IN
DEGREE PROJECT INFORMATION AND COMMUNICATION TECHNOLOGY,
SECOND CYCLE, 30 CREDITS STOCKHOLM SWEDEN 2020,
Simulation-Based Stochastic Blockage Model for
Millimeter-wave Communication
MIHRET GETYE SIDELEL
KTH ROYAL INSTITUTE OF TECHNOLOGY
www.kth.se
Simulation-Based Stochastic
Blockage Model for Millimeter-wave Communication
MIHRET GETYE SIDELEL
Master of Science Thesis
Supervisor: Dr. Hossein Shokri-Ghadikolaei
Examiner: Prof. Carlo Fischione
Abstract
Recently, the growing demand for high data rates in wireless communication, to- gether with the scarcity of spectrum in existing microwave bands, has motivated the use of millimeter-wave (mmWave) bands for 5G and future wireless communi- cations. Even though mmWaves are potential candidates for fulfilling this rising demand, they come along with their own drawbacks that need to be addressed.
Sensitivity to blockages is one of these drawbacks. It is a major channel impair- ment that is of concern in the design of mmWaves communication systems. As such, different industrial and academic research activities have been performed and are in progress for modeling and characterizing blockages in mmWave communi- cation systems. However, most of the proposed blockage models failed to capture the temporal correlation of the blockages and the dynamics of the channel’s envi- ronment.
In order to address this issue, this thesis work aims to develop a simple Stochastic Blockage Model for mmWave communication channels. The model uses two-states (ON and OFF states) to represent Line of Sight (LoS) and Non-Line of Sight (NLoS) conditions, respectively. Using simulation-based analysis, the behavior and probability of the LoS and the NLoS situations of a communication link over time have been analyzed. It is demonstrated that the proposed blockage model can capture the behaviors of the probability of a link being blocked or not in a dynamic environment. It was also found to be adequate to model and characterize the effects of blockage in mmWave communication systems. The accuracy of the model was evaluated to be satisfactory by validating the results against a bench- mark which was derived from actual data. It is possible to characterize mmWave communication on a system-level by using this model. Thus, this work provides researchers with a simple simulation-based blockage model to help facilitate the
Sammanfattning
Den växande efterfrågan på höga nedladdningshastigheter i trådlösa kommunika- tionssystem, i kombination med en brist på tillgängliga frekvensband i nuvarande mikrovågsband, har medfört att millimetervågsbandet ses som ett attraktivt alter- nativ för 5G och andra framtida trådlösa kommunikationssystem. Även om det är troligt att millimetervågsbandet kommer att vara en del av lösningen för att upp- fylla efterfrågeökningen har det en del negativa egenskaper som måste beaktas och tas hänsyn till. Känslighet för blockering är en sådan typisk nackdel som avsevärt försämrar radiokanalen i ett millimetervågssystem. Både från näringslivets sida och inom den akademiska världen har det forskats inom detta område. Den har bestått av karakterisering och framtagning av modeller som beskriver kommunika- tionssystem på dessa frekvensband med avseende på blockering. Emellertid har de flesta föreslagna modellerna har misslyckats fånga upp de temporala korrelation av de blokeringar och de dynamiken av kanalens miljö.
Den här avhandlingen har som mål att utveckla en enkel stokastisk blockerings- modell för millimetervågsbandet för att ta itu med just dessa frågor. Modellen använder två tillstånd (ON och OFF tillstånd) för att representera Line of Sight (LoS) respektive Non-Line of Sight (NLoS) utbredning. Simuleringar av kanalen har gjorts för att analysera de tidsmässiga egenskaperna och sannolikheten för ut- bredning via direktvåg respektive skuggning. Det visas att den föreslagna skugg- ningsmodellen kan beskriva det dynamiska beteendet och sannolikheten för att länken är blockerad. Den konstateras också vara adekvat för att modellera och karakterisera kommunikationssystem för millimetervågsbandet med avseende på blockering. Modellens noggrannhet har utvärderats och den anses vara tillfreds- ställande genom att resultaten validerats mot ett riktmärke som är baserat på verkligt data. Det är möjligt att karakterisera millimetervågskommunikation på systemnivå genom att använda denna modell. Detta verk förser således forskare med en enkel simuleringsbaserad blockeringsmodell som främjar studier och fram-
Acknowledgements
First and foremost, I would like to thank God the Almighty for giving me the opportunity and the strength to undertake this study and complete it. The thesis appears in its current form due to the assistance and guidance of several individ- uals. At the very outset, I would like to express my deepest sense of gratitude to my examiner Professor Carlo Fischione and my supervisor Dr. Hossein Shokri- Ghadikolaei, who welcomed me and gave me the opportunity to join them in this thesis work with warm encouragement and thoughtful guidance. Specially, Dr.
Hossein Shokri-Ghadikolaei, thank you very much for your support, constructive feedbacks and guidance as well as your patience the whole time. I would like to offer my sincere thanks to Igor Maria Di Paolo for helping me to get started with the first simulation tool. I want to express my appreciation to Ayda Kiyar, Tsion Abebaw and Mattias Heinze for helping me with the Swedish translation of the Abstract part of this report. Moreover, I would like to take the opportunity to thank all my friends and family for encouraging me and assisting me in all they can.
Last but not the least, to my beloved husband, thank you for your unconditional
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Contents
List of Figures ix
List of Tables xi
1 Introduction 1
1.1 Millimeter-Wave Technology . . . 2
1.2 Millimeter-wave Communication Characteristics . . . 3
1.2.1 Path Loss . . . 3
1.2.2 Deafness and Blockage . . . 4
1.3 Related Works . . . 4
1.4 Contribution of the Thesis . . . 6
1.5 Organization of the Thesis . . . 7
2 System Model 8 2.1 Mobility Model . . . 8
2.2 Link Model . . . 9
2.3 Obstacle Model . . . 10
2.4 LoS and NLoS Evolution Model . . . 11
2.5 Neural Network . . . 12
3 Simulation 16 3.1 First Simulation Phase . . . 16
3.1.1 Simulation Tool . . . 17
3.1.2 Simulation Parameters . . . 17
3.1.3 Simulation Assumptions and Procedures . . . 18
3.2 Second Simulation Phase . . . 21
3.2.1 Simulation Tool . . . 21
3.2.2 Layers and Activation Functions . . . 22
3.2.3 Optimization Method . . . 23
3.2.4 Cost Function . . . 23
4 Results and Discussions 25 4.1 Comparison of ON-OFF Model parameters . . . 26
4.2 Comparison of NLoS probability . . . 28
4.3 Comparison of LoS and NLoS Duration CCDFs . . . 32
4.3.1 Comparison of LoS Duration CCDF . . . 33
4.3.2 Comparison of NLoS Duration CCDF . . . 36
4.4 Performance of the Neural Network . . . 39
5 Conclusions and Future Works 42 5.1 Summary . . . 42
5.2 Future Work . . . 43
Bibliography 44
viii
List of Figures
1.1 Exponential growth in the data transfer rates in the wireless com-
munication; reproduced from . . . 1
1.2 MmWave frequencies identified at WRC-15 . . . 3
1.3 Human and building blockage in mmWave networks . . . 4
2.1 Tx-Rx pair and the respective link model . . . 10
2.2 Representation of LoS and NLoS Links . . . 10
2.3 ON-OFF Link Blockage Model. . . 11
2.4 State diagram of LoS and NLoS states . . . 12
2.5 Basic Components of a Neural Network. . . 13
2.6 Neural Net Input Output Diagram. . . 15
3.1 Distinction between initial simulation area and actual simulation area. 19 3.2 Sample mobility of Tx and Rx nodes of the tagged link for a config- uration C at some random round: where the red triangles represent the start and end points of the mobility for each node while indi- vidual steps are indicated by a * marker. . . 20
3.3 Different Realizations (Extended Topologies) of a Configuration C. . 20
3.4 First Phase Simulation Procedure for One Configuration Scenario. . 21
3.5 Neural Network Architecture Used. . . 22
3.6 Comparison of different optimization algorithms on multilayer neu- ral network training . . . 24
4.1 Impact of mean speed of Tx and Rx Nodes on the Probabilities that a Link remains in LoS and NLoS states fixing the density and mean size of Obstacles at 0.01 and 1.0 m respectively. . . 26
4.2 Impact of density of obstacles on probabilities that a Link remains in LoS and NLoS states fixing the mean speed of Tx and Rx Nodes and mean size of Obstacles at 1.79 m/s and 1.0 m respectively. . . . 27
4.3 Impact of mean size of obstacles on probabilities that a Link remains in LoS and NLoS states fixing the mean speed of Tx and Rx Nodes and density of Obstacles at 1.79 m/s and 0.01 respectively. . . 28
4.4 Impact of mean speed of Tx and Rx Nodes on the probability that a link will be in a NLoS state after n time slot steps given that it was in LoS state at time 0 fixing the density and mean size of Obstacles at 0.01 and 1.0 m respectively. . . 29 4.5 Impact of density of obstacles on the probability that a link will be
in a NLoS state after n time slot steps given that it was in LoS state at time 0 fixing mean speed of Tx and Rx Nodes and mean size of Obstacles at 1.79 m/s and 1.0 m respectively. . . 30 4.6 Impact of mean size of obstacles on the probability that a link will
be in a NLoS state after n time slot steps given that it was in LoS state at time 0 fixing the mean speed of Tx and Rx Nodes and density of Obstacles at 1.79 m/s and 0.01. . . 31 4.7 Impact of mean speed of Tx and Rx Nodes on LoS duration keeping
the density and mean size of Obstacles constant at 0.01 and 1.0 m respectively. . . 33 4.8 Impact of density of obstacles on LoS duration while fixing the mean
speed of Tx and Rx Nodes and mean size of Obstacles constant at 1.79 m/s and 1.0 m respectively. . . 34 4.9 Impact of mean size of obstacles on LoS duration while fixing the
mean speed of Tx and Rx Nodes and density of Obstacles constant at 1.79 m/s and 0.01 respectively. . . 35 4.10 Impact of mean speed of Tx and Rx Nodes on NLoS duration while
keeping the density and mean size of Obstacles constant at 0.01 and 1.0 m respectively. . . 37 4.11 Impact of density of obstacles on NLoS duration keeping the mean
speed of Tx and Rx Nodes and mean size of Obstacles constant at 1.79 m/s and 1.0 m respectively. . . 38 4.12 Impact of mean size of obstacles on NLoS duration keeping the mean
speed of Tx and Rx Nodes and density of Obstacles constant at 1.79 m/s and 0.01. . . 39
x
List of Tables
3.1 Simulation Parameters . . . 18 4.1 Comparison of WD for Different Number of Training Samples for
the two parameters of the ON-OFF Blockage Model. . . 40 4.2 Comparison of Averaged WD for Different Number of Training Sam-
ples. . . 40
Chapter 1
Introduction
Currently there are around 7.9 billion mobile users and it is increasing in a two percent rate annually. The subscription for smartphones is 60% of all mobile users [1]. The existing wireless communication technology is unable to meet the significant mobile traffic demand and spectrum requirements. Figure 1.1 shows how the new technologies in wireless communications are exponentially faster than the old ones as well as the trends for the near future, perhaps to address the emerging requirements for higher data rate services including Augmented Reality, Virtual Reality uncompressed high quality video delivery, etc. [2], [3].
Figure 1.1: Exponential growth in the data transfer rates in the wireless communication; reproduced from [4].
Besides, the smart device to device communication, Internet of Things (IoT), big data and so on make the task of meeting these demands formidable. In order to support these growth, there should be a means to raise the transmission rate of up to multi gigabit-per-second peak throughputs and tens of Mbps cell edge rates very easily [5]. However, this is becoming difficult to accomplish with the existing sub-6 Ghz bands which is highly crowded [6]. Low propagation loss makes the frequency band less than 6 GHz preferable and usable for a long period of time while the frequency above 6 GHz has been considered as only suitable for special applications with short coverage distances due to the high propagation loss they have. However, driven by the demand described above recent studies around mmWave mobile networks changed the view around the feasibility of using mmWave bands for mobile communication [3]. Among the major use cases of 5G, Enhanced mobile broadband is one of them, by which the smart future requires fast and wide bandwidth for diverse communications [7].
1.1 Millimeter-Wave Technology
As it has been already mentioned, the current communication system which is operating in the microwave band (MW) under 3GHz, is becoming congested and scarce. 5G technology and the future network needs extra spectrum which is above the microwave because its requirement for higher data rate support. Therefore, shifting to the new spectrum of under utilized millimeter-wave (mmWave) comes with the hope of improvement of network capacity. MmWave system uses the frequency between 30 GHz and 300 GHz which gives a short millimeter wavelength ranging from 1-100mm [8].
The 5G tech is expected to exploit these band and step up the current traffic requirements and system capacity shortage one step ahead. Several industrial standards tried to recommend different bandwidth for 5G networks with respect to coexistence with it and achieving better coverage and performance. GSMA recommends IMT identifications in the 26 GHz (24.25-27.5 GHz), 40 GHz, 50 GHz (37.5-43.5 GHz), (45.5-52.6 GHz) and 66 GHz (66-71 GHz) bands while RSPG (Radio Spectrum Policy Group within which France is represented by ANFR) focuses mainly in 26,32 and 42 GHz bands [9]. On the other hand, mmWave frequencies identified at World Radiocommunications Conference (WRC-15) are shown on Figure 1.2.
These frequency bands are wide so that they can accommodate a huge amount of data flow, and as such, the mmWave technology can easily achieve 10 Gbps
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Figure 1.2: MmWave frequencies identified at WRC-15 [7].
data rate for communication. Due to this fact, mmWave technology is well suited for modern smart devices and mobile phones, which are supposed to be efficient and small in size due to its tiny component size. In addition, mmWaves can be used for HD video applications, satellite communications, automotive and radar applications, body scanners, VR headsets, and medical applications like mmWave therapy [2].
1.2 Millimeter-wave Communication Characteris- tics
Though mmWave is the best solution for spectrum scarcity and network require- ments, it has some constraints that need to be taken care of. The main drawbacks of mmWave propagation are higher path loss and blockage. These are discussed below.
1.2.1 Path Loss
The propagation loss for microwave frequency communications is not as significant as the millimeter band communications. Increasing the carrier frequency from the microwave to mmWave will increase the power loss regardless of the transmission distance, and the larger bandwidth contributes to noise power. Atmospheric atten- uation due to water drops and oxygen is in order of 10-20 dB/km. Some range of bands is less affected while others are sensitive to it. In addition to that, a Line-of- Sight (LoS) path which does not have any obstruction between the transmitting and receiving nodes has less propagation loss than a Non-Line-of-Sight (NLoS) with an obststruction present in between the transmitter and the receiver [10].
Under one of the illustrations depicted in Figure 1.3, a pictorial representation to clarify this difference between the LoS and NLoS paths can be found.
Figure 1.3: Human and building blockage in mmWave networks [12].
1.2.2 Deafness and Blockage
Deafness refers to the case where the beams of the transmitter and receiver are not aligned, making them unable to hear each other. While it prevents the com- munication link establishment, it helps with a significant interference reduction in mmWave communication [11]. On the other hand, mmWaves are vulnerable to blockage with a human body or other materials like buildings [12]. The attenu- ation due to obstacle in mmWave can reach up to 35 dB in the case of a human body based on the Friis free-space path loss formula. It reduces the bandwidth gains expected in these spectrum bands. In a NLoS situation, the path loss is higher than the microwave bands [13].
1.3 Related Works
Even though mmWaves are the potential technologies for 5G networks, it is crucial to be able to understand their specific features and adequately analyse them in order to design a system that involves such technologies correctly. Accordingly, research works including [14] and [15] with their focus on channel measurement and analysis have been performed at some mmWave frequencies to capture the channel characteristics and help to model and design 5G mmWave communica- tion systems. And several measurement-based blockage and channel models and techniques to improve existing channel models have been presented in [16–22] at different mmWave frequency bands for various scenarios, including use cases from IEEE802.15.3c and IEEE802.11ad.
Furthermore, statistical models for dynamic and self blockages have been intro- duced, and the effects of obstacles on system performance has been analyzed in [23–26] for both indoor and outdoor deployments of mmWave communication
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systems based on either existing data or experimental or simulation analysis. For example, the statistical blockage model presented in [23] is based on both elec- tromagnetic simulations and measurements on an experimental 28 GHz mmWave prototype. While it was able to mix measurements for best estimation of signal loss and time-scales at which disruptions occur due to blockage and simulations which considers the difficulties of getting measurement-based estimates for vehicles as blockers in the outdoor deployments, it did not consider the mobility of users as well as did not clearly show the behavior of blockage probability over a period of time for such systems. Similarly, the reference [27] proposes a dynamic blockage model caused by humans for urban mmWave deployments taking into account the density and dimension of transmitter-receiver pairs as well as human blockages.
Mathematical and analytical frameworks and models have also been developed and introduced in [28–30], for characterizing the effects of blockages in mmWave com- munication systems based on experimental data. For example, the work in [28]
proposed a mathematical blockage model that captures the time-dependent con- ditional probability of having blockage and the time spent in blocked/unblocked states for a stationary user at mmWave frequencies where an analysis of three different 3GPP scenarios has been considered using stochastic geometry in com- bination with renewal process theory and queuing models. However, this model did not cover the scenario where the users are moving. Similarly, an analytical expression for blockage probability has been derived for mmWave mesh network at 60 GHz by the writers of [31] in order to investigate their interference perfor- mance. References [32] and [33] have used a boolean blockage model in order to analyze the connectivity of mmWave networks with multi-hop relaying and the ef- fects of blockage on urban cellular networks, respectively. However, the temporal correlation of the blockage is not reflected.
On the other hand, another perspective of channel modeling can be seen in [34], where a neural network framework for time-varying channel modeling together with shadow fading and simulation has been proposed based on outdoor measurements at 28 GHz. While the effects of shadow fading has been considered as an add-on to the path loss model presented in this paper, the behavior of how the probability of the communication link being blocked or not changes over time has not been investigated and the effects of obstacles in the link has not been taken into account in the channel model.
Moreover, a preliminary overview of existing and ongoing campaign efforts tar- geting the 5G channel measurements and modeling has been presented in [35], which include: NIST 5G mmWave Channel Model Alliance, NYU WIRELESS, COST2100/COST, METIS2020, ETSI mmWave, IC1004, MiWEBA, and mm- Magic. Similarly, reference [36] presents a survey of projects contributing to chan-
nel modeling of mmWave communication systems, among other things. It demon- strates that even though there had been many works in the literature concerning mmWave channel modeling, there are still some limitations that need to be ad- dressed for the fact that not all characteristics of mmWaves have been sufficiently characterized to be applicable for such systems. Lack of scenarios as a potential technology for future communication systems and a ‘dual mobility’ scenario where a pair of moving nodes is feasible are among the limitations that this paper lists down. For instance, the reference [37] models the blockage loss and the path loss as a whole for vehicle-to-vehicle communication scenarios. However, it does not provide a means to predict how the probability of being blocked changes or be- haves over time. On the other hand, in the references [38] and [39], an analytical model to represent a dynamic and self blockage has been presented apart from other Quality of Service (QoS) parameters for mmWave cellular systems. Consid- ering an open-park like scenario and using stochastic geometry, these two papers, have derived closed-form expressions for the probability and duration of blockages for a LOS link as a function of blocker density, velocity, height, and link length.
However, Non-Line-of-Sight (NLOS) links, and a scenario for mobile users have not been considered.
1.4 Contribution of the Thesis
This thesis work aims to derive a simple and dynamic two-state ON-OFF blockage model using a neural network based on simulation. To the best of the author’s knowledge, there are no prior works on blockage models which incorporate all of the following features:
• An easy simulation-based two-state ON-OFF blockage model using neural networks where results can be replicated easily by just manipulating the settings of a simulator for different scenarios instead of performing various experiments.
• A model that can predict how the probability of being blocked changes or behaves over time.
• A model takes takes into account the ‘dual mobility’ scenario where the movement of users is typical like in device to device communications.
Our novel mmWave blockage model enables one to capture the temporal correlation of the blockage, which is almost ignored in all the existing works. Moreover, due to
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its simplicity, it allows for tractable mathematical analysis, which is very important for the design and optimization of robust mmWave cellular networks.
1.5 Organization of the Thesis
The rest of this thesis paper is organized as follows. First, Chapter 2 presents how the whole system is modeled. Chapter 3 summarizes the simulation details, including the assumptions made and procedures followed to address the problem.
Then, Chapter 4 presents the results and discusses the observations from those results. Finally, Chapter 5 presents the conclusions made along with possible future work ideas.
Chapter 2
System Model
This section describes how the communicating nodes, the communication link, the obstacles, and the mobility of the nodes are modeled for simulating and analyzing the blockage probability behavior in mmWave networks.
2.1 Mobility Model
In this thesis work, a Gauss Markov Mobility model has been used to mimic the movement behavior of the transmitter-receiver pairs under simulation. This model, which has a temporal dependency where a node’s actual movement is influenced by its past movement, has been chosen as this work is targeting on deriving the behavior of link blockage over time.
Similar to [40], given an initial speed and direction of a mobile node, its movement at fixed intervals of time t, is modeled by updating its speed and direction in this mobility model. To be exact, the value of speed and direction at the tth interval is calculated based upon the value of speed and direction at the (t - 1)th interval and a random variable as follows [40]:
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st= αst−1+ (1 − α)s +q
(1 − α2)sx(t−1) (2.1)
dt= αdt−1+ (1 − α)d + q
(1 − α2)dx(t−1) (2.2)
where stand dtare the new speed and direction of the mobile node at time interval t; α, where 0 ≤α ≤ 1, is the tuning parameter used to vary the randomness; s and d are constants representing the mean value of speed and direction as t→ ∞; and sx(t−1) and dx(t−1) are random variables from a Gaussian distribution.
On the other hand, the next position of the mobile node at each time interval is then calculated based on the current position, speed, and direction of movement.
Thus, the mobile node’s location at time interval t is calculated as follows:
xt= x(t−1)+ s(t−1)cos d(t−1) (2.3)
yt= y(t−1)+ s(t−1)sin d(t−1) (2.4)
where (xt , yt) and (x(t−1), y(t−1) ) are the x and y coordinates of the mobile node’s location at the tthand (t-1)thinstances, respectively, while s(t−1) and d(t−1)are the speed and direction of the mobile node at the (t-1)th time interval respectively.
2.2 Link Model
The transmitter-receiver pairs are modeled as two-dimensional points with x and y coordinates and some initial mean speed each. This, in turn, means that the link between transmitter-receiver (Tx-Rx) pair is represented as a line segment with the transmitter (Tx) and receiver (Rx) as end points. Both of these representations are illustrated in Figure 2.1. For the sake of simplicity, the transmitter is initialized at the origin (0,0) while the receiver is initialized at (1, 1) with a configured initial mean speed. Then, through time, the Gauss Markov mobility model that was discussed in the previous sub-section is applied to both the Tx and Rx, where their location, speed, and orientation is updated at each time interval accordingly.
(a) Tx-Rx pairs model as points
(b) Link model with Tx and Rx as end points
Figure 2.1: Tx-Rx pair and the respective link model
2.3 Obstacle Model
The obstacles between the transmitter and the receiver ends are modeled as a line segment with random size, position, and orientation. Obstacles are randomly dropped within the simulation area with a uniformly distributed position with size and orientation following a Poisson point process. It is assumed that if the line
(a) LoS Link Representation (b) NLoS Link Representation
Figure 2.2: Representation of LoS and NLoS Links
segment representing the link between the transmitter-receiver pairs is intersected by the line segment representing any of the obstacles, then the link is blocked and we have a Non-Line-of-Sight (NLoS) link state and Line-of-Sight (LoS) link state otherwise based on the assumption that mmWave signals can not penetrate obstacles similar to [41]. This assumption is shown in Figure 2.2, where the line
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segments representing the obstacles are drawn as buildings for the sake of clarity.
2.4 LoS and NLoS Evolution Model
The characteristics of LoS and NLoS probabilities against time is represented by a simple two-state (ON-OFF) model to imitate LoS and NLoS states. As can be shown in Figure 2.3, this model can be used to show the time that we remain on a good channel situation with low NLoS probability and the time that we go to a bad channel situation with high NLoS probability.
Figure 2.3: ON-OFF Link Blockage Model.
In this model, ON represents that the link is not blocked, and hence it is in LoS situation while the OFF represents that the link is blocked, and hence it is in NLoS situation. Additionally, TON and TOFF denote the time duration that the link will remain in LoS and NLoS states, respectively.
For the purpose of analysis, it can be modeled in the state diagram given in Figure 2.4 and a state transition probability matrix (P) given by Equation (2.7) as well. And it is used as a reference for LoS and NLoS conditions to calculate the two parameters (α and β) for a given configuration (a set of specific values of the topology parameters such as mean speed of communicating nodes, obstacle density, and size) which in turn can be used to find the probability of moving from LoS/NLoS state to NLoS/LoS state. Then a neural network can be trained to learn these two parameters from this ON-OFF model.
The two parameters α and β in Figure 2.4 represent the probabilities that the link remains in OFF(NLoS) and ON(LoS) states, respectively. And for each configu- ration C, they are calculated as:
Figure 2.4: State diagram of LoS and NLoS states
αc= P
i
P
jI{Bij > 0, Bij+1 > 0}
Rmax∗P
jI{Bij ≥ 0} (2.5)
βc= P
i
P
jI{Bij = 0, Bij+1 = 0}
Rmax∗P
jI{Bij ≥ 0} (2.6)
where Rmax represent the maximum number of different realizations of the config- uration C.
P =
α 1 − α
1 − β β
(2.7) Where α and β represent the probabilities that the link remains in NLoS and LoS states while 1 - α and 1 - β denote the probabilities that the link goes to LoS and NLoS state from NLoS and LoS states respectively.
2.5 Neural Network
A neural network (NN), inspired by biological neural networks, is an interconnected assembly of simple processing units or nodes which send signals to each other in
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order to abstract the relations between a given input and output data in order to solve complex problems that can be encountered in real-world situations. For example, there are problems with many subtle factors that can not be formulated as an algorithm like the purchase price of a real estate. NNs can learn to explore this kind of complex problems by generalizing and associating data from training samples. By doing so, they are capable of solving and finding reasonable solutions very efficiently, for similar problems of the same class that were not explicitly trained [42], [43], [44].
Neural networks are often used for statistical analysis and data modeling as an alternative to standard non-linear regression or cluster analysis techniques. They are used, for example, in image and speech recognition, textual character recogni- tion, medical diagnosis, stock market forecast, geological survey for oil as well as forecasting the number of tourists or hotel stays in a country [42], [43].
Figure 2.5 depicts the basic components of a NN, which include the processing units, which are called neurons, the inter-neuron connections, and an activation function. While each circle in the figure represents an individual neuron, the arrows represent the connections between individual neurons and indicate the fact that signals from the previous unit are transferred into the next via those connections.
Figure 2.5: Basic Components of a Neural Network.
The inter-neuron connections are defined by assigned weights, which represent the strength of the connection between the units and control the input signal’s effect on the connected neuron. These weights are obtained through training from a set of input/output data/patterns. As can be seen in Figure 2.5, the weighted sum of the values from the neurons connected to Neuron X i.e., from Neurons 1, 2 ... n is passed into an activation function (AF). Activation or transfer functions in neural networks are crucial components and mathematical representations that determine the output of the NN given a set of inputs and weights. The function
is attached to each neuron in the network and determines whether it should be activated or not based on whether each neuron’s input is relevant for the model’s prediction. According to the relevance of a neuron’s input for the prediction of the model, the AF that is attached to this neuron in the network determines if the neuron should be activated or not. Moreover, by introducing non-linearity into the neuron’s output, the AF makes the NN capable of learning and performing more complex tasks [42], [43].
A typical NN is organized in layers which are made up of interconnected neurons, and the basic structure consists of the following three kinds of layers [42], [44]:
1. Input layer: which provides information from the outside world to the net- work. Each of the neurons that make up the input layer represents an in- dividual feature from each sample within the dataset that will pass to the data model.
2. Hidden layers: which are the abstraction layers of the NN, which perform all computations on the features entered through the input layer and transfer the result to the output layer.
3. Output layer: which brings up the information learned by the network to the outside world.
The neural network (NN) used in this thesis work aims to learn the two parameters (α and β) of the ON-OFF model for different configurations (C). The different configurations are obtained by changing the size and density of obstacles in the area as well as the initial mean speed of the transmitting and receiving nodes. Then, for each of the configurations, the probability of the NLoS conditions (PNLoS), the α and β are mathematically computed from the status of the link being blocked or not at different time intervals which depends on the locations of the transmitting and receiving nodes as well as that of the obstacles in the area. The PNLoS situation for a configuration C at a time interval j is calculated as:
PN LoSj = P
iI{Bij > 0}
P
iI{Bij ≥ 0} (2.8)
where i is the number of realizations of C. Thus, for a configuration C, the series of PNLoS situations can be written as a list of the PNLoS situations at every trajectory.
PN LoSC = [PN LoS1, PN LoS2, ..., PN LoSM] (2.9) where M is the number of trajectories.
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On the other hand, the two parameters, α, and β, are computed using Equations (2.5) and (2.6), respectively. This, in turn, results in one set of values (C, α, β) per configuration C as one sample dataset for training the NN. Thus, the task of the NN is to find the mapping between C as inputs (in terms of the probability of NLoS conditions) and α and β for the same configuration as expected outputs.
Thus, one set of values for this dataset (input-output chain) of the NN for a single configuration C can be shown in Figure 2.6.
Figure 2.6: Neural Net Input Output Diagram.
In this chapter, simplified models for the different components of a mmWave com- munication system has been shown and thoroughly described. In the next chapter, how these models are applied and combined together to introduce a new blockage model for mmWave networks will be presented.
Chapter 3
Simulation
In this section, the simulation tools used, assumptions, parameter choices made, as well as the simulation procedures performed for this work, will be presented.
This thesis work involves two different simulation phases.
1. The first phase was to generate the evolution of the mobility of the nodes, which gives the trajectories and the probability of the LoS and NLoS con- ditions of the link under test over time. The name tagged link is used from now onwards to mean the link under test in this paper. Hence, the purpose of the first phase will be to obtain a dataset that will be processed to be used as an input of the second simulation phase.
2. The second phase was to use the results from the first phase as an input to a neural network (NN) and train the NN to generate a 2-state model to represent the probabilities of being in LoS and NLoS conditions for the tagged link.
3.1 First Simulation Phase
The first simulation phase involves generating the data set that will be manip- ulated to create the input data for the next simulation stage i.e., for training a neural network, and it was performed for three different car scenarios with mean speeds [45], [46] of:
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• 8.33 m/s - Typical car speed on residential and busy city roads
• 13.89 m/s - Typical car speed on city roads
• 19.44 m/s - Typical car speed on highway
and three different pedestrians scenarios with mean speeds [47], [48] of:
• 1 m/s - Slow pedestrian speed
• 1.4 m/s - Average human walking speed
• 1.79 m/s - Brisk walking speed
with different combinations of parameters for:
• Round (Number of Extended Topologies (ETs) per configuration) = 1000
• Interval Limit (Number of trajectories per extended topology) = 49
3.1.1 Simulation Tool
A Java-based simulator which was developed at KTH for generating a two-dimensional random topology of communicating nodes and obstacles was used as a basis of the first simulation phase. After generating the initial topology, a module for the mo- bility model, and some more algorithms were added to the simulator to generate all required data that can be used in the next phase.
3.1.2 Simulation Parameters
Different combinations of the simulation parameters shown in Table 3.1 were used to create a total of 48 configuration scenarios, which are used as a basis for the simulations to evaluate the evolution of the trajectory and LoS and NLoS prob- abilities of the tagged link with time. Then, the resulting outputs were used for the neural network to get trained in the next stage.
Initial Simulation Area (m2) 10 x 10
Simulation Area (m2) 800 x 800
Simulation Time (min) 20
Round of Simulations
(Number of Realizations) 1000
Sampling Interval (sec) 19
Obstacle Mean Size (m) 0.5, 1.0
Obstacle Density 0.0025, 0.005, 0.0075, 0.01 Mean Speed of Nodes (m/s) 1.0, 1.4, 1.79, 8.33, 13.89, 19.44
Table 3.1: Simulation Parameters
3.1.3 Simulation Assumptions and Procedures
The following assumptions have been made for simplicity reasons in the first sim- ulation phase:
1. The nodes constituting the tagged link are initialized within the initial sim- ulation area at:
• The origin (0.0, 0.0) for the Transmitter (Tx) and
• (1.0, 1.0) for the Receiver (Rx)
2. The obstacles are stationary and randomly distributed over the simulation area with a uniform distribution.
The initial simulation area indicated in Table 3.1 is a small area (10x10 m2) where the nodes constituting the tagged link are initialized before the start of the actual simulation. On the other hand, the actual simulation is performed within the whole simulation area (800x800 m2) where the obstacles are randomly initialized, and the mobility of the nodes takes place. This distinction between the initial simulation area and the actual simulation area can be shown in Figure 3.1.
And then, the Gauss Markov mobility model is applied to the nodes throughout the simulation time to generate how the trajectory for those nodes; apparently, the tagged link looks with respect to time. The parameters of the mobility model are chosen as follows:
• While the tuning parameter to vary randomness for the mobility model (al- pha) is a configurable parameter in the designed simulator, a medium value
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Figure 3.1: Distinction between initial simulation area and actual simulation area.
of 0.5 has been chosen for the simulations in this thesis work.
• sxn-1 and dxn-1 are chosen from a random gaussian distribution with mean equal to zero and standard deviation equal to one.
• The initial mean speed of the transmitting and receiving nodes is set to one of the above car or pedestrian scenarios per configuration. It will then be used in calculating the next value of the mobility speed over time.
• An initial value of π/2 radians is considered for the mean direction that will be used in calculating the next value of the direction of mobility over time.
A sample evolution of the mobility of the Tx and Rx nodes can be seen in Fig- ure 3.2, which was plotted from a trajectory output picked from one random round of one of the configuration scenarios. Meanwhile, as the nodes move around the simulation area, the state of being blocked or not i.e., whether there are obsta- cles encountered between the Tx and Rx nodes or not, is evaluated and stored.
The simulation stores the generated trajectories and obstacle conditions for each configuration consisting of 1000 rounds in a CSV file for later usage.
For each configuration scenarios, 49 trajectories for the tagged link and the state of any obstacles being in the path of the tagged link or not for each of the trajectories have been generated for 1000 rounds. Thus 1000 ETs of 49 trajectories were derived for the tagged link during the first simulation phase constituting of the
Figure 3.2: Sample mobility of Tx and Rx nodes of the tagged link for a configuration C at some random round: where the red triangles represent the
start and end points of the mobility for each node while individual steps are indicated by a * marker.
trajectories for the tagged link and the availability of obstacles in the path of the tagged link, as shown in Figure 3.3. The 49 trajectories were obtained from the first simulation phase with a simulation time of approximately 20 minutes, where successive samples were executed about every 19 seconds.
Figure 3.3: Different Realizations (Extended Topologies) of a Configuration C.
Next, the probability of Non-Line of Sight (PNLoS) situation for each of the con- figuration scenarios was calculated at each of the trajectories of the tagged link
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according to Equation (2.8) presented in the previous section based on the ex- tended topologies that were obtained from this simulation. Then, the PNLoS series specified in Equation (2.9) is the one that is being used as an input parame- ter to the neural network in the second simulation phase. Figure 3.4 shows a visual summary of the procedures that were taken during the first simulation phase.
Figure 3.4: First Phase Simulation Procedure for One Configuration Scenario.
3.2 Second Simulation Phase
The second simulation phase involves training a neural network (NN) using the outputs of the previous simulation phase as input parameters to the NN in order to predict the probability of the channel remaining either in LoS (β) or NLoS (α) states.
3.2.1 Simulation Tool
In this phase, a python based simulator with different modules to read and pro- cess the raw data from the previous phase, train the NN and eventually generate
and document the results was developed. The NN python implementation from nimblenet [49] was used with some customization in order to train the above data.
Nimblent is an implementation of a fully connected neural network in NumPy, which can be trained by a variety of learning algorithms. Furthermore, the choices made for the NN based on some theoretical suggestions, as well as trial and error methods are briefly described in the following sections.
3.2.2 Layers and Activation Functions
Apart from an input layer of 49 neurons representing the 49 PNLoS derived earlier in the first phase and an output layer of 2 neurons representing the probability of the channel remaining either in LoS (β) or NLoS (α) states, only a single hidden layer has been used for the NN. The number of neurons in the hidden layer has been chosen to be approximately two-thirds of the sum of the number of neurons in the input and output layers. Adding more hidden layers did not improve the performance of the NN, as it has been noticed during trial and error. Thus, the usage of the number of hidden layers in this work had been limited to one. An overview of the NN architecture used for this thesis work is shown in Figure 3.5.
Figure 3.5: Neural Network Architecture Used.
For the simulation that is performed in this thesis work, a Rectified linear unit (ReLU) activation function has been used on the hidden layer as it takes less time to train and converges faster; while a sigmoid activation function which is also called logistic activation function has been used in the output layer since we want
22
to predict a probability as an output. A ReLU function which outputs the inputs directly if it is positive and zero otherwise is mathematically defined as:
f (x) = max(0, x) (3.1)
And the sigmoid function is characterized by an S-shaped curve and is defined as the ratio of the exponential of the input value and the sum of the exponential value of the input value and one as can be seen in Equation (3.2).
f (x) = ex
1 + ex (3.2)
3.2.3 Optimization Method
In the context of neural networks, optimization means minimizing a cost function by iteratively tuning the trainable parameters, which in turn means to find a set of parameters that minimize the cost function of the neural network on a training data set. This, in turn, would optimize some of the performance measures of the learning algorithm for a machine learning model and improve the performance on a test data set.
In this thesis work, an algorithm that uses adaptive learning rates, the Adam (Adaptive Moment Estimation) optimizer is used as an optimization algorithm for training the neural network since it tends to efficiently solve practical deep learning problems by combining the merits of RMSProp and momentum optimizers. This efficiency, as compared to other optimization algorithms, can be clearly seen in Figure 3.6 as it has been presented in [50].
3.2.4 Cost Function
A sum squared error cost function is used to train the neural network since the problem that needed to be solved is given the Non-Line of Sight probabilities of different configuration scenarios, the neural network needs to learn the probability that the channel is in a good/bad state.
Figure 3.6: Comparison of different optimization algorithms on multilayer neural network training [50].
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Chapter 4
Results and Discussions
Following the training of a NN to learn the two parameters of the ON-OFF blockage model (α and β) from the probability of NLoS condition that was obtained directly from data as described in Chapter 3, in this section, first, the analysis of those two parameters was performed. Going forward, the actual versus the simulation results of the ON and OFF duration and that of the NLoS probability of the link given that it started in ON state is demonstrated. Moreover, the validation of the ON-OFF blockage model is performed by comparing simulation results obtained by training a NN with actual results which were obtained directly from data for different configuration scenarios.
For validating the ON-OFF blockage model, the Wasserstein Distance (WD) of order one between the actual and simulation results for different probability distri- butions has been used for quantifying the difference between them. The lower the value of WD, the more similar the probability measures being compared are and vice versa. The WD of order r (r ≥ 1) between any two probability measures p and q on a finite space X = {x1, x2, . . . , xN} is computed in the following manner [51]:
Wr(p, q) = min
w∈π(p,q)
X
x,x0∈X
dr(x, x0)wx,x0 1/r
(4.1)
where π(p, q) is the set of all probability measures on X x X with probability measures p and q, respectively.
4.1 Comparison of ON-OFF Model parameters
The NN described in the last section was able to be trained with an error limit of 0.0008 with a number of training samples of half of the 48 datasets. A plot of the simulation and actual results for the α and β of different configuration scenarios is shown in Figures 4.1, 4.2 and 4.3.
Figure 4.1: Impact of mean speed of Tx and Rx Nodes on the Probabilities that a Link remains in LoS and NLoS states fixing the density and mean size of
Obstacles at 0.01 and 1.0 m respectively.
Figure 4.1 illustrates the trend of actual and simulated values of alpha and beta for different configurations with the same density and mean size of obstacles while varying the mean speed of Tx-Rx nodes. It can be seen that there was more than 50% reduction in the probability of the link remaining in LoS state. At the same time, there has been about a 15% rise in the probability of the link remaining in NLoS state from the slowest pedestrian scenario of 1 m/s to the typical car scenario on the highway with 19.44 m/s speed.
Overall, whether it is with the simulation results or the actual values from direct data, as the mean speeds at which the Tx and Rx nodes make their movement increases, we can see a clear upward trend in the probability that a link remains in NLoS state. At the same time, there is a downward trend in the probability that a link remains in the LoS state.
26
Figure 4.2: Impact of density of obstacles on probabilities that a Link remains in LoS and NLoS states fixing the mean speed of Tx and Rx Nodes and mean size
of Obstacles at 1.79 m/s and 1.0 m respectively.
Similarly, Figure 4.2 gives information about actual and simulated values of α and β for different configurations with the same mean speed of Tx and Rx nodes and mean size of obstacles while varying the density of obstacles. It can be seen that there was a very slight decrease in the probability of the link remaining in the LoS state. In contrast, the probability of the link remaining in NLoS state has decreased by about 8% from an obstacle density of od = 0.0025 to an obstacle density of 0.005. And then, it shows a very slight increase afterward except for the deviations seen with the simulated results.
The trend of actual and simulated values of alpha and beta for different configura- tions with the same density of obstacles and mean speed of Tx and Rx nodes while varying the mean size of obstacles has been demonstrated in Figure 4.3. It can be seen that there was a slight decrease in the probabilities of the link remaining in LoS and NLoS states as the mean size of obstacles increased from 0.5m to 1.0 m.
Some unexpected behaviors were observed, like the decrease in the probability of remaining in NLoS state with increasing mean size of obstacles in Figure 4.3. This can be due to the effect of the randomness of the location and size of the obstacles as well as the trajectories that were taken by the Tx and Rx nodes as another group of datasets that were not included in the results show otherwise.
Figure 4.3: Impact of mean size of obstacles on probabilities that a Link remains in LoS and NLoS states fixing the mean speed of Tx and Rx Nodes and density
of Obstacles at 1.79 m/s and 0.01 respectively.
4.2 Comparison of NLoS probability
Given the transition probability matrix of the ON-OFF state model (P), the prob- ability that a Markov chain will be in state j after n steps starting in state i is the same as the ijth entry Pij(n) of the n-step transition probability matrix Pn [52].
Based on this, the probability of a link being in a NLoS state after n steps given that it was in LoS state at time 0 was calculated and compared between the actual and simulated results for different configuration scenarios.
The conditional probability that a link will be in NLoS state at the nth time interval given that it starts at a LoS state at time 0 is depicted in Figures 4.4 - 4.6 for different configurations over a time period of approximately 20 minutes.
How this conditional probability behaves over time when the mean speed of the Tx and Rx nodes are changing while all other parameters are kept constant is illustrated in Figure 4.4. It can be seen from the figure that during the first 10 time intervals, the probability rises up, and then it saturates afterward for all scenarios of different mean speeds. This could be due to the increase in the mean speed of the communicating devices is triggering an increase in the distance between them, which in turn makes the link more susceptible to blockage. Another interesting trend that can be seen from the figure is that there is a significant gap between the probabilities for pedestrian scenarios and car scenarios. The slowest
28
(a) Probability that a link will be in a NLoS state after n time slot steps given that it was in LoS state at time 0
(b) WD between the actual and simulated probabilities
Figure 4.4: Impact of mean speed of Tx and Rx Nodes on the probability that a link will be in a NLoS state after n time slot steps given that it was in LoS state
at time 0 fixing the density and mean size of Obstacles at 0.01 and 1.0 m respectively.
car configuration has conditional NLoS probability of more than twofold of the fastest (brisk walking) pedestrian scenario. Overall, as the mean speed at which the nodes move around increases, the probability that the link will be NLoS state at a specific time given that it starts in a LoS state increases.
The deviations that can be observed between the actual and simulated curves in Figure 4.4 (a) are quantified with their respective WD distances in Figure 4.4 (b).
For example, a maximum deviation was observed between curves with a mean speed of 1.79 m/s followed by the ones with a mean speed of 1.0 m/s, which is illustrated as WD values of about 0.1 and 0.04, respectively. Red dotted horizontal lines are used to indicate if a configuration dataset was one of the training samples that was used to train the NN. This helps to demonstrate the relative performance of the NN with trained and untrained datasets. For instance, configurations with a mean speed of 19.44 m/s and 1.0 m/s were subsets of the training samples, as indicated in the figure. Even though they have small WD values relative to the maximum value encountered, some of the other configurations which were not part of the training dataset have even smaller values.
(a) Probability that a link will be in a NLoS state after n time slot steps given that it was in LoS state at time 0
(b) WD between actual and simulated probabilities
Figure 4.5: Impact of density of obstacles on the probability that a link will be in a NLoS state after n time slot steps given that it was in LoS state at time 0 fixing mean speed of Tx and Rx Nodes and mean size of Obstacles at 1.79 m/s
and 1.0 m respectively.
Similarly, how conditional probability behaves over time when the obstacle density is changing while all other parameters are kept constant is illustrated in Figure 4.5.
It can be seen from the figure that during the first 15 to 20 time intervals, the probability rises up. Then, it leveled off at the peaks afterward for all scenarios of different obstacle densities. It has also been observed that as the density of
30
obstacles increases, the probability that the link will be NLoS state at a specific time given that it starts in LoS state interval also increases.
As it is depicted in Figure 4.5 (b), a minimum deviation of the actual and simulated curves is encountered with a WD value of 0.01585 for a configuration with an obstacle density of 0.0075. This configuration was also part of the training dataset.
It can also be observed that all the other configurations which were not part of the training sample have higher deviations with a maximum difference with a WD value very close to 0.1 between the curves for a configuration with 0.01 obstacle density.
(a) Probabilities that a link will be in a NLoS state after n time slot steps given that it was in LoS state at time 0
(b) WD between actual and simulated probabilities
Figure 4.6: Impact of mean size of obstacles on the probability that a link will be in a NLoS state after n time slot steps given that it was in LoS state at time 0 fixing the mean speed of Tx and Rx Nodes and density of Obstacles at 1.79 m/s
and 0.01.
Another scenario of the conditional NLoS probability has been obtained by chang- ing the mean size of obstacles while keeping all other parameters constant. This
scenario has been depicted in Figure 4.6. Similar to the scenarios shown in Fig- ure 4.5 for varying the obstacle density, the scenario observed from varying ob- stacles’ mean size is that during the first 20 time intervals, there is a rise in the probability and goes into a steady-state for the rest of the time intervals. More- over, it can also be seen that the larger the obstacles’ mean size, the larger the probability that the link will be in NLoS state at a time interval provided it started in a LoS state will be.
The difference in the actual and simulated probabilities is illustrated with the part (b) of the figure with a maximum of almost 0.1 WD between them, which also reflects the highest gap that can be seen in part (a) of the figure. The distance at an obstacle mean size of 0.5 m is about 0.07 lower than the one at an obstacle size of 1.0 m mean size.
The findings demonstrated in Figures 4.4 - 4.6 can be summarized as there is a tradeoff between LoS probability and size and density of obstacles as well as the mean speed of communicating devices, which are also in accordance with what is reported by [32] and [41].
4.3 Comparison of LoS and NLoS Duration CCDFs
Given the transition probability matrix of the ON-OFF state model (P) by Equa- tion (2.7) as has been provided in Chapter 2, the complementary cumulative dis- tribution function (CCDF) of LoS condition duration i.e., the probability that the link will be in LoS situation for a duration of n discrete time slots or longer is calculated as follows [53]:
FLoSC (n) = lim
N →∞
N
X
i=n
βi(1 − β) n = 1, 2, 3, ...N (4.2)
Similarly, the probability that the link will be in NLoS situation for a duration of n discrete time slots or longer is expressed as follows [53]:
FN LoSC (n) = lim
N →∞
N
X
i=n
αi(1 − α) n = 1, 2, 3, ...N (4.3)
32
4.3.1 Comparison of LoS Duration CCDF
It can be observed from Figure 4.7 that in case of scenarios with car speeds, the probability of LoS duration for more than 10 time intervals (more than 3 minutes) is lower than 0.05.
(a) CCDF of LoS Duration
(b) WD between actual and simulated probabilities
Figure 4.7: Impact of mean speed of Tx and Rx Nodes on LoS duration keeping the density and mean size of Obstacles constant at 0.01 and 1.0 m respectively.
The probability of a longer LoS duration for example, for more than 45 time intervals (more than 14 minutes) is more than 0.05 for all of the scenarios with pedestrian speeds. This result is consistent with the results found in Section 4.1 for the two parameters of the ON-OFF model, demonstrating that the LoS duration probability is sensitive to the mean speed of the communicating devices. The faster
the speed, the lower the LoS duration.
(a) CCDF of LoS Duration
(b) WD between actual and simulated probabilities
Figure 4.8: Impact of density of obstacles on LoS duration while fixing the mean speed of Tx and Rx Nodes and mean size of Obstacles constant at 1.79 m/s and
1.0 m respectively.
Moreover, the gaps between the actual and simulated results can be demonstrated by the WD between them for each of the configurations, as shown in part (b) of the figure. The configuration with a mean speed of 1.0 m/s and 19.44 m/s are labeled with an additional horizontal dotted line to indicate they were part of the training samples used by the NN while the others were used only in testing samples. It can be seen that the maximum WD between the actual and simulated results is 0.14 at a mean speed of 1.0 m/s while the minimum is lower than 0.01 at a mean speed of 19.44 m/s for the distributions shown in part (a) of the figure.
34
When we look at the LoS duration results for different configurations of varying obstacle density as illustrated in Figure 4.8 (a) and (b), it can be clearly seen that the LoS duration is inversely related to the density of obstacles which is consistent with the observations in Section 4.1 as well. The inconsistency with simulated results between an obstacle density of 0.0075 and 0.01 which could be a combined effect of the fact that the deviation at an obstacle density of 0.01 is 0.11 more than that at an obstacle density of 0.0075 as shown in part (b) of the figure while the actual distribution values are lower than the corresponding values for configurations of smaller densities by one to more than three folds.
(a) CCDF of LoS Duration
(b) WD between actual and simulated probabilities
Figure 4.9: Impact of mean size of obstacles on LoS duration while fixing the mean speed of Tx and Rx Nodes and density of Obstacles constant at 1.79 m/s
and 0.01 respectively.
Furthermore, a maximum of about 0.276 WD at an obstacle density of 0.0025 and a minimum of about 0.028 WD at an obstacle density of 0.0075, which was the only configuration being part of the training samples among the configurations plotted the figure was observed.
Similar to the density of obstacles, it can be deduced from Figure 4.9 that the mean size of obstacles affects the LoS duration probability with an inverse relationship;
the higher the obstacle mean size, the lower the LoS duration probability will be.
For example, at a mean obstacle size of 1.0 m, the link will be in a LoS state for more than 40 time intervals (more than 12 minutes) with a probability of less than 0.2 while the same LoS duration can be achieved with a probability of more than 0.5 at a mean obstacle size of 0.5 m.
On the other hand, the WD between the actual and simulated results for the two configurations shown in part (a) of the figure are illustrated in part (b) of the figure with a WD of about 0.14 at an obstacle mean size of 1.0 m and 0.05 at an obstacle size of 0.5 m.
4.3.2 Comparison of NLoS Duration CCDF
It can be seen from Figure 4.10 that the probability of NLoS duration is directly proportional to the mean speed of the communicating devices, complementing the results observed in subSection 4.3.1 where increasing the mean speed of commu- nicating devices reduces the probability of LoS duration.
The two configurations which were part of the training samples comprise the lowest and highest WD values of 6.2x10-4 at a mean speed of 1.0 m/s and 3.9x10-2 at a mean speed of 19.44 m/s respectively. All the other configurations are not part of the training samples, and their WD values are in the range of the minimum and maximum values shown. Furthermore, the ups and downs of the WD values in Figure 4.10 (b) clearly reflect the gaps between the actual and simulated curves plotted in Figure 4.10 (a).
The CCDF of NLoS duration for configurations of different obstacle densities is illustrated in Figure 4.11 (a). As the number of time intervals increases, the probability that the link will remain in NLoS state for a duration of a specific number of time intervals or more is shown to decrease quickly. For example, starting with a probability of more than 0.7 for NLoS duration for a period of 1 time interval (19 seconds) or more, the probability drops to less than 0.2 for an NLoS duration of 12 time intervals (approximately 4 minutes) or more.
The actual and simulated CCDFs experienced the highest difference between them with a WD value of around 0.075 at an obstacle density of 0.0025 followed by WD values approximately 0.02 at obstacle densities of 0.005 and 0.01 as can be seen
36
(a) CCDF of NLoS Duration
(b) WD between actual and simulated probabilities
Figure 4.10: Impact of mean speed of Tx and Rx Nodes on NLoS duration while keeping the density and mean size of Obstacles constant at 0.01 and 1.0 m
respectively.
in Figure 4.11 (b) with the configuration of obstacle density of 0.0075 having the lowest distance being part of the training samples.
Similar to the previously presented CCDFs of the NLoS duration probabilities, it is evident from Figure 4.12 (a) that the probability of NLoS duration for a period of a specific time interval or more has a downward trend with respect to the number of time intervals. Unexpected behavior has been observed as a configuration with an obstacle mean size of 0.5 shows higher NLoS duration probability than another configuration with an obstacle mean size of 1.0 which is consistent with what
(a) CCDF of NLoS Duration
(b) WD between actual and simulated probabilities
Figure 4.11: Impact of density of obstacles on NLoS duration keeping the mean speed of Tx and Rx Nodes and mean size of Obstacles constant at 1.79 m/s and
1.0 m respectively.
was observed in Figure 4.3 which was speculated to be due to randomness of the topology parameters for the specific dataset.
As can be observed from Figure 4.12 (b), both the configuration scenarios were not part of the training samples as there were no horizontal dotted red lines with a maximum WD value of a little more than 0.025 is encountered at an obstacle mean size of 0.5.
38
(a) CCDF of NLoS Duration
(b) WD between actual and simulated probabilities
Figure 4.12: Impact of mean size of obstacles on NLoS duration keeping the mean speed of Tx and Rx Nodes and density of Obstacles constant at 1.79 m/s
and 0.01.
4.4 Performance of the Neural Network
From the WD results obtained between the actual and simulated probability pa- rameters that were demonstrated in the previous sections, it can be concluded that the NN is able to give good results for different configuration scenarios regardless of a configuration being in training datasets or not. It was clearly demonstrated that untrained datasets of configurations can also have even lower WD values than the ones in trained datasets.
Furthermore, the performance of the NN with multiple training samples is demon- strated in terms of the WD between the actual and simulated results in Table 4.1
and Table 4.2. In Table 4.1, the WD values between actual and simulated sequence of values for the two ON-OFF model parameters (α and β) is presented. On the
Number of Training Sample
Datasets WD (α) WD (β)
5 0.0428776341193 0.0429217237102
15 0.0164288216993 0.0177197841075
24 0.011061631265 0.00763180332194
30 0.0101585506625 0.0075314960101
Table 4.1: Comparison of WD for Different Number of Training Samples for the two parameters of the ON-OFF Blockage Model.
other hand, for each simulation with a specific number of training samples, the performance comparison is shown in Table 4.2 as the averaged value of WD (W D) of each of the configuration scenarios, which is obtained as follows.
W D =
48
X
n=1
W Dn (4.4)
where WDn is the WD for the nth configuration.
As can be seen in Tables 4.1 and 4.2, as the number of training sample datasets
Number of Training Sample
Datasets
W D (PNLoS)
W D (LoS Duration
Probability)
W D
(NLoS Duration Probability)
5 0.1036 0.2312 0.0489
15 0.0485 0.1137 0.0271
24 0.0220 0.0523 0.0159
30 0.0178 0.0492 0.0124
Table 4.2: Comparison of Averaged WD for Different Number of Training Samples.
40
increases, the NN can learn with less WD between the actual and simulated prob- ability distributions, which in turn leads to better modeling of the blockage with the proposed two-state ON-OFF model.
