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  1. (School of Computer Science and Engineering, Kyungpook National University / Daegu 41566, Korea {duddmd0219, neloyou} )

TDMA, Broadcasting, Propagation delay

1. Introduction

Most military networks need to broadcast shared data to every friendly force. Thus, TDMA is widely used in military networks because it adequately ensures broadcasting without collisions by allocating the same frequency to each user in a time slot. In particular, airborne military networks require guard time to prevent collisions owing to the large propagation delay. However, use of a guard time causes waste and degrades network performance, but reducing the time interval while ensuring broadcasting is a challenge.

In this paper, we propose Adaptive Guard Time with Inter-transmitter Propagation Delay (AGT-IPD), a scheme for reducing guard time while ensuring broadcasting. AGT-IPD does not require a central node, and assumes that all nodes are synchronized and share prior information (e.g., propagation delay). Each transmitter adjusts the guard time considering the propagation delay for the next time slot owner, referred to as PD-NEXT. AGT-IPD also provides a distributed mechanism that uses PD-NEXT for propagation delay estimation and time synchronization. AGT-IPD does not provide tight time synchronization. Thus, we consider additional guard time to compensate for errors due to rough time synchronization. We consider a network initialization mode in which all nodes are unsynchronized and use a fixed guard time. After network initialization mode, each node adjusts the guard time adaptively by using PD-NEXT, which was estimated in the previous frame. We constructed analytical and simulated models of AGT-IPD, showing through numerical results that AGT-IPD provides higher link utilization than other schemes, regardless of packet length, maximum communication range, the number of nodes, and the number of errors.

2. Related Works

Most studies have focused solely on reducing the guard time in underwater wireless sensor networks (UWSNs) [1-4]. UWNSs are shaped as tree-based multi-hop networks. The objective of a UWSN is to deliver data to the sink node for ocean exploration, monitoring tasks, and target tracking. To achieve high link utilization when changing data between nodes, the guard time is set longer than the transition time in the modem [1]. By setting the optimal time slot length, the guard time is reduced to reach efficient throughput. However, the scheme does not ensure broadcasting, and a way to reduce guard interval itself was not devised. The scheme proposed in [3] considers how to select the nearest node and how to broadcast between adjacent nodes, but assumes that each sensor is fixed. In these schemes, the TDMA method provided is not suitable for military networks that must handle dynamic movement and broadcast tactical data.

In general, military networks require high reliability and stability. The traditional centralized TDMA, a method in which a particular node allocates a time slot centrally, is likely to paralyze the entire network if a problem arises with the node managing the resource. On the other hand, distributed TDMA is a method of allocating distributed time slots without a separate node. Therefore, research on tactical data links has focused on distributed TDMA techniques rather than centralized TDMA. Distributed TDMA has been studied in various fields. The scheme in [5] proposes efficient time slot adjustment to minimize vehicle-to-vehicle collisions in a vehicle ad hoc network. The authors in [6] showed that localization accuracy is achieved by quickly allocating all idle time slots to maximize channel ranging and communication in mobile UWB networks.

There are several types of tactical data link, among which Link-16 is a representative airborne military communication system with a maximum range of 300 nautical miles (nm) [7]. It uses a fixed guard time considering the maximum propagation delay in accord with the maximum communication range. In the worst-case scenario, it causes an unnecessary waste of time when communicating between nodes at short distances, and leads to poor network performance. In [4], an optimal TDMA scheme that uses an adaptive guard time considering the propagation delay from the time slot owner to its farthest neighbor was defined. However, this scheme does not provide optimal performance, and assumes that each node has already determined the propagation delay to its farthest neighbor. To avoid ambiguity, we refer to that scheme as AGT-LPD.

3. The Proposed Scheme

We consider a single-hop, distributed TDMA network with a large propagation delay. The network consists of $\textit{N}$ nodes that are unsynchronized. We do not consider a time slot allocation procedure. We focus solely on guard time control and time synchronization by using PD-NEXT. Therefore, we assume that each node has one time slot per frame according to a predefined order, and that order is already stored in all nodes before the system starts, as in Link-16 [7]. We also assume that all nodes transmit packets of the same length.

We define a number of variables. A frame consists of $\textit{N}$ time slots, each of which consists of several mini-slots. Let $\textit{T}$$_{frame}$ denote the frame length. We can express $\textit{T}$$_{frame}$ as

$ T_{\textit{frame}}=\sum _{i=1}^{N}T_{S,i} $

where $\textit{T}$$_{S,i}$ is the length of the $\textit{i-th}$ time slot and is obtained as follows:

$ T_{S,i}=\left\lceil \frac{T_{P}+T_{G,i}}{T_{MS}}\right\rceil \times T_{MS} $

where $\left\lceil x\right\rceil $ is the smallest integer greater than or equal to $\textit{x, T}$$_{P}$ is the packet length, $\textit{T}$$_{G,i}$ is the guard time length of the $\textit{i-th}$ time slot, and $\textit{T}$$_{MS}$ is the mini-slot length. For guard time control, we define four variables: $\textit{TSO}$$_{i}$, $\textit{t}$$_{s,i}$, $\textit{t}$$_{r,i,i+1}$, and $\textit{p}$$_{i,i+1}$. $\textit{TSO}$$_{i}$ and $\textit{t}$$_{s,i}$ denote the owner and starting time, respectively, of the $\textit{i-th}$ time slot. Then, $\textit{TSO}$$_{i+1}$ starts to receive the packet that was transmitted by $\textit{TSO}$$_{i}$ at $\textit{t}$$_{r,i,i+1}$. In Fig. 1, $\textit{TSO}$$_{1}$ broadcasts a packet at $\textit{t}$$_{s,1}$, and $\textit{TSO}$$_{2}$ records $\textit{t}$$_{r,1,2}$, at which time $\textit{TSO}$$_{2}$ starts to receive the packet. We denote with $\textit{p}$$_{i,i+1}$ the PD-NEXT for $\textit{TSO}$$_{i}$, i.e. the propagation delay between $\textit{TSO}$$_{i}$ and $\textit{TSO}$$_{i+1}$.

Fig. 1. Example of the AGT-IPD frame and packet structure in normal mode.

In each frame, guard time control and time synchronization are performed with PD-NEXT, which was estimated in the previous frame. However, in the first frame, none of the nodes can perform these procedures because PD-NEXT has not yet been estimated. Therefore, AGT-IPD provides two modes: network initialization mode and normal mode.

3.1 Network Initialization Mode

The network initialization mode is used for estimating PD-NEXT while all nodes are unsynchronized in the first frame. $\textit{TSO}$$_{1}$ starts the network by broadcasting a packet with $\textit{t}$$_{s,1}$. As soon as each node receives the packet, it sets the local time to $\textit{t}$$_{s,1}$ and starts the first frame. Because all nodes are still unsynchronized, a fixed guard time is used to prevent collisions, and its length is denoted as $\textit{T}$$_{MAX\backslash \_ RTT}$, which is the maximum round trip time.

After the first time slot, each node estimates PD-NEXT by exchanging a packet. The packet of $\textit{TSO}$$_{i}$ contains $\textit{t}$$_{s,i}$ and $\textit{t}$$_{r,i-1,i}$ as well as the data. In the $\textit{i-th}$ time slot, $\textit{TSO}$$_{i}$ broadcasts the packet, and $\textit{TSO}$$_{i+1}$ records $\textit{t}$$_{r,i,i+1}$. Subsequently, in the ($\textit{i+1}$)$\textit{-th}$ time slot, $\textit{TSO}$$_{i+1}$ broadcasts the packet containing $\textit{t}$$_{s,i+1}$ and $\textit{t}$$_{r,i,i+1}$ as well as the data. Then, $\textit{TSO}$$_{i}$ records $\textit{t}$$_{r,i+1,i}$ and obtains $\textit{p}$$_{i,i+1}$ with the following calculation: {($\textit{t}$$_{r,i+1,i}$ - $\textit{t}$$_{s,i}$) - ($\textit{t}$$_{s,i+1}$ - $\textit{t}$$_{r,i,i+1}$)}/2. However, $\textit{TSO}$$_{i+1}$ does not yet have $\textit{p}$$_{i,i+1}$. In particular, $\textit{TSO}$$_{N}$ regards $\textit{TSO}$$_{1}$ as the next time slot owner in order to estimate PD-NEXT.

3.2 Normal Mode

After network initialization mode (i.e., for the first frame), all nodes switch to normal mode. All nodes perform guard time control and time synchronization with PD-NEXT estimated in the previous frame. In addition, all nodes estimate PD-NEXT to be used in the next frame.

A packet of $\textit{TSO}$$_{i}$ contains $\textit{t}$$_{s,i}$, $\textit{t}$$_{r,i-1,i}$, and $\textit{p}$$_{i,i+1}$ as well as the data, as shown in Fig. 1. When $\textit{TSO}$$_{i+1}$ receives this packet, it obtains $\textit{t}$$_{s,i}$ and $\textit{p}$$_{i,i+1}$. Thus, $\textit{TSO}$$_{i+1}$ can achieve time synchronization with $\textit{TSO}$$_{i}$ by setting the local time as the sum of $\textit{t}$$_{s,i}$ and $\textit{p}$$_{i,i+1}$. It also determines $\textit{t}$$_{s,i+1}$ as follows:

$ t_{s,i+1}=t_{s,i}+T_{S,i} $

where $\textit{T}$$_{S,i}$ is obtained from (2) and depends on $\textit{T}$$_{G,i}$. In particular, $\textit{TSO}$$_{1}$ regards $\textit{TSO}$$_{N}$ as the previous time slot owner for time synchronization. Therefore, $\textit{t}$$_{s,1}$ is obtained from $\textit{t}$$_{s,N}$ + $\textit{T}$$_{S,N}$.

When PD-NEXT is used for guard time control and time synchronization, errors occur because PD-NEXT was estimated in the previous frame. Hence, an additional guard time is used to compensate for these errors. More specifically, $\textit{T}$$_{G,i}$, which is not $\textit{T}$$_{MAX\backslash \_ RTT}$ as in the first frame, is expressed as

$ \begin{array}{l} T_{G,i}=p_{i,i+1}+e_{MAX}\;\;\;\;\;\;\;\; \text{ for }i=1,\cdots ,N-1\\ T_{G,N}=p_{N,1}+e_{MAX} \;\;\;\;\;\;\;\; \text{ for }i=N \end{array} $

where $\textit{e}$$_{MAX}$ denotes the additional guard time to compensate for errors of propagation delay estimation and time synchronization. Our error model is the same as in [4]. We can express $\textit{e}$$_{MAX}$ as 2(${\varepsilon}$+${\sigma}$) where ${\varepsilon}$ is the maximum error experienced in estimating the propagation delay between any two nodes, and ${\sigma}$ is the maximum time synchronization error due to drift before time synchronization. Because each of the errors between any two nodes differs by at most two times, we define $\textit{e}$$_{MAX}$ as twice the size of ${\varepsilon}$+${\sigma}$. We assume that $\textit{e}$$_{MAX}$ is a value derived from experiments before the system starts.

In Fig. 1, we depict an example of the AGT-IPD frame structure and packet structure in normal mode when $\textit{N}$ is 4 and the predefined order is 1${\rightarrow}$3${\rightarrow}$2${\rightarrow}$4. At $\textit{t}$$_{s,1}$, $\textit{TSO}$$_{1}$ broadcasts a packet that includes the values of $\textit{t}$$_{s,1}$, $\textit{t}$$_{r,4,1}$, and $\textit{p}$$_{1,2}$. As soon as $\textit{TSO}$$_{4}$ and $\textit{TSO}$$_{2}$ receive the packet, they record $\textit{t}$$_{r,1,4}$ and $\textit{t}$$_{r,1,2}$, respectively. $\textit{TSO}$$_{4}$ estimates the new PD-NEXT by calculating $\textit{p}$$_{4,1}$, which will be used in the next frame, as follows: {($\textit{t}$$_{r,2,1}$ - $\textit{t}$$_{s,1}$) - ($\textit{t}$$_{s,2}$ - $\textit{t}$$_{r,1,2}$)}/2. $\textit{TSO}$$_{2}$ achieves time synchronization with $\textit{TSO}$$_{1}$ by setting its local time with $\textit{t}$$_{s,1}$ + $\textit{p}$$_{1,2}$. It then determines $\textit{t}$$_{s,2}$ by calculating $\textit{t}$$_{s,2}$ = $\textit{t}$$_{s,1}$ + $\textit{T}$$_{S,1}$ from (3). In $\textit{T}$$_{S,1}$, $\textit{T}$$_{G,1}$ is obtained by calculating $\textit{T}$$_{G,1}$ = $\textit{p}$$_{1,2}$ + $\textit{e}$$_{MAX}$ from (4). After $\textit{TSO}$$_{2}$ determines $\textit{t}$$_{s,2}$, it starts to broadcast at $\textit{t}$$_{s,2}$. All nodes repeatedly estimate a new PD-NEXT, achieving time synchronization with the owner of the next time slot, and determining the starting time of their own time slots with the adaptive guard time. As shown in Fig. 1, each time slot has a different length attributed to the adaptive guard time.

4. Models for Simulation and Analysis

In this section, we describe the simulation model and the analytical model for AGT-IPD. We use link utilization as the performance metric. Let $\textit{U}$ denote link utilization during one frame in normal mode. We obtain $\textit{U}$ with

$ U=\frac{N\times T_{P}}{T_{\textit{frame}}} $

where $\textit{T}$$_{frame}$ is obtained by using (1), (2), and (4).

4.1 Simulation Model

We performed 100 simulations and averaged the results to obtain link utilization. In each simulation, $\textit{N}$ nodes were deployed in a uniform distribution for sphere of radius $\textit{R}$/2, where $\textit{R}$ is the maximum communication range. Thus, all nodes can communicate directly. In spherical coordinates, the location of a node is specified by ($\textit{r}$, ${\theta}$, ${\varphi}$), where $\textit{r}$ is the radial distance, ${\theta}$ is the polar angle, and ${\varphi}$ is the azimuth [8]. Thus, for each node deployed, three uniform random variables, ($\textit{r}$, ${\theta}$, ${\varphi}$), are selected from 0 ${\leq}$ $\textit{r}$ ${\leq}$ $\textit{R}$, 0 ${\leq}$ ${\theta}$ ${\leq}$ ${\pi}$, and 0 ${\leq}$ ${\varphi}$ ${\leq}$ 2${\pi}$, respectively. We assume that each node has one time slot per frame, that the order of time slot allocation is random, and that all nodes already have the order before the system starts. After the completion of node deployment, each scheme estimated $\textit{U}$.

We use fixed guard time (FGT) and AGT-LPD as the comparison schemes. FGT uses a guard time of fixed length, as in Link-16, and AGT-LPD uses adaptive guard time. For the comparison schemes, but not AGT-IPD, we assumed that all the nodes are synchronized. We also assumed that each node in AGT-LPD has the propagation delay between it and the node from which it is the farthest. In FGT, the time slot length was set as $\textit{T}$$_{P}$ + $\textit{P}$$_{MAX}$ + $\textit{e}$$_{MAX}$, where $\textit{P}$$_{MAX}$ is the maximum propagation delay in accord with the maximum communication range. Thus, $\textit{T}$$_{frame}$ for FGT was $\textit{N}$($\textit{T}$$_{P}$ + $\textit{P}$$_{MAX}$ + $\textit{e}$$_{MAX}$). In AGT-LPD, the length of the $\textit{k-th}$ time slot was set at $\textit{T}$$_{P}$ + $\textit{P}$$_{k}$ + $\textit{e}$$_{MAX}$, where $\textit{P}$$_{k}$ is the propagation delay between $\textit{TSO}$$_{k}$ and its farthest node. Thus, the $\textit{T}$$_{frame}$ of AGT-LPD was the total length of $\textit{N}$ time slots.

4.2 Analytical Model

We constructed an analytical model to check the performance of AGT-IPD. Before estimating $\textit{U}$ in the analytical model, we need to estimate the expected propagation delay between any pair of nodes. Therefore, we defined a node deployment rule for its estimation.

The node deployment rule is that all nodes are distributed evenly in each dimension. We deployed $\textit{N}$ nodes within a sphere of radius $\textit{R/2}$. We defined $\textit{N}$$_{D}$ as the number of nodes per dimension. Thus, $\textit{N}$$_{D}$ is the cube root of $\textit{N}$. Let $\textit{l}$$_{n}$ be the location of node $\textit{n}$ for 1 ${\leq}$ n ${\leq}$ $\textit{N}$. For a given $\textit{n}$, we determined three variables ($\textit{i}$, $\textit{j}$, $\textit{k}$), where $\textit{i}$ is the quotient of ($\textit{n}$ - 1) divided by $\textit{N}$$_{D}$$^{2}$, $\textit{j}$ is the quotient of ($\textit{n}$ - 1 - $\textit{iN}$$_{D}$$^{2}$) divided by $\textit{N}$$_{D}$, and $\textit{k}$ is ($\textit{n}$ - 1) modulo $\textit{N}$$_{D}$. Then, $\textit{n}$ = $\textit{iN}$$_{D}$$^{2}$ + $\textit{jN}$$_{D}$ + ($\textit{k}$ + 1). After determining the three variables, $\textit{l}$$_{n}$ can be specified by the spherical coordinates ($\textit{r}$$_{i}$, ${\theta}$$_{j}$, ${\varphi}$$_{k}$) where $\textit{r}$$_{i}$ = $\textit{iR}$/($\textit{N}$$_{D}$ - 1), ${\theta}_{j}$ = $j{\pi}/(N_{D}$ - 1), and ${\varphi}$$_{k}$ = 2$k{\pi}$/($N_{D}$ - 1) for 0 ${\leq}$ $\textit{i}$, $\textit{j}$, $\textit{k}$ < $\textit{N}$$_{D}$.

After the nodes were deployed, we could calculate $\textit{E}$[$\textit{P}$], which denotes the expected propagation delay between any pair of nodes and is expressed as

$ E\left[P\right]=\sum _{n=1}^{N}\sum _{m=1,n\neq m}^{N}\frac{d\left(l_{n},l_{m}\right)}{c}p\left(l_{n},l_{m}\right) $

where $\textit{d}$($\textit{l}$$_{n}$, $\textit{l}$$_{m}$) is the distance from node $\textit{n}$ to node $\textit{m}$, $\textit{c}$ is the signal propagation speed, and $\textit{p}$($\textit{l}$$_{n}$, $\textit{l}$$_{m}$) is the probability that node $\textit{m}$ is selected after node $\textit{n}$ is selected. We obtained $\textit{d}$($\textit{l}$$_{n}$, $\textit{l}$$_{m}$) = {($\textit{x}$$_{n}$ - $\textit{x}$$_{m}$)$^{2}$ + ($\textit{y}$$_{n}$ - $\textit{y}$$_{m}$)$^{2}$ + ($\textit{z}$$_{n}$ - $\textit{z}$$_{m}$)$^{2}$}$^{\mathrm{1/2}}$, where ($\textit{x}$$_{n}$, $\textit{y}$$_{n}$, $\textit{z}$$_{n}$) and ($\textit{x}$$_{m}$, $\textit{y}$$_{m}$, $\textit{z}$$_{m}$) are the Cartesian coordinates of $\textit{l}$$_{n}$ and $\textit{l}$$_{m}$, respectively. If the spherical coordinates of $\textit{l}$$_{n}$ are ($\textit{r}$$_{i}$, ${\theta}$$_{j}$, ${\varphi}$$_{k}$), then ($\textit{x}$$_{n}$, $\textit{y}$$_{n}$, $\textit{z}$$_{n}$) is obtained as follows: $\textit{x}$$_{n}$ = $\textit{r}$$_{i}$sin${\theta}$$_{j}$cos${\varphi}$$_{k}$, $\textit{y}$$_{n}$ = $\textit{r}$$_{i}$sin${\theta}$$_{j}$sin${\varphi}$$_{k}$, and $\textit{z}$$_{n}$ = $\textit{r}$$_{i}$cos${\theta}$$_{j}$. Regardless of $\textit{n}$ and $\textit{m}$, $\textit{p}$($\textit{l}$$_{n}$,$\textit{l}$$_{m}$) is expressed as {$\textit{N}$($\textit{N}$ - 1)}$^{-1}$.

Now, we can obtain $\textit{U}$ in the analytical model. In (4), $\textit{T}$$_{G,i}$ becomes $\textit{E}$[$\textit{P}$] + $\textit{e}$$_{MAX}$ for all $\textit{i}$. In (1), $\textit{T}$$_{frame}$ becomes $\textit{NT}$$_{S,i}$ because all time slot lengths are the same. Therefore, in the analytical model, $\textit{U}$ for AGT-IPD can be derived by

$ U=\frac{T_{P}}{\left\lceil \left(T_{P}+E\left[P\right]+e_{MAX}\right)/T_{MS}\right\rceil \times T_{MS}} $

4.3 Numerical Results

We compared $\textit{U}$ of AGT-IPD with those of AGT-LPD and FGT. To verify AGT-IPD, we compared the analytical results with the simulated results.

In airborne networks such as Link-16 [7] and Tactical Targeting Network Technology (TTNT) [9], a radio frequency (RF) signal with a propagation speed of 3${\times}$10$^{8}$ m/s is used. Because the maximum communication range is 300nm, the maximum propagation delay is 1.852~ms. In TTNT, the maximum number of nodes is 200.

For simulation and analysis, we selected the values of $\textit{N}$ and $\textit{R}$ based on Link-16 and TTNT. $\textit{R}$ and $\textit{N}$$_{D}$ were set at 300~nm and 6 to make the environments similar to TTNT. We also altered $\textit{R}$, $\textit{N}$$_{D}$, $\textit{e}$$_{MAX}$, and $\textit{T}$$_{P}$ for various comparisons. We considered an error-free single channel.

Fig. 2 shows $\textit{U}$ according to $\textit{T}$$_{P}$ when $\textit{R}$ = 300 nm, $\textit{N}$ = 216, and $\textit{e}$$_{MAX}$ = 0 ms. All schemes provided a high $\textit{U}$ when $\textit{T}$$_{P}$ was large. FGT showed the lowest $\textit{U}$ because the guard time length, which was set at the maximum propagation delay, was the largest. AGT-LPD provided a higher $\textit{U}$ than FGT owing to the use of the adaptive guard time considering the propagation delay between the time slot owner and the farthest node. AGT-IPD provided a much higher $\textit{U}$ than FGT or AGT-LPD because it uses an adaptive guard time considering PD-NEXT. If the next time slot owner is the farthest node in a certain time slot, then the guard time length of the time slot is the same as in AGT-LPD, even though it was the worst case in AGT-IPD. Therefore, $\textit{U}$ for AGT-LPD cannot be higher than $\textit{U}$ for AGT-IPD. To verify our simulation model, we compared it with the analytical model of AGT-IPD. We can see that both showed almost the same performance.

Fig. 2. Comparison of link utilizations according to TP (R = 300 nm, N = 216, $e_{MAX}$ = 0).

Fig. 3 shows $\textit{U}$ according to $\textit{R}$ when $\textit{N}$ = 216 and $\textit{e}$$_{MAX}$ = 0 ms. In each time slot, the ratio of $\textit{T}$$_{P}$ to guard time length, which is affected by $\textit{R}$, affected $\textit{U}$ directly. When $\textit{R}$ was 300 nm, the maximum propagation delay was 1.852 ms. We considered two types of packet: one with a length shorter than the maximum propagation delay (0.1 ms) and another with a length that is longer (3.0 ms). As shown in Fig. 3, $\textit{U}$ was high when $\textit{T}$$_{P}$ was large. Regardless of $\textit{T}$$_{P}$, AGT-IPD consistently provided the highest $\textit{U.}$ The analytical and simulated models of AGT-IPD also showed almost identical performance.

Fig. 4 shows $\textit{U}$ according to $\textit{N}$$_{D}$ when $\textit{R}$ = 300 nm and $\textit{e}$$_{MAX}$ = 0 ms. When $\textit{N}$$_{D}$ was less than 5, AGT-LPD was only affected by $\textit{N}$$_{D}$. Regardless of $\textit{T}$$_{P}$, AGT-IPD and FGT were hardly affected by $\textit{N}$$_{D}$. AGT-IPD also provided the highest $\textit{U}$.

Fig. 5 shows $\textit{U}$ according to $\textit{e}$$_{MAX}$ when $\textit{R}$ = 300 nm and $\textit{N}$~= 216. In each scheme, $\textit{U}$ decreased when $\textit{e}$$_{MAX}$ was large. In particular, when $\textit{T}$$_{P}$ was large, all schemes were greatly affected by $\textit{e}$$_{MAX}$. When $\textit{e}$$_{MAX}$ was 2.0 ms, which is greater than the maximum propagation delay, and when $\textit{T}$$_{P}$ was 0.1~ms, the difference in $\textit{U}$ between any pair of schemes was very small because $\textit{e}$$_{MAX}$ is constant with no mechanism to reduce it. Nevertheless, AGT-IPD still provided the highest $\textit{U}$.

Fig. 3. Comparison of link utilizations according to R (N = 216, $e_{MAX}$ = 0).
Fig. 4. Comparison of link utilizations according to $N_{D}$ (R = 300 nm, $e_{MAX}$ = 0).
Fig. 5. Comparison of link utilizations according to $e_{MAX}$ (R = 300 nm, N = 216).
Table 1. Description of Parameters.



The number of nodes per dimension


The location of node $\textit{n}$


The distance from node $\textit{n}$ to node $\textit{m}$

$\textit{d}$($\textit{l}$$_{n}$, $\textit{l}$$_{m}$)

The probability that node $\textit{m}$ is selected after node $\textit{n}$ is selected.

$\textit{p}$($\textit{l}$$_{n}$, $\textit{l}$$_{m}$)

The quotient of ($\textit{n}$ - 1) divided by $\textit{N}$$_{D}$$^{2}$


The quotient of ($\textit{n}$ - 1 - $\textit{iN}$$_{D}$$^{2}$) divided by $\textit{N}$$_{D}$


($\textit{n}$ - 1) modulo $\textit{N}$$_{D}$


The signal propagation speed


5. Conclusion

In this paper, we proposed AGT-IPD to reduce guard time while ensuring broadcasting in single-hop wireless networks. We found the analytical and simulated results of AGT-IPD were almost identical. In addition, AGT-IPD consistently provided the highest link utilization, regardless of the settings for $\textit{T}$$_{P}$, $\textit{R}$, $\textit{N}$$_{D}$, and $\textit{e}$$_{MAX}$.


This research was supported by Kyungpook National University Research Fund, 2021.


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Youngeun Cho

Youngeun Cho is currently pursuing a B.S. from the School of Computer Science and Engineering at Kyungpook National University in Daegu, South Korea, and graduates in February 2023. Her research interests include wireless communications and networks, UAV systems, and military communications and networks.

Hoki Baek

Hoki Baek received his B.S, M.S., and Ph.D. from the Department of Computer Science at Ajou University in Suwon, South Korea, in 2006, 2008, and 2014, respectively. From March 2014 to February 2015, he served as a full-time researcher at Ajou University's Jangwee Defense Research Institute, and from March 2015 to February 2021, he was a Lecture Professor in the Department of Military and Digital Convergence at Ajou University. Currently, he is an Assistant Professor for the School of Computer Science and Engineering at Kyungpook National University. He is a life member and a director of the Korean Institute of Communications and Information Sciences (KICS), and is an editorial board member for the Journal of the Korean Institute of Communications and Information Sciences (J-KICS). He is a member of the Defense Information Technology Standards (DITA) Standard Working Group (SWG) for the Ministry of National Defense, serving from June 2020 to May 2024. His research interests include 5G/6G communications and networks, UAV networks, Wi-Fi, IoT, military communications and networks, and positioning and time synchronization.