Performance Modeling and Analysis of BASUR-CARQ Protocol Based on Interrelay Interference Cancellation

Abstract

To recover the performance loss of nodes in half-duplex mode, this paper proposes a buffer-aided successive relay protocol based on cooperative automatic repeat request mechanism (BASUR-CARQ). Based on the fact that interrelay interference (IRI) will occur when relay nodes transmit or receive simultaneously, an interference cancellation operator is proposed to determine whether the interference is eliminated to reduce the outage probability. Moreover, a delay model for data frame transmission is proposed based on CARQ mechanism, and a closed-form expression for the average delay is derived. A 6-state discrete-time Markov chain (DTMC) model is developed to obtain the system throughput, and a closed-form expression for the system energy efficiency under M-ary modulation is derived. Finally, the simulation results show that with the setting of parameters that can balance the main performance, the delay performance of BASUR-CARQ protocol is significantly enhanced compared to the traditional protocols, and the throughput of BASUR-CARQ protocol is also optimized at high signal-to-noise ratio (SNR). Meanwhile, the energy efficiency of BASUR-CARQ protocol is significantly improved for the successive relay communication system without interference cancellation technique.

This work is licensed under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.

1. Introduction

Cooperative communication (CC) is a communication technique to obtain diversity gain in wireless communication, which can shorten the transmission distance and increase network coverage [1]. The common means of relay forwarding include amplify-and-forward (AF) and decode-and-forward (DF). The AF relay amplifies the source signal and transmits it directly, while the DF relay decodes the source signal and then reencodes it for transmission. When either link is poor at both ends of relay, the traditional DF relay forwards the reencoded data directly at the next time slot, which leads in the impairment of system performance [2]. Thus, buffer-aided relays were proposed to adaptively select transmission links at each time slot based on channel state information (CSI) and the number of buffers, which provided significant performance gains [3, 4]. Hajipour et al. [5] showed that buffer-aided relay led to higher system throughput and lower average end-to-end packet delay. In CC systems, at least two time slots are required to complete the transmission, resulting in a halving of the end-to-end rate. To recover the performance loss of half-duplex (HD) mode, [6, 7] allowed the source and relay nodes to transmit simultaneously to achieve virtual full-duplex (FD). Thus, the buffer-aided successive relay (BASUR) was formed to achieve the spatial diversity gain of single antenna nodes. However, the interrelay interference (IRI) would be generated, which was the key problem in BASUR system.

The receiving relay receives the new source signal, and the transmitting relay forwards the recoded source signal, causing IRI by concurrent transmissions from two transmitters [8]. Therefore, the interference cancellation (IC) is required at relay to avoid performance degradation. Wei et al. [9] caused relays to actively store the source signals as priori knowledges to cancel IRI. Marey and Moustafa [10] separated the transmission from source and forwarding relay using carriers with the same frequency but in phase quadrature to achieve IRI-free. In addition, [11] proposed that multiple relays shared a common package to eliminate the effects of IRI imposed on receiving relay node through successive IC. However, the above methods to solve IRI were complex and difficult to implement. Briefly, the condition for interference signal to be decoded was that the interference had been subtracted at relays before decoding the source signals [12]. Therefore, we adopt the IC technique in this paper.

In multi-BASUR systems, reasonable relay selection can avoid the bandwidth waste, improve the system throughput, and reduce the system outage probability. Nomikos et al. [13] summarized the relay selection algorithms based on infinite buffer size, such as max-max relay selection, max-link selection, and optimal relay-pair selection strategies. In recent studies, [14] proposed a priority-based max-link selection relay scheme, dividing the buffer into three priority levels, and the best relay node corresponded to the link with the highest channel gain among the priority level. Jabeen et al. [15] proposed a joint power allocation and adaptive link selection protocol based on orthogonal frequency division multiplexing network to maximize the average throughput by power loading on different subcarriers at source and relay. Xu et al. [16] used buffers and randomness to determine link selection, indicating that different trade-offs between outage probability and average packet delay could be achieved. To avoid ideal assumptions, considering the limited buffer, CSI, and buffer status, various link selection protocols in BASUR system were summarized in [17]. Some of them were analyzed for a specific number of buffer sizes. The scheme proposed in [4] had a lower outage probability to achieve full diversity with a smaller buffer size. Also, the scheme based on buffer states in [18] reduced the average delay when the buffer size was greater than or equal to 3 compared to the scheme proposed in [4]. Raza et al. [19] proposed that the selection of the optimal relay depended on the buffer size and link quality, showing that the system obtained the maximum diversity gain when the buffer size was greater than or equal to 3. Abou-Rjeily [20] showed the effect of buffer size on hierarchical order, coding gain, and delay by establishing a discrete-time Markov chain (DTMC) model to analyze the optimization parameters that minimized the system outage probability and average packet delay. El-Zahr and Abou-Rjeily [21] used a DTMC model to demonstrate that a buffer size of 3 can achieve the ability to improve system performance and achieve an outage-delay trade-off over the Rayleigh fading channels. Also, in terms of confidential outage performance, [22] concluded that the case of smaller buffers was more advantageous than the case of larger buffers. The above literature shows that a smaller buffer is sufficient to demonstrate the capability of BASUR in improving the system performance.

The state of the buffer is related to the state of the previous time slot and the state of the next time slot. According to DTMC theory, the parameter values of the time and state processes are all discrete Markov processes, and the transition of the state is only related to the state before and after the transition. Therefore, most of the literatures established the DTMC models for discrete buffer data queue lengths and used the DTMC model to analyze the performance of the system [20–24]. Bapatla and Prakriya [23] modeled the energy buffer using the discrete-time continuous-state DTMC model to analyze the outage and throughput performance of the system. Based on the buffer state information, [24] used the Markov reward process to minimize the average queuing delay, thus overcoming the delay challenge posed in two-hop buffer-aided relay networks. However, these methods ignore the fact that when the transmission of data is based on the CARQ mechanism, the transmission model produces multiple states, and the transitions of these states are only related to the states before and after the transition. Chen et al. [25] developed a generalized DTMC model based on the number of retransmissions and used the steady-state probability of transition to destination node in the successfully decoded state as the throughput of the system. Zhou, Qian et al and Zhou, Wang et al. [26, 27] used the above approach to build a DTMC model and then derived the analytical expressions for throughput, energy efficiency (EE), and delay performance according to outage probability and one-step state transition probability matrix. Therefore, for the buffer-aided successive relay cooperative automatic repeat request (BASUR-CARQ) protocol, we consider various states of the transmission model and establish a DTMC model to calculate its performance. The main contributions of this paper are as follows:

(1) The BASUR-CARQ protocol is proposed to realize the virtual FD. To improve the performance of the system, the IC operator is used to eliminate the IRI, and the closed-form expressions for outage probability of links are derived

(2) The CARQ mechanism is used to enhance the reliability of the system. The system analyzes the average packet transmission delay based on ACK feedback and timers at transmitting node. A DTMC model is developed to derive the system throughput by stable distribution. In addition, the total energy consumption model of the system under M-ary modulation is proposed to derive the closed-form expression of the energy efficiency of the system

(3) The optimal parameters that can trade-off the system performance are set. Numerical results show that the proposed BASUR-CARQ protocol has better delay, throughput, and energy efficiency performance compared to the traditional protocols

The rest of this paper is organized as follows: Section 2 describes the model of the BASUR-CARQ protocol. In Section 3, the closed-form expressions for outage probability of links of the proposed system are derived, respectively. The system delay model and the closed-form expression for the average delay are given in Section 4. Moreover, Section 5 establishes a DTMC model to derive system throughput, and the total system energy consumption under M-ary modulation is analyzed in Section 6 to derive the energy efficiency of the system. Section 7 provides the numerical simulation results and discussions. Finally, Section 8 concludes the work of this paper.

2. System Transmission Model

As shown in Figure 1, a wireless communication consists of a source node $S$, a destination node $D$, and a relay cluster $ℝ\in R_j,1\le j\le J$. The distance between $S$ and $D$ cannot communicate directly but can only through $R_j$ forwarding. Suppose that DF relay nodes are equipped with a single antenna and work in HD. Virtual FD is implemented by equipping each $R_j$ with a buffer $Q_j,j\in 1,\cdots ,J$ to improve the spectrum efficiency, which not only obtains the gain of FD but also improves the system performance. The decoded data frames are stored in the buffer $Q_j$ for subsequent transmission $Q_j=I,I\ge 2$, and the queue obeys the first-come-first-service (FCFS) rule. In addition, the target transmission rate is $R_{\text{th}}$ bpz/Hz. To prevent $Q_j$ from being successively empty,$S$is in a saturated state, which data frames are to be transmitted in each time slot. The channel between two nodes obeys the Rayleigh fading channel model; $h_{{\text{SR}}_j}$, $h_{R_{j}D}$, and $h_{R_b{R}_j}$ represent the instantaneous channel fading of $S-R_j$, $R_j-D$, and $R_b-R_j$ links, respectively. The instantaneous channel gains ${h_{{\text{SR}}_j}}^2$, ${h_{R_{j}D}}^2$, and ${h_{R_b{R}_j}}^2$ obey exponential distributions of mean value ${\lambda }_{{\text{SR}}_j}$, ${\lambda }_{R_{j}D}$, and ${\lambda }_{R_b{R}_j}$, respectively, and ${h_{{\text{SR}}_j}}^2\sim \exp {\lambda }_{{\text{SR}}_j}$, ${h_{R_{j}D}}^2\sim \exp {\lambda }_{R_{j}D}$, and ${h_{R_b{R}_j}}^2\sim \exp {\lambda }_{R_b{R}_j}$. Since the distance within $R_j$ is relatively close, and the distance between $R_j$ and D is much shorter than the distance between $S$ and $D$, thus we assume that ${\lambda }_{R_b{R}_j}>{\lambda }_{{\text{SR}}_j}>{\lambda }_{R_{j}D}$. Finally, we assume that the channel noise $n_R$ and $n_D$ in communication are additive white Gaussian noise with mean value of 0 and variance of ${\sigma }^2$, $n\sim \text{CN}0,{\sigma }^2$.

[figure(s) omitted; refer to PDF]

The data packet is divided into multiple data frames, and each data frame is transmitted in a time slot. In Figure 1, the black line represents the transmission link. In same time slot, $R_j,j\ne b$ receive the data frame by $S$, and $R_b$ transmit data frame in $Q_b$, forming the BASUR. Assuming that the feedback channel is error-free, the ACK signaling of the transmitting node is fed back through the green dashed line in Figure 1. In the same time slot, we divide it into $R_b-D$ and $S-R_j$ links to analyze the mathematical model.

2.1. Transmission on $R_b-D$ Link

$S$ broadcasts a data frame $x_k$ to $R_j$, and the selected best relay node $R_b$ transmits the data frame in $Q_b$ to $D$. Therefore, at the beginning of each time slot, the corresponding $R_b$ of $x_h$ is selected firstly, according to $R_i\in {\Phi }_{\text{RD}}h$, where ${\Phi }_{\text{RD}}h$ represents the decoded relay set successfully for data frame $x_h$. The highest signal-to-noise ratio (SNR) of $R_i\in {\Phi }_{\text{RD}}h$ is selected to forward that recoded signal ${\widehat{x}}_h$ to $D$. Without loss of generality, let ${\widehat{x}}_h=x_h$, and the signal energy is 1, ${\rm E}{x_k}^2={\rm E}{x_h}^2=1$. Therefore, the $R_b$ is expressed as $$\begin{array}{}\text{(1)}& R_b=\arg \underset{R_i\in {\Phi }_{\text{RD}}h}{\max }{\gamma }_{R_{i}D}=\arg \underset{R_i\in {\Phi }_{RD}h}{\max }{h_{R_{i}D}}^2.\end{array}$$

The signals received at $D$ in this time slot as $$\begin{array}{}\text{(2)}& y_{D}k=\sqrt{P_R}{h}_{R_{b}D}{x}_h+n_D,\end{array}$$where $P_R$ is the transmit power of $R_b$ and $n_D$ is the noise of $R_b-D$ link.

Since there are no other interference signals on $R_b-D$ link, the received SNR of $R_b-D$ link is expressed as $$\begin{array}{}\text{(3)}& {\gamma }_{R_{b}D}=\frac{P_R{h_{R_{b}D}}^2}{{\sigma }^2}\end{array}$$

2.2. Transmission on $S-R_j$ Link

$S-R_j$ and $R_b-D$ links are transmitting at the same time. Since the transmitting relay $R_b$ is selected, $R_j,j\ne b$ receives $x_k$ from $S$. However, due to the broadcast characteristics of nodes, so it will generate IRI for $R_j,j\ne b$ when $R_b$ transmits $x_h$ to $D$, as shown by the red dotted line in Figure 1. Then, the signal received by $R_j,j\ne b$ in this time slot as $$\begin{array}{}\text{(4)}& y_{R_j}k=\sqrt{P_S}{h}_{{\text{SR}}_j}{x}_k+\sqrt{P_R}{h}_{R_b{R}_j}{x}_h+n_R,\end{array}$$where $P_S$ is the transmit power of $S$ and $n_R$ is the noise of $S-R_j$ link.

To eliminate IRI, we assume $\Delta R_b,R_j$ as an IC operator to indicate whether IRI satisfies the elimination factor. The IC condition is that $R_j,j\ne b$ can successfully decode $x_h$ transmitting by $R_b$; otherwise, it is the opposite. $$\begin{array}{}\text{(5)}& \Delta R_b,R_j=\begin{array}{cc}0,\hfill & \frac{P_R{h_{R_b{R}_j}}^2}{P_S{h_{{\text{SR}}_j}}^2+{{\sigma }_R}^2}\ge {\gamma }_0,\hfill \\ 1,\hfill & \frac{P_R{h_{R_b{R}_j}}^2}{P_S{h_{{\text{SR}}_j}}^2+{{\sigma }_R}^2}<{\gamma }_0.\hfill \end{array}\end{array}$$

According to Shannon’s formula, ${\gamma }_0=2^{2R_{\text{th}}}-1$. If relay $R_j,j\ne b$ successfully decodes $x_h$, IC can be performed, $\Delta R_b,R_j=0$ ($\Delta R_b,R_j$ is abbreviated as $\Delta$ in the subsequent sections). The received SNR of $S-R_j$ link with IC is $$\begin{array}{}\text{(6)}& {\gamma }_{{\text{SR}}_j}^{1}k=\frac{P_S{h_{{\text{SR}}_j}}^2}{{\sigma }^2}.\end{array}$$

Otherwise, IC is not performed. IRI still exists, so $\Delta =1$. The received signal-to-interference-to-noise ratio (SINR) is $$\begin{array}{}\text{(7)}& {\gamma }_{{\text{SR}}_j}^{2}k=\frac{P_S{h_{{\text{SR}}_j}}^2}{P_R{h_{R_b{R}_j}}^2+{\sigma }^2}.\end{array}$$

Thus, the SINR of $S-R_j$ link as $$\begin{array}{}\text{(8)}& {\gamma }_{{\text{SR}}_j}=\frac{P_S{h_{{\text{SR}}_j}}^2}{P_R{h_{R_b{R}_j}}^2\Delta R_h,R_j+{{\sigma }_R}^2}.\end{array}$$

3. Performance Analysis of Outage Probability

In this section, the outage probability of each link is analyzed. An outage event occurs if the instantaneous received SNR of $a-b$ link is less than the transmitted SNR threshold ${\gamma }_0$, that is ${\gamma }_{\text{ab}}<{\gamma }_0$. Therefore, the closed-form expressions of the outage probability of $S-R_j$, $R_b-D$ links and the probability of IC are $$\begin{array}{c}\text{(9)}& {\text{Pr}}_{R_{b}D}=\text{Pr}{\gamma }_{R_{b}D}<{\gamma }_0=\text{Pr}\frac{P_R{h_{R_{b}D}}^2}{{\sigma }^2}<{\gamma }_0=1-\exp -\frac{{\gamma }_0{\sigma }^2}{P_R{\lambda }_{R_{b}D}},{\text{Pr}}_{{\text{SR}}_j}=\begin{array}{cc}{\text{Pr}}_{{\text{SR}}_j}^1=\text{Pr}{\gamma }_{{\text{SR}}_j}^1<{\gamma }_0=\text{Pr}{h_{{\text{SR}}_j}}^2<\frac{{\gamma }_0{\sigma }^2}{P_S}=1-\exp -\frac{{\gamma }_0{\sigma }^2}{P_S{\lambda }_{{\text{SR}}_j}},\hfill & \Delta =0,\hfill \\ \begin{array}{c}{\text{Pr}}_{{\text{SR}}_j}^2=\text{Pr}{\gamma }_{{\text{SR}}_j}^2<{\gamma }_0=\text{Pr}{h_{{\text{SR}}_j}}^2<{\gamma }_0{P}_R{h_{R_b{R}_j}}^2+{\sigma }^2/P_S\hspace{1em}\hfill \\ ={\int }_0^{\infty }{F}_{{h_{{\text{SR}}_j}}^2}{\gamma }_0{P}_{R}x+{\sigma }^2/P_S\cdot f_{{h_{R_b{R}_j}}^2}xdx\hfill \\ =1-\frac{P_S{\lambda }_{{\text{SR}}_j}}{{\gamma }_0{P}_R{\lambda }_{R_b{R}_j}+P_S{\lambda }_{{\text{SR}}_j}}\exp -\frac{{\gamma }_0{\sigma }^2}{P_S{\lambda }_{{\text{SR}}_j}},\hfill \end{array}\hfill & \Delta =1,\hfill \end{array}\\ \text{Pr}\Delta =\begin{array}{c}\text{Pr}\Delta =1=\text{Pr}\frac{P_R{h_{R_b{R}_j}}^2}{P_S{h_{{\text{SR}}_j}}^2+{\sigma }^2}<{\gamma }_0=1-\frac{P_R{\lambda }_{R_b{R}_j}}{{\gamma }_0{P}_S{\lambda }_{{\text{SR}}_j}+P_R{\lambda }_{R_b{R}_j}}\exp -\frac{{\gamma }_0{\sigma }^2}{P_R{\lambda }_{R_b{R}_j}},\hfill \\ \text{Pr}\Delta =0=\text{Pr}\frac{P_R{h_{R_b{R}_j}}^2}{P_S{h_{{\text{SR}}_j}}^2+{\sigma }^2}\ge {\gamma }_0=\frac{P_R{\lambda }_{R_b{R}_j}}{{\gamma }_0{P}_S{\lambda }_{{\text{SR}}_j}+P_R{\lambda }_{R_b{R}_j}}\exp -\frac{{\gamma }_0{\sigma }^2}{P_R{\lambda }_{R_b{R}_j}}.\hfill \end{array}\end{array}$$

4. Average Transmission Delay

Assuming that the transmission delay of data packet length $L$ is $t_T$, the propagation delay (feedback delay) is $t_P$, and the data packet is divided into data frames of length $L=1$, thus the transmission delay and propagation delay are $t_T/L$, $t_P/L$, respectively. Set a timer at the transmitting nodes to work when transmission starts, and the timer is set to $\tau =t_T/L+2t_P/L$. The data frame is discarded normally when the transmitting node receives ACK signaling from the receiving node. However, the transmitting node will directly discard the current data frame when timer is 0 to avoid buffer congestion and data frame continuity.

Data frame transmission delay model is shown in Figure 2. The first time slot is received by $R_j,1\le j\le J$, and $S$ first transmits frame 0 to $R_j,1\le j\le J$. If at least one of $R_j,1\le j\le J$ is decoded successfully, ACK signaling is fed back to $S$, and $S$ will discard frame 0. The time of this time slot is $t_T/L+t_P/L$.

[figure(s) omitted; refer to PDF]

In the next time slot, the best relay $R_b\in {\Phi }_{\text{RD}}0$ will be selected. $R_j,j\ne b$ receives frame 1 from $S$, and $R_b$ transmits frame 0 to $D$. If all the data frames corresponding to $R_j,j\ne b$ and $D$ are decoded successfully, then $R_j,j\ne b$ feedbacks ACK signaling to $S$ and $R_j$, respectively. $S$ discards frame 1, $R_i\in {\Phi }_{\text{RD}}0$ discards frame 0, while frame 1 enters $Q_i$ of $R_i\in {\Phi }_{\text{RD}}1$. The time of this time slot is $t_T/L+t_P/L$.

The next time slot selects the best relay $R_b\in {\Phi }_{\text{RD}}1$, $R_j,j\ne b$ receives frame 2 from $S$, and $R_b$ transmits frame 1 to $D$. If $R_j,j\ne b$ decodes frame 2 successfully, while $D$ decodes frame 1 unsuccessfully. $R_j,j\ne b$ feedbacks ACK signaling to $S$, $S$ discards frame 1, while frame 2 enters $Q_i$ of $R_i\in {\Phi }_{\text{RD}}2$ and does not receive ACK signaling after timer is 0, and $R_i\in {\Phi }_{\text{RD}}1$ discards frame 1. The time of this time slot is $\tau$.

The next time slot selects the best relay $R_b\in {\Phi }_{\text{RD}}2$, $R_j,j\ne b$ receives frame 3 from S, $R_b$ transmits frame 2 to $D$. If all the data frames corresponding to $R_j,j\ne b$ and $D$ are decoded unsuccessfully, ACK signaling is not received after the timer is 0, $S$ discards frame 3, and $R_i\in {\Phi }_{\text{RD}}2$ discards frame 2. The time of this time slot is $\tau$.

Due to BASUR, all $R_j$ work at the same time, and the transmission of two data frames occurs in the same time slot. Therefore, it can be regarded as only one transmission delay $t_T/L$ and propagation delay $t_P/L$ for transmitting a data frame. Then, the average delay of a data frame can be expressed as $$\begin{array}{}\text{(10)}& Et=\text{Pr}{D}_{\text{suc}},R_{\text{suc}}\cdot \frac{t_P+t_T}{L}+\text{Pr}{D}_{\text{out}},R_{\text{suc}}+\text{Pr}{D}_{\text{suc}},R_{\text{out}}+\text{Pr}{D}_{\text{out}},R_{\text{out}}\cdot \tau =1-{\text{Pr}\Delta =1{\text{Pr}}_{{\text{SR}}_j}^2+\text{Pr}\Delta =0{\text{Pr}}_{{\text{SR}}_j}^1}^{J-1}1-{\text{Pr}}_{R_{b}D}\cdot \frac{t_P+t_T}{L}+\begin{array}{c}1-{\text{Pr}\Delta =1{\text{Pr}}_{{\text{SR}}_j}^2+\text{Pr}\Delta =0{\text{Pr}}_{{\text{SR}}_j}^1}^{J-1}{\text{Pr}}_{R_{b}D}\\ +{\text{Pr}\Delta =1{\text{Pr}}_{{\text{SR}}_j}^2+\text{Pr}\Delta =0{\text{Pr}}_{{\text{SR}}_j}^1}^{J-1}1-{\text{Pr}}_{R_{b}D}\\ +{\text{Pr}\Delta =1{\text{Pr}}_{{\text{SR}}_j}^2+\text{Pr}\Delta =0{\text{Pr}}_{{\text{SR}}_j}^1}^{J-1}{\text{Pr}}_{R_{b}D}\end{array}\cdot \tau .\end{array}$$

The average delay of a data packet is $ET$, $ET=L\cdot Et$.

The first part of (10) is the probability of successful decoding by the receiving node, and the delay occupied by the transmission data packet is $t_P+t_T$. The second part is the probability of decoding failure of at least one receiving node, and the delay occupied by the transmission data packet is $2t_P+t_T=L\tau$.

5. Throughput Analysis

In this section, we establish a discrete-time Markov chain (DTMC) model, deriving closed-form expressions for state transition probability and steady-state distribution. Then, we derive the system throughput based on steady-state distribution, which is defined as the average number of data frames successfully decoded per unit time slot. In addition, we assume that the channel fading coefficient of the same data frame remains constant in all transmission time slots.

5.1. Establish a DTMC Model

According to the system model and transmission delay model, it can be seen that the entire system has 6 states, whose explanations are as follows:

State S1: $S$ transmits $x_k$ to $R_j,1\le j\le J$, $R_j$ feedbacks ACK to $S$ when at least one $R_j$ decodes $x_k$ successfully. In the next time slot, selecting $R_b\in {\Phi }_{RD}k$ transmits $x_k$ to $D$, and $S$ transmits a new data frame $x_{k+1}$ to $R_j,j\ne b$.

State S2: $S$ transmits $x_k$ to $R_j,1\le j\le J$, and there is no ACK if $R_j,1\le j\le J$ decode unsuccessfully. After $\tau$, $S$ discards $x_k$. In the next time slot, $S$ transmits $x_{k+1}$ to $R_j,1\le j\le J$.

State S3: $D$ feedbacks an ACK to $R_j,1\le j\le J$ when D decodes $x_h$ from $R_b$ successfully. Then, $R_i\in {\Phi }_{\text{RD}}h$ discards $x_h$. At the same time, $R_i\in {\Phi }_{\text{RD}}k$ feedbacks ACK to $S$ when at least one $R_j,j\ne b$ decodes $x_k$ from $S$ successfully. In the next time slot, selecting $R_b\in {\Phi }_{\text{RD}}k$ transmits $x_k$ to $D$, and $S$ transmits $x_{k+1}$ to $R_j,j\ne b$.

State S4: $D$ feedbacks an ACK to $R_j,1\le j\le J$ when D decodes $x_h$ from $R_b$ successfully, and then, $R_i\in {\Phi }_{\text{RD}}h$ discards $x_h$. At the same time, $R_j,j\ne b$ decodes $x_k$ from $S$ unsuccessfully. After $\tau$, $S$ discards $x_k$. In the next time slot, $S$ transmits $x_{k+1}$ to $R_j,1\le j\le J$.

State S5: $D$ decodes $x_h$ from $R_b$ unsuccessfully. After $\tau$, $R_i\in {\Phi }_{\text{RD}}h$ discards $x_h$. At the same time, $R_j,j\ne b$ decodes $x_k$ from $S$ unsuccessfully. After $\tau$, $S$ discards $x_k$. In the next time slot, $S$ transmits $x_{k+1}$ to $R_j,1\le j\le J$.

State S6: $D$ decodes $x_h$ from $R_b$ unsuccessfully. After $\tau$, $R_i\in {\Phi }_{\text{RD}}h$ discards $x_h$. At the same time, $R_i\in {\Phi }_{\text{RD}}k$ feedbacks an ACK to $S$ when at least one $R_j,j\ne b$ decodes $x_k$ from $S$ successfully. In the next time slot, selecting $R_b\in {\Phi }_{\text{RD}}k$ transmits $x_k$ to $D$, and $S$ transmits $x_{k+1}$ to $R_j,j\ne b$.

All the states are simplified to Figure 3. The state of time slot $t+1$ is related to time slot $t$. The state of time slot $t+1$ depends on the time slot $t$, which can establish a complete 6-state DTMC model.

[figure(s) omitted; refer to PDF]

5.2. State Transition Probability and One-Step Transition Probability Matrix

According to the DTMC model and the outage probability performance analysis, the one-step state transition probability can be expressed as follows: $$\begin{array}{c}\text{(11)}& p_{\text{S}2⟶\text{Sm}}=p_{\text{S}4⟶\text{Sm}}=p_{\text{S}5⟶\text{Sm}}=0,m=3,4,5,6,p_{\text{Sm}⟶\text{S}1}=p_{\text{Sm}⟶\text{S}2}=0,m=1,3,6,\\ p_{\text{Sn}⟶\text{S}1}=1-{{\text{Pr}}_{{\text{SR}}_j}^1}^J;p_{\text{Sn}⟶\text{S}2}={{\text{Pr}}_{{\text{SR}}_j}^1}^J,n=2,4,5,\\ p_{\text{Sm}⟶\text{S}3}=1-{\text{Pr}\Delta =1{\text{Pr}}_{{\text{SR}}_j}^2+\text{Pr}\Delta =0{\text{Pr}}_{{\text{SR}}_j}^1}^{J-1}1-{\text{Pr}}_{R_{b}D},m=1,3,6,\\ p_{\text{Sm}⟶\text{S}4}={\text{Pr}\Delta =1{\text{Pr}}_{{\text{SR}}_j}^2+\text{Pr}\Delta =0{\text{Pr}}_{{\text{SR}}_j}^1}^{J-1}1-{\text{Pr}}_{R_{b}D},m=1,3,6,\\ p_{\text{Sm}⟶\text{S}5}=1-{\text{Pr}\Delta =1{\text{Pr}}_{{\text{SR}}_j}^2+\text{Pr}\Delta =0{\text{Pr}}_{{\text{SR}}_j}^1}^{J-1}{\text{Pr}}_{R_{b}D},m=1,3,6,\\ p_{\text{Sm}⟶\text{S}6}={\text{Pr}\Delta =1{\text{Pr}}_{{\text{SR}}_j}^2+\text{Pr}\Delta =0{\text{Pr}}_{{\text{SR}}_j}^1}^{J-1}{\text{Pr}}_{R_{b}D},m=1,3,6,\end{array}$$where $p_{\text{Sn}⟶\text{Sm}}$ represents the transition probability from state $\text{Sn}$ to state $\text{Sm}$. The closed-form expressions of the transition probability are $$\begin{array}{c}\text{(12)}& p_{\text{Sn}⟶\text{S}1}=1-{{\text{Pr}}_{{\text{SR}}_{\text{j}}}^1}^J=1-{1-\exp -\frac{{\gamma }_0{\sigma }^2}{P_S{\lambda }_{{\text{SR}}_j}}}^J,p_{\text{Sn}⟶\text{S}2}={{\text{Pr}}_{{\text{SR}}_j}^1}^J={1-\exp -\frac{{\gamma }_0{\sigma }^2}{P_S{\lambda }_{{\text{SR}}_j}}}^J,\\ p_{\text{Sm}⟶\text{S}3}=1-1-\frac{P_R{\lambda }_{R_h{R}_j}}{{\gamma }_0{P}_S{\lambda }_{{\text{SR}}_j}+P_R{\lambda }_{R_h{R}_j}}\exp -\frac{{\gamma }_0{\sigma }^2}{P_R{\lambda }_{R_h{R}_j}}1-\frac{P_S{\lambda }_{{\text{SR}}_j}}{{\gamma }_0{P}_R{\lambda }_{R_h{R}_j}+P_S{\lambda }_{{\text{SR}}_j}}\exp -\frac{{\gamma }_0{\sigma }^2}{P_S{\lambda }_{{\text{SR}}_j}}{+\frac{P_R{\lambda }_{R_h{R}_j}}{{\gamma }_0{P}_S{\lambda }_{{\text{SR}}_j}+P_R{\lambda }_{R_h{R}_j}}\exp -\frac{{\gamma }_0{\sigma }^2}{P_R{\lambda }_{R_h{R}_j}}1-\exp -\frac{{\gamma }_0{\sigma }^2}{P_S{\lambda }_{{\text{SR}}_j}}}^{J-1}\times 1-\exp -\frac{{\gamma }_0{\sigma }^2}{P_R{\lambda }_{R_{b}D}},\\ p_{\text{Sm}⟶\text{S}4}=1-\frac{P_R{\lambda }_{R_b{R}_j}}{{\gamma }_0{P}_S{\lambda }_{{\text{SR}}_j}+P_R{\lambda }_{R_b{R}_j}}\exp -\frac{{\gamma }_0{\sigma }^2}{P_R{\lambda }_{R_b{R}_j}}1-\frac{P_S{\lambda }_{{\text{SR}}_j}}{{\gamma }_0{P}_R{\lambda }_{R_b{R}_j}+P_S{\lambda }_{{\text{SR}}_j}}\exp -\frac{{\gamma }_0{\sigma }^2}{P_S{\lambda }_{{\text{SR}}_j}}{+\frac{P_R{\lambda }_{R_b{R}_j}}{{\gamma }_0{P}_S{\lambda }_{{\text{SR}}_j}+P_R{\lambda }_{R_b{R}_j}}\exp -\frac{{\gamma }_0{\sigma }^2}{P_R{\lambda }_{R_b{R}_j}}1-\exp -\frac{{\gamma }_0{\sigma }^2}{P_S{\lambda }_{{\text{SR}}_j}}}^{J-1}\times 1-\exp -\frac{{\gamma }_0{\sigma }^2}{P_R{\lambda }_{R_{b}D}},\\ p_{\text{Sm}⟶\text{S}5}=1-1-\frac{P_R{\lambda }_{R_b{R}_j}}{{\gamma }_0{P}_S{\lambda }_{{\text{SR}}_j}+P_R{\lambda }_{R_b{R}_j}}\exp -\frac{{\gamma }_0{\sigma }^2}{P_R{\lambda }_{R_b{R}_j}}1-\frac{P_S{\lambda }_{{\text{SR}}_j}}{{\gamma }_0{P}_R{\lambda }_{R_b{R}_j}+P_S{\lambda }_{{\text{SR}}_j}}\exp -\frac{{\gamma }_0{\sigma }^2}{P_S{\lambda }_{{\text{SR}}_j}}{+\frac{P_R{\lambda }_{R_b{R}_j}}{{\gamma }_0{P}_S{\lambda }_{{\text{SR}}_j}+P_R{\lambda }_{R_b{R}_j}}\exp -\frac{{\gamma }_0{\sigma }^2}{P_R{\lambda }_{R_b{R}_j}}1-\exp -\frac{{\gamma }_0{\sigma }^2}{P_S{\lambda }_{{\text{SR}}_j}}}^{J-1}\times \exp -\frac{{\gamma }_0{\sigma }^2}{P_R{\lambda }_{R_{b}D}},\\ p_{\text{Sm}⟶\text{S}6}=1-\frac{P_R{\lambda }_{R_b{R}_j}}{{\gamma }_0{P}_S{\lambda }_{{\text{SR}}_j}+P_R{\lambda }_{R_b{R}_j}}\exp -\frac{{\gamma }_0{\sigma }^2}{P_R{\lambda }_{R_b{R}_j}}1-\frac{P_S{\lambda }_{{\text{SR}}_j}}{{\gamma }_0{P}_R{\lambda }_{R_b{R}_j}+P_S{\lambda }_{{\text{SR}}_j}}\exp -\frac{{\gamma }_0{\sigma }^2}{P_S{\lambda }_{{\text{SR}}_j}}{+\frac{P_R{\lambda }_{R_b{R}_j}}{{\gamma }_0{P}_S{\lambda }_{{\text{SR}}_j}+P_R{\lambda }_{R_b{R}_j}}\exp -\frac{{\gamma }_0{\sigma }^2}{P_R{\lambda }_{R_b{R}_j}}1-\exp -\frac{{\gamma }_0{\sigma }^2}{P_S{\lambda }_{{\text{SR}}_j}}}^{J-1}\times \exp -\frac{{\gamma }_0{\sigma }^2}{P_R{\lambda }_{R_{b}D}},\end{array}$$

The one-step state transition probability matrix $\mathbf{P}$ (sum of each $\text{row}=1$) is listed as follows: $$\begin{array}{}\text{(13)}& \mathbf{{\rm P}}=\begin{array}{cccccc}0& 0& p_{\text{S}1\text{S}3}& p_{\text{S}1\text{S}4}& p_{\text{S}1\text{S}5}& p_{\text{S}1\text{S}6}\\ p_{\text{S}2\text{S}1}& p_{\text{S}2\text{S}2}& 0& 0& 0& 0\\ 0& 0& p_{\text{S}3\text{S}3}& p_{\text{S}3\text{S}4}& p_{\text{S}3\text{S}5}& p_{\text{S}3\text{S}6}\\ p_{\text{S}4\text{S}1}& p_{\text{S}4\text{S}2}& 0& 0& 0& 0\\ p_{\text{S}5\text{S}1}& p_{\text{S}5\text{S}2}& 0& 0& 0& 0\\ 0& 0& p_{\text{S}6\text{S}3}& p_{\text{S}6\text{S}4}& p_{\text{S}6\text{S}5}& p_{\text{S}6\text{S}6}\end{array}.\end{array}$$

5.3. Steady-State Distribution

According to the balance equation $$\begin{array}{c}\text{(14)}& \pi \mathbf{{\rm P}}=\pi ,\sum _{i=1}^6{\pi }_i=1.\end{array}$$

By substituting (13) into (14), the steady-state distribution of DTMC is listed as: $$\begin{array}{c}\text{(15)}& {\pi }_k=\frac{p_{\text{SnSk}}{p}_{\text{SmS}4}+p_{\text{SnSk}}{p}_{\text{SmS}5}}{A},k=1,2,\begin{array}{cc}{\pi }_g=\frac{1-p_{\text{SnS}2}{p}_{\text{SmSk}}}{A},& g=3,4,5,6,\end{array}\end{array}$$where $A=p_{\text{SmS}4}-p_{\text{SnS}2}+p_{\text{SmS}5}+1$.

5.4. Throughput

Assuming that the state transition probability in the first row of $\mathbf{P}$ starts from state $\text{S}1$, the steady-state distribution of the DTMC model is $\pi ={\pi }_1,{\pi }_2,\cdots ,{\pi }_6$. When the data frame of $R_b$ is successfully decoded by $D$, the steady state of $\text{S}3$ and $\text{S}4$ are expressed as the average number of data frames successfully decoded per unit time slot, and then, the throughput can be calculated as the steady-state distribution: $$\begin{array}{}\text{(16)}& TH={\pi }_3+{\pi }_4=\frac{1-p_{\text{SnS}2}{p}_{\text{SmS}3}}{A}+\frac{1-p_{\text{SnS}2}{p}_{\text{SmS}4}}{A}=\frac{1-p_{\text{SnS}2}{p}_{\text{SmS}3}+p_{\text{SmS}4}}{A}.\end{array}$$

6. Energy Efficiency

In wireless communication system, the protocols usually focus on their reliability or effectiveness. In fact, the energy consumption of each node also needs to be concerned. Therefore, we analyze the EE performance of the proposed system. One method to improve the EE is to adopt M-ary modulation; that is, one symbol represents $b$ bits, and then, the bit rate is $R_b=R_s{\log }_{2}M$, where $R_s$ denotes the symbol rate and $b={\log }_{2}M$ is the modulation level [28]. It is assumed that the data packet length is $L$ and the power amplification loss factor is $\beta$, which is related to the modulation scheme.

According to [27], the total energy consumption $P_c$ from data communication can be simply described as $P_c=P_{\text{PA}}+P_{\text{TR}}+P_{\text{RE}}$. Among that, $P_{\text{PA}}$ is the energy consumption of power amplifier, and $P_{\text{PA}}$ has a linear relationship with the output power $P_{\text{out}}$ and power amplification loss factor $\beta$, $P_{\text{PA}}=1+\beta P_{\text{out}}$. $P_{\text{RE}}$ and $P_{\text{TR}}$ are the energy consumption of the receiving node and the transmitting node, respectively. EE is defined as the ratio of the success probability of packet transmission to total energy consumption, and then, the system EE can be expressed as $$\begin{array}{c}\text{(17)}& \eta =\frac{{\text{Pr}}_{\text{suc}}}{P_c},{\text{Pr}}_{\text{suc}}=1-\text{PER}=1-{{\text{Pr}}_{{\text{SR}}_j}^1}^J+{\text{Pr}\Delta =1{\text{Pr}}_{{\text{SR}}_j}^2+\text{Pr}\Delta =0{\text{Pr}}_{{\text{SR}}_j}^1}^{J-1}+1-{{\text{Pr}}_{{\text{SR}}_j}^1}^J{\text{Pr}}_{R_{b}D}+1-{\text{Pr}\Delta =1{\text{Pr}}_{{\text{SR}}_j}^2+\text{Pr}\Delta =0{\text{Pr}}_{{\text{SR}}_j}^1}^{J-1}{\text{Pr}}_{R_{b}D},\end{array}$$where $\text{PER}$ represents the outage probability of data packet.

The outage probability of the proposed system in this paper can be divided into two parts. The first part is that, in the traditional system, $R_j,1\le j\le J$ decode unsuccessfully, and at least one $R_j,1\le j\le J$ decode successfully, while $D$ decodes unsuccessfully. The second part is that in the BASUR system, $R_j,j\ne b$ decodes unsuccessfully, and at least one $R_j,j\ne b$ decodes successfully, while $D$ decodes unsuccessfully. These two parts constitute the outage probability of the system (the PER of the system). The energy consumption of the proposed system is divided into the following situations:

$R_j,1\le j\le J$ decode unsuccessfully: $$\begin{array}{}\text{(18)}& P_0={{\text{Pr}}_{{\text{SR}}_j}^1}^J{P}_{\text{PA}}+P_{\text{TR}}+J\cdot P_{\text{RE}}\cdot \frac{L}{R_b}.\end{array}$$

At least one $R_j,1\le j\le J$ decode successfully, while D decodes unsuccessfully: $$\begin{array}{}\text{(19)}& P_1=1-{{\text{Pr}}_{{\text{SR}}_j}^1}^J{\text{Pr}}_{R_{b}D}2P_{\text{PA}}+2P_{\text{TR}}+J+1\cdot P_{\text{RE}}\cdot \frac{L}{R_b}.\end{array}$$

Both at least one $R_j,j\ne b$ and D decode successfully: $$\begin{array}{}\text{(20)}& P_2=1-{{\text{Pr}}_{{\text{SR}}_j}^1}^{J}1-{\text{Pr}}_{R_{b}D}2P_{\text{PA}}+2P_{\text{TR}}+J+1\cdot P_{\text{RE}}\cdot \frac{L}{R_b}.\end{array}$$

$R_j,j\ne b$ decodes unsuccessfully: $$\begin{array}{}\text{(21)}& P_3={\text{Pr}\Delta =1{\text{Pr}}_{{\text{SR}}_j}^2+\text{Pr}\Delta =0{\text{Pr}}_{{\text{SR}}_j}^1}^{J-1}{P}_{\text{PA}}+P_{\text{TR}}+J-1\cdot P_{\text{RE}}\cdot \frac{L}{R_b}.\end{array}$$

At least one $R_j,j\ne b$ decodes successfully, while D decodes unsuccessfully: $$\begin{array}{}\text{(22)}& P_4=1-{\text{Pr}\Delta =1{\text{Pr}}_{{\text{SR}}_j}^2+\text{Pr}\Delta =0{\text{Pr}}_{{\text{SR}}_j}^1}^{J-1}{\text{Pr}}_{R_{b}D}2P_{\text{PA}}+2P_{\text{TR}}+J\cdot P_{\text{RE}}\cdot \frac{L}{R_b}.\end{array}$$

Both at least one $R_j,j\ne b$ and D decode successfully: $$\begin{array}{}\text{(23)}& P_5=1-{\text{Pr}\Delta =1{\text{Pr}}_{{\text{SR}}_j}^2+\text{Pr}\Delta =0{\text{Pr}}_{{\text{SR}}_j}^1}^{J-1}1-{\text{Pr}}_{R_{b}D}2P_{\text{PA}}+2P_{\text{TR}}+J\cdot P_{\text{RE}}\cdot \frac{L}{R_b}.\end{array}$$

Therefore, the total energy consumption of the communication system is given by $$\begin{array}{}\text{(24)}& P_c=\sum _{i=0}^5{P}_i.\end{array}$$

By substituting (24) into (17), the EE of the system is as follows: $$\begin{array}{}\text{(25)}& \eta =\frac{{\text{Pr}}_{\text{suc}}}{P_c}=\frac{1-\text{PER}}{{\sum }_{i=0}^5{P}_i}.\end{array}$$

7. Numerical Simulation

The parameters in the following numerical simulation are assumed to be ${\lambda }_{{\text{SR}}_j}=1$, ${\lambda }_{R_{b}D}=0.5$, $\text{SNR}=P_S/{\sigma }^2=P_R/{\sigma }^2=15$ dB, $R_{\text{th}}=0.5,1$ bps/Hz, and $J\ge 2$. The data packet length is $L$, $t_P=0.1\cdot L$, $t_T=1.1\cdot L$, $R_b=15$, $P_{\text{out}}=0.1$ dB, $P_{\text{TR}}=0.01$ J, and $P_{\text{RE}}=0.02$ J. According to the above parameters, the numerical simulation results of the performance of the proposed system, such as delay, outage probability, interference cancellation probability, throughput, and energy efficiency, are given.

For the BASUR-CARQ protocol, Figures 4 and 5 show the effect of SNR on interference cancellation probability and outage probability of $S-R_j$ link with $R_{\text{th}}=0.5$ bps/Hz, respectively. The channel gains of $R_b-R_j$ and $S-R_j$ links obey independent exponential distributions with means ${\lambda }_{R_b{R}_j}$ and ${\lambda }_{{\text{SR}}_j}$, respectively. Without loss of generality, the values of ${\lambda }_{R_b{R}_j}$ and ${\lambda }_{{\text{SR}}_j}$ relate to the distance between nodes, due to the distance between relay nodes within the relay cluster $ℝ$ that is much closer than $S$ to $R_j$, thus ${\lambda }_{R_b{R}_j}>{\lambda }_{{\text{SR}}_j}$. As observed from Figure 4, as SNR increases, the interference cancellation probability $\text{Pr}\Delta =0$ is highest when ${\lambda }_{R_b{R}_j}=2$. On the contrary, the outage probability of $S-R_j$ link is lowest when ${\lambda }_{R_b{R}_j}=2$ in Figure 5. The trade-off between interference cancellation probability and outage probability of $S-R_j$ link can be obtained with different parameter settings, which achieves the goal of eliminating IRI. Therefore, we set ${\lambda }_{R_b{R}_j}=2$ to optimize other performances.

[figure(s) omitted; refer to PDF]

In the traditional relay system, a data frame needs to be transmitted in different time slots on $S-R_j$ and $R_b-D$ links, and at least two transmission delays and two propagation delays are required. Therefore, the average delay of a data packet of length $L$ is divided into two parts, and the delay of transmitting a data packet is $t_P+t_T$ and $2t_P+t_T$, respectively.

Figure 6 shows the numerical simulation results of the data packet length $L$ and the average system delay of different transmission systems under the constraints of $R_{\text{th}}=0.5\text{bps}/\text{Hz}$, $\text{SNR}=15\text{dB}$, and $J$. Set $t_P=0.1\cdot L$, $t_T=1.1\cdot L$. It can be seen that as $L$ increases, the average delay of the three transmission systems increases linearly. Compared with the traditional transmission system, the average delay of the BASUR system is significantly reduced, and the delay performance is improved by 50%. In addition, the BASUR system has lower delay than the DH-MSMR-CARQ system in [26], and the delay reduced by about 10%. The reason of this appearance is that the relay nodes can receive and transmit simultaneously in the virtual FD, which greatly reduces the delay. However, we find that $J$ does not have much effect on the delay. The reason is that the transmitting nodes are all configured with fixed-time timers, and there is no error in the feedback delay, which leads to the average delay only depending on ACK feedback.

[figure(s) omitted; refer to PDF]

Figure 7 shows the numerical simulation results of SNR and throughput of the system under different $R_{\text{th}}$ and $J$ conditions. As shown in Figure 7, the throughput of the system clearly tends to increase as $J$ increases. At low SNR, the throughput at $R_{\text{th}}=0.5\text{bps}/\text{Hz}$ is higher for same $J$, because the throughput depends on the probability of successful transmission. When the target rate is low, the probability of successful decoding of data frames is high. At high SNR, there is a slight advantage in the throughput performance at $R_{\text{th}}=1\text{bps}/\text{Hz}$ when $J=2,3$, because the increase of $J$ compensates for the increase of the outage probability, so that the system throughput tends to 1 and reaches the optimal value when the number of relay nodes is greater than 5.

[figure(s) omitted; refer to PDF]

Figure 8 shows the numerical simulation results of power loss factor $\beta$ and energy efficiency under the constraints of $R_{\text{th}}=0.5\text{bps}/\text{Hz}$, $J=5$, $\text{SNR}=15\text{dB}$, and $L$. As observed from Figure 8, with the increase of $L$, the energy efficiency of the system obviously shows a decreasing trend. The higher the $\beta$ is, the lower the energy efficiency will be. It means that the greater the loss of energy provided by the transmitting nodes in per unit time, the greater the energy consumption generated, and then, the energy efficiency decreases. It can also be seen from Figure 8 that the energy efficiency performance of $L=1$ is significantly greater than that of $L=5$, indicating that the actual application should appropriately reduce the packet length to improving the system energy efficiency.

[figure(s) omitted; refer to PDF]

Figure 9 depicts the numerical simulation results of SNR and the energy efficiency of the BASUR-CARQ and the system without interference cancellation technique under the constraints of $\beta =1$, $L=3$, $J=5$, and different $R_{\text{th}}$. As observed from Figure 9, as SNR increases, the energy efficiency of both systems clearly tends to increase. For both systems, the energy efficiency with $R_{\text{th}}=1\text{bps}/\text{Hz}$ is significantly lower than that of $R_{\text{th}}=0.5\text{bps}/\text{Hz}$. In addition, the energy efficiency of proposed system with interference cancellation technique improves the energy efficiency without interference cancellation technique by 50% regardless of $R_{\text{th}}$.

[figure(s) omitted; refer to PDF]

From the above numerical simulation results of outage probability, interference cancellation probability, system delay, throughput, and energy efficiency performances, we can infer that the optimal parameters that can trade off the above performance of the BASUR-CARQ protocol are $J=5$, $R_{\text{th}}=0.5\text{bps}/\text{Hz}$, $L=3$, and ${\lambda }_{R_b{R}_j}=2$.

8. Conclusion

In order to improve the delay and throughput performance of single antenna communication system, we use buffer to assist relay nodes in HD mode to realize virtual FD mode. Firstly, an ACK-based BASUR-CARQ protocol is proposed, and its transmission model is analyzed. We propose an interference cancellation operator to determine whether to eliminate IRI and thus derive the closed-form expressions of outage probability of each link and interference cancellation probability. Secondly, the system delay model based on ACK feedback is described, and then, the average delay of the system is derived. In addition, the DTMC model is established to derive the system throughput using stable-state distribution and state transition matrix. Moreover, the total energy consumption model under M-ary modulation is proposed to obtain energy efficiency. Finally, the numerical simulation results show that the outage probability, delay, throughput, and energy efficiency performance can be measured under the optimal parameters. The delay performance of the proposed system is improved by 50% compared to the traditional relay system and the delay reduced by about 10% compared to DH-MSMR-CARQ system. The target data rate has almost no effect on throughput, and the throughput tends to be optimal with high SNR. In addition, the energy efficiency performance of the proposed system is also improved by 50% compared to the system without interference cancellation technique.

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 PhD Research Startup Fund of Lanzhou University of Technology (05-061405), the Hongliu Fund of First-class Disciplines of Lanzhou University of Technology, and the 2021 Graduate Research Exploration Fund of Lanzhou University of Technology, China.

References

[1] A. Nosratinia, T. E. Hunter, A. Hedayat, "Cooperative communication in wireless networks," IEEE Communications Magazine, vol. 42 no. 10, pp. 74-80, DOI: 10.1109/MCOM.2004.1341264, 2004.

[2] R. U. Nabar, H. Bolcskei, F. W. Kneubuhler, "Fading relay channels: performance limits and space-time signal design," IEEE Journal on Selected Areas in Communications, vol. 22 no. 6, pp. 1099-1109, DOI: 10.1109/JSAC.2004.830922, 2004.

[3] H. M. Zhang, Y. Li, D. P. Jin, M. M. Hassan, A. Alelaiwi, S. Chen, "Buffer-aided device-to-device communication: opportunities and challenges," IEEE Communications Magazine, vol. 53 no. 12, pp. 67-74, DOI: 10.1109/MCOM.2015.7355587, 2015.

[4] N. Zlatanov, R. Schober, "Buffer-aided relaying with adaptive link selection—fixed and mixed rate transmission," IEEE Transactions on Information Theory, vol. 59 no. 5, pp. 2816-2840, DOI: 10.1109/TIT.2013.2238607, 2013.

[5] J. Hajipour, R. Ruby, A. Mohamed, V. C. M. Leung, "Buffer-aided relaying improves both throughput and end-to-end delay," EURASIP Journal on Wireless Communications and Networking, vol. 2015 no. 1,DOI: 10.1186/s13638-015-0482-3, 2015.

[6] M. Oiwa, S. Sugiura, "Generalized virtual full-duplex relaying protocol based on buffer-aided half-duplex relay nodes," GLOBECOM 2017 - 2017 IEEE global communications conference,DOI: 10.1109/glocom.2017.8254954, .

[7] T. Mishina, M. Oiwa, R. Nakai, S. Sugiura, "Buffer-aided virtual full-duplex cooperative networks exploiting source-to-relay broadcast channels," 2019 IEEE 90th vehicular technology conference (VTC2019-fall),DOI: 10.1109/vtcfall.2019.8891481, .

[8] C. Zhai, L. Zheng, W. Guo, "Cognitive decode-and-forward relaying with successive interference cancelation," EURASIP Journal on Wireless Communications and Networking, vol. 2018 no. 1,DOI: 10.1186/s13638-018-1256-5, 2018.

[9] J. J. Wei, J. Wei, S. L. Hu, W. Chen, "Successive decode-and-forward relaying with privacy-aware interference suppression," IEEE Access, vol. 8, pp. 95793-95806, DOI: 10.1109/ACCESS.2020.2989503, 2020.

[10] M. Marey, H. Moustafa, "Interference mitigation for two-path successive relaying systems," IEEE Wireless Communications Letters, vol. 10 no. 9, pp. 2022-2026, DOI: 10.1109/LWC.2021.3091006, 2021.

[11] G. Srirutchataboon, J. Kochi, S. Sugiura, "Hybrid buffer-aided relay selection based on half-duplex and virtual full-duplex transmission," Proc. IEEE Global Commun. Conf, .

[12] N. Nomikos, T. Charalambous, N. Pappas, D. Vouyioukas, R. Wichman, "LoLa4SOR: leveraging successive transmissions for low-latency buffer-aided opportunistic relay networks," IEEE Open Journal of the Communications Society, vol. 2, pp. 1041-1054, DOI: 10.1109/OJCOMS.2021.3077036, 2021.

[13] N. Nomikos, T. Charalambous, I. Krikidis, D. N. Skoutas, D. Vouyioukas, M. Johansson, C. Skianis, "A survey on buffer-aided relay selection," IEEE Communications Surveys & Tutorials, vol. 18 no. 2, pp. 1073-1097, DOI: 10.1109/comst.2015.2512441, 2016.

[14] B. R. Manoj, R. K. Mallik, M. R. Bhatnagar, "Performance analysis of buffer-aided priority-based max-link relay selection in DF cooperative networks," IEEE Transactions on Communications, vol. 66 no. 7, pp. 2826-2839, DOI: 10.1109/TCOMM.2018.2808287, 2018.

[15] T. Jabeen, Z. Ali, W. U. Khan, F. Jameel, I. Khan, G. A. S. Sidhu, B. J. Choi, "Joint power allocation and link selection for multi-carrier buffer aided relay network," Electronics, vol. 8 no. 6,DOI: 10.3390/electronics8060686, 2019.

[16] P. Xu, Z. Yang, Z. G. Ding, I. Krikidis, Q. Chen, "A novel probabilistic buffer-aided relay selection scheme in cooperative networks," IEEE Transactions on Vehicular Technology, vol. 69 no. 4, pp. 4548-4552, DOI: 10.1109/TVT.2020.2975611, 2020.

[17] M. El‐Rajab, C. Abou‐Rjeily, R. Kfouri, "Buffer-aided relaying: a survey on relay selection policies," IET Communications, vol. 14 no. 21, pp. 3715-3734, DOI: 10.1049/iet-com.2020.0532, 2020.

[18] R. Nakai, M. Oiwa, S. Sugiura, "Generalized buffer-state-based relay selection for fixed-rate buffer-aided cooperative systems," 2017 IEEE 85th vehicular technology conference (VTC spring),DOI: 10.1109/vtcspring.2017.8108243, .

[19] W. Raza, H. Nasir, N. Javaid, M. Imran, M. Guizani, "Buffer size and link quality based cooperative relay selection in wireless networks," 2017 13th international wireless communications and Mobile computing conference (IWCMC), pp. 1489-1494, DOI: 10.1109/iwcmc.2017.7986504, .

[20] C. Abou-Rjeily, "Optimal two-way buffer-aided relaying: achieving the best outage and delay performance with small buffer sizes," IEEE Transactions on Wireless Communications, vol. 20 no. 5, pp. 2888-2901, DOI: 10.1109/twc.2020.3045219, 2021.

[21] S. El-Zahr, C. Abou-Rjeily, "Threshold based relay selection for buffer-aided cooperative relaying systems," IEEE Transactions on Wireless Communications, vol. 20 no. 9, pp. 6210-6223, DOI: 10.1109/TWC.2021.3072561, 2021.

[22] C. Wei, Z. F. Yin, W. D. Yang, Y. Cai, "Enhancing physical layer security of DF buffer-aided relay networks with small buffer sizes," IEEE Access, vol. 7, pp. 128684-128693, DOI: 10.1109/ACCESS.2019.2939272, 2019.

[23] D. Bapatla, S. Prakriya, "Performance of two-hop links with an energy buffer-aided IoT source and a data buffer-aided relay," IEEE Internet of Things Journal, vol. 8 no. 6, pp. 5045-5061, DOI: 10.1109/jiot.2020.3036130, 2021.

[24] R. Kumar, A. Hossain, "Delay performance of two-hop buffer-aided relay network with wireless assisted links," Wireless Personal Communications, vol. 121 no. 3, pp. 1725-1738, DOI: 10.1007/s11277-021-08694-8, 2021.

[25] H. L. Chen, Y. M. Cai, W. W. Yang, D. Zhang, Y. Hu, "Throughput and energy efficiency of a novel cooperative ARQ strategy for wireless sensor networks," Computer Communications, vol. 35 no. 9, pp. 1064-1073, DOI: 10.1016/j.comcom.2011.08.005, 2012.

[26] Y. Q. Zhou, H. Qian, Q. H. Wang, S. P. Li, "Performance modeling analysis of D-MSMR-CARQ with relay selection in wireless sensor networks," Security and Communication Networks, vol. 2021,DOI: 10.1155/2021/5533926, 2021.

[27] Y. Q. Zhou, B. Wang, H. Qian, S. P. Li, "Performance modeling and analysis of CMIMO-SM-ARQ protocol in intelligent transportation system," Application Research of Computers, vol. 38 no. 8, pp. 2449-2453, 2021.

[28] K. Feher, D. K. Feher, Wireless Digital Communications: Modulation and Spread Spectrum Applications, 1995.