Wireless Powered Cooperative Communication Network for Dual-Hop Uplink NOMA With IQI and SIC Imperfections

Non-orthogonal multiple access (NOMA) is currently one of the promising techniques for the 6th generation (6G) wireless mobile networks, which can be combined with different technologies, such as cooperative communications and radio frequency (RF) wireless power transfer. RF can transmit energy over a wireless medium and has been seen as an essential application of systems. On the other hand, due to mismatched components and poor circuit fabrications, the transceiver suffers from RF front-end effects in actual situations, such as in-phase and quadrature-phase imbalance (IQI) which degrade the performance of the system. In this paper, we investigate the harvest-then-cooperate assisted NOMA for a wireless-powered cooperative communication network (HTC-NOMA-WPCCN) with practical constraints such as IQI and imperfect successive interference cancellation (ISIC). We thereafter extend the analysis to the multi-helper-user scheme to improve the performance of our considered system. The linear and non-linear EH are considered in our proposed system. We analyze the outage probability (OP), ergodic capacity (EC) and throughput. We discuss the effect of the IQI, ISIC, image rejection ratio and power allocation on the proposed HTC-NOMA-WPCCN. Our theoretical analysis is validated by Monte Carlo simulations. The simulation results demonstrate that the IQI and ISIC can significantly degrade the OP, EC and throughput performances of HTC-NOMA-WPCCN. The linear EH achieves better performance gain than the non-linear EH. Furthermore, this latter is influenced more by IQI and SIC imperfections, which closely approach a practical transmission. On the other hand, we compare the proposed system with UL NOMA without EH, and the results clearly showed the superiority of the proposed system. Finally, the system performance is influenced by changes in image rejection ratio, power allocation and WPCCN parameters which effects the IQI and SIC on the RF impairments.


I. INTRODUCTION
Non-orthogonal multiple access (NOMA) has been identified as a promising technology for 6th generation (6G) wireless The associate editor coordinating the review of this manuscript and approving it for publication was Francisco Rafael Marques Lima . mobile networks [1]. In order to improve spectral efficiency, quality of service (QoS) and the coverage area, the interplay between cooperative communication and NOMA has attracted tremendous attention from researchers [2], [3], [4]. With the rapid growth of the Internet of Things (IoT) and the increasing number of mobile devices, energy harvesting (EH) has attracted much interest as a sustainable means of extending the lifespan of wireless networks that are energy-limited [5].
In [6], the coverage probability, ergodic rate, and energy efficiency have been analyzed for downlink (DL) cooperative NOMA-assisted simultaneous wireless information and power transfer (CNOMA SWIPT). The optimal power allocation factor and optimal time switching (TS) with the effect of imperfect successive interference cancellation (ISIC) for DL CNOMA EH are derived to minimize the outage probability (OP) and maximize the system throughput [7]. The authors of [8] maximize the sum rate of PS and TS for DL CNOMA EH. The adaptive power allocation with full duplex CNOMA under TS protocol has been performed to improve OP and throughput performance [9]. With the perfect SIC and ISIC, the authors of [10], [11], and [12] evaluate ergodic capacity (EC), throughput and OP performance of the DL CNOMA SWIPT for IoT. Furthermore, the authors of [13] and [14] investigated the achievable rate, sum throughput and energy efficiency for DL and uplink (UL) jointly with power splitting (PS)-based SWIPT multiple-input multipleoutput (MIMO)-NOMA systems. In [15], UL NOMA with EH jammers has been analyzed in terms of OP and secrecy OP. On the other hand, a novel wireless network type known as a wireless-powered communication network (WPCN) has received increasing interest as a viable research subject. In this wireless network type, wireless stations are only powered by wireless energy transfer and use the collected energy to transfer information [16]. In [17], the capability of the resource allocation and time scheduling algorithms for a NOMA-based device-to-device (D2D) and WPCN system has been investigated. A sum-throughput maximization problem for a NOMA WPCN with cluster-specific beamforming was developed by the authors of [18]. In [19], a multi-cell WPCN based on NOMA has been analyzed, along with a proposed algorithm to increase the sum throughput of the network. In [20] and [21], a newly emerged NOMA and WPCNs with the aid of intelligent reflecting surface (IRS) technology has been carried out for sum-rate maximization.
As we observe above, most of the existing studies consider a linear EH model, in which the energy actually harvested by the EH circuit rises linearly with the energy received from the RF signal. However, the reality is that the practical EH circuits have non-linear properties. An incremental CNOMA with non-linear EH has been analyzed in terms of OP and throughput [22]. In [23], the OP of full-duplex (FD) CNOMA with non-linear EH has been performed. The authors of [24] and [25] investigate the OP, throughput and sum rate of cognitive radio CNOMA-assisted multi-antenna with non-linear EH. In [26], FD-CNOMA with non-linear EH has been analyzed in terms of OP and throughput. In [27], CNOMA with linear and non-linear EH has been evaluated in terms of OP. The DL CNOMA has been adopted for linear and non-linear EH with power beacon in terms of OP and throughput [28].
All aforementioned works consider the ideal RF front-end operating conditions. However, in reality, the transceiver RF front-end is prone to in-phase/quadrature-phase imbalance (IQI) since non-ideal mixers and phase shifters are used [29], [30], [31]. In [32] and [33], the OP and the error probability are evaluated with the effects of IQI and ISIC. The authors of [29] and [34] analyzed the OP and ergodic rate of the DL FD/half-duplex (HD) CNOMA with ISIC. In [35], the OP and intercept probability (IP) are obtained, to explore the reliable and secure performance of a cognitive ambient backscatter for NOMA with an internet-of-vehicle maritime transportation systems network when the IQI is considered for practical proposes. The OP and IP are derived for non-linear EH DL NOMA multi-relay with IQI and imperfect channel state information (ICSI) [36]. The OP of CNOMA-aided EH has been examined with the effect of residual hardware impairments (RHWI) and ICSI [37].
As we have mentioned above, the OP of the DL SWIPT CNOMA has been analyzed in [6], [7], [8], [9], [10], [11], and [12] with and without ISIC under ideal RF front-end condition when the EH is linear. In [22], [23], [24], [25], [26], and [28], the non-linear EH for DL SWIPT CNOMA has been performed. Likewise, the UL NOMA with SWIPT in terms of the OP, throughput and energy efficiency are examined in [13], [14], and [15], where the RF front-end condition is ideal and the EH is linear. Also, the OP and ergodic rate with the IQI imperfections for DL SWIPT CNOMA has been evaluated in [29], [32], [33], and [34] for linear EH and non-linear in [36]. Moreover, the throughput and sum rate of WPCN based on NOMA has been performed in [17], [18], [19], [20], and [21]. The impact of practical proposals such as IQI with WPCN or EH has not received extensive attention in the literature. Therefore, it is important to consider practical proposals in the literature to evaluate the performance of systems. To the best of the authors' knowledge, the UL CNOMA assisted WPCN with non-linear EH has not been studied in the literature. Moreover, most papers neglected the negative impact of the RF front-end deficiencies on UL CNOMA with or without SWIPT. Therefore, this topic is critical to the actual implementation of practical systems, which is considered the first investigation in the open literature with non-linear EH. Motivated by this, we propose harvest-then-cooperate assisted NOMA for a wireless-powered cooperative communication network (HTC-NOMA-WPCCN), where the wireless power transfer (WPT) in the DL and wireless information transmission (WIT) in UL. The linear and non-linear EH are considered in our investigation. To make the investigation more realistic and practical, we take into account the IQI and SIC imperfections. Thus, the main contributions of this paper are given as follows • For a more realistic scenario, the ideal and non-ideal IQI with ISIC have been considered in our system. We derive closed-form analytical expressions for OP and throughput with linear and non-linear EH. We obtained accurate analytical expressions of EC for our proposed system with linear and non-linear EH under the effects of IQI and ISIC.
• We employ the commonly utilized image-rejection ratio (IRR) metric to evaluate the impacts of IQI. Hence, we discuss the effect of the IQI and SIC imperfections with different WPCCN parameters and power allocation on the proposed scheme. We validate our numerical derivations by simulation results.
• As a benchmark, we compare the proposed scheme with the UL NOMA without EH. The simulation results validate the presented analyses and show the superiority of the proposed scheme over the benchmark. Moreover, the IQI has negative effects on OP, EC and the throughput of systems. In a non-linear model, IQI and ISIC have a significant impact on system performance. The rest of the paper is presented as follows. The considered HTC-NOMA-WPCCN system model is introduced in Section II. Section III analyzes the OP, EC and throughput of our considered schemes. The numerical results are presented in Section IV to validate the analysis. Finally, Section V concludes the paper.

II. SYSTEM MODEL
The proposed system consists of one access point (AP), one far user (U F ) and L near users U NJ users, where J = 1, 2, 3, . . . , L as shown in Fig. 1. We assume that the U NJ works as assistant users in DF protocol to improve the received signal of U F at AP. It is assumed that each node works in HD mode and the communication links experience Rayleigh fading. It is assumed that the channel coefficients between each other are independent. We consider that all users have no other embedded energy supply, and they collect energy 1 from the AP in the DL, which can be stored in a rechargeable battery and afterward utilized to transmit the signal to the AP in the UL. Is assumed that CSI is available at all nodes.
We assume that the RF impairment is described as IQI in both TX and RX, which is the phase and/or amplitude imbalance between the in-phase (I) and quadrature-phase (Q) branches. Hence, the baseband form of the IQI-impaired signal is written by [34] where µ t/r and ν t/r are the IQI coefficients at the TX/RX respectively, is the baseband transmit signal and (.) * denotes conjugation. It is noticed that in the absence of IQI, µ t = µ r = 1 and ν t = ν r = 0. The IQI coefficients µ t/r 1 The WPCN is assumed to be used in our proposed system. A WPCN is only powered by wireless energy transfer and uses the harvested energy to transfer information i.e., the nodes need to harvest energy during the first time and then use it to forward information during the second time [16].  and ν t/r are expressed by [34] , where ϵ t/r and φ t/r are the amplitude and the phase imbalances levels of TX/RX, i = √ −1 is the unit of the imaginary. The IRR calculates the frequency band used for images' attenuation. The IRR is generally between 20 and 40 dB in the literature for practical analog RF front-end circuits [38], [39], [40]. Thus, the IRR is expressed by As shown in Fig. 2, in the first τ T time slot, the users harvest energy from AP. Both linear and non-linear EH models are adopted in this article. In the linear EH model, the harvested energy during the power transfer phase in each user is given as Nevertheless, taking into account the non-linear feature of a practical EH circuit, the corresponding expressions during the power transfer phase in each user can be given by where P t and P th are the total transmit power and the saturation threshold respectively, h AF and h ANJ are the channels 76508 VOLUME 11, 2023 Authorized licensed use limited to the terms of the applicable license agreement with IEEE. Restrictions apply.
between AP-U F and AP-U NJ , η is the energy harvesting efficiency, in which 0 ≤ η ≤ 1, τ is the energy transfer factor and T is the transmission block period. The remaining fraction (1 -τ ) of the block is divided into two-time slots with an equal length of (1 − τ )T /2 for cooperative information transmission in the UL (please see Fig. 2).
Accordingly, in the linear EH model, the transmit power of users in the second (UL) phase is given as However, in the non-linear EH model, the transmit power of users in the second (UL) phase is given as where are the channels between AP-U F and AP-U NJ and ι is the path loss factor.
During the first time slot (1 − τ )T /2 of the UL WPCCN NOMA, the U F transmits its signal x 1 to AP and U NJ . The received signals at AP and U NJ are given respectively as where are the channels between U F -AP and U F -U FNJ , 2 n is the Additive white Gaussian noise (AWGN), x 1 is the signal of U F , µ t,FNJ /r,FNJ , µ t,FA/r,FA , ν t,FNJ /r,FNJ , and ν t,FA/r,FA are the IQI coefficients at the TX/RX and equal to µ t/r and ν t/r in (1). P ð F denotes the transmit power of U F , which is depending on the linear or non-linear EH models as in (7) and (9), where ð = Lin, NL.
The AP and U NJ decode x 1 using maximum likelihood detection. In the linear model, the signal-to-interference plus noise ratios (SINRs) during the first (1 − τ )T /2 time at AP and U NJ are given as 2 Since the transmission of power and information occurs in two different phases (i.e., in DL and UL), it is supposed that However, in the non-linear model, the SINRs during the first (1 − τ )T /2 time at AP and U NJ are given as During the second (1 − τ )T /2 time, all U NJ combines their own signal x 2 with the coming signal from U F in a superimposed coding signal 3 and transmits the total signal simultaneously using the harvested power to AP. Thus, the AP received the same signal from L U NJ (i.e., L path). Hence, the received signal by AP in the channel corresponding to U NJ is given by where X = √ α 1 x 1 + √ α 2 x 2 . α 1 and α 2 are the power allocation coefficients of x 1 and is the channel between L U NJ and AP. µ t,NJA/r,NJA and ν t,NJA/r,N ȷA are the IQI coefficients at the TX/RX and equal to µ t/r and ν t/r in (1). P ð NJ denotes the transmit power of U NJ , which is depending on the linear or non-linear EH models as in (8) and (10), where ð = Lin, NL.
At AP, x 1 is detected firstly using MLD and x 2 is detected using the SIC. Thus, during this time, the SINRs of the linear model to detect x 1 and x 2 in the channel corresponding to U NJ at AP can be expressed as in (18) and (19), shown at the bottom of the next page.
Likewise, the SINRs of the non-linear model to detect x 1 and x 2 in the channel corresponding to U NJ at AP can be expressed as in (20) and (21), shown at the bottom of the next page. where r,NJA ) and ϱ is the effect of the SIC process. The AP receives multiple signals from L U NJ and U F . Thus, the AP received the signals from multi-path. Hence, the selection combining (SC) technique is assumed to be used at AP to select the best-received signal 4 based on all received signals from L U NJ and U F . Hence, the SINRs of x 1 and x 2 when the SC is implemented in the linear or non-linear models are given as where ð = Lin, NL.

III. PERFORMANCE ANALYSIS
In this section, we derive the OP, throughput and EC expressions of HTC-NOMA-WPCCN with linear and non-linear EH models under IQI and SIC imperfections.
The AP received the signal x 1 from different sources i.e., U F and U NJ . The SC is implemented at AP, where only the signal with the highest SINR among those received is utilized for detection. The OP of the SC for x 1 at AP can be written as Thus, (24) can be written as 4 It is assumed that the selection in the SC technique at the receiver is based on the higher channel quality of the received signals similar to the antenna selection strategy [42]. Generally, we can obtain a selection signal according to the higher-received SINR at AP [42].
By employing the probability density function (PDF) and the cumulative distribution function (CDF) of the dedicated Rayleigh fading channel as in [43], (25) can be calculated as (26), shown at the bottom of the next page.
By using [44, Eq. (3.324.1)], the integral of (26) can be written as where is defined for notation simplification with K 1 (·) denoting the modified Bessel function of the second kind with first order [44]. It is noted that through (27), the effects of IQI and ISIC influence OP performance.
Also, the OP of x 2 occurs when AP can not successfully decode the x 1 signal and x 2 signal. Based on these events, the OP of x 2 can be expressed as in [3], [4], and [34] as (28), shown at the bottom of the next page.
Each term of (28) is calculated as in (29) and (30) (shown at the bottom of the next page), respectively, where 1−τ − 1, r 2 is the target rate of x 2 and θ 2 is the transmission threshold of x 2 .
By substituting (29) and (30) into (28), we find the OP of x 2 at AP as given in (31), shown at the bottom of the next page. Through (29) and (30), it appears that the IQI and ISIC affect the OP performance of x 1 and x 2 respectively, and this leads to influences the OP performance of x 2 in (31).

2) NON-LINEAR EH
The outage performance of NOMA can be utilized in the non-linear EH model. In this instance, when implementing wireless power transfer architecture, our focus is on the threshold power of harvested value. Thus, to transmit the signal in the NOMA scheme, we take into account two instances of harvested power or transmit power deployed. As a result, the analytical formulas can be obtained using a method similar to that of the preceding sub-subsection, which dealt with a linear EH model. Thus, in the non-linear case, the outage behavior for x 1 at AP can be expressed as Thus, (32) can be re-written as [23] and [27] P SC where |h NJA | 2 < ζ 1 NJ , P t |h ANJ | 2 ≤ P th ) and I 4 = P (|h NJA | 2 < ζ 1 NJ ,1 , P t |h ANJ | 2 > P th ). We compute each term of (33) respectively below. I 1 can be written as Thus, (34) can be obtained as [23] and [27] Also, we obtain I 2 as By employing the PDF and CDF of the dedicated Rayleigh fading channel as in [4], [23], and [27], (36) is obtained as By using the same way, we obtain I 3 and I 4 respectively as given in (38) and (39) (shown at the bottom of the next Thus, to find the OP for x 1 at AP of the non-linear model, we substitute the (35), (37), (38) and (39) into (33) as given in (40) (shown at the bottom of the next page).
Likewise, the OP of x 2 in the non-linear model can be expressed as (41), shown at the bottom of the next page.
The term M 1 of (41) is calculated in (42) shown at the bottom of the next page.
Thus, to find the OP for x 2 at AP of the non-linear model, we substitute the (42) and (46) into (41) as given in (47) (shown at the bottom of the page 9).
The integral of equations (40) and (47) cannot be obtained in closed forms based on the authors' knowledge. However, they can be easily determined by numerical tools.

B. ERGODIC CAPACITY 1) LINEAR EH
Since the AP receives signals from multiple sources (U F , U NJ ), the SC is implemented to select the highest SINR from all received signals as given in (22) and (23) to employ it for detection. Thus, the achievable (Shannon) rate of x 1 can be written as By averaging R 1,Lin over SINRs in (48), we obtain the EC of x 1 as where f γ 1,Lin SC (z) is the PDF of γ SC 1,Lin . Recalling, dz where F Z (z) is the CDF of Z [44]. Thus, the EC of x 1 is given by where where ζ a Likewise, the achievable rate of x 2 at AP can be written as By averaging R 2,Lin , we obtain the EC of x 2 as where f γ SC

2,Lin
(z) is the PDF of γ SC 2,Lin . Hence, the EC of x 2 at AP can be expressed as 76512 VOLUME 11, 2023 Authorized licensed use limited to the terms of the applicable license agreement with IEEE. Restrictions apply. where . To the best of the authors' knowledge, (50) and (54) cannot be determined mathematically in closed forms. However, they can be easily determined by numerical tools.
Hence, (63) can be re-written as By averaging (64), we obtain where f ℑ 3 (z) and f ℑ 4 (z) is the PDF of ℑ 3 and ℑ 4 respectively. Hence, the (65) can be expressed as where 76514 VOLUME 11, 2023 Authorized licensed use limited to the terms of the applicable license agreement with IEEE. Restrictions apply.  We compute I 8 as To find the EC for x 1 at AP of the non-linear model, we substitute the (60), (61) and (62) into (59). Also, we obtain the EC for x 2 at AP of the non-linear model, we substitute the (67), (68) and (69) into (66). To the best of the authors' knowledge, the integral of (59) and (66) cannot be determined mathematically in closed forms. However, they can be easily determined by numerical tools.

C. THROUGHPUT
In this subsection, we analyze the throughput (with linear and non-linear EH) which is defined as the number of signals transmitted per period of time successfully. Thus, the throughput (for linear and non-linear EH) is formulated as [45] ℶ,ð = where P SC x ℶ ,ð (out) is the OP of x 1 and x 2 at AP for linear or non-linear EH and are obtained in (27), (31), (40) and (47).

IV. NUMERICAL RESULTS
In this section, we compute Monte Carlo simulations to prove the theoretical analysis. The lines in all figures indicate the simulation results, while the markers indicate the theoretical derivations. For a fair comparison, it is supposed that σ 2 =1 [46], SNR= Pt /σ 2 and SNR th = Pth /σ 2 . The parameters used in all simulations are given [47], ϱ = 0.01, η = 0.95, As a benchmark scheme, we consider that the UL NOMA scheme has two users far U F and near U N 1 from the AP. It is assumed that the users transmit their signal with their own power to the AP simultaneously, where the U N 1 has higher energy than U F . For fairness, as described in [11], [48], and [49], transmitted energy by users in the UL NOMA is equal to the total power P t while the transmitted energy by the users in HTC-WPCCN-NOMA is equal to P t /τ . The SIC is implemented at AP, where the U N 1 signal is detected directly using MLD due to its higher power, then using the SIC, U F signal is detected. To improve the performance of the VOLUME 11, 2023 76515 Authorized licensed use limited to the terms of the applicable license agreement with IEEE. Restrictions apply. U F , the HTC-NOMA-WPCCN is proposed as presented in Section II. The comparison between UL NOMA and our proposed scheme (with linear and non-linear EH model) under ideal and non-ideal IQI with ISIC when r 1 =0.2, r 2 = 0.3, and IRR=20 dB is presented in Fig. 3. In this figure, we observe that the OP of U F of our scheme with linear and non-linear EH outperforms the UL NOMA while the OP of U N 1 with ideal/non-ideal IQI was better only with J =1 and when J >1, the U NJ with ideal/non-ideal IQI and linear/non-linear EH outperforms the U N 1 of UL NOMA. In the non-linear EH, the U N 1 with ideal/non-ideal IQI in the high SNR regions was better than U NJ . It can be seen that the OP in the non-linear EH reaches a performance floor when SNR th =5 dB. The presence of IQI and ISIC in the non-linear EH increases the error floor at the high SNR regions and degrades the performance. It is clear that the non-linear EH with IQI affects the SIC performance and the detection signals at AP. We observe also the OP of both signals U F and U NJ improved as the number of J increased with ideal/non-ideal IQI, linear/ non-linear EH and with perfect/imperfect SIC. Moreover, it can be easily seen that the OP of both users with ideal IQI with all J is superior to the non-ideal condition. Also, the ISIC with linear/non-linear EH degrades the OP performance of the U NJ signal with ideal/non-ideal IQI conditions. In the case of an ISIC, the residual detection of the x 1 affects the detection of the x 2 signal, and this leads to a decrease in the OP performance of the x 2 with all U NJ .
In Fig. 4, we evaluate the effect of τ on the OP performance of both users' signals with U NJ under ideal/non-ideal IQI and linear/non-linear EH with ISIC when r 1 =0.009, r 2 =0.01, SNR= 10 dB and IRR= 20 dB. We observe that in the linear and non-linear EH, the OP of both users' signals decreased as τ increased with all J values under ideal/non-ideal IQI conditions. Again, the OP of both users' signals with J values under ideal IQI is superior to the non-ideal condition in all τ values. It can be seen also the non-linear EH degrades the performance of both signals, which more closely approaches a practical transmission.
As known in NOMA schemes, power distribution is important in detecting signals at receivers for evaluating systems performance. To evaluate the impact of α 2 on our system, Fig. 5, presents the OP of both users' signals with linear and 76516 VOLUME 11, 2023 Authorized licensed use limited to the terms of the applicable license agreement with IEEE. Restrictions apply.  non-linear EH w.r.t α 2 with U NJ under ideal and non-ideal IQI with ISIC when r 1 =0.05, r 2 =0.01, SNR= 20 dB and IRR= 20 dB. In the linear/non-linear EH, we observe that incrementing α 2 increases the performance of U F and decreases the performance of U NJ for the ideal/non-ideal IQI conditions. The non-linear EH degrades the OP performance of both users in all α 2 values. Again, the OP of both users' signals with J values under ideal IQI with the linear/non-linear EH outperforms the non-ideal condition in all α 2 values. It is clearly also with increasing J , the gaps between the ideal and non-ideal curves increase. Increasing α 2 with ideal/ non-ideal IQI conditions and linear/non-linear EH affects the SIC process and the detected signals at AP, however, the non-ideal IQI and non-linear EH have more influence on the SIC process because it creates more errors in the system, which emphasizes the significant influence of power allocation on the RF impairment.
In Fig. 6, we evaluate the impact of IRR on the OP of both users' signals for linear and non-linear EH with J values under ideal and non-ideal IQI with ISIC when r 1 =0.05, r 2 =0.01, and SNR= 20 dB. It is clear that as the IRR grows, the OP performance of the users for linear and non-linear EH with all J values increases and becomes almost exact to that of the ideal scenario (ideal IQI) in the high IRR. It means that a low IRR is a more severe condition of IQI. Also, the non-linear EH degrades the performance of both users. It more closely corresponds to practical transmission. Again, increasing J improves the OP of users with ideal/ non-ideal conditions at the AP. It is seen that the IQI has a variety of effects on the OP performance of the users in our considered system, according to the gaps between the curves representing perfect IQ matching and the IQI. These results present and emphasize the detrimental impacts of IQI and underscore the importance of bringing RF impairments into consideration. Fig. 7 presents the EC performance of HTC-NOMA-WPCCN and UL NOMA with ideal/non-ideal IQI, linear/ non-linear EH and perfect/imperfect SIC when SNR= 20 dB and IRR= 20 dB. It can be seen that the EC of U F of our proposed scheme outperforms the U F UL NOMA with ideal-non ideal IQI and linear/non-linear EH while the U N 1 for UL NOMA has better performance than U NJ despite increasing J . It is due to a higher power in the UL NOMA. Since the U F is targeted for improvement in all CNOMA schemes in the literature, the U N 1 of UL NOMA has better EC performance than U NJ . It can be seen also the EC performance decreases significantly in the non-linear EH case compared to linear EH, and the performance decreases more in the presence of IQI and ISIC. We observe also the EC performance of both users with linear/non-linear EH increases as J increases in all imperfections cases (ideal/non-ideal IQI and perfect/imperfect SIC). Also, it is seen that the ISIC decreases the EC performance of U NJ with ideal/non-ideal IQI conditions. The ISIC has a more significant impact in the presence of non-linear EH and non-ideal IQI. Furthermore, the EC performance of the ideal IQI outperforms the non-ideal case and the non-ideal decreases the EC performance of U NJ more than U F . It is due to the different power allocations of each user's signal and SIC process.
In Fig. 8, we present the EC performance of our considered system with linear and non-linear EH w.r.t τ with ideal/non-ideal and SIC imperfections when SNR=10 dB and IRR=20 dB. We observe that the optimal τ is proportional to the number of U NJ denoted as J with ideal/non-ideal conditions. It can be seen again the ideal IQI is superior to non-ideal conditions. The non-linear EH degrades the performance at high SNR regions compared to linear EH, which reflects the practical transmission. The change of τ values has more effects on the EC performance of the non-ideal IQI, which explains the influence of τ on the RF impairment of our system.
In order to examine the impact of α 2 on the EC performance of our system, Fig. 9, presents the EC performance of our considered system with linear and non-linear EH w.r.t α 2 with ideal/non-ideal IQI and SIC imperfections when SNR=20 dB and IRR=20 dB. In both linear and non-linear EH, it is observed that increasing α 2 increases the EC performance of U NJ and decreases the EC performance of U F with all J values for ideal/non-ideal IQI. Also, the EC performance of the users with all J values decreases in the presence of non-ideal IQI imperfections compared to the ideal IQI. Moreover, the non-linear EH degrades the EC performance compared to linear EH in all α 2 and the performance is more degraded in the presence of non-ideal IQI. It can be stated that the change in α 2 in the presence of non-ideal IQI conditions and non-linear EH affects the SIC and the detected signals at AP, highlighting the substantial effect of α 2 on RF impairment. 76518 VOLUME 11, 2023 Authorized licensed use limited to the terms of the applicable license agreement with IEEE. Restrictions apply. To examine the impact of IRR on the EC performance of our system, Fig. 10, presents the EC performance of our considered system with linear and non-linear EH w.r.t IRR with ideal/non-ideal IQI and SIC imperfections when SNR=20 dB. In both linear and non-linear EH, it is evident that when IRR increases, the EC performance of the users with all J values rises and closely matches the ideal case (ideal IQI) in the high IRR. Again, the non-linear EH decrease the EC performance compared to linear EH and the performance get worse in the presence of non-ideal IQI. Besides, increasing J increases the OP of users in the ideal/non-ideal IQI conditions. According to the gaps between the curves depicting perfect IQI matching and the non-ideal IQI, it can be shown that the non-ideal IQI has a range of effects on the EC performance of the users in the considered system which demonstrate the negative effects of IQI on RF impairments.
In Fig. 11, we present the throughput performance of our considered system with linear and non-linear EH compared to UL NOMA with ideal/non-ideal IQI and ISIC when r 1 =0.2, r 2 =0.3 and IRR=20 dB. It is observed that U F in the HTC-NOMA-WPCCN with linear and non-linear EH outperforms its counterpart in the UL NOMA scheme with the ideal/non-ideal IQI while U N 1 in the UL NOMA is superior to U NJ in HTC-NOMA-WPCCN with the ideal/non-ideal IQI and linear/non-linear EH. It is due to the different distribution of power allocation levels for users between the UL NOMA and HTC-NOMA-WPCCN. Also, the non-linear EH limits throughput performance and is affected more by the presence of non-ideal IQI, which more closely matches the practical operation of the transmission. It can be seen also the IQI has more effect on the U F than U N 1 in the UL NOMA. Also, we can observe a big impact of the IQI on all U NJ in HTC-NOMA-WPCCN with linear/non-linear EH compared to U F . It is due to the SIC process to detect U F signal in the systems. In this figure, we observe also the throughput performance with linear/non-linear EH increases with the increase of the J values in the ideal/non-ideal IQI and ISIC. The throughput performance of the ideal IQI outperforms the non-ideal condition. Furthermore, the ISIC with ideal/nonideal IQI conditions decreases the throughput performance with linear/non-linear EH despite the increase in J values. Fig. 13 presents the throughput performance with idea/non-ideal IQI and linear and non-linear EH under ISIC w.r.t τ when r 1 =0.01, r 2 =0.009, IRR=20 dB and SNR=10 dB. In both linear and non-linear EH, we observe that the increase τ increases the throughput performance of both users with ideal/non-ideal IQI in all J values. Besides, the increasing VOLUME 11, 2023 J improves the throughput performance with ideal/non-ideal IQI conditions. Again, the non-linear EH degrades the performance and is more impacted in the presence of non-ideal IQI conditions. It is observed that the choice of optimal τ is fully correlated with the number of J values to improve throughput performance, and this latter is affected by the IQI imperfections.
In order to examine the impact of α 2 on the throughput performance of our system, in Fig. 14, we present the throughput performance of our considered system with linear and non-linear EH w.r.t α 2 with ideal/non-ideal IQI and SIC imperfections when r 1 =0.2, r 2 =0.1, SNR=20 dB and IRR=20 dB. In both linear and non-linear EH, we observe that the change of α 2 affects the throughput performance of users with all J values for ideal/non-ideal IQI. Again, the non-linear EH degrades the performance of the system, which is more influenced by non-ideal IQI conditions. Also, the throughput performance of the users increases with all J values in the presence of ideal/non-ideal IQI conditions. It can be concluded that the SIC and the detected signals at AP are impacted by the change in α 2 and non-linear EH when the non-ideal IQI condition is available, emphasizing the significant impact of α 2 and non-linear EH on RF impairment.
To evaluate the effect of IRR on our system, Fig. 15, present the throughput performance with idea/non-ideal IQI and linear/non-linear EH under ISIC when r 1 =0.3, r 2 =0.2 and SNR=20dB. In both linear/non-linear EH, we observe that the increase in the throughput performance is proportional to an increase in J values. Also, throughput performance degrades in the non-linear EH and the impact increases with non-ideal IQI. Besides, the growth of the IRR increases the throughput performance of both users with all J values for linear/non-linear EH and is nearly matching the ideal IQI in the high IRR. It is clear that IQI has a negative impact on the RF impairments in our system.
To evaluate the effect of SNR th on our system, Fig. 15, presents the OP, EC and throughput performance w.r.t. SNR th with ideal/non-ideal IQI under ISIC when r 1 =0.3, r 2 =0.2 and SNR=20dB. We observe that in the OP, EC and throughput, the system performance improves as SNR th increases and creates an error floor at the high SNR th . Although the curves indicate enhanced performance when SNR th is high, this is