=512\) reaches 2 b/s/Hz. Blind RISIRFNOMA, for example, with \(N=32\) reflecting elements, achieves a maximum throughput of 2 b/s/Hz at \(\approx\) 15 dB. It is also been noted that the increase in N decreases the SNR requirement to reach the target throughput. It is also obvious that the Monte Carlo simulation curves for blind RISIRFNOMA system closely match closedform analytical curves.
The outage probability of RISRSUFNOMA far vehicle for varying N is shown in Fig. 8. For \(N=32\), \(N=64\), \(N=128\) and \(N=256\) reflecting elements, the far vehicle attains an outage probability of \({10}^{4}\) at \(\approx\) 29 dB, \(\approx\) 26 dB, \(\approx\) 23 dB, \(\approx\) 20 dB. The SNR gain grows as N increases. Based on the outage expression in (32), analytical curves for various N are obtained. For all N, there is a close match between the Monte Carlo simulation curves and the analytical curves. The outage probability of the RISRSUFNOMA near vehicle for varying N is shown in Fig. 9. The analytical curves for various N are drawn based on the outage expression in (41). When comparing Figs. 8 and 9, it is evident that the far vehicle’s outage performance is better to the near vehicle’s. Figure 9’s other trends follow Fig. 8. In Fig. 10, the throughput (b/s/Hz) performance of blind RISRSUFNOMA is compared for different numbers of RIS elements and \({\widetilde{R}}_{\mathrm{nv}}\) = \({\widetilde{R}}_{\mathrm{fv}}=1\) b/s/Hz. Figure 7’s explanations are applicable to Fig. 10.
To demonstrate the efficacy of the suggested RISaided approaches, comparisons are made with classic time division multiple access (TDMA), FNOMA [18], ONOMA [18], CNOMA [29], and SWIPTCNOMA [30]. \(N=64\) reflective elements are assumed in the RIS. The probability of outage attained by the far vehicle using various systems is shown in Fig. 11. The outage probability of far vehicle for OMA (TDMA), FNOMA, ONOMA, CNOMA, and SWIPTNOMA is given by
where \(c_{\mathrm{fv}}\)=\(2^{2{\widetilde{R}}_{\mathrm{fv}}}1\).
where \(\frac{1}{\delta _{H}^{2}}\)=\(\frac{1}{\delta _{\mathrm{fv}}^2}+\frac{1}{\delta _{\mathrm{nv}}^2}\)
where \(\delta _{\mathrm{nf}}^{2}\) is the average gain of channel between near and far vehicle.
where \(\sigma ^{2}\) is the variance of noise and \(P_{H}\) is the harvested energy during direct transmission. The outage probability of near vehicle for OMA (TDMA), FNOMA, ONOMA, CNOMA, and SWIPTNOMA is given by
where \(c_{\mathrm{nv}}\)=\(2^{2{\widetilde{R}}_{\mathrm{nv}}}1\).
where \(\varphi =\max \left\{ \frac{R_{\mathrm{fv}}}{\left( \beta _{\mathrm{fv}}\beta _{\mathrm{nv}}R_{\mathrm{fv}}\right) \rho _s},\ \frac{R_{\mathrm{nv}}}{\beta _{\mathrm{nv}}\rho _s}\right\}\).
where \(\psi\) is the fraction for energy harvesting. To simulate SWIPTCNOMA system, \(\delta _{\mathrm{nf}}^{2}=2\), \(\psi =0.5\) and efficiency of energy harvesting circuit \(\eta _{\mathrm{eff}}=0.7\) are considered. The increase in transmit power at RSU improves the outage performance of all the systems. Both proposed RISaided FNOMA systems (IR and RSU) perform nearly equally well and reach the desired outage probability of \({10}^{4}\) at \(\approx\) 29 dB. FNOMA and CNOMA systems outperform other NOMA variants due to their higher power allocation and selection diversity. Because of the constraints on resources, TDMA performs poorly. SWIPTNOMA’s performance is subpar compared to other systems due to constraints on resources and fractional harvested power used for relaying. The suggested RISaided FNOMA systems outperform TDMA, FNOMA, ONOMA, CNOMA, and SWIPTCNOMA systems by \(\approx\) 16 dB, \(\approx\) 11 dB, \(\approx\) 13 dB, \(\approx\) 12 dB, and \(\approx\) 23 dB, respectively.
The probability of outage achieved by the near vehicle using various methods is compared in Fig. 12. It is obvious that the suggested RISaided system performs better than all previous systems, particularly up to \(\approx\) 25 dB SNR. After \(\approx\) 25 dB, ONOMA performs better since user channel gains determine the order of decoding. Here, \(N=64\) is used by the RISaided systems. Increasing the number of RIS elements improves the performance of the RISaided system over other systems. Due to very lower power allocation, FNOMA performs poor than ONOMA. When compared to all other systems, CNOMA and SWIPTCNOMA perform the worst due to time resource constraints. The recommended RISaided FNOMA systems outperform TDMA, FNOMA, CNOMA, and SWIPTCNOMA systems by \(\approx\) 9 dB, \(\approx\) 14 dB, \(\approx\) 20 dB, and \(\approx\) 25 dB, respectively. In comparison with other OMA and NOMA variants, the outage probability of far and near vehicles is relatively low for blind RISassisted schemes in high SNR regions. As the SNR increases, the gain of blind RISassisted methods becomes substantially higher.
The throughput attained by various systems is compared in Fig. 13. At \(\approx\) 10 dB SNR, the RISassisted systems achieve the target throughput of 2 b/s/Hz. ONOMA, FNOMA, and TDMA systems achieve the desired throughput by \(\approx\) 25 dB, \(\approx\) 29 dB, and \(\approx\) 29 dB, respectively. Even at 30 dB SNR, desired throughput is not achieved with CNOMA and SWIPTCNOMA. Even though the ONOMA near vehicle outperforms the suggested RISaided systems with \(N=64\) in terms of outage probability, the proposed systems exhibit a \(\approx\) 15 dB SNR gain in terms of throughput over ONOMA system.
4 Conclusions
This paper has presented the blind RISIRFNOMA and RISRSUFNOMA systems’ closedform analytical outage probability and throughput expressions for downlink V2I scenarios. The analytical and Monte Carlo simulation curves are almost identical. To guarantee QoS fairness, FNOMA gives far vehicles more power than nearby vehicles. As a result, for both blind RISIRFNOMA and RISRSUFNOMA systems, the far vehicle’s outage performance is better than the near vehicle’s. As the number of reflecting elements grows, so does the outage and throughput performance. The blind RISIRFNOMA and RISRSUFNOMA systems outperform the OMA and NOMA variants in terms of outage probability and throughput. RISassisted FNOMA is better than NOMA variants for vehicular environments because of its massive connectivity, stronger reliability, and ability to give improved outage and throughput even without channel knowledge. As RISRSUFNOMA system performs identically to RISIRFNOMA system in terms of throughput and outage performance and more realistic in practical circumstances, it could be a viable contender for vehicular applications.
Blind RIS can be substituted with discrete phase shifterassisted RIS in the future, and its usefulness in vehicular environments can be studied. Random power allocations for FNOMA are performed in the suggested study, which could be changed to achieve optimal power allocation. The proposed systems can be tested with multiple vehicles by considering user pairing. The performance of far vehicles can be improved further by employing a CNOMA system, in which cooperative combining is performed at the far vehicle. The proposed RISaided system can be modified with CNOMA in the future, and its performance for uplink and downlink transmissions can be tested.
Availability of data and materials
Not applicable
Abbreviations
 AP:

Access point
 BS:

Base station
 CLT:

Central limit theorem
 FNOMA:

Fixed NOMA
 IR:

Intelligent reflector
 ITS:

Intelligent transportation system
 MIMO:

Multiple input–multiple output
 NOMA:

Nonorthogonal multiple access
 OMA:

Orthogonal multiple access
 PLS:

Physical layer security
 QoS:

Quality of service
 RIS:

Reconfigurable intelligent surfaces
 RSU:

Roadside unit
 SNR:

Signaltonoise ratio
 6G:

Sixthgeneration
 SIC:

Successive interference cancellation
 3GPP:

Thirdgeneration partnership project
 V2X:

Vehicletoeverything
 V2I:

Vehicletoinfrastructure
 V2V:

Vehicletovehicle
 VANET:

Vehicular ad hoc network
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This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2021R1A6A1A03043144).
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Appendices
Appendices
1.1 Appendix 1. Condition for outage at far vehicle
Taking antilog on both sides of (7)
Simplifying this results in expression (8).
1.2 Appendix 2. Probability of outage expression for far vehicle
Substituting \(r_{\mathrm{fv}}\) results in expression (11).
1.3 Appendix 3. Condition for decoding of the far vehicle’s signal fails at the near vehicle
Taking antilog on both sides of (18)
Simplifying this results in expression (19).
1.4 Appendix 4. Condition for decoding of the near vehicle’s signal fails at the near vehicle
Taking antilog on both sides of (21)
1.5 Appendix 5. Probability of outage expression for near vehicle
Substituting \(r_{\mathrm{nv}}\) results in expression (26).
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Kumaravelu, V.B., Selvaprabhu, P., Han, D.S. et al. Blind reconfigurable intelligent surfaceaided fixed nonorthogonal multiple access for intelligent vehicular networks. J Wireless Com Network 2023, 83 (2023). https://doi.org/10.1186/s1363802302291y
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DOI: https://doi.org/10.1186/s1363802302291y