Abstract
In this paper, a combination of energy harvesting (EH) and cooperative nonorthogonal multiple access (NOMA) has been proposed for full-duplex (FD) relaying vehicle-to-vehicle (V2V) networks with two destination nodes over a Rayleigh fading channel. Different from previous studies, here both source and relay nodes are supplied with the energy from a power beacon (PB) via RF signals, and then use the harvested energy for transmitting the information. For the extensive performance analysis, the closed-form expressions for the performance indicators, including outage probability (OP) and ergodic capacity of both users, have been derived rigorously. Additionally, the effect of various parameters, such as EH time duration, residual self-interference (RSI) level, and power allocation coefficients, on the system performance has also been investigated. Furthermore, all mathematical analytical results are confirmed by Monte-Carlo simulations, which also demonstrate the optimal value of EH time duration to minimize the OP and maximize the ergodic capacity of the proposed system.
1. Introduction
Under the fast development of Internet of Things (IoT) devices and future wireless networks, e.g., the fifth generation (5G) of mobile communications and numerous solutions to improve the spectrum efficiency have been proposed and experimented. Among those solutions, the advanced techniques such as full-duplex (FD) relaying, nonorthogonal multiple access (NOMA), and massive multiple-input multiple-output (MIMO) have been arising as the most promising candidates [1–3]. Therefore, a lot of studies and experiments have been conducted to investigate those systems in practical scenarios to verify the potential of capacity increasing. Due to the fact that the FD communication can achieve double of system capacity compared to half-duplex (HD) with perfect self-interference (SI) cancellation, the study of FD systems becomes a hot topic. On the contrary, NOMA can improve the average system capacity in comparison with the traditional orthogonal multiple access (OMA) because it can help exchange information among multiple users at the same time, in the same frequency band, only with different power allocation coefficients.
The combination between FD communication and NOMA technique has been studied in the literature such as [4–7]. In [4], the authors analyzed the down-link NOMA system with a FD amplify-and-forward (AF) relay. In that work, the direct link from the source node to near user has been considered. Through numerical calculation, the authors obtained the analytical expressions to indicate the system performance, including outage probabilities (s) and ergodic capacities of both users. Based on that, the impact of residual self-interference (RSI) and power allocation coefficients were also investigated. In another aspect, Yue et al. [6] have utilized a cooperative NOMA system where the near user was employed as a relay, which can operate in either HD or FD mode and with decode-and-forward (DF) protocol. The authors considered two cases, i.e., with or without a direct link from the base station (BS) to the far user. expressions, ergodic rate, and energy efficiency have been derived for system performance analysis. Similar to [6], Zhang et al. [7] also considered a NOMA system, in which the near user operated as a FD relay to forward the signal to the far user. The authors derived the expressions of both users and compared with the conventional NOMA and OMA schemes.
Recently, various techniques have been applied for energy supply for wireless networks, including RF energy harvesting (EH) [5, 8–11]. Specifically, wireless devices first harvest energy from radio frequency signals and then use the harvested energy for exchanging data. Therefore, the EH technique is a promising solution for battery-limited devices. Due to the advantage of wireless charging, EH becomes popular in real-world applications such as personal mobile phones. Furthermore, to increase the amount of harvested energy at the transmitters, power beacon (PB) may be utilized to supply energy wirelessly to both source and relay before information transmission [10, 12–14].
In the literature, there have been several studies on the combination of EH, FD, and NOMA [5, 9, 15–17]. In [9], the authors considered a down-link NOMA system, where the source node transmits two signals to two users via a FD decode-and-forward relay node. In this model, the relay node has constrained power supply and must harvest energy through RF signals transmitted by the source. Based on the theoretical analysis, the authors derived of the considered system over Nakagami-m fading channel. Additionally, the optimal harvesting time and optimal power allocation coefficients to minimize were also obtained. In 2018, Alsaba et al. [5] investigated a cooperative NOMA system, where a strong user operated at the FD mode and forwarded the signal to a weak user. The authors successfully derived expressions for both users and studied the impact of imperfect self-interference and EH circuit on the system performance. Wang and Wu [15] and Guo et al. [16] investigated a similar system where the strong user (which is an EH-FD relay node) harvested energy from the source node for transmitting information messages. Furthermore, [17] extended this model to M relay nodes and K users. Different from [5, 9, 15, 16], the work in [17] investigated the case that the users harvest energy from the source. In summary, the previous studies considered either only FD relay (strong user) or weak user can harvest energy from the source. The case that both source and relay harvest energy from the power beacon has not been investigated.
Although the EH, FD, and NOMA are advanced techniques that play a key role for future wireless networks, the coexistence of these techniques in a unique system raises the complexity of processing to a very high level. However, with the fast development of circuit design as well as analog and digital processing techniques, hopefully the proposed system can be implemented in very near future. On the contrary, in practical networks, not only the relay node but also the source node has limited power supply. That leads to the idea of providing the energy to the source node before message transmission by using the power beacon (PB). With tremendous number of applications in many areas [18], FD communication has been considered particularly for vehicle-to-vehicle (V2V) communication networks. When vehicles move on the road, the end-to-end delay of the information transmission among them can be reduced significantly by applying FD communication. Moreover, with the ability to send and receive data simultaneously, the innovative technologies, such as cooperative, semiautonomous, and autonomous driving, can be supported. As a result, road and passenger safety is enhanced and traffic congestion is reduced. Because of the mobility of vehicles, it is difficult to supply energy to the wireless devices on the vehicle. To maintain the connectivity to other devices, they need to harvest energy from the RF signals for powering the data transmission. Therefore, EH is a promising solution for V2V networks.
Motivated by all these above facts, in this paper, we investigate an EH-FD-NOMA system, in which both source and relay nodes harvest energy from . After that, they utilize suitable circuits to transform the harvested energy to power for transmitting information. Furthermore, the relay node operates in the FD mode while the source node and two users operate in the half-duplex (HD) mode. Two users are located in different location from the relay. In particular, there is a strong user and the other is a weak user. Based on the analytical expressions of outage probability and ergodic capacities at both users, we investigate the system performance of the proposed system. The contributions of this paper can be summarized as follows:(i)We proposed a novel combination of EH, FD, and NOMA techniques in V2V networks. It is noted that in the previous studies about the similar combination, only the case that a strong user acts as a relay has been considered. In addition, only the relay can harvest the energy from the source node. In our model, we assume that both the source node and the FD relay node, which is not any one of the receiving users, harvest the energy from the power beacon through RF signals. This assumption leads to the complexity in mathematical derivations of the proposed system performance, compared with previous works. However, our model can be applied for V2V communication systems and future wireless networks, thus it is vital to investigate.(ii)We derive the exact theoretical expressions for the system performance in terms of outage probability, throughput, and ergodic capacity of both users in the case of imperfect self-interference cancellation at the FD relay node over Rayleigh fading channel.(iii)We analyze the system performance through analysis and simulation. The numerical results show that, with the suitable power allocation coefficients for both users, the performance measures of both users are the same. On the contrary, the impact of imperfect self-interference cancellation and the time for harvesting are also analyzed. In fact, there exists an optimal time duration for EH to minimize outage probability and maximize ergodic capacity. Finally, we conduct Monte-Carlo simulations to validate the analytical results.
The rest of this paper is organized as follows: Section 2 presents the system model, while Section 3 derives the system performance in terms of and capacity. Section 4 discusses about the numerical results and finally, Section 5 concludes this paper.
2. System Model
In this section, we introduce a system model that combines three techniques EH, FD, and NOMA, as illustrated in Figure 1. Here, the source node () simultaneously transmits two messages to both users ( and ) under the assistance of relay node (). We assume that and do not have their all power supplies due to their inconvenient locations. As a result, they must harvest the energy from RF signals. To supply enough power for and , we use a power beacon () to transmit energy to them. After the energy harvesting phase, and convert the received energy to the power for transmitting signals. As shown in Figure 1, , , , and are single-antenna devices while is equipped with two antennas. In this system, only operates at the FD mode, while other devices operate in the HD mode. In many analytical studies and experiments, can use one shared-antenna for transmitting/receiving the signal. However, in this work, we deploy two-antenna relay to identify clearly the SI and get the better SI cancellation. To transmit simultaneously two messages to two users, applies the NOMA technique in the power domain. Assume that the distances from two users to are different. In particular, is a far user and is a near user.
The operation of the EH-FD-NOMA system of interest is divided into two stages. During the first stage, transmits a RF signal to and . and harvest the energy through this RF signal and then convert it to the supply power. During the second stage, by using the harvested energy, transmits a message to , and at the same time transmits the decoded message from the previous block to and . Let T be the length of the entire transmission block. The time duration for the first stage is , while the time duration for the second stage is , where α is called time-switching ratio, . Figure 2 illustrates the time duration for EH and for information transmission.
Let and denote the harvested energies at and during the EH phase . Therefore, and are given as [19].where η is a constant that represents the energy conversion efficiency. Its value depends on the converting hardware and method (); P is the average transmit power of ; and and are, respectively, the fading coefficients of the channels from to and from to . As illustrated in Figure 1, in this paper, we investigate the case that only uses one antenna for EH. In practical systems, can use all antennas for harvesting energy by using suitable hardware resources [20]. Furthermore, and have a super capacitor to store the harvested energy. After the time duration of EH, and can fully use the harvested energy for transmitting information during the time . Therefore, the transmit power at and can be calculated as [21].where and are channel gains of the links and , respectively.
During the time duration , transmits a signal to . Simultaneously, forwards a signal to both users and on the same frequency band. That results in SI at . It is also noted that the message that is transmitted by are the combination of two messages for two users and . The messages transmitted by are the decoded messages at during the previous symbol block (as long as decodes successfully the received message). The received signal at can be calculated aswhere and are, respectively, the fading coefficients of the channels from and from the transmitting to the receiving circuits of ; and are NOMA coefficients with ; and are average transmit powers at and , respectively; are two messages for two users and , respectively; is the transmitted signals at ; and is the additive white Gaussian noise (AWGN) with zero-mean and variance of , i.e., .
From (3), the SI at is calculated by
In FD devices, various SI cancellation techniques can be applied to reduce the effect of RSI on the system performance such as isolation, propagation domain, and digital and analog cancellation. In fact, the relay definitely knows the transmit signal , so by using the results of SI channel estimation of , it can apply digital processing methods to subtract the SI from the received signals [22–25]. However, due to the hardware impairment and the imperfect estimation of the SI channel, SI may still exist in the system after applying various SI cancellation methods and degrade the system performance. Typically, the RSI, which is denoted by , can be modeled by the complex Gaussian distribution [23, 25–28] with zero-mean and variance , where . It is also noted that denotes the SI cancellation capability of the relay node. After SI cancellation, (3) becomes
From (5), (signal-to-interference-plus-noise ratio) to detect the message at (denoted by ) is calculated aswhere is the channel gain from .
After detecting , removes all ’s components from received signals and then detect . Thus, to detect message at (denoted by ) is given by
Due to the FD mode, during the time duration of , transmits the signals to both destinations and . We assume that the delay caused by signal processing at the relay is equal to one symbol period. Therefore, the transmitted signals at are the received signals in the previous period after processing. Then, the received signals at and are, respectively, given bywhere and are fading coefficients of channels from and , respectively and and are the AWGN terms with zero-mean and variance of , i.e., and .
By the principle of NOMA systems, the far user (user 1, denoted by in our paper) decodes its own message while user 2’s message is considered as interference. The near user (user 2 or in this paper) first subtracts the signal of the user through successive interference cancellation (SIC) to remove the interference from the far user . Then, it decodes its own message. In this paper, we assume that can perfectly remove interference. After that, the received signal at from (9) can be rewritten as
From equations (8)–(10), s at and can be calculated aswhere and are the channel gains of the links and , respectively.
It is also noted that, for DF relaying protocol, the end-to-end is calculated as
Therefore, the end-to-end s at and can be written as follows:
3. Performance Analysis
3.1. Outage Probability Analysis
In this section, the outage probability of the considered EH-FD-NOMA system is derived to evaluate the system performance. The system is the probability that makes the instantaneous falling below a predefined threshold [29]. To derive s for this system, let and (bit/s/Hz) be the minimum required data rates for the users and , respectively. By assuming the fairness of the users in this systems, we set . Then, at , denoted by , can be calculated aswhere is derived in (13). Let be the threshold. Then, the expression (15) can be rewritten as
At destination , the outage occurs when it does not decode successfully the signal or its own message . Therefore, we have
Theorem 1. The s at and of the cooperative EH-FD-NOMA system under the impact of RSI over Rayleigh fading channel are determined, respectively, as follows:where , and . Here, where and denote the average and instantaneous channel gains of the Rayleigh fading channel, respectively (); denotes the expectation operator; and is the first-order modified Bessel function of the second kind [30].
Proof of Theorem 1. To calculate and , from equations (16) and (17), we apply the probability rule in [31] to getOn the contrary, the cumulative distribution functions (CDFs) and probability distribution functions (PDFs) of the Rayleigh distribution can be determined as follows:By using equations (20)–(23) and doing some algebras, we can derive (18) and (19) in Theorem 1. For details of the proof, see in appendix A.
3.2. Ergodic Capacity Analysis
The ergodic capacity of the FD relay system is calculated bywhere γ is the end-to-end of the considered system and is the PDF of γ. To derive the closed-form expression of the ergodic capacity of the system, we rewrite (24) after some algebras aswhere is the CDF of the end-to-end of the considered system.
Theorem 2. The ergodic capacities of both users and are, respectively, given bywhere N is the complexity-accuracy trade-off parameter, , , , and .
Proof of Theorem 2. From (25), we calculate the ergodic capacities at () and () by replacing in (25) by and in (18) and (19), respectively. Therefore, and are calculated asBy applying the integral formulas in [32], we obtain the ergodic capacities at and in (26) and (27) after some mathematical transforms. In appendix B, we provide the details of proof.
4. Numerical Results
In this section, the EH-FD-NOMA system performance in terms of and ergodic capacity is plotted by using the expressions in Theorem 1 and Theorem 2. In addition, we also conduct the Monte-Carlo simulations on and ergodic capacity to demonstrate the correctness of theoretical formulas. The system performance is evaluated for different values of the average , where is the ratio between the transmit power of and the variance of AWGN, i.e., . In our simulations, we choose parameters for evaluating the system performance as follows: the power allocation coefficients are and , the energy harvesting efficiency at each node is , the average channel gains , and . The simulation results were obtained by using channel realizations.
In Figure 3, we consider the s of both users and versus the average . In this figure, we use the results of Theorem 1 to plot theoretical curves ((18) for and (19) for ) with , bit/s/Hz, and SI cancellation capability . It is obvious that the simulation curves exactly match with the theoretical ones. As can be seen from the figure, s of both users have the same performance and diversity order. They decrease when increases. On the contrary, at high regime (), the s of both users decrease slowly. If we continuously increase , the s will go to outage floor due to the RSI and NOMA coefficients. It is easy to see that, even if the RSI is very small and with high transmit power at , from (6) we have . If the RSI is larger, the outage floor will be reached sooner. Therefore, it is necessary to apply various SI cancellation techniques for the FD mode to avoid performance loss of the FD communication systems.
Figure 4 illustrates the throughput of the EH-FD-NOMA system versus average with various data transmission rates bit/s/Hz. It is also noted that the system throughput is defined by and . The other simulation parameters are the same as those in Figure 3. Figure 4 shows that at low regime (i.e., ), with low data transmission rate, i.e., , the throughput will reach the best value among three considered cases. When increases, such as from 14 to 26 , the optimal throughput is obtained when . In the case of the system throughput reaches the maximal value with . Therefore, depending on the transmit power at , we can suitably choose the data transmission rate for the considered system to get the optimal throughput and improve the overall system performance.
Figure 5 shows the impact of EH time-switching ratio α on the s of the considered system with bit/s/Hz and . As can be seen from the figure, there is an optimal value of α corresponding to a pretransmit power of . For example, with , the optimal value is . In the case of , the value is , and in the case of , . Consequently, based on the transmit power at , we can adjust the EH time-switching ratio in order to improve the system performance.
Figure 6 illustrates the ergodic capacity of both users under the impact of SI cancellation capability with . In this figure, the theoretical curves are plotted by using equations (26) and (27) in Theorem 2, while the marker symbols are plotted by Monte-Carlo simulations. It is obvious that the ergodic capacity increases when increases, especially when RSI is small such as . In the case of , the ergodic capacity at both users increases about 0.6 bit/s/Hz comparing with the case of . The gain for the system capacity is about 1.2 bit/s/Hz. Figure 6 shows the strong impact of RSI on the capacity of the considered system. Thus, to deploy this system in realistic scenarios, wireless researchers and designers need to design circuits and build algorithms in order to improve the SI cancellation.
Finally, Figure 7 plots the ergodic capacities of the EH-FD-NOMA system with various time durations of α in the case of . This figure shows that the ergodic capacities of users and increase when α increases. For example, the ergodic capacity in the case of is the best capacity compared with the case of and . However, at high , such as , the ergodic capacities of three considered cases are the same. The results in Figure 7 are compatible with those in Figure 5. By combining Figures 5 and 7, we can clearly see that when , we choose to get the best performance and best capacity of the considered system.
5. Conclusion
In this paper, we propose a novel combination of three advanced techniques, namely, EH, FD, and NOMA, in a so-called EH-FD-NOMA communication system, which can be applied for V2V communication networks. By mathematical analysis, we derive exact expressions of outage probability and ergodic capacity at both users under the impact of residual self-interference at the FD relay node. Our results show that the two users can obtain the same performance and capacity, i.e., the fairness is guaranteed. Depending on the transmit power at the power beacon, there is an optimal value for EH time-switching ratio to minimize the outage probability and maximize the capacity. Furthermore, the impact of data transmission rate, residual self-interference level, and time-switching factor α is also investigated. Numerical results demonstrate the importance of self-and-successive-interference cancellation on the performance of the considered system. Those results serve as important references for wireless researchers and designers in deployment of the EH-FD-NOMA system in practice.
Appendix
A. Proof of Theorem 1
In this appendix, we provide step-by-step procedure of how to derive the expressions of outage probability at both users of the proposed EH-FD-NOMA system over Rayleigh fading channels.
For , from (20), we calculate in (A.1) and in (A.2) as follows:
It is noted that, in the case of , the probabilities in (A.1) and (A.2) always occur. Therefore, and , which lead to . After doing some algebras and applying [30, 3.324.1], we derive and at the end of (A.1) and (A.2). By substituting (A.1) and (A.2) into (20), we obtain in (18) in Theorem 1.
For , based on the equation (21), we can calculate as in (A.3) and as in (A.4):
It is also noted that when , we always have . In the case of , we have , that means . Otherwise, we have . Therefore, we can transform the second line to the third line of (A.3) and (A.4). After doing some algebraic manipulations and using [30, 3.324.1], we obtain the final expressions of in the last line of (A.3) and in the last line of (A.4). After that, we can substitute (A.3) and (A.4) into (21) to achieve (19) as in Theorem 1.
The proof is complete.
B. Proof of Theorem 2
This appendix is used to provide the detailed proof of Theorem 2. From (29) and (30), we have
Due to the complexity of equations (B.1) and (B.2), it is difficult to derive the closed-form expressions for ergodic capacity at both users. In this case, we apply the Gaussian–Chebyshev quadrature method in [32] to obtain the ergodic capacity for both users.
The first and second terms in (B.2) are, respectively, calculated as
By substituting (B.3) and (B.4) into (B.2), we obtain the capacity of user as in (27). Similarly, the capacity of user is obtained as in (26).
The proof is complete.
Data Availability
The simulation data used to support the findings of this study are included within the article.
Conflicts of Interest
The authors declare that they have no conflicts of interest.
Acknowledgments
This research is funded by the Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 102.04-2017.317.