Active, Passive, and Absorptive RIS-Aided 6G Network Under Non-Orthogonal CCI

Received 2 June 2025; accepted 19 June 2025. Date of publication 26 June 2025; date of current version 1 August 2025. The review of this article was coordinated by Editor Ping Wang. Digital Object Identifier 10.1109/OJVT.2025.3583545 Active, Passive, and Absorptive RIS-Aided 6G Network Under Non-Orthogonal CCI VOLKAN ÖZDURAN 1(Senior Member, IEEE), EHSAN SOLEIMANI-NASAB 2, NIKOLAOS NOMIKOS 3(Senior Member, IEEE), IMRAN SHAFIQUE ANSARI 4(Senior Member, IEEE), AND PANAGIOTIS TRAKADAS 3 1˙ Istanbul University-Cerrahpa¸sa, 34320 Istanbul, Türkiye 2Department of Electrical and Computer Engineering, Graduate University of Advanced Technology, Kerman, Iran 3Research and Development Department, Four Dot Infinity, 16777 Elliniko, Greece 4James Watt School of Engineering, University of Glasgow, G12 8QQ Glasgow, U.K. CORRESPONDING AUTHOR: VOLKAN ÖZDURAN (e-mail: [email protected]). This work was supported by the 6G-LEADER Project funded by Smart Networks and Services Joint Undertaking through the European Union’s Horizon Europe Research and Innovation Programme (6g-leader.eu) under Grant 101192080. ABSTRACT This paper investigates the impact of randomly deployed non-orthogonal co-channel interference (CCI), originating from the information exchange process among non-orthogonal multiple access (NOMA) users, in an active, passive, and absorptive reconfigurable intelligent surface (RIS)-assisted dualhop network. More specifically, the study considers that the information exchange process involves the source utilizing active, passive, or absorptive RIS architecture, along with a line of sight (LOS)/non-line of sight (NLOS) link between source and destination terminals. Additionally, this study considers the limited non-orthogonal CCI affecting the destination terminal in an independent and identically distributed (i.i.d.) non-orthogonal CCI scenario. Theoretical insights and Monte Carlo-based simulations collectively demonstrate that non-orthogonal CCI severely degrades system performance, particularly in high signalto-noise ratio conditions, leading to notable losses in system coding gain. Meanwhile, results also reveal that increasing the number of RIS elements stabilizes the system and mitigates the impact of CCI on its performance. INDEX TERMS Reconfigurable intelligent surface, active, passive, absorptive, co-channel interference, performance analysis. I. INTRODUCTION As millimeter and terahertz-waves are susceptible to fading between building blocks, the reconfigurable intelligent surface (RIS) architecture has emerged as an essential component for improving wireless propagation in sixth-generation (6G) wireless mobile communications [1],[2]. The evolution initiated by passive RISs [1] is now advancing with the introduction of active [3],[4],[5], hybrid [6],[7], absorptive [8], distributed, zero-energy [9], and simultaneous transmission and reflection (STAR)-RIS paradigms [10]. RIS technology distinguishes itself from traditional relaying by providing notable advantages in spectrum and energy efficiency. Unlike relays, passive RIS units solely reflect received signals without processing, differentiating them from relay modes, such as half-duplex (HD) [11] and full-duplex (FD) [12]. Notably, relay operating modes still contend with challenges like the pre-log factor and loop-interference drawbacks [13].Inrecent years, active RIS has also received great attention due to its capability to amplify the incident signal and reflect to other direction [3],[5],[14],[15]. Meanwhile, academic and industrial stakeholders in the telecom domain are expecting a dramatic increase in the number of mobile terminals [16]. This trend is anticipated to increase co-channel interference (CCI) occurrences in the near future. Prominent examples © 2025 The Authors. This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ 2048 VOLUME 6, 2025 include leakage interference from beamforming side lobes and information exchange among non-orthogonal multiple access (NOMA) users [17].1 Thereby, some of the studies in the literature scrutinize this issue and investigate the detrimental effects of CCI on RIS-assisted systems. The study in [18] investigates the system outage performance of a multiple decode-and-forward (DF)-based HD relay-assisted communication under Rayleigh fading. In addition, [18] considers that the source terminal has Nreflecting elements and relay-destination terminals experience CCI. Moreover, [18] presents an opportunistic relay selection strategy to minimize the system outage performance and overhead. The authors in [19] consider a wireless network with a RIS-assisted source, which has N1reflecting elements, communicating with a destination via KRIS-assited multiple HD-DF relay nodes, having N2reflecting units. Furthermore, [19] considers that relay and destination terminals are affected by an arbitrary number of CCI terminals under Rayleigh fading conditions. Meanwhile, opportunistic relay selection is adopted in [19], which is based on succeeded the decoding received signal. Finally, results reveal that the proposed selection algorithm achieves increased cooperative diversity order and the interference at the destination is more detrimental than the interference at the relay terminal on the system outage performance. The paper in [20] investigates the constructive interference effects on a downlink network, where a multi-antenna base station (BS) communicates with Kmobile terminals via a RIS with Mreflecting elements. To enhance the system’s error-rate performance, optimization techniques are employed to redesign the phase shifts at the RIS unit, also utilizing a greedy algorithm to minimize the error floors at medium-to-high signal-to-noise ratio (SNR). Then, the work in [21] investigates the CCI effects on the outage and bit error rate (BER) performance of RIS and DF-based HD relay-assisted mixed free-space optical communication and radio frequency systems. In addition, the authors assume that the destination terminal is affected by a limited number of CCI terminals subject to Rayleigh fading conditions. Here, the direct-link between source and destination terminals does not exist due to excessive fading and path-loss. Reference [22] investigates the system performance of RISassisted wireless powered interference-limited networks. In greater detail, the destination terminal is affected by a limited number of CCI and the direct-link between source and destination terminals does not exist. Meanwhile the authors assume Generalized-Kand Nakagami-mfading environments for the RIS and interference links, respectively. The study in [23] focuses on a topology where the source communicates with the destination through a RIS unit, which has Nreflecting unit, under Rayleigh fading conditions. At the same time, 1It is worth noting that while practical RIS implementations often encounter significant interference from quantization lobes due to discrete phase shifts, our focus remains on analyzing the CCI arising from the information exchange among NOMA users. Expanding the scope to include multi-antenna interference sources and the impact of RIS quantization lobes would undoubtedly enrich the analysis; however, such considerations are left for future work. the paper does not consider a direct-link between the source and destination and communication is established only via the RIS unit. Moreover, [23] considers that the destination terminal is affected by a limited number of independent, equally powered CCIs. Since the aforementioned system operates in interference-limited regime, [23] neglects the thermal noise effects over the system performance. [23] investigates the system performance by means of outage probability, error probability, and average channel capacity. [23] also provides asymptotic analysis to get more insight of the derived analytical results. In addition, [23] utilizes binary phase shift keying and differential phase shift keying modulations to investigates the system BER performance. Moreover, [23] also takes into consideration the ideal and practical phase shift effetcs on the system outage performance in the presence of CCI. [23] investigates the effects of the different numbers and powers of interferers and also different numbers of reflecting unit effects on the system performance. Next, the work in [24] investigates the outage and average bit error rate performance of single and multiple RIS-assisted dual-hop networks without a direct-link. The presented analysis and performance evaluation consider that the destination terminal is affected by a limited number of independent and identically distributed (i.i.d.) CCI subject to Rayleigh fading. Additionally, a best RIS selection algorithm for the multiple RIS-assisted system is presented, enhancing the network’s reliability. The authors in [25] shed light on how CCI, which is caused by active uplink transmissions, can be minimized by using RISs in the RIS-aided FD networks. The authors consider two scenarios, with and without direct-link, and adopt various optimization techniques. Results reveal that a larger RIS is required for efficient CCI cancellation. Another work investigates the outage and achievable-rate performance of passive RIS-aided dual-hop network [26]. The investigation considers that source and destination terminals do not have a direct-link and all information exchange is completed via passive RIS and destination terminal is affected by a limited number of CCI. The paper in [27] investigates the CCI effects on the RIS-aided multiple-input single output wireless communication system. Here the outage probability, bit-error rate, and ergodic capacity performance metrics are analyzed. The study in [28] investigates the performance of RIS-aided FD network. The authors assume that users and RIS terminal are affected by CCI and because of the FD information exchange process, user terminals suffer from the self-interference that is caused by transmitting and receiving at the same time. In this setting, the authors focus on the analysis of the outage and ergodic capacity performance of the RIS-aided FD network. Furthermore, the authors in [29] study a network where mobile terminals introduce CCI on a passive RIS-aided dual-hop network. More specifically, it is considered that the destination terminal is affected by a limited number of mobile CCI terminals. The obtained results reveal that mobile CCI has severe effects on the system performance compared to static CCI. Then, the study in [30] investigates the performance of RIS-aided systems in the presence of interference. Aiming to reduce phase adjustment overheads, the VOLUME 6, 2025 2049 ÖZDURAN ET AL.: ACTIVE, PASSIVE, AND ABSORPTIVE RIS-AIDED 6G NETWORK UNDER NON-ORTHOGONAL CCI authors adopt quasi-static phase shifting where the phase shifts do not vary with the instantaneous channel state information (CSI), offering an attractive performance-complexity trade-off. Vega-Sánchez et al. [31] investigates the achievable secrecy performance of RIS-aided dual-hop network in the presence of a single eavesdropper. The investigation also considers that RIS terminal is affected by electromagnetic interference. The work in [32] focuses on the performance of RIS-aided downlink power-domain NOMA in Nakagami-m fading channels with CCI. Considering the Gamma approximation, they provide closed-form expressions for the ergodic capacity and outage probability, under the impact of CCI. Moreover, Monte Carlo simulations are presented highlighting that RIS-NOMA outperforms RIS-OMA for varying numbers of users and reflecting elements. Finally, the authors in [33] investigate the performance of passive RIS-aided downlink two-users NOMA network. The investigation considers that BS has an access to user one via IRS terminal while it has a direct access to user two. The investigation also considers that two NOMA users are affected by a limited number of CCI. Likewise, [34] investigates the outage performance of passive and absorptive RIS-aided uplink NOMA networks in the presence of CCI affecting the BS. The literature comparison table is presented in Table I. Aiming to build on prior works in RIS-aided NOMA networks, in this study, we investigate the impact of randomly deployed non-orthogonal CCI, introduced from NOMA communication between different users, in a dual-hop RIS-aided network. Furthermore, we analyzed the performance under three different RIS modes, i.e. active, passive, and absorptive. While prior studies have analyzed RIS-assisted systems under generalized fading and hardware impairments [35],[36],[37], [38], these works typically address specific fading environments or hardware limitations in isolation, without jointly considering the interplay between RIS operation modes and non-orthogonal CCI. In contrast, our study develops a unified analytical framework comparing active, passive, and absorptive RIS operation under randomly deployed non-orthogonal CCI, a realistic and practically motivated interference scenario that has not been jointly addressed in the RIS literature. More specifically, this work provides the following contributions: rAiming to provide a generalized view on RIS-aided networks, we include in our study three different RIS operation modes. The first mode corresponds to Nreflecting element equipped active RIS, with power amplifiers and no signal processing capabilities, then, we present an analysis on passive RISs, and finally we present results for absorptive-RISs, the wireless topology we focus herein consists of a line-of-sight (LOS)/direct-link and non-LOS (NLOS), between source and destination. To cater for real-world impairments, we assume that the destination is affected by a limited number of randomly deployed i.i.d. non-orthogonal CCI subject to Rayleigh fading. Differently from [23], instead of constant transmit power, the investigation in this paper considers proportional transmit power associated with source FIGURE 1. Active, passive, and absorptive RIS-assisted dual-hop network in the presence of non-orthogonal CCI. terminal’s transmit power and Euclidean distance for the interference. rFor this topology, we provide a thorough theoretical analysis, in terms of outage probability (OP), error probability (EP), throughput, energy and spectral efficiency. Analytical and asymptotic derivations regarding the aforementioned performance metrics are provided and verified by means of Monte-Carlo based intensive computer simulations. The remaining parts of the investigation are as follows: Section II provides detailed descriptions regarding the investigated system model along with channel statistics. Section III presents the analytical and asymptotic derivations of performance metrics. Then, Section IV presents the numerical result, and finally Section Vconcludes the investigation. The list of acronyms and Notations are presented in Tables Iand III, respectively. Notations: Throughout the paper, the superscripts “a”, “p”, and “abs” denote the operating modes of active, passive, and absorptive RIS, respectively. The Fh(.) represents the cumulative distribution function (CDF) of a random variable (RV) h.Thefh(.) term represents the probability density function (PDF) of a random variable h.(.) is the Gamma function [39, Eq. (8.310.1)].γ(a,b) is the lower incomplete Gamma function [39, Eq. (8.350.1)] and (a,b) is the upper incomplete Gamma function [39, Eq. (8.350.211)].B(x,y)is the Beta function [39, Eq. (8.384.1)].(a)nis the Pochhammer symbol [39] and x yis the Binomial coefficient [39]. All log are base 2 unless stated otherwise. The operator E[.] stands for expectation, while Pr(.) represents probability. Gm,n p,q[.] is the Meijer’s G-Function [39, Eq. (9.301)]. pFq(a1,...,ap;b1,...,bq;x) is the generalized hypergeometric function [39, Eq. (9.14)].TheCN(μ, σ2) is complex Gaussian RV with mean of μand variance of σ2. II. SYSTEM MODEL & CHANNEL STATISTICS Fig. 1present a RIS-aided network, under non-orthogonal CCI, where three different operation modes are adopted, i.e. 2050 VOLUME 6, 2025 TAB LE 1. Comparison of Existing Works and This Study VOLUME 6, 2025 2051 ÖZDURAN ET AL.: ACTIVE, PASSIVE, AND ABSORPTIVE RIS-AIDED 6G NETWORK UNDER NON-ORTHOGONAL CCI TAB LE 2. List of Acronyms active RIS with power amplifiers, without signal processing capabilities, passive RIS, and absorptive RIS. Moreover, a single antenna equipped mobile terminal (MT) makes information exchange with a single antenna equipped destination, which is BS, via RIS with NLOS and RIS with LOS/directlink between source. In this study, we assume a single-antenna BS to analyze the fundamental impact of RIS operational modes in a NOMAbased network. While modern 5G and 6G networks frequently employ massive multiple-input multiple-output (MIMO), the single-antenna BS model remains relevant in scenarios such as low-power edge nodes, small cells, and Internet of Things (IoT) applications, where large antenna arrays may not be feasible. Additionally, this assumption allows for analytical tractability and closed-form performance derivations without excessive complexity [40]. It is worth noting that while practical RIS implementations may introduce additional factors such as scatterers, beamforming side lobes, quantization lobes, and energy losses, our study adopts an idealized model to focus on the TAB LE 3. List of Notations fundamental performance impact of active, passive, and absorptive RIS modes in a NOMA-based communication system. This approach is widely used in analytical studies to derive closed-form expressions and fundamental insights [41], [42]. The energy reflection coefficient of RIS elements is assumed to be 1 in passive mode, following conventional models that establish theoretical performance limits before incorporating practical impairments [42]. While losses due to hardware constraints and multiplicative fading are valid concerns, analyzing them in detail would significantly increase model complexity and require numerical evaluations, which fall outside the scope of this work. However, extending this 2052 VOLUME 6, 2025 analysis to include such impairments could be an interesting direction for future research [43],[44]. The RV hi,∀i=1,...,N, represents the channel impulse response between MT →RIS. hiis a complex Gaussian RV with zero mean and σ2 hid−ν MT−RIS variance. i.e. hi∼ CN(0,σ2 hid−ν MT−RIS), where dMT−RIS is the distance between MT →RIS and νis the pathloss exponent and takes values between 2 −6[45].gi∼CN(0,σ2 gid−ν RIS−BS) is the channel impulse response RIS →BS, where dRIS−BS is the distance between RIS →BS. Next, f∼CN(0,σ2 fd−ν MT−BS)is the channel impulse response between MT and BS, where dMT−BS is the distance between MT →BS. In addition, mj∼CN(0,σ2 mjd−ν mj−BS), ∀j=1,...,M, is the channel impulse response between jth CCI →BS, where dmj−BS is the distance between jth CCI →BS. The distances, channel impulse responses, and power allocation coefficients of the CCI terminals are sorted as: dmj−BS ≤,...,≤dmM−BS, |mj|2≥,...,≥|mM|2, and 1 >α j≥,...,≥αM>0, where M j=1αj=1, respectively. The amplitudes of all channels are distributed according to Rayleigh distribution. It should be noted that the i.i.d. case is considered for modeling the CCI subject to Rayleigh fading. According to Fig. 1, MT transmits information to the destination via active, passive, and absorptive RIS with LOS/direct-link. The received signals at BS for the active, passive, and absorptive RIS modes are written as follows: ya+d BS =Psfx+Ps N  i=1 hiθigix+ N  i=1 niθigix + M  j=1Pjαjmjaj+wn,(1) yp+d/abs+d BS =Psfx+Ps N  i=1 hiθigix + M  j=1Pjαjmjaj+wn,(2) where Psis the transmit power of MT. xis the transmit information, which has a unit variance E[|x|2]=1. The niis the noise term from the amplifier at ith reflecting element which follows CN 0,σ2 ni.θi=ρiejφi,∀i=1,...,N, and = diag ρ1ejφ1,...,ρ iejφi,...,ρ NejφN represent reflecting phase shifting matrix of RIS. The term ρiis the energy coefficients of the ith element for reflecting responses. The term φi∈[0,2π) is the adjustable phase at the ith reflected unit in the RIS. Considering ρi=ρ[4],theterm can be written as: =ρdiag ejφ1,...,ejφi,...,ejφN. In practical implementations, the phase shift φiat each RIS element is typically optimized based on CSI to enhance received signal strength. In this study, we assume an idealized continuous phase shift model, which provides an upper-bound performance analysis and allows for analytical tractability. However, in practical RIS hardware, discrete phase shifts are often employed due to quantization constraints, which can introduce additional performance losses [46]. While our model does not explicitly incorporate phase quantization, its fundamental insights remain applicable. By setting ρ>1, the active mode is obtained. Conversely, by setting the term ρto 1 and σ2 ni to 0, the passive mode is obtained. Likewise, in absorptive mode, which neither involves an amplification process at the RIS nor amplifies noise, the term ρtakes values in the range 0≤ρ≤1[8],[47].P jis the transmit power at jth CCI. aj, where E[|aj|2]=1, is the transmit information of the jth CCI. wnis the thermal noise at BS and modeled as additive white Gaussian noise (AWGN). Utilizing (1), the signal-tointerference plus noise ratio (SINR) at BS is written as: γa+d BS = Ps|f|+ρN i=1|hi||gi| 2 ρ2N i=1σ2 ni|gi|2+M j=1Pjαj|mj|2+σ2 wn (3) By setting the term ρto 1 and σ2 nito 0, the SINR expression for the passive and absorptive modes is obtained as: γp+d/abs+d BS = Ps|f|+ρN i=1|hi||gi| 2 M j=1Pjαj|mj|2+σ2 wn (4) Note that passive and absorptive modes have the same SINR expression with a different ρvalue. In passive mode, ρterm is set to 1 and in absorptive mode, ρterm is a value between 0≤ρ≤1. III. PERFORMANCE ANALYSIS This section provides the analytical and asymptotic derivations of outage probability, error probability, throughput, energy and spectral efficiency performance metrics. A. OUTAGE PROBABILITY Below, an outage analysis is presented for the considered dualhop RIS-aided network under the impact of non-orthogonal CCI. Pa+d out (γ)=1 (ρb)a+1f(a+4)σ2 ngN(PJm)M(M)(N)γ Psa+3 2∞  k=0 (1+k)(3/2+k) (3/2) ((a+4)/2+k)((a+5)/2+k) ((a+4)/2)((a+5)/2) k!−γ 2Psfk ×∞  u=0 (a+2k+5 2) (u+1)(a+2k−2u+5 2) u  t=0u tρ2(u−t)(N+u−t) 1 σ2 ngN+u−t (M+t) 1 PJmM+t(5) VOLUME 6, 2025 2053 ÖZDURAN ET AL.: ACTIVE, PASSIVE, AND ABSORPTIVE RIS-AIDED 6G NETWORK UNDER NON-ORTHOGONAL CCI Proposition 1: The OP analytical derivations are presented at the top of the next page. Note that for the case of active RIS with direck link (5) shown at the bottom of the previous page, passive RIS with direct link (6) shown at the bottom of this page, active RIS without direct link (7) shown at the bottom of this page, and passive RIS without direct link (8) shown at the bottom of this page. Proof: See Appendix A. B. ERROR PROBABILITY With the help of [48, Eq. (27)], the CDF-based EP performance metric can be formulated as ¯ Pe=p 2q π∞ 0 exp (−qx) √xF(x)dx,(9) where p=q=1 represents the binary phase shift keying (BPSK) and p=q=2 represents quadrature phase shift keying (QPSK) modulations. The analytical derivations for the EP performance metric are presented in the following proposition. Proposition 2: The EP for the proposed model is derived in the following expressions, which are presented in the middle of the next page. For the case of active RIS with direct link (10) shown at the bottom of this page, passive RIS with direct link (11) shown at the bottom of this page, active RIS without direct link (12) shown at the bottom of the next page, and passive RIS without direct link (13) shown at the bottom of the next page. Proof: See Appendix B. C. THROUGHPUT The CDF-based throughput performance metric is formulated with the help of [49, Eq. (15(a))] as: τBS =Rth 1−FγBS (γth)(14) Substituting (3) and (4) into (14), the throughput analytical expressions are obtained. Due to space limitations, the derivations are omitted and only utilized in the performance evaluation results in Section IV. Pp+d out (γ)=1 (ρb)a+1f(a+4)(M)(PJm)Mγ Psa+3 2∞  k=0 (1+k)(3/2+k) (3/2) ((a+4)/2+k)((a+5)/2+k) ((a+4)/2)((a+5)/2) k!−γ 2Psfk ×∞  u=0 (a+2k+5 2) (u+1)(a+2k−2u+5 2) (M+u) 1 PJmM+u(6) Pa out(γ)=1 ρaba+1(a+1)(a+1)(M)(N)σ2 ngN(PJm)Mγ Psa+1 2∞  u=0 (a+3 2) (u+1)(a+3−2u 2) × u  t=0u tρ2(u−t)(N+u−t) 1 σ2 ngN+u−t (M+t) 1 PJmM+t(7) Pp out(γ)=1 ρaba+1(a+1)(a+1)(M)(PJm)Mγ Psa+1 2∞  u=0 (a+3 2) (u+1)(a+3−2u 2) (M+u) 1 PJmM+u(8) ¯ Pea+d =1 2√π(ρb)a+1f(a+4)Pa+3 2 sσ2 ngN(PJm)M(M)(N) ∞  k=0 (1+k)(3/2+k) (3/2) ((a+4)/2+k)((a+5)/2+k) ((a+4)/2)((a+5)/2) k! ×−1 2Psfk∞  u=0 (a+2k+5 2) (u+1)(a+2k−2u+5 2) u  t=0u tρ2(u−t)(N+u−t) 1 σ2 ngN+u−t (M+t) 1 PJmM+t(a+2k+4 2) (10) ¯ Pep+d =1 2√π(ρb)a+1f(a+4)Pa+3 2 s(PJm)M(M) ∞  k=0 (1+k)(3/2+k) (3/2) ((a+4)/2+k)((a+5)/2+k) ((a+4)/2)((a+5)/2) k!−1 2Psfk ×∞  u=0 (a+2k+5 2) (u+1)(a+2k−2u+5 2) (M+u) 1 PJmM+u(a+2k+4 2) (11) 2054 VOLUME 6, 2025 D. ENERGY EFFICIENCY By definition, the energy efficiency (EE) is calculated as the system throughput over the total power consumption [50, Eq. (3)]. EE =τBS Ps ,(15) E. SPECTRAL EFFICIENCY The spectral efficiency (SE) is measured in bits/s/Hz and formulated as [51],[52]. SE =τBS B,(16) where B is the bandwidth used in the transmission. F. ASYMPTOTIC ANALYSIS To get additional insights from the derived analytical results, this subsection focuses on the high SNR regime. In greater detail, we evaluate the asymptotic performance for the following performance metrics: 1) OUTAGE PROBABILITY Considering the small values of j,kterms, the asymptotic outage representations are obtained for the case of active RIS with direct link (17), passive RIS with direct link (18), active RIS without direct link (19), and passive RIS without direct link (20), all shown at the bottom of this page. ¯ Pea=1 2√πρaba+1(a+1)(a+1)Pa+1 2 sσ2 ngN(PJm)M(M)(N) ∞  u=0 (a+3 2) (u+1)(a+3−2u 2) × u  t=0u tρ2(u−t)(N+u−t) 1 σ2 ngN+u−t (M+t) 1 PJmM+ta+2 2(12) ¯ Pep=1 2√πρaba+1(a+1)(a+1)(M)(PJm)MPa+1 2 s ∞  u=0 (a+3 2) (u+1)(a+3−2u 2) (M+u) 1 PJmM+ua+2 2(13) Pa+d,∞ out (γ)=1 (ρb)a+1f(a+4)σ2 ngN(PJm)M(M)(N)γ Psa+3 2 × 1  k=0 (1+k)(3/2+k) (3/2) ((a+4)/2+k)((a+5)/2+k) ((a+4)/2)((a+5)/2) k!−γ 2Psfk1  u=0 (a+2k+5 2) (u+1)(a+2k−2u+5 2) × u  t=0u tρ2(u−t)(N+u−t) 1 σ2 ngN+u−t (M+t) 1 PJmM+t(17) Pp+d,∞ out (γ)=1 (ρb)a+1f(a+4)(M)(PJm)Mγ Psa+3 21  k=0 (1+k)(3/2+k) (3/2) ((a+4)/2+k)((a+5)/2+k) ((a+4)/2)((a+5)/2) k!−γ 2Psfk × 1  u=0 (a+2k+5 2) (u+1)(a+2k−2u+5 2) (M+u) 1 PJmM+u(18) Pa,∞ out (γ)=1 ρaba+1(a+1)(a+1)(M)(N)σ2 ngN(PJm)Mγ Psa+1 21  u=0 (a+3 2) (u+1)(a+3−2u 2) × u  t=0u tρ2(u−t)(N+u−t) 1 σ2 ngN+u−t (M+t) 1 PJmM+t(19) Pp,∞ out (γ)=1 ρaba+1(a+1)(a+1)(M)(PJm)Mγ Psa+1 21  u=0 (a+3 2) (u+1)(a+3−2u 2) (M+u) 1 PJmM+u(20) VOLUME 6, 2025 2055 ÖZDURAN ET AL.: ACTIVE, PASSIVE, AND ABSORPTIVE RIS-AIDED 6G NETWORK UNDER NON-ORTHOGONAL CCI 2) ERROR PROBABILITY Following a similar procedures as in the OP asymptotic representations, the EP asymptotic representations are also obtained. The obtained derivations are omitted, being only applied in Section IV. 3) THROUGHPUT Considering the asymptotic OP representations and utilizing it in the throughput formula, the asymptotic throughput represantation is obtained. To ensure readability, the obtained derivations are omitted, being only utilized in Section IV. 4) ENERGY EFFICIENCY Considering the asymptotic throughput expressions and using it in the (15), the asymptotic EE representation is obtained. As for the previous two performance metrics, the derivations are omitted, being only evaluated in Section IV. G. DIVERSITY ORDER ANALYSIS The relation between diversity order and coding gain is expressed as [53] Pout =(Gcγ)−Gd,(21) where Gdis the diversity order and Gcis the coding gain. Regarding the passive RIS with NLOS, its system asymptotic CDF derivation, when Ps→∞,1 (PJm)M,( 1 PJm)M+u, and (1 Ps)a+1 2terms approximate zero and become neglible, and γbecomes dominant. The power of γ, which is a+1 2, yields the diversity order. Note that, as it is clearly expressed in Appendix A, the a term is dependent on the number of reflecting elements. In other words, the number of reflecting elements defines the diversity order. Substituting the values of a term in Appendix A,a+1 2is calculated as 0.8N.The obtained result is consistent with the diversity order analysis. On the other hand, the remaining constant terms, which are presented in the following, represent the system coding gain, which is Gp c=1 ρaba+1(a+1)(a+1)(M)1 u=0 (a+3 2)(M+u) (u+1)(a+3−2˜u 2). Regarding the asymptotic performance of the active RIS with NLOS, when Ps→∞,1 (PJm)M,( 1 PJm)M+t, and ( 1 Ps)a+1 2 approximate zero and become neglible, and γbecomes dominant. The power of γ, which is a+1 2, yields the diversity order. Substituting the values of a term in Appendix Asection, a+1 2is calculated as 0.8N. The obtained result is consistent with the diversity order analysis. The remaining constant terms, which are presented below, represent the system coding gain, which is Ga c=1 ρaba+1(a+1)(a+1)(M)(N)(σ2 ng)N× 1 u=0 (a+3 2) (u+1)(a+3−2˜u 2)u t=0u tρ2(u−t)(N+u−t)(M+t) (1 σ2 ng)N+u−t. Regarding the asymptotic performance of the passive RIS with LOS, when Ps→∞,1 (PJm)M,( 1 PJm)M+t,( 1 Ps)a+1 2, and (−1 2Psf)k=0approximate to zero and become neglible and the γterm becomes dominant. The power of γ, which is a+3 2+k, yields the diversity order. Substituting the values of a term in Appendix Asection, a+3 2is calculated as TAB LE 4. System Configurations 1+0.8N. The obtained result is consistent with the diversity order analysis. The remaining constant terms, which are presented below represents the system coding gain, which is Gp+d c=(a+2) (ρb)a+1(a+1)(a+1)f(a+4)(M)1 u=0 (a+5 2)(M+u) (u+1)(a−2u+5 2). Regarding the active RIS with LOS asymptotic performance, when Ps→∞,1 (PJm)M,( 1 PJm)M+t,(1 Ps)a+1 2, and (−1 2Psf)k=0terms approximate to zero and become neglible and γterm becomes dominant. The power of γ, which is a+3 2+k, yields the diversity order. Substituting the values of a term in Appendix Asection, a+3 2is calculated as 1+0.8N. The obtained result is consistent with the diversity order analysis. The remaining constant terms, which are presented below represents the system coding gain, which is Ga+d c=(a+2) (ρb)a+1(a+1)(a+1)f(a+4)(σ2 ng)N(M)(N)× 1 u=0 (a+5 2) (u+1)(a−2u+5 2)u t=0u tρ2(u−t)(N+u−t)(M+t) (1 σ2 ng)N+u−t. IV. NUMERICAL RESULTS This section validates the analytical and asymptotic derivations by means of Monte-Carlo-based computer simulations. The Matlab©environment is considered for the related performance analysis and 106channel realizations are generated. The following parameters are considered for the system model configuration. The number of reflection unit, which is N,isset to 2, 4, 6, 12, 30, 50, 60, and 100 for different performance metrics. The number of CCI terminals, which is M,issetto 0, 1, and 2. The parameters dMT−RIS,dRIS−BS, and dMT−BS are set to 10. Since the non-orthogonal CCI terminals are randomly deployed, dmj−BS is set to 1 and 10 for near and far NOMA users, respectively. Further, the vterm is set to 2 and 3. The transmit power of the source terminal, which is Ps, is set to P and the transmit power of the jth interferer, which is Pj,issettoP jd−v mj−BS. The target rate, which is Rth, is set to 10 bps/Hz. The ρterm is set to 1.1, 1, and 0.5 for active, passive, and absorptive modes, respectively. The simulation parameters are also presented in Table IV.The 2056 VOLUME 6, 2025 ×∞ 0 (γF+1)a+3 2+kγM−1 Fe−γF PJmdγF   I7 .(34) By means of [39, Eq. (1.110)],I7is further simplified as ∞  u=0 (a+2k+5 2) (u+1)(a+2k−2u+5 2)∞ 0 γM+u−1 Fe−γF PJmdγF   I8 .(35) By means of [39, Eq. (3.381.4)], the integral expression in I8is solved as I8=(M+u) 1 PJmM+u.(36) In summary, the final expression is obtained as in (6). Regarding the system model that communicates via active RIS with NLOS, bypassing the direct link in (3),(22), and (23), the following expression is written Fa A(γ)=Pr ρ N  i=1|hi||gi|≤γ =Pr N  i=1|hi||gi|≤γ ρ =γ 0 FN i=1|hi||gi|γ ρdγ =1 ba+1(a+1)ρaγ 0 γaexp −γ ρbdγ. (37) By means of [39, Eq. (3.381.1)],(37) is solved as ρ (a+1)γa+1,γ ρb.(38) By definition [60, Eq. (11)],(38) is obtained as: Fa A(γ)=ρ−ρ (a+1,γ ρb) (a+1) .(39) By means of [59, Eq. (06.06.06.0001.02)],Fa A(γ)= ρ(γ ρb)a+1/(a+1)(a+1). Utilizing the obtained results in (39), following expressions are obtained. Fγa BS (γ)=Fa Aγ Psρ2γG+γF+11 2.(40) In this regard, substituting the approximated (39) into (40), the following integral expression is obtained Fγa BS (γ)=1 ρaba+1(a+1)(a+1) γ Psa+1 2 ×∞ 0∞ 0ρ2γG+γF+1a+1 2fγG(γG)fγF(γF)dγGdγF   I9 . (41) Substituting the related PDF expressions into (41),I9is written as 1 σ2 ngN1 PJmM1 (M)(N) ×∞ 0∞ 0ρ2γG+γF+1a+1 2   ×γN−1 Ge−γG σ2 ngγM−1 Fe−γF PJmdγGdγF   I10 .(42) By means of [39, Eq. (1.110)],I10 is further simplified as: ∞  u=0 (a+3 2) (u+1)(a+3−2u 2)∞ 0∞ 0ρ2γG+γFu   ×γN−1 Ge−γG σ2 ngγM−1 Fe−γF PJmdγGdγF   I11 .(43) Note that since (a+1)/2 is not an integer in a+1 2 u,x y= (x+1) (y+1)(x−y+1)[39] is utilized for further simplification. By performing basic algebraic manipulations and using [39, Eq. (1.111)],I11 is further simplified as u  t=0u tρ2(u−t)∞ 0 γN+u−t−1 Ge−γG σ2 ngdγG   ×∞ 0 γM+t−1 Fe−γF PJmdγF   I12 .(44) By means of [39, Eq. (3.381.4)], the integral expressions in I12 are solved as I12 =(N+u−t) 1 σ2 ngN+u−t (M+t) 1 PJmM+t.(45) In summary, the CDF expression of active-RIS with NLOS is presented in (8). Regarding the passive RIS with NLOS counterpart, by setting the active RIS amplification coefficient to 1 in (37) and also eliminating the active-RIS companent in (40),the following passive expression is obtained. Note that the term ρis retained in the derivations for the absorptive counterpart. Fγp BS (γ)=Fp Aγ Ps (γF+1)1 2,(46) Substituting the approximated (39), which is Fp A(γ)= ρ(γ ρb)a+1/(a+1)(a+1), into (46), the following expression is obtained Fγp BS (γ)=1 ρaba+1(a+1)(a+1) γ Psa+1 2 VOLUME 6, 2025 2063 ÖZDURAN ET AL.: ACTIVE, PASSIVE, AND ABSORPTIVE RIS-AIDED 6G NETWORK UNDER NON-ORTHOGONAL CCI ×∞ 0 (γF+1)a+1 2fγF(γF)dγF   I13 .(47) Substituting the related PDF expressions into (47),I13 is written as 1 PJmM1 (M) ×∞ 0 (γF+1)a+1 2γM−1 Fe−γF PJmdγF   I14 .(48) By means of [39, Eq. (1.110)],I14 is further simplified as ∞  u=0 (a+3 2) (u+1)(a+3−2u 2)∞ 0 γM+u−1 Fe−γF PJmdγF   I15 ,(49) Since (a+1)/2 is not an integer in a+1 2 u,x y= (x+1) (y+1)(x−y+1)[39] is utilized for the further simplification. By means of [39, Eq. (3.381.4)], the integral expressions in I15 are solved as I15 =(M+u) 1 PJmM+u.(50) APPENDIX B PROOF OF PROPOSITION 2 Starting with the active RIS when the source has a LOS link with the destination terminal, substituting the related CDF expression, (5), into EP formula, (9), following integral expression is obtained ¯ Pea+d=1 2√π∞ 0 γa+2k+2 2exp(−γ)dγ. (51) By means of [39, Eq. (3.381.4)],(51) is solved as: a+2k+4 2. The final expression is written as in (10).Likewise, for passive RIS with LOS/direct-link, following a similar procedure and utilizing (6) and (9), and also solving the integral expression, a+2k+4 2is obtained. The final EP expression for passive RIS with LOS / direct-link is presented in (11). 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Papoulis and U. Pillai, Probability, Random Variables and Stochastic Processes, 4th ed. New York, NY, USA: McGraw-Hill, 2001. [59] Wolfram Research, “The wolfram functions site,” 2025. Accessed: Jun. 1, 2025. [Online]. Available: http://functions.wolfram.com/ [60] E. W. Weisstein, “Gamma function.” Accessed: Jun. 1, 2025. [Online]. Available: https://mathworld.wolfram.com/GammaFunction.html VOLKAN ÖZDURAN (Senior Member, IEEE) received the graduation degree from the Department of Electronics, Söke Technical High School, Aydın, Türkiye, in 1997, the A.Sc. (with First Hons.) degree in industrial electronics, and the B.Sc., M.Sc., and Ph.D. degrees in electrical and electronics engineering from Istanbul University, Istanbul, Türkiye, in 2002, 2005, 2008, and 2015, respectively. During the Ph.D. studies he was with the Department of Electrical Engineering, Dynamic Spectrum Management (DSM) research group led by Prof. Dr. John M. Cioffi, best known as the “father of DSL”, Stanford University, Stanford, CA, USA, and Department of Electrical Engineering, California Institute of Technology, Pasadena, CA, and Princeton University, Princeton, NJ, USA, respectively. His research focuses on various aspects of the 6G wireless networks. He received the Doçent title from the Turkish Interuniversity Council, Ankara, Türkiye in 2022. VOLUME 6, 2025 2065 ÖZDURAN ET AL.: ACTIVE, PASSIVE, AND ABSORPTIVE RIS-AIDED 6G NETWORK UNDER NON-ORTHOGONAL CCI EHSAN SOLEIMANI-NASAB received the B.Sc. degree in electrical engineering from the Iran University of Science and Technology, Tehran, Iran, in 2006, and the M.Sc. and Ph.D. degrees in communication systems from the K. N. Toosi University of Technology, Tehran, Iran, in 2009 and 2013, respectively. From April 2012 to October 2012, he was a Visiting Researcher with the Department of Signals and Systems, Chalmers University of Technology, Gothenburg, Sweden. From June 2014 to August 2014, he worked as a Research Associate with the Department of Electrical and Electronics Engineering, Özye˘ gin University, Istanbul, Türkey. Since 2014, he has been with the Graduate University of Advanced Technology, Kerman, where he is currently an Associate Professor. From 2022 to 2023, he was a Guest Researcher with the Department of Electrical and Electronics Engineering, Koç University, Istanbul, Turkey. He has author or coauthor of more than 60 journal and conference publications. His research interests include optical wireless communications, radio wireless communications, and signal processing in communications. He was on the technical program committees for various IEEE conferences. He has been on the editorial board of FRONTIERS IN COMMUNICATIONS AND NETWORKS. He is an active reviewer for various IEEE TRANSACTIONS and other journals. NIKOLAOS NOMIKOS (Senior Member, IEEE) received the Diploma in electrical engineering and computer technology from the University of Patras, Patras, Greece, in 2009, and the M.Sc. and Ph.D. degrees from the Information and Communication Systems Engineering Department, University of the Aegean, Samos, Greece, in 2011 and 2014, respectively. Since 2025, he has been an Assistant Professor of Mobile and Satellite Communications Systems, Department of Information and Communication Systems Engineering, University of the Aegean, Samos, Greece. Moreover, he is a Project Manager with Four Dot Infinity P.C. His research interests include cooperative communications, nonorthogonal multiple access, non-terrestrial networks, and machine learning for wireless networks optimization. Prof. Nomikos is an Editor of IEEE TRANSACTIONS ON COMMUNICATIONS and Associate Editor for Frontiers in Communications and Networks. He is a Member of the IEEE Communications Society and the Technical Chamber of Greece. IMRAN SHAFIQUE ANSARI (Senior Member, IEEE) received the B.Sc. degree in computer engineering from the King Fahd University of Petroleum and Minerals (KFUPM), Dhahran, Saudi Arabia, in 2009 (with First Honors) and the M.Sc. and Ph.D. degrees from King Abdullah University of Science and Technology (KAUST), Saudi Arabia, in 2010 and 2015, respectively. Since 2018, he has been a Lecturer (Assistant Professor) with University of Glasgow, Glasgow, U.K. He has been affiliated with IEEE since 2007 and was in various capacities. He is currently on IEEE European Public Policy Committee from 2023 to 2024 and IEEE LEO SatS Future Directions since 2022. He was on the IEEE Nominations and Appointments (N&A) Committee from 2020 to 2021 and IEEE Communication Society Young Professionals (ComSoc YP) Board from 2016 to 2021. Sicne 2017, he has been a part of the IEEE 5G Tech Focus Publications Editorial Board. He is an active reviewer for EPSRC research grants, various IEEE Transactions and various other journals. He has authored or coauthored more than 100 journal and conference publications. His current research interests include free-space optics (FSO), satellite communications, underwater communications, physical layer secrecy issues, and reconfigurable intelligent surfaces / intelligent reflective surfaces (RIS / IRS), among others. He was also a TPC for various IEEE conferences. He is a recipient of appreciation for an exemplary reviewer for IEEE Transaction on Communications (TCOM) in 2018 and 2016, respectively, a recipient of appreciation for an exemplary reviewer for IEEE Wireless Communications Letters (WCL) in 2017 and 2014. He was also the recipient of Postdoctoral Research Award (PDRA) (first cycle) with Qatar national research foundation (QNRF) in 2014, KAUST Academic Excellence Award (AEA) in 2014, and IEEE Richard E. Merwin Student Scholarship Award in 2013. He has co-organized the GRASNET’2016, 2017, 2018 workshops in conjunction with IEEE WCNC’2016, 2017 and IEEE Globecom 2018. PANAGIOTIS TRAKADAS received the Dipl. Ing. degree in electrical and computer engineering and the Ph.D. degree from the National Technical University of Athens (NTUA). He has worked with Hellenic Aerospace Industry (HAI), as a Senior Engineer, on the design of military wireless telecommunications systems, and the Hellenic Authority for Communications Security and Privacy, where he was the the Director of the Division for the Assurance of Infrastructures and Telecommunications Services Privacy. He is currently an Associate Professor with the National and Kapodistrian University of Athens, and a Technical Manager with Four Dot Infinity P.C. He has been actively involved in many EU FP7 and H2020 Research Projects. He has authored or coauthored more than 130 papers in magazines, journals, and conference proceedings. His research interests include the fields of wireless and mobile communications, wireless sensor networking, network function virtualization, and cloud computing. He is a reviewer in several journals, including IEEE TRANSACTIONS ON COMMUNICATIONS and IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY journals. 2066 VOLUME 6, 2025