Coverage and Capacity Analysis of LEO Satellite
Network Supporting Internet of Things
Haotian Zhou, Liang Liu, Huadong Ma
Beijing Key Laboratory of Intelligent Telecommunication Software and Multimedia Beijing University of Posts and Telecommunications, Beijing, China
Email:{zhouhaotian, liangliu, mhd}@bupt.edu.cn
Abstract— In this paper, we focus on the coverage and capacity
analysis for LEO satellite network supporting Internet of Things. We propose a metric of coverage degree to measure average cover level during a return circle of a satellite constellation in different latitudes, and furter consider the spot beam communication process with TDMA as a discrete time queueing process to caculate the number of devices in a unit area, which can be accessed during a period. Finally, we derive the relationship among device density, maximum tolerant delay, and coverage degree of the satellite constellation. The obtained theoretical results are verified by extensive simulation experiments.
I. INTRODUCTION
With the coming of IoT Era, massive devices need to be connected in the future, which may be thousands of times more than that number in current Networks. There are many approaches to deal with this challenge on the ground such as NB-IoT and MIMO. But there still exists many areas, e.g. desert and sea, which cannot be covered by information netowrks, beacuse it is difficult to depoy infrastructures in these areas.
Because of the characteristics of low orbit, large bandwidth, and full coverage, LEO satellite network can provides all-around access not bound by geographic positions. It provides an effective way to connect IoT devices which are deployed in inaccessible areas. Then, LEO satellite network supporting Internet of Things (LEO-IoT for short) has attracted many attentions recently. Paper [1] proposes the concept of Internet of Remote Things and discusses issues and solutions of satellite communication systems supporting IoT in different application scenarios. Paper [2] gives an overview on LEO satellite constellation structure for Internet of Things, and discusses the issues of spectrum allocation, heterogeneous networks compatibility and etc.
However, there are still a lot of problems that have not been considered in previous researches. Polar orbit or near-polar orbit usually used in LEO satellite constellations will result in uneven coverage with different latitudes. Because all orbits meet near the two poles, satellite constellation provide relatively dense and sparse covarage for polar and equator regions, respectively. This uneven coverage restricts the number of devices which can be accessed in the network because of the using of spot beam antennas controlled by phased array targeting at high antenna gain.
It is important to model the uneven coverage for quan-titatively analyzing the relationship between parameters and
performance of LEO-IoT. It can also solve many problems in LEO satellite network design and applications. For example, in different latitudes, how many users can be served at the same time or how many satellites are needed to serve a certain amount of users. In this paper, we focus on two problems that 1) how to measure the uneven coverage with the change of latitude and 2) how many IoT devices can be accessed simultaneously with the change of coverage.
To solve the problems, we first proposed a metric of Cov-erage Degree to measure avCov-erage cover level during a return circle of a satellite constellation in different latitudes. We use an indicator function to represent whether the observation point is covered with a satellite. Second, considering the spot beam communication process with TDMA as a discrete time queueing process, we put forward the metric of Device Density to express the number of devices can be accessed in a unit area during a period. Finally, we derive the relationship between device density and some important parameters such as maximum tolerant delay and the coverage degree of the satellite constellation. We use STK 10 and MATLAB to simulate the satellite constellation and the access process of IoT devices. The experiment result shows that the coverage and the capacity are influenced by many factors.
The contribution of this paper lies below:
• We set up the coverage model of LEO-IoT which can quantificationally describe the coverage level of the LEO satellite network to the earth. It gives an analyzable result to future researches on the deployment of LEO satellite network which aims to support large-scale IoT devices. • We come up with the concept of device density to
define the relationship between device number and other parameters which will guide collaboratively disposition of LEO satellite network and IoT. Precisely, that can be of great significance in guiding how to support more IoT devices with less LEO satellites.
• We use simulated experiments to verify our models. With the increasing of latitude, the coverage changes more and more sharply. The user number that can be accommodated by the system tends to increase when the number of beams and slots increase. The average waiting time tends to decrease when the number of beams increases or that of slots decreases.
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II. RELATEDWORK
Since the birth of the artificial satellite in the 1950s, scien-tists around the world begin to research on satellites. With the development of artificial satellite technology, more and more satellites are launched to form Networks in the space. Satellite Networks are applicated in many fields, such as TV, naviga-tion, telecommunication and so on. People are also beginning to study on the coverage problem of the ground by satellite networks. Walker first derived the relationship between the minimum number of satellites and ground coverage in [3] at 1970, which solved continuous coverage problem using circular orbit. Then he further came up with delta constellation in [4], which is a classic constellation model. Later Beste first studied on the design of constellations for optimal continuous coverage to the earth in [5]. He came to the conclusion about the relationship between the number of satellites, latitude and coverage radius of satellites. In 1980 Ballard designed Rosette constellations in [6], which further enriched the configuration of the satellite constellation. The above research is mainly focused on how to continuously cover the earth continuously. Draim focused on how to achieve continuous full coverage of the earth with fewer satellites in [7]. He designed a satellite constellation using only four satellites. Matossian discussed the constellation generation algorithm in [8] for low or medium orbit small satellites and took into account multiple situations of full coverage and partial coverage. Later people begin to use algorithms to generate parameters of the satellite constellation. He Quan did a research on optimize constellation parameters using Ant System Algorithm in [9]. Cui used Hermite interpolation technique and ordinal optimization to optimize the satellite constellation configuration design in [10]. Yuri considered continuous or discontinuous coverage for a geographic area for practical application in [11]. William applied GRIPS on solving complex cover missions in satellite constellation design in [12]. Li did a research on coverage performance of LEO satellite constellation in 2016 in [13]. This article presents an indicator for assessing the coverage performance of LEO constellations using a method similar to scoring a golf course. But it thinks that the smaller the coverage overlap between satellites, the better the coverage performance. This article only focused on how to realize full coverage of the satellite constellation to the earth rather than how to provide multi-coverage as more as possible.
III. MODELASSUMPTIONS
Some assumptions in our model are introduced in this section. There is an LEO satellite network overhead the earth with inter-satellite links which is responsible for the realization of multi-hop communication (see Fig. 1). Every satellite has four laser links with two inner-orbit satellites in the front and back and two inter-orbit satellites in the left and right. The satellite constellation use polar orbit or near-polar orbit and all orbits are circular orbits. There are n orbital planes and m satellites in each orbit. The total amount of satellite in the constellation isI = m × n.
Fig. 1. Communication scenario of satellite network and users.
Users on the ground use terminals which have receiving antenna to communicate with the satellite network. Users can deliver all kinds of data to the satellite network. The data can be any size: up to multimedia data and down to sensor data. Suppose any user can request a communication at any time so the number of users is unlimited.
There are four channels between satellites and terminals on the ground for communication: uplink signaling channel, downlink signaling channel, the uplink traffic channel and downlink traffic channel. Satellites use the low gain broadcast antenna in downlink signaling channel to broadcast downward signaling. Terminals on the ground use the high gain antenna in uplink signaling channel to upload communication requests. In traffic channel, satellites use spot beams to send and receive downlink and uplink data. Phased array is used to control directions of spot beams on satellites. Spot beams can accurately point to a terminal by the phased array through changing phases of beams. Spot beams can hops from one direction to another only using few milliseconds which can be ignored. TDMA (Time Division Multiple Address) is used in every spot beam to serve more users in the meantime. One frame is divided into many slots and every slot can be assigned to different users. The beam will be controlled by the phased array at the beginning moment of the slot to jump from one user to another beam in one satellite and its adjacent satellites use different frequencies so collision will not occur when two beams point to the same position at the same time. That is, using TDMA + FDMA + SDMA (Space Division Multiple Address), b beams in each satellite and s slots in one frame in a beam can provide at most K = b × s accesses by one satellite at the same time.
The communication process includes two parts: the access process and the data transmission process. When a user what to communicate with another user or a server, he should first join into the satellite network. Through the uplink signaling channel, user send an access request using a terminal by the high gain antenna. Satellites in the network which keep listening to signals from the ground receive the request and execute access operations. Access operations include identi-fication, IP allocation and channel allocation. The satellite network verifies the identity of the user by searching the identification code on the terminal who initiated the request
3 6
Fig. 2. The covered area of a satellite.
6
6
Fig. 3. The overlap part of two satellites’ covered area.
in its identity database. After the identification, the satellite which is currently connected to the terminal allocates an IP address to this terminal for next communication process. Then the satellite checks if there are available slot can be provided to the terminal in the traffic channel. If yes, the available slot is allocated to the terminal. Otherwise, the terminal should wait until there is a new available slot released. Users queue to wait for slots according to the FIFO (First In First Out) rule. Once a terminal obtains a slot by the satellite, it begins transmit data through the traffic channel according to the time division multiplexed protocol. When all the data of the user has finished transmission by the terminal, the slot will be released for another terminal.
IV. COVERAGE
With such a satellite-terrestrial communication network as described in the last chapter, the coverage degree of the satellite network to the ground has become an important indicator on measuring communication capabilities of this satellite network. However, since orbital planes of the polar or near-polar orbit meet at two poles, the coverage of the earth by the entire satellite network is uneven. The coverage area of a satellite’s signal to the ground is a spherical crown which is the red part shown in Fig. 2. In order to realize full coverage on the earth, there must be overlap part among two or three satellites’ cover areas (shown in Fig. 3). The higher the latitude, the larger the overlap area of adjacent satellites. So the uneven level is higher near two poles. In order to quantify the uneven level, we introduce a concept of Coverage Degree to describe the variation of satellite density with latitude.
Definition 1: During a period T , a region on the earth in a certain latitude is covered by how many satellites on average is defined as Coverage Degree D on this latitude of the satellite network.
Because the coverage to every point on the earth of the satellite network is uneven at the same time, we consider an average coverage level during a period. The periodT is the regression period of the satellite network. Regression period refers to the period taken by a satellite to pass the same substellar point twice. But not all satellite networks are regressive. Actually, regressive satellite constellation is only an idea condition because of the orbit perturbation and the gravity. Hence, we consider a long period as an approximate regression period.
To quantificationally express Coverage Degree of a satellite network in different altitude, we count how many satellites
2
DL
5© ¶
Fig. 4. Use spherical coordinates to express a point on the earth.
2 6
¸
Fig. 5. Half cone angleψ.
covered an area in a certain latitude during an approximate regression periodT . We introduce an indicator function Ii(t) to show the visibility of the satellite i to the ground. If a satellite is visible to a specified point on the ground at time t, it’s indicator function equals 1, otherwise it’s indicator function equals 0. A satellite is visible to the specified point on the ground means that the point is in the communication radius of the satellite, which implies the point is covered by the satellite. Then, the indicator function
Ii(t) =
1, e ∈ Aiat timet, 0, e /∈ Aiat timet,
(1) wherei is the serial number of the satellite. e is the coordinates of the observation point. Ai is a point set of all points within the coverage area of satellite i.t ∈ T , T is the approximate regression period of the satellite network. We use spherical coordinates to express a point on the earth surface just with its latitude and longitude(see Fig. 4). The substellar point of satellite i can be express in ai(R, θi, Φi), in which
⎧ ⎪ ⎨ ⎪ ⎩ R = earth radius θ =π2− latitude Φ = longitude (2)
The point set Ai of all points within the area covered by satellite i can be express in:
Ai={x(R,θ,Φ)|sinθsinθicos(Φ−Φi)+cosθcosθi≤cosψ}, (3) where ψ is the half cone angle of the covered area to the earth’s core. It is shown in Fig. 5.
For every point e(R, θj, Φ) (shown in Fig. 6), integrate the indicative function Ii(t) of all satellites in the satellite network during the regression periodT . We can obtain average numbers covered by the satellite network refer to different latitudes, that is, Coverage Degree D.
D = 1 T T i Ii(t)dt. (4)
Azimuth angle Φ of point e is a certain longitude because Coverage Degree D is uniform in the longitude direction due to periodic rotation of the earth and satellites in the regression period. Coverage Degree D only changes with latitude θj.
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Fig. 6. Find Coverage Degree of point e with different latitude.
V. CAPACITY
Due to the uneven of coverage to every point on the earth of the satellite network at the same time, the capacity of the satellite network is also uneven. That is, how many users can be served by the satellite network at the same time is uneven at different places on the earth because of the uneven coverage of the satellite network. At a moment, the maximum number of served users in the meantime in a certain area covered by two satellites is two times than that covered by one. That is, when an area is covered by k satellites, the maximum served user number turns into k times. We introduce a concept named Device Density N to describe the system Capacity quantitatively. We define the Device Density N as follow:
Definition 2: In a period time Delay, the maximum number of device averagely accessed in the meantime in a unit area on a certain latitude is called Device DensityN of that latitude. If that area is covered only by a satellite, it’s Device Density is called Basic Device DensityN0 of the latitude.
In definition 2, the period timeDelay is the maximum trans-mission delay tolerated by users. The unit area is considered as the region we defined in definition 1. According to the aforementioned relationship between Device Density N and Coverage Degree D, we obtain the relationship between Basic Device DensityN0 and them of the same latitude:
N = D × N0. (5)
To calculate Basic Device Density N0 quantitatively, we
abstract the communication access process as a discrete time queuing model. This is a multi-servers queuing system of the access process in a satellite. Servers provide services according to the FIFO(First-in-First-out) rule. The arrival process of users obeys geometric distribution. A user will wait in a queue if servers are full when it arriving. Every server can serve multiple users in the same frame using the Time-Division Multiplexing. The service time of every user’s traffic also obeys geometric distribution. Users are considered to arrive only at the beginning of a frame and to leave at the ending of a frame.
This is a Geom/G/b discrete time queuing process. The arrive process is a Bernoulli process with a parameterp(0 < p < 1), so the arrival interval obeys geometry distribution with the parameter p. Service time, or the departure interval
of users, is a general distribution because of the Time-Division Multiplexing used in every server. The service time of every service is independent identically distributed. It’s distribution, mean and PGF(Probability Generating Function) are:
dk= P {S = k} , k ≥ 1, d = E(S). (6) G(z) = E(zS) = ∞ k=1 zkdk. (7)
The arrival interval and the service time of every service are independent. The number of servers is b, which is exactly number of beams on a satellite. The average waiting time of this queuing process is the maximum tolerant delay of users. The average length of the queue when the system tends to be steady is the maximum accessed user number.
We use{Qn, n ≥ 0} to express the number of users in the system at moment n. The user who leaves at the moment n does not count inQn. Because the leaving process of the queue system does not obey the geometry distribution, Qn is not a Markov Chain. So we only focus on the moment when a user leaves. Use the embedded Markov Chain method to solve the queue problem. Let Ln be the number of users in the system at the moment after the nth user leaves the system. Then Ln is a Markov Chain and it is the embedded Markov Chain of Qn. Ln+1= Ln− x + A, Ln≥ 0, A, Ln = 0, (8)
where A is the number of arrived users during a leaving interval. b × s ≥ x ≥ 0. The distribution of A is:
aj=P{A =j}= ∞ r=j
P {S = r}P {j users arrive in r frames} = ∞
r=j
drrj pjpr− j,
(9)
wherep = 1 − p. The PGF(Probability Generating Function) of A is: A(z) = ∞ j=0 zjaj= ∞ r=1 dr(p + pz)r= G[λ(z)], (10)
where λ(z) = p + pz and the average arrived user number during a departure interval is:
ρ = E(A) = A(1) = pd, (11)
whereρ is the ratio of average service time and average arrival interval. Then, we can write the probability transfer matrix of
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the Markov ChainLn. The probability transfer matrixP is:
P = ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ k0 k1 k2 k3 k4 · · · k0 k1 k2 k3 k4 · · · k0 k0 k1 k2 k3 · · · k0 k0 k0 k1 k2 · · · .. . ... ... . .. ... ··· k0 k0 k0 k0 k0 · · · 0 k0 k0 k0 k0 · · · 0 0 k0 k0 k0 · · · .. . ... . .. ... ... ... ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ ,
where the number ofk0 in the first column equals K + 1.
Ifρ < 1, the distribution of stable queue length exists. The steady state equation is:
Π · P = Π, (12)
whereΠ = {πj, j ≥ 0} denotes the distribution of the steady state. SubstituteP into above equation we obtain:
πj = π0kj+ j+1 r=1 πrkj+1−r+ (K − 1)k0 j+K h=j+2 πh. (13) To obtian the PGF of the length of the queue when the queuing system is under steady state, we multiplyzj on both sides and sum onj:
L(z)= ∞ j=0 zjπj=π0 ∞ j=0 zjkj+ ∞ j=0 zj j+1 r=1 πrkj+1−r + (K − 1)k0 ∞ j=0 zj j+K h=j+2 πh =π0A(z)+1 z[L(z)−π0]A(z)+(K−1)k0[(K−1)L(z) − (K − 1)π0− K−1 h=1 (K − h)zhπ h]. (14)
Using the normalization conditionL(1) = 1, we derives: (K − 1)π0+
K−1 h=1
(K − h)πh= K − 1. (15)
From Eq. (12) and Eq. (15) we can obtain thatπh(K −1 ≥ h ≥ 0) has a solution but it is hard to express in a general term. We will further discuss it in experiment part with specific numerical values.
Then L(z) can be derived and the PGF W (s) of waiting timeW can be calculate from:
L(z) = W (s)G[λ(z)], s = λ(z). (16)
To obtain the average waiting time and the average queue length, we need to calculate the general distribution dk. We first focus on one server using Time-Division Multiplex-ing. The business package length of users is independent identically distributed and obeys geometry distribution with parameter μ. It’s distribution is μμm−1, (m ≥ 1), thereinto,
μ = 1 − μ. It means the probability of service time lasting m slots in m frame is μμm−1. Therefore, the distribution of leaving interval in a server P {l = k} is:
∞ i=1
P {le1= i} P {le2− le1= k|le1= i} = ∞ i=1 P {le1= i}P {le2= k + i, le1= i} P {le1= i} = μ 1 − μμk. (17)
In Eq. (17), le1 and le2 express the moment when the first
and second departing users leave respectively.
We can further obtain the distribution of dk = P {S = k}: ∞ i=1 P {Sl1= i} P {Sl2− Sl1= k|Sl1= i} = ∞ i=1 P {Sl1= i}P {Sl2= k + i, Sl1= i} P {Sl1= i} = μk+2 1 + μ3. (18)
The mean ofdk is:
d = E(S) = G(1) = 2μ
4(2 − μ2)
(1 − μ)2(1 + μ)5. (19)
Combine aforesaid results together the average queue length L and average waiting time W can be calculated:
L = L(1), W = W(1). (20)
The average queue lengthL can be seen as N0then the Device
Density N is:
N = D × L. (21)
VI. EXPERIMENT
A. Coverage
We use the Iridium constellation as the example to ana-lyze change properties of Coverage Degree D with different latitudes. The Iridium constellation is an LEO satellite com-munication network with polar circular orbit. There are totally 66 satellites in the Iridium constellation: 6 orbital planes in the constellation and 11 satellites in each orbit. The orbital altitude of the Iridium constellation is about 780 km and the orbital inclination is 86.4◦.
We use STK 10 (Satellite Tool Kit) developed by Analytical Graphics to simulate the satellite constellation. Fig. 7 shows the simulation result of the Iridium system. We set longitudeΦ at0◦ and calculate Coverage DegreeD at different latitudes. Fig. 8 shows the experiment results. The half cone angle ψ is set to 60◦,61◦ and62◦ respectively. The maximum value of the half cone angle ψ is 62◦ because the line between the satellite to the farthest covered point is tangent to the ground when ψ = 62◦. As can be seen from Fig. 8, the Coverage Degree D changes gently at low latitudes. Then it gradually increased in the middle latitudes and rapidly increased near the polar regions. The larger the half cone angle ψ is, the larger the coverage degree. That because the half cone angle ψ of the satellite is larger means the coverage area of a satellite is larger.
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Fig. 7. Iridium system simulated by STK 10.
0 10 20 30 40 50 60 70 80 90 Latitude 0 2 4 6 8 Coverage Degree 62 deg 61 deg 60 deg
Fig. 8. Coverage Degree with different latitudes and half cone angleψ.
B. Capacity
We use MATLAB R2016b to simulate the scenario we described in section 3. There is a full covered LEO satellite network overhead the earth. Its constellation is like the Iridium system. Every satellite use spot beams to communicate with users on the ground using Time-Division Multiplexing. We simulate the scenario for 10 minutes (6 × 105ms). The length
of a slot is 100 ms so there are totally 6000 slots in this experiment. We set the arrival strengthp as 0.6 and the service time parameterμ as 0.1.
Fig. 9 and Fig. 10 show the change of average queue length and average waiting time when beam number and slot number take values from 2 to 6 and 2 to 20 respectively. The results show that with the increasement of the number of slots, the average queue length increases, and the average waiting time also shows an increasing trend. On the other hand, with the increasement of the number of beams, the average queue length increases but the average waiting time tends to decrease. The average queue length increases both when the number of beams and slots increase. This is because more beams and more slots can obviously accommodate more users in the system. However, the trend of the average waiting time is opposite. Because more beams can lead to more users accessing at the same moment, the average waiting time increases with the increasing of beam number. Conversely, the increasement of the slot number implies users need to wait for more slots to be served. This results in the increasement of the average waiting time. To access more users, increase number of slots and beams is a good way. But limited by power and frequency resource on satellites, beam cannot be too much. Moreover, too many slots will make the delay very large. This requires a balance between delay and user number.
VII. CONCLUSION
With the coming of the 5G Era, the average number of devices of everyone that needs to access the Internet is
0 50
6
Average Queue Length 7 5
Beam Number 100 Slot Number 4 3 2 2
Fig. 9. Average Queue Length vs beam number and slot number.
0 1000
6
Average Waiting Time(ms) 7
Beam Number 5 2000 Slot Number 4 3 2 2
Fig. 10. Average Waiting Time vs beam number and slot number.
increasing. As a good complement to the terrestrial network, LEO satellite networks will certainly be used on accessing more IoT devices. This paper looks into the future application of LEO satellite networks together with massive IoT devices. We present a mathematical model describing the coverage of the earth and access capacity of device of the LEO satellite network in that scenario. Simulation experiments are used to show the variation tendency of the coverage and the capacity in different latitudes.
ACKNOWLEDGEMENT
This work was supported in part by National Key R&D Program of China 2017YFB1003000, National Natural Sci-ence Foundation of China (61632008, 61722201), and the 111 Project (B18008).
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