Performance Evaluation of Cooperative NOMA-based Improved Hybrid SWIPT Protocol

In the proposed CNOMA-IHS scheme, $x_{1}$ is transmitted from $S$ to the users using $A_{1}$ signal with transmitted power $P$. So, $A_{1}$ can be expressed as below:

where $x_{1}$ denotes a data symbol for $UE_{2}$. In addition, $x_{1}$ is transmitted to $UE_{1}$, which harvests the energy during the first segment of phase 1 ($\theta T$). Moreover, $A_{1}$ is received by $UE_{2}$ and $UE_{2}$ decodes $x_{1}$ during the first segment of phase 1 ($\theta T$). The received signals at $UE_{1}$ and $UE_{2}$ are expressed by the following equations:

where $n_{1}\sim CN(0,\sigma^{2})$ and $n_{2}\sim CN(0,\sigma^{2})$ are the complex white Gaussian noises at $UE_{1}$ and $UE_{2}$, respectively, with variance $\sigma^{2}$ and zero mean. The received SINR for $x_{1}$ at $UE_{2}$ can be derived as follows:

where $\rho\triangleq\frac{P}{\sigma^{2}}$ denotes the transmit signal-to-noise ratio (SNR) and $\sigma^{2}$ denotes the additive white Gaussian noise variance for all received signals described in this study [20]. Following the principles of DL NOMA, during the second segment of phase 1 (($(1-\theta)T/3$)), $S$ transmits the superposition signal ($A_{2}$) to $UE_{1}$ and $UE_{2}$, as indicated below:

where $x_{2}$ and $x_{3}$ denote the data symbol for $UE_{1}$ and $UE_{2}$, respectively [11–12]. $UE_{1}$ acquires $x_{2}$ using SIC. The imperfect SIC is assumed at $UE_{1}$. Thus, the residual interference due to imperfect SIC is quantified by $\beta$ ($0\leq\beta\leq 1$). So, $\beta=1$ refers to imperfect SIC and $\beta=0$ refers as perfect SIC [22]. So, the received signals at $UE_{1}$ can be expressed by the following equation:

The received SINR corresponding to the symbols, $x_{2}$ ($\gamma_{x_{2}}^{t_{1}}$) and $x_{3}$ ($\gamma_{x_{3}->x_{2}}^{t_{1}}$) at $UE_{1}$ by SIC can be expressed as follows [11-13,23]:

Furthermore, IHS-based SWIPT is used at $UE_{1}$ [11–13, 23]. According to Figure 2, $UE_{1}$ uses the $\delta$ proportion of the received power for EH. Moreover, $UE_{1}$ uses the fraction ($1-\delta$) of the received power for information decoding (ID). In addition, the directly received signal at $UE_{2}$ from $S$ is expressed as follows:

Furthermore, $x_{3}$ is directly decoded by $UE_{2}$ using the direct link from $S$. The received SINR corresponding to $x_{3}$ ($\gamma_{x_{3}}^{t_{1}}$) at $UE_{2}$ can be expressed as follows:

During phase 2 (($(1-\theta)T/3$), $\hat{x}_{3}$ is transmitted by $P_{1}$ from $UE_{1}$ to $UE_{2}$ by utilizing the harvested energy (Figure 2). It can be assumed that $UE_{1}$ can perfectly decode the $x_{3}$ symbol during the second segment of phase 1 (($(1-\theta)T/3$)) (Figure 2) [11, 20, 23–24]. The power splitting (PS)-based SWIPT is implemented by $UE_{1}$ for EH to relay the decoded $\hat{x}_{3}$ from $UE_{1}$ to $UE_{2}$. The signal received by the DF relaying from $UE_{1}$ to $UE_{2}$ can be expressed as follows:

Thus, the received SINR at $UE_{2}$ from $UE_{1}$ corresponding to the symbol $\hat{x}_{3}$ ($\gamma_{x_{3}}^{t_{2}}$) owing to the DF relay can be expressed as follows :

Thus, the DF relaying from $UE_{1}$ to $UE_{2}$ is performing by the transmitted power $P_{1}$ from $UE_{1}$. $P_{1}$ utilizing the harvested energy which can be expressed as follows by [11–13]:

where $E_{1}=\eta\rho|h_{S,1}|^{2}\theta T+\eta\delta\rho|h_{S,1}|^{2}(1-\theta)T/3$ is the harvested energy at $UE_{1}$ by IHS protocol [11-13]. Moreover, $\eta$ represents the energy conversion efficiency that relies on the EH circuit and $0<\eta<1$ [11–13,20]. Moreover, $S$ directly transmitted a signal ($A_{3}=\sqrt{p_{N}P}x_{4}$) from $S$ to $UE_{1}$ by $p_{N}P$ during $t_{2}$. Because, $x_{4}$ is only transmitted for $UE_{1}$. So, the signal received at $UE_{1}$ during $t_{2}$ can be expressed as follows:

Thus, the received SINR for $x_{4}$ at $UE_{1}$ during phase 2 owing to direct transmission can be represented as follows:

By assuming normalized total time duration and total transmit power, the capacity of $x_{1}$ can be calculated as follows:

Moreover, the achievable capacities of $x_{2}$ and $x_{3}$ can be calculated as follows [2,9,11–13,20]:

In addition, the achievable capacities of $x_{4}$ can be calculated as follows [2,9,11–13]:

Thus, the achievable SC can be calculated using the following equations [2,9,11–13,20]:

where E[.] represents the mean or expectation operator. Moreover, $C_{1}$, $C_{2}$, and $C_{sum}$ denote the respective channel capacities of $UE_{1}$, $UE_{2}$, and ESC for the proposed CNOMA-IHS scheme.

The analytical ergodic capacity (EC) of $UE_{1}$ can be expressed by Theorem 1. The values of the variables are considered identical. Various variables are assumed for information transfer by transmitting various symbols (i.e., $x_{2}$ and $x_{4}$) from $S$ in different phases for $UE_{1}$, utilizing different power allocations from $S$ in the case of the proposed scheme. The EC in the case of $UE_{1}$ for the proposed scheme can be analytically expressed using Theorem 1.
Theorem 1. The EC of $UE_{1}$ ($C_{1}^{erg}$) in the case of CNOMA-IHS is expressed by the following equation:

where $g\triangleq(1-\delta)\lambda_{S,1}\rho p_{N}$ and $h\triangleq\lambda_{S,1}\rho p_{N}$ due to direct transmission of $x_{2}$ by superimposed signal along with PS based EH and direct transmission of $x_{4}$ during $t_{1}$ and $t_{2}$, respectively. Moreover, Ei(.) denotes the exponential integral function.

The EC of $UE_{2}$ for the proposed CNOMA-IHS scheme can be analytically derived using Theorem 2
Theorem 2. The EC of $UE_{2}$ ($C_{2}^{erg}$) for the CNOMA-IHS scheme is expressed as follows:

where, $l=\frac{1}{\lambda_{S,1}\rho(1-\delta)}$, $q=\frac{1}{\lambda_{1,2}\rho}$, $r=\frac{1}{\lambda_{S,1}\rho p_{N}(1-\delta)}$, $s=\frac{1}{\lambda_{1,2}\rho p_{N}}$, $u={\lambda_{S,2}\rho}$, and Ei(.) represents the exponential integral function.

By adding (25) and (29), the analytical expression of ESC of the proposed CNOMA-IHS can be derived as follows:

The evaluation of EE and the optimization technique of EE for the proposed CNOMA-IHS scheme is describe in this subsection. $UE_{1}$ uses the energy harvested by the proposed CNOMA-IHS scheme to conduct a relay operation. The relay of $\hat{x_{3}}$ from $UE_{1}$ to $UE_{2}$ is conducted during phase 2 of the proposed IHS protocol using $P_{1}$. Thus, EE is the ratio of the ESC ($C_{sum}$) to the total transmit power for direct transmission ($2P$ and $p_{N}$) and transmit power of $UE_{1}$ for DF-based relay operation ($P_{1}$) [28]. Therefore, the EE corresponding to the proposed CNOMA-IHS scheme can be derived using the following equation:

As $\theta$ is the dominating factor than $\delta$ in case of HS SWIPT protocol [11–13]. Hence $\theta$ based EE optimization technique is considered for the proposed CNOMA-IHS scheme [18]. Thus, the optimal $\theta$ ($\theta^{*}$) can be derived to achieve EE maximization by below equation:

As benchmark, OMA-IHS scheme is considered and compared with the proposed CNOMA-IHS scheme for fair comparisons. In the case of OMA, time division multiple access has been considered in this study. In this scenario, $S$ directly delivers different information signals to $UE_{1}$ and $UE_{2}$ separately using various independent time slots. Furthermore, one additional time slot is required to perform TS-based EH at $UE_{1}$. Moreover, an additional time slot is required to perform the DF relay of $\hat{x}_{3}$ from $UE_{1}$ to $UE_{2}$. Various independent time slots are allocated for $UE_{1}$ and $UE_{2}$ related to various symbols for information transfer (e.g., $x_{1}$, $x_{2}$, $x_{3}$, and $x_{4}$), EH (e.g., EH at $UE_{1}$) and for DF relaying of $\hat{x}_{3}$ are denoted by $t_{1}$, $t_{2}$, $t_{3}$, $t_{4}$, $t_{5}$, and $t_{6}$, respectively, because the IHS protocol is a combination of TS and PS-based SWIPT. Total six time slots are used in case of OMA-IHS scheme. Among them, four time slots are used for information transfer from $S$ to the users and one time slot is using for TS-based EH and another for DF relaying. At first, $x_{1}$ is transmitted to $UE_{1}$ during $t_{1}$ for the TS-based EH. Then, $x_{1}$ is transmitted to $UE_{2}$ during $t_{2}$ for information transfer. In addition, $x_{2}$ is transmitted from $S$ to $UE_{1}$ by $t_{3}$ for information transfer. In the case of PS-based SWIPT, $UE_{1}$ uses a fraction ($\delta$) of the received power for EH. Furthermore, the rest of the fraction ($1-\delta$) of the received power is used for ID during time slot $t_{3}$ [17, 20]. Subsequently, $x_{3}$ is transmitted from $S$ to $UE_{2}$ by $t_{4}$ for information transfer. Moreover, $\hat{x}_{3}$ relays from $UE_{1}$ to $UE_{2}$ during $t_{5}$ using the power ($P_{1}$) which utilizing the harvested energy. Afterwards, $x_{4}$ is directly transmitted to $UE_{1}$ from $S$ during $t_{6}$ for information transfer as well. All these transmissions are performed by the total transmit power of $P$ from $S$. In addition, $t_{1}=t_{2}=t_{3}=t_{4}=t_{5}=t_{6}=\frac{1}{6}$ are considered in this study for the OMA-IHS scheme to complete all the EH, information transfer, and relaying. Thus, the capacity of $x_{1}$ at $UE_{2}$ in the case of OMA-IHS can be expressed as follows [2,20,25–26]:

In addition, the achievable capacities of $x_{2}$ and $x_{3}$ corresponding to the OMA-IHS scheme can be calculated as follows [2,20,24,26]:

where $\gamma_{x_{1}}^{OMA}={\rho{{|h_{S,2}|^{2}P}}}$. $\gamma_{x_{2}}^{OMA}={(1-\delta)\rho{{|h_{S,1}|}^{2}}P}$, $\gamma_{x_{3}}^{OMA}={(1-\delta)\rho{{|h_{S,1}|}^{2}}P}$, $\gamma_{x_{4}}^{OMA}=\rho{{{|h_{S,1}|}^{2}}P}$, $\gamma_{\hat{x}_{3}}^{OMA}={\rho{{|h_{1,2}|}^{2}}P_{1}^{OMA}}$, $\gamma_{x_{4}}^{OMA}={\rho{{|h_{1,2}|}^{2}}P}$, and $P_{1}^{OMA}=\eta\rho|h_{S,1}|^{2}(\frac{6\theta}{1-\theta}+\delta)$. Thus, the ESC of the OMA-IHS scheme can be expressed as follows [2,20,25–26]:

Here, E[.] denotes the expectation operator. $C_{1}^{OMA}$, $C_{2}^{OMA}$, and $C_{sum}^{OMA}$ denote the respective channel capacities of $UE_{1}$, $UE_{2}$, and ESC in case of the OMA-IHS scheme. Moreover, the associated EE for the OMA-IHS can be derived using the following equation [13,15,28]:

Therefore, the aforementioned equation demonstrates that EE is related to $C_{sum}^{OMA}$, $P$, and $P_{1}^{OMA}$.

Figure 3 illustrates that the proposed scheme exhibits a higher capacity than the conventional schemes for different transmit SNRs ($\rho$). The parameters, $T=1$, $d_{S,1}=0.6$, $d_{S,2}=1$, $\eta=1$, $\delta=\theta=0.4$, $R_{th,1}=R_{th,2}=0.3$, $\beta=1$, $v=2$, and $d_{1,2}=d_{S,2}-d_{S,1}$, are considered for the MATLAB simulation. Moreover, for each value of $\rho$, the ESC of the proposed CNOMA-IHS scheme is significantly higher than those of the other schemes. This is because the additional symbols ($x_{1}$ and $x_{4}$) are transmitted to $UE_{2}$ and $UE_{1}$, respectively, using the CNOMA-IHS scheme without consuming any additional resource. Hence, the user channel capacities and ESC improvement is achieved for the proposed scheme. Thus, the proposed scheme exhibits higher ESC than the other compared schemes. Moreover, the analytical results validate the simulation results of ESC for the proposed CNOMA-IHS scheme which depicted in Figure 3.

Figure 4 illustrates that owing to an increase in $d_{S,1}$, the ESC corresponding to the proposed scheme is higher than those corresponding to other compared schemes. The parameters, $T=1$, $d_{S,2}=1$, $\eta=1$, $\delta=\theta=0.4$, $\rho=15dB$, $R_{th,1}=R_{th,2}=0.3$, $\beta=1$, $v=2$, and $d_{1,2}=d_{S,2}-d_{S,1}$, are considered for the simulation. The position of the relaying node ($UE_{1}$) varies depending on the variations of $d_{S,1}$. But $x_{1}$ and $x_{4}$ are transmitted towards $UE_{1}$ and $UE_{2}$ during phase-1 and phase-2, respectively. Thus, the achieved ESC is significantly higher than the other compared schemes. Furthermore, in the case of the proposed scheme, the amount of energy harvested is higher than those of the other schemes, as CNOMA-IHS comprises PS- and TS-based SWIPT protocols. Thus, the harvested energy is sufficient for the relay operation by $UE_{1}$ in the case of higher values of $d_{S,1}$ corresponding to the proposed CNOMA-IHS scheme.

The comparative analysis depicted in Figure 5 indicates that increasing $\theta$ influences the ESC of the proposed CNOMA-IHS scheme. The parameters, $T=1$, $d_{S,1}=0.6$, $d_{S,2}=1$, $\rho=15dB$, $\delta=0.4$, $\eta=1$, $R_{th,1}=R_{th,2}=0.3$, $\beta=1$, $v=2$, and $d_{1,2}=d_{S,2}-d_{S,1}$, are considered for the MATLAB simulation. For increasing values of $\theta$, ESC decreases significantly in the case of conventional TS-SWIPT protocol based schemes (CNOMA-HS [11], WP-CNOMA [14], and CNOMA-TS [20]) but ESC increases significantly in the case of the proposed CNOMA-IHS scheme. Because of the higher value of $\theta$ can enhance the harvested energy at $UE_{1}$ for relaying. Hence, only $\theta T$ segment of phase-1 is directly involved to perform TS-based EH at $UE_{1}$ in the case of conventional TS-SWIPT protocol based schemes (CNOMA-HS[12] (HS protocol is the combination of TS and PS based SWIPT), WP-CNOMA[22], and CNOMA-TS[20]). Hence, the remaining time segments are not sufficient which are used for NOMA-based direct transmission, and DF relaying [11–13,20,23]. Therefore, higher values of $\theta$ degrade the user capacities of the conventional TS-based SWIPT schemes. Hence, the ESC of the CNOMA-HS [12], WP-CNOMA [14], and CNOMA-TS [20] schemes, is degraded owing to the increasing values of $\theta$. In contrast, $x_{1}$ is transmitted to $UE_{2}$ during the first segment of phase-1 ($\theta T$) along with the TS-based EH at $UE_{1}$, which enhances the capacity of $UE_{2}$ as well as ESC of the proposed CNOMA-IHS scheme. Though other time segments of the protocol for the proposed CNOMA-IHS scheme are not sufficient to perform direct transmission and DF relaying. Thus, the proposed CNOMA-IHS scheme provides higher ESC than other compared TS-SWIPT based CNOMA schemes owing to increasing values of $\theta$.

The comparative analysis illustrated in Figure 6 indicates that $\delta$ influences the ESC of the proposed CNOMA-IHS scheme. The parameters,$T=1$, $d_{S,1}=0.6$, $d_{S,2}=1$, $\rho=15dB$, $\theta=0.4$, $\eta=1$, $R_{th,1}=R_{th,2}=0.3$, $\beta=1$, $v=2$, and $d_{1,2}=d_{S,2}-d_{S,1}$, are considered for the MATLAB simulation. The ESC is decreasing in the case of the proposed and PS-based schemes (CNOMA-IHS, CNOMA-HS[12], and CNOMA-PS[20]) for increasing values of $\delta$. Due to the higher value of $\delta$, the harvested energy at $UE_{1}$ is increase but the ID cannot perform successfully because ($1-\delta$) amount of energy is used for ID at $UE_{1}$ which is degraded due to the higher value of $\delta$. Hence, the relaying cannot perform effectively by $UE_{1}$ since the signal decoding cannot perform successfully by less amount of energy due to the higher value of $\delta$. Furthermore, in the case of the proposed CNOMA-IHS scheme, additional symbols ($x_{1}$ and $x_{4}$) are transmitted to $UE_{2}$ and $UE_{1}$ without consuming any additional resources or interference. Hence, the higher individual user channel capacities and higher ESC are also achieved for the proposed scheme due to different values of $\delta$.

The comparative analysis depicted in Figure 7 indicates the impact of $\eta$ on the ESC of the proposed scheme and the other conventional schemes. The parameters, $T=1$, $d_{S,1}=0.6$, $d_{S,2}=1$, $\rho=15dB$, $\delta=\theta=0.4$, $R_{th,1}=R_{th,2}=0.3$, $\beta=1$, $v=2$, and $d_{1,2}=d_{S,2}-d_{S,1}$, are considered for the MATLAB simulation. Figure 7 illustrates that $\eta$ does not have much influence on the ESC in the case of the proposed scheme and other compared schemes. However, CNOMA-IHS transmits the additional symbols ($x_{1}$ and $x_{4}$) to the users utilizing different phases without consuming any additional resources or any interference issue. Hence, the user channel capacities, as well as ESC, corresponding to the proposed CNOMA-IHS scheme are significantly higher compared with the other schemes for different values of $\eta$.

The EE comparisons between the proposed CNOMA-IHS scheme and the other compared schemes are depicted in Figure 8 with and without the EE optimization technique. The parameters, $T=1$, $d_{S,1}=0.5$, $d_{S,2}=1$, $\eta=1$, $\delta=\theta=0.4$, $\rho=15dB$, $R_{th,1}=R_{th,2}=0.3$, $\beta=1$, $v=2$, and $d_{1,2}=d_{S,2}-d_{S,1}$, are considered for the MATLAB simulation. The CNOMA-IHS exhibits higher EE than other TS-based compared schemes (e.g., CNOMA-HS[11], WP-CNOMA[14], CNOMA-TS[20], and OMA-IHS). This phenomenon occurs because additional symbols ($x_{1}$ and $x_{4}$) are transmitted to the users by the proposed CNOMA-IHS scheme to enhance the ESC of the proposed compared scheme. This leads to the use of additional power by the proposed scheme but significantly higher ESC is also achieved by the proposed CNOMA-IHS scheme. Thus, the proposed scheme outperforms the other schemes in case of EE without EE optimization. In addition, due to the optimized value of $\theta$ ($\theta^{*}$), significant EE gain can be achieved in the case of the proposed CNOMA-IHS scheme with EE optimization compared to the proposed scheme without EE optimization.