Optimal Achievable Transmission Capacity Scheme for Full-Duplex Multihop Wireless Networks

Full-duplex (FD) communication has been attractive as the breakthrough technology for improving attainable spectral efficiency since the 5G mobile communication system. Previous research focused on self-interference cancellation and medium access control (MAC) protocol to realize the FD system in wireless networks. This paper proposes an optimal achievable transmission capacity (OATC) scheme for capacity optimization in the FD multihop wireless networks. In this paper, the proposed OATC scheme considers the temporal reuse for spectral efficiency and the spatial reuse with transmit power control scheme for interference mitigation and capacity optimization. OATC scheme controls the transmit power to mitigate interference and optimizes the transmission capacity, which leads to the optimal achievable network capacity. We conduct the performance evaluation through numerical simulations and compare it with the existing FD MAC protocols. The numerical simulations reveal that considering only the concurrent transmissions in the FD system does not guarantee optimal transmission capacity. Moreover, the hybrid mechanism, including the sequential transmissions, is also crucial because of the interference problem. Besides, numerical simulation validates that the proposed OATC scheme accomplishes the optimal achievable network capacity with lower interference power and higher achievable throughput than the existing MAC protocols.


Introduction
Full-duplex (FD) is well-known as the potential communication technology to improve the spectral efficiency of the transmission for the wireless system. FD communication simultaneously allows the transmission and reception in a single frequency channel. Several research works have focused on realizing FD communication by proposing the protocols and designing the system in different approaches in the networks of wireless LAN and mobile wireless [1][2][3][4][5][6]. For example, refs. [1,2] proposed the MAC protocols to realize the FD communication using the carrier sense multiple access with collision avoidance (CSMA/CA) concepts. The FD MAC protocols with the primary hand-shaking mechanism of request-to-send (RTS)/clear-to-send (CTS) were proposed in [3,4]. In the ad hoc network, Rahman et al. proposed Adhoc-FDMAC using the distributed coordination function (DCF) MAC standard [5]. Marlali et al. proposed the synchronized contention window FD (S-CW FD) protocol for synchronization in enabling the FD transmission, which can operate in both ad hoc and infrastructure modes of WLAN [6].
Unlike half-duplex (HD) communication, FD communication benefits in throughput gain, collision avoidance, hidden terminal problem reduction, and end-to-end delay mitigation in the wireless system. However, the concurrent transmissions in the FD system could bring possible increased traffic, higher interference, degraded link reliability, higher packet loss rate, and synchronization issues [7]. Therefore, there are several challenges in implementing FD communication in the wireless system. One of the challenges is the strong the HD MAC protocol. Similar research work with CSMA/CA-based FD MAC protocol in [23], Kim et al. considered user scheduling for further capacity improvement. Their simulation results show a significant throughput gain than the loss due to collision because of high transmission probability even when the number of users increases in the network. In addition, in the hybrid approach with FD/HD system, the research in [24] analyzed the system throughput with adaptive communication mode of FD and HD based on the interference strengths of the FD wireless nodes.
On the other hand, plenty of research has focused on capacity optimization with interference mitigation in the FD system in both wireless LAN and mobile wireless networks. For example, in mobile wireless, Tang et al. derived capacity optimization by cancelling IUI from other transmissions [17]. The simulation result shows that the perfect cancellation can bring more than 60% capacity gain even in a dense network environment. In similar research on mobile wireless, Wu et al. proposed the IUI suppression scheme by transmitting the additional reversed signal at the base station [16]. However, transmitting the additional signal can cause further energy-consuming. Therefore, as the different perspectives to approach the interference mitigation problem, the transmit power control (TPC) scheme is considered to mitigate IUI [19]. For example, Qu et al. proposed the multiuser FD MAC protocol, which considers the power control to manage the uplink for interference [25]. In their research, the simulation result shows that the lower transmit power that satisfies the signal-to-interference-plus-noise ratio (SINR) threshold can bring a better network capacity. Another relevant research work is [18], which proposed the limited area-based interference control scheme in mobile wireless using TPC. In addition, Samy et al. designed the transmit power optimization problem to maximize the sum-rate and received SINR in the wireless relay network [26]. Furthermore, Kai et al. presented the joint user scheduling and power control scheme as the performance optimization in the wireless LAN [27]. In their simulation results, the proposed scheme brings up to 80% of capacity improvement compared to the HD system. In [28], the use-up-link-capacity iterative algorithm formulates the throughput optimization, which pairs the transmission with binary scheduling variables in FD cellular network. Similar to [14], the proposed distributed joint user scheduling and power allocation achieved nearly twice the capacity improvement in an indoor multicell network.
The existing FD MAC protocols only consider concurrent transmissions with temporal reuse for capacity optimization in the wireless network. Even in the hybrid approach with FD/HD system, the MAC protocol only considers the concurrent transmission (CT) scheme in FD mode and the sequential transmission scheme in HD mode. With the motivation of lack to consider both the concurrent transmission and sequential transmission in the FD system, we proposed a mixture of concurrent and sequential transmission (MCST) scheme for capacity optimization in the FD multihop wireless networks by considering both the advantages of concurrent transmission and sequential transmission in [29]. However, we lack to consider the tradeoff between the interference power and capacity gain of the transmission. In [30], we also studied the consensus transmit power control (CTPC) scheme for capacity optimization through power control in the FD multihop wireless networks and elucidated that the CTPC with optimal consensus coefficient value improves the throughput with the minimum transmit power and interference power. Therefore, the reviewed literature shows that FD communication is worth studying and still needs investigation for capacity optimization in future advanced wireless networks.

Contributions
This paper investigates capacity optimization in the FD multihop wireless networks with the aid of the relay node. The contributions of this paper are summarized as follows.
• This paper contributes that the findings of the CT scheme only and the MCST scheme only cannot provide the best achievable network capacity all the time, even with the aid of transmit power control scheme in the FD multihop wireless networks. As a result, the OATC scheme is proposed to combine these two schemes to achieve the optimal achievable capacity. • This paper introduces an algorithm for the OATC scheme to choose either the CT scheme or MCST scheme by using the tradeoff threshold, which is the tradeoff to consider both the interference power and the received power of the ongoing transmission. • Through numerical simulation results, this paper reveals that the proposed OATC scheme not only applies the high ratio of the CT scheme when the network is not dense to achieve the optimal achievable capacity but also reduces total interference power.
We note that [31] presented a part of the contributions to the OATC scheme as a preliminary study of saturation throughput analysis. However, we assumed the consensus coefficient is one as a constant in the CTPC algorithm. Therefore, compared to [31], the consensus coefficient impact is considered in this paper for a complete OATC scheme of the considered research problem.
The organization of the paper is as follows. Section 2 presents the system model, and Section 3 introduces the proposed OATC scheme. Section 4 presents the numerical simulation scenarios and settings, evaluation metrics, results, and discussion. Finally, Section 5 concludes the paper.

System Model
This section presents the system model with the distributed wireless network without the central control nodes. In the network, we consider a single relaying transmission flow in which a source node (S) communicates to a destination node (D) with the help of a relay node (R), as illustrated in Figure 1. We assume that all the wireless nodes are enabled as a shared-antenna FD system [32]. They can transmit and receive simultaneously in a single frequency band through the use of a circulator. In the wireless system, the FD-enabled relay node adopts the SIC technique to suppress SI. Therefore, we assume SI can be suppressed until the noise level and omit the effect of SI as in [17]. The FD relaying system can apply the decode-and-forward and amplify-and-forward relaying strategies. However, we assume this research applies no relaying strategies for simplicity. In this work, we also assume the relay node knows the perfect channel state information (CSI) from other nodes. Hence, we define the basic relaying flow (BRF) transmission as the combination of source-relay (SR) transmission and relay-destination (RD) transmission by omitting the time synchronization problem. In addition, due to the shadowing effects, we assume that there is no direct transmission link from S to D as in [33]. Let N = {1, . . . , n, . . . , N} denote the set of nodes where N is the total number of nodes. Each BRF transmission can be selected from the set of BRF transmission M = {1, . . . , m, . . . , M} where M is the number of BRF transmissions and M = N/3. In this research, to consider the tradeoff between the total interference power level and the achievable network capacity in the presence of TPC, the selection of node combinations in a single BRF transmission is random for the theoretical analysis purpose in the single network.

Channel Model
The attenuation of the transmission link over a communication channel depends on the signal propagation model of the Log-distance pathloss model. With the Friis free space model, the channel gain in the unit of decibel [dB] at the receiving node j from the transmitting node i, where i, j ∈ N is defined as where PL 0 = 20 · log 10 (d 0 ), α is the attenuation constant, d 0 is the decorrelation distance which is 1 m, d ij is the euclidean distance between node i and node j, W ij is the wall attenuation and X σ is the additive and Gaussian random variable with zero mean and standard deviation of σ. Then, the received power ratio between transmitting node i and receiving node j is (2)

SINR Model
A successful transmission occurs only if the SINR is above a certain threshold. The SINR obtained at the receiving node j from the transmitting node i is computed as where P i is the transmit power of the node i, η j is the noise level at node j, B is the channel bandwidth, and I is the set of interfering nodes to the ongoing transmission from node i to node j. SNR-based interference model is assumed to compute I when there are concurrent transmissions in the vicinity of the transmission medium [29]. An interference model determines the interfering nodes according to the received signal-to-noise ratio (SNR) of the ongoing transmission from node i to node j and is computed as For example, if node k is the concurrent transmitting node in the same transmission medium, the SNR of node k to transmitting node i and receiving node j of the ongoing transmission is SNR ki and SNR kj , respectively. Then, if SNR ki and/or SNR kj is less than SNR ij , the transmitting node k is called interfering node and k ∈ I.

Link Capacity Model
Using the Shannon theorem [34], the transmission rate [bit/s] over a communication channel for the ongoing transmission from node i to node j is defined as

Achievable Single BRF Transmission Capacity
In the FD system, several transmissions can proceed simultaneously in the single time/frequency band through the CT scheme. As shown in Figure 1, the relay node R can receive the transmission from the source node S and proceed to the destination node D simultaneously. Figure 2a shows an example of a CT scheme for a BRF transmission, and the achievable transmission capacity is computed as where R con SR and R con RD are the transmission rates R SR and R RD based on SI NR SR of SR transmission and SI NR RD of RD transmission, respectively. Through the cooperative MCST scheme, the achievable transmission capacity of a BRF transmission can be maximized as presented in [29]. MCST performs the concurrent transmissions in the time fraction τ of the timeslot and sequential transmission in the remaining time of the timeslot. MCST optimizes the achievable transmission capacity by selecting the time fraction τ and the sequential transmission as shown in Figure 2b. The time fraction τ can be computed as the following equation RD are the transmission rates R SR and R RD based on SNR SR of SR transmission and SNR RD of RD transmission, respectively. Then, the achievable transmission capacity of a BRF transmission is computed by choosing the sequential transmission, which gives the optimal transmission capacity as the following where τ SR and τ RD are the τ values as SR transmission and RD transmission are the choice of sequential transmissions, respectively.

Transmit Power Control Scheme
We obtain the achievable transmission capacity from the previous section. Hereafter, the TPC scheme is applied to advance the transmission capacity while mitigating the interference, subjective to the minimum transmit power of the nodes. We apply the CTPC scheme in this research work among the existing TPC schemes. CTPC converges all the transmitting nodes to an average transmission rate by adjusting the transmit power of each node [30,35]. In CTPC, the algorithm maximizes the minimum transmission rate of the ongoing transmissions by adjusting the transmit power. As a result, all transmission rates converge on the average transmission rate of all existing BRF transmissions, which optimizes the achievable network capacity. Therefore, we aim to attempt the capacity optimization of the transmissions while satisfying the SINR constraints, and the optimization problem for TPC is formulated as where R ij is the transmission rate from node i to node j of a BRF transmission, F is the minimum link rate of each BRF transmission, C is the consensus coefficient that depends on the node-to-node distance of the network topology, A is the average link rate of all BRF transmissions, P i is the transmit power of node i, P max is the transmit power budget, and β is the SINR threshold.

Optimal Achievable Transmission Capacity Scheme
This section describes an optimal achievable transmission capacity (OATC) scheme to optimize the achievable transmission capacity of the BRF transmission in the FD multihop wireless networks. By applying the temporal reuse mechanism, OATC allows the relay node cooperatively select the CT scheme or MCST scheme to achieve the optimal achievable transmission capacity of the BRF transmission. By applying the hybrid scheduling policy of [14], OATC applies the MCST scheme, which gives its advantage of capacity gain. Otherwise, it applies the default CT scheme for BRF transmission. Besides, OATC integrates with the TPC mechanism to mitigate the IUI of the concurrent transmissions and accomplishes the objective function of achievable transmission capacity while satisfying the SINR threshold. The existing transmission schemes tend to achieve the optimal achievable transmission capacity without considering the tradeoff between interference power and capacity gain of the transmission. Therefore, the achievable transmission capacity is still limited when the network becomes dense. OATC attempts to overcome the interference issues and optimize the achievable transmission capacity by integrating the temporal and spatial reuse mechanisms.
The proposed OATC scheme attains the optimal achievable transmission capacity under the transmit power constraint with three main steps. The first step computes the transmission rate of each ongoing transmission through the CT scheme and MCST scheme. The second step applies the CTPC scheme to the CT and MCST scheme to obtain the appropriate transmit power for optimizing the achievable transmission capacity while mitigating the total interference power. Third, the operational transmission scheme, either the CT scheme or MCST scheme with TPC, is determined according to the defined tradeoff threshold. The tradeoff threshold T is the ratio of interference power to the received power of the receiving node in the BRF transmission and computed as where I * = ∑ k∈I,k =i G kj · P k is the interference power and G * = G ij · P i is the received power of the ongoing transmission. OATC selects the operational transmission scheme with the lower T for higher achievable transmission capacity. The lower tradeoff threshold gives the lower interference power and the higher achievable transmission capacity, which optimizes the achievable network capacity of the entire network. OATC scheme works cooperatively according to the three algorithms executed in the relay node by using the simple compute-and-compare mechanism as in [36]. As illustrated in Algorithm 1, CT with CTPC computes the required transmit power, transmission rate of each transmitting node as the choice transmission rate R, and its threshold for the BRF transmissions through the CT scheme. In the algorithm, step 2 computes the transmission rate through the CT scheme from the SINR received. And then, CTPC is applied to optimize the achievable transmission capacity. Algorithm 2 describes the operation of MCST with CTPC. In the algorithm, step 2 to step 11 optimally chooses the transmission rate of the ongoing transmission through the MCST scheme. And then, CTPC is applied to mitigate the interference power by satisfying the required threshold condition for successful transmission. Finally, Algorithm 3 determines the operational transmission scheme of either CT scheme or MCST scheme according to the T and results in the transmit power and the transmission rate for the transmission.

Algorithm 1 CT with CTPC Algorithm
Definition: TC ct (P ct , R ct , T ct ) is transmission control set, P is the transmit power and R is the choice transmission rate, T is the threshold of CT, t is timeslot, i is the transmitting node, j is the receiving node Input: SNR SR , SNR RD , SI NR SR , SI NR RD Output: TC ct (P ct , R ct , T ct ) function CT/CTPC Calculate R con SR (t), R con RD (t) Calculate target rate of each flow F(t) where F(t) ⇐ mean{R con SR (t), R con RD (t)} Calculate next target rate of all flows A(t + 1) where

Algorithm 2 MCST with CTPC Algorithm
Definition: TC mcst (P mcst , R mcst , T mcst ) is transmission control set, P is the transmit power and R is choice transmission rate, T is the threshold of MCST, t is timeslot, i is the transmitting node Input: SNR SR , SNR RD , SI NR SR , SI NR RD Output: TC mcst (P mcst , R mcst , T mcst ) end if 12: Calculate target rate of each flow F(t) where F(t) ⇐ mean{R(t)}

13:
Calculate next target rate of all flows A(t + 1) where A(t) ⇐ mean{∀F(t)}

Numerical Simulations
This section evaluates the network performance of the proposed OATC scheme through simulations. The performance evaluation compares the existing FD MAC protocols with RTS/FCTS [4], which considers only the concurrent transmissions without any sequential transmissions, and FD-MCST [29] with both concurrent and sequential transmissions in the multihop wireless networks. Both existing FD MAC protocols are not considering the TPC scheme.

Simulation Scenarios and Settings
The simulation parameters and settings are listed in Table 1 with the standard specification of IEEE802.11ac [37]. In this paper, the simulation program is written using MATLAB R2021a. It consists of two scenarios: the influence on the DATA length in a 30-node random topology scenario and the influence on the network density with fixed DATA length. Figure 3 illustrates the block diagram of the numerical analysis. In the network model, a different network topology is randomly generated with a uniform distribution of the node allocation in the network coverage area. As an assumption, all the wireless nodes are identical; they are equipped as the FD system and have equal initial transmit power. Besides, the node combination in a single BRF transmission is randomly selected in the network. In the traffic model, we assume the transmission is the single relaying transmission flow with a relay node, and all transmitting nodes always have a DATA frame of the same size. This paper considers only one transmission per DATA frame for theoretical study purposes without a retransmission scenario. Therefore, the backoff timer is set to the initial backoff contention window for any collision. With the log-distance pathloss model as the channel model, the transmission rate is computed based on the SINR model, and link capacity model. And then, the numerical analysis of the proposed OATC scheme, RTS/FCTS, and FD-MCST is conducted for performance evaluation. The simulation results are based on an average of 1,000 different experiments. In the output model, we consider the performance matrices of achievable network capacity, average achievable throughput, and average achievable transmission overhead with the SINR threshold of 6 dB.

Evaluation Metrics
This section provides the evaluation metrics of the proposed OATC scheme in terms of achievable network capacity, achievable throughput, and achievable transmission overhead ratio.

Achievable Network Capacity
The achievable network capacity, C a is the total of the achievable transmission capacity of every single BRF transmission in the network and computed as where C m is the achievable transmission capacity, C of mth BRF transmission.

Achievable Throughput
The two-state Markov Chain model, i.e., success and collision, as in [1] is applied to evaluate the proposed OATC scheme. A transmission collision will happen when a transmitting node starts transmission in a backoff slot, and one or more other stations start transmission in the same backoff slot. In the discrete-time Markov Chain, the next state of the transmission depends on the previous state, and the transmission collision occurs according to the conditional collision probability (p) of a transmission which is computed as where p is the probability that the transmitting node observes the collision. By simply considering the FD system in a saturated traffic condition with no retransmission and the MAC protocol with the specification of IEEE802.11, the calculations for conditional collision probability and saturation throughput are similar as in [29]. Therefore, the saturation throughput, S of the transmission, is given as where p t is the probability of transmission, L and C are the successful transmission time and transmission collision time, respectively.
The average achievable throughput, S a is the average value of the total number of successfully transferred data in a second by a transmitting node in the network and is formulated as where p s is the probability of successful transmission based on the SINR constraint condition of the transmission and S m is the saturation throughput, S of mth BRF transmission.

Achievable Transmission Overhead
Suppose that the transmission is successful with the schematic analysis of frame exchange of CT scheme and MCST scheme as in [29]. We suppose that T DIFS is the duration of DCF interframe space (DIFS), T SIFS is the duration of short interframe space (SIFS), T RTS is the duration for request-to-send (RTS) frame, T CTS is the duration for clear-to-send (CTS) frame, T ACK is the duration for acknowledgement (ACK) frame, T PHY is the time of physical preamble and header, H is the size of MAC header and trailer, and R base is the basic rate. Therefore, the overhead time T o for CT scheme and MCST scheme defined by T CT o and T MCST o , respectively, are And then, the successful time of transmission to transmit an l-byte DATA length, T s for CT scheme and MCST scheme defined by T CT s and T MCST s , respectively, are where T BK is the time of the initial backoff timer for the DCF mechanism and R MCST is the transmission rates of SR transmission and RD transmission, which is given as On the other hand, by assuming the collision is detected during the initial stage of data transmission in the DCF mechanism, the time of transmission in the collision condition, T c is computed as The average achievable transmission overhead, O a is the average value of the overhead which is required to successfully carry out a transmission without considering the retransmission for any collision scenario in the network and is computed as where O m is the transmission overhead ratio, O of mth BRF transmission, which is given as Figure 4 compares the performance of average achievable throughput and average achievable transmission overhead versus DATA length for the 30-node random topology scenario. As we can observe, OATC accomplishes its superiority in achievable throughput over RTS/FCTS and FD-DMAC regardless of the DATA length. Quantitatively, when the DATA length is 1500 bytes, OATC gives 40.02 Mbps, while RTS/FCTS and FD-MCST bring 29.84 Mbps and 38.42 Mbps, respectively. It means OATC accomplishes 34% and 4% of achievable throughput improvement compared to RTS/FCTS and FD-MCST, respectively. This is because OATC optimizes the achievable transmission capacity by considering the tradeoff threshold with the temporal and spatial reuse mechanisms. Compared to the other two protocols, when the DATA length increases, the achievement of OATC in average achievable throughput increases with high average achievable transmission overhead. However, the optimal achievable transmission capacity leads to a shorter successful transmission time and results a higher achievable transmission overhead. We can conclude that OATC is superior to the achievable throughput with the reasonably achievable transmission overhead regardless of the number of BRF transmissions and DATA length in the network.  Table 2 shows the performance comparison between the proposed OATC scheme, RTS/FCTS, and FD-MCST in terms of achievable network capacity and average achievable throughput for the network with single BRF transmission and fixed DATA length of 1500 bytes. The simulation result shows that there is no interference in the network with single BRF transmission. As we can observe, OATC achieves a better achievable network capacity and average achievable throughput by taking advantage of higher achievable transmission capacity through the MCST scheme. And then, Table 3 shows the performance of RTS/FCTS and FD-MCST with and without CTPC compared to OATC. With the fixed DATA length of 1500 bytes, we can observe that the CTPC scheme can achieve higher average achievable throughput to both the RTS/FCST and FD-MCST. However, by taking the advantage of temporal reuse and spatial reuse and considering the tradeoff threshold between the interference power and capacity gain, OATC can accomplish higher average achievable throughput compared to RTS/FCTS and FD-MCST.  Figure 5 describes the performance comparison of achievable network capacity and total interference power versus the number of BRF transmissions in the multihop wireless network environments. As we can observe from the graph, OATC gives a better achievable network capacity compared to RTS/FCTS. In particular, OATC achieves 781.63 Mbps while RTS/FCTS achieves 529.45 Mbps when the number of BRF transmissions is 50. OATC can bring the 36% to 48% of better achievable network capacity given by RTS/FCTS when the number of BRF transmissions changes from 10 to 50 in the network. However, when the network is dense, OATC has a lower achievable network capacity than the FD-MCST. Quantitatively, OATC has around 4% lower achievable network capacity given by FD-MCST when the number of BRF transmissions is 50, which is neglectful compared to the achievement over RTS/FCTS. This is because OATC controls the transmit power with the CTPC scheme with the consensus coefficient to mitigate the interference power. Besides, the algorithms of OATC choose the operational transmission scheme subject to the minimum total interference power. In addition, Figure 5 depicts that the total interference power increases when the network density is high. The comparison shows that the OATC is superior to RTS/FCTS and FD-MCST in total interference power. We can conclude that OATC can accomplish a higher achievable network capacity and mitigate the interference power regardless of the number of BRF transmissions and density of the network. Figure 6 illustrates the performance comparison in terms of average achievable throughput and average achievable transmission overhead versus the number of BRF transmissions. OATC depicts the superiority of average achievable throughput compared to RTS/FCTS and FD-MCST with a fixed DATA length of 1500 bytes. This is because OATC optimizes the transmit power with the CTPC scheme and mitigates the interference power while satisfying the SINR constraint of the transmission. As a result, OATC converges the transmission rate of ongoing transmissions and maximizes the number of successful transmissions. The figure shows that the average achievable throughput decreases when the number of BRF transmissions increases. This is because the average transmitter-toreceiver distance decreases in the fixed network coverage area; on the other way, the network becomes dense. However, regardless of the number of BRF transmissions, OATC achieves the maximum achievable throughput over the other two protocols. Besides, the figure shows that the average achievable transmission overhead of OATC is higher than RTS/FCTS and FD-MCST, significantly when the number of BRF transmissions increases. In particular, OATC gives the average achievable overhead ratio of 83% while RTS/FCTS and FD-MCST give 77% and 81%, respectively, when the number of BRF transmissions is 50. This is because the higher transmission rate achieved by OATC gives a shorter successful transmission time of transmission compared to RTS/FCTS and FD-MCST.   Table 4 lists the performance analysis of concurrent transmissions in the OATC scheme. When the number of BRF transmissions increases, the network becomes dense, leading to high total interference. As we can observe, the ratio of the CT scheme operating as the operational transmission scheme in OATC is decreasing to mitigate the interference because of the concurrent transmissions. As a result, reducing the CT scheme in OATC increases the achievable network capacity and average achievable throughput gain. Furthermore, it decreases total interference power compared to the purely CT scheme, i.e., RTS/FCTS, when the number of BRF transmissions increases. However, the total interference reduction becomes merely less when the number of BRF transmissions is 50 due to the selection of BRF transmission that leads to the close distance between source and destination. In summary, the proposed OATC accomplishes its superiority in terms of achievable network capacity, total interference power, and achievable throughput compared to FD MAC protocol with RTS/FCTS and FD-MCST in multihop wireless networks.

Conclusions
This paper proposes an OATC scheme for capacity optimization in FD multihop wireless networks with the relaying system. We investigated the capacity optimization in terms of achievable network capacity, achievable throughput, and interference mitigation compared to the existing FD MAC protocol with RTS/FCTS and FD-MCST. Numerical simulation results reveal that only a concurrent transmission scheme and a mixture of concurrent and sequential transmission scheme do not guarantee the optimal transmission capacity in the FD system. Therefore, it is crucial to consider the sequential transmission and the aid of transmit power control scheme because of the interference. By combining the concurrent transmission scheme and a mixture of concurrent and sequential transmission scheme, the proposed OATC scheme optimizes the achievable network capacity with the tradeoff between the interference power and the received power of the transmission. Compared to the FD MAC with only concurrent transmissions, the simulation results show that the proposed OATC scheme is superior in interference mitigation and significantly accomplishes a higher achievable network capacity. In addition, the proposed OATC outperforms the other protocols in achievable throughput regardless of the number of BRF transmissions and DATA length. Mainly, OATC can accomplish 56% and 14% higher achievable throughput of RTS/FCTS and FD-MCST, respectively, in the FD multihop wireless network. As the preliminary research study, this paper only considers the FD system with a single relaying transmission flow with a relay node. The proposed OATC scheme can be easily extended for the wireless network with multiple relay nodes as well as the relaying selection, which is left as a further research topic for capacity optimization. The significant research attention on the FD system for capacity optimization is timely and ongoing in the trend of future 6G mobile communication systems. In future research work, we will conduct the performance investigation of the OATC scheme in multihop wireless networks with multiple relay nodes and highly dynamic environments such as vehicular scenarios. Furthermore, we will investigate OATC with the multi-channel allocation scheme for additional interference mitigation and capacity optimization in the FD multihop wireless networks.

Conflicts of Interest:
The authors declare no conflict of interest.

Abbreviations
The following abbreviations are used in this manuscript: Request-to-send/clear-to-send mechanism RTS/FCTS Request-to-send/full-duplex clear-to-send MAC protocol SI Self-interference SIC Self-interference cancellation SINR Signal-to-interference-plus-noise ratio SNR Signal-to-noise ratio SR Source-relay transmission TPC Transmit power control scheme