Map-based Placement and Trajectory Design in UAV-aided Wireless Networks 

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Research Methodology and Assumptions

In order to solve the UAV placement problems in UAV-aided wireless communication, various approaches are here studied. In this thesis, we speci cally focus on how to e ciently exploit the knowledge of a 3D map of the environment to guarantee the performance predicted by the proposed algorithms.
First, we study the problem of UAV placement and the communication trajectory design to maximize the performance of the network in terms of the worst user throughout. The critical components for the UAV placement and the trajectory design are the radio channel parameters of the environment where the UAV is deployed and the location awareness of the nodes in the network. During the communication phase, we assume that these pieces of information are available, while they often have to be estimated from the UAV-borne measurements.
To deal with this problem, we also formulate the problem of learning the channel parameters from a set of measurements which has been collected by the UAV while following an arbitrary trajectory over the network. To minimize the error of the esti-mated channel parameters we then optimize the UAV learning trajectory for collecting measurements. Note that, we are treating the learning and the communication phases that are separated in time. This allows us to obtain optimal trajectories for both phases independently, i.e., if one is only interested in learning or communication scenario this solution serves the purpose.
To learn the channel parameters we assume that the locations of the ground nodes are known while may not be true in most of the cases. For this, in a separate chapter of this thesis, we study the problem of node localization in wireless networks by capitalizing on the city 3D map information. Similarly, a node in the network can be localized from UAV-borne radio measurement. Note that, to localize a node the radio channel parameters need to be known, hence the UAV requires not only to localize the users but also to learn the channel at the same time. Similar to channel learning, we rst address the node localization from a given set of measurements when the UAV follows an arbitrary trajectory and then we optimize the UAV trajectory for the further improvement in the localization accuracy.
All the aforementioned algorithms build on the availability of the city 3D map while in some cases the map information may not available or costly to access. To cope with this problem, we propose a method to construct a 3D model of a city just by exploiting the radio measurements collected by the UAV from the outdoor ground nodes, whose locations are known, in the city.
We nally investigate the problem of cellular-enabled UAV communication. A novel approach will be proposed to design the shortest trajectory for a UAV to guarantee a seamless connection to the infrastructure on the grounds (i.e. ground BS) all along the UAV path while allowing the completion of the UAV mission. To this end, the trajectory design algorithm leveraging a coverage map that can be obtained with a combination of 7
3D map of the environment, radio propagation models, and the locations of the ground BSs. In table 1.1, we summarized all the key assumptions and information which are required for each algorithm proposed in this thesis.

Segmented Channel Model

The quality of channel models lies in their ability to correctly predict power attenuation as a function of distance, frequency, as well as to characterize seemingly random blockage. While some models encompass multipath fading, the placement optimization time scale is usually much longer than the fast fading coherence time, hence fast fading can be averaged out in the rst approximation. A simple received signal strength indicator (RSSI) model then ensues [26; 27]: s = s s ; s 2 f1; ; Sg; (2.1).
where s is a class index, s is a path loss exponent, s is a channel gain o set, and s is a random variable that captures additional non-predictable behavior (log-normal shadowing, additional noise sources, etc.), and d is the distance between the receiver and the transmitter. The model in (2.1) is often referred to as segmented, with s called the segment value, re ecting the degree of link’s obstruction and its strong dependence on local terrain scenario. A simpli ed analysis may consider a single segment (S = 1), e.g free space propagation or LoS everywhere. The next most popular scenario just distinguishes between S = 2 segments, with s 2 fLoS; NLoSg links. In a deterministic segmented channel model, the segment value s is directly predicted from a 3D terrain map or possibly from UAV radio measurements. For example regarding the LoS/NLoS classi cation of a link, we can leverage the knowledge of a 3D city map [28]. Based on such map, we can predict LoS (un)availability on any given links from a trivial geometry argument: For a given UAV position, the BS is considered in LoS to the UAV if the straight line passing through the UAV’s and the ground node’s position lies higher than any buildings in between. The channel gain in dB can be written as gs = s s’(d) + s; (2.2).
where gs = 10 log10 s, s = 10 log10 s; ’(d) = 10 log10 (d), s = 10 log10 s, and s is modeled as a Gaussian random variable with N (0; s2).
For a greater reality match, one may increase the number S of segments to account for meaningful intermediate degrees of obstruction such as concrete building vs. wood-walled structure vs. foliage, etc. [29]. Of course, expanding the segment values means added complexity as well as a greater noise sensitivity when doing model classi cation on the basis of real link strength measurements. Note that in reality, the segment value can be considered stable while the UAV is ying over some limited neighborhood, while sharply transitioning to another value as the UAV goes over a street corner or ies behind a large building. A piece-wise quasi-static behavior of s is typically assumed for segmented channel models. In g. 2.1, an illustration of the segmented channel model by considering two ground users in a given city is shown. The status of each ground node-UAV link is determined by leveraging the 3D map of the city.
It is noteworthy that channel measurements and modeling for UAV communications are still ongoing research. Incorporating various issues into the channel modeling would be bene cial for the precise performance analysis and the practical design of the UAV communication systems. For example, analyzing the e ects of UAV mobility patterns and the blades rotation on the channel, the multiple input multiple output (MIMO) and massive MIMO channel modeling [30; 31], the millimeter wave UAV channel modeling [32], etc. Such aspects remain however beyond the scope of this thesis.

Probabilistic Link Attenuation Models

As mentioned in the previous section, in a deterministic segmented channel model, the segment value s is directly predicted from a 3D terrain map or possibly from UAV radio measurements. However, in the absence of maps, probabilistic segmented models can be employed, whereby the segment value is simply governed by a likelihood parameter [15; 33]. The two-segment case (S = 2), has been particularly used in the literature to date as it naturally lends itself to closed-form tractability. In this case, a given link l between a ground node and the UAV is simply classi ed as LoS or NLoS where the LoS probability pLoS(l) follows a parametric model. A popular model is as follows [15]: pLoS(l) = 1 ; (2.3) 1 + exp ( a l + b).
where l denotes the elevation angle between the horizontal plane and the axis between the drone and the ground node. Finally, fa; bg are the model coe cients which are speci c for the city that the UAV is deployed and can be learned via a tting method using labeled training data points, for instance using prior radio measurements or a terrain map. In order to infer the average link gain, a weighted average of s over random value s, accounting for the segmented probability, can be carried out as follows: s2f X g (l) = sps(l); (2.4) .

Trajectory Design in UAV-aided Wireless Networks

The key advantage of using UAVs in wireless communication lies in the high mobility and fast deployment of the UAVs which can bring signi cant gains to the performance of the network besides the traditional communication designs such as scheduling and resource allocation. For the performance optimization of the UAV communication systems, the generic mathematical problem can be considered as follows [13].
max U(v(t); A(t)) (2.14a).
v(t); A (t).
s.t. fi(v(t)); i 2 [1; I1]; (2.14b).
gi(A(t)); i 2 [1; I2]; (2.14c).
hi(v(t); A(t)); i 2 [1; I3]; (2.14d).
where A(t) is a set of variables pertaining to the all communication relevant design over the time, such as scheduling, transmit power control, etc., and U(:; 🙂 denotes the desired utility function to be maximized and depending on the application can be any of the metrics introduced in the previous section. fi(:) represents the constraints related to the UAV trajectory at any time t, gi(:) captures all the communication related constraints, and hi(:; 🙂 involves both UAV trajectory and communication variables such as the SNR constrained which is a function of the UAV location and the communication parameters. Note that problem (2.14) is recast as a static placement problem if the UAV location is independent of the time t which is a special case of the trajectory design problem, in other words v(t) = v; 8t.
The UAV trajectory constraints can depend on the type of the UAV, the application, the mission requirement, etc. In the following we refer to some of the common UAV trajectory constraints: Altitude range: In practice, a maximum and a minimum ying altitude need to be considered for the UAV. Typically, the maximum ying altitude is limited by the regulation depending on the ying area, and the minimum altitude is chosen to avoid the collision with the obstacles (i.e. in a city the minimum altitude can be set as the height of the tallest building in the city).
Initial/destination locations: In most of the cases, it’s required that the UAV starts from an initial point and terminates in a pre-determined destination location. Thus, the initial and destination location constraints can be expressed as v(0) = vI; v(T ) = vF; (2.15).

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Cellular-connected UAV Trajectory Design

The enabling of safe cellular controlled UAVs beyond visual line of sight is expected to open important future opportunities in di erent domains. A key challenge in this area lies in the design of trajectories which, while allowing the completion of the UAV mission, can guarantee reliable cellular connectivity all along the path. In general, the problem of designing a trajectory for the UAV under cellular connectivity constraints can be formulated as follows:
max U(v(t)) (2.17a).
v(t);A(t).
s.t. fi(v(t)); i 2 [1; I1]; (2.17b).
gi(A(t)); i 2 [1; I2]; (2.17c).
hi(v(t); A(t)); i 2 [1; I3]; (2.17d).
where A(t) is a set of variables pertaining to the all communication relevant designs over the time, and U(:) is the desired utility function to be maximized. In the context of cellular-connected UAV trajectory design, the utility function is mainly the UAV energy consumption (or equivalently the ying time if the UAV movies with a constant velocity over the time). fi(:) represents the constraints related to the UAV trajectory at any time t and can be any of the constraints listed in the previous section. gi(:) contains all the communication related constraints. One of the common communication related constraints is the minimum SNR constraint which is as follows: 0mintT k max k (v(t)) min ; (2.18). where k(v(t)) denotes the SNR of the link between the UAV at time t and the k-th ground BS. Constraint (2.18) implies that the minimum SNR obtained by the UAV during the mission needs to be greater than or equal to the threshold min. Constraints hi(:; 🙂 involves both UAV trajectory and communication variables. In Chapter 7, the problem of trajectory design for a UAV under cellular connectivity constraint is discussed in details.

Optimal Trajectory Design for an Intelligent Data Har-vesting

A wireless communication system where a UAV-mounted ying BS serving K static ground level nodes (IoT sensors, radio terminals, etc.) in an urban area is considered. The k-th ground node, k 2 [1; K], is located at uk = [xk; yk]T 2 R2: By no means the ground level node assumption is restrictive, the proposed algorithms in this work can in principle be applied to a scenario where the nodes are located in 3D. The UAV’s mission consists of a communication phase of duration T . We assume that the propagation parameters of the environment have been learned beforehand by collecting the radio measurements from the ground users (for more details see Chapter 4). These parameters are then used to optimally serve the ground nodes. The time-varying coordinate of the UAV/drone is denoted by v(t) = [x(t); y(t); z(t)]T 2 R3; 0 t T , where z(t) represents the altitude of the drone.
For the ease of exposition, we assume that the time period T is discretized into N equal-time slots. The time slots are chosen su ciently small such that the UAV’s location, velocity, and channel gains can be considered to remain constant in one slot. Hence, the UAV’s position v(t) is approximated by a sequence v[n] = [x[n]; y[n]; z[n]]T; n 2 [1; N]: (3.1).
We assume that the ground nodes and the drone are equipped with GPS receivers, hence the coordinates uk; 8k and v[n]; n 2 [1; N] are known.

LoS Probability Model Using Map Compression

Statistical map compression approach relies on converting 3D map data to build a reliable node location dependent LoS probability model. The LoS probability for the link between the drone located at altitude z and the k-th ground node in the n-th time slot is given by pk[n] = 1 ; (3.7). where k[n] = arctan(z=rk[n]) denotes the elevation angle and rk[n] is the ground projected distance between the drone and the k-th node located at uk in the time slot n, and fak; bkg are the model coe cients.
The LoS probability model coe cients fak; bk g are learned (i.e. by utilizing logistic regression method[52]) by using a training data set formed by a set of tentative UAV locations around the k-th ground node along with the true LoS/NLoS label obtained from the 3D map. Interestingly, the model in (3.7) can be seen as a localized extension of the classical (global) LoS probability model used in [15; 40]. The key di erence lies in the fact that, a local LoS probability model will give performance guarantees which a global model cannot.
Using (3.7), the average channel gain of the link between the drone and the k-th ground node in the n-th time slot is E[ k[n]] = (dk[n])(A 1) LoS B + B LoS ; (3.8) 1 + exp( ak k + bk) (dk[n]) NLoS NLoS NLoS where B = ; A = 1, and dk[n] = z 2 + (rk[n]) 2 is the distance between.

Table of contents :

Abstract
Abrege [Francais]
Acknowledgements
Contents
List of Figures
List of Tables
Acronyms
Notations
1 Introduction 
1.1 Background and Motivations
1.1.1 Role Played by Node Localization
1.2 Aims and Objectives
1.3 Research Methodology and Assumptions
1.4 Outline of the Thesis
2 System Model 
2.1 Introduction
2.2 Channel Models
2.2.1 Segmented Channel Model
2.2.2 Probabilistic Link Attenuation Models
2.3 Communication Performance Metric
2.3.1 SINR
2.3.2 Outage
2.3.3 UAV Energy Consumption
2.3.4 Communication Throughput
2.4 Trajectory Design in UAV-aided Wireless Networks
2.5 Cellular-connected UAV Trajectory Design
3 Map-based Placement and Trajectory Design in UAV-aided Wireless Networks 
3.1 Introduction
3.2 Optimal Trajectory Design for an Intelligent Data Harvesting
3.2.1 Communication System Model
3.2.2 Joint Scheduling and Trajectory Optimization
3.2.3 LoS Probability Model Using Map Compression
3.2.4 Proposed Solution for Communication Trajectory Optimization
3.2.5 Iterative Algorithm
3.2.6 Proof of Convergence
3.2.7 Trajectory Initializing
3.3 Optimal UAV Relay Placement in LTE Networks
3.3.1 Communication Model
3.3.2 UAV Placement Optimization
3.4 Numerical Results
3.5 Conclusion
4 Active Learning for Channel Estimation: Map-based approaches 
4.1 Introduction
4.2 UAV Kinematic Model
4.3 Learning Trajectory Design
4.3.1 Measurement Collection and Channel Learning
4.3.2 Optimization Problem
4.3.3 Dynamic Programming
4.4 Numerical Results
4.5 Conclusion
5 UAV-aided Radio Node Localization 
5.1 System Model
5.2 User Localization and Channel Model Learning
5.2.1 PSO Techniques
5.2.2 Single User Case
5.2.3 Multi User Case
5.3 Trajectory Design for Accelerated Learning
5.3.1 Fisher Information Matrix
5.3.2 Cramer-Rao Bound Analysis
5.3.3 Trajectory Optimization
5.3.4 Greedy Trajectory Design
5.4 Numerical Results
5.5 Conclusion
6 3D City Map Reconstruction from Radio Measurements 
6.1 Introduction
6.2 System Model
6.3 LoS vs. NLoS Classication
6.3.1 Target User Clustering
6.3.2 Optimization of Target User Group
6.3.3 Radio Propagation Parameter Learning
6.3.4 User Classication
6.4 3D City Map Reconstruction
6.4.1 Optimum UAV Altitude
6.5 Numerical Results
6.6 Conclusion
7 UAV Trajectory Design Under Cellular Connectivity Constraints
7.1 Introduction
7.2 System Model
7.2.1 Communication Model
7.2.2 Problem Formulation
7.3 Feasibility Check
7.4 Trajectory Optimization
7.5 Numerical Results
7.6 Conclusion
8 Experimental Studies 
8.1 Introduction
8.2 System Design
8.2.1 UAV Design
8.2.2 OAI eNBs
8.2.3 Autonomous Placement
8.3 UAV Placement
8.3.1 Channel Parameter Estimation
8.3.2 Placement Algorithm
8.4 Experimental Results
8.5 Conclusion and Discussion
8.5.1 Design Improvement
8.5.2 Channel Models
9 Conclusion 
Appendices 
A Chapter 3 Appendices 
A.1 The derivation of the average channel gain
A.2 Proof of Lemma 3.2.1
A.3 Proof of Proposition 3.2.1
B Chapter 5 Appendices 
B.1 Proof of convergence for multi-user localization
B.2 Derivation of FIM
C The estimate of the map reconstruction error 
D Chapter 7 Appendices 
D.1 Proof of Proposition 7.2.1
D.2 Proof of Proposition 7.3.1
D.3 Proof of Lemma 7.4.1
Resume [Francais] 

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