 Research
 Open Access
Inband fullduplex medium access control design for heterogeneous wireless LAN
 Md. Abdul Alim^{1, 2}Email author,
 Makoto Kobayashi^{1},
 Shunsuke Saruwatari^{1} and
 Takashi Watanabe^{1}
https://doi.org/10.1186/s1363801708676
© The Author(s) 2017
 Received: 1 July 2016
 Accepted: 19 April 2017
 Published: 5 May 2017
Abstract
Fullduplex (FD) wireless communication is evolving into a practical technique, and many studies are being conducting in this area, especially regarding the physical layer. However, to exploit FD benefit successfully, efficient medium access control (MAC) protocols are crucial as well as physical layer advances. Numerous FDMAC protocols have been proposed, but these MAC protocols cannot address all the issues encountered in this area. In addition, many halfduplex (HD) capable devices are present in existing wireless local area networks (WLANs), so there is an urgent need to integrate FD clients and HD clients in the same WLAN. We refer to this type of WLAN as a heterogeneous WLAN (HetWLAN). In this paper, we propose an FDMAC for HetWLAN, which considers all possible types of FD transmissions. Our proposed FDMAC protocol suppresses interuser interference. Simulation results demonstrated that a significant throughput gain (about 96%) could be achieved by using our proposed FDMAC compared with traditional HD communications. Moreover, our proposed MAC obtained better performance (average throughput gain of about 11%) compared with another existing FDMAC design. In addition, probability analysis suggested that the total probability of FD transmissions increased rapidly as the WLAN approached saturation conditions.
Keywords
 Fullduplex
 MAC protocol
 HetWLAN
 FDMAC
1 Introduction
In general, traditional radio transceivers cannot transmit and receive simultaneously using the same frequency band because of selfinterference at the receiver end. However, recent technological advances in antenna design and radio frequency interference cancellation techniques can reduce selfinterference by up to 110 dB [1]. Similar studies have also been conducted regarding the physical layer by [2–4]. The latest technologies for selfinterference cancellation allow us to transmit and receive signals simultaneously using the same frequency, which is known as inband fullduplex (IBFD) communication [5]. However, a suitable medium access control (MAC) is crucial to exploit the full advantages of IBFD technology in wireless local area networks (WLANs) because the current IEEE standard MAC protocols do not support IBFD communications. IBFD is one of the techniques with the greatest potential for supporting the huge traffic demands in the near future, and researchers are attracted to IBFD because it can increase the spectral efficiency without requiring any additional frequency resources [5]. IBFD can also double the ergodic capacity of a multipleinput multipleoutput system [1, 3].
All of the user terminals or nodes in existing WLANs are traditional HD capable. Therefore, it is not possible to replace all of these HD nodes (HDNs) with FD nodes (FDNs) overnight, so it is necessary to incorporate FDNs in existing WLANs in a manner that allows HDNs and FDNs to operate simultaneously. A WLAN that comprises HDNs and FDNs is referred to as a heterogeneous WLAN (HetWLAN) because it has different types of clients or nodes.
The symmetric length of the uplink and downlink data traffic is considered in the design of our FDMAC protocol. This type of traffic is very common in different areas, such as cellular mobile communications, distant health monitoring, online video games, peertopeer (P2P) TV, P2P file sharing, and video conferencing [7]. Moreover, IBFD wireless communications should be designed in such a way, where the symmetric traffic length plays a vital role. Otherwise, the link (downlink or uplink) that finishes its data transmission earlier will be idle for the remainder of the time of that round.

An FDMAC is proposed for a HetWLAN that contains FDNs and HDNs.

The proposed FDMAC considers all possible types of FD transmissions in this HetWLAN.

We compared performance of our proposed FDMAC with traditional HD communications and another existing FDMAC protocol.

A comprehensive probability analysis was performed for the proposed HFDMAC.
The remainder of this paper is organized as follows. In Section 2, we provide a brief description of related research in this area. In Section 3, we present the problem statement regarding FDMAC. In Section 4, we explain the proposed MAC design. In Section 5, we give a brief description of the method for combating interuser interference. In Section 6, we present the mathematical analysis. The results and performance analysis are given in Section 7. In Section 8, we give our conclusions.
2 Related works
Many studies in the area of IBFD wireless communication have aimed to minimize selfinterference, which are related to the physical layer. For example, a single antenna was used to support IBFD WiFi radio by [1], where both analog and digital selfinterference cancelation techniques were used. Various techniques have been proposed to reduce selfinterference, which are related to advances in IBFD wireless communication in the physical layer [2, 4, 8–11].
Although several MAC designs have been proposed for WLANs using IBFD, they do not consider all possible types of IBFD transmissions. In addition, some were proposed for distributed wireless networks or ad hoc networks, where all the clients were treated as FDNs [12, 13]. An FD multichannel MAC (FDMMAC) was proposed to mitigate multichannel hidden terminal (HT) problems, which targeted for eliminating controlling signals [12]. During data transmission between two nodes, the receiver transmits a beacon packet backtoback until the data transmission is complete. This beacon packet does not contain any user data. Hence, in terms of user data communications, the FD capability is not fully utilized in FDMMAC. In addition, TNFD communication is not possible because PR always needs to transmit beacon packets while receiving data from PT. Another MAC protocol was proposed by [13] for IBFD adhoc networks, where all the clients were considered as FDNs. The interuser interference is not considered during TNFD communications, and thus, TNFD communications will be affected greatly by interuser interference problems. The MAC design proposed by [14] can be used in both ad hoc and infrastructurebased WLANs. In this design, all the nodes are considered to be FD capable. Moreover, in the case of sourcebased TNFD transmissions, collisions will occur if more than two clients select the same subcarrier and AP also selects that subcarrier. Furthermore, this MAC does not include a procedure to allow the network allocation vector (NAV) to update the timing in different nodes.
An infrastructurebased MAC protocol for IBFD wireless communications was proposed that includes a shared random backoff mechanism [15], where all the nodes are treated as FDNs and the nodes can switch to the HD or FD mode based on the traffic availability. According to this MAC, all the nodes first participate in the normal contention period, before HD transmission occurs. Subsequently, any FD transmission (BFD or TNFD) can be performed after the shared random backoff period. Hence, a HD transmission should be performed earlier before initiating an FD communication. Moreover, the method proposed by [15] restricts TNFD transmission to this case only, where AP wins in the shared random backoff period. A powercontrolled MAC (PoCMAC) was proposed recently for IBFD WiFi networks [16]. This MAC utilizes a contentionbased receiver selection scheme to mitigate interuser interference during FD transmissions, but only FDAP and HD clients are considered in the network. The AP cannot initiate any transmissions in PoCMAC. Another FDMAC design was proposed for a WiFi network, where both HD and FD clients are available [17]. However, the authors limit FD communications when a mobile node and AP have packets for each other.
An FDMAC was proposed for a WLAN by [18], where AP is FD capable and all the clients are traditionally HD capable. In this method, AP and all the clients need to calculate and update the signaltointerference ratio map continuously, which may increase the computational load as well as the complexity. Transmissions always need to be initiated by clients to establish IBFD communications. If AP wins in the contention period, IBFD communication cannot be established for two reasons: the clients do not support IBFD transmissions or the clients cannot make decisions about which can start the TNFD transmission. Another APbased MAC protocol was proposed by [19], where all of the clients and AP are FD capable. This protocol has a pollingbased MAC design, where AP always needs to initiate the transmission. However, the control frame formats were not described clearly in this MAC design.
Other studies have considered different issues on IBFD communications, such as relay transmissions or power controlbased FD [20–22], but they did not consider the MAC design.
3 Problem statement
The hidden and exposed terminal problems are not so significant when the network is considered to be an APbased WLAN and communication is performed using a requesttosend (RTS) and cleartosend (CTS) handshake mechanism. This is because all the clients in a WLAN can update their NAVs by using the control frames transmitted by AP.
4 Proposed MAC protocol: HFDMAC
4.1 New control frames
Description of duplexing indicator
Value of DI  Meaning of DI 

00  Not used 
01  Sender can Rx only 
10  Sender can Tx only 
11  Sender can Tx and Rx simultaneously 
Control frames’ transmission capability
Control frame  Tx capability  

AP  FDN  HDN  
RTSD  ○  ○  × 
CTSD  ○  ○  × 
RTS  ○  ×  ○ 
CTS  ○  ×  ○ 
NCTS  ○  ×  × 
NDI  ○  ×  × 
4.2 Possible FD transmission in HetWLAN
 1.Case 1: TNFD communications
 (i)
AP initiates the transmission
 (ii)
Any HDN initiates the transmission
 (iii)
Any FDN initiates the transmission
 (i)
 2.
Case 2: BFD communications
In HFDMAC, the TNFD communication is performed between the AP and two other nodes, which can be an HDN or FDN. The BFD communication is performed between the AP and an FDN when they have data for each other. However, HD transmissions may also occur in the proposed MAC.
4.3 Description of the proposed HFDMAC
The working principle of this HFDMAC is based on the distributed coordination function (DCF) in IEEE 802.11. This protocol uses CSMA/CA and a backoff mechanism to access the channel and to avoid collisions. For simplicity, the DCF interframe space (DIFS) time and backoff time are not shown in the figures, but the short interframe space (SIFS) time is shown by “S” in all of the figures. In this MAC, a node ignores collisions or the reception of erroneous packets during the NAV period. Moreover, it is assumed that FDNs can perform selfinterference cancelation perfectly.
According to the IEEE 802.11 standard, a number of management frames are exchanged between the AP and nodes when nodes or devices join the WLAN [23]. For example, after exchanging the prob request and response, the AP grants access to the device if the device can satisfy the authentication and association procedure. Some optional bits in these management frames can be used by the nodes to indicate their FD capabilities. For example, during the joining process, a node moves to the association phase after the authentication procedure and an association request is sent to the AP. The node can indicate its FD capability using this association request because several optional bits are available. Therefore, the AP can determine which MAC address has an FD capability and which has an HD capability. Hence, the AP sends an RTSD to the FDN and an RTS to the HDN. In addition, RTS and RTSD are transmitted by HDNs and FDNs, respectively.
The description of this MAC protocol is given below for the cases mentioned above.
4.3.1 Case 1: TNFD communications
(i) AP initiates the transmission
(ii) Any HDN initiates the transmission
(iii) Any FDN initiates the transmission
After winning in the contention period, an FDN initiates a transmission by sending an RTSD to AP with a DI value of 11. AP does not have data to send the corresponding FDN, and thus, it is a TNFD communication. However, AP has data for another node (may be another FDN or any HDN). Hence, AP transmits an NCTS. The subsequent procedure is the same as that described in the previous subsection for case 1 (ii). Therefore, sending an NCTS after receiving an RTSD from AP indicates that AP has data for another node.
4.3.2 Case 2: BFD communications
BFD transmission occurs between AP and one FDN when they have data for each other. In this case, either AP or an FDN wins in the contention period and sends an RTSD. For example, AP sends an RTSD with a DI value of 11 to an FDN. The corresponding FDN also sends a CTSD with a DI value of 11 because the FDN has data for AP. BFD transmission then occurs.
It should be noted that an RTSD is always sent with a DI value of 11. The corresponding data transmission may be BFD, TNFD, or HD, which depends on the reply of the CTSD and other control frames.
5 Combating interuser interference

SDTC1: “An ST can hear an RTS from AP but cannot hear the corresponding CTS from PR.”

SDTC2: “An ST can hear an RTSD from AP and cannot hear the corresponding CTSD from PR, but can hear the NDI from AP.”

SDTC3: “An SR cannot hear an RTS/RTSD from the PT but can hear the corresponding NCTS from AP.”
SDTC1 is applied to TNFD communication where AP initiates the transmission to a HDN. Similarly, SDTC2 is applied in the case of TNFD where AP initiates the transmission to an FDN. Thus, after initiating the transmission by the AP to a FDN, if an ST wants to send data to the AP, the ST needs to satisfy SDTC2, i.e., if the ST has data to send to AP and satisfies SDTC2, it stops its NAV and starts the selftimer, and the corresponding procedures occur for the TNFD communication, as described in the previous section. In addition, SDTC3 is used in the case where an HDN/FDN initiates the TNFD communication. These FDMAC mechanisms prevent interuser interference during TNFD communications.
6 Mathematical analysis
Declaration of variables
Variables  Explanation 

m  Number of HDNs 
n  Number of FDNs 
γ  Percentage of total nodes as hidden terminals 
λ _{AP}  Packet arrival rate at AP for all clients (packets/s) 
λ _{APH}  Packet arrival rate at AP for each HDN (packets/s) 
λ _{APF}  Packet arrival rate at AP for each FDN (packets/s) 
λ _{H}  Packet generating rate by each HDN for AP (packets/s) 
λ _{F}  Packet generating rate by each FDN for AP (packets/s) 
P _{BFD}  Probability of bidirectional FD communication 
P _{TNFD}  Probability of TNFD communication 
P _{HD}  Probability of HD communication 
T _{RTS}  Time for RTS 
T _{CTS}  Time for CTS 
T _{RTSD}  Time for RTSD 
T _{CTSD}  Time for CTSD 
T _{SIFS}  Time for SIFS 
T _{NDI}  Time for NDI 
where μ is the average service rate of AP.
The probability analysis is described in the following subsections.
6.1 BFD communications
To derive the probability of bidirectional FD communications (P _{BFD}), we present Lemmas 1 and 2.
Lemma 1
After sending an RTSD to an FDN by the AP, BFD will occur only if the corresponding FDN also has data to send to the AP.
Proof
To calculate the probability of BFD occurring when AP initiates the transmission to a FDN, we need to calculate the following two probabilities. (a) The conditional probability that the packet arriving at AP is for an FDN, which is \(\frac {n\lambda _{\text {APF}}}{\lambda _{\text {Total}}}\). (b) The probability that the corresponding FDN also has a packet to send to the AP within the time T _{1}, where T _{1}= T _{RTSD}+T _{SIFS}+T _{ w }. The probability that the FDN has at least one packet to send to AP within time T _{1} is \(\Big (1  e^{ \lambda _{\mathrm {F}} T_{1} }\Big)\phantom {\dot {i}\!}\). By multiplying (a) and (b), we can calculate the probability of BFD occurring in this case. □
Lemma 2
After sending an RTSD to the AP by an FDN, BFD will occur only if the AP also has data to send to the corresponding FDN.
Proof
To calculate the probability of BFD occurring when an FDN initiates the transmission, we need to calculate the following two probabilities. (a) The conditional probability that the packet arriving at AP is sent by an FDN, which is \(\frac {n\lambda _{\mathrm {F}}}{\lambda _{\text {Total}}}\). (b) The probability that AP also has a packet to send to FDN within the time T _{1}. The probability that AP has at least one packet to send to the corresponding FDN within time T _{1} is \(\Big (1  e^{ \lambda _{\text {APF}} T_{1} }\Big)\phantom {\dot {i}\!}\). By mltiplying (a) and (b), we can calculate the probability of BFD occurring in this case. □
6.2 TNFD communications
To derive the probability of the TNFD communication (P _{TNFD}), we present Lemmas 3–6 as follows.
Lemma 3
After initiating the transmission by a HDN to the AP, TNFD communications will occur only if AP also has data to send to any other node that cannot hear the RTS from the HDN.
Proof
To calculate the probability of TNFD occurring in the case when an HDN initiates the communication, we need to calculate the following two probabilities. (a) The conditional probability that the packet arriving at AP is sent by an HDN, which is \(\frac {m\lambda _{\mathrm {H}}}{\lambda _{\text {Total}}}\). (b) The probability that AP also has a packet to send to any other node that cannot hear the RTS from the HDN within time T _{2}, where T _{2}= T _{RTS}+T _{SIFS}+T _{ w }. The probability that AP has at least one packet for one of the hidden nodes within time T _{2} is \(\Big (1  e^{ \{(m1)\lambda _{\text {APH}}+ n\lambda _{\text {APF}} \}T_{2} }\Big)\gamma \phantom {\dot {i}\!}\). By multiplying (a) and (b), we can calculate the probability of TNFD occurring in this case. □
Lemma 4
After initiating the transmission by a FDN to the AP, TNFD communications will occur only if (i) the AP has no data for the corresponding FDN and (ii) the AP has data for another node that cannot hear the RTSD from the FDN.
Proof
To calculate the probability of TNFD occurring in this case, we need to calculate the following three probabilities. (a) The conditional probability that an FDN has a packet to send to AP, which is \(\frac {n\lambda _{\mathrm {F}}}{\lambda _{\text {Total}}}\). (b) The probability that AP has no data to send to the corresponding FDN within time T _{1}, which is \(\Big (e^{ \lambda _{\text {APF}}T_{1}}\Big)\phantom {\dot {i}\!}\). (c) The probability that the AP has a packet for another node that cannot hear the RTSD from the FDN within time T _{1}, which is \(\Big (1  e^{ \{m\lambda _{\text {APH}}+ (n1)\lambda _{\text {APF}} \}T_{1}}\Big)\gamma \phantom {\dot {i}\!}\). We can calculate the probability of TNFD communications occurring in this case by multiplying (a), (b), and (c). □
Lemma 5
After initiating the transmission by the AP to a HDN, TNFD communications will occur only if another node that cannot hear the RTS has data to send to AP.
Proof
To calculate this probability, we need to calculate the following two probabilities. (a) The conditional probability that the AP has a packet to send a HDN, which is \(\frac {m\lambda _{\text {APH}}}{\lambda _{\text {Total}}}\). (b) The probability that any other node that cannot hear the RTS has packets for the AP within time T _{3}, where, T _{3}= T _{RTS}+T _{SIFS}+T _{CTS}+T _{ w }. This probability can be written as T _{3} is \(\Big (1  e^{ \{(m1)\lambda _{\mathrm {H}}+ n\lambda _{\mathrm {F}} \}\gamma T_{3}}\Big)\phantom {\dot {i}\!}\). By multiplying (a) and (b), we can calculate the probability of TNFD occurring in this case. □
Lemma 6
After initiating the transmission by the AP to a FDN, TNFD will occur only if (i) the corresponding FDN has no data to send to the AP and (ii) any other node that cannot hear the RTSD has data for the AP.
Proof
To calculate the probability of TNFD communications occurring in this case, we need to calculate the following three probabilities. (a) The conditional probability that the AP has a packet to send to an FDN, which is \(\frac {n\lambda _{\text {APF}}}{\lambda _{\text {Total}}}\). (b) The probability that the corresponding FDN has no data to send to the AP within time T _{1}, which is \(\Big (e^{ \lambda _{\mathrm {F}}T_{1}}\Big)\phantom {\dot {i}\!}\). (c) The probability that any other node that cannot hear the RTSD has data for the AP within time T _{4}, where T _{4}= T _{RTSD}+2T _{SIFS}+T _{CTSD}+T _{NDI}+T _{ w }. This probability is calculated as \(\Big (1  e^{ \{m\lambda _{\mathrm {H}}+ (n1)\lambda _{\mathrm {F}} \}{\gamma }T_{4}}\Big)\phantom {\dot {i}\!}\). We can calculate the probability of TNFD occurring in this case by multiplying (a), (b), and (c). □
6.3 HD communications
To derive the probability of HD communication (P _{HD}), Lemmas 7–10 are presented as follows.
Lemma 7
After initiating the transmission by a HDN, HD communications will occur if (i) AP has no data to send any other node or (ii) AP has data to send to another node that is exposed to the corresponding HDN. Because although the AP has data for the nodes that are exposed to the corresponding HDN, the SDTC3 cannot be satisfied, and thus, a HD communication will occur.
Proof
To calculate the probability of HD communications occurring in this case, we need to calculate the following probabilities. (a) The conditional probability that the HDN initiates a transmission and the probability that the AP has no data to send to other nodes within time T _{2}, which is calculated as \(\frac {m\lambda _{\mathrm {H}}}{\lambda _{\text {Total}}}\Big (e^{ \{(m1)\lambda _{\text {APH}}+ n\lambda _{\text {APF}} \}T_{2} }\Big)\phantom {\dot {i}\!}\). (b) The probability that the HDN initiates the transmission and the AP has at least one packet for the nodes that are exposed to the HDN, which is calculated as \(\frac {m\lambda _{\mathrm {H}}}{\lambda _{\text {Total}}}\Big (1  e^{ \{(m1)\lambda _{\text {APH}}+ n\lambda _{\text {APF}} \}T_{2} }\Big)\Big (1\gamma \Big)\phantom {\dot {i}\!}\).
By adding (a) and (b), we can calculate the probability of HD communications occurring in this case. □
Lemma 8
After initiating the transmission by an FDN, HD communications will occur if (i) The AP has no data to send to any other node including the corresponding FDN or (ii) The AP has data to send to another node that is exposed to the corresponding FDN. SDTC3 cannot be satisfied so HD communications will occur in this case.
Proof
To calculate the probability of HD communications occurring in this case, we need to calculate the following probabilities. (a) The conditional probability that the FDN initiates the transmission and the probability that the AP has no data to send to other nodes, including the FDN, within time T _{1}, which is calculated as \(\frac {n\lambda _{\mathrm {F}}}{\lambda _{\text {Total}}}\Big (e^{ \lambda _{\text {AP}}T_{1}}\Big)\phantom {\dot {i}\!}\). (b) The probability that after initiating the transmission by a FDN, the AP has no data for the corresponding FDN and the AP has at least one packet for the nodes that are exposed to the FDN within time T _{1}, which is calculated as \(\frac {n\lambda _{\mathrm {F}}}{\lambda _{\text {Total}}}\Big (e^{ \lambda _{\text {APF}}T_{1}}\Big)\Big (1  e^{ \{m\lambda _{\text {APH}}+ (n1)\lambda _{\text {APF}} \}T_{1}}\Big (1\gamma \Big) \). By adding (a) and (b), we can calculate the probability of HD communications occurring when an FDN initiates the transmission. □
Lemma 9
After initiating the transmission by the AP to an HDN, HD communications will occur if other nodes that cannot hear the RTS have no data for AP.
Proof
To calculate the probability of HD communications occurring in this case, we need to calculate the following two probabilities. (a) The conditional probability that the AP has a packet to send to an HDN, which is \(\frac {m\lambda _{\text {APH}}}{\lambda _{\text {Total}}}\phantom {\dot {i}\!}\). (b) The probability that other nodes that satisfy SDTC1 have no data for the AP within time T _{3}, which is calculated as \(\Big (e^{ \{(m1)\lambda _{\mathrm {H}}+ n\lambda _{\mathrm {F}} \}\gamma T_{3}}\Big)\phantom {\dot {i}\!}\). By multiplying (a) and (b), we obtain the probability of HD communications occurring in this case. □
Lemma 10
After initiating the transmission by the AP to an FDN, HD communications will occur if (i) the corresponding FDN has no data for the AP and (ii) other nodes that cannot hear the RTSD have no data for the AP.
Proof
To calculate the probability of occurring HD in this case, we need to calculate the following three probabilities. (a) The conditional probability that the AP has a packet to send to an FDN, which is \(\frac {n\lambda _{\text {APF}}}{\lambda _{\text {Total}}}\). (b) The probability that the corresponding FDN has no data to send to the AP within time T _{1}, which is \(\phantom {\dot {i}\!}\Big (e^{ \lambda _{\mathrm {F}}T_{1}}\Big)\). (c) The probability that other nodes that cannot hear the RTSD have no data for the AP within time T _{4}, which can be written as \(\Big (e^{ \{m\lambda _{\mathrm {H}}+ (n1)\lambda _{\mathrm {F}} \}{\gamma }T_{4}}\Big)\phantom {\dot {i}\!}\). By multiplying (a), (b), and (c), we can calculate the probability of HD communications occurring in this case. □
7 Result and performance analysis
Simulations were performed in MATLAB to analyze the performance of the proposed HFDMAC. The performance analysis for HFDMAC is presented in the following two subsections in terms of the probability analysis and throughput analysis.
7.1 Probability analysis
The probability analysis was performed in unsaturated conditions, where every node did not have data to send at all times. By contrast, in saturation conditions, all clients and the AP always have packets to transmit [24]. The saturation condition represents the maximum load in a stable condition, i.e., the queue for arriving packets is assumed to always be nonempty for each node in the network.
The simulation results in Fig. 9 show that the probability of HD communications decreased significantly as PAR increased at AP for each node, whereas P _{TNFD} increased significantly as PAR increased for each node. Moreover, P _{BFD} also increased. Thus, the total probability of FD communications (P _{TNFD} + P _{BFD}) increased significantly. Moreover, the figures present the effects of HTs on the probability of different communications. As shown in the figures, it is observed that the higher percentage of HTs in the network had higher probability of FD communications and lower probability of HD communications as compared between two subfigures in Fig. 9. However, even with a small percentage of HTs (10% of total nodes), the HFDMAC provided about 70% FD communications out of all possible communications in saturation conditions (Fig. 9 a).
Based on this probability analysis, it is observed that the probability of FD communications (P _{TNFD} and P _{BFD}) increased significantly and the probability of HD communications decreased substantially as the system moved toward the saturation condition from an unsaturated condition. FD communications could not always be performed under saturation conditions because the SDTC was not always satisfied when HDNs initiated the transmission. In addition, the figures show that the sum of all the probabilities (P _{TNFD}, P _{BFD}, and P _{HD}) always equals 1, thereby validating the derivation of the equations.
7.2 Throughput analysis
Simulation parameter
Packet payload (data)  2000 bytes 
RTS  20 bytes 
CTS  14 bytes 
RTSD  20.25 bytes 
CTSD  14.25 bytes 
ACK  14 bytes 
NDI  14.25 bytes 
Data rate  54 Mbps 
Control frame (RTS, CTS, etc.) rate  6 Mbps 
DIFS time  34 μs 
SIFS time  16 μs 
Slot time  9 μs 
Minimum backoff window size (C W _{min})  15 
PLCP preamble duration  16 μs 
PLCP header duration  4 μs 
Maximum time of selftimer  50 μs 
We assumed that the reception of any control frame and data is successful if the receiving node lies within the range of the transmitter. A typical topology for an APbased WLAN was considered for this simulation, as shown in Fig. 11. As mentioned earlier, satisfying the SDTCs is crucial for performing TNFD communications in HFDMAC. Moreover, satisfying SDTC depends on the topology, where some hidden nodes exist. A WLAN was considered in this simulation with 30% hidden nodes on an average. For example, as shown in Fig. 11, if node B is a PT, then node E and D cannot hear the signal transmitted from B, i.e., E and D are HTs with respect to node B. Similarly, node F is the HT with respect to node C. Therefore, if B initiates the transmissions, E or D can participate in TNFD communications because they satisfy the SDTC. Similarly, if C initiates the transmissions, only F can participate in the TNFD communications.
As shown the Fig. 12, there were two FDNs and HDNs initially, and each number was then increased by two, whereas only one AP was considered. In this simulation, we used 10 samples as the throughput with each different number of nodes and then calculated the average throughput, as shown in Fig. 12. The results show that the mean average throughput with HFDMAC was 55.17 Mbps, whereas the values were 28.12 and 49.69 Mbps for the traditional HD and existing FDMAC [17], respectively. Thus, the mean average throughput increased by 96.19 and 11.03% using our proposed MAC compared with the traditional HD and existing FDMAC, respectively.
In this simulation, we considered that about 30% of total nodes were hidden when a particular node was considered. Satisfying the SDTC depends on the number of hidden nodes in the network. The throughput with HFDMAC was lower than that using the existing FDMAC when the number of nodes was less than 10 because the SDTC cannot always be satisfied if the number of nodes is lower. However, this SDTC condition is not required by the FDMAC proposed by [17]. Hence, either BFD or HD communication occurred when using FDMAC. Therefore, the average throughput was higher using FDMAC than the proposed HFDMAC when the number of nodes was less than 10. In addition, the average throughput decreased with FDMAC [17] when the number of nodes increased. When the number of nodes increased, BFD communications did not increase as much compared with TNFD communications. Therefore, the average throughput decreased with FDMAC ([17]) because TNFD communications were not considered here. However, the probability of HD communications decreased greatly whereas that of TNFD increased significantly as the number of nodes increased, and thus, the average throughput increased in our proposed HFDMAC.
Some differences are observed between the simulation throughput and the throughput that is calculated analytically as in Fig. 12. The reason is that the percentage of hidden terminals are fixed in the mathematical derivations. However, there are some variations of this number in different network topology in the simulation. Moreover, the contention period for channel access may vary in simulations, and thus, the exact time of the transmission also changes. On the other hand, a fixed average transmission time is assumed in the mathematical analysis. Therefore, some variations are observed between the simulation throughput and the analytical throughput. The mean average throughput is achieved by the simulation and the mean analytical throughput are 55.17 and 54.29 Mbps, respectively, which are very close to each other.
The average HT ratio is considered as 30% for the simulation in Fig. 12. This consideration is clarified by the following discussion. The MAC design is proposed for an infrastructurebased WLAN by using the game theory [25]. The authors evaluated the performance in the presence of HT and consider the percentage of HT from 10 to 60% [25]. The performance of IEEE 802.11 DCF is analyzed in the presence of HT, where the HT ratio is varied from about 5 to 60% [26]. The effect of HT on the performance of MAC protocol based on IEEE 802.11 standard are analyzed in [27]. The authors considered the HT ratio from 10 to 30% in that paper. The average HT ratio in practical radio environment can vary depending on various parameters, such as network topology, line of sight, and transmitting power or range. Therefore, we chose the average HT ratio as 30% for this simulation in Fig. 12.
The MAC design for this kind of HetWLAN is very important, as the coexistence of HDNs and FDNs in the same WLAN will be inevitable in near future. Some FDMAC were proposed, where FDNs can switch between FD and HD mode [14, 15]. However, this is not sufficient because there are some differences in terms of MAC protocols between the WLAN that consists of only FDNs and the WLAN that contains both HDNs and FDNs. Although the FDN can switch between FD and HD mode, it depends on the packet availability and also on the response of the respective FDN (type 1). However, it is fixed that the HDN always performs HD transmission, which does not depend on packets arrival rate (type 2). The decision in type 1 is taken by the node and the AP acts accordingly. However, the decision in type 2 is always fixed, and the AP takes decision without getting any feedback from the HDN. Therefore, different MAC protocols are required for these two kinds of networks.
8 Conclusions
In this paper, we proposed an FDMAC protocol for the HetWLAN, which comprises FDNs, HDNs, and an FDAP. In our proposed HFDMAC, all possible FD transmissions were considered in HetWLANs. This protocol minimizes the interuser interference during FD transmissions by using SDTCs. The simulation results showed that HFDMAC increased the overall throughput significantly compared with that using traditional HD transmissions. In addition, the performance of HFDMAC protocol was better than that of another existing FDMAC. The probability analysis results suggested that the total probability of IBFD transmission increased significantly as the WLAN approached saturation conditions. This type of FDMAC may be very important for supporting highspeed FDWLANs in the near future.
Declarations
Acknowledgements
This research and development work was supported by the MIC/SCOPE # 155007006. This work was also supported by JSPS KAKENHI Grant Number JP16H01718.
Competing interests
The authors declare that they have no competing interests.
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References
 D Bharadia, E McMilin, S Katti, Full duplex radios. ACM SIGCOMM Comput. Commun. Rev.43(4), 375–386 (2013).View ArticleGoogle Scholar
 JI Choi, M Jain, K Srinivasan, P Levis, S Katti, in Proc. of the Sixteenth Annual International Conference on Mobile Computing and Networking. Achieving single channel, full duplex wireless communication (ACMChicago, 2010), pp. 1–12.View ArticleGoogle Scholar
 D Bharadia, S Katti, in Proc. of 11th USENIX Symposium on Networked Systems Design and Implementation (NSDI 14). Full duplex MIMO radios (Seattle, 2014), pp. 359–372.Google Scholar
 M Jain, JI Choi, T Kim, D Bharadia, S Seth, K Srinivasan, P Levis, S Katti, P Sinha, in Proc. of the 17th Annual International Conference on Mobile Computing and Networking (MobiCom). Practical, realtime, full duplex wireless (ACMLas Vegas, 2011), pp. 301–312.Google Scholar
 D Kim, H Lee, D Hong, A survey of inband fullduplex transmission: from the perspective of PHY and MAC layers. IEEE Commun. Surv. Tutorials. 17(4), 2017–2046 (2015).View ArticleGoogle Scholar
 KM Thilina, H Tabassum, E Hossain, DI Kim, Medium access control design for full duplex wireless systems: challenges and approaches. IEEE Commun. Mag.53(5), 112–120 (2015).View ArticleGoogle Scholar
 Literature on asymmetry of the working document, SE19(13)49 Annex 5, 2013 (2013). http://cept.org/documents/se19/10171/se19.
 E Everett, M Duarte, C Dick, A Sabharwal, in Proc. of the Forty Fifth Asilomar Conference on Signals, Systems and Computers (ASILOMAR). Empowering fullduplex wireless communication by exploiting directional diversity (IEEEPacific Grove, 2011), pp. 2002–2006.Google Scholar
 M Duarte, A Sabharwal, in Proc. of the Forty Fourth Asilomar Conference on Signals, Systems and Computers. Fullduplex wireless communications using offtheshelf radios: feasibility and first results (IEEEPacific Grove, 2010), pp. 1558–1562.Google Scholar
 A Tang, X Wang, Balanced RFcircuit based selfinterference cancellation for full duplex communications. Ad Hoc Netw.24:, 214–227 (2015).View ArticleGoogle Scholar
 M Sakai, H Lin, K Yamashita, in Proc. of IEEE Global Communications Conference (GLOBECOM). Adaptive cancellation of selfinterference in fullduplex wireless with transmitter IQ imbalance (IEEEAustin, 2014), pp. 3220–3224.Google Scholar
 Y Zhang, L Lazos, K Chen, B Hu, S Shivaramaiah, in Proc. of IEEE INFOCOM Conference on Computer Communications. FDMMAC: combating multichannel hidden and exposed terminals using a single transceiver (IEEEToronto, 2014), pp. 2742–2750.Google Scholar
 W Cheng, X Zhang, H Zhang, in Proc. of IEEE Global Communications Conference (GLOBECOM). RTS/FCTS mechanism based fullduplex MAC protocol for wireless networks (IEEEAtlanta, 2013), pp. 5017–5022.Google Scholar
 S Goyal, P Liu, O Gurbuz, E Erkip, S Panwar, in Proc. of Asilomar Conference on Signals, Systems and Computers. A distributed MAC protocol for full duplex radio (IEEEPacific Grove, 2013), pp. 788–792.Google Scholar
 A Sahai, G Patel, A Sabharwal, arXiv preprint arXiv:1107.0607 (2011).Google Scholar
 W Choi, H Lim, A Sabharwal, Powercontrolled medium access control protocol for fullduplex wifi networks. IEEE Trans. Wirel. Commun.14(7), 3601–3613 (2015).View ArticleGoogle Scholar
 M Duarte, A Sabharwal, V Aggarwal, R Jana, K Ramakrishnan, CW Rice, N Shankaranarayanan, Design and characterization of a fullduplex multiantenna system for wifi networks. IEEE Trans. Veh. Technol.63(3), 1160–1177 (2014).View ArticleGoogle Scholar
 A Tang, X Wang, Aduplex: medium access control for efficient coexistence between fullduplex and halfduplex communications. IEEE Trans. Wirel. Commun.14(10), 5871–5885 (2015).View ArticleGoogle Scholar
 JY Kim, O Mashayekhi, H Qu, M Kazandjieva, P Levis, Janus: A novel MAC protocol for full duplex radio. CSTR. 2(7), 23 (2013).Google Scholar
 T Riihonen, S Werner, R Wichman, E Zacarias, in Proc. of the 10th Workshop on Signal Processing Advances in Wireless Communications. On the feasibility of fullduplex relaying in the presence of loop interference (IEEEPerugia, 2009), pp. 275–279.Google Scholar
 W Cheng, X Zhang, H Zhang, in Proc. of IEEE INFOCOM Conference. Full/half duplex based resource allocations for statistical quality of service provisioning in wireless relay networks (IEEEShanghai, 2012), pp. 864–872.Google Scholar
 T Riihonen, S Werner, R Wichman, Hybrid fullduplex/halfduplex relaying with transmit power adaptation. IEEE Trans. Wirel. Commun.10(9), 3074–3085 (2011).View ArticleGoogle Scholar
 IEEE Standards Association, 802.112012IEEE standard for information technology—telecommunications and information exchange between systems local and metropolitan area networks—specific requirements part 11: wireless lan medium access control (MAC) and physical layer (PHY) specifications (2012). http://standards.ieee.org/about/get/802/802.11.html.
 G Bianchi, Performance analysis of the IEEE 802.11 distributed coordination function. IEEE J. Sel. Areas Commun.18(3), 535–547 (2000).View ArticleGoogle Scholar
 SM Najafabadi, CC Constantinou, in Proc. of IEEE 24th International Symposium on Personal Indoor and Mobile Radio Communications (PIMRC). A game theoretic model for wireless medium access control in the presence of hidden terminals (IEEELondon, 2013), pp. 1731–1736.Google Scholar
 H Wu, F Zhu, Q Zhang, Z Niu, in in Proc. of IEEE Global Telecommunications Conference. WSN021: analysis of IEEE 802.11 DCF with hidden terminals (IEEESan Francisco, 2006), pp. 1–5.Google Scholar
 S Khurana, A Kahol, AP Jayasumana, in Proc. in IEEE Conference on Local Computer Networks (LCN’98). Effect of hidden terminals on the performance of IEEE 802.11 MAC protocol (IEEELowell, 1998), pp. 12–20.Google Scholar