Fundamental performance analysis ofmillimeter wave relay networks

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Fundamental performance analysis of millimeter wave relay networks

ROBERTO CONGIU

Master’s Degree Project Stockholm, Sweden September 2015

TRITA-EE 2015:74

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KTH, Kungliga Tekniska Högskolan

Master Thesis

Fundamental performance analysis of millimeter wave

relay networks

Author:

Roberto Congiu

Supervisor:

Hossein Shokri Ghadikolaei

Examiner:

Prof. Carlo Fischione

A thesis submitted in fulfilment of the requirements for the degree of Telecommunications Engineering

in the

Automatic Control Department School of Electrical Engineering

October 18, 2015

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KTH, KUNGLIGA TEKNISKA HÖGSKOLAN

Abstract

Automatic Control School of Electrical Engineering Telecommunications Engineering

Fundamental performance analysis of millimeter wave relay networks

by Roberto Congiu

Due to spectrum scarcity in the microwave bands, used by legacy communication technologies, the millimeter wave (mmWave) bands are considered as a promising candidate to extremely high data rate access in future wireless networks. MmWave communications exhibit high attenuations, vulnerability to obstacles, and sparse-scattering environments. The small wavelengths of mmWave signals make it possible to incorporate many antenna elements both at the transmitters and at the receivers, which lead to high antenna gains. This demands a reconsideration of almost all design aspects in mmWave networks compared to the traditional networks, espe- cially at the medium access control (MAC) layer. Blockage affects heavily the performance of mmWave networks. How to model blockage and its impacts on the key performance indicators are largely open problems.

In this thesis, a new blockage model is introduced, which allows evaluating the impact of penetration loss due to obstacles on the fundamental performance indicators including achievable throughput and delay. Using this blockage model, the achievable throughput and delay of two solution ap- proaches to overcome blockage, namely fallback and relay, is investigated.

The analysis highlights an interesting correlation between blockage period and the importance of using one technique or the other one. Afterwards, a delay analysis is proposed to focus on more realistic scenarios. Such an analysis is then used to characterize the throughput-delay tradeoff. The latter section allows to explore the impact of the main network parameters such as beamwidth, obstacle occurrence, blockage period, transmission time and alignment overhead. A general framework is proposed, in which it is shown under which condition which option is preferable, from throughput-delay perspective, at the transmitter to mitigate the blockage problem. More- over, it shows the situations under which these two techniques are not feasible in order to fulfil some throughput-delay requirements. Simulations are presented in order to validate the equations used at the performance analysis.

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Acknowledgements

First of all, I would like to thank my supervisor Hossein for the patience and his constantly help during the development of this thesis work. He taught me the basic of being a researcher, motivating me step by step during all this period. Thank you. Moreover, I have to thank Prof. Carlo Fischione for all the opportunities he gave me during this year at KTH, Stockholm. He helped me with the design of my studies plan, coordinating each aspect of my career during all our cooperation time. I learned a lot, both as person and as student. Furthermore, I have to thank all the amazing people met during this year, as Erasmus project. I would not have done so much without all of you and I will not forget all the moment spent together I promise. In the end, I thank my family and my girlfriend that although so far from me were able to be always so close, helping me in the worse moments. I do not know if I will have enough time to reciprocate.

To all of you.

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List of Figures

2.1 Simple network model considered . . . 6

2.2 Time slots divided in phases . . . 6

3.1 Time slot in a queuing system . . . 12

3.2 Queuing system; general scheme with infinite buffer capacity and servers . . . 12

3.3 M|M|1|1 system . . . 13

3.4 Countless obstacles can cause blockage . . . 13

3.5 Markov chain of M |M |∞ . . . 14

4.1 Option choice related to µ [1/s] . . . 18

4.2 Option choice related to the virtual time slot (inter-LoS- interval) [s] . . . 18

4.3 Option choice related to the blockage time [%] . . . 19

4.4 Option choice related to the blockage time [%], with energy saving consideration . . . 19

4.5 Throughput analysis function of blockage time, beamwidth=5^o 20 4.6 Throughput analysis function of blockage time, beamwidth=20^o 20 4.7 Throughput analysis finite regime epsilon=1e-6, m=100 . . . 21

4.8 Throughput analysis finite regime epsilon=1e-6, m=1000 . . 21

4.9 Throughput analysis finite regime epsilon=1e-6, m=50 . . . 22

4.10 Threshold sensibility for blocklength=100 . . . 22

4.11 Threshold sensibility for blocklength=10 . . . 23

4.12 Threshold sensibility for different blocklength in function of block error probability . . . 24

4.13 Impact of 33% of blockage probability . . . 25

4.14 Impact of 8% of blockage probability . . . 25

4.15 Simulation and analytical result of throughput analysis [1.0] 26 4.16 Simulation and analytical result of throughput analysis [2.0] 26 5.1 Delay-Throughput tradeoff for a beamwidth= 20^◦ . . . 30

5.2 Delay-Throughput tradeoff for a different transmission time 30 5.3 Delay-Throughput tradeoff for a different blockage time . . 31

5.4 Delay-Throughput tradeoff for a different beamwidth= 5^◦ . 31 5.5 General framework for high payload applications . . . 32

5.6 Threshold function for the feasible range . . . 33

5.7 General framework for low payload applications . . . 34

5.8 Threshold function for the feasible range [2.0] . . . 34 5.9 Throughput-Beamwidth tradeoff for blockage period=48% . 35 5.10 Throughput-Beamwidth tradeoff for blockage period=55% . 35

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5.11 Throughput-Beamwidth threshold choice, blockage=50% . . 36 5.12 Throughput-Beamwidth trade off for different blockage pe-

riod=48% [2.0] . . . 36 5.13 Throughput-Beamwidth trade off for different blockage pe-

riod=55% [2.0] . . . 37 5.14 Throughput-Beamwidth threshold choice,blockage=50% [2.0]

. . . 37 5.15 Simulation for Fallback option; M|D|1 system . . . 37 5.16 Simulation for Relay option; M|D|1 system . . . 38

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List of Tables

2.1 Summary of main notations . . . 8

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List of Abbreviations

MAC Medium Access Control LoS Line of Sight

NLoS Non Line of Sight SNR Signal to Noise Ratio

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Chapter 1 Introduction

Growing demands for higher data rates are always parts of almost all wireless applications. The increased data rate, besides improving the QoS of previous applications, enable many new use cases, including mobile back- hauling/fronthauling and offloading (minimum 20 Gbps), 8K video transfer at smart homes (minimum 25 Gbps) and wireless backup links in data cen- ters (minimum 40 Gbps) [1]. The state of the art in conventional technologies in cellular networks (LTE-advanced release 11-12 with peak data rate of 1 up to 3 Gbps [2,3]) and short range networks (IEEE 802.11ac with peak data rate of 6.9 Gbps [4]) can less likely support those future applications with extremely high data rates. The main reason is relatively short amount of bandwidth available at the microwave bands. The promising solution is going to higher frequency and using (mmWave) communications. mmWave communications appear as a future step of wireless communication to alleviate the imminent spectrum scarcity and to meet the growing demands of extremely high data rate application. In fact, current mmWave standards such as IEEE 802.11ad can support up to 6.7 Gbps and its extension, re- cently formed as IEEE 802.11ay, is envisioned to have more than 40 Gbps data rate.

The mmWave bands refer to the electromagnetic spectrum between 30 and 300 GHz, which correspond to the wavelengths from 10 mm to 1 mm. On the negative side, the channel attenuation in the mmWave bands is gener- ally higher than that of conventional microwave bands (below 6 GHz).

Moreover, huge bandwidth leads to order(s) of magnitude higher noise power accumulated at the receiver, which in turn can substantially reduce signal-to-noise ratio (SNR). On the positive side, small wavelength of the mmWave signals facilitates the integration of numerous antenna elements in the current size of radio chips, which promises a significant antenna gain both at the transmitter and at the receiver. These antenna gains can completely compensate for the higher channel attenuation as well as the higher noise power, and provide the same (if not higher) SNR level as the traditional microwave networks over order of magnitude higher operating bandwidth. A direct consequence is supporting Gbps data rates.

Blockage and deafness are two important problems in mmWave communication [5]. Blockage is high penetration loss in mmWave networks due to solid materials. Examples include 35 dB due to the human body and 20/30 dB due to the furniture in the environment [5–7]. Deafness refers

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2 Chapter 1. Introduction to a misalignment between main beams of the transmitter and receiver, prohibiting establishment of a high quality mmWave link. To avoid deafness, a source-destination pair should execute a time consuming alignment procedure [8].

1.1 Addressing blockage

These extreme attenuations cannot be compensated by increasing the transmission power. Upon appearance of an obstacle in the direct link between a transmitter and a receiver, there are two promising options to alleviate the blockage: relaying [9] and fallback [8]. In the relaying techniques, the source node bypasses the obstacles and communicates with the destination using an intermediate station, called relay. Note that cause of high directionality in mmWave communication, the receiver is able to receive signal either from the direct or from the relay path. This is different from conventional microwave networks, where the superposition of signals received from both direct and relay paths is used for decoding. Using relaying options, the source node has to solve deafness with an alignment overhead procedure, which is time-consuming, but it keeps on transmitting at mmWave bands. The other solution, called fallback, is to switch to the microwave bands (e.g., 2.4 GHz) during blockage and return to the mmWave bands once the obstacle(s) disappears. In this case, there is no beam searching overhead, but some performance loss due to smaller bandwidth. To efficiently address blockage, the main question is if a mmWave transmitter- receiver pair should establish a new path using a relay node, which may cost extra alignment overhead, or it should go for the fallback option until the the direct link becomes obstacle-free. To have a comparative analysis, we have derived closed-form expressions for the throughput and delay of both options.

1.2 Blockage model

The obstacle occurrence is modelled as the packets arriving into a queue system, and the blockage time is modelled as the busy time of the server.

Two different systems have been explored, M|M|1 and a M|M|inf, which model a configuration with low rate of obstacles and high probability of blockage, respectively. M means markovian process, so memoryless and Poisson/Exponential distributed.

For the delay-throughput tradeoff, a queuing system is analyzed, in which the payload is characterized by a Poisson distribution and the service time is constant, according to the choice of deterministic path loss and so a deterministic channel capacity. It is shown that, in applications in which the payload is considerably high, the relay option overcomes the fallback one for some fixed periods of blockage time. On the other hand, in short- packets context, the relay is better for other blockage periods, pointing up

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Chapter 1. Introduction 3 a different behaviour. The analysis highlights several parameters such as beam angle, transmission time, obstacle presence and obstacle occurrence.

A decision rule from which the source is capable to overcome blockage at the best of his possibilities is proposed; it is shown how this rule depends on all the parameters which have been introduced. The last contribution of this work is giving an original framework to characterize mmWave net- working, where blockage, unlikely for microwave links, can be a critical problem. The results of this thesis have the potentiality to be valuable for the standardization of future mmWaves systems.

1.3 Contributions of this thesis

A first original contribution of this thesis is using queuing theory to model the blockage. There are several models adopted for blockage in mmWave communications like [7,9–11], but none of those have never used queuing tools. In [12], a blockage model is proposed for a delay/throughput performance analysis, highlighting the transitional behaviour of mmWave networks from noise-limited to interference-limited regime. Precisely, this model is used to study the correlation between adjacent LoS links, addressing the interference; indeed, it does not ponder the dynamic nature of obstacles, which may leave a link after a certain time: this characteristic is considered by the proposed blockage model and so it could be adopted in that context.

Instead, in [13,14], the important topic of resource allocation for 60 GHz wireless access networks is faced. In these works, the blockage problem is identified without the use of a specific model: the blockage is only addressed at the problem formulation for resources allocation about the instability of the wireless channel and the abrupt performance degradations; the proposed model in this thesis can be used in order to improve those works identifying, in a better way, the role of blockage at the resource allocation side.

Moreover, a first deep analysis/comparison has been faced for the first time between fallback and relay techniques: so far, there are different works which have presented and studied the main features of fallback [8] and relay [9], but no one has tried to present a framework which provide for the choice of one option compared to the other under certain conditions (blockage probability, beamwidth, throughput and delay constraints). Several results emerged, in order to be valuable for future standardization about wireless applications at mmWave bands.

1.4 Structure of the document

The thesis is organized as follows. In Chapter 2, we present the system model and generic problem formulation. The analytical development is also presented without considering the delay impact, which will be done

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4 Chapter 1. Introduction afterwards. The proposed blockage model is introduced in Chapter 3. After this background, the throughput analysis is provided in Chapter 4, followed by a delay analysis in Chapter 5. Simulations are then presented in the last two chapters in order to validate the equations used in both the analysis.

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Chapter 2 Problem formulation

2.1 System model

The communication of a transmitter-receiver pair, operating at the mmWave frequencies, is analyzed. The configuration treated in this thesis is in Fig- ure 2.1. There are three nodes in which a source, a destination and an half-duplex relay node are identified. During a communication between the source and the destination in a millimeter system, the situation of non line of sight is analyzed.

At these frequencies, cause of the high directionality of the antenna to face the high path-loss, obstacles between the direct path would cause a significant decrease of the received signal power. On preserving the communication of such a configuration, the source can set up a new communication with the relay node passing by the obstacles, but this approach does not guarantee the absence of blockage on the alternative path and is time consuming too.

It assumes that the source is able to sense the presence/absence of obstacles on its link to the receiver without delay or error. Given this perfect sensing,

interesting to find the average throughput and delay of option 1 and option 2.

Further, the statistic distribution of the presence of obstacles is known to the source and the relay paths are free of obstacles. This last assumption will be removed afterwards, showing the impact of the error probability for the relay technique.

Let the energy consumption be not considered in the analysis and t_w be a waiting time after which the source will choose the best option; the following remark is given:

Remark 1 : t_w = 0 is the optimal waiting time.

Proof. Since the energy consumption component is not considered, being silent for t_w seconds (t_w > 0) reduces the transmission time and, therefore, the throughput, irrespective of using option 1 or 2. Therefore, adopting t_w = 0 is throughput optimal.

The time needed to set up the alternative route is: T_align. Let X_i and Y_i be the two phases which compose the variable T_i. The latter is named as

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6 Chapter 2. Problem formulation

Figure 2.1: Simple network model considered

Figure 2.2: Time slots divided in phases

inter-LoS-interval. The inter-LoS-interval indicates "virtual transmission time", namely the available time the source has to transmit. The phases are realizations of the random variables X and Y which indicate NLoS and LoS period, respectively. The inter-LoS-interval is defined as a concatenation of X_i followed by Y_i, as illustrated in Figure 2.2. The randomness in X_i and Y_i poses implied duration for a transmission time slot. Now all the possible scenarios after a blockage are itemized, considering T_i, . Three different transmission rates [bit/s] are identified:

• C_dx : transmission rate of direct path during time X_i

• Cdy : transmission rate of direct path during time Yi

• C_r : transmission rate of relaying path

To explain more clearly the configurations above, it refers to Figure 2.3c.

For option 1, the source transmits with rate C_dx during X_i, turning on rate C_dy during Y_i; poorly speaking, during the blockage time the source transmits in fallback at the direct path and when the obstacles pass by, during Y_i, it turns back transmitting in mmWave bands: it communicates from a transmission rate of C_dx to a transmission rate C_dy. On the other hand, with relay option, the source sets the alternative route, transmitting with rate C_r: it goes directly for relay path transmitting in mmWave rate and, recalling the half-duplex condition, the transmission time is the half.

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Chapter 2. Problem formulation 7

(a) Phase 1: NLoS period

(b) Phase 2: LoS period

(c) Figure 3: First inter-LoS-interval T0

2.2 Analytical development

Two throughputs are defined for each scenario, in terms of bit transmitted:

they are random variables with realization for the i − th inter-LoS-interval:

TS1(i) = C_dxXi+ C_dyYi, T_S₂(i) = C_r

2 · max ((X_i+ Y_i− T_align) , 0) . (2.1) The half-duplex relay transmission is responsible for the factor 0.5 in the second throughput. The next step is to define a decision rule; the latter can be adopted by the source to mitigate blockage. It corresponds in maximizing the throughput represented by a random variable (2.1), at first approach; the impact of the delay is explored afterwards. For this aim, the expected values of these probability distributions should be considered , so:

E[TS1] = E[X]Cdx+ E[Y ]Cdy, E[TS2] = C_r

2 · max (E [(X + Y − Talign)] , 0) . (2.2)

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8 Chapter 2. Problem formulation Table 2.1: Summary of main notations

Parameter Description

X Phase 1 duration, random variable Y Phase 2 duration, random variable C_dx Capacity LoS channel during X, microWave C_dy Capacity LoS channel during Y , mmWave

Cr Capacity relay channel , mmWave T_align Time needed for establishing relay path

The following Proposition is given:

Proposition 1. Consider the equations in 2.2 and the inter-LoS-interval defined in Figure 2.2. Let X and Y be the distributions of NLoS and LoS period, respectively. If T_align is the needed time for the alignment procedure and E is the expectation operator, then:

If T_align >E[X + Y ] E[TS2] =0 .

Proof. On average, if Talign is higher than the average length of the transmission time, the source always adopts fallback option, otherwise there is no time left to transmit.

If Proposition 1 does not hold, the formulation of the decision rule follows, consisting in the comparison between the two mean values in (2.2).

So it states:

E[CdxX + C_dyY ] > C_r

2 E [(X + Y − Talign)] , C_dxE[X] + CdyE[Y ] > Cr

2 E[X] + Cr

2 E[Y ] −TalignCr

2 ,

C_dx− C_r 2

E[X] +

C_dy− C_r 2

E[Y ] > −

T_alignC_r

2 . (2.3)

If (2.3) holds, the throughput of fallback is higher than relay one, in average: the source uses the fallback technique. The channel capacities are taken at the maximum values, scalar ones; they do not depend on X and Y in terms of specific realization. T_align is a scalar too. It has to recall, that this first approach does not consider the impact of the delay of the the two option, so the decision rule is based on the asymptotic regime of throughput (maximum bit rate in infinite time). Table 2.1 resumes the parameters in the scenario.

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Chapter 2. Problem formulation 9

2.3 Chapter conclusion

In this chapter, the simplified network model has been shown, which will be used in all the document. It can represent a simple WLAN indoor network in which the position of the relay node is unknown to the source: in this context the alignment-overhead procedure is justified. After that the problem to solve is pointed out, which is blockage due to obstacles, an analytical development is presented in order to introduce the equations which govern the analysis afterwards. In the next chapter, all the parameters will be characterized, studying a feasible model for the obstacle occurrence at the LoS: a closed-form formula for E[X] and E[Y ] is given.

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Chapter 3 Model obstacle presence

Now, it is interesting to compute the mean values in (2.3). It resorts to queuing theory because there are several similarities between the line of sight of the source-destination pair and the busy time of servers in a queuing system. Moreover, using queuing tools, the incoming obstacles at the direct path can be modelled with the customers arriving at the queuing system; the permanence of obstacles in the link is modelled like the service time of the servers. Poorly speaking, blockage and clear path are modelled such as busy period and idle period of a system of servers in a queuing scheme, respectively.

Figure 2.2 introduces the inter-LoS-interval, which consists in a series of phases where obstacles are present and absent, respectively. In terms of queuing system, considering the obstacles permanence like a service time of a server, the situation is analogous to Figure 3.1. The next observation is the following: the random variables, X and Y can be modelled with the distributions of busy time and idle slot.

The probability distributions of the systems are:

• Poisson distribution for arriving and exponential distribution for de- parture

The configuration is expressed in Figure 3.2. The rate of obstacles coming and the average permanence of an obstacle in the link are modelled with λ and 1/µ = x, respectively. Two strategies can be adopted: modelling this situation like a M |M |1|1 system, considering only the presence of one obstacle in the LoS path, or considering that multiple obstacles can occur causing blockage, that is M |M |∞|∞. It recalls that M states of Markovian process.

3.1 M|M|1|1

From the Figure 3.3 two states are identified: state 0 and state 1. In the first there are no obstacles in the system, meaning that the direct path is free; on the other hand the state 1 means that there is the blockage and the system is full. (it remarks that in M |M |1|1 there is just one available position) The numerical importance of λ and µ is not highlighted in this section, the analysis will be done afterwards; for the stability of the system

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12 Chapter 3. Model obstacle presence

Figure 3.1: Time slot in a queuing system

Figure 3.2: Queuing system; general scheme with infinite buffer capacity and servers

is remarked that the following relation holds:

ρ = λ

µ < 1 . (3.1)

Other equations of the system are given below:

λp₀− µp₁ = 0 , p₀ + p₁ = 1 ,

p₀ : % time free by obstacle ,

p₁ : % time obstacle presence . (3.2) To know the wished values, it states that the idle slot distribution is given by the arriving distribution, which is Exponential(λ, t):

f_Y(y) =







λe^−λt if t ≥ 0 ,

0 if t < 0 . (3.3)

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Chapter 3. Model obstacle presence 13

Figure 3.3: M|M|1|1 system

Figure 3.4: Countless obstacles can cause blockage

From (3.3):

E[Y ] = 1

λ. (3.4)

In this case, the busy time of the server corresponds to the service time.

The latter is Exponential(µ, t) distributed. So:

E[X] = 1

µ. (3.5)

3.2 M |M |∞

The previous model works perfectly, but it can be seen such as too simplified one. In fact, that configuration works well in a context in which very few obstacles in the workspace are expected; a hypothesis that may not hold in several cases. For this reason, M |M |∞| is presented, in which a ∞ number of independent obstacles can occur causing blockage. In Figure 3.4, the situation under analysis is visible. In this case, after that a single obstacle occurs, the arriving/departures of others is expected, so the Markov chain of before does not hold anymore: Figure 3.5 reports the new configuration.

Under the queuing theory perspective, the main features of this process are:

• Arrivals occur at rate λ according to a Poisson process and move the process from state i to i + 1

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14 Chapter 3. Model obstacle presence

Figure 3.5: Markov chain of M |M |∞

• Service times have an exponential distribution with parameter µ and there are always sufficient servers such that each arriving job is served immediately. Transitions from state i to i − 1 are at rate iµ

For the same stability reason already discussed, the ratio: ρ = λ/µ < 1 is kept. Now, like before, the main value to formalize is the busy period of the servers: the time under which, after the occurrence of the first obstacle, it turns back in the clear path. The generalization of this time is also known like congestion period, which is the length of time the process spends above a fixed level c, starting timing from the instant the process transitions to state c + 1. This period has mean value [15]:

1 λ

X

i>c

c!

i!

λ µ

!i−c

. (3.6)

For the treated case with c = 0 , E[X] = 1

λ

e^λ^µ − 1

. (3.7)

About the idle slot distribution, the result of the previous model is kept, so it refers to (3.3) and (3.4).

3.3 Chapter conclusion

In this chapter, the main contribution of this document is given. The blockage model has been presented and characterized with the help of queuing theory. Two situations have been investigated: M |M |1|1 and M |M |∞ sys- tem. Both of them can be adopted, but it remarks that the first one is used more for theoretical reasons than practical ones: hereafter, in fact, the LoS of the source-destination pair will be modelled like an M |M |∞ system. In the next chapter the analysis starts. First results will be given and several situations will be studied. Delay impact will not be face though, however, the main features of fallback and relay techniques will be visible.

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Chapter 4 Throughput analysis

From (2.3) it is clear that the channel capacities C_1i and C₂ and the needed time to set up the relay path, T_align, still remain to be characterized.

4.1 Alignment overhead

Such as it has already been said, in a mmWave system, deafness is an important problem that is solved with a beam-searching procedure [16];

the latter introduces an alignment overhead which is the required time to find the best beams. Let T_p be the time required for a pilot transmission, which has to be performed for each possible direction, and {φ^t_i, θ^t_i} and {φ^r_i, θ_i^r} be sector-level and beam-level beamwidths at the transmitter and receiver sides of link i, respectively. The total duration of this searching (alignment) procedure within a given sector is [16]:

T_align(θ_i^t, θ_i^r) =

&

φ^t_i θ_i^t

' &

φ^r_i θ^r_i

'

T_p, (4.1)

where de is the ceiling function, returning the smallest following an integer, since the number of pilots has to be integer.

4.2 Channel capacities

In the configuration shown in Figure 2.1, the network consists in one single- active link in which there is no interference experienced by the receiver. The situation analyzed states in a communication between source and destination in which there is no time alignment overhead. If the SNR of this path is defined like SNR_sd, according to Shannon formula, this link can achieve a rate of log₂(1 + SNR_sd). If W is the bandwidth of the signal the source has to transmit, the throughput will be:

R = W

2 · log₂(1 + SNR_sd) [ bit/s] . (4.2) Now, the throughput related to fallback and relay is analyzed, starting from (2.2). About fallback, it is clear that for each phase, it has a dif- ferent transmission rate, according to the technique used. If W₁ and W₂

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16 Chapter 4. Throughput analysis are the bandwidths of the transmitted signals in mmWave and microwave respectively, the overall throughput is:

E[TS1] = E[X]W₂

2 log₂(1 + SNR^M_sd) + E[Y ]W₁

2 log₂(1 + SNR^m_sd) , (4.3) where the channel capacities are the following:

• C_dx = W₂/2 · log₂(1 + SNR^M_sd) with SN R^M_sd computed in microwave condition;

• C_dy = W₁/2 · log₂(1 + SNR^m_sd) with SN R^m_sd computed in mmWave condition;

With the other option, the source sets up the alternative route for relay transmission, immediately. The time slot is divided in:

• E[X + Y ]/2, source ⇒ relay

• E[X + Y ]/2, relay ⇒ destination

Defining the transmission rates for these two links R₁ and R₂, it follows:

R₁ = E [X + Y − Talign] 2

W₁

2 · log₂(1 + SNR^m_sr) , R₂ = E [X + Y − Talign]

2

W₁

2 · log₂(1 + SNR^m_rd) . (4.4) The statements below are implicitly assumed in (4.4):

1. the alignments overhead between source-relay and relay-destination are equal.

2. SN R^m_sr states for SNR between source and relay 3. SN R^m_rd states for SNR between relay and destination

The same transmission rate for both the links has to be ensured, so the throughput of relay option will be given by:

R = min(R₁, R₂) . (4.5)

Now, comparing (2.2) and (4.5), the channel capacity has been already computed:

C_r = min

1

2log₂(1 + SNR_sr^m),1

2log₂(1 + SNR^m_rd)

. (4.6)

In the end, the formula to compute the SNR at the i − th link is given . Let g_i,j^c denote channel gain between the transmitter of link i and the receiver j, capturing both path loss and block fading, n be the power of white Gaussian noise and p_i be the transmission power of transmitter

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Chapter 4. Throughput analysis 17 i. Moreover let g_i,j^t and g_i,j^r be the transmission and reception gains at transmitter i and receiver j toward each other and z be the side gain of the antenna patterns. The formula is the following [16]

SNR_i= g_i,i^c p_i n

2π − (2π − θ^t_i)z θ^t_i

! 2π − (2π − θ_i^r)z θ_i^r

!

(4.7) where:

• g_i,j^t =^{2π−(2π−θ}_θt ^tⁱ^)z i

• g_i,j^r =^{2π−(2π−θ}_θr ^rⁱ^)z i

All the parameters have been defined, so it is possible to proceed with the numerical analysis.

4.3 Numerical results

The results presented are computed considering the M |M |∞ model intro- duced before. A WPAN scenario with three nodes has been chosen: a source, a destination and an half-duplex relay node, operating at 68 GHz in mobility condition; the maximum transmission power is 2.5 mW which is a typical value in bluetooth-based WPAN. [16]. The sector-level beams both at transmitter and receiver side are equal to 90^◦ and the directivity gain on the side lobe (z) is equal to 0.05. The distance considered is 10 meters. About the path loss model, the log-distance for both microwave and mmWave transmissions is chosen. There is the need of considering two bandwidths and two white noise powers which are: W₁ = 2.16 GHz, n₁ = −80.7 dBm and W₂ = 20 MHz, n₂ = −101 dBm. To compute the alignment overhead, based on (4.1), according to IEEE 802.15.3c, a single pilot transmission time is 20µs. The given results depend on the choice of λ and µ, which fix the length of the inter-LoS-interval, blockage time and clear path. For the following results, a beamangle of 20^o for the transmitter, half-duplex relay and receiver is adopted. The outputs have been discussed in two sections: infinite block-length and finite block-length regime, respectively.

4.3.1 Infinite block-length regime

From Figure 4.1, a set up is shown, in which the throughputs are visible for a rate of 5 obstacles/s and several values of µ from 5 to 10. The source constantly adopts the second option until µ > 6.8; after that the fallback option overcomes the relay one. To show more clearly the relation of these parameters with the inter-LoS-interval and blockage it refers to the following figures. In Figure 4.2 it is possible to observe the same output, but related to the inter-LoS-interval, to highlight the meaning of µ and

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18 Chapter 4. Throughput analysis

Figure 4.1: Option choice related to µ [1/s]

Figure 4.2: Option choice related to the virtual time slot (inter-LoS-interval) [s]

λ in terms of transmission time. Recalling that the virtual time slot, in average, is E[T ] = E[X] + E[Y ] from which the mathematical formulations are (3.4) and (3.7), for a fixed value of λ is clear that more µ grows, more E[T ] is short. From Figure 4.3, the quantity of bit transmitted in function of blockage time is presented. The result is surprising and interesting.

Despite there is up to 50 % of blockage, with the given configuration, the source should adopt the first option, which is fallback. It is visible that until 52 % of blockage, the fallback option gives, in average, almost 1.35 Gb transmitted; after that point, the relay option starts to overcome the fallback one, giving up to 1.70 Gb transmitted with more than 62%

of blockage. It recalls that these values of throughput are given without considering the delay impact. The alignment overhead for the parameters chosen is: 3.2 · 10⁻⁴ s. Looking at the analyzed figures, it notes that while the relay option gives an output related to the blockage/µ/time slot values, the fallback does not seem to be sensitive to them. If the expression of the fallback in (2.1) is analyzed, it is possible to observe that the main contribution, in terms of throughput, is given by the component E[Y ]Cdy, which is constant. This brings to the natural consideration of a third option in which the source stays silently during blockage and transmits only

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Chapter 4. Throughput analysis 19

Figure 4.3: Option choice related to the blockage time [%]

Figure 4.4: Option choice related to the blockage time [%], with energy saving consideration

during E[Y ]. Figure 4.4 proves the latter result. Although there is a slight difference of bits between option 2 and option 3, this gap allows to consider another scenario in which the source could save energy simultaneously to transmit the maximum quantity of bits. Of course, it must be said, that if the energy consumption is considered all the model has to be formalized again, so the adopted one may not hold; in any cases Figure 4.4 shows that a future analysis is encouraged, but it will not be part of this work.

The last consideration that can be done is about the beamwidth: changing the latter will bring consequences mainly in two aspects:

• Directivity gain

• Alignment overhead

Figure 4.5 and 4.6 show two configurations for an extreme choice of λ = 49 and µ = 50 : 100 highlighting the beamwidth impact. Decreasing the beamwidth triggers the increase of directivity gain, which causing a boost of the SNR for both the situations, will let the options have more bit transmitted. At the same time, it will cause an increase of the alignment

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Figure 4.5: Throughput analysis function of blockage time, beamwidth=5^o

Figure 4.6: Throughput analysis function of blockage time, beamwidth=20^o

overhead, which will let the relay option be less desirable; the threshold between the two choices is augmented: with 5^o of beamwidth, the fallback option overcomes the relay one until 57 % of blockage time.

4.3.2 Finite blocklength regime

Using Shannon equation to derive the channel capacity has made it possible giving important results about how the decision rule can be applied by the source; though, in terms of throughput, it is of vital interest to assess the backoff from the required capacity to sustain the desired error probability at a given fixed finite blocklength. As presented in [17] a bound is used, which shows that the backoff from channel capacity C is accurately characterized by a parameter, which is referred to channel dispersion V : it measures the stochastic variability of the channel relative to a deterministic one with the same capacity. This parameter, together with normal approximation, gives the correct framework. For the AWGN channel, which has been considered in this study, with certain SNR value, block error probability  and blocklength m, the channel capacity, in terms of bits per channel use,

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Figure 4.7: Throughput analysis finite regime epsilon=1e-6, m=100

is expressed by:

R = C −

sV

nQ⁻¹() + 1

nO(log n) [bit] , (4.8) where:

C = 1

2log₂(1 + SNR) , V = SNR

2

SNR + 2

(SNR + 1)²log₂e . (4.9) To relate equation (4.8) to (4.2), considering in each scenario the appropri- ate bandwidth and SNR, the following step is:

R = R · W [bit/s] . (4.10)

With normal approximation, the term O(logn) can be removed, replacing it with 1/2log₂n. Several results are given for different parameter choices.

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Figure 4.10: Threshold sensibility for blocklength=100

Figures 4.7, 4.8 and 4.9 show the throughputs of the options related to the blockage time. The three schemes are different in terms of blocklength, but with same error probability. The first consideration is that the transmission rate, compared to the infinity regime is lower as it was expected. On the other hand, with m = 1000 almost the same values of the infinity regime one are visible: it means that for enough large window of transmission the bound designed by the Shannon capacity is reached. Now, it wishes to show the relation between the threshold from which the source adopts either option 1 or option 2, and the blocklength. Figures 4.10 and 4.11 highlight an interesting result. Both the pictures show the two options at infinite and finite regime: at both the configurations, the threshold point seems to remain unchanged, pointing up that the blocklength does not play an important role about the decision rule. Now, it presents a short analysis about the impact of the block error probability on the option choice. In Figure 4.12 it is possible to note that even the block error probability does not bring any relevant changes to the cited threshold. Moreover, it highlights how for a large blocklength, for instance m = 100, the impact of the probability of error is negligible even for the throughput. In the

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Figure 4.11: Threshold sensibility for blocklength=10

end, after this short analysis, it is possible to affirm that the Shannon bound does not change the results in terms of decision choice, compared to the finite-blocklength regime; it is true, on the other hand, that there are differences on the quantity of bit transmitted, but for a qualitative analysis, which is the purpose of the thesis, it states that there are no relevant errors proceeding with Shannon formula.

4.4 Blockage probability for relay option

In this section the impact of the blockage probability for the relay option is explored. So far, results have been presented under ideal condition, for which the relay path is not affected by blockage. Although the latter is not such a strong assumption, because it is always possible to assume that the source is able to find a relay path with high SNR level, (similar work is presented in [9]), the impact of the blockage for relay option is analyzed, highlighting the importance of the fallback technique in those circumstances. The relay path has been modelled like an M |M |∞ system, as it was done for the LoS, so the blockage probability is computed using a queuing formula, once again. In stationary conditions, recalling the Markov chain for the M |M |∞ system in Figure 3.5, the stationary probability mass function is a Poisson distribution [18]:

πk= (λ/µ)^ke^(−λ/µ)

k! k ≥ 0 . (4.11)

So, for the state k = 0 which indicates the probability of having zero obstacles in the system, it has:

p₀ = e^(−λ/µ), (4.12)

and so:

p₁ = 1 − p₀ Probability of blockage . (4.13)

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Figure 4.12: Threshold sensibility for different blocklength in function of block error probability

The relay option now is weighted in this way:

C_r⁰ = C_rp₀+ C_r1p₁, (4.14) where C_r is already computed in (4.6) and C_r1 is computed in similar manner, but considering a further attenuation of 37 dB [19] in the SNR, caused by blockage in mmWave condition. Now that the theory has been presented, it starts to analyze the following results. Figures 4.14 and 4.13 show the main consequence of introducing the blockage probability for relay technique: for a considerable blockage probability it observes how the fallback option overcomes the relay one for a higher value of the percentage blockage time. This switch threshold point decreases for lower p₁.

Therefore, the importance of fallback option has been again highlighted , which can be preferred in most of the cases if the contest implies high blockage probability for the relay option.

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Figure 4.13: Impact of 33% of blockage probability

Figure 4.14: Impact of 8% of blockage probability

4.5 Simulation of M |M |∞

In order to validate the obtained results about the throughput analysis, it should refer to equations (2.1) and (2.2). Modelling the LoS like an M |M |∞ system has given the opportunity to find a simple closed formula for E[X] and E[Y ]. These formula come from the behaviour of the queuing system considered and so, this latter will be emulated with the simulations.

Figure 4.15 and 4.16 show the difference between the simulations and the analytical results for a fixed configuration. Actually it is possible to appreciate that there is no gap, but this output was expected, indeed: the equations have been deeply explored and analyzed from the queuing network community; they only have been proposed under another perspective to model the blockage frequency of the LoS between two nodes.

4.6 Chapter conclusion

In this chapter, the throughput analysis was shown. Interesting results emerged from that: the fallback option revealed to be important because it overcomes the relay option in many situations. It has shown, for a specific

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Figure 4.15: Simulation and analytical result of throughput analysis [1.0]

Figure 4.16: Simulation and analytical result of throughput analysis [2.0]

set up, that if the blockage time percentage is less than 50% the source uses fallback to mitigate the issue. The impact of finite blocklength regime communication has been explored as well. It emerged that it does not affect the decision choice significantly; therefore the Shannon capacity can be used in order to lighten the calculations giving valid results. Simulations have confirmed the robustness of the used equations. In the next chapter, the impact of the delay for the options will be investigated, introducing

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Chapter 4. Throughput analysis 27 first a new queuing model and analytical results afterwards. In the end of the chapter a proper framework is derived, in which the decision rule is well defined.

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Chapter 5 Delay evaluation

In this section, the transmission delay brought by the two options is investigated . So far, the impact of these techniques has been studied, in terms of throughputs, without analysing if the reached bit-rates are feasible in a finite time. A natural scheme is given, in which the throughput-delay tradeoff is explored. The considered channel capacities are the ones taken in consideration in the finite blocklength regime, with a window size of 100 and block error probability of 0.1. The transmission time T_i is the inter-LoS-interval in Figure 3.1; here his average value for fixed λ and µ is considered, which determines the blockage time and clear path; in short E[T ] = E[X] + E[Y ]. To lighten the notation, the expect-value symbols are removed, considering T=X+Y. For modelling the introduced situation, it recurs once again to the queuing systems. Specifically, the two options are modelled like M |D|1 systems in which:

• the bits generated and eventually retransmitted by the source follow the Poisson distribution with rate G [bits/s]

• the source has an infinite buffer-length, so all the bits are served.

• the constant service times for both the options are D₁ for fallback and D₂ for relay.

So it has:

D₁ =

C_microX

T + C_mmWaveY T

⁻¹

[s] , (5.1)

D₂ =

C_mmWave· Teff

T

⁻¹

[s] , (5.2)

where C_micro and C_mmWave are the capacities widely introduced in the pre- vious sections in [bits/s] rate; T_eff = (T − T_align)/2 in which the original transmission time has been reduced for the alignment overhead and the half duplex communication. The total mean delay brought by these two systems is given by:

τ = 1

2S · 2 − ρ

1 − ρ, (5.3)

defining ρ = G/S as the utilization and S = 1/D. As long as the queue system remains stable, (ρ < 1), the throughput consists in the amount of

29

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30 Chapter 5. Delay evaluation

Figure 5.1: Delay-Throughput tradeoff for a beamwidth=

20^◦

Figure 5.2: Delay-Throughput tradeoff for a different transmission time

bits generated by the source, (G), served with delay τ . When the system is unstable the throughput is bounded by S, the average service time.

Instability means that the server is not able anymore to empty its queue, so the traffic starts to increase going to saturation. The throughput-delay tradeoff is proposed as a function of several parameters, for different amount of generated bits.

In Figure 5.1 is shown the delay-throughput tradeoff for a fixed value of transmission time T , blockage time and beamwidth. For this configuration is visible that the fallback option ensures the same throughput for less delay until 2250 Mbps/s, but then it becomes unstable, reaching the saturation before the other option. All the visible results, from the latter figure, depend on many parameters in the chosen scheme; to highlight this feature, other schemes are introduced.

In Figure 5.2 the same blockage time % and beamwidth of Figure 5.1 are kept, changing the transmission time. With T considerably shorter, it is clear that the alignment overhead seems to have an important weight in the system and the relay technique goes to instability region before than fallback one. This ending is logical: when the length of T is comparable to

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Chapter 5. Delay evaluation 31

Figure 5.3: Delay-Throughput tradeoff for a different blockage time

Figure 5.4: Delay-Throughput tradeoff for a different beamwidth= 5^◦

the alignment overhead, all the time available to transmit will be "wasted"

in turning through the relay, so no time is left for the transmission and the system cannot empty its queue. In Figure 5.3 the blockage time percentage with the transmission time are changed, as the latter has been defined at the previous chapters. Anyway, T is kept enough far from T_align, so only the blockage effect is highlighted. With lower blockage period, the fallback option can exploit the mmWave communications for more time and so it overcomes the relay one, in terms of delay for high throughput, compared to Figure 5.1.

The last configuration, Figure 5.4, introduces a set up in which the beamwidth was decreased to 5^◦. As it is clear from the picture, this change has brought a considerable improvement for the fallback option. This is because, decreasing the beamwidth, the option 1 will gain in terms of channel capacity and so in faster service time without paying any cost; for the relay option we always have a tradeoff between T_align and channel gain, so compared to Figure 5.1, the maximal reached throughput is higher, but this aug- ment is paid with higher delay. For all this reasons, in this configuration, the fallback is always adopted. Among all the obtained results, it notes

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5 10 15 20 25 30 35 40 45 50 55 60 80

75 70 65 60 55 50 45 40 35 30

Blockage %

Beam angle ° Fallback

Relay High Throughput

Λ=2000 Mbps

In this case, for the beam angle- blockage time considered the throughput is not

fulfilled

S1,W1: service and waiting time

Fallback S2,W2:service and waiting time Relay Tal=Alignment overhead: function of

beam angle X/T=blockage time % Y/T=clear path %

Cmicro: Channel capacity microwave CmmWave: Channel capacity mmWave

W1+S1>W2+S2+Tal

W1+S1<W2+S2+Tal

W=(ΛS^2)/[2(1-ΛS)]

S1=[Cmicro(X/T)+CmmWave(Y/T)]^-1 S2=[CmmWave(T-Tal/2T)]^-1 Option choise

depending on blockage time %

Always Fallback option

Fallback option for limited values of

blockage %

Figure 5.5: General framework for high payload applications

that it is not so straightforward to give a general framework from which the source can adopt one option in order to maximise its performance: all the parameters play a central role in this context, so it has to restrict the configuration, fixing some parameters, to reach such an achievement.

5.1 Framework for fixed throughput demand

In Figure 5.5 is presented a configuration in which the throughput to meet is considerable, 2000 Mbps; in x-axis there is the beamwidth in y-axis the blockage period % and the coloured zones identify the option which guarantees a better performance in terms of delay. The blockage period variates from 30% to 80% and the beamwidth is from 5^◦ to 60^◦. This figure gives a clear scheme in which, among the several situations that may occur, the source can adopt the best solution to mitigate blockage. For a beamwidth range 5/10^◦ whatever is the blockage period, the fallback option must be used to ensure the wished throughput with lower delay.

The same behaviour is visible for a beamwidth higher than 45^◦, but in that

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Figure 5.6: Threshold function for the feasible range

case, the blockage time period has to be limited in the range showed in the picture, otherwise the data demand is not fulfilled. For a range of 10^◦/45^◦ the option choice depends on the blockage time. To better appreciate this option choice on the mixed zone, it proposes a further analysis, with higher resolution, expressed in Figure 5.6. In Figure 5.7 is presented the same configuration but for lower data rate demand. It is surprising to observe how the behaviour is different. The beamwidth range reaches 70^◦ now, because with lower throughput scenario it is possible to decrease the directivity gain, first consequence of this change and still to fulfil the requirements. For this scheme, the fallback option is used until 20^◦ for all the considered blockage periods. After 20^◦ the option depends on the blockage period once again and, as long as the beamwidth increases, the range in which the relay is preferred grows. As it was done before, in Figure 5.8 is proposed a picture which shows the curve of the threshold indicating the switching options point.

5.2 Framework for fixed delay demand

Keeping going on this direction, it proposes a further analysis similar to the one just analyzed. A configuration in which the maximum allowed delay is given can be analyzed and it is interesting to observe the throughput- beamwidth tradeoff. In Figures 5.9 and 5.10 the output for the described situation is given, in which the maximum allowed delay is 0.001 s. The first consideration to be done is that increasing the beamwidth the throughput will decrease because this effect is caused by the change of the directivity gain. The observable outputs are even more interesting. It is clear that depending on which blockage period are considered, for a fixed delay, one option will definitely overcome the other one for whatever value of beamwidth.

From Figure 5.11, the threshold from which the source adopts either fallback option or the relay one appears to be 50%; it concludes that, for the presented schemes, if the blockage period is higher than 50% the source

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5 10 15 20 25 30 35 40 45 50 55 60 65 70 80

75 70 65 60 55 50 45 40 35 30

Blockage %

Beam angle ° Fallback

Relay Low Throughput

Λ=1Mbps

S1,W1: service and waiting time

Fallback S2,W2:service and waiting time Relay

Tal=Alignment overhead: function of beam angle X/T=blockage time %

Y/T=clear path % Cmicro: Channel capacity microwave CmmWave: Channel capacity mmWave W1+S1>W2+S2+Tal

W1+S1<W2+S2+Tal

W=(ΛS^2)/[2(1-ΛS)]

S1=[Cmicro(X/T)+CmmWave(Y/T)]^-1 S2=[CmmWave(T-Tal/2T)]^-1 Option choise

depending on blockage time %

Always Fallback option

Figure 5.7: General framework for low payload applications

Figure 5.8: Threshold function for the feasible range [2.0]

adopts the relay option to maximize the throughput, the fallback one otherwise. It further says that this result holds for other transmission times, but if the situation in which T is comparable to the alignment-overhead is analyzed, it will be visible the well-known tradeoff delay-throughput caused by the beamwidth variation. In Figures 5.12,5.13 and 5.14 this

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Figure 5.9: Throughput-Beamwidth tradeoff for blockage period=48%

Figure 5.10: Throughput-Beamwidth tradeoff for blockage period=55%

phenomenon is highlighted. For the relay option, is visible this concave behaviour where the maximal throughput is reached for 13^◦. For lower angles and fixed delay of 0.001 s, the throughput decreases up to 0 for 7^◦. After the maximum is reached, the behaviour is approximately the same compared to Figures 5.9, 5.10 and 5.11.

5.3 Simulation of M |D|1

In order to validate the results about the delay analysis, a simulation of the M|D|1 queuing system is given. In this case, such as for the throughput analysis, a gap between the analytical results and the simulations is not expected . For computational reason, a figure that has not been treated during chapter 5 is shown, in which only the waiting time is visible. It recalls, once again, that the treated equations for this study have been already analyzed by the queuing theory community which guarantees their validations.

Figures 5.15 and 5.16 confirm what it has been said.

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Figure 5.11: Throughput-Beamwidth threshold choice, blockage=50%

Figure 5.12: Throughput-Beamwidth trade off for different blockage period=48% [2.0]

5.4 Chapter conclusion

In this chapter, a new queuing model has been used to introduce the delay component in the analysis. Several throughput-delay tradeoffs emerged, highlighting the behaviour of fallback and relay in different situations.

Once certain parameters have been fixed, several frameworks have been presented, for specific throughput demand and maximum allowed delay.

Simulations once again confirmed the validity of the adopted model. In the next chapter the conclusion of the entire thesis work is reported.

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Figure 5.13: Throughput-Beamwidth trade off for different blockage period=55% [2.0]

Figure 5.14: Throughput-Beamwidth threshold choice,blockage=50% [2.0]

Figure 5.15: Simulation for Fallback option; M|D|1 system

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Figure 5.16: Simulation for Relay option; M|D|1 system