Modeling of NOMA-MIMO-Based Power Domain for 5G Network under Selective Rayleigh Fading Channels

: The integration of multiple-input multiple-output (MIMO) and non-orthogonal multiple access (NOMA) technologies is a hybrid technology that overcomes a myriad of problems in the 5G cellular system and beyond, including massive connectivity, low latency, and high dependability. The goal of this paper is to improve and reassess the bit error rate (BER), spectrum efﬁciency (SE) of the downlink (DL), average capacity rate, and outage probability (OP) of the uplink (UL) in a 5G network using MIMO. The proposed model utilizes QPSK modulation, four users with different power location coefﬁcients, SNR, transmit power, and two contrasting bandwidths 80 and 200 MHz under selective frequency Rayleigh fading channels. The proposed model’s performance is evaluated using the MATLAB software program. The DL results found that the BER and SE against transmitted power showed the MIMO-NOMA enhanced the BER performance for the best user U4 from 10 − 1.7 to 10 − 5.2 at 80 MHz bandwidth (BW), and from 10 − 1.5 to 10 − 5 at 200 MHz for transmitting power of 40 dBm. In contrast, the SE performance for the best user U4 is enhanced from 24 × 10 − 3 to 25 × 10 − 3 bits/second/Hz at 80 MHz BW and from 19.8 × 10 − 3 to 20 × 10 − 3 bps/Hz at 200 MHz BW. Although the outcomes for the UL were obtained in terms of average capacity rate and OP versus SNR at 80, and 200 MHz BW, the MIMO-NOMA result showed that the average capacity rate for the best user U4 performance improves by 12 bps/Hz for 1 dB SNR and the OP is reduced by 15 × 10 − 3 for 80 MHz BW and by 12 × 10 − 3 for 200 MHz BW at an SNR of 0.17 dB. As the BW increased the BER, the average capacity rate increased while the SE and OP decreased. For both DL/UL NOMA with and without MIMO, closed-form expressions for BER, SE, average capacity rate, and OP were obtained. All users’ performance, even those whose connections were affected by interference or Rayleigh fading channels signiﬁcantly improved, when MIMO-NOMA was implemented. was investigated and analyzed for various distances, power location coefﬁcients, transmitted power, and BW, whereas the average capacity rate and OP performance of UL NOMA were examined for various distances, SNR, and BW. The DL NOMA system results showed that using 64 × 64 MIMO enhanced the performance of BER, and SE, and solved the near–far user’s problem, where the performance of all users becomes close to each other’s for different transmitted power, distance, and power location coefﬁcients parameters when compared without MIMO DL NOMA performance. The results demonstrated that the 64 × 64 MIMO DL NOMA enhances the BER performance for the best user U4 from 10 − 1.7 to 10 − 5.2 at 80 MHz BW, and from 10 − 1.5 to 10 − 5 at 200 MHz BW at a transmitter power of 40 dBm. In contrast, the SE performance for the best user U4 is improved by 0.8% bps/Hz for 80 MHz BW and by 1.01% bps/Hz for 200 MHz BW at a transmitter power of 40 dBm. The UL NOMA systems results obtained using 64 × 64 MIMO enhanced the average capacity rate performance by 12 bps/Hz, reduced the OP by 0.0150 for 80 MHz BW at SNR of 1 dB, improved the average capacity rate performance by 12 bps/Hz, and decreased the OP by 0.0120 for 200 MHz BW at SNR of 0.17 dB for the best user U4. In general, an increase in BW increases BER and average capacity rate while decreasing SE and OP. MIMO signiﬁcantly improves the performance of all users. In the future, it will be looked into how MIMO cooperative NOMA and cognitive radio work together.


Introduction
Due to the compelling multimedia applications and the popularity of smart mobile devices, wireless communication has developed at a breakneck pace over the last decade [1,2]. Non-orthogonal multiple access (NOMA) has been offered as a possible strategy for achieving mass accessibility with keeping spectral efficiency [3,4]. NOMA achieves multiple access by modifying the power level of overlay user signals at the transmitter and receiving the signal using successive interference cancellation (SIC) in receivers, with noise-limiting • Two different bandwidths (BWs) for the NOMA system over a Rayleigh fading channel are proposed and investigated; • Improvements in the system have been examined when NOMA and MIMO are used together to handle four users.
The article addresses the NOMA technique which is considered one of the main bullets of 5G technology. Our main innovative idea in the article is remodeling NOMA-MIMO for the power domain for a higher data rate, capacity, and throughput. This has been performed by proposing a new power domain scheme for NOMA-MIMO.
The remainder of the paper is structured as follows: Section 2 contains previous and related works. Section 3 discusses the proposed system mathematical model. Simulation and simulation parameters are presented in Section 4. The results and discussions are presented in Section 5 and, finally, Section 6 concludes the paper and presents further future work.

Related Work
Multiple beams forming with a single carrier are utilized in NOMA systems to accommodate numerous users as a two-stage beam forming solution for modular beam forming vectors, according to the author in [32]. A reduced total transmission packet shaping issue is built to identify both users' packet-shaping vectors and power.
The author in [33], established successful precoding and detecting procedures to produce a considerable difference between users' effective channel gains, allowing NOMA's potential to be achieved even when the users' initial channel conditions are comparable. The author investigated the performance of MIMO-NOMA when numerous users are aggregated into a group, finding that MIMO-NOMA outperforms MIMO-OMA in terms of total channel capacity and total practical capacity [34].
Using statistical channel state information at the transmitter, the ergodic capacity maximization problem for selective Rayleigh fading MIMO-NOMA systems was investigated in [30]. The MIMO-NOMA schemes greatly outperform the conventional OMA scheme, according to numerical results.
Following a review of the concept of integrating NOMA downlink with MIMO, an experiment was carried out to assess the performance of NOMA downlink combined with MIMO under realistic settings in [35]. In UL, the user connection. The author investigated NOMA in [36], considering numerous specified power allocation techniques. It has been demonstrated that NOMA with the suggested user pair technique outperforms NOMA with the previously described signal realignment.
The author looked in [37] at many NOMA DL and UL user power field-based communication systems with different fading bindings for all users who can follow one of the many conceivable distributions. At high SNRs, analytical expressions of the OP for the NOMA DL and UL systems were derived.
An unmanned aerial vehicle-assisted NOMA network with UL and DL transmissions was explored, and analytical expressions of OP as the major measure were derived in [38]. The author explores a novel UL/DL NOMA system with a uniform relay and set decode order that involves the use of statistical channel state information, resulting in enhanced fairness and applicability [39]. The author evaluated the potential of UL and DL resource utilization, adaptive control, and power control for wireless communications systems under the assumptions of in-band full-duplex BSs, NOMA operation, and queue stability limitations.
A method is proposed for solving by finding a correlation similarity in [40]. The efficacy of different NOMA plots over the tapping delay line channel in both normal and fast UE speed and correlation-level modeling was explored by the author in [40][41][42]. With UE's normal and fast speed, NOMA methods work differently.

DL Scenario
Consider a wireless network with four DL NOMA users and a 64 × 64 MIMO system (as depicted in Figure 1). 1, 2, 3, and 4 are the four users with different bandwidths of 80 and 200 MHz [43]. Let 1, 2, 3, and 4 represent their various BS distances, 1 > 2 > 3 > 4 indicating the preferred order. Depending on the distance, 1 is the weak/far user while U4 is the strong/near user from BS. Let ℎ , ℎ , ℎ , and ℎ identify which selective Rayleigh fading coefficients they correspond to |ℎ | < |ℎ | < |ℎ | < |ℎ | . The total Rayleigh fading channel for each user is given by [44]: where, = 1,2,3,4 is the number of users, and = 64 is the number of channels. , , and show their respective power coefficients. According to the NOMA (power domain) principles, the lower user must have more power and the better user should have less power [45,46]. As a result, the power coefficients must be modified as > > > . Let , , and be the QPSK-formed messages to send to BS 1, 2, 3, 4. The BS's encoded overlay signal is then given by as in [47].
1 decodes directly when it has maximum power, interfering with the 2nd, 3rd, and 4th signals. As a result, the first possible rate is The obtained rate is for 2 after SIC eliminated 1 data.
The achieved rate is for 3 after SIC deleted U1 and 2 data. The total Rayleigh fading channel for each user is given by [44]: where, i = 1, 2, 3, 4 is the number of users, and M = 64 is the number of channels. α 1 , α 2 , α 3 and α 4 show their respective power coefficients. According to the NOMA (power domain) principles, the lower user must have more power and the better user should have less power [45,46]. As a result, the power coefficients must be modified as α 1 > α 2 > α 3 > α 4 . Let x 1 , x 2 , x 3 and x 4 be the QPSK-formed messages to send to BS U1, U2, U3, and U4. The BS's encoded overlay signal is then given by as in [47].
U1 decodes y 1 directly when it has maximum power, interfering with the 2nd, 3rd, and 4th U signals. As a result, the first possible U rate is The obtained rate is for U2 after SIC eliminated U1 data. The achieved rate is for U3 after SIC deleted U1 and U2 data.
The acquired rate is for U4 after SIC deleted U1 data, U2 data, and U3 data.
To calculate the spectrum efficiency.
where the SE is spectrum efficiency, Th is the throughput and BW is the bandwidth.

UL Scenario
The power domain multiplexing for uplink NOMA is almost entirely different. In downlink NOMA, the BS employed superposition coding to offer power domain multiplexing; however, the user's transmit power is limited only by their battery capacity in the uplink. That is, both users can transmit at full strength. Changes in the users' channel gains cause variation in the power domain at the receiver side of BS.
Let x 1 , x 2 , x 3 and x 4 represent the messages that will be sent by four UL NOMA users U1, U2, U3, and U4, accordingly. Suppose that both users' signals have the same strength and consider the 64 × 64 MIMO system and BW equal to 80 MHz on a wireless network (as depicted in Figure 2). Let d1 > d2 > d3 > d4 denote the various BS distances, with d1 > d2 > d3 > d4 being the preferred order. U1 from BS is the weak/far user, while U4 is the strong/near user, depending on the distance. Let h T1 , h T2 , h T3 , and h T4 determine which selective Rayleigh fading coefficients they relate to |h T1 | 2 < |h T2 | 2 < |h T3 | 2 < |h T4 | 2 .
The acquired rate is for 4 after SIC deleted 1 data, 2 data, and 3 data.
To calculate the spectrum efficiency.
where the is spectrum efficiency, ℎ is the throughput and is the bandwidth.

UL Scenario
The power domain multiplexing for uplink NOMA is almost entirely different. In downlink NOMA, the BS employed superposition coding to offer power domain multiplexing; however, the user's transmit power is limited only by their battery capacity in the uplink. That is, both users can transmit at full strength. Changes in the users' channel gains cause variation in the power domain at the receiver side of BS.
Let , , and represent the messages that will be sent by four UL NOMA users 1, 2, 3, 4 , accordingly. Suppose that both users' signals have the same strength and consider the 64 × 64 MIMO system and BW equal to 80 MHz on a wireless network (as depicted in Figure 2). Let 1 > 2 > 3 > 4 denote the various BS distances, with 1 > 2 > 3 > 4 being the preferred order. 1 from BS is the weak/far user, while 4 is the strong/near user, depending on the distance. Let ℎ , ℎ , ℎ , ℎ determine which selective Rayleigh fading coefficients they relate to |ℎ | < |ℎ | < |ℎ | < |ℎ | . The total Rayleigh fading channel for each user is given by: where = 1,2,3,4 is the number of users and = 64 is the number of channels. The signal was received at the BS. The total Rayleigh fading channel for each user is given by: where j = 1, 2, 3, 4 is the number of users and N = 64 is the number of channels. The signal was received at the BS.
where w is the noise power.

Capacity Rates Achievable of Four Users UL NOMA
The signal from the close user is decoded first, with the signal from the distant users being treated as interference. Therefore, the rate at which the BS can decode the data of a nearby user is, according to [48,49].
After the SIC has been calculated, the maximum rate U3 can be obtained.
After the SIC has been calculated, the maximum rate U2 that can be accomplished After the SIC has been calculated, the maximum rate of U1 can be achieved.

OP of Four Users UL NOMA
Consider that the four users have different target rates.
The capacity U4 is calculated as follows: U3 s capacity is calculated as follows: U2 s capacity is calculated as follows: U1 s capacity is calculated as follows: For U1, the OP condition is: The OP of U1: For U2, the OP condition is: The OP of U2: For U3, the OP condition is: The OP of U3: For U4, the OP condition is: The OP of U4: where N is the number of transferred samples.

Simulation Parameters
The system model and simulator parameters for the DL and UL NOMA power domains in 5G networks with and without MIMO were implemented using the MATLAB software program. Tables 1 and 2 show the simulation parameters that are properly considered in the simulation model.  The DL NOMA system results showed that using 64 × 64 MIMO improved the SE and BER performance. The near-far user's problem is also resolved, where the performance of all users becomes close to each other's for different power location coefficients, transmitted power, and distance parameters when compared without MIMO DL NOMA performance. Figure 3 depicts the DL NOMA BER performance versus transmitted power at 80 MHz BW. The findings indicate that the BER performance decreases as transmitted power increases. As an outcome, the U4 BER performance is best for all users, because U4 is the nearest one. At a transmitter power of 25 dBm, the BER rate for U1, U2, U3, and U4 is found to be 20%, 28%, 22%, and 8%, respectively. Figure 4 shows the DL NOMA BER performance against transmitted power at 200 MHz BW; the findings show that the BER performance decreases as transmitted power increases. As a result, the U4 BER performance is best when compared with all users because U4 is the nearest one. At a transmit power of 25 dBm, the BER rates for U1, U2, U3, and U4 are found to be 27%, 36%, 31%, and 13%, respectively. The 64 × 64 MIMO DL NOMA enhances the performance of BER for the best user U4 from 10 −1.7 to 10 −5.2 at 80 MHz then, from 10 −1.5 to 10 −5 at 200 MHz BW at a transmitter power of 40 dBm in Figure 4. In contrast, the SE performance for the best user U4 is improved by 8 × 10   At 80 MHz BW and 64 × 64 MIMO, Figure 5 shows the DL NOMA BER performance versus transmitted power. When transmitted power is 20 dBm, the BER rate for U1, U2, U3, and U4 is found to be 19 × 10 −4 , 18 × 10 −4 , 8 × 10 −4 , and 5 × 10 −4 , respectively. Figure 6 shows the DL NOMA BER performance against transmitted power at 200 MHz BW and 64 × 64 MIMO, at a transmitted power of 25 dBm, the BER rates for U1, U2, U3, and U4 are found to be 46 × 10 −4 , 43 × 10 −4 , 19 × 10 −4 , and 7 × 10 −4 , respectively. The MIMO system reduces the BER performance. At 80 MHz BW and 64 × 64 MIMO, Figure 5 shows the DL NOMA BER performance versus transmitted power. When transmitted power is 20 dBm, the BER rate for U1, U2, U3, and U4 is found to be 19 × 10 −4 , 18 × 10 −4 , 8 × 10 −4 , and 5 × 10 −4 , respectively. Figure 6 shows the DL NOMA BER performance against transmitted power at 200 MHz BW and 64 × 64 MIMO, at a transmitted power of 25 dBm, the BER rates for U1, U2, U3, and U4 are found to be 46 × 10 −4 , 43 × 10 −4 , 19 × 10 −4 , and 7 × 10 −4 , respectively. The MIMO system reduces the BER performance.     Figure 7 shows the performance of the DL NOMA SE vs. transmitted power at 80 MHz BW, with the outcomes demonstrating that SE performance improves as transmitted power increases. As an outcome, the U4 BER performance is best for all users, because U4 is the nearest one. There is a clear separation of SE performance for all users from one another until the transmitted power reaches 5 dBm. Figure 8 depicts the DL NOMA SE performance versus transmitted power at 200 MHz BW, with the results indicating that increasing transmitted power improves SE performance. The U4 SE performance is best when compared with all users because U4 is the nearest one. The outcomes are superior to those of the best U2 users in [38], with an improvement rate of 10 −2.3 in the BER.  Figure 7 shows the performance of the DL NOMA SE vs. transmitted power at 80 MHz BW, with the outcomes demonstrating that SE performance improves as transmitted power increases. As an outcome, the U4 BER performance is best for all users, because U4 is the nearest one. There is a clear separation of SE performance for all users from one another until the transmitted power reaches 5 dBm. Figure 8 depicts the DL NOMA SE performance versus transmitted power at 200 MHz BW, with the results indicating that increasing transmitted power improves SE performance. The U4 SE performance is best when compared with all users because U4 is the nearest one. The outcomes are superior to those of the best U2 users in [38], with an improvement rate of 10 −2.3 in the BER.    The performance of the DL NOMA SE in terms of transmitted power at 80 MHz BW and 64 × 64 MIMO is shown in Figure 9. At the transmitting power of 5 dBm, the SE for all users is relatively close. Figure 10   The performance of the DL NOMA SE in terms of transmitted power at 80 MHz BW and 64 × 64 MIMO is shown in Figure 9. At the transmitting power of 5 dBm, the SE for all users is relatively close. Figure 10

The Outcomes of the UL Scenario
The UL NOMA average capacity rate vs. SNR at 80 MHz BW is depicted in Figure  11. The result shows that the average capacity rate for U4 is best for all users because U4 is the closest. At SNR of 1 dB, the average capacity rate for U1, U2, U3, and U4 is found to be 1.6873, 2.8718, 6.4960, and 12.7814, respectively. Figure 12 shows the UL average capacity rate against SNR at 200 MHz BW. At SNR of 1 dB, the average capacity rate for U1, U2, U3, and U4 is found to be 2.6015, 3.9841, 7.7910, and 14.1068, respectively. The results reveal that when an SNR increases, the average capacity rate performance rises as well. The 64 × 64 MIMO improved the performance of the capacity average rate by 12 bps/Hz

The Outcomes of the UL Scenario
The UL NOMA average capacity rate vs. SNR at 80 MHz BW is depicted in Figure 11. The result shows that the average capacity rate for U4 is best for all users because U4 is the closest. At SNR of 1 dB, the average capacity rate for U1, U2, U3, and U4 is found to be 1.6873, 2.8718, 6.4960, and 12.7814, respectively. Figure 12 shows the UL average capacity rate against SNR at 200 MHz BW. At SNR of 1 dB, the average capacity rate for U1, U2, U3, and U4 is found to be 2.6015, 3.9841, 7.7910, and 14.1068, respectively. The results reveal that when an SNR increases, the average capacity rate performance rises as well. The 64 × 64 MIMO improved the performance of the capacity average rate by 12 bps/Hz and reduced the OP by 15 × 10 −3 for 80 MHz BW at SNR of 1 dB; it enhanced the performance capacity average rate by 12 bps/Hz, and decreased the OP by 12 × 10 −3 for 200 MHz BW at 0.17 dB SNR for the user U4. In general, an increase in BW increases the capacity average rate and BER while decreasing OP and SE. MIMO significantly enhances the throughput of all users.    The average capacity rate performance for UL NOMA versus SNR at 80 MHz BW and 64 × 64 MIMO is obtained in Figure 13. The outcomes were achieved for four users 12.7881, 14.4423, 18.4489, and 24.7815, respectively. Figure 14 shows the average capacity rate performance versus SNR for UL NOMA at 200 MHz BW and 64 × 64 MIMO. The results show that the average capacity rate performance improves as the SNR increases. The average capacity rate performance for UL NOMA versus SNR at 80 MHz BW and 64 × 64 MIMO is obtained in Figure 13. The outcomes were achieved for four users 12.7881, 14.4423, 18.4489, and 24.7815, respectively. Figure 14      The BW and average capacity rate have a positive relationship, with an increase in BW leading to an increase in average capacity rate. The average capacity rate increases dramatically when the system is enhanced using the MIMO scheme.
The UL NOMA of OP vs. SNR correlation is shown in Figure 15 at 80 MHz BW. When SNR is 0.17 dB, the results for U1, U2, U3, and U4 are 99.9 × 10 −2 , 98.9 × 10 −2 , 44.3 × 10 −2 , and 15 × 10 −3 , respectively. Figure 16 depicts the UL NOMA of OP versus the SNR at 200 MHz BW. At an SNR of 0.17 dB, the results for U1, U2, U3, and U4 are 0.9989, 0.9715, 0.3709, and 0.0120, respectively. The findings show that as the SNR improves, the OP performance decreases. Results achieved have an improvement in average capacity rate and are superior to those of the best U2 users in [35]. The BW and average capacity rate have a positive relationship, with an increase in BW leading to an increase in average capacity rate. The average capacity rate increases dramatically when the system is enhanced using the MIMO scheme.
The BW and OP have an inverse connection, with an increase in BW resulting in a drop in OP. The OP drops dramatically when the system is optimized utilizing the MIMO technique. With an improvement rate of 10 −1.9 in OP, the results are superior to those of the top U2 users in [38].

Conclusions and Future Work
This paper demonstrated the performance of DL and UL NOMA PD in a 5G network with and without 64 × 64 MIMO technologies. The BER and SE performance of DL NOMA was investigated and analyzed for various distances, power location coefficients, transmitted power, and BW, whereas the average capacity rate and OP performance of UL NOMA were examined for various distances, SNR, and BW. The DL NOMA system results showed that using 64 × 64 MIMO enhanced the performance of BER, and SE, and solved the near-far user's problem, where the performance of all users becomes close to each other's for different transmitted power, distance, and power location coefficients parameters when compared without MIMO DL NOMA performance. The results demonstrated that the 64 × 64 MIMO DL NOMA enhances the BER performance for the best user U4 from 10 −1.7 to 10 −5.2 at 80 MHz BW, and from 10 −1.5 to 10 −5 at 200 MHz BW at a transmitter power of 40 dBm. In contrast, the SE performance for the best user U4 is improved by The BW and OP have an inverse connection, with an increase in BW resulting in a drop in OP. The OP drops dramatically when the system is optimized utilizing the MIMO technique. With an improvement rate of 10 −1.9 in OP, the results are superior to those of the top U2 users in [38].

Conclusions and Future Work
This paper demonstrated the performance of DL and UL NOMA PD in a 5G network with and without 64 × 64 MIMO technologies. The BER and SE performance of DL NOMA was investigated and analyzed for various distances, power location coefficients, transmitted power, and BW, whereas the average capacity rate and OP performance of UL NOMA were examined for various distances, SNR, and BW. The DL NOMA system results showed that using 64 × 64 MIMO enhanced the performance of BER, and SE, and solved the near-far user's problem, where the performance of all users becomes close to each other's for different transmitted power, distance, and power location coefficients parameters when compared without MIMO DL NOMA performance. The results demonstrated that the 64 × 64 MIMO DL NOMA enhances the BER performance for the best user U4 from 10 −1.7 to 10 −5.2 at 80 MHz BW, and from 10 −1.5 to 10 −5 at 200 MHz BW at a transmitter power of 40 dBm. In contrast, the SE performance for the best user U4 is improved by 0.8% bps/Hz for 80 MHz BW and by 1.01% bps/Hz for 200 MHz BW at a transmitter power of 40 dBm. The UL NOMA systems results obtained using 64 × 64 MIMO enhanced the average capacity rate performance by 12 bps/Hz, reduced the OP by 0.0150 for 80 MHz BW at SNR of 1 dB, improved the average capacity rate performance by 12 bps/Hz, and decreased the OP by 0.0120 for 200 MHz BW at SNR of 0.17 dB for the best user U4. In general, an increase in BW increases BER and average capacity rate while decreasing SE and OP. MIMO significantly improves the performance of all users. In the future, it will be looked into how MIMO cooperative NOMA and cognitive radio work together.