# Performance Analysis for the CMSA/CA Protocol in UAV-based IoT network

Xianzhen Guo, Bin Li, Kebang Liu
Department of Communication Engineering, Northwestern Polytechnical
University, Xi’an, China 710072

###### Abstract

UAV-based base station (UBS) has played an important role in the air-ground
integration network due to its high flexibility and nice air-ground wireless
channels. Especially in Internet of Things (IoT) services, UBS can provide an
efficient way for data collection from the IoT devices. However, due to the
continuous mobility of UBS, the communication durations of devices in
different locations with the UBS are not only time-limited, but also vary from
each other. Therefore, it is a challenging task to analyze the throughput
performance of the UAV-based IoT network. Accordingly, in this paper, we
consider an air-ground network in which UAV flies straightly to collect
information from the IoT devices based on CSMA/CA protocol. An analytical
model analyzing the performance of this protocol in the network is proposed.
In detail, we set up the system model for the network, and propose a new
concept called quitting probability. Then, a modified Markov chain model
integrating the quitting probability is introduced to describe the
transmission state transition process and an accurately theoretical analysis
of saturation throughput is given. In addition, the effects of the network
parameters are discussed in the simulation section.

###### Index Terms:

Air-Ground integration network, CSMA/CA, IoT, Markov chain model, UAV

This work is partially supported by National Natural Science Foundation of
China (Nos. 61601365, 61571370), Natural Science Basic Research Plan in
Shaanxi Province (No. 2019JM-345), National Civil Aircraft Major Project of
China (No. MIZ-2015-F-009), China Postdoctoral Science Foundation(No.
2018M641020)

##  I Introduction

Wireless communication with unmanned aerial vehicles (UAVs) has been adopted
widely in air-ground integration network for military, public and emergency
applications [1]. Compared with the terrestrial communication system, UAV-
based air-ground network is not only easy to deploy, but also has better
wireless channels [2]. Therefore, numerous UAV-based wireless communication
systems have been developed [3, 4, 5, 6]. One typical application is the UAV-
based data collection network in the air-ground IoT system, where UAV is
deployed as a UBS flying over the IoT devices to collect the information. In
this way, the system avoids the complex routing design and improves the
efficiency of data collection greatly. However, there are still some
challenges in developing UAV-based data collection system.

One of the challenges is that it is difficult to analyze the performance of
the MAC protocol performance for the mobility of the UBS. Generally, the
fixed-wing UAV is usually a priority in data collection scenario for its high
altitude and long endurance. However, the UAV of this type cannot hover over a
predetermined location and must fly continuously, causing the time-varying
channels between the UAV and the devices. Moreover, the UAV is usually
equipped with directional antennas for energy-efficient transmission, making a
circular signal coverage on the ground. In this case, the devices in different
locations can communicate with UBS for different durations. These
characteristics make it difficult to develop an accurate and efficient
theoretical model to analyze the performance of a UAV-based communication
system. Given the wide application of the CSMA/CA in data collection network,
we focus on the performance analysis of CSMA/CA considering the continuous
mobility of UBS.

Some work has been made to analyze the performance of the UAV-based data
collection system. [7] analyzes the influence of the distance between two UAVs
on the system performance, but the UAV’s mobility was not taken into
consideration. In [8], the location of UAV is updated periodically to obtain
the optimized locations of UAV. However, it only involves the rotor crafts
which could hover over the predetermined locations to collect the information.
[9] gives a simple but extremely accurate model to calculate the throughput of
CSMA/CA protocol using Markov chain model, and [10] extends the multi-
dimensional Markov chain model by considering the impacts of both non-ideal
channel and capture effects. Unfortunately, both of them can only be applied
in terrestrial communication system with fixed base station.

In this paper, we propose a new quitting probability based on the CMSA/CA
protocol to deal with the communication heterogeneity among the devices caused
by UBS’s mobility. In detail, we divide the devices into different clusters
according to their communication durations with the UBS. Then, a modified
Markov chain model integrating the quitting probability is introduced to
describe the transition of the devices’ state and an accurate analytical model
of saturation throughput is given.

Our main novelty and contributions are given as follows.

  * •

We analyze the characters of the UAV-based IoT network and propose a new
quitting probability in the Markov chain model to model the devices access
process where the different locations among the devices are considered.

  * •

We set up an accurate theoretical analysis model and calculate the saturation
throughput of CSMA/CA protocol in UAV-based IoT network.

The rest of this paper is organized as follows. System model is presented in
Section II. Section III analyzes the Markov model process and gives the
computation of throughput. Numerical results are shown in Section IV. Finally,
Section V concludes the paper.

##  II System Model

###  II-A UAV-based Air-ground Network Model

Figure 1: System model.

We consider a scenario where UBS collects the information from a set of IoT
devices distributed normally on the 2-D plane. Let $({x_{u}},{y_{u}},{z_{u}})$
and $({x_{i}},{y_{i}},{z_{i}})$ denote the locations of the UBS and
$s_{i},i=1,2,...,K$, where $K$ is the total number of devices in the UAV’s
coverage. The UBS is assumed to move in a straight trajectory over the devices
which try to access the UBS for data uploading. The access process between the
devices and the UBS follows CSMA/CA protocol.

During the data collection, for energy efficiency, the UBS deploys the
directional antennas for communications and forms a circular coverage on the
ground, as shown in Fig. 1. Compared with the traditional communication system
with terrestrial infrastructures, the communication durations between UBS and
devices are time limited because of the UBS’s mobility. The devices turn into
the active mode and ready to send the information to the UBS once they are
inside the coverage while the wireless links will break when the UBS flies
away. In addition, the UBS-Devices communication durations are also different
under the straight trajectory because of the different locations of the
devices. The communication duration for device $s_{i}$ can be expressed as:

${T_{i}}=\frac{{2R\cos{\theta_{i}}}}{v},$ (1)

where $R$ is the radius of the UAV coverage, ${\theta_{i}}\in(0,\pi/2)$ is the
locations of the device and can be calculated as
${\theta_{i}}=\arcsin({x_{i}}/R)$ and $v$ is the velocity of UAV. How to
generate the cluster will be described in detail in Section II-D.

###  II-B Markov Chain Model

To analyze the network performance, we propose a Markov chain model to explore
the access process of the devices in the network. We divide all the devices in
the coverage into $N$ band-shaped clusters along the flight trajectory. In
each cluster $\mathbb{C}_{i}$ ($i=1,...,N$), there are $n_{i}$ devices and
each of them is assumed to always have a packet available for transmission.
Assume that all the packet collide with constant and independent probability
regardless of the number of retransmission suffered.

Generally, the CSMA/CA access scheme employs a binary exponential backoff
technique. During the transmission, the backoff time is uniformly chosen in
the range of $(0,{W_{i,j}})$, where ${W_{i,j}}$ is the contention window in
the $j$th backoff stage for the devices in cluster $\mathbb{C}_{i}$. For the
first access round, the $W_{i,0}$ equals to $C{W_{\min}}$. After each failed
access, contention window will be doubled, up to the maximum $C{W_{\max}}$.
Therefore, the size of contention window in stage $j$ is
${W_{i,j}}{\rm{=}}{2^{j}}{W_{i,0}},~{}0\leq j\leq{L}$, where $L$ is the retry
limit.

To clearly describe Markov chain model, we introduce three coefficients ($i$,
$j$ and $b(t)$) to represent the Markov process. Here $b(t)$ represents the
backoff counter for a certain device at time $t$. The backoff counter
decreases if the channel is sensed idle and stops when the channel is busy.
Let $s(t)$ be the stochastic process representing the devices’ backoff stage
$(j=0,...,m,s(t)=j)$ at time $t$. The backoff stage changes after any
unsuccessful access transmission until to the maximal value. A three-
dimensional Markov process with $i$, $j$ and $b(t)$ can be defined and the
detailed stage transition process is shown in Fig. 2, where the ellipses with
parameters ($i$, $j$ and $b(t)$) represent the states of this Markov process.
The arrows show the direction of the state transmission. The formulas along
the arrows, like $(1-Q_{i})(1-q_{i}),(1-Q_{i})q_{i}+Q_{i}$, are the
probabilities for one-step transmission. $Q_{i}$ is the quitting probability
and the details are given in Section II-C. $q_{i}$ is the probability that the
devices in the $i$th cluster sense the channel busy in a backoff stage and it
is derived in Section III-A.

According to Fig. 2, the one-step transmission probabilities of the Markov
process is shown below.

$\displaystyle\\{\begin{array}[]{l}P_{i,j,k|i,j,k+1}=(1-Q_{i})(1-q_{i})\\\
j\in[0,L],~{}k\in[0,W_{i,j}-2]\end{array},$ (2c)
$\displaystyle\\{\begin{array}[]{l}{P_{i,j,k|i,j,k}}=(1-{Q_{i}}){q_{i}}+{Q_{i}}\\\
~{}j\in[0,{L}],~{}k\in[1,{W_{i,j}}-1]\end{array},$ (2f)
$\displaystyle\\{\begin{array}[]{l}{P_{i,0,k|i,j,0}}=\frac{{(1-{Q_{i}})(1-{q_{i}})}}{{{W_{i,0}}}}\\\
~{}j\in[0,{L}-1],~{}k\in[1,{W_{i,0}}-1]\end{array},$ (2i)
$\displaystyle\\{\begin{array}[]{l}{P_{i,0,k|i,{L},0}}=\frac{1}{{{W_{i,0}}}}\\\
~{}k\in[1,{W_{i,0}}-1]\end{array},$ (2l)
$\displaystyle\\{\begin{array}[]{l}{P_{i,j,k|i,j-1,0}}=\frac{{(1-{Q_{i}}){q_{i}}+{Q_{i}}}}{{{W_{i,j}}}}\\\
~{}j\in[1,{L}],~{}k\in[0,{W_{i,j}}-1],\end{array}$ (2o)

where $P_{i_{1},j_{1},k_{1}|i_{0},j_{0},k_{0}}$ is a short notation and it is
defined as

$\begin{split}&P_{i,j_{1},k_{1}|i,j_{0},k_{0}}~{}=\\\
&~{}P\\{i,~{}s(t+1)=j_{1},~{}b(t+1)=k_{1}~{}|~{}i,~{}s(t)=j_{0},~{}b(t)=k_{0}\\}.\end{split}$
(3)

The equation (2a) means that the backoff counter deceases in the beginning of
each time slot with the probability that the device stays in the coverage area
and the channel is idle at the same time. (2b) tells us the probability that
the device stays in the same stages because it quits the coverage or the
channel is sensed busy. (2c) and (2d) represent the probability that the
backoff stages return to 0 from the former stages. For devices in stages
$(i,j,0)$, they will transmit to $(i,0,k)$ after a successful transmission or
quit the network. For the stages in $(i,L,0)$, they will return to stages 0
anyway. The last equation gives the probability of rescheduling a contention
state after an unsuccessful transmission.

Figure 2: Markov chain model.

###  II-C Quitting Probability

Since the mobility of the UBS, the devices on the ground will quit the access
process if it is removed from the signal coverage. To model this special
scenario, a new concept called quitting probability is proposed to define this
quitting behavior. Since the devices have different communication durations
with the UBS, their packets for transmission will go through the Markov
process for different times. The longer they stay in UBS’s coverage, the
higher probability they can transmit packets successfully because they have
higher opportunities to retry the network access.

To calculate the quitting probability of the devices in cluster
$\mathbb{C}_{i}$, we first consider a situation where a packet traverses all
the backoff stages, which indicates that the device does not quit the network
in the whole access process. In this case, the transmission state transfers to
state $(i,L,0)$. Here we use $P_{b}$ to denote the stationary probability of
state $(i,L,0)$. Obviously, $(1-P_{b})$ represents the probability that the
packet quits the access process during the process.

While for cluster $\mathbb{C}_{i}$, the quitting probability ${Q_{i}}$ can be
defined as the probability that the device quits the access process after
$m_{i}$ times, where $m_{i}$ shows the maximal access times for cluster $i$.
Accordingly, ${Q_{i}}$ can be shown as

${Q_{i}}={(1-{P_{b}})^{{m_{i}}}},$ (4)

where $m_{i}=\frac{{{T_{i}}}}{\Delta}$. ${\Delta}$ is the time duration after
the packet traverses all the stages and the details can be find in Section
II-D.

By introducing the quitting probability into the Markov chain model, we can
insight the transmission process in the UAV-based network.

###  II-D The Division of the Devices Clusters

${q_{i}}=1-\prod\limits_{h=1}^{i-1}{(\sum\limits_{n=0}^{\infty}{{f_{h}}(n)}{{(1-{\tau_{h}})}^{{n_{h}}}})(\sum\limits_{n=1}^{\infty}{{f_{i}}(n)}{{(1-{\tau_{i}})}^{n-1}}})\prod\limits_{h=i+1}^{N}{(\sum\limits_{n=0}^{\infty}{{f_{h}}(n)}{{(1-{\tau_{h}})}^{{n_{h}}}})}$
(19)

${b_{i,j,k}}=\frac{{{W_{i,j}}-k}}{{{W_{i,j}}}}\left\\{{\begin{array}[]{*{20}{l}}{(1-{q_{i}})(1-{Q_{i}})\sum\limits_{j=0}^{{L_{j}}-1}{{b_{i,j,0}}+{b_{i,{L},0}},~{}j=0}}\\\
{[{q_{i}}(1-{Q_{i}}){\rm{+}}{Q_{i}}]{b_{i,j-1,0}},~{}j\in[1,L]}\end{array}}\right.$
(20)

${b_{i,0,0}}=\frac{{2{P_{a}}{P_{b}}}}{{2{W_{i,0}}{P_{eq}}[{P_{a}}(1-{{(2{P_{eq}})}^{{L}}})-(1-P_{eq}^{{L}}){P_{b}}]+2{P_{b}}(1-P_{eq}^{{L}+1})+{P_{b}}[(1-{q_{i}})(1-{Q_{i}})(1-P_{eq}^{{L}})+{P_{a}}P_{eq}^{{L}}]({W_{i,0}}-1)}}$
(22)

As mentioned before, the devices in different locations have different time to
access the UBS. To insight the network property, we divide the devices into
different clusters according to how many times they can traverse the whole
Markov process. For example, one device will be allocated into the cluster
$\mathbb{C}_{i}$ if it can traverse the Markov process for $l_{i}$ times. Here
$l_{i}$ can be expressed as

$l_{i}=\left\lfloor\frac{{T_{i}}}{\Delta}\right\rfloor=\left\lfloor\frac{{2Rcos\theta_{i}}}{v*\Delta}\right\rfloor,$
(5)

where $\left\lfloor x\right\rfloor$ represents the rounding down to $x$.
$\Delta$ is the time for a packet to traverse all the Markov stages. According
to [11], $\Delta$ is shown as

$\begin{split}\Delta=&E({B_{i}})\delta+E({F_{i}})[\frac{{{P_{si}}}}{{{P_{bi}}}}{T_{s}}+\frac{{({P_{bi}}-{P_{si}})}}{{{P_{bi}}}}{T_{c}}]\\\
&+{L}({T_{c}}+{T_{o}}),\end{split}$ (6)

where ${P_{si}}$ and ${P_{bi}}$ are the probabilities that the devices in
$\mathbb{C}_{i}$ transmit a packet successfully and the probability that there
is at least one device transmitting the packet, respectively. ${B_{i}}$
represents the total number of backoff counter and $E({B_{i}})$ is the average
number of backoff counter during the backoff stage, which can be shown as

$E({B_{i}})=\sum\limits_{j=0}^{{L}}{\frac{{{W_{i,j}}-1}}{2}}.$ (7)

Assume that ${F_{i}}$ is the overall time when the counter freezes and
$E({F_{i}})$ is shown as

$E({F_{i}})=\frac{{E({B_{i}})}}{{1-{q_{i}}}}{q_{i}}.$ (8)

Let $T_{s}$ and $T_{c}$ in (6) denote the average time that the channel is
sensed busy and the average time for a collision. $T_{o}$ is the time that a
device has to wait after the access collision before the next channel sensing.

Here the basic access mechanism is a two-way handshaking technique while the
RTS/CTS is a four-way handshaking technique, which are the most common
mechanisms in 802.11 [12] and [13]. The definitions of $T_{s}$, $T_{c}$ and
$T_{o}$ are different in the basic access mechanism and RTS/CTS mechanism. For
clarity, we use $T_{s}^{b}$, $T_{c}^{b}$, $T_{o}^{b}$ and $T_{s}^{r}$,
$T_{c}^{r}$, $T_{o}^{r}$ to denote the parameters in basic access mechanism
and RTS/CTS mechanism, respectively. Then, we have

$T_{s}^{b}=T_{\rm{H}}+T_{\rm{E}}+\rm{SIFS}+T_{\rm{ACK}}+\rm{DIFS}+2*\delta,$
(9) $T_{c}^{b}=T_{\rm{H}}+T_{\rm{E}}+\rm{DIFS}+\delta,$ (10)
$T_{o}^{b}=\rm{SIFS}+T_{\rm{ACK\\_timeout}},$ (11)
$\begin{split}T_{s}^{r}=&T_{\rm{RTS}}+T_{\rm{CTS}}+T_{\rm{H}}+T_{\rm{E}}+3*\rm{SIFS}+\\\
&T_{\rm{ACK}}+\rm{DIFS},\end{split}$ (12)
$T_{c}^{r}=T_{\rm{RTS}}+\rm{SIFS}+T_{\rm{ACK}}+\rm{DIFS},$ (13)
$T_{o}^{r}=\rm{SIFS}+T_{\rm{CTS\\_timeout}},$ (14)

where $T_{\rm{H}}$, $T_{\rm{E}}$, $T_{\rm{ACK}}$, SIFS, DIFS, $T_{\rm{RTS}}$
and $T_{\rm{CTS}}$ denote the time to transmit the header (including MAC
header, physical header), the time to transmit a payload with length E, the
time to transmit an ACK, the time durations of a SIFS and DIFS, and the time
to transmit a RTS and CTS , respectively. $T_{\rm{CTS\\_timeout}}$ and
$T_{\rm{ACK\\_timeout}}$ denote the duration of the ACK and CTS timeouts
respectively. $\delta$ denotes the duration for an idle time slot.

Under this division strategy, the devices located in the center band of the
UBS’s coverage can connect with the UBS for the longest time. If these devices
repeat the backoff process for $N$ times, they belong to the cluster
$\mathbb{C}_{N}$ and $N=\left\lfloor\frac{t_{N}}{v*\Delta}\right\rfloor$. In
this way, all the devices in the coverage can be divided into $N$ clusters and
each devices in the cluster $\mathbb{C}_{i},(i=1,2,...,N)$ can repeat the
Markov process for $i$ times.

On the other hand, we assume the devices are uniformly distributed in the
UBS’s coverage with density $\rho$, the number of the devices in the area
follows the Poission distribution according to [14]. The probability that
there are $n$ devices in the cluster $\mathbb{C}_{i}$ can be shown as

${f_{i}}(n)=\frac{{{{(\rho{A_{i}})}^{n}}{e^{-\rho{A_{i}}}}}}{{n!}},n=0,1,2,...,\infty,$
(15)

where ${A_{i}}$ is the area of $\mathbb{C}_{i}$. This distribution can help us
to analyze the saturation throughput of the network in the following section.

##  III Performance Analysis

This section analyzes the Markov chain process and gives the solution of the
saturation throughput.

###  III-A Markov Chain Process Analysis

Before the analysis, we first define the stationary distribution of the chain
${b_{i,j,k}}$ as

$\begin{split}{b_{i,j,k}}=&\mathop{\lim}\limits_{t\to\infty}P\\{cluster=i,s(t)=j,b(t)=k\\},\\\
&~{}j\in[0,L],~{}k\in[0,{W_{i,j}}].\end{split}$ (16)

Then, for a device in the cluster $i$, we get

${b_{i,j,0}}={P_{eq}}{b_{i,j-1,0}}=P_{eq}^{j}{b_{i,0,0}},~{}{\rm{j}}\in{\rm{[0,}}{{\rm{L}}_{\rm{i}}}{\rm{]}},$
(17)

where $P_{eq}$ can be expressed as

$P_{eq}=(1-{Q_{i}}){q_{i}}+{Q_{i}},$ (18)

where $q_{i}$ is the probability that the channel is busy when the device is
in the backoff stage. During the access process, according to the CSMA/CA
protocol, once a device in the cluster $\mathbb{C}_{i}$ connects to the UBS,
other devices either in the cluster $\mathbb{C}_{i}$ or not cannot transmit
information to the UBS. Combining the Poission distribution of the number of
the devices in (15), we can calculate the $q_{i}$ as (19).

According to the chain regularities, each value of the backoff counter
$k\in[1,{W_{i,j}}-1]$ can be obtained by (20).

By substituting (17) in (20), all the values ${b_{i,j,k}}$ can be expressed as
a function of ${b_{i,0,0}}$. Then, considering the normalization condition, we
can easily obtain:

$\begin{split}1&=\sum\limits_{j=0}^{{L}}\sum\limits_{k=0}^{{W_{i,j}}-1}{{b_{i,j,k}}}\\\
&=\sum\limits_{j=0}^{{L}}{{b_{i,j,0}}}+\sum\limits_{k=1}^{{W_{i,j}}-1}{{b_{i,0,k}}}+\sum\limits_{j=1}^{{L}}\sum\limits_{k=1}^{{W_{i,j}}-1}{{b_{i,j,k}}},\end{split}$
(21)

where ${P_{a}}=(1-{P_{eq}}),{P_{b}}=(1-2{P_{eq}})$. Therefore, we can obtain
the expression of $b_{i,0,0}$, as shown in (22).

According to the Markov chain, the devices stop the transmission when their
backoff counters decrease to 0. Thus, the probability $\tau_{i}$ that one
device in the cluster $i$ transmits a packet in a randomly selected time slot
can be shown as:

${\tau_{i}}=\sum\limits_{j=0}^{{L}}{{b_{i,j,0}}=\frac{{1-P_{eq}^{{L}+1}}}{{1-{P_{eq}}}}{b_{i,0,0}}}.$
(23)

By combining (19) and (23), we can calculate the value of parameters
$\tau_{i}$ numerically.

###  III-B Saturation Throughput Computation

Let $P_{tr}$ be the probability that there is at least one device doing the
transmission for a certain time. According to [9], it can be shown as

${P_{tr}}=1-\prod\limits_{h=1}^{N}{(\sum\limits_{n=0}^{\infty}{{f_{h}}(n)}{{(1-{\tau_{h}})}^{n}})}.$
(24)

For the devices in cluster $\mathbb{C}_{i}$, the probability of successful
transmission $P_{s_{i}}$ can be calculated as

$\begin{split}{P_{{s_{i}}}}=&\left[\sum\limits_{n=1}^{\infty}{{f_{h}}(n)}n{\tau_{i}}{(1-{\tau_{i}})^{n-1}}\right]\times\\\
&\prod\limits_{h=0,h\neq
i}^{N-1}\left[{\sum\limits_{n=0}^{\infty}{{f_{h}}(n)}{{(1-{\tau_{h}})}^{n}}}\right].\end{split}$
(25)

Therefore, in the whole coverage, the overall probability ${P_{s}}$ of
successful packet transmission to UBS can be shown as
${P_{s}}=\sum\limits_{i=1}^{N}{{P_{{s_{i}}}}}$. Finally, by combining (24) and
(25), the throughput of the network can be shown as

$S=\frac{{{P_{s}}{P_{tr}}E[P]}}{{(1-{P_{tr}})\sigma+{P_{s}}{P_{tr}}{T_{s}}+{P_{tr}}(1-{P_{s}}){T_{c}}}}.$
(26)

##  IV Simulation and Numerical Results

In this section, we validate our system model firstly by comparing the
theoretical results with those obtained by the Monte Carlo simulation. Then,
the effects of the network parameters, such as UBS’s velocity and the density
of the devices, on the throughput are analyzed. An idle time slot $\delta$ is
50$\mu s$, ${\rm{ACK}_{\rm{timeout}}}$= 300 $\mu s$,
${\rm{CTS}_{\rm{timeout}}}$= 300 $\mu s$, ACK= 112 $\mu s$, RTS= 160 $\mu s$,
CTS= 112 $\mu s$, SIFS=28 $\mu s$, DIFS= 128 $\mu s$. Assume the channel data
rate is equal to $1Mbit/s$ and the frame size , denoted by EP, is fixed at
$8k$ Bytes. The radius of the coverage is assumed to be 1000m unless stated
otherwise.

Figure 3: Saturation throughput vs. velocity of the UBS.

Fig. 3 indicates the normalized saturation throughput versus the velocity of
the UBS under different parameters for the theoretical model and the
simulation, marked as ‘Mod’ and ‘Sim’ in legends respectively. To fully verify
the network performance, we validate the results in both basic access and
RTS/CTS cases. The user density in this simulation is $\rho=50/{km}^{2}$ and
the retry limit is $L=7$ for all devices. In addition, we adopt two values of
the initial contention window size ($CW_{min}=8,16$) to explore the network
performance. It is clear to see that the theoretical results (lines) match the
simulation results (symbols) well, which perfectly confirm our model.
Moreover, the saturation throughput of proposed model decreases with the
increasing of the UBS’s velocity. This is because the device can connect with
the UBS for a shorter time when the UBS flies faster. It is hard for all the
devices to access the channel and fewer packets can be transmitted
successfully because of the short communication duration, leading to the the
lower throughput.

In Fig. 4(a), we plot the normalized saturation throughput vs. the density of
the devices for both basic access and RTS/CTS mechanisms under two different
UBS’s velocities ($v=10,20m/s$). The density of the devices increases from
$50/{km}^{2}$ to $100/{km}^{2}$. It can be seen that the density of the
devices influences the performance negatively. The throughput decreases along
with the increase of the devices’ density. This is because with the constraint
of the spectrum resource, the more devices participate in the access process
at the same time, the more access collisions will happen, which makes it
harder to transmit a packet successfully and result in the lower throughput.
In addition, by comparing the throughput of those two mechanisms, we can find
that the RTS/CTS performs better than the basic access mechanism in saturation
throughput. Compared with the basis mechanism, RTS/CTS is designed to combat
the problem of hidden terminal and it can reduce the duration of a collision
to increase the system performance. Therefore, RTS/CTS is more likely to give
better performance than the basic one especially when long messages are
transmitted.

(a) Density of the devices.

(b) Retry limit.

Figure 4: Saturation throughput vs. device density and retry limit.

In the simulations, we also implement some experiments to analyze the
influence of the retry limit on the saturation throughput for both basic
access and RTS/CTS mechanisms, shown in Fig. 4(b). From Fig. 4(b), we can see
that the increase of the retry limit (from 7-14) has negative impact on the
throughput. It is because that the devices have more opportunities to retry
the transmission with larger retry limit, which will cause more collisions and
it is more difficult to transmit a packet successfully in the network. As a
result, the throughput will be influenced negatively.

(a) Initial contention window size.

(b) UBS’s coverage.

Figure 5: Saturation throughput vs. initial contention window size and UBS’s
coverage.

The impacts of the initial contention window size are also analyzed in Fig.
5(a). According to Fig. 5(a), we can conclude that the effects of the initial
contention window size is serious. For basic access mechanism, the throughput
declines to almost zero when the initial contention window size climbs to 256.
For RTS/CTS mechanism, the effects cannot be ignored either. The throughput
drops to below 0.1 in this scenario. The reason is that if the initial
contention window increases, the devices will spend more time in the backoff
process. Therefore, the channel is more likely to stay in idle state, causing
the waste for the part of the channel resource. On the other hand, the
transmission delay will be longer for larger window size which also influences
the throughput performance.

Finally, the impacts of UBS’s coverage are considered. Since the UBS’s
coverage is a circle, we just analyzes the effects of the radius of the
coverage. Here we set the density of the devices is $\rho=50/{km}^{2}$ and the
radius of the coverage increases from 1000 m to 2000 m. The results for basic
access mechanism and RTS/CTS mechanism are given in Fig 5(b).

The throughput drops with the increasing of the radius both in basic access
mechanism and RTS/CTS mechanism. For larger coverage area, more devices will
connect with the UBS and transmit the packet simultaneously, leading to the
more congestion. Accordingly, the system’s throughput decreases both for basic
and RTS/CTS mechanisms. Though both increasing the density of the devices and
UBS’s coverage radius enlarge the number of the devices that the UBS serves,
there is sitll some difference between these two methods. The larger coverage
not only increases the number of the devices, but also improves the
communication duration between the devices and the UBS. Thus, the results are
different between Fig. 4(a) and Fig. 5(b).

##  V Conclusions

In our paper, a scenario where a UBS flies straightly to collect data from a
set of IoT devices is considered. Based on the characteristics of the UAV-
based network, we propose a quitting probability and develop a Markov chain
model to calculate the saturation throughput of CSMA/CA in this UBS data
collection system. In addition, we also analyze the impacts of different
network parameters including retry limit, initial contention window size,
UBS’s velocity, the density of the devices and the UBS’s coverage.

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