Optimal Power Allocation and Cooperative Relaying under Fuzzy Inference System (FIS) Based Downlink PD-NOMA

Abstract

Optimal power allocation (PA) is a decisive part of the power domain non-orthogonal multiple access (PD-NOMA) technique. In PD-NOMA, users are served at the same time and using the same frequency band, but at differing power levels. In this paper, the optimization problem for PA is formulated with distance (d), signal-to-noise ratio ($SNR$), and foliage depth ($d_f$) constraints. A fuzzy inference system (FIS) addresses the optimization problem by allocating the optimal power factors (power levels) to each user in the vicinity of a 5G base-station (gNodeB). The proposed system incorporates a cooperative relaying technique at the near-user to assist the far-user facing signal degradation and greater path losses. A realistic 5G micro-cell is analyzed for downlink PD-NOMA where superposition coding (SC) is used at the transmitter side, a successive interference cancellation (SIC) scheme at the near-user, and a maximum ratio combining (MRC) technique at the far-user’s receiver, respectively. For both simple PD-NOMA and cooperative relaying PD-NOMA, the presented technique’s bit-error-rate (BER) performance is evaluated against various SNR values, and it is concluded that cooperative PD-NOMA outperforms simple PD-NOMA. By combining the presented FIS system with cooperation relaying, the proposed FIS method guarantees user fairness in PD-NOMA systems while also significantly improving performance.

1. Introduction

The demand for novel wireless communication techniques is at an all-time high to meet capacity targets and envision a new era for 5G and beyond technologies. In this regard, some promising fifth generation (5G) techniques have been acknowledged, such as non-orthogonal multiple access (NOMA) [1,2,3], interleave division multiple access (IDMA) [4,5], sparse code multiple access (SCMA) [6], low-density spreading multiple access (LDSMA) [7], pattern division multiple access (PDMA) [8], massive multiple input and multiple output (massive MIMO) [9], cooperative communication [10], and so on. Each of the above 5G techniques is unique in its own right and is classified based on a diverse range of quality of service, user fairness, spectral efficiency, low latency, and a diverse degree of freedom.

The power domain NOMA (PD-NOMA) is a 5G wireless technique that incorporates all of the above properties into a single package. In PD-NOMA [11], users around the 5G base-station (gNodeB) are served at the same frequency and time but with varying powers. Considering the downlink PD-NOMA, the superposition coding (SC) is performed at the gNodeB and SIC schemes on the serving user’s side. After decoding an undesirable user’s signal, the SIC technique [12,13] is used to eliminate its effect by subtracting it from the received signal. The PD-NOMA system has been broadly investigated for a maximum of two users in [14,15]. To achieve the capacity goals in congested NOMA networks, some recent work has been proposed in [16,17] that effectively addresses the multi-user PD-NOMA systems. The overall performance of PD-NOMA is thoroughly dependent on power allocation (PA) and user clustering techniques. The PA is established through a distance-based power allocation algorithm (DBPA) in [16,18], whereby the near-user is allocated a lower power and the far-user a higher power. User clustering techniques (Best with Best and Best with Poor models) were proposed by Hussain et al. in [19,20]. In the Best with Best model, users having the same channel conditions are grouped into the same cluster, while the Best with Poor model has users in descending order of their channel gains. Orthogonal and non-orthogonal spreading codes such as(Pseudo-Noise (PN) and Walsh codes are used to distinguish equidistant users from the gNodeB in multi-cluster PD-NOMA [18]. As a result, the inter-cluster interference is overcome with the help of spreading codes and intra-cluster interference over the SIC technique.

Consider the practical 5G micro-cells with foliage or vegetation close to the gNodeB, which operates using millimeter wave (mmWave) communication at gigahertz (GHz) frequencies. At such higher frequencies, the mmWave signals are obstructed by small particles. As a result, the signal is attenuated more, which leads to substantial path losses. For the sake of simplicity, we include the foliage part in our simulation because it weakens the signal but does not totally block it, as do buildings wall and other barriers. To address such path loss issues, multiple advanced techniques have been introduced, such as unmanned-aerial-vehicle (UAV) assisted communication [21], re-configurable intelligent surfaces (RIS) or meta-surfaces [22,23] and cooperative communication [24]. UAVs mostly help in providing a direct line-of-sight (DLOS) path between transmitter and receiver where chances of signal blockage and attenuation are reduced effectively. The RIS is installed on the surfaces of building walls to direct the phase-shifted and amplified version of the incident signal with negligible attenuation [25]. To shift the trend in mmWave communication from using probabilistic radio channels to deterministic channel modeling, an efficient radio technique called Ray-tracing [26] is being used nowadays. Ray tracing was first introduced in the 1990s [27] but is currently attracting the attention of most researchers due to its reliability in high-frequency communication. Ray tracing consumes more time at lower frequencies while effectively working at higher frequencies such as in GHz and THz communication [28]. Cooperative relaying is used to enhance the performance of far-users by using the near-users as relay nodes in the system [29].

Moreover, the power optimization problem is a crucial part of PD-NOMA to deal with. In the previously mentioned work, the power allocation has no such dedicated and optimal power allocation strategies. Most of them performed the power allocation process using classical methods such as DBPA, and some used random power factors for PD-NOMA users. The limitation of the previous methods for power allocation strategies such as in [16,17,18] is the user-fairness. Considering only the distance parameter is not enough for accurate power distribution among NOMA users. However, it is urgently needed to propose a power allocation strategy that is optimal and ensures user-fairness. To address this issue, we are proposing a human intuition-based fuzzy inference system approach that not only considers the distance separation of users from the gNodeB but also incorporates other parameters as well, such as signal-to-noise ratio ($SNR$) and foliage depth ($d_f$) during the power allocation process. The purpose of considering these multi-input parameters is to make the power allocation process accurate and optimal so that each user is served with equity and fair-play during power distribution. For the allocation of relay nodes, a fuzzy logic-based method is utilized, which effectively improves the choice of adaptive data rates and assigning power for NOMA transmission in [30]. To optimize the productivity of conventional and complex fuzzy systems, the Mamdani complex fuzzy inference system (Mamdani CFIS) was developed by Selvachandran et al. in [31]. It has been shown that the suggested Mamdani CFIS is simpler, faster, and provides a more efficient way of dealing with time information and time-periodic events than any other fuzzy IS identified in the literature to date. Similarly, the Fuzzy-System Kernel Machines, a family of machine learning techniques concerning the relationship of FIS systems and kernel machines, were introduced by Guevara et al in [32]. The fundamental motivation for utilizing FL to solve these problems is that they are difficult to model with mathematical equations. Instead, systems that replicate people’s behaviors can easily manage them. Power control, traffic control, and channel selection are some of FL’s application fields. Cellular systems and bandwidth allocation in cognitive radio networks [33,34] are two notable areas where FL is productive. An approach to generating a fuzzy inverse matrix has been introduced in [35]. Using this method, the fuzzy system is turned into an identical structure of crisp polynomial equations. The eigenvalue approach is used to calculate the solutions to the crisp polynomial equations. Fuzzy systems have a wide range of applications [36,37,38,39,40]. In [40], a fuzzy inference system is used in the medical field for the intensive care of patients where depth of anesthesia (DOA) estimation approach is designed using a machine learning algorithm and an adaptive neuro-fuzzy model.

This paper presents two different and important aspects of PD-NOMA in 5G-based micro-cells: optimal PA and cooperative relaying. We developed a fuzzy logic-based system that assigns each PD-NOMA user the optimal power levels. Furthermore, we incorporate a cooperative relaying technique into the PD-NOMA system that effectively addresses the raised issues at far-user due to intense path losses. The proposed paper’s primary contributions are as follows;

• The power optimization problem is coordinated through multi-input parameters such as distance (d), signal-to-noise ratio ($SNR$), and foliage depth ($d_f$) for each user in PD-NOMA;
• The optimization problem for equity power allocation is solved through an FIS-based system that guarantees user-fairness in terms of the optimal power distribution among PD-NOMA users;
• In realistic 5G micro-cells, the Weissberger model is being used to analyze the impact of foliage on channel conditions between the gNodeB and users;
• The proposed methodology employs the decode and forward (D&F) cooperation relaying mechanism at the cell-center level to improve BER performance at the cell-edge level, where a maximum ratio combining (MRC) is used for detection.

The rest of the paper is organized as follows. Section 2 presents the system model, optimal PA and cooperative relaying PD-NOMA is discussed in Section 3, respectively. Section 4 provides the simulation results. Finally, conclusions are drawn in Section 5.

2. System Model

An ideal 5G micro-cell with a coverage radius of 200 m is shown in Figure 1. This micro-cell consists of a gNodeB which serves two users U${}_1$ (near-user) and U${}_2$ (far-user), via downlink PD-NOMA communication. The gNodeB and two users (U${}_1$ and U${}_2$) are installed with single antennas. In the downlink PD-NOMA, the gNodeB is considered the controlling unit which allocates different powers to each serving user at the same time and frequency. The fuzzy inference system (FIS) based optimal PA strategy is used in the proposed methodology. To obtain user fairness, U${}_1$ is given a minimum power and U${}_2$ a maximum power, as demonstrated in Figure 1.

At the gNodeB, random symbol bits for the ith user are generated, which is given by:

$$r_i\left(t\right)=\sum _l{b}_i^l\delta (t-i{T}_s),$$

(1)

where $r_i\left(t\right)$ represents the randomly generated symbol bits and $b_i^l$ is the $ith$ user’s $lth$ symbol. $\delta$ and $T_s$ represent the Dirac delta function and the sampling rates, respectively. For each user the absolute power factor is computed through FIS as shown in Section 3 and Appendix A. The output of the FIS system is normalized to obtain the actual power factors for each user and is given by:

$$P_i=\frac{p_i^{{}^{\prime }}}{{\sum }_{i=1}^2{p}_i^{{}^{\prime }}},$$

(2)

where $P_i$ and $p_i^{{}^{\prime }}$ are the normalized and absolute power factors for $ith$ user, respectively. The total normalized power for all users is constrained by:

$$\sum _{i=1}^2{P}_i=1.$$

(3)

Each user’s signal is modulated with Binary Phase Shift Keying (BPSK) along distinct phase offsets and assigned with corresponding power factors via FIS at the gNodeB, and is given by:

$$c_i\left(t\right)=\sqrt{P_i}{r}_i\left(t\right)=\sqrt{P_i}\sum _l{b}_i^{\left(l\right)}g(t-i{T}_s),$$

(4)

where $c_i\left(t\right)$ is the $ith$ user’s power multiplexed signal and $g\left(t\right)$ stands for the transmitting pulse. The combined signal for both users is given by:

$$x\left(t\right)=\sum _{i=1}^2\sqrt{P_i}{c}_i\left(t\right).$$

(5)

The combined signal $x\left(t\right)$ after passing through root raised cosine filter (RRCF) for pulse shaping is transmitted over a channel in the presence of additive white Gaussian noise (AWGN). Each user (U${}_i)$ obtains the transmitted combined signal after it has been subjected to large-scale fading and is given by:

$$Y_i\left(t\right)={\alpha }_{i}x\left(t\right)+n_i\left(t\right),$$

(6)

where $Y_i\left(t\right)$ is the received combined signal at the $ith$ receiver, ${\alpha }_i$ is the channel gain and $n_i\left(t\right)$ is the AWGN with zero mean and standard deviation $\sigma$. The message signal is decoded by each receiver based on power levels. Signals with higher multiplexed power are decoded first, followed by those with lower power levels in descending order. The far-user (U${}_2$) will decode its signal immediately due to maximum power, whereas the near-user U${}_1$ will conduct SIC to negate the influence of the U${}_2$ signal and then decode its signal, which is provided by:

$$\widehat{x_i}\left(t\right)=Y_i\left(t\right)-x_{i^{\prime }}\left(t\right).$$

(7)

$\widehat{x_i}\left(t\right)$ is the decoded signal and $x_{i^{\prime }}\left(t\right)$ is the SIC term. Here, $i^{\prime }=2$ for near-user (U${}_1$) and $i^{\prime }=1$ for far-user (U${}_2$). The proposed framework is represented in Figure 2, which illustrates a step-by-step block diagram of the proposed framework, where each user signal is given different phase shifts and assigned the associated power factors by employing an FIS-based system. All of the users’ signals are superimposed, then sent over the channel after passing through a root-raised cosine filter (RRCF) for pulse shaping. At the receiving end, the incoming signal is processed once more by RRCF before being decoded using the SIC technique. The near-user U${}_1$ is used for cooperation to assist the far-user U${}_2$ using the D&F technique, which is further discussed in Section 3.2.

3. Optimal Power Allocation (PA), Cooperative Relaying and Channel Models in PD-NOMA

3.1. Fuzzy Inference System for Optimal PA

In comparison to conventional logic systems, fuzzy logic is largely reliant on human reasoning in spirit and is considerably closer to natural language. The fuzzy logic controller mimics the actions of a human operator by modifying the input signal. The proposed technique uses an FIS-based system to address the issue of power allocation. Normally, in the downlink PD-NOMA users’ signals are assigned different power levels at the gNodeB but this is not the optimum solution for practical implementation of the NOMA system. To solve this issue, we proposed an FIS-based optimization technique that effectively distributes the total power among all the user signals at the gNodeB. The FIS system uses a fuzzy rule-based system (FRBS) that takes different input variables and mimics them identically as humans perform. The power optimization problem is solved using the FIS system, which allocates an optimal power factor to each user surrounding the gNodeB. Fuzzy logic (FL) is relatively less complicated and simpler to configure the model for solving non-convex and multi-objective systems with greater efficiency [41]. A normal fuzzy system is composed of three different levels: fuzzification, rule base, and defuzzification. The input values are transformed to fuzzy values in the fuzzification stage. The output of the fuzzification stage is executed depending on the different fuzzy rules from the fuzzy rule matrix (FRM) in the rule base. The fuzzy results from the rule base are turned into final output values via defuzzification.

3.1.1. Selection of Fuzzy Sets

At this stage, the fuzzy inputs and their respective membership functions (MFs) are chosen to enfold the complete range of inputs and outputs. The FIS system takes different input signals at the gNodeB, such as d, $SNR$, and $d_f$ for each serving user in its vicinity. Each input has three triangular MFs, which are labeled as low (L), moderate (M), and high (H). In the fuzzification stage, all three input variables are transformed into fuzzy values: ${\mu }_d$, ${\mu }_{SNR}$ and ${\mu }_{d_f}$. Our proposed FIS system is implemented for d = 200 m, $SNR$ = 30 dB, and $d_f$ = 30 m. However, if the universe of discourse changes, the same MF should be utilized to cover the entire range of input parameters. The output function is also triangular and consists of five MFs: very low (VL), low (L), moderate (M), high (H), and very high (VH). All the three inputs and output MFs are shown in Figure 3, Figure 4, Figure 5 and Figure 6, respectively. The triangular MFs are produced with min-max (and-or) operations [42] for implication/aggregation. With a high point ($\alpha ,h$) and end points ($e,0$) and ($f,0$), the triangular membership function $T\left(s\right)$ is given by:

$$T\left(s\right)=\left\{\begin{array}{c}h\left(\frac{s-e}{\alpha -e}\right)\mathrm{for}e\le s\le \alpha \hfill \\ h\left(\frac{s-f}{\alpha -f}\right)\mathrm{for}\alpha \le s\le f\hfill \\ 0\mathrm{otherwise}\hfill \end{array}\right..$$

(8)

Here, s is the input parameter such as d, $SNR$, and $d_f$.

3.1.2. Fuzzy Rule Matrix (FRM) for Optimal PA

The FRM is the decision-taking stage of the FIS system. At this stage, the output of the fuzzification stage is passed through the FRM for execution. The FRM depends on the input parameters and their respective MFs for each fuzzy value. It uses IF-THEN logical statements for the appropriate execution of fuzzy inputs. The proposed system gives more weight to the input variable $SNR$ for each user signal. It means if $SNR$ is low, comparatively more power will be allocated to that user. In other words, the impact of input variable $SNR$ on PA is comparatively greater than the other inputs, such as distance and foliage depth. The FRM is made up of 27 possible rule combinations based on the input variables and their respective MFs: d = {$d_L,d_M,d_H$}, $SNR$ = {$SN{R}_L,SN{R}_M,SN{R}_H\}$, and $d_f$ = {$d{f}_L,d{f}_M,d{f}_H\}$. The FRM observes the fuzzy inputs and takes decisions, which are then used as inputs to the defuzzification stage.

Table 1. Human Intuition based FIS system for Optimal PA in PD-NOMA.

S.no	d	SNR	d${}_{\mathit{f}}$	Power Level
1	L	L	L	L
2	L	L	M	M
3	L	L	H	H
4	L	M	L	L
5	L	M	M	L
6	L	M	H	M
7	L	H	L	VL
8	L	H	M	L
9	L	H	H	L
10	M	L	L	M
11	M	L	M	H
12	M	L	H	H
13	M	M	L	L
14	M	M	M	M
15	M	M	H	H
16	M	H	L	L
17	M	H	M	L
18	M	H	H	M
19	H	L	L	H
20	H	L	M	H
21	H	L	H	VH
22	H	M	L	M
23	H	M	M	H
24	H	M	H	H
25	H	H	L	L
26	H	H	M	M
27	H	H	H	H

, depicts the fuzzy rule-based system for three inputs. To better understand the Table 1, we have three input variables, d, $SNR$, and $d_f$ each consisting of three different triangular MFs: L, M, and H. So a combination of 27 different rules are implemented using these input variables. The outcome of the FIS-based system has five MFs (VL, L, M, H, and VH), that are completely dependent on the arrangements of input parameters: d, $SNR$, and $d_f$.

3.1.3. Defuzzification

In the defuzzification, the center of area (COA) technique [42] is used to calculate the optimal power factors using the proposed FRBS system. For various numbers of fuzzy rules, the defuzzifier’s output is obtained by:

$$p_i^{{}^{\prime }}=\frac{{\sum }_i{\mu }_{Ci}(\Delta \mu )\Delta \mu \left(Ci\right)}{{\sum }_i\Delta \mu \left(Ci\right)}.$$

(9)

For the rule $Ci$, $\Delta \mu \left(Ci\right)$ specifies the peak value of the fuzzy set’s membership degree and ${\mu }_{Ci}$ represents the centroid of the associated output membership function. Using Equation (9), each user is assigned an absolute power factor based on the FRM, which is then normalized through Equation (2) to produce real power factors. Figure 7 shows the graphical representation of the FIS system’s output as a function of d and $SNR$. The foliage depth is kept constant at $d_f$ = 14 m for a 3D graphical view. The output power factors for input d, $SNR$, and $d_f$ are maximum for combinations (H, L, H) and minimum for combinations (L, H, L). For a better understanding of Table 1 in terms of the FIS system’s outcome for the different power levels, we assumed the input arrangements for row 21 (H, L, and H). The FIS system will result in maximum power levels for each user if the distance is high (H), the SNR is low (L), and the foliage depth is high (H). The same intuition is tabulated for all the power levels calculated.

3.2. Cooperative Relaying and Channel Models in PD-NOMA

In cooperative relaying communication, the strong node is used as a relay to assist the weak node in the system. A strong node has better channel conditions than a weak node. In the proposed model, the strong and weak nodes are U${}_1$ and U${}_2$, respectively, as shown in Figure 8. The weak node faces critical signal losses due to multiple issues such as greater distance separation, foliage depth, and low signal-to-noise ratio. Although PD-NOMA assigns higher power to far users’ signals to ensure user fairness, it is further needed to assist them from strong nodes as well, which provide indirect line-of-sight (LOS) paths between the gNodeB and the far-users (U${}_2$ here).

In Figure 8, U${}_2$ being located at a maximum distance and foliage depth faces signal degradation and results in intense path losses. To address this issue that occurs in ordinary PD-NOMA, the proposed model incorporates cooperative relaying into the existing system by treating U${}_1$ as a relay that uses the decode and forward (D&F) method to assist U${}_2$. Specifically, during the time slot ($t_1$), both users U${}_1$ and U${}_2$ receives the combined signal. The U${}_1$ first decodes the U${}_2$ signal using basic NOMA principles and performs SIC on the U${}_2$ signal to retrieve its signal. The U${}_2$ signal is regenerated from the previously decoded signal at U${}_1$ and forwarded to the U${}_2$ receiver at time slot ($t_2$). Cooperation in the system can be implemented at the expense of increased bandwidth consumption. Now U${}_2$ has two signals: a degraded signal from the gNodeB with higher path losses and a D&F signal from node U${}_1$. The maximum ratio combining (MRC) technique is then used by the U${}_2$ receiver to decode its signal.

We used three types of channel models: NYUSIM, Rician, and Rayleigh channels, to study the behavior of the proposed model. The NYUSIM [43] channel model, which was created specifically for 5G wireless communication protocols and covers a frequency range of 500 MHz to 100 GHz. The path loss (PL) calculated for each user signal by passing it through the NYUSIM channel model is given by:

$$\begin{array}{c}\hfill \mathrm{PL}(f_c,d)\left[\mathrm{dB}\right]=\mathrm{FSPL}(f_c,1\mathrm{m})\left[\mathrm{dB}\right]+10n{\log }_{10}(d/d_0)+\mathrm{AT}\left[\mathrm{dB}\right]+X_{\sigma }.\end{array}$$

(10)

$f_c$ is the carrier frequency in gigahertz and d is the 3D distance between each user and the gNodeB. $d_o$ is the reference distance of 1 m, n denotes the path loss exponent, and AT denotes the attenuation effect from the surrounding environment. $X_{\sigma }$ represents a Gaussian random variable with zero mean and a variance of 2.52. The free space path loss (FSPL) in Equation (10) is given by:

$$\begin{array}{c}\hfill \mathrm{FSPL}(f_c,1\mathrm{m})\left[\mathrm{dB}\right]=20{\log }_{10}\left(\frac{4\pi \times f_c\times {10}^9}{c}\right)\\ \hfill =32.4\left[\mathrm{dB}\right]+20{\log }_{10}\left(f_c\right),\end{array}$$

(11)

where, c denotes speed of light. The 3-D distance separation is given by:

$$d=\sqrt{d_{2D}^2+{(h_t-h_r)}^2},$$

(12)

where $d_{2D}$ denotes the 2-D distance separation for each user from the gNodeB, $h_t$ and $h_r$ are the gNodeB and each user heights, respectively. The environment attenuation is given by:

$$\mathrm{AT}\left[\mathrm{dB}\right]=\beta [\mathrm{dB}/\mathrm{m}]\times d\left[\mathrm{m}\right].$$

(13)

Here, $\beta$ represents the factor of attenuation from the surrounding environment and $d\left[\mathrm{m}\right]$ is the 3D distance separation. The proposed model is also simulated in the Rician and Rayleigh fading channels. In the Rician fading channel, the SUI-3 (Stanford University Interm channel model 3) parameters are used in the simulation. The K-factor (line of sight paths) is equal to 1, the path delay vector is [0 0.4 0.9], the path gain vector in dB is [0 −5 −10], and a doppler spread equal to 0.5 is chosen. For the Rayleigh fading channel, SUI-6 parameters are used, such as K-factor equal to 0, path delay vector is [0 14 20], path gain vector in dB is [0 −10 −14], and a doppler spread equal to 0.5.

In practical scenarios, the 5G micro-cell may consist of plants or foliage. This foliage drastically affects high-frequency communications, such as mm-Wave communication at GHz frequencies. The losses are proportional to the foliage depths ($d_f$) and carrier frequency. In the proposed model, we use the ITU-developed Weissberger model [44,45], which accounts for propagation losses related to foliage.

$$P{L}_{d_f}=\left\{\begin{array}{c}1.33f_c^{0.284}{d}_f^{0.588},14 \mathrm{m}<d_f\le 400 \mathrm{m}\hfill \\ 0.45f_c^{0.284}{d}_f,0 \mathrm{m}<d_f\le 14 \mathrm{m}\hfill \\ ,\hfill \end{array}\right.$$

(14)

where $P{L}_{d_f}$ denotes the path loss due to foliage, f denotes the frequency in GHz and $d_f$ is the foliage depth. We simulate the Weissberger model at 28 GHz with different foliage depths as shown in Figure 9. As the foliage distance between the BS and the user increases, the path loss increases as well, as shown in Figure 9. So it is recommended that for larger foliage depths among the gNodeB and users, higher power will be assigned to those users.

The total path losses for a user are calculated by adding NYUSIM path losses ($\mathrm{PL}(f_c,d)$) and foliage losses $\left({\mathrm{PL}}_{d_f}\right)$ which is given by:

$${\mathrm{PL}}_{total}=\mathrm{PL}(f_c,d)+{\mathrm{PL}}_{d_f}.$$

(15)

In the results section, we conclude from Figure 10 and Figure 11, that incorporating the cooperative relaying technique into ordinary PD-NOMA systems improves the BER performance of U${}_2$.

4. Simulation Results

In this section, the proposed system’s simulation results are discussed in detail. A frequency of 28GHz is employed as the operational frequency. The system is implemented for two users (U${}_1$& U${}_2$) in SISO downlink cooperative relaying PD-NOMA with different pairs of optimal powers. The FIS system is used to allocate these powers (optimal power factors).

Table 2. Parameters used in implementation of System Model.

Parameters	Values
Carrier frequency ($f_c$)	28 GHz
gNodeB radius	200 m
gNodeB and U${}_i$ antenna	(SISO) 1,1
gNodeB height ($h_t$)	10 m
$\beta$	0.0019 (Collective)
Users (U${}_i$) height ($h_r$)	1 m
Path Loss exponent (n)	2
Modulation schemes	BPSK
Phase shifts	$\pi /2,0$
$X_{\sigma }$	Mean 0, variance 2.52

lists the parameters utilized in the simulation model. The coverage radius of the gNodeB is set to 200 m, which is ideal for 5G BS (gNodeB). For simplicity, single antennas are installed on both the gNodeB and the users (U${}_i$) sides. The heights of the gNodeB and the users have been set to 10 m and 1 m, respectively. The path loss exponent is set to 2, which is the standard value for the free space, and the modulation scheme of BPSK is used to avoid large interference issues. The proposed FIS system is compared based on optimal PA and user fairness. For comparison analysis, the proposed method simulates the existing the existing DBPA algorithm from [18] for two users in the PD-NOMA system. The FIS system is then utilized to assign optimal power to each user, and the two power distribution strategies are compared in terms of performance. The bit-error-rate (BER) for each user signal is calculated using Monte Carlo simulations to determine the difference between transmitted and received bits. The BER curves at 10${}^{-3}$ along the Y-axis are used to compare the results, and hence they are plotted against different SNR values.

The comparison of BER curves for PD-NOMA employing DBPA and the proposed FIS-based optimal PA schemes is shown in Figure 10. The distance separation of near-user U${}_1$ and far-user U${}_2$ from gNodeB is $d_1=60$ m and $d_2=180$ m, respectively. Using the DBPA scheme, U${}_1$ is allocated with $P_1=0.23$ and U${}_2$ with $P_2=0.77$. The FIS system uses three parameters to determine optimal powers for each user: ($d_1$ = 60 m, $d_{f1}$ = 10 m and $SN{R}_1$ = 14 dB) for user U${}_1$ and ($d_2$ = 180 m, $d_{f2}$ = 28 m and $SN{R}_2$ = 10 dB) for user U${}_2$. Here, $P_1=0.34$ and $P_2=0.66$ are the calculated power factors for users U${}_1$ and U${}_2$, respectively. The FIS system ensures fairness by providing optimal powers with equity. Fairness can be seen from the obtained SNR levels at a threshold BER of 10${}^{-3}$. The proposed methodology integrates D&F cooperation in addition to assigning optimal powers. Due to the D&F cooperation scheme implemented at the near-user level U${}_1$ helps to enhance the performance of far-users U${}_2$. Using DBPA scheme, the obtained SNR levels at a threshold BER is 10 dB for user U${}_1$ and 5 dB for user U${}_2$, subsequently. While using the FIS system, the obtained SNR levels are: U${}_1$ at 8.8 dB; U${}_2$ at 7 dB (in only PD-NOMA), and 6 dB (in D&F PD-NOMA). In the case of DBPA scheme, the difference between the obtained SNR levels is 5 dB, while it is only 2.8 dB in the FIS-based system. In this context, the largest SNR difference in DBPA scheme indicates that powers are not distributed fairly, whereas the minimal SNR level in the FIS-based system establishes justice between users in terms of PA. Similarly, another attempt was made to test and compare the proposed FIS-based methodology with the DBPA scheme in Figure 11, for distinct input signals. Here in DBPA scheme, U${}_1$ with $d_1$ = 40 m is assigned with $P_1$ = 0.32 and U${}_2$ with $d_2$ = 80 m is allocated with $P_2$ = 0.68. As a result, U${}_2$ obtains an SNR of 5.4 dB and U${}_1$ obtains an SNR of 9 dB. So, the obtained SNR difference between the users is 3.6 dB. On the other hand, the FIS-based system uses ($d_1$= 40 m, $d_{f1}$ = 5 m, and $SN{R}_1$ = 15 dB) and ($d_2$=80 m, $d_{f2}$ = 10 m, and $SN{R}_2$ = 10 dB) for U${}_1$ and U${}_2$, subsequently. Here, the FIS system results in $P_1$ = 0.44 and $P_2$ = 0.56. The obtained SNR level is 8 dB for U${}_1$; 6.3 dB and 6.6 dB for U${}_2$ with D&F cooperation and only PD-NOMA, respectively. Here, the highest SNR difference is 1.7 dB, which indicates that power is fairly distributed among users and hence user fairness is established.

Furthermore, simulation is carried out for the proposed FIS-based model in the Rician and Rayleigh channels. The SUI-3 and SUI-6 models are utilized as standard parameter values for Rician and Rayleigh fading channels, respectively. The BER performance for the proposed FIS-based system is compared with the DBPA in Figure 12 and Figure 13 under the Rician and Rayleigh fading channels, respectively. Similar to previous results from NYUSIM models, the proposed technique again outperforms under these two channels in terms of user-fairness. In the Rician channel, the proposed FIS-based system achieves a threshold BER of 10${}^{-3}$ at an SNR of 11.4 dB for U${}_1$ ($P_1$ = 0.34); 8.2 dB and 8.4 dB for U${}_2$ ($P_2$ = 0.66) with D&F cooperation and only PD-NOMA, respectively. While utilizing the DBPA scheme, the threshold BER is achieved at SNRs of 13.2 dB for U${}_1$ and 8 dB for U${}_2$, respectively. The DBPA allocates $P_1$ = 0.23 to U${}_1$ and $P_2$ = 0.77 to U${}_2$, respectively. Here, again, we can see the difference in the achieved SNRs between U${}_1$ and U${}_2$ is less in the case of the proposed FIS-based than the DBPA. As we can see in Figure 12 the SNR difference in FIS-based is 3.2 dB while it is 5.2 dB for DBPA. Similarly, Figure 13 also ensures that an FIS-based system outperforms the DBPA schemes in terms of optimal power allocation and user-fairness. The lower the difference between the achieved SNR levels, the larger the user-fairness and vice versa. User-fairness is the key capability of the NOMA technique that differentiates it from other OMA techniques. In comparison with the power allocation scheme of DBPA, the proposed FIS-based allocates optimal power factors with equity and fair-play and hence ensures user-fairness. The BER performance when utilizing the Rician channel is comparatively better than that of the Rayleigh channel. This is because the Rician channel has more line-of-sight (LOS) paths (K-factor) than the Rayleigh channel, which has no LOS paths and more delays.

In the DBPA scheme, the far-user is allocated higher power and the near-user with lower power, but this is the case when power is distributed among users based on distance separation from the gNodeB. However, the proposed FIS system decides the PA based on multi-input parameters. Given the foregoing, it is possible that, despite being close to the gNodeB, a near-user (U${}_1$) has poor channel condition due to low input SNR and high foliage depth, as compared to a far-user (U${}_2$) having high input SNR and low foliage depth. In this case, the proposed FIS system assigns maximum power to U${}_1$ and minimum power to U${}_2$. The simulation is performed for a scenario in which U${}_1$ has ($d_1$ = 90 m, $SN{R}_1$ = 15 dB, and $d{f}_1$ = 25 m) and U${}_2$ has ($d_2$ = 110 m, $SN{R}_2$ = 25 dB, and $d{f}_2$ = 8 m) from the gNodeB. The FIS-based system assigns optimal power factors of $P_1$ = 0.64 and $P_2$ = 0.36 to U${}_1$ and U${}_2$, respectively. In this case, U${}_1$ will not be used as a relay node to assist the far-user U${}_2$. The reason is simple: U${}_1$ suffers from greater signal losses due to low input SNR and high foliage depth, and hence its contribution as a relay node is negligible. It is observed that U${}_1$, which is closer to gNodeB and has higher power, directly decodes its signal from the combined signal, whereas U${}_2$, which is further away and has a lower power factor, uses the SIC technique to negate the effect of the U${}_1$ signal from the combined signal to retrieve its U${}_2$ signal. As shown in Figure 14, the BER threshold of 10${}^{-3}$ is obtained at an SNR of 6 dB and 8 dB by U${}_1$ and U${}_2$, respectively. The degraded U${}_2$ performance is caused by using the SIC technique on the U${}_1$ signal.

Table 3. Performance analysis of two users in PD-NOMA and Cooperative PD-NOMA with PA through DBPA and the FIS-based strategies.

Users	d	i/p SNR	d${}_{\mathit{f}}$	Power Factor (DBPA)	Power Factor (FIS)	SNR Level Obtained (DBPA)	SNR Level Obtained (FIS)
UE${}_1$	60 m	14 dB	10 m	0.23	0.34	10 dB	8.8 dB
UE${}_2$	180 m	10 dB	28 m	0.77	0.66	5 dB	6 dB (with D&F), 7 dB (No D&F)
UE${}_1$	40 m	15 dB	5 m	0.32	0.44	9 dB	8 dB
UE${}_2$	80 m	10 dB	10 m	0.68	0.56	5.4 dB	6.3 dB (with D&F), 6.6 dB (No D&F)
UE${}_1$	90 m	15 dB	25 m	–	0.64	–	6 dB
UE${}_2$	110 m	25 dB	8 m	–	0.36	–	8 dB (No D&F)

contains a detailed description of the parameters and the results obtained in various attempts. The complexity of the FIS system increases with the number of inputs and outputs, the number of MFs used for the universe of discourse, and the selection of different rule base sets.

5. Conclusions

Key aspects of power domain NOMA (PD-NOMA) and cooperative relaying PD-NOMA are successfully presented in this study. An FIS-based system is used to precisely address the power optimization problem, which is a fundamental aspect of PD-NOMA. The proposed system evaluates the performance of PD-NOMA in a scenario where mmWave signals are degraded around the gNodeB. Overall, the proposed system achieves user-fairness, and system performance is considerably improved thanks to FIS-based power optimization and cooperative relaying. Future studies on the proposed technique can include multiuser clustering systems with multiple cooperation stations, allowing multiple cell-center users to cooperate with the cell-edge users for performance improvement in denser PD-NOMA networks.