Abstract
To extend the lifetime of energy-constrained wireless networks, this paper proposes a three-node model of the wireless-powered cooperative communication network (WPCCN). The model consists of an energy-constrained source node, an energy-sufficient relay node, and a destination node and considers two different cochannel interference (CCI) sources at the relay and destination nodes. To ensure the reliability of data transmission, we introduce the cooperative automatic retransmission request (CARQ) protocol, propose the energy-constrained source that harvests and cooperates automatic retransmission request (ECS-HTCARQ) protocol in interference scenario, derive a closed-form expression for the outage probability under Rayleigh fading channels, and establish a discrete-time Markov chain (DTMC) model to analyze the system throughput. The relationship between parameters such as the energy harvesting time allocation factor and energy harvesting efficiency on the outage probability and the system throughput is obtained. Numerical results show that the difference in system throughput is small as the increasing number of transmissions at a high signal-to-interference ratio (SIR), but there is a significant reduction in the outage probability. Finally, the optimal value of the energy harvesting time allocation factor is given under this model.
1. Introduction
In recent years, for energy-constrained wireless networks, replacing or charging batteries is costly and not easily achievable; besides, it is not an effective and sustainable approach, while energy harvesting (EH) has received much attention from researchers as a reliable and sustainable technology that can prolong the network lifetime [1–3]. EH technology collects energy in two primary ways: one is to use natural energy, including wind energy, solar energy, and water energy; the other is to adopt electromagnetic radiation, where wireless radio frequency energy harvesting (RFEH) technology is advantageous, because energy-constrained nodes through the RF signal radiated in the environment for energy harvesting and then harvested energy for information transmission. The authors in [4] studied the optimization of network delay, power allocation, and energy transfer in wireless sensor networks (WSNs) for EH. Literature [5] adopted RFEH technology in wireless body area networks (WBANs) and proposed an energy-efficient sleep scheduling algorithm with work-on-demand to prolong the network life. With the further development of antenna technology and EH technology, RFEH technology was widely adopted in WSNs, WBANs, and wireless charging systems (WCS) [4–6].
Wireless energy transfer is transferring energy to other devices in a wireless way. Two technologies are using RFEH for powering wireless network devices: one is simultaneous wireless information and power transfer (SWIPT) and the other is the wireless-powered communication network (WPCN). In [7, 8], addressing the trade-off between energy transfer and information transmission, the authors compared the rate-energy (RE) domain and outer boundaries of two EH receivers (i.e., time switching (TS) and power splitting (PS)) under the SWIPT network architecture and provided a solution for designing the best practical receiver. For the problem of optimal power allocation, literature [9–11] investigated the PS receiving mechanism of SWIPT and gave solutions according to different allocation standards. To increase the transmission range in the heterogeneous network (HetNet) environment, literature [12] proposed a hybrid backscatter communication model suitable for WPCN and adopted the harvest-then-transmit (HTT) mechanism to study the throughput maximization problem under this model. In [13], for addressing the information transmission problem of secondary networks under cognitive WPCN, the authors proposed a novel hybrid HTT and backscatter communication. However, this does not apply to long-distance energy supply and data transmission. Literature [14] investigated a hybrid relay node (HRN) relay-assisted WPCN, adopted a harvest-then-cooperate (HTC) mechanism, and gave an optimization algorithm for the energy efficiency of the joint duration and power allocation problems in amplify-and-forward (AF) and decode-and-forward (DF) strategies. In this paper, we focus on studying the trade-off between energy transfer and information transmission under the WPCN structure, consider energy supply by an energy-sufficient relay node, adopt the HTC mechanism, and discuss the relationship between the impact of parameters such as the time allocation factor on outage probability and system throughput.
The cooperative communication (CC) technique used relay nodes for assisting the source node to transmit information to the destination node, which enhanced the performance of system outage probability, throughput, and energy efficiency [15–20]. In cooperative relay networks, AF and DF are two relay-forwarding strategies used frequently. AF strategy has lower complexity and is usually used in network environments with poor channel quality, while DF has higher complexity and is used for better channel quality [21, 22]. Thus, this paper adopts the DF relay-forwarding strategy in the high signal-to-interference ratio (SIR) environment. To further improve performances such as outage probability and throughput of the communication network, literature [23, 24] introduced the CARQ technology, which significantly improved the network performances compared to the traditional ARQ. In WSNs, [25] proposed a novel CARQ technology and established a discrete-time Markov chain (DTMC) model, which outperformed the traditional ARQ with an increasing number of transmissions at long-distance communication. In [26], the authors used the Go-Back-N ARQ (GBn-ARQ) technology to study the error control system for underwater wireless sensor networks and also analyzed the performance of throughput and delay under different system parameters. Inspired by the literature [14, 25], we consider introducing CARQ technology to establish a three-node model of the wireless-powered cooperative communication network (WPCCN), further improving the performance of the considered network.
Due to the limited spectrum of resources in nature, it was essential to consider interference factors [27, 28]. For wireless communication networks in the interference scenario, literature [27, 28] used DF and AF strategies to study their systems, respectively, which gave solutions to improve the reliability of data transmission in the interference scenario. Since the interfering transmitter affects the quality of received signals at the relay and destination nodes, literature [29] investigates the energy efficiency performance of SWIPT-enabled collaborative relay networks with the interfering transmitter. Discovering a model where the relay collects both the interference and the source node signal has a higher energy efficiency than a model where the relay harvests only the source node signal. In this paper, we consider the existence of cochannel interference (CCI) at the receptive nodes, introduce CARQ technology to improve the network system performance, and study the network performance under the WPCCN. Finally, the energy-constrained source that harvests and then cooperates automatic retransmission request (ECS-HTCARQ) protocol in the interference scenario is proposed, modeled, and analyzed.
The main contributions of this paper are summarized as follows.(1)To be more actual, we consider that there are different CCI nodes at the received signal nodes, use the DF relay forwarding strategy, and adopt selection combining (SC) to perform signal merging at the destination node. Finally, a three-node model of WPCCN in the interference scenario is given.(2)This paper adopts the HTC mechanism to harvest energy and then cooperative transmission. This model studies the problem of supplying energy from energy sufficient relay node to an energy-constrained source node, which has the advantage of a wider energy supply and transmission range compared with the nonrelay node, so it is more suitable for the medium and long-distance scenario.(3)We establish the DTMC model of ECS-HTCARQ. Based on this model, we derive the closed-form expressions of the outage probability and system throughput, obtain the relationship of parameters such as the time allocation factor on the outage probability and system throughput, and give the optimal time allocation factor under different parameter settings.
The remainder of this paper is organized as follows: Section 2 shows the system model and transmission mechanism, Section 3 gives the closed-form expression for the outage probability, Section 4 analyzes the system throughput, Section 5 is the numerical simulation section, and Section 6 gives the future work and outlook.
2. System Model and Transmission Process
Aiming at the improvement problem of WPCCN performance in an interference scenario, the ECS-HTCARQ protocol under the interference scenario is proposed. The system model is shown in Figure 1. The model consists of an energy-constrained source node , a destination node , an energy-sufficient relay node , and cochannel interference sources and near and . Among them, the channel fading coefficient is expressed as , the channel gain obeys an exponential distribution with mean , and , .
As shown in Figure 1, the system model consists of two parts: first, the energy-constrained source node harvests the RF signal broadcasted by the energy-sufficient relay node ; second, after the source node harvests end, the data transmission will take place. To improve the reliability of data transmission, the CARQ protocol with incremental redundancy is considered in this paper. The receiver has the memory of past data and accumulates mutual information for decoding data frames. During data transmission, the data packet is divided into multiple data frames, and when the data frame is received, and also receive the interference signal of and , respectively. This paper sets that harvests energy each time which is only used for this data frame transmission, i.e., before transmits a data frame, which needs to harvest energy in advance (Note: This is determined by the energy storage space of the energy-constrained source node). Considering fails to decode but successfully decodes, when and retransmit the data frame, will forward the data frame in DF strategy and use SC for data merging at ; all nodes among the entire system work in half-duplex mode. In addition, let be the time from energy harvesting to the end of one frame data transmission, which is recorded as a data frame transmission process of the system (including energy harvesting and data frame transmission).
2.1. Energy Harvesting (RF Signal)
Figure 2 shows the transmission process of the ECS-HTCARQ protocol. For the energy harvesting part, we adopt the HTC mechanism and introduce the time allocation factor . Within time, harvests the RF signal with energy from , after the energy is collected, which is used for this transmission process.
2.2. Data Frame Transmission Process
As in Figure 2, performs data frame transmission within . The transmission process of the ECS-HTCARQ protocol in the interference scenario is as follows: In this paper, we set the probability of successfully receiving the RF signal as 1. During the first stage , broadcasts its RF signal carrying energy, which will be used for the next stage of data transmission. In the second stage , uses the energy harvested in the previous stage to broadcast the data frames to and . The data frame transmission stages are divided into the following three situations:(1)If successfully decodes the data frame from , then will feedback an acknowledgment (ACK) to . At this point, whether or not successfully decodes the data frame or not, will send a new data frame on the next transmission.(2)Neither nor successfully decodes the data frame from , then both feedback a negative acknowledgment (NACK) to , and request to rebroadcast the data frame. If the maximum number of transmissions specified by the system has been reached but still fails to decode the data frame, the data frame will be discarded and will transmit a new data frame.(3)If successfully decodes the data frame and fails to decode it, they will feedback ACK and NACK to , respectively; then, will request to retransmit the decoded failed data frame. Since has successfully decoded the data frame in the previous transmission, will not receive the data frame in the retransmission, but and will send the data frame to at the same time. If fails to decode successfully after reaching the maximum transmission times specified by the system, the data frame will be discarded, and will transmit a new data frame.
In addition, we define as the successful decoding of a data frame from by at the lth time.
When = 3 and = 2, Figure 3 gives the successful transmission of one data frame for the ECS-HTCARQ protocol in the interference scenario.
3. Outage Probability Analysis
In this section, we calculate the outage probability of the ECS-HTCARQ protocol in the interference scenario. According to Figure 1, the receiver of an energy-constrained source node harvests energy from the RF signal that can be expressed aswhere is the energy harvesting efficiency and is the transmit power of the relay node.
Since transmits the data frame within , the transmit power of is
According to the system model, we consider the existence of interference sources during each transmission process and give expressions for the received signals of the , , , and links, which are expressed by , , , and , respectively:where source node and interference sources and that emit the normalized signals are , , and , respectively.
We give the SIR received by the above four links in formulas (4)–(7):
We analyze the outage probability of the system under long-term static channels. In the long-term static channel, the channel fading coefficients are constant during each transmission and between frames are independent and identically distributed.
When an outage event occurs, the outage probability can be expressed as the transmission error probability of a data frame in a transmission. Assuming that the outage rate of the data link is r bits/transmission time/Hz, the outage links can be indicated as
In the lth transmission, , , , and are used to denote the outage probability of each link, and since the ARQ protocol with incremental redundancy is considered, we have
In the appendix, we derive the closed-form expressions of equations (9)–(12), which can be expressed as equations (13)–(16):
4. System Throughput Analysis
Based on the transmission mechanism, we establish a DTMC model with states under the condition that the maximum number of transmissions is , as shown in Figure 4. As shown in Table 1, we give the meanings of states in the DTMC model. What needs to be pointed out is that we assume the relay can successfully decode the data frame in the next transmission once it decodes the data frame correctly in the transmission. In other words, the state can only shift to the state , or .
Based on the DTMC model, the one-step transition probabilities are yielded:
We define the throughput as the average number of frames successfully decoded by the destination node in , which can be computed as the average number of time that the DTMC spends in the state , i.e., the product of the steady-state probability of state and the transmission time.
Assuming that both the first row and the first column of the one-step transition probability matrix of the DTMC model start from state , the steady-state distribution of the model is , where is the steady-state probability of that decodes a data frame successfully. can be obtained from the following equilibrium equation and normalization condition:
In particular, the system throughput is calculated for and .
When , the one-step transition probability matrix of the DTMC model is given as
According to (18) and (19), we have
Using (20), we can solve for , which can be expressed as
To find the steady-state probability when , the one-step transition probability matrix of the DTMC model is given as
Similarly, there is an equationwhere can be computed aswhere and are expressed by the following equations:
Adopting the one-step transition probabilities, respectively, reduces to
Substituting (27) and (28) back into (24), we obtain the final expression for :
The data frames are transmitted within . To simplify the calculation, let , and then the throughput of and can be expressed as follows, respectively:
5. Numerical Results and Discussion
In this section, we present numerical results to analyze the impact of the system parameters on the end-to-end outage probability and throughput performance and compare the ECS-HTCARQ protocol and the Noncooperative automatic retransmission request (non-CARQ) protocol under this system model. The trade-off of the throughput and outage probability on the time allocation factor is further investigated. Since this paper considers the destination node to use SC for data fusion and in many practical applications, the system performance at high SIR is of great importance and use [30]. Therefore, the basic parameters are set as follows: , , , and .
Figure 5 shows the variation of with under the parameter settings of , , , and , , . It can be seen that the outage probability also tends to 0 when tends to 0, but as increases, the outage probability increases and reaches 1 in all cases. When is fixed, as increases, the outage probability decreases significantly; when is constant, as grows, the outage probability also improves obviously; when and increase simultaneously, the outage probability saturates to 1 and the value is extended, which is more suitable for high scenario. In addition, we compare the outage probability under the non-CARQ and find the CARQ technique can effectively reduce the outage probability. Because the redundant information of each retransmission improves the coding efficiency when the number of transmissions increases, which reduces the data frame transmission error rate. When the increases, the energy-constrained source node can collect more energy through the RF signal, which will reduce the end-to-end outage probability.
In Figure 6, the variation of with is compared for the parameter settings of , , , and , , . As increases, the source node can obtain more energy to ensure data transmission, which will reduce the outage probability. When goes from 0.1 to 0.8, it is observed that the outage probability decreases and becomes relatively saturated, the reason is that when reaches a certain value, the source node has collected sufficient energy and ensured reliable data transmission. When and increase simultaneously, the ECS-HTCARQ protocol shows a significant reduction in outage performance compared to the non-CARQ protocol.
In Figure 7, we investigate the variation of with for the parameter settings of , , , and , , . When is higher, the improvement of outage performance is more significant. In practice, the outage probability is reduced by improving the intrinsic circuit structure of the network nodes to increase energy harvesting efficiency. As and increase simultaneously, there is a significant reduction in the outage probability.
In Figure 8, the variation of throughput with is considered for the cases of non-CARQ, , , and , , . The numerical result finds the difference in throughput is small as increases, with an overall trend of increasing and then decreasing. When tends to 0 or 1, based on the closed-form expression of throughput, the two curves both tend to 0 as well as conform to the rising and then falling trend of the image. Combined with Figure 6, there is a significant decrease in the outage probability with increasing , but the value cannot be increased to 1. To maximize the system throughput, Figure 8 demonstrates there exists an optimal for all cases. In addition, the optimal for the ECS-HTCARQ protocol is smaller than the non-CARQ protocol because only the redundant information is retransmitted each time, not the entire data frame. Although the difference in throughput is smaller as increases, there is a significant decrease in outage probability. Thus, we introduce the CARQ technology as effective.
Figure 9 compares the variation of throughput with for non-CARQ, , and , , ; it shows an overall increasing trend. When the increases to , the ECS-HTCARQ protocol is superior to the non-CARQ protocol, and the throughput curves tend to be the same for , and , , . Combined with Figure 6, when and increase simultaneously, the two throughput curves converge but the outage probabilities decrease significantly.
According to Figures 6 and 8 and 10, further consider the optimal versus for non-CARQ, , , , , and , . Note that the optimal can easily be obtained by a one-dimension exhaustive search. It can be seen that the optimal decreases when increases and the relay successfully decode early, and the optimal is smaller such that there is more sufficient time for data transmission. When , the optimal values are 0.41, 0.3, 0.2, and 0.24 for the cases of the non-CARQ, , , , , and , , respectively.
6. Conclusion
In this paper, we propose the ECS-HTCARQ protocol in the interference scenario. The three-node model of WPCCN and data frame transmission mechanism are described, the DTMC model is established, and the closed-form expressions for the outage probability and the throughput are derived under Rayleigh fading channels. Numerical results show that the introduction of CARQ technology leads to smaller differences in throughput. However, with an increasing number of transmissions, a significant reduction in outage probability and CARQ technology further improves the reliability of the overall system data transmission. The optimal for a specific and value is given. It is found when increases and the relay successfully decode early, the optimal is smaller, which is beneficial to enhance the data frame transmission time. To further improve the system performance of the considered networks, future work will extend this model to the case of multiple relays to give the optimal relay selection scheme.
Appendix
Before expanding the calculation, let , , , , , and .
To compute the closed-form expression of equation (9), we give the following proposition.
Proposition 1. When and are the random variables and is a constant, , can be calculated asEquation (9) can be expanded aswhere , is the th order modified Bessel function of the second kind, , and .
To further derive the closed-form expression for equation (9), query the integral expressions for the product of the th order modified Bessel function of the second kind, exponential, and power functions according to the literature [31], and from 6.631(3), we havewhere is the Whittaker function.
Substituting equation (A 4) into equation (A 3), we finally obtain the closed-form expression of equation (9) asSimilarly, the closed-form expression of equation (10) is obtained aswhere and .
The closed-form expression of equation (11) iswhere and .
The closed-form expression of equation (12) is
Data Availability
The data used to support the findings of this study are from previously reported studies and datasets, which have been cited.
Conflicts of Interest
The authors declare that they have no conflicts of interest.
Acknowledgments
This work was supported by the Gansu Provincial Department of Education, Innovation Fund Project (2022A-019), the National Natural Science Foundation of China (61663024), the Ph.D. Research Startup Fund of Lanzhou University of Technology (05-061405), and the Hongliu Fund of First-class Disciplines of Lanzhou University of Technology, China.