Underlay Drone Cell for Temporary Events: Impact of Drone Height and Aerial Channel Environments

Providing seamless connection to a large number of devices is one of the biggest challenges for the Internet of Things (IoT) networks. Using a drone as an aerial base station (ABS) to provide coverage to devices or users on ground is envisaged as a promising solution for IoT networks. In this paper, we consider a communication network with an underlay ABS to provide coverage for a temporary event, such as a sporting event or a concert in a stadium. Using stochastic geometry, we propose a general analytical framework to compute the uplink and downlink coverage probabilities for both the aerial and the terrestrial cellular system. Our framework is valid for any aerial channel model for which the probabilistic functions of line-of-sight (LOS) and non-line-of-sight (NLOS) links are specified. The accuracy of the analytical results is verified by Monte Carlo simulations considering two commonly adopted aerial channel models. Our results show the non-trivial impact of the different aerial channel environments (i.e., suburban, urban, dense urban and high-rise urban) on the uplink and downlink coverage probabilities and provide design guidelines for best ABS deployment height.

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01/18/2018

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I Introduction

The Internet of Things (IoT) is at present rapidly evolving and will connect a massive number of devices, both machine and human operated, in the near future. The applications of IoT will improve all aspects of our life, ranging from smart homes, such as self-managed household appliances, personal wearables and healthcare, to smart cities, like manufacturing management, infrastructure monitoring and vehicle communications. This requires effective and reliable wireless connectivity, high data rates and ultra low latency. It is not possible to rely solely on the conventional wireless networks (e.g., cellular system) to support IoT. The high data rates and the numerous number of connected network nodes would quickly and constantly overload base stations and put pressure on network resources. Moreover, in locations which experience poor coverage by base stations, IoT devices may not be able to connect to the base station. Furthermore, wireless network coverage may not reach all locations where smaller IoT devices are placed, such as rural areas, forest and sea. In this regard, the use of drones as aerial base stations (ABSs), to form drone cells and to provide flexible and agile coverage is a potential network solution for IoT applications [2, 3, 4, 5].

I-a Motivation

Recently in [2], eight scenarios have been identified for drone cell deployment, with drones providing service to: (i) rural areas, (ii) urban areas, (iii) users with high mobility, (iv) congested urban areas, (v) congested backhaul, (vi) temporary events, (vii) temporary blind spots and (viii) sensor networks. The literature to date [6, 7, 8, 9, 10, 11] has focused on the downlink, generally for Scenarios (i)–(iii). In this work, we focus on the use of drone cell for Scenario (vi), i.e., using ABS to provide additional coverage for temporary events, such as concerts or sports events. Such temporary events are happening more frequently in cities all over the world with very high number of users gathering. A large number of IoT devices are expected to be deployed in a stadium to help the event operators to provide superior experience to event participants efficiently and effectively. For example, security cameras being used to monitor all corners of the venue and keep the crowd safe. Sensors being used to provide up-to-date information on queues for merchandise stalls. Temperature sensors being used to monitor and control the air conditioning system. These devices all need to be connected to the core network. Therefore, assessing the usefulness of ABSs to provide coverage for temporary events is an important open problem in the literature which has great practical importance as well. Note that network users inside a stadium are not limited to smartphones, but can also be security cameras, noise and temperature sensors inside the stadium and performance monitoring devices on the sports players.

I-B Related Work

The investigation of drone cells has drawn attention in the literature from different perspectives, such as drone channel modeling [12, 13, 14, 15, 16], drone deployment and optimization of trajectories [17, 18, 19, 20, 21, 22, 23, 15] and performance analysis of drone enable cellular systems [6, 7, 8, 9, 10, 24, 25].

The work in [12] presented a comprehensive overview of existing research related to aerial (also known as air-to-ground (A2G)) channel measurements, including large and small-scale fading channel models. Models for path-loss exponents and shadowing for the aerial radio channel between drones and cellular networks were presented in [13, 14] based on field measurements. Using the general geometrical statistics of various environments provided by the International Telecommunication Union (ITU-R), the authors proposed location and environment dependent path-loss model for low altitude platforms in [15, 16].

Optimal drone trajectory was designed for a drone base station in cellular network in [17] and for a drone enabled relaying network in [18]. An analytical model for finding optimal placement of a drone was provided in [19] to maximize the number of covered users and optimal height and antenna beamwidth was found in [20] for throughput optimization. Optimal density of the underlay drones was investigated in [21] and optimal placement for multiple drones in a large-scale network was studied in [22]. The work in [23] studied the joint user scheduling and drone trajectory optimization for maximizing the minimum average rate of ground users. In [15], the authors derived the optimal altitude enabling a single drone to achieve a maximum coverage radius on the ground.

Some previous works investigated the performance of drone network using stochastic geometry. Note that stochastic geometry is a powerful mathematical tool, which can be used to capture the randomness of the nodes’ locations and fading channels. Specifically, [24] investigated the uplink performance of a drone cell in the presence of a Poisson field of ground interferers. The downlink performance of a single static drone and a single mobile drone with underlay device-to-device users was studied in [6], while [7] analyzed the downlink coverage of a finite network formed by multiple drones. The downlink coverage probability of a network with multiple directional beamforming drones was investigated in [8]. The downlink coverage performance of multiple drones in an urban environment was studied in[9]. In [10], the authors studied the downlink in a cellular network with multiple ground base stations and a drone user equipment. The downlink coverage and rate in a Poisson field of drone base stations was investigated in [25].

We focus on the performance analysis of drone in a temporary event scenario using stochastic geometry. Recently, there are some works investigating the application of drone in temporary events from different perspectives. Specifically, the Aerial Base Stations with Opportunistic Links for Unexpected and Temporary Events (ABSOLUTE) project in Europe aims to provide reliable network coverage through a combination of aerial, terrestrial and satellite links for unexpected and temporary events [26]

. A heuristically accelerated reinforcement learning based framework was proposed in

[27] for dynamic spectrum sharing in a temporary event scenario. In [28], the authors constructed a non-cooperative game and studied the equilibrium beaconing durations in terms of energy efficiency of the competing drones for temporary events. A proactive drone cell deployment scheme was investigated in [29] to cope with flash crowd traffic in different scenarios, including stadiums. A limited feedback scheme for non-orthogonal multiple access was designed for millimeter wave drone to provide coverage over a stadium in [30].

I-C Contributions

In this work, we consider a drone system coexisting with a single-cell cellular network, where an ABS is designated to provide service to IoT devices (namely the ABS-supported devices (AsDs), such as smartphones, security cameras, noise and temperature sensors and performance monitoring devices) inside a stadium for a temporary event (e.g., a concert or a sporting event). Since the ABS shares the same spectrum resources (i.e., in an underlay fashion) with the terrestrial base station (TBS), the concurrent transmission of both systems can cause interference to each other and impact the network performance. To the best of our knowledge, this scenario and its study have not yet been presented in the literature to date. In our preliminary work [1], we considered a simplified aerial channel model and used stochastic geometry to assess the uplink coverage performance for an underlay drone cell. In this work, we consider a general aerial channel model and both uplink and downlink network performance. The novel contributions of this paper are summarized as follows:

  • Leveraging tools from stochastic geometry, we develop a general analytical framework to analyze the uplink coverage probability of the TBS and the ABS and the downlink coverage probability of the TBS-supported user equipment (TsUE) and the AsD. The proposed framework is able to accommodate any aerial channel model.

  • Our proposed framework depends on the Laplace transforms of the interference power distribution at the TBS, the ABS, the TsUE and the AsD. We derive the key factors that determining the Laplace transforms of the interference power distribution, the distribution function of the 3-D distance between the ABS and an independently and uniformly distributed (i.u.d.) AsD and the distribution function of the 3-D distance between the ABS and an i.u.d. TsUE. Note that such distance distributions take into account the hole effects (i.e., the TsUE are prohibited from the ABS serving region and the AsD are contained in the ABS serving region).

  • Our results show that for urban environment and dense urban environment the ABS is best deployed at a low height (e.g., 200 m or lower), regardless of the distance between the center of the stadium and the TBS. However, for suburban environment and high-rise urban environment the best ABS deployment height depends on the distance between the center of the stadium and the TBS and the task of the system (i.e., prioritize the terrestrial link or the aerial link, prioritize the uplink or the downlink communication).

Symbol Definition
Radius of the network region of TBS
Radius of the stadium
Distance between the center of the stadium and the TBS
Path-loss exponent of terrestrial link
Path-loss exponent of LOS aerial link
Path-loss exponent of NLOS aerial link
Additional attenuation factor for LOS aerial link
Additional attenuation factor for NLOS aerial link
Nakagami- fading parameter for LOS aerial link
Nakagami- fading parameter for NLOS aerial link
Uplink receiver sensitivity of TBS
Uplink receiver sensitivity of ABS
AsD maximum transmit power
TBS transmit power
ABS transmit power
Uplink SINR threshold of TBS
Uplink SINR threshold of ABS
Downlink SINR threshold of TsUE
Downlink SINR threshold of AsD
Noise power
TABLE I: Summary of Main Symbols Used in the Paper.

I-D Notation and Paper Organization

The following notation is used in this paper. indicates the probability measure and denotes the expectation operator.

denotes the probability density function (pdf) of a random variable

. denotes the Laplace transform of a random variable . A list of the main mathematical symbols employed in this paper is given in Table I.

The rest of the paper is organized as follows: Section II describes the system model and assumptions. Section III focuses on the uplink coverage probability at the TBS and the ABS. Section IV details the analysis of the downlink coverage probability at the TsUE and the AsD. Section V presents the results and the effect of the system parameters on the network performance. Finally, Section VI concludes the paper.

Ii System model

A two-cell communication network comprised of a TBS and an ABS is considered in this paper, where the network region is a disk with radius , i.e., and a TBS is located at the center. We assume that there is a temporary event held inside a stadium within the network region and a large number of IoT devices are active inside the stadium. The stadium’s building area is modeled as a disk with radius and its center is at a distance from the TBS. A drone is placed as an ABS111Current drone regulations prohibit a drone from flying over stadiums or sports events. This is expected to change in the future. to provide additional resources for the event. The ABS is assumed to be deployed at a height of above the center of the stadium, as shown in Fig. 1. The TsUEs served by the TBS are uniformly distributed over the network region excluding the stadium, i.e., . At the same time, the AsDs are independently uniformly deployed on the ground inside the stadium . For tractability, we assume that all AsDs are connected to the ABS only. In this work, we focus our analysis on one terrestrial cell and its underlay drone cell without inter terrestrial cell interference. This is based on the assumption that the terrestrial adjacent cells use different frequencies, while the TBS and the underlay ABS share the same spectrum resource. Hence, the interference from far away cells becomes negligible and can be ignored [29, 31]. Note that the single terrestrial cell model is commonly used in literature for underlay network analysis [32, 33].

Ii-a Channel Model

There are two types of communication links in the considered system model: aerial links and terrestrial links. The link between the TsUE and the TBS and the link between the AsD and the TBS are terrestrial links. The link between the TsUE and the ABS and the link between the AsD and the ABS are aerial links.

Terrestrial links: A general power-law path-loss model is considered for terrestrial links, in which the signal power decays at a rate with the propagation distance and

is the path-loss exponent. Furthermore, we assume the terrestrial links experience small-scale Rayleigh fading and additive white Gaussian noise (AWGN) with variance

.

Aerial links: The channel characteristics of the aerial links (or known as A2G links) are significantly different from the terrestrial links. Depending on altitude and type of the drone, elevation angle and type of propagation environment, the aerial links can be either line-of-sight (LOS) or non-line-of-sight (NLOS) with different probabilities of occurrence and [16].

The path-loss of the NLOS link is higher than LOS one, because of the shadowing effect and the reflection of signals from obstacles. Following [6], the path-loss of the aerial link is modeled as

(1)

where is the 3-D propagation distance between the TsUE and the ABS and between the AsD and the ABS, and is the path-loss exponent of LOS aerial link and NLOS aerial link respectively, and is the additional attenuation factor for LOS aerial link and NLOS aerial link respectively and .

Most previous works using aerial channel model ignore the impact of small-scale fading [6, 19]. However, small-scale fading characteristics are measured and reported in the literature recently for various aerial propagation environments [12]. In this paper, the small-scale fading of the aerial link is modeled as Nakagami- fading, which is a flexible model that mimics various fading environments. For example, Nakagami- fading is equivalent to Rayleigh fading when equals to 1 and Nakagami- fading can also closely approximate Rician fading by matching the values. The fading parameter for the LOS aerial link and NLOS aerial link is denoted by and respectively. The difference between including and ignoring the small-scale fading will be discussed in the result section. The aerial links also experience AWGN with variance .

(a) 3D view.
(b) Projection on the ground.
Fig. 1: Illustration of the system model.
(2)

 

Ii-B Uplink Network Model

For uplink, we assume that orthogonal multiple access technique is employed [34]. Hence, there is no interference among TsUEs (or AsDs). However, both the TBS and the ABS share the same spectrum resource, i.e., in an underlay fashion. We assume that the number of the TsUEs and the AsDs are sufficiently high. That is to say, there will always be one TsUE and one AsD to be served per each channel at the same time. Therefore, interference exists between TsUEs and AsDs. In this work, we focus our analysis on one uplink channel since other channels share the same interference statistics.

For reliable and successful uplink communication, the TsUE controls its transmit power such that the average signal received at the TBS is equal to the receiver sensitivity . Power control is deployed at the AsD as well. Perfect channel state information (CSI) knowledge is assumed at TsUE and AsD. We also set a maximum transmit power constraint at the AsD, to avoid the transmit power for AsD going to very large when the ABS is placed at a high altitude. In other words, the AsD compensates for the path-loss to keep the average signal power at the ABS equal to the receiver sensitivity if the transmit power required for the path-loss inversion is less than . Otherwise, the AsD tries to establish an uplink connection with the ABS by transmitting with a power of . Therefore, the instantaneous transmit power for the AsD, , depends on the propagation distance between the AsD and the ABS and can be shown as (2) at the top of this page, where is the Euclidean distance between the AsD and the ABS and the conditions are:

(3)
(4)
(5)

where (in and ) is for LOS case or for NLOS case. These conditions come from the fact that AsD will transmit with its maximum power regardless of where it is located inside the stadium, if the ABS is placed at a high enough altitude. On the other hand, the AsD will always be under full channel inversion if the altitude of the ABS is low.

SINR: For the considered setup, the instantaneous uplink signal-to-interference-plus-noise ratio (SINR) at the TBS is given as

(6)

where is the TsUE transmit power. and

are the uplink fading power gain between the TsUE and the TBS and between the AsD and the TBS, respectively, which follow exponential distribution.

and are the Euclidean distance between the TsUE and the TBS and between the AsD and the TBS, respectively. The transmit power of the AsD is given in (2).

The instantaneous uplink SINR at the ABS is given as

(7)

where and

are the uplink fading power gain between the AsD and the ABS and between the TsUE and the ABS, respectively, which follow Gamma distribution.

and are the Euclidean distance between the AsD and the ABS and between the TsUE and the ABS, respectively.

Ii-C Downlink Network Model

Different from uplink transmission, the TBS and ABS are assumed to transmit at a constant power and respectively.

SINR: For the considered setup, the instantaneous downlink SINR at the TsUE is given as

(8)

where is the downlink fading power gain between the TsUE and the TBS, which follow exponential distribution and is the downlink fading power gain between the TsUE and the ABS, which follow Gamma distribution.

The instantaneous downlink SINR at the AsD is given as

(9)

where is the downlink fading power gain between the AsD and the ABS, which follow Gamma distribution and is the downlink fading power gain between the AsD and the TBS, which follow exponential distribution.

(11)

 

Iii Uplink Coverage Probability

In this section, we propose the analytical framework to compute the uplink performance by adopting coverage probability as the performance metric. The uplink coverage probability is formally defined as

(10)

where superscript is for TBS and for ABS, and is the uplink SINR threshold. and can be found in (6) and (7), respectively. The results for the uplink coverage probability of the TBS and the ABS are presented in the next two subsections.

Iii-a TBS Uplink Coverage Probability

First we present two lemmas, which are used in deriving the coverage probability of the TBS in Theorem 1.

Lemma 1

The Laplace transform of the interference power distribution at the TBS is given as (11) at the top of this page, where

(12)

and is given in (3) and (5) respectively and the other conditions are given below:

(13)
(14)
(15)
(16)
(17)
(18)

These conditions come from the fact that as the height of the ABS increases, the AsD is first under full channel inversion and then reaches its maximum power constraint. Depending on whether is greater or smaller than , we can further specify conds. 1N, 2L, 2N and 3L as the conditions above.

Proof:

See Appendix A.

From Lemma 1, we can see that the transmit power of the AsD and the distance between the AsD and the TBS are related to the distance between the AsD and the ABS . This important distance distribution is presented in the following lemma.

Lemma 2

The pdf of the distance between the ABS at height above the center of and an i.u.d. AsD inside is

(19)
Proof:

See Appendix B.

(25)

 

Theorem 1

Based on the system model in Section II, the uplink coverage probability of the TBS is

(20)

where , , and is given by Lemma 1.

Proof:

Using the fact that the link between the TsUE and the TBS experiences Rayleigh fading with a pdf of , we can derive the TBS uplink coverage probability.

Substituting (11) and (19) into (20), we can obtain the uplink coverage probability of the TBS.

Iii-B ABS Uplink Coverage Probability

We begin by presenting three lemmas, which will then be used to compute the uplink coverage probability of the ABS in Theorem 2.

Lemma 3

The Laplace transform of the interference power distribution at the ABS is

(21)

where

(22)

and .

Proof:

See Appendix C.

The pdf of the distance between the TsUE and the ABS , and the conditional pdf of the angle, , between the ground projection of and are given in Lemma 4 and Lemma 5, respectively.

Lemma 4

The pdf of the distance between the ABS at height above the center of and an i.u.d. TsUE inside is

(23)
Proof:

See Appendix D.

Lemma 5

The pdf of the angle, , between the ground projection of and conditioned on is

(24)
Proof:

This lemma can be proved by using cosine rule and simple trigonometry.

Theorem 2

Based on the system model in Section II, the uplink coverage probability of the ABS is given as (25) at the top of this page, where

(26)

and is given by Lemma 3 and

(27)

and is given by Lemma 3. The pdf of the distance between the AsD and the ABS is provided in Lemma 2. , , 4–9 are given in (3), (5) and (13)–(18). These conditions come from the fact that the AsD is first under full channel inversion and then transmits with its maximum power as the height of the ABS increases. Note that we can further specify conds. 1N, 2L, 2N and 3L as conds. 4–9 depending on whether is larger or smaller than .

Proof:

See Appendix E.

Combining Lemma 34, and 5 with Theorem 2, we can calculate the uplink coverage probability of the ABS.

Iv Downlink Coverage Probability

In this section, we present the analytical framework to analyze the performance metric, the downlink coverage probability, which is formally defined as

(28)

where superscript is for TsUE and for AsD, and is the downlink SINR threshold. and can be found in (8) and (9), respectively. The next two subsections investigate the downlink coverage probability of the TsUE and the AsD.

Iv-a TsUE Downlink Coverage Probability

First we present a lemma, which is used in deriving the coverage probability of the TsUE in Theorem 3

Lemma 6

The conditional Laplace transform of the interference power distribution at the TsUE is

(29)
Proof:

The proof follows the same lines as Lemma 3 and is skipped for the sake of brevity.

Theorem 3

Based on the system model in Section II, the downlink coverage probability of the TsUE is given as