A Spatially Fair and Low Conflict Medium Access Control Protocol for Underwater Acoustic Networks

Abstract

The large propagation delay in underwater acoustic networks results in spatial and temporal uncertainty between communication links. This uncertainty, in turn, leads to problems with spatial unfairness and packet collision in media access control (MAC) solutions. To address these issues, this research paper proposes a spatially fair and low-conflict media access control (SFLC-MAC) protocol. Within the protocol, a contention window spatial fairness adjustment strategy is designed, including random and fair states. Nodes autonomously adjust their contention states based on the perceived network information. Nodes in the fair state increase their listening time to ensure that nodes in the random state can successfully access the channel, thereby overcoming the fairness issues in channel access. A method based on postponing data packet transmission is proposed to avoid collisions between data packets and neighbors’ control packets. By scrutinizing the spatio-temporal constraints pertinent to these conflicts, the exact duration of the delay required for this method is ascertained. Simulation results demonstrate that SFLC-MAC effectively improves network throughput, reduces end-to-end delay, decreases network energy consumption, and enhances channel access fairness among nodes.

1. Introduction

In recent years, Underwater Acoustic Networks (UANs) have been widely used in marine observation, pollution detection, marine ranching, and assisted navigation [1,2,3]. As an important part of UANs, the Medium Access Control (MAC) protocol is responsible for ensuring the efficient and fair delivery of data to the next hop. How to maximize the network throughput by optimizing rules under fair and low conflict rates is the key challenge of MAC protocol [4,5].

Compared with terrestrial wireless networks, there are large propagation delays, low transmission rates, and dynamic communication environments in UANs. Due to these characteristics, designing MAC protocols has become a difficult and challenging task. In the distributed topology scene of UANs, there is no central management node, and data can be exchanged between nodes [6]. The contention-based MAC protocol shows high applicability in the highly dynamic distributed topology, which can be divided into random access protocol and reservation protocol. Slot ALOHA is a typical random access protocol. It divides the network time into equal slots and allows nodes to send data only at the beginning of the slot [7]. This protocol can suppress the problem of high data collision rate of ALOHA protocol under long propagation delay. Compared with random access mode, reservation MAC protocol requires nodes to acquire channels by interacting request-to-send (RTS) and clear-to-send (CTS) packets before transmitting data [8]. Slotted floor acquisition multiple access (Slotted-FAMA) is a reservation MAC protocol based on RTS/CTS handshaking [9]. The protocol solves the problem of hidden terminals by using the slot reservation transmission mechanism and using the maximum propagation delay as the basis for slot allocation. However, its long slot will result in a large amount of idle time in the channel.

The large propagation delay leads to the problem of spatial-temporal uncertainty in UANs [10]. The spatial-temporal uncertainty problem can be defined as two-dimensional uncertainty. The packets sent simultaneously by different senders may arrive at the receiver sequentially due to different propagation delays, and then can be received without collision. The packet collisions may still occur at the receiver even if no packets are sent at the same time. From the above problems, it can be concluded that the collision problem in UANs is caused by the joint effect of the location and transmission time of the nodes. Therefore, it is necessary to consider the spatial-temporal uncertainty in dealing with data collision problems of the MAC protocol in UANs.

Due to spatial-temporal uncertainty, there is a spatial unfairness of channel access and collisions between control packets and DATA packets in reservation-based protocols. The spatial unfairness of channel access is caused by differences in propagation delays between communication links. Links with a shorter propagation delay require less time to complete the RTS/CTS exchange and, therefore, access channels preferentially compared to links with a longer propagation delay. To ensure collision-free reception of DATA packets, the receiver notifies its neighbors to remain silent by sending a CTS packet. However, the neighbor node may have sent a control packet before receiving the CTS packet from the receiver, resulting in a collision with the DATA packet at the receiver due to long propagation delays.

To address these issues, this paper proposes a spatially fair and low-conflict medium access control (SFLC-MAC) protocol. The paper’s multiple contributions include the following:

• A contention window spatial fairness adjustment strategy is presented to address the issue of spatial unfairness in channel access. The  mechanism divides the contention state into random and fair. In random state, nodes possess similar channel access priorities. Conversely, in fair state, nodes proactively lower their priority by increasing channel listening time, ensuring other nodes can access the channel. The state transition strategy is formulated to minimize network performance degradation caused by extended listening time while maintaining channel access fairness among nodes.
• To address the problem of collisions between control packets from neighbors and DATA packets, we propose a conflict avoidance approach that allows the sender to postpone the transmission of DATA packets. By examining the spatio-temporal constraints associated with these conflicts, we derive the precise delay time necessary for effective conflict resolution.
• A node state transition strategy is proposed, wherein nodes perform different operations based on their own state and the type of packets received. This strategy allows nodes to adapt their behavior according to the current network status, ensuring an efficient and stable operation of the network.

The remainder of the paper is structured as follows. Section 2 provides an overview of existing MAC protocols for UANs. Section 3 outlines the problem definition. Section 4 presents a detailed description of the SFLC-MAC protocol. Section 5 evaluates the performance of the SFLC-MAC protocol through simulation and compares it to other protocols. Finally, Section 6 concludes the paper.

2. Related Work

The MAC protocols in UANs can be divided into contention-based and scheduling-based protocols. The scheduling-based protocols allocate channel resources, such as time slots, frequency bands, and orthogonal codes, to all nodes by a centralized control center, thereby ensuring contention-free network transmission. According to the type of resource, they can be divided into time division multiple access (TDMA), frequency division multiple access (FDMA), and code division multiple access (CDMA) [11,12,13].

The spatial-temporal MAC protocol [10] utilizes the spatio-temporal unpredictability of UANs to construct a network conflict graph and then proposes a heuristic approach to address the issue of coloring this conflict graph. This approach increases channel reuse, which consequently enhances the throughput of the network. The continuous-time TDMA (CT-TDMA) protocol [14] constructs a local conflict state graph with the sender at the center and continuous time as the unit of measurement. It proposes a distributed construction algorithm that takes advantage of the difference in link delay between the same receiver and different senders to reduce the idle time between frames received at the destination. Based on spatiotemporal uncertainty, a deep-reinforcement learning-based medium access control (DL-MAC) protocol [15] uses deep Q-learning algorithms to propose synchronous and asynchronous optimal MAC policies to improve network performance. The FDMA enables users to access channels simultaneously by assigning different frequencies to each user. SeaWeb’98 and SeaWeb’99 were the first ocean observation networks to utilize FDMA [16]; however, they experienced issues such as low-frequency utilization and susceptibility to interference. The CDMA enables multiple users to share a single frequency channel simultaneously. Spread spectrum communication provides better robustness to frequency selective fading channels caused by multipath propagation [17]. In [18], it proposes a transmitter-based distributed code division protocol that optimizes power allocation and spreading code length, aiming to improve network throughput, reduce channel access delay, and lower energy consumption. The energy-efficient adaptive hiErarchical and robust architecture (EDETA) protocol is based on a clustering mechanism [19], which ensures that communication between clusters is free of conflicts by using a CDMA mechanism and aggregating data within clusters using TDMA.

The scheduling-based protocols are generally applicable to static and fixed topological structures and often require a central node to schedule compliance with all the network nodes. They are mostly used in star or clustered networks. Compared to contention-based protocols, scheduling-based protocols have higher requirements for auxiliary mechanisms such as clock synchronization and positioning algorithms. These auxiliary mechanisms have higher implementation costs in randomly distributed, highly dynamic scenarios.

There are many works on contention-based MAC protocols, which can be divided into random access protocols and reservation protocols.

Table 1. Summary of the contention-based MAC protocols.

Procotol	Classification	Network Topology	Spatial Unfairness of Channel Access	Collisions between Control Packets and DATA Packets
PDT-ALOHA [20]	RA	DT	N	–
UW-SEEDEX [21]	RA	DT	Y	–
SF-MAC [22]	H	ST	Y	–
MACA-MN [23]	H	DT	N	N
MACA-DT [24]	H	DT	N	N
SFAMA-DT [25]	H	DT	N	Y
MultiACK-SFAMA [26]	H	DT	N	Y
QL-UACW [27]	H	DT	Y	N
OPMAC [28]	H	DT	N	Y

RA: Random Access, H: Handshaking, ST: Star topology, DT: Distributed topology, Y: Deal with the problem, N: Ignore the problem, –: The problem does not exist.

summarizes the performance of the main contention-based protocols in addressing spatial unfairness in channel access and packet collision issues.

The random access protocol is mainly based on the ALOAH protocol [29]. In ALOHA, the sender does not need to listen to the channel in advance, but instead sends their data packets directly. However, the terrestrial ALOHA protocol cannot be directly applied to the underwater environment due to the large propagation delay. In [20], it found that the synchronization advantage of the Slot-ALOHA protocol was weakened due to the problem of spatial-temporal uncertainty. Its propagation delay tolerant ALOHA (PDT-ALOHA) algorithm reduced the collision rate of the Slot-ALOHA protocol by increasing the protection interval in each time slot. In [30], it deduced the theoretical performance of the PDT-ALOHA protocol, proved that the network throughput would not decrease with an increase in the protection interval, and obtained the theoretical upper limit of the network throughput under different network load conditions. In [31], it revealed the time-coupling relationship of the underwater Slot-ALOHA protocol in conflict-free scenarios and proposed a low-complexity heuristic scheduling algorithm, which improved the network performance of Slot-ALOHA in a star topology. A seedex-based protocol for UANs (UW-SEEDEX) [21] is proposed. The protocol begins with an initial phase in which nodes within two hops exchange the seeds of their respective pseudo-random methods. Each node then randomly sets the state to receive or transmit within each time slot according to its respective seed. Each node estimates the state of each node within two-hop based on the random seeds of its neighbors and, thus, decides whether to transmit data or not. Compared to ALOHA-based protocols, UW-SEEDEX can achieve higher network performance because the nodes in UW-SEEDEX can predict the two-hop node states.

The reservation-based protocols are used to reserve channels through the exchange of RTS and CTS packets [32]. These protocols can be divided into two categories: receiver-centric multi-access control protocols and sender-driven reservation-based protocols. In multi-access protocols, since only one receiver is considered, the handshake mechanism can be designed based on the spatial-temporal constraints between the links. The main challenge in multi-access protocols is addressing fairness issues caused by spatio-temporal uncertainty. The spatially fair MAC (SF-MAC) protocol [22] makes it possible to receive RTS packets from multiple senders by deferring CTS packets. In this protocol, the receiver calculates the potential transmission time of each competitor and selects the sender for this transmission while taking fairness into account. A conflict avoidance fairness protocol is proposed in [33] to address the issue of RTS packet collisions at the receiver. This protocol divides the receiver’s neighbors into two groups based on their average propagation delay and ensures that packets sent by two senders within each group will never collide at the receiver by considering the earliest sending time.

In wireless networks, sender-driven reservation-based protocols are primarily based on either the multiple access with collision avoidance (MACA) or floor acquisition multiple access (FAMA) protocol [34]. Since the next hop in a packet in the cache queue to be sent may be different, a MACA-based protocol with packet train to multiple neighbors (MACA-MN) [23] alleviates network congestion and reduces the collision rate by sending a single RTS packet to multiple neighboring nodes for simultaneous handshaking. The MACA-based protocol with delay tolerant (MACA-DT) [24] improves channel utilization and reduces end-to-end delay through the use of adaptive silent time and simultaneous handshake technique. The Slotted-FAMA based protocol with data train (SFAMA-DT) [25] is proposed. It simultaneously established communication links by sequencing RTS/CTS packets, thereby increasing the channel utilization of Slotted-FAMA. In [26], it proposed a multi-ACK mode for Slotted-FAMA to address the issue of retransmission due to lost acknowledgment packets by increasing the likelihood of successful ACK reception. In [27], an adaptive contention window adjustment backoff algorithm based on Q-learning (QL-UACW) is proposed to address issues of unfairness access to the dynamic channel. This algorithm utilizes the concept of reinforcement learning to adjust the contention window. Simulations have shown that the protocol can achieve high network performance under different traffic loads.

The slotted FAMA-based protocols can be effective in avoiding collisions between control packets from neighbors and DATA packets. However, due to the limitation of fixed slots, these protocols are only suitable for low-load network scenarios. The protocols described [28,35] attempt to avoid collisions by deferring CTS packets or DATA packets. Both the fixed slot and deferral approaches increase the time cost of each handshake round, thus, reducing network efficiency.

The issue of spatial unfairness in channel access is not often taken into account in distributed topology scenarios of UANs. However, in certain application scenarios, this fairness issue must be addressed. For instance, in a routing network where energy balance is the indicator, relay nodes closer to the Sink tend to select the next hop closer to themselves, while nodes further away from the Sink tend to select the next hop closer to them. This can lead to the closer communication link blocking the more distant communication link persistently.

3. Problem Definition

In the reservation-based MAC protocol, the spatial-temporal uncertainty leads to channel access unfairness and packet collision. This section analyses the spatial-temporal constraints of these problems.

3.1. Spatial Unfairness in Channel Access

The issue of spatial unfairness in channel access mainly arises from the difference in propagation delay between communication links. Examining the interplay between two links can shed light on this problem. As illustrated in Figure 1, let us assume that nodes A and C need to transmit data to nodes B and D, respectively. Four interfering links directly affect the links AB and CD. Analyzing these interfering links enables us to investigate the spatial unfairness problem between communication links. The four interfering links are representative examples of typical scenarios involving exposed and hidden terminals in transmission and reception processes.

Assuming node C transmits an RTS packet before node A, the First-In-First-Out (FIFO) principle dictates that node C should be granted priority access to the communication channel. However, due to the long propagation delay inherent in underwater environments, neighboring nodes may experience asynchronous reception of control packets, potentially causing node A to occupy the channel when node C should have been given access priority. As a result, the intended FIFO mechanism is disrupted, leading to spatial unfairness, as nodes with longer propagation delays may be at a disadvantage when attempting to establish communication links.

Figure 2 presents the timing diagrams for various packet interactions that lead to spatial unfairness across the four scenarios depicted in Figure 1. In Figure 2a, node C receives an RTS packet from node A before the expected CTS packet due to the closer proximity to node A and the greater distance from node D. Similarly, in Figure 2b, node D receives an RTS packet from node A before receiving the RTS from node C because of the same distance factors. The handshake rules state that a node will remain silent upon receiving an RTS packet intended for another node. As a result, the handshake process for Link CD is disrupted by node A’s RTS packet in both scenarios a and b. In Figure 2c, the handshake process between nodes A and B completes quickly due to their close proximity. However, node C’s greater distance from node D and closer proximity to node B cause it to receive node B’s CTS packet before node D’s CTS packet, interrupting the handshake process for Link CD. In contrast, Figure 2d shows that if node C sends the RTS packet before node A does, the handshake process for Link CD remains uninterrupted. Since node D is the hidden receive terminal of node A, and the distance from node A to node D is greater than the maximum effective propagation distance, the RTS packet sent by node C reaches node D before the CTS packet sent by node B.

In summary, spatial unfairness in Links AB and CD emerges due to location factors in scenarios a, b, and c. Therefore, it is necessary to investigate these scenarios to analyze the problem’s constraints.

If node A and C send RTS packet at the time $T_2$ and $T_1$, respectively, the temporal-spatial constraints for the unfairness problem in Figure 2a–c are as follows:

$$\begin{array}{cc}\hfill \left(\mathrm{a}\right)& :\left\{\begin{array}{c}{T}_3<T_4\\ T_5<T_6\end{array}\right.\hfill \\ \hfill \left(\mathrm{b}\right)& :T_3<T_4\hfill \\ \hfill \left(\mathrm{c}\right)& :\left\{\begin{array}{c}{T}_3<T_4\\ T_5<T_6\end{array}\right.\hfill \end{array}$$

(1)

where $T_5<T_6$ in scenarios a and c ensure that link AB can successfully complete the handshake, and $T_3<T_4$ in all scenarios is the condition required for link CD to be interrupted.

Equation (1) is converted into the constraint relationship between RTS packet sending time and propagation delay, as shown in the following equation:

$$\begin{array}{cc}\hfill \left(\mathrm{a}\right)& :\left\{\begin{array}{c}{T}_2-T_1<2D_{CD}+T_{RTS}+T_{CTS}-D_{AC}\\ T_2-T_1<D_{AC}-2D_{AB}-T_{RTS}-T_{CTS}\end{array}\right.\hfill \\ \hfill \left(\mathrm{b}\right)& :T_2-T_1<D_{CD}+T_{RTS}-D_{AD}\hfill \\ \hfill \left(\mathrm{c}\right)& :\left\{\begin{array}{c}{T}_2-T_1<2D_{CD}+T_{CTS}-D_{AB}-D_{BC}\\ T_2-T_1<D_{BC}-D_{AB}-T_{RTS}\end{array}\right.\hfill \end{array}$$

(2)

where $T_{RTS}$ and $T_{CTS}$ are the RTS and CTS packet duration, respectively. $D_{ij}$ denotes the propagation delay between node i and node j.

In conclusion, it can be seen that if the relationship between the transmission time and the spatial location of any two links satisfies Equation (2), there is a channel access spatial unfairness issue in the network.

3.2. The Collision between Control Packet from Neighbors and DATA Packet in Hidden Terminal Scene

The RTS/CTS handshake mechanism can effectively reduce the impact of hidden terminal problems, but Figure 3 shows that, due to the large propagation delay, successful handshakes do not guarantee collision-free reception of data packets.

In Figure 3, the temporal-spatial constraints for the collision between the control packet and the data packet need to be satisfied:

$$T_5\le T_6\le T_8\vee T_5\le T_7\le T_8$$

(3)

Since the node needs to enter the quiet state when it receives a control packet that is intended for another node (xRTS or xCTS), the time $T_3$ and $T_2$ when Node B or C sends the control packet needs to satisfy:

$$T_2\le T_4\wedge T_3\le T_6$$

(4)

As shown in Equation (5), for each time point, it can be represented by the time of sending the RTS packet, the link propagation delay, and the duration of various packets.

$$\left\{\begin{array}{c}{T}_3=T_1+D_{AB}+T_{RTS}\hfill \\ T_4=T_1+D_{AB}+T_{RTS}+D_{BC}\hfill \\ T_5=T_1+D_{AB}+T_{RTS}+D_{AB}+T_{CTS}+D_{AB}\hfill \\ T_6=T_2+D_{BC}\hfill \\ T_7=T_2+D_{BC}+T_{RTS}\hfill \\ T_8=T_1+D_{AB}+T_{RTS}+D_{AB}+T_{CTS}+D_{AB}+T_{DATA}\hfill \end{array}\right.$$

(5)

where $T_{DATA}$ is the DATA packet duration.

Substituting Equation (5) into Equation (3), we can get.

$$\begin{array}{c}3T_{AB}-T_{BC}+T_{CTS}\le T_2-T_1\le 3T_{AB}-T_{BC}+T_{CTS}+T_{DATA}\\ \vee \\ 3T_{AB}-T_{BC}+T_{RTS}+T_{CTS}\le T_2-T_1\le 3T_{AB}-T_{BC}+T_{RTS}+T_{CTS}+T_{DATA}\end{array}$$

(6)

Simplification Equation (6) can be obtained.

$$3T_{AB}-T_{BC}+T_{CTS}\le T_2-T_1\le 3T_{AB}-T_{BC}+T_{RTS}+T_{CTS}+T_{DATA}$$

(7)

Substituting Equation (5) into Equation (4), we can get.

$$T_{AB}+T_{RTS}-T_{BC}\le T_2-T_1\le T_{AB}+T_{RTS}+T_{BC}$$

(8)

If the times $T_1$ and $T_2$ at which nodes A and C send their respective control packet satisfy Equations (7) and (8), then the control packet from node C and the data packet from node A will collide at node B.

4. SFLC-MAC

In this section, we first present an overview of the SFLC-MAC protocol. Then, the spatial fairness adjustment strategy of the contention window and packet collision avoidance mechanism are described, respectively. Finally, the state transition strategy of the protocol is discussed in detail.

4.1. Overview of SFLC-MAC

In the SFLC-MAC protocol (As shown in Figure 4), when node S needs to transmit data to node R, it uses the competition window spatial fairness algorithm to calculate its listening period. If no packet is overheard from other nodes during this period, node S sends an RTS packet. Node R calculates the waiting time for the DATA packet and records this time in the CTS packet after receiving the RTS packet. Node S then sends the DATA packet according to the waiting time. If node R does not receive the DATA packet, it will immediately send a negative acknowledgment (NACK) packet to node S, requesting that the DATA packet be retransmitted. Upon receiving the NACK packet, node S will immediately retransmit the corresponding DATA packet. Node R will then send an acknowledgment (ACK) packet immediately after receiving the DATA packet. Upon receiving the ACK packet, Node S will check if the cache queue with the destination address node R is empty. If it is not, node S will continue to send the next DATA packet.

4.2. Contention Window Spatial Fairness Adjustment Strategy

In the reservation-based MAC protocol, to avoid multiple nodes accessing the channel at the same time, nodes need to randomly select their listening periods before sending an RTS packet. During the listening period, the node detects the status of the channel. If it overhears that the channel is busy, the node will stop the competition and remain silent. The listening period $T_{CTD}$ can be expressed as

$$T_{CTD}=Random\left[0,1\right]\times \omega$$

(9)

where $Random\left[0,1\right]$ means taking a random number between 0 to 1, $\omega$ is the contention window value.

As the density of nodes and the load on the network increase, the likelihood of congestion increases. Previous research has typically addressed this issue by decreasing the packet send rate. That is to use a large contention window to reduce the sending rate of each node. The node’s current level of congestion is measured by the length ($L_{sq}$) of the queue of data packets in the buffer at nodes. The $\omega$ of the node can be expressed as

$$\omega =min(⌈\frac{L_{sq}}{L_{th}}⌉,C{W}_{max})\left(\tau +T_{RTS}\right)$$

(10)

where $C{W}_{max}$ is the maximum contention window counter; $\tau$ is the maximum propagation delay; $L_{th}$ is the range of congestion levels per level. For the Equation (10), the larger the $L_{sq}$, the larger the $\omega$.

In Figure 1, node A can increase its listening time after completing a data transmission to give node C a chance to access the channel. However, due to spatial unfairness, Node A may still shake hands successfully even if its listening time is greater than that of node C. Therefore, the listening time of node A has to take into account the spatial relationship with node C.

As demonstrated in Figure 1, the spatial unfairness problem is primarily present in scenarios a, b, and c. Figure 5a–c illustrate that for node C to successfully handshake, the following conditions need to be met.

• In scenario a, the RTS packet from node A cannot reach node C before node C receives the CTS packet from node D.
• In scenario b, the RTS packet from node A cannot reach node D before node D receives the RTS packet from node C.
• In scenario c, node B receives an RTS packet from node C before it receives an RTS packet from node A.

Combining the above, if $T_3\le T_4$ in Figure 5, node C can successfully complete the control packet exchange with node D.

The $T_3\le T_4$ is converted into the relationship between $T_1$, $T_2$, propagation delay and packet duration as follows.

$$\begin{array}{cc}\hfill \left(\mathrm{a}\right)& :T_1+2D_{CD}+T_{RTS}+T_{CTS}\le T_2+D_{AC}\hfill \\ \hfill \left(\mathrm{b}\right)& :T_1+D_{CD}+T_{RTS}\le T_2+D_{AD}\hfill \\ \hfill \left(\mathrm{c}\right)& :T_1+D_{BC}\le T_2+D_{AB}\hfill \end{array}$$

(11)

If nodes A and C are ready to access the channel at time 0, then the values of $T_1$ and $T_2$ are equivalent to the listening times of nodes A and C. The maximum value of $T_1$ is w, the value of $T_2$ is shown below.

$$\begin{array}{cc}\hfill \left(\mathrm{a}\right)& :T_2=w+2D_{CD}-D_{AC}+T_{RTS}+T_{CTS}\hfill \\ \hfill \left(\mathrm{b}\right)& :T_2=w+D_{CD}+T_{RTS}-D_{AD}\hfill \\ \hfill \left(\mathrm{c}\right)& :T_2=w+D_{BC}-D_{AB}\hfill \end{array}$$

(12)

The $T_2$ value in scenario b is less than that in scenario a, so node A chooses the maximum value from scenarios a and c as the listening time to ensure that node C can successfully access the channel in all three scenarios.

Assuming that the sender is i and the destination node is j, according to Equation (12), to ensure that the neighbors can successfully access the channel, node i uses the following equation to calculate its listening time.

$$T_{CTD}^{ij}=\omega +T_{SF}^{ij}$$

(13)

where $T_{SF}^{ij}$ is the spatial fairness waiting time.

The above discussion is based on a two-link scenario, but each node may have more than one neighbor. In Equation (12), the acquisition of the $D_{CD}$ and $D_{BC}$ require node A to maintain the location information of all nodes within its 2-hop range. However, the dynamic nature of the underwater environment makes it costly for a node to obtain the location of nodes within its 2-hop range. We use the maximum propagation delay from node C or D to its neighbors as the value of $D_{CD}$. The $D_{BC}$ is acquired using the same method. The value of $T_{SF}^{ij}$ is shown below.

$$T_{SF}^{ij}=max(T_{SF}^{\left(a\right)},T_{SF}^{\left(c\right)}),\left\{\begin{array}{c}{T}_{SF}^{\left(a\right)}=max(2D_k^{max}-D_{ik}+T_{RTS}+T_{CTS})\hfill \\ T_{SF}^{\left(c\right)}=D_j^{max}-D_{ij}\hfill \end{array}\right.$$

(14)

where $max\left(\right)$ means take the maximum value among the values in the brackets. $T_{SF}^{\left(a\right)}$ and $T_{SF}^{\left(c\right)}$ denote the spatially fair waiting time under scenario a and c, respectively. k is the neighbor node of node i. $D_k^{max}$ and $D_j^{max}$ represent the maximum propagation delays from nodes k and j to their neighbors, respectively.

For node C to successfully access the channel, node A and C must make decisions at the same time. If node C sends the RTS packet later than $T_1$, the method may be invalid. Figure 1a,c show that if the scenario is exposed or hidden transmit terminal, node C can obtain the specific time for link AB to complete data transmission through xRTS or xCTS packet, and then can start the channel competition mechanism with A at the same time in the next transmission. Figure 1b shows that when node D receives xRTS, it will enter the quiet state. At this time, node C will not be able to get the CTS packet from node D after sending the RTS packet, so node C will implement a random backoff mechanism (for example, binary exponential backoff mechanism [36]). This prevents nodes A and C from starting the channel contention mechanism synchronously.

If link $ij$ successfully handshake, this indicates that the node in i’s two-hop range has not accessed the channel. To increase the likelihood of a non-synchronous decision node accessing the channel, node i must further increase its listening time in the next transmission. Equation (15) demonstrates that node i’s listening period is increased exponentially.

$$T_{CTD}^{ij}=2^{N_{TxOk}^{ij}}\omega +T_{SF}^{ij}$$

(15)

where $N_{TxOk}^{ij}$ represents the number of successful handshakes between node i and j.

This paper adopts the same binary exponential backoff mechanism as in [36]. To ensure the access channel of the node for asynchronous decision, the maximum value of $T_{CTD}$ should not be less than the maximum backoff time. Assuming that the maximum backoff counter is $B_{max}$, the maximum backoff time is $\left(\tau +T_{rts}\right)B_{max}$. That is, the maximum value $N_{MAX-TxOk}^{ij}$ of $N_{TxOk}^{ij}$ should meet the following.

$$2^{N_{MAX-TxOk}^{ij}}\omega \ge \left(\tau +T_{RTS}\right)B_{max}$$

(16)

Based on the analysis presented, this protocol sets the node contention state to G, which is divided into a random period (G = RD) and a fair period (G = FA). The listening time $T_{CTD}^{ij}$ for each contention state G is determined by the equation presented below.

$$T_{CTD}^{ij}=\left\{\begin{array}{cc}Random\left[0,1\right]\times \omega ,\hfill & \hfill G_{ij}=RD\\ min\left\{2^{N_{TxOk}^{ij}}\omega ,B_{max}(\tau +T_{RTS})\right\}+T_{SF}^{ij},\hfill & \hfill G_{ij}=FA\end{array}\right.$$

(17)

where, during the random period, the listening time is selected randomly based on the size of the contention window. During the fair period, a node increases its listening time actively in accordance with the number of successful handshakes. Compared to the RD state, nodes in the FA state extend their listening time to the channel. In other words, while nodes maintain a consistent channel access priority in the RD state, they proactively reduce their channel access priority in the FA state by increasing their listening time.

The calculation method for a node’s listening time is illustrated in Algorithm 1. First, nodes compute the basic contention window $\omega$ based on their current buffer queue length. If the present state is FA, nodes iterate through all neighbors to acquire the maximum $T_{SF}^{\left(a\right)}$ value and subsequently calculate the $T_{SF}^{\left(c\right)}$ value according to the destination node. The larger value between $T_{SF}^{\left(a\right)}$ and $T_{SF}^{\left(c\right)}$ is chosen as $T_{SF}$, and the final $T_{CTD}$ value is determined using Equation (17). Conversely, if the current state is RD, a random value within the basic contention window range is selected as the listening time.   

Algorithm 1: Algorithm for the calculation of listening time.

Input:  the sender i, the receiver j, the contention state $G_{ij}$, the number of successful handshakes $N_{TxOk}^{ij}$, the set of node i’s neighbors $F_{nei}$, and  the length of the data queue $L_{sq}$.

Output: the listening time $T_{CTD}^{ij}$

    The above method ensures the fairness of other nodes accessing the channel by increasing the listening time, which may reduce the end-to-end delay performance of the network. To ensure fairness and optimize end-to-end delay performance, the transition between states should be carefully evaluated.

To achieve high network performance, nodes must monitor the current network status and adjust the G accordingly. In a distributed topology, a node can gather information about itself within a two-hop range. A node can assess the success of data transmission by checking if it receives an acknowledgment packet from the destination node. To determine if there is an active communication link within two hops, the node should consider the following:

• If it does not receive a CTS packet after sending an RTS, this may indicate that the destination node is in a quiet state, possibly due to an active communication link within one hop of the destination node.
• If it receives an xRTS or xCTS during the idle state, listening time, or while waiting for the CTS packet, this can also indicate the presence of an active communication link within two hops.

The node adjusts the state G according to the perceived information. The state transition rules are as follows.

• In RD state, it will be transferred according to the following conditions:
  • When a data packet is successfully transmitted, it sets $N_{TxOk}^{ij}=N_{TxOk}^{ij}+1$. If  $N_{TxOk}^{ij}==N_{th}^{RD}$, the node sets $G_{ij}=FA$, $N_{TxOk}^{ij}=0$. Where, $N_{th}^{RD}$ is a certain number. This is because the contention window of FA is larger, resulting in a longer listening time and reducing the channel utilization rate. To prevent FA from occupying a large portion of the entire network cycle, this protocol specifies that $G_{ij}$ cannot switch to RD until $N_{th}^{RD}$ successful transmissions have been completed.
  • When the node does not receive the CTS packet after sending an RTS packet, it will increase its backoff counter, $B_{cnt}^i$. If CTS is not received multiple times, the backoff counter $B_{cnt}^i$ will increase exponentially. If $B_{cnt}^i$ reaches the maximum backoff counter, it indicates that the node has been in the backoff state for a longer period. At this time, the protocol compensates for the node by reducing the $N_{TxOk}^{ij}$ value to ensure that the node has more opportunities to be in the RD state in the future, thus, increasing the number of times the node accesses the channel. That is to say, if $N_{TxOk}^{ij}>-N_{th}^{RD}$ and $B_{cnt}^i==B_{max}$, it then sets $N_{TxOk}^{ij}=N_{TxOk}^{ij}-1$.
• In FA state, it will be transferred according to the following conditions:
  • If the transmission of the DATA packet is successful, it then sets $N_{TxOk}^{ij}=N_{TxOk}^{ij}+1$. If $N_{TxOk}^{ij}==N_{MAX-TxOk}^{ij}$, this means that there is a high probability that no other node needs to access the channel within the node’s 2-hop range. So, there is no need to keep the fair state and set $G_{ij}=RD$, $N_{TxOk}^{ij}=0$.
  • If there is a communication link within 2-hops, it sets $N_{TxFail}^{ij}=N_{TxFail}^{ij}+1$ and $N_{TxOk}^{ij}=0$. However, as there may be more than one node waiting to access the channel within the 2-hop range, this node must still remain in its current state. Assuming that the maximum number of waits specified by the protocol is $N_{th}^{FA}$, if $N_{TxFail}^{ij}==N_{th}^{FA}$, then the node enters the random period and sets $G_{ij}=RD$, $N_{TxOk}^{ij}=0$, $N_{TxFail}^{ij}=0$.

The process of updating the contention window state is shown in Algorithm 2. In Algorithm 2, assuming that the sender is i and the destination is j, node i maintains the G, $N_{TxOk}^{ij}$, and $N_{TxFail}^{ij}$, where $N_{TxFail}^{ij}$ represents the number of times node i has successfully relinquished the channel.   

Algorithm 2: Contention window state update algorithm.

Input:  the sender i, the receiver j, the destination node of the last time k, the contention state $G_{ij}$, the number of successful handshakes $N_{TxOk}^{ij}$, the number of times node i has successfully relinquished the channel $N_{TxFail}^{ij}$, and the backoff counter, $B_{cnt}^i$.

Output: the contention state $G_{ij}$

When the destination node changes, the communication distance will also change. Since the problem of spatial unfairness is determined by the distance between nodes, if the communication distance changes slightly, the new link will still have a continuous impact on the surrounding nodes. Therefore, if the change in the communication distance is less than the threshold ${\Delta }_{th}$, the new link will still continue the calculation process of the listening period of the previous link. Assume that the destination nodes of the last time and this time are k and j, respectively. If $\left|d_{ij}-d_{ik}\right|\le {\Delta }_{th}$, then $G_{ij}=G_{ik}$, $N_{TxOk}^{ij}=N_{TxOk}^{ik}$ and $N_{TxFail}^{ij}=N_{TxFail}^{ik}$. If $\left|d_{ik}-d_{ij}\right|>{\Delta }_{th}$, then $G_{ij}=RD$, $N_{TxOk}^{ij}=0$ and $N_{TxFail}^{ij}=0$. Where, $d_{ab}$ represents the euclidean distance between nodes a and b.

4.3. Avoid Collisions between Control Packets from Neighbors and DATA Packets

In Figure 6, node A delays sending the DATA packet for some time after receiving the CTS packet to ensure that the DATA packet does not collide with the control packet sent by node C at node B. $T_3$ and $T_4$ are the moments when the control packet of node C and the data packet of node A arrive at node B, respectively. To avoid collisions, the following conditions must be satisfied.

$$T_3\le T_4$$

(18)

Equation (18) is converted into the relationship between $T_1$, $T_2$, the waitting time $T_W^{ABC}$, propagation delay, and packet transmission time as follows.

$$T_2+D_{BC}+T_{RTS}\le T_1+3D_{AB}+T_{RTS}+T_{CTS}+T_W^{ABC}$$

(19)

The range of $T_W^{ABC}$ can be obtained.

$$T_W^{ABC}\ge T_2-T_1+D_{BC}-3D_{AB}-T_{CTS}$$

(20)

According to Equations (7) and (8), the sets $F_1^{ABC}$ and $F_2^{ABC}$ can be obtained. The time difference between $T_2$ and $T_1$ of the collision case is the intersection of sets $F_1^{ABC}$ and $F_2^{ABC}$.

$$\left\{\begin{array}{c}{F}_1^{ABC}=\left[3T_{AB}-T_{BC}+T_{CTS},3T_{AB}-T_{BC}+T_{RTS}+T_{CTS}+T_{DATA}\right]\hfill \\ F_2^{ABC}=\left[T_{AB}+T_{RTS}-T_{BC},T_{AB}+T_{RTS}+T_{BC}\right]\hfill \end{array}\right.$$

(21)

Let $T_{MAX}^{ABC}$ be the maximum value of $F_1^{ABC}\cap F_2^{ABC}$, and if $T_W^{ABC}\ge T_{MAX}^{ABC}+D_{BC}-3D_{AB}-T_{CTS}$, the collision probability between control packets from neighbors and DATA packets is 0. The value of $T_W^{ABC}$ is as follows.

$$T_W^{ABC}=T_{MAX}^{ABC}+D_{BC}-3D_{AB}-T_{CTS}+\delta$$

(22)

where $\delta$ is a protection interval designed to prevent short-term distance errors caused by node drift. The likelihood of a collision increases if the intersection of sets $F_1$ and $F_2$ is larger. Therefore, the receiver needs to choose the hidden terminal of the sender with the largest intersection value to calculate the waiting time.

As shown in Figure 6, the collision problem between control packets from neighbors and data packets can be effectively prevented. However, collisions between data packets may still occur due to the waiting time. To address this issue, we incorporate the stop-and-wait automatic repeat request (ARQ) scheme from the [37] into the protocol.

Assuming that the sender is node i and the receiver is node j, then node j uses the following process and Algorithm 3 to calculate the waiting time, $T_W^{ij}$.

• The receiver can obtain the set $F_{Hidden}$ of the sender’s hidden terminals among the receiver’s neighbors by using the location information.
• After receiving the RTS packet from the sender i, the receiver j calculates the waiting time of the DATA packet by traversing the location information of the set $F_{Hidden}$. Node j selects the node k with the largest $P_W^{ijk}$ to calculate its waiting time $T_W^{ij}$. Node j informs node i of the waiting time through the CTS packet.
• If node j does not receive the DATA packet, it will immediately send a negative NACK packet to node i. Upon receiving the NACK packet, node i will immediately retransmit the corresponding DATA packet.
• Node j will then send an ACK packet immediately after receiving the DATA packet. Upon receiving the ACK packet, Node i will check if the cache queue with the destination address node j is empty. If it is not, node i will continue to send the next DATA packet.

Algorithm 3: Waiting time selection algorithm.

Input:  the sender i, the receiver j and the sender’s hidden terminals among the receiver’s neighbors $F_{Hidden}$.

Output: the waiting time $T_w^{ij}$

4.4. Packet Structure

As shown in Figure 7, the packet structures for RTS, CTS, DATA, ACK, and NACK are designed to enable nodes to efficiently acquire information and accomplish data transmission tasks. In the design of each packet structure, apart from the fundamental fields such as packet type, source address, and destination address, we have incorporated additional fields to support the protocol algorithm effectively. The node maintains the location information of its neighbors in the neighbor table by receiving the spatial position coordinates in the RTS or CTS packet. Through the neighbor table, the node can easily obtain the hidden terminal set of its sender in Algorithm 3. Nodes typically obtain their position coordinates in the network periodically using a positioning algorithm. However, due to the fact that underwater nodes drift with the current, there can be errors in the propagation delay of nodes to neighbors obtained by coordinates. The timestamp in each packet records when the packet was sent, and the receiver can obtain the propagation delay of the sender through the timestamp. The link delay in CTS, DATA, and ACK/NACK is set to record the propagation delay of the communication link, and neighboring nodes can then set the quiet time based on this information. The maximum propagation delay to neighbors is set in RTS and CTS, so the sender can use this information to get a spatially fair waiting time. In the DATA, ACK, and NACK packet structures, the “Has Next” field indicates whether there is another DATA packet to be sent or received. Neighbors can get the end time of the communication link based on this field. The “Data ID” and “Data” fields represent the identification and specific content of the DATA packet, respectively.

4.5. State Transition Policy

The state transition strategies are typically an essential part of contention-based MAC protocols. These strategies define the rules for nodes to transition between different states, such as idle, backoff, and transmission, based on the perceived network conditions and the protocol’s requirements. The state transition strategy consists of two components: state transition rules and state hold time. The State hold time determines the duration that a node remains in a specific state. To effectively determine the state holding times for each state, it is crucial to analyze the timing of various packet interactions within the proposed MAC protocol.

Suppose the source node is i, the destination node is j, and node k is a neighbor of node i and node j. The timing diagram of SFLC-MAC is shown in Figure 8. When node j receives an RTS packet from node i, it waits for a duration of $2D_{ij}+T_{\mathrm{DATA}}+T_{\mathrm{CTS}}+T_w$ to receive the DATA packet. After receiving the DATA packet, if there is a subsequent packet, node j waits for a duration of $2D_{ij}+T_{\mathrm{DATA}}+T_{\mathrm{ACK}}$ to receive the next packet. After sending the DATA packet, node i waits for a duration of $2D_{ij}+T_{\mathrm{DATA}}+T_{\mathrm{ACK}}$ to receive the ACK packet from node j. If there is another packet to be sent, the same waiting time applies. Neighboring node k must remain silent when receiving packets from nodes i or j. Upon receiving an xRTS packet from node i, node k cannot determine the location of node j, so the silence duration for node k should be $2\tau +T_{CTS}+T_{DATA}$. If node k receives an xCTS packet from node j, the silence duration can be easily determined as $2T_{link}^{ij}+T_w^{ij}+T_{DATA}+T_{ACK}$ from the timing diagram. When receiving an xDATA packet from node i, node k must determine whether there will be another DATA packet received based on the data packet information; if so, the actual silence duration is $2T_{link}^{ij}+T_{DATA}+T_{ACK}$. Similarly, when node k receives an xACK packet from node j, the same silence strategy is employed.

By providing a clear and organized overview of the protocol’s operation, the state transition diagram is shown in Figure 9. It visually represents the possible states that a node can be in, as well as the conditions and events that trigger transitions between these states. The SFLC-MAC has six states, namely, IDLE, CONTEND (CTD), WFCTS, WFDATA, WFACK, and QUIET. The state transition strategies in Figure 9 can be described as follows:

• In IDLE state, it will be transferred according to the following conditions:
  • If there is a DATA packet to be sent in the cache, the state is switched to the CTD, and the CTD state’s hold time is calculated according to Algorithm 1.
  • Overhear RTS packet, it calculates the DATA packet waiting time $T_w$ according to Algorithm 3, writes the $T_w$ into CTS packet, and broadcast the packet. Then, its state switches to the WFDATA, and the state’s hold time is $2D_{ij}+T_{\mathrm{DATA}}+T_{\mathrm{CTS}}+T_w+T_{\mathrm{PRO}}$. Where $T_{PRO}$ is a protection interval.
  • Overhear xRTS packet, its state switches to the QUIET, and the state’s hold time is $2\tau +T_{CTS}+T_{DATA}+T_{PRO}$.
  • Overhear xCTS packet, its state switches to the QUIET, and the state’s hold time is $2T_{link}+T_w+T_{DATA}+T_{ACK}+T_{PRO}$. Where $T_{link}$ and $T_w$ are the link delay and waiting time recorded in the packet, respectively.
  • Overhear DATA packet that is intended for another node (xDATA), its state switches to the QUIET. If the HasNext flag of the packet is 1, the state’s hold time is $2T_{link}+T_{DATA}+T_{ACK}+T_{PRO}$. If the flag is 0, the state’s hold time is $2T_{link}+T_{ACK}+T_{PRO}$.
  • Overhear ACK or NACK packet that is intended for another node (xACK or xNACK). If the HasNext flag of the packet is 1, its state switches to the QUIET, and the state’s hold time is $2T_{link}+T_{DATA}+T_{ACK}+T_{PRO}$.
• In CTD state, it will be transferred according to the following conditions:
  • After the state hold time is over, the node sends an RTS packet. The state then switches to WFCTS and the state hold time is $2\tau +T_{\mathrm{RTS}}+T_{\mathrm{CTS}}+T_{\mathrm{PRO}}$.
  • Overhear RTS packet, the node executes the policy consistent with IDLE.
  • Overhear packet sent to other nodes, the node executes the policy consistent with IDLE.
• In the WFCTS state, it will be transferred according to the following conditions:
  • Overhear the CTS packet, the node sends the DATA packet immediately after the waiting time. Then, its state switches to the WFACK and the state’s hold time is $2D_{ij}+T_{\mathrm{DATA}}+T_{\mathrm{ACK}}+T_{\mathrm{PRO}}$.
  • After the hold time expires, it means that the handshake fails. The node updates the backoff value $B_{\mathrm{cnt}}$ according to the BEB algorithm. Then, its state switches to the CTD and the state’s hold time is $Random\left[0,B_{\mathrm{cnt}}\right]\left(\tau +T_{\mathrm{RTS}}\right)$.
  • Overhear packet sent to other nodes, the node executes the policy consistent with IDLE.
• In the WFDATA state, it will be transferred according to the following conditions:
  • Overhear DATA packet, the node write the HasNext into ACK packet and broadcast the packet. If the HasNext flag of the packet is 1, its state switches to the WFDATA and the state’s hold time is $2D_{ij}+T_{\mathrm{DATA}}+T_{\mathrm{ACK}}+T_{\mathrm{PRO}}$. If the flag is 0, its state switches to the IDLE.
  • After the hold time expires, it means that the DATA packet has not been received. If the DATA packet does not exceed the maximum number of retransmissions, the node immediately sends a NACK packet to request retransmission, and maintains the WFDATA state for a duration of $2D_{ij}+T_{\mathrm{DATA}}+T_{\mathrm{ACK}}+T_{\mathrm{PRO}}$. If the DATA packet exceeds the maximum number of retransmissions, the state is switched to IDLE.
• In the WFACK state, it will be transferred according to the following conditions:
  • Overhear ACK packet, the node detects whether there is still data in the queue to be sent this time. If there is, it immediately sends a DATA packet, and the state is changed to WFACK, and the hold time is $2D_{ij}+T_{\mathrm{DATA}}+T_{\mathrm{ACK}}+T_{\mathrm{PRO}}$. If the queue is empty, the state is switched to IDLE.
  • Overhear NACK packet, the node detects whether the corresponding DATA packet exceeds the maximum number of retransmissions. If not, the node immediately sends the corresponding DATA packet, switches the state to WFACK, and the hold time is $2D_{ij}+T_{\mathrm{DATA}}+T_{\mathrm{ACK}}+T_{\mathrm{PRO}}$. If it exceeds, the DATA packet will be discarded immediately, and the state will be set to IDLE.
  • After the hold time expires, the node executes the policy consistent with WFCTS.
• In QUIET state, it will be transferred according to the following conditions:
  • After the hold time expires, the node detects whether the channel is busy. If it is busy, the node will continue to maintain the QUIET state, and the state hold time is $\tau +T_{\mathrm{RTS}}$. If it is idle, the state is changed to the IDLE state.
  • Overhear packet sent to other nodes, the node calculates the new hold time according to the policy in the IDLE state. It compares the new hold time with the current remaining hold time, and selects the largest hold time as the hold time of this state.

5. Simulation Results

In this paper, we use the NS3 simulation to compare the performance of SFLC-MAC with QL-UACW, Slotted-FAMA, and UW-SEEDEX.

Table 2. Simulation parameter settings.

MAC Parameter	Value
Maximum transmission range	3 km
Date rate	3000 bps
DATA packet size	$300,500,1000$ bytes
Transmission power	10 W
Receiver power	3 W
Idle power	8 mW
$T_{PRO}$	$0.01$ s
$C{W}_{max}$	5
$L_{th}$	5
${\Delta }_{th}$	300 m
$N_{th}^{RD}$	5
$N_{th}^{FA}$	4
$B_{max}$	8

shows the simulation parameters, while Figure 10 depicts the scenarios of a distributed topology. In Figure 10a,b, nodes A and C transmit packets to nodes B and D, respectively. We assume that the maximum transmission range is R, with $d_2$ being a random number r ranging from 0 to R. Furthermore, $d_1$ and $d_3$ are random numbers in the range of $R-r$ to R, ensuring that the scene is either an exposed or hidden terminal. In Figure 10c, we divide the 6 km × 6 km sea area into 16 grids of 1.5 km × 1.5 km each and randomly deploy one node in each grid.

In all scenarios, the time interval for each sender to generate DATA packets satisfies the Poisson distribution. In Figure 10c, each time the sender generates a DATA packet, it randomly selects a neighbor node as the destination address. A total of 100 simulations were conducted randomly, each lasting $10,000$ s, and the results were averaged across all simulations.

Four metrics are utilized to evaluate the performance of these protocols: network throughput, end-to-end delay, average energy consumption, and spatial fairness index. Network throughput is quantified as the amount of data successfully transmitted during the simulation period. End-to-end delay is determined as the duration from the time a packet is generated by the sending node to the time it is received by the destination node. Average energy consumption is calculated by computing the average energy consumed to successfully receive a packet. To evaluate the fairness of the protocols, we adopted Jain’s Fairness Index [38]:

$$\mathrm{Fairness}\mathrm{Index}=\frac{{\left({\displaystyle \sum _{i=1}^N}{x}_i\right)}^2}{N\times {\displaystyle \sum _{i=1}^N}{x}_i^2}$$

(23)

where $x_i$ denotes the throughput of node i ($1\le i\le N$), and N is the number of nodes in the network.

5.1. Evaluating Contention Window Spatial Fairness Adjustment Strategy

To verify the effectiveness of the contention window adjustment algorithm, we conducted simulation experiments using QL-UACW in scenarios with exposed, hidden, and random topologies. The simulation results for a packet size of 500 bytes are presented in Figure 11.

5.1.1. 4-Node Topology

In Figure 11a,c,e we show the performance differences between SFLC-MAC and QL-UACW in the 4-node scenario. Equation (2) reveals that the unfairness in channel access is linked to the distance of link; therefore, the simulation experiments were conducted with varying values of $d_1$. To assess the impact of short communication links on the network and maintain generality, we set the random range of values for $d_1$ in Figure 10 to $[100$ m$,500$ m] and $[100$ m$,2900$ m], respectively.

Figure 11a shows that the difference in the fairness index between SFLC-MAC and QL-UACW is close to 0 in both exposed and hidden terminal scenarios when the load is less than $0.1$ pkt/s. However, as the load increases, the difference between the two MAC protocols also increases. While re-handshaking can solve the unfairness problem when the network congestion is low due to a small load, it becomes more difficult for nodes to access the channel through re-handshaking as the network load increases.

In the same topology scene, it was observed that SFLC-MAC had a higher fairness index when $d_1$ was between 100 m and 500 m than when $d_1$ was between 100 m and 2900 m. This is because SFLC-MAC addresses issues related to spatial fairness, which are more likely to occur when $d_1$ is small. In contrast, QL-UACW does not take problems of spatial fairness into account.

In the same range of $d_1$, SFLC-MAC has a greater fairness advantage in the topology scenario shown in Figure 10a than in Figure 10b. This is because Figure 10a shows the exposed terminal scenario and the degree of competition among senders is high, which affects the self-learning process of QL-UACW. In SFLC-MAC, the sender periodically switches to the fair period, which enhances the cooperation ability among nodes and ensures the orderly transmission of links. As shown in Figure 11c, SFLC-MAC requires the node that has successfully completed its DATA transmission to increase its listening time, thus, paying a high end-to-end delay cost in scenario in Figure 10a to ensure fairness.

As shown in Figure 11c,e, SFLC-MAC has a better end-to-end delay and higher throughput performance for the hidden terminal scenario. In Figure 10b, if the sender does not receive a CTS packet, it will enter the backoff state. The backoff time can effectively reduce the conflict rate between nodes and improve fairness. Therefore, the fairness advantages of QL-UACW and SFLC-MAC are similar in the hidden terminal scenario. This can be attributed to SFLC-MAC’s consideration of the asynchronous decision problem that exists in hidden terminals, which guarantees fair access to the channel for hidden terminals by actively deferring access to the channel. In contrast, QL-UACW has to wait longer to update its policy.

5.1.2. 16-Node Topology

In Figure 11b,d,f we show the performance differences between SFLC-MAC and QL-UACW in the 16-node scenario.

As shown in Figure 11b, it can be concluded that the SFLC-MAC protocol provides higher fairness than the QL-UACW after $0.05$ pkt/s. In this scenario, each packet from a node randomly selects a neighboring node as its destination address, resulting in rapid changes in the network. The QL-UACW uses a greedy strategy based on Q-learning, which does not consider the cooperation of neighboring nodes. Furthermore, Q-learning algorithms require some time to reach a converged state. In comparison, the fairness algorithm in this paper allows nodes to actively or postpone competing for channels while considering the spatial fairness issue, ensuring orderly communication between nodes. As a result, SFLC-MAC has clear advantages in both the spatial fairness problem and the rapidly changing network transmission environment.

In Figure 11f, it can be observed that when the load exceeds $0.05$ pkt/s, the throughput of SFLC-MAC is lower than that of QL-UACW. With reduced fairness, certain nodes will continuously occupy the channel, leading to fast packet delivery for these nodes, while packets from other nodes may be consistently blocked. Consequently, a low fairness approach may result in higher network throughput. In Figure 11d, the end-to-end delay of SFLC-MAC is slightly higher than that of the QL-UACW protocol. As shown in Equation (10), this study employs a fixed step size for adjusting the basic contention window value, whereas QL-UACW adopts an adaptive adjustment strategy, which leads to a loss of delay performance. Nonetheless, although the end-to-end delay and throughput performance of SFLC-MAC are slightly lower than those of QL-UACW, its fairness is significantly higher than QL-WACW when the load exceeds $0.05$ pkt/s.

In summary, under various scenarios, the contention window adjustment mechanism in SFLC-MAC can achieve higher fairness while ensuring good end-to-end delay and throughput performance. This ensures that each node in the network can access the channel fairly, regardless of the specific scenario.

5.2. Evaluating the Mechanism of Postponing DATA Packet Transmission

To evaluate the effectiveness of the collision avoidance mechanism, we modified the waiting time for DATA packets sent in the SFLC-MAC protocol to 0, and named the modified protocol SFNW-MAC. We then compared the performance differences between the SFLC-MAC and SFNW-MAC protocols in scenarios with 4 nodes (Figure 10b) and 16 nodes (Figure 10c). The simulation results are depicted in Figure 12.

5.2.1. Hidden Terminal Scenario of 4-Node

Based on Equations (7) and (8), it becomes evident that the probability of collisions between control packets and DATA packets is associated with the DATA packet size and the distance between the links. Therefore, for the purpose of the simulation experiments, we chose packet sizes of 300 bytes and 1000 bytes, and set the $d_2$ values within the ranges of $[100$ m$,500$ m] and $[1000$ m$,1500$ m]. In Figure 12a,c, we show the performance differences between SFLC-MAC and SFNW-MAC in the 4-node scenario.

As depicted in Figure 12c, the difference in end-to-end delay between SFLC-MAC and SFNW-MAC is more significant when the packet length is 300 bytes than when it is 1000 bytes. This is because shorter packets require less transmission time, resulting in an increased number of handshakes within the same network time. This increase in handshakes leads to a higher probability of collisions between control and DATA packets. The performance of SFLC-MAC can be improved by waiting a certain amount of time before sending DATA packets, depending on the probability of control packets colliding with DATA packets. Consequently, SFLC-MAC performs better in shorter packet scenarios within the same simulation time. The performance advantage of SFLC-MAC is more noticeable when the distance $d_2$ is in $[1000$ m$,1500$ m]. This is because a larger $d_2$ corresponds to a higher probability of collision between control and DATA packets.

In Figure 12a, regarding throughput performance, the SFLC-MAC demonstrates higher throughput than the SFNW-MAC. With the same data packet size, the larger the range of $d_2$, the greater the difference in throughput. These performance trends are related to the end-to-end delay performance in their respective scenarios. This is because as the end-to-end delay decreases, the number of data packets transmitted per unit of time increases, consequently leading to higher throughput.

5.2.2. 16-Node Topology

In the 16-node topology, as shown in Figure 12d, the end-to-end delay difference between the two schemes is approximately −30 s, while in the hidden terminal scenario, the difference is approximately −100 s. The probability of collision between control packets and DATA packets is lower in the 16-node topology. Thus, the advantage of SFLC-MAC in terms of end-to-end delay is smaller in this scenario. Nevertheless, the end-to-end delay of SFLC-MAC is still lower than that of SFNW-MAC in the 16-node topology. As shown in Figure 12b, when the packet size is increased from 300 to 1000 bytes, the throughput difference is significantly higher. This is because larger packet lengths result in more DATA being received by the node for a similar end-to-end delay, thus, leading to an increase in the throughput difference.

In conclusion, this paper has shown that the proposed waiting time algorithm can effectively reduce end-to-end delay and increase throughput in both hidden terminal and random scenarios, with a particularly significant improvement in the hidden terminal scenario.

5.3. Comparing SFLC-MAC with Other Protocols in Randomly Deployed Networks Topology

This paper compares the performance of SFLC-MAC with that of Slotted-FAMA and UW-SEEDEX in the 16-node topology.

Under different loads, UW-SEEDEX demonstrates excellent fairness, as depicted in Figure 13d. The SFLC-MAC protocol maintains fairness of over 0.95 at loads lower than $0.01$ pkt/s. At higher loads, network congestion increases, which affects the fairness of SFLC-MAC but remains above 0.85. The Slotted-FAMA protocol, which employs a fixed time slot algorithm, cannot handle network congestion under high loads, resulting in a significant drop in fairness after $0.05$ pkt/s. In contrast, SFLC-MAC addresses fairness issues caused by spatio-temporal uncertainty at low loads and maintains fairness similar to UW-SEEDEX, and higher than the Slotted-FAMA protocol.

Both UW-SEEDEX and Slotted-FAMA use fixed time slots to transmit DATA packets, as shown in Figure 13a, resulting in a convergence of throughput at $0.05$ pkt/s due to the limited number of time slots. UW-SEEDEX, which employs a collision avoidance mechanism, has a lower packet collision rate than Slotted-FAMA, resulting in higher throughput. SFLC-MAC performs similarly to UW-SEEDEX when the load is not higher than $0.007$ pkt/s. However, when network congestion occurs, as shown in Figure 13a,c, SFLC-MAC adjusts the competition window time according to the degree of congestion and reduces the degree of congestion, resulting in higher throughput and end-to-end performance than UW-SEEDEX and Slotted-FAMA. The average energy consumption of the UW-SEEDEX network significantly increases at a load of $0.01$ pkt/s, compared to the load of $0.007$ pkt/s required to reach the full load state of UW-SEEDEX, and convergence is maintained as the load increases, as shown in Figure 13b. Slotted-FAMA is unable to adapt to the high congestion state of the network at $0.01$ pkt/s, resulting in an increase in the average energy consumption of its network. SFLC-MAC can effectively manage network congestion and independently coordinate network resources, ensuring that the average energy consumption of the network remains stable.

In the 16-node topology, the SFLC-MAC protocol demonstrates lower end-to-end delay, higher network throughput, and lower average energy consumption than other protocols due to its ability to address unfairness caused by spatio-temporal uncertainty and reduce the probability of collision between control and DATA packets.

6. Conclusions

SFLC-MAC is a reservation-based protocol for UANs. The protocol optimizes the contention window adjustment mechanism, handshake mechanism, and state transfer strategy. The protocol formulates a contention window state transition strategy based on the locally perceived information of the nodes. Through this strategy, nodes can autonomously switch between random and fair contention states. This not only ensures fairness in channel access, but also minimizes performance degradation caused by prolonged listening time. This protocol reduces the packet collision rate by making the receiver responsible for calculating the waiting time for sending DATA packets from the sender. Finally, a node state transition strategy is established to regulate the behavior of nodes under different network conditions. Based on the timing of data packet interactions, the maintenance durations of various states are refined under different conditions. Through experiments in the exposed terminal, hidden terminal, and 16-node topology scenarios, the protocol achieved high performance in terms of throughput, end-to-end delay, network energy consumption, and fairness, demonstrating its effectiveness. Future work will evaluate the performance of this protocol in combination with routing protocols and aim to enhance its advantages in end-to-end networks.