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Powerefficient fullduplex near user with power allocation and antenna selection in NOMAbased systems
EURASIP Journal on Wireless Communications and Networking volume 2024, Article number: 64 (2024)
Abstract
This paper proposes a power scaling (PS) technique aimed at mitigating the outage floor problem commonly encountered in multiuser fullduplex (FD) nonorthogonal multiple access (NOMA) systems. Two antenna modes denominated as adaptive antenna mode (AAM) and fixed antenna mode (FAM) are utilized in this work for L FD near users in close proximity. In addition, a combined method of selecting both antenna mode and near user integrated with PS is employed to improve the overall network performance. Moreover, a power allocation between the chosen near user and far user is considered. In the lowtomoderate power regions, by AAM and FAM, we achieve twice of full diversity gain and full diversity gain, respectively. The research presents mathematical expressions for deriving the average capacity and outage probability and supports the theoretical findings with simulationbased evidence. The results of this work show that PS method not only contributes to a greater spatial diversity but also leads to superior performance compared to traditional FD NOMA systems. Moreover, our proposed method overcomes the outage floor and capacity ceiling. Furthermore, the work can be developed to 6G massive MIMO technology in multiuser FD cooperative NOMA systems.
1 Introduction
The increasing demand for wireless networks has provided the necessity for effective spectrum utilization in 6G Networks [1]. To enhance spectral efficiency in 6G networks, nonorthogonal multiple access (NOMA) was introduced as an appropriate option [2, 3]. While various NOMA designs have been explored, cooperative NOMA has shown potential for enhancing system performance and extending communication coverage [4, 5]. Authors in [6] have evaluated the performance of fullduplex (FD) near user in IRSaided NOMA systems. Some works have considered cooperative structure for mobile edge computing (MEC) in wireless networks which can improve the system performance [7,8,9,10]. Additionally, employing FD structures has emerged as a promising idea to address bandwidth efficiency concerns, allowing in the same frequency band for simultaneous reception and transmission[11]. However, imperfect selfinterference cancellation in FD relay systems can impact on the performance, particularly in Rayleigh fading channels [12, 13].
Beamforming methods, such as those detailed in [14,15,16], multiplies the transmitted signal from each antenna in a complex number to improve performance parameters as detailed in [17]. Additionally, a beamforming design for AF FD twoway relays has been considered in [18]. Furthermore, a FD relaying protocol with cochannel interference was studied in [19]. In [20], the authors introduced a joint relay and antenna selection structure for FD DF cooperative system over Rayleigh fading environments.
The concept of relay selection is considered as an efficient method to improve diversity while keeping complexity at a minimum level. In the context of halfduplex structures, initial considerations regarding relay selection were outlined in [21]. A rate maximization was conducted for AF relaying in which relay selection has been employed[22]. Additionally, relay selection for halfduplex DF relays has been evaluated in [17, 23], but it has a loss in spectral efficiency because of the halfduplex structure. To solve this, FD relay selection was used in [24, 25]. However, designs presented in [24, 26, 27] encountered a performance floor for highpower regime. The study in [28] evaluates the performance of a FD twoway relaying network, including the simultaneous impact of CEE, CCI and RSI.
In existing literature, joint beamforming (BF) and virtual MISO relaying has been explored in [29], with a relay selection approach introduced. Furthermore, various antenna selection strategies were introduced to improve the performance of relaying networks with multiple antenna relays in [30, 31], resulting in a significant performance improvement. Moreover, [32] has investigated the outage performance of the FD DF system over Nakagamim fading environment. The authors in [33] have supposed fixed receive and transmit antennas in DF FD relay structures, necessitating efficient algorithms to remove the error floor.
1.1 Motivations and related works
NOMA techniques are more efficient in terms of spectral usage in comparison with orthogonal multiple access (OMA), making them a better option for advanced communication systems like 5 G and beyond. Additionally, FD nodes have the potential to increase spectral efficiency. In this work, the research focuses on a multiuser FD cooperative NOMA system that integrates FD capabilities to take the advantages of both NOMA and FD techniques. The existing literature given in Table 1 indicates that current methods could not achieve full diversity order. To improve the system performance, the study introduces nearuser selection and antenna mode selection methods in multiuser FD NOMA systems to obtain additional spatial diversity gain. One major challenge in FD systems is the presence of outage floor, particularly when there is no direct channel between the base station (BS) and far user. Existing studies have not been able to effectively address this outage floor, highlighting the need for solutions to enhance the performance of FD systems in such scenarios.
In this work, we introduce a power scaling (PS) technique that addresses the issue of outage floor, even in scenarios where there is no direct channel between the base station (BS) and far user. This method significantly enhances the system performance in comparison with traditional FD NOMA systems and eliminates the capacity ceiling. In the situations that it is not possible to have a direct channel between the BS and far user due to large obstacles, long distances and power limitations, our proposed method is an optimal choice for transmission. Furthermore, we utilize nearuser selection and antenna mode selection to gain additional spatial diversity. To the best of our knowledge, the combination of antenna mode selection, nearuser selection, and power scaling in the analysis of multiuser FD cooperative NOMA systems has not been explored in existing literature. In addition, this work can be extended to 6G massive MIMO technology in the multiuser FD cooperative NOMA systems.
1.2 Contributions
In this paper, a power scaling technique is introduced to tackle the issue of outage floor in the multiuser FD cooperative NOMA systems even when there is no direct channel between the BS and far user. The system consists of L FD near users operating over a Rayleigh fading scenarios. To enhance the system performance, joint near user and antenna mode selection methods are applied in multiuser FD cooperative NOMA systems. Each FD near user has multiple antennas for receiving and transmitting information. The selection of receiving and transmitting antennas is according to the instantaneous channel conditions, and one near user is chosen to optimize the signaltointerference and noise ratio (SINR) of the multiuser FD cooperative NOMA system. The main contributions of this research are outlined as follows:

(1)
The paper introduces two antenna selection designs, denominated as adaptive antenna mode (AAM) and fixed antenna mode (FAM), for the multiuser FD cooperative NOMA systems (see Fig. 1). These schemes involve selecting one near user according to instantaneous channel variations. The process of antenna mode selection for FAM and AAM is performed by the optimization problems for the chosen near user, taking into consideration the power allocation between the chosen near user and far user. The AAM and FAM designs enable the multiuser FD cooperative NOMA system to achieve almost twice of full diversity gain and full diversity gain for small to moderate power regime, respectively.

(2)
By applying the power scaling technique at the base station, the outage floor attributed to residual selfinterference (RSI) is eliminated. Diversity gain for the multiuser FD cooperative NOMA system with L FD near users approaches 2L and L for the AAM and FAM designs, respectively. The power scaling technique mitigates the effect of RSI, changing the highSNR diversity gain from zero to roughly 2L and L for the AAM and FAM designs, respectively.

(3)
New closedform expressions for outage probability and average capacity are derived for the proposed AAM and FAM designs in the multiuser FD cooperative NOMA systems, taking into consideration the impact of imperfect selfinterference cancellation. The asymptotic behavior of the system is investigated to gain more insights, which indicates an outage floor in highpower regions. By proposing an efficient PS method, the aforementioned outage floor attributed to selfinterference is eliminated, and the system obtains diversity gain for low selfinterference levels. Furthermore, the capacity ceiling is removed by the aforementioned PS method. The work emphasizes the importance of this method in enhancing the system performance. The review of existing literature shows that whereas past studies have investigated combined antenna and relay selection in general FD cooperative systems, none have specifically examined nearuser selection and AAM integrated with PS in multiuser FD cooperative NOMA systems. The evaluation of performance metrics shows enhancements compared to previous researches.

(4)
The performance analysis of the system, taking selfinterference into account, is validated using MonteCarlo simulations, and the impacts of various parameters are assessed.
1.3 Organizations and notations
The remainder of this paper is organized as follows. In Section II, the methods for the multiuser FD cooperative NOMA system are provided in which study design, setting, participants or materials, interventions and different analyses are described. Results and discussion are given in Section III. Section IV concludes the paper.
Notation: erfc(w) and Q(w) specify the complementary error function and Gaussian Qfunction, respectively.
2 Methods/experimental
2.1 Study design
In this paper, a power scaling technique is introduced to tackle the issue of outage floor in the multiuser FD cooperative NOMA systems even when there is no direct channel between the BS and far user. The system consists of L FD near users operating over a Rayleigh fading environment. To enhance the system performance, joint near user and antenna selection methods are applied in multiuser FD cooperative NOMA systems. Each FD near user has multiple antennas for receiving and transmitting the signals. An optimization problem is formulated to select the receiving and transmitting antennas according to instantaneous channel conditions, and one near user is chosen to enhance the SINR of multiuser FD cooperative NOMA system.
Monte Carlo simulations are conducted to verify the theoretical analysis, focusing on the outage probability of the multiuser FD cooperative NOMA system, and the performance of adaptive antenna mode (AAM) and fixed antenna mode (FAM) structures. The simulations consider different values for the number of near users (L) and the selfinterference level (\(\eta\)). Additionally, the effects of proposed methods are investigated, and the results based on performance metrics are compared.
2.2 Setting
The paper discusses a multiuser FD cooperative NOMA system in which a far user communicates with a BS with the aid of multiple near users. The research was carried out in a simulated environment specifically designed to simulate this system. This simulation setup provided a controlled setting to evaluate proposed techniques aimed at improving the system performance. Various scenarios were examined and simulated to obtain the effectiveness of proposed techniques. The assumption was made that there is no direct channel between BS and far user due to power constraints over long distances. In the case of extending the proposed scheme to the scenario with direct link between BS and far user, the analysis of diversity order could not be tractable and complicated integrals are required to be computed. Moreover, performance metrics will not have closedform solution and the complexity increases, and thus, we have omitted the aforementioned scenario in this paper.
The near users work in FD mode for receiving and transmitting information, denoted by \(U_k, k=1,2,...,L\). Moreover, \(h_\textsf{S,j}^{u}\) and \(h_{j,\mathsf D}^{r}\) represent the channel fading coefficients from the BS to the receive antenna u, \(u=1,2,...,B/2\), of near user j, \(j=1,2,3,...,L\), i.e., \(U_j\), and from \(U_j\)’s transmit antenna r, \(r=B/2+1,...,B\), \(r\ne u\), to far user, respectively. Each FD near user has multiple antennas for receiving and transmitting the signals. The selection of the optimal combination of antennas for transmission and reception is crucial, and a specific near user is chosen to enhance the SINR of the system.
The primary challenge of the considered system is the residual selfinterference (RSI) at the FD near user, which arises from imperfect selfinterference cancellation, adding complexity to the performance analysis of the system. The RSI which is considered as the primary drawback of the FD system is attributed to outdated CSI throughout the process of selfinterference cancellation. In a block fading model, it is considered as a channel estimation error. This assumption stands to the reason that RSI is a result of channel estimation error which is unchanged over a block. This permits the system to obtain the information contained in the RSI by accurately evaluating the channel. As a result, the RSI channel can be effectively modeled as a block Rayleigh fading channel, and the selfinterference channel at near user \(U_j\) is denoted by \(I_{j,j}^{r\rightarrow u}\)[25, 34].
All channels are assumed to be under Rayleigh flat fading and additive white Gaussian noise (AWGN), with the assumption of independence among these channels. If near user \(U_j\) at time m is chosen to collaborate in the message transmission, the BS sends its symbol.
The received signal at \(U_j\) is obtained as
The notation \(z_j(m)\) stands for additive white Gaussian noise (AWGN) with zero mean and unit variance. \(x_{2}(m)\) and \(x_{1}(m)\) denote the signals for the far user and selected near user, respectively. Additionally, \(\hat{x}(m  m_0)\) indicates the selfinterference signal, where \(m_0\) signifies the processing delay at the near user. Power allocation coefficients for the far user and chosen near user are denoted by \(a_2\) and \(a_1\), with the condition that \(a_2 > a_1\) and \(a_1 + a_2 = 1\) to ensure fairness among users. The near user can utilize successive interference cancellation (SIC) to initially detect the far user, who has higher transmitted power and less interference signal. Then, the signal of the far user can be obtained from the superposed signal, assuming perfect SIC implementation at the near user. Moreover, the received SINR at the jth near user to identify the signal for far user is written as
where \(\sigma ^2\) denotes the noise power spectral density. Moreover, \(w=1\) and \(w=0\) denote FD and halfduplex (HD) modes, respectively. The received signal at far user is
The transmitted power from BS and the selected near user is denoted by \(P_\textsf{S}\) and \(P_\textsf{U}\), respectively. Additionally, \({w_D}(m)\) represents an AWGN noise with variance equal to 1 and zero mean. The received signaltonoise ratio (SNR) at far user is given by
In the case of imperfect successive interference cancellation (SIC), OTFSBased NOMA can be used which mitigates the aforementioned interference. In [35], an iterative SIC turbo receiver is proposed for OBNOMA system which can overcome imperfections in the SIC process and uncertainties in the channel state information (CSI).
2.3 Participants or materials
This research involved one far user, multiple FD near users and one base station (BS) in a multiuser FD cooperative NOMA system which are considered as simulation nodes. These nodes simulated the behaviors and communication capabilities of the participants. Additionally, binary phase shift keying (BPSK) modulation was used within the simulation setup to generate source data for evaluating the system performance.
2.4 Interventions and comparisons
This paper considers two modes for the FD near user. Moreover, PS method is proposed in the following subsections which can overcome the outage floor caused by imperfect interference cancellation at FD near user. The research was performed in a simulated environment that models a multiuser FD cooperative NOMA system. The theoretical and simulation results are used to investigate the methods for improving the system performance through our proposed methods. Different scenarios were analyzed and simulated to assess the effectiveness of the methods. Different values for number of near users (L) and selfinterference level (\(\eta\)) are considered in the simulations. Moreover, the effects of proposed methods are investigated, and the results based on performance metrics are compared to each other. The interventions in this work composed of comparing the performance metrics achieved through two different methods:

(1)
FAM configuration: In this structure, multiple labeled receiving and transmitting antennas are utilized. These antennas are designated with specific labels and cannot change their role as transmitting or receiving antennas. The selected near user (SN) can be determined as follows:
$$U_{\text {SN}}= \arg \mathop {\max }\limits _{j} {W_j},$$(5)$${W_{j}} = \min \left\{ {\gamma _{D\rightarrow D_{j}}^{r \rightarrow u},\gamma _{D\rightarrow D}^{{r} \rightarrow {u}}} \right\} ,$$(6)where \({\gamma _{D\rightarrow U_{j}}^{r \rightarrow u}}\) and \({\gamma _{D\rightarrow D}^{r \rightarrow u}}\) are defined as in Eqs. (2) and (4).

(2)
AAM configuration: In this setup, there are multiple antennas at the FD near users. Each antenna can work as either a transmitter or a receiver, and they have the flexibility to switch roles between transmitting and receiving. Consequently, the selected near user is determined as
$$U_{\text {SN}} = \arg \mathop {\max }\limits _{j} \max \left\{ {{W_{1}},{W_{2}}} \right\} ,$$(7)$${W_{1}} = \min \left\{ {\gamma _{D\rightarrow D_{j}}^{r \rightarrow u},\gamma _{D\rightarrow D}^{{r} \rightarrow {u}}} \right\} ,$$(8)$${W_{2}} = \min \left\{ {\gamma _{D\rightarrow D_{j}}^{u \rightarrow r},\gamma _{D\rightarrow D}^{{u} \rightarrow {r}}} \right\} ,$$(9)To simplify the analysis, we specifically consider the case where the number of antennas at FD near user is equal to 2.
2.5 Analysis of FAM
This section investigates the performance of the system utilizing a fixed antenna mode. The investigation focuses on determining the performance metrics. Furthermore, it examines the finiteSNR diversity gain in situations characterized by minor selfinterference levels and highpower regime.
2.5.1 Outage probability
In FAM design, the near user with highest SINR is adopted in the system with the FAM scheme. The outage probability of this configuration, which the system involves L near users, is then determined as
Furthermore, \(\lambda _{1}=\lambda _{S,j}\), \(\lambda _{3}=\lambda _{j,D}\), and \(\lambda _{LI}\) represent the rate parameters of the random variables \({{\left {h_{S,j}^{u}} \right }^2}\), \({{\left {h_{j, D}^{r}} \right }^2}\) and \({{\left {I_{j,j}^{r \rightarrow u}} \right }^2}\), respectively. It is assumed that \({\eta _j} = {\lambda _1}/{\lambda _{LI}}\). The detailed derivation of this relation is provided in Appendix A. In the highSNR region where \(P_{S}\) and \(P_{U}\) tend to infinity, the function \(H_{j}^{(\infty )}(x)\) approaches
This phenomenon occurs because the SINR is primarily influenced by the selfinterference at the FD near user, and increasing the transmitted power does not mitigate this interference. Consequently, alternative strategies like interference cancellation or optimizing relay placement can provide more efficiency in enhancing system performance under these circumstances.
We have two types of diversity gain. The first one is finiteSNR diversity gain and the second one is highSNR diversity gain. Diversity gain is the same as diversity order (DO) which can be defined as the asymptotic slope of the logarithmic plot of outage probability against SNR (in dB). Higher values of diversity gain indicate superior performance compared to lower values of diversity gain. The finiteSNR diversity gain can be written as
Here, \(\gamma\) represents the average SNR of the link between the BS and near user, while \(P_\text {out}\) indicates the outage probability at SNR \(\gamma\). By conducting certain algebraic simplifications, the finiteSNR diversity gain is obtained as
Furthermore, employing Taylor series expansions, \(\text {DO}\) is approximated as
where \({\kappa _j} = \frac{{{P}{\eta _i}}}{\lambda _{j,\textsf{D}} + \lambda _{\textsf{S},j}}\). Therefore, DO is related to the transmitted power, channel gains, selfinterference level at FD near user and the number of near users. In scenarios where the selfinterference is minimal (\(\eta _j\rightarrow 0\)), \(\text {DO}\) approaches L and the system performance improves. Additionally, when the value of selfinterference is nonnegligible (\(\eta _j\ne 0\)) and the SNR is high, \(P_{U}\rightarrow \infty\) and \(\kappa _j\rightarrow \infty\). This situation results in a diversity order of zero due to existing the outage floor imposed by selfinterference at FD near user.
2.5.2 Average capacity
The outage probability in relation (10) is written as
In the given formulation, let \(\mathcal {S}=\{1,2,\ldots ,L\}\), \(\mathcal {A}\) be a subset of \(\mathcal {S}\), and the sum is performed over all feasible subsets of \(\mathcal {S}\) [36]. Consequently, the average capacity is determined as
where \(\mathcal {A}\) specifies the size of \(\mathcal {A}\) and
Employing the residue theorem, B(x) is given as
where a and \(b_i\) can be written as
By using the following identity [36],
The average capacity is written as
where \(E_{i}(\cdot )\) is the exponential integral function and \(\beta ={\sum \limits _{j \in A}( {\frac{{{\lambda _1}x}}{{P\left( {{a_2}  {a_1}x} \right) }} + \frac{{{\lambda _3}x}}{P}}) }\). In the case of tending SNRs to infinity, the average capacity can be obtained as
Utilizing the identity \(\int {\frac{1}{{b + ax}}} dx = \frac{1}{a}\ln \left {ax + b} \right\), the following integral transforms into:
Furthermore, by equating B(x) in (17) and (18) as \(x\rightarrow \infty\), it is demonstrated that \(a + \sum \limits _{j \in \mathcal {A}} {\frac{{{b_j}}}{{{\eta _j1}}}} = 0\). Utilizing this, \(X(\infty )\) can be determined as
Substituting (24) and \(X(0)=0\) into (22) yields
This analysis demonstrates that there exists a rigid limitation on the average capacity even when the transmitted powers grow infinitely. This limit arises from the nonzero value of selfinterference.
2.6 Analysis of FAM with power scaling
For equal power allocation (\(P_\textsf{S}=P_\textsf{U}\)), a significant outage floor emerges in highSNR region, affecting the highSNR diversity gain. To tackle this issue, the system performance is evaluated by applying power scaling at the BS, which effectively alleviates the outage floor. This strategy enables the system to achieve full diversity order.
Moreover, the transmit power of the BS is adjusted according to the instantaneous channel fluctuations from the BS to the selected near user. This method facilitates the system in realizing its full diversity gain, mitigates the outage floor, and ultimately enhances the overall system performance.
In this case, \(\Pr \left( {{\gamma _{D\rightarrow U_{j}}^{r \rightarrow u}}> x} \right)\) can be derived as,
where \(a = {\left {{h_{LI,j}}} \right ^2}\), \(k = \sqrt{\frac{{wPa + x}}{{P^2\left( {{a_2}  {a_1}x} \right) }}}\), \(f = \frac{x}{{P^2\left( {{a_2}  {a_1}x} \right) }}\), and \({k_2} = \sqrt{\frac{w}{{P\left( {{a_2}  {a_1}x} \right) }}}\). Hence, the outage probability is obtained as
where \({F_{\gamma _i}}\) is obtained as
where the following identity from [36] is employed in the aforementioned derivation.
By utilizing the identity \(erfc(x) \le \exp \left( {  {x^2}} \right)\), along with the two subsequent characteristics, an upper bound on the outage probability can be achieved.
where \({G_{i}}\) can be provided as
In highpower regions, as \({k_2} \rightarrow 0\), the system achieves full diversity gain L. Moreover, the average capacity can be obtained as
Then, the approximation of average capacity can be obtained as
As seen, the lower bound gets infinity. Then, we do not have any capacity ceiling for our proposed design.
2.7 Analysis of AAM
If the roles for the receiving and transmitting antennas are interchanged, the selfinterference channel remains unchanged for our scheme. Furthermore, the optimization problem can be formulated as
Therefore, the CDF of \(\gamma _i\) can be derived as
Next, let us define \({\gamma _{\max }}={\max }\{\gamma _1,\ldots ,\gamma _L\}\). Then, the cumulative distribution function (CDF) of \(\gamma _{\max }\) is given by \(F_{\gamma _{\max }}(x)=\prod \limits _{j= 1}^L F_{\gamma _j}(x)\). The proof of aforementioned derivation is presented in Appendix B. By using Taylor series expansion, \(\text {DO}\) is approximately obtained as
where \({\zeta _j} = \frac{{{P}{\eta _j}}}{{{{\lambda _{\textsf{S},j}} + {\lambda _{j,\textsf{D}}}}}}\). Therefore, DO is related to the transmitted power, channel gains, selfinterference level at FD near user and the number of near users. Notably, as \({\eta _j} \rightarrow 0\), \({\zeta _j} \rightarrow 0\), and the diversity order (DO) approaches 2L. This signifies that with AAM structure, the number of effective channels between the BS and L near users, and between L near users and the far user, reaches 2L. Consequently, in the scenario where selfinterference diminishes to zero, the diversity order converges to 2L.
Overall, power scaling technique can help to overcome the outage floor observed in highSNR regime. This can lead to improved performance and reliability in highSNR regions. As PS is utilized, the CDF of \(\gamma _i\) is obtained as
To prove that \(\text {DO}\rightarrow 2L\), we can employ the Taylor series expansion of the diversity gain function \(\text {DO}(\text {SNR})\) around \(\text {SNR} = \infty\). Since the diversity gain typically increases linearly with SNR for most communication systems, we can write \(\text {DO}(\text {SNR}) = a\text {SNR} + b\) where a and b are constants. Taking the derivative of \(\text {DO}(\text {SNR})\) with respect to \(\text {SNR}\), we get \(\frac{dDO(\text {SNR})}{d(\text {SNR})} = a\). Thus, the finiteSNR diversity order \(\text {DO}\) is simply a, which is a constant. Since the diversity gain increases linearly with SNR, the slope a in the Taylor series expansion is the rate at which the diversity order grows as SNR approaches infinity. Therefore, in this case, we have proved that \(\text {DO} = 2L\). It stands to the reason that \(\text {DO}\) approaches a constant value of 2L as SNR goes to infinity.
3 Results and discussion
This section evaluates the performance of previously discussed system in details. The simulations are performed in MATLAB R2021b, and different functions in this software are used to generate Rayleigh fading channel coefficients and noise components. The configuration of the system is given in Fig. 2. Based on this figure, all nodes composed of BS, L FD near users and a far user (FU) are considered in a square region, and proposed methods are employed to transmit the signal from the BS to far user. When no power scaling is applied, the transmit power of the BS and near user is set as equal, i.e., \(P_S=P_U\), and without loss of generality, all channel gains are all set to one.
The power spectral density of noise (\(\sigma ^2\) ) is considered to be constant and we suppose that \(\sigma ^2 =1\). We consider BPSK modulation in the evaluation of outage probability and average capacity performance. Furthermore, all numerical results are averaged over \(10^6\) channel realizations. Additionally, the power allocation coefficients for chosen near user and far user are considered as \(a_1=0.2\) and \(a_2=0.8\), respectively. The Monte Carlo simulations have confirmed the theoretical analysis, highlighting the outage probability of the multiuser FD cooperative NOMA system and the performance of FAM and AAM schemes. Different values for number of near users (L) and selfinterference level (\(\eta\)) are considered in the following simulations. Moreover, the effects of proposed methods are investigated, and the results based on performance metrics are compared to each other.
3.1 Impacts of fullduplex near user on outage probability
The results in Fig. 3 for different values of \(\eta\) with \(L=2\) indicate an outage floor for AAM and FAM, which is a direct result of the impact of the selfinterference in Eq. (10). According to the outage floor which occurs in the systems with FD users, the value of outage probability decreases as SNR increases, until a point where increasing the value of SNR does not provide any significant reduction in the value of outage probability so that diversity order gets zero. The cause of this phenomenon is that there exists the selfinterference channel at FD near users and increasing the value of SNR does not mitigate the aforementioned interference. Moreover, increasing the selfinterference level at FD near users degrades the system performance.
3.2 Impacts of employing power scaling method at the BS on the system performance
As observed in Fig. 3, employing power scaling method demonstrates superior performance compared to other schemes. The aforementioned power scaling leads to removing outage floor and achieving diversity order so that diversity order changes from zero to a nonzero value. Moreover, applying antenna mode selection at FD near users results in better performance compared to the case in which antenna mode selection is not used.
3.3 Impacts of selfinterference level on the system performance
Figure 3 illustrates that the outage probability of AAM with power scaling is directly proportional to \(\eta\), whereas its value is less affected by changes in \(\eta\) demonstrating that our proposed structure is robust to variations in selfinterference level. Furthermore, in the highSNR region, FAM with power scaling outperforms “AAM without power scaling”, even when it experiences higher levels of selfinterference.
These results verify the effectiveness of the proposed system and its power scaling approach in improving the performance. Moreover, they indicate the robustness of multiuser FD cooperative NOMA system. However, the proposed AAM with power scaling demonstrates superior performance compared to other structures and achieves diversity gain in highSNR regime.
3.4 FiniteSNR diversity order analysis
Figure 4 depicts the finiteSNR diversity gain of AAM and FAM designs for \(L = 3\) and different values of selfinterference. It is observed that although in highpower regime, diversity gain of FAM and AAM gets zero due to the presence of selfinterference, the diversity of AAM exceeds that of the FAM structure in the small to moderate power regime. Moreover, the finiteSNR diversity order for \(\eta =0\) is also illustrated in the figure.
Specifically, finiteSNR diversity gain of the AAM becomes 2L when the selfinterference level at the near user is zero, whereas the aforementioned gain is L for FAM design. Furthermore, finiteSNR diversity order of the AAM for \(\eta =0.001\) almost approaches 2L before reaching the outage floor which verifies our theoretical results.
3.5 Comparison of outage probability of AAM and FAM structures
Figure 5 illustrates the outage probability of FAM in the system with 4 near users and selfinterference level \(\eta =0.001\). The figure also indicates the performance of the AAM structure. It is noted that in “AAM with power scaling”, the transmitted power of the BS changes according to the instantaneous conditions of the channel. As expected, the AAM with power scaling method leads to superior performance compared to the AAM design without power scaling so that outage floor is removed, i.e., diversity order changes from zero to a nonzero value. Furthermore, the simulation results verify the theoretical findings. These results show the effectiveness of the proposed AAM and its ability to outperform the FAM structure, as well as the verification of theoretical results through simulations.
3.6 Impacts of L and power scaling on the average capacity of the system
Figure 6 depicts the average capacity of “AAM” and “AAM with power scaling” structures for \(L = 3, 5\). The figure illustrates that there exists a capacity ceiling for AAM design, whereas there is no capacity ceiling for AAM with power scaling (AAMPS). These observations indicate the potential advantages of AAMPS over AAM. Additionally, it shows that the capacity of the system increases as L increases, highlighting the scalability of the AAM design in accommodating more near users.
3.7 Comparison of energy efficiency of FD NOMA and HD NOMA systems
Figure 7 compares the energy efficiency of proposed FD NOMA and halfduplex NOMA (HD NOMA) systems, where energy efficiency is considered as the ratio of the throughput to total energy consumption. The figure shows that in the highSNR region, the increase in SNR has a minimal effect on the energy efficiency of FD NOMA systems, while for HD NOMA systems, energy efficiency improves as SNR approaches infinity.
Moreover, it provides insights into the energy efficiency differences between FD NOMA and HD NOMA systems so that the aforementioned metric for FD NOMA system is lower than that of HD NOMA system. Moreover, there exists a point where after that point, energy efficiency remains constant. The aforementioned point for FD NOMA system is smaller than that of HD NOMA systems.
3.8 Discussion
The effectiveness of our proposed approach in 6G Massive MIMO systems is explored in this section. Our suggested methodology is particularly suitable for deployment in 6G Massive MIMO systems which the outage probability decreases to zero and indicates the optimum performance. Hence, our proposed framework emerges as a suitable option for massive MIMO systems. For largescale MIMO near users equipped with a considerable number of receive and transmit antennas, based on the following steps, an optimization problem by machine learning algorithms can be formulated.

(1)
Identify all receive and transmit antennas at FD near users.

(2)
Segment the step 1 into some distinct subsets.

(3)
Employ max–min on the aforementioned subsets.

(4)
Obtain the maximum value of the results obtained from step 3.
4 Conclusion
The paper has presented a novel approach that combines adaptive antenna mode (AAM), power scaling, nearuser selection and power allocation for multiuser FD cooperative NOMA systems. The near user helps the BS to transmit information to the far user, but an outage floor issue has been identified in highpower regions. Power scaling techniques have been developed to address this issue and enhance the system performance. The evaluation of the asymptotic structure shows that the use of PS technique increases achievable diversity. Specifically, the FAM scheme achieves full diversity order for low selfinterference values, while the AAM scheme achieves twice of full diversity order. These results demonstrate significant improvements in diversity through the proposed techniques. Additionally, the research indicates that PS techniques can overcome the capacity ceiling and outage floor in multiuser FD cooperative NOMA systems, potentially enhancing the overall performance and reliability, especially in highpower regions.
Abbreviations
 NOMA:

Nonorthogonal multiple access
 FD:

Full duplex
 FAM:

Fixed antenna mode
 IRS:

Intelligent reflecting surface
 6G:

Sixth generation
 CDF:

Cumulative distribution function
 AAM:

Adaptive antenna mode
 CEE:

Channel estimation error
 RSI:

Residual selfinterference
 CCI:

Cochannel interference
 AWGN:

Additive white Gaussian noise
 SN:

Selected near user
 SINR:

Signaltointerference plus noise ratio
 MIMO:

Multiple input multiple output
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Funding
This study was supported by the Ministry of Science and Higher Education of the Republic of Kazakhstan through project AP13068587, titled “57–65 GHz Wireless Communication FrontEnd for Secure 5 G Applications.”
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Mahsa Shirzadian Gilan proposed the main idea and analyzed the results. She conducted simulations, evaluation, methodology, investigation, and edited the paper. Behrouz Maham contributed to reviewing and editing the paper. Both authors have read and approved the manuscript.
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This study was supported by the Ministry of Science and Higher Education of the Republic of Kazakhstan through project AP13068587, titled “5765 GHz Wireless Communication FrontEnd for Secure 5G Applications”.
Appendices
Appendix A
Proof of the expression in (10)
In this part, the outage probability of the multiuser FD cooperative NOMA system is calculated as specified in Eq. (10). By utilizing Eqs. (5) and (6), we obtain
where \({W_j}\) can be written as,
By replacing the provided expressions for \(\Pr \left\{ {{\gamma _{D\rightarrow U_{j}}^{r \rightarrow u}} > x} \right\}\) and \(\Pr \left\{ { {\gamma _{D\rightarrow D}^{r \rightarrow u}} > x} \right\}\), the outage probability is determined in the following equations
Appendix B
Proof of Eq. (34)
In this part, the CDF of \(\gamma _j\) is calculated as specified in Eq. (34). The outage probability is expressed as
In this context, the CDF of \(\gamma _j\) for AAM is denoted as \(\Pr \left\{ {{\beta _j} < z} \right\}\). Referring to the includingexcluding rule [36], the expression for \(\Pr \left\{ {\max \left\{ {{W_1},{W_2}} \right\} < z} \right\}\) is formulated as
In this case, the expressions for \(\Pr \left\{ {{W_1} >z } \right\}\), \(\Pr \left\{ {{W_2} > z } \right\}\), and \(\Pr \left\{ {{W_1}> z,\,{W_2} > z } \right\}\) are derived as
where \(W_1\), \(W_2\) are given in relations (8) and (9), respectively. After performing certain algebraic simplifications, the outage probability is obtained as detailed in Section III.
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Shirzadian Gilan, M., Maham, B. Powerefficient fullduplex near user with power allocation and antenna selection in NOMAbased systems. J Wireless Com Network 2024, 64 (2024). https://doi.org/10.1186/s13638024023913
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DOI: https://doi.org/10.1186/s13638024023913