1 This project has received funding from Horizon 2020, European Union’s Framework Programme for Research and Innovation, under grant agreement No. 761794 Deliverable D4.3 TERRANOVA’s resource management optimisation framework for THz networks Work Package 4 - THz Wireless Access and Resource Management TERRANOVA Project Grant Agreement No. 761794 Call: H2020-ICT-2016-2 Topic: ICT-09-2017 - Networking research beyond 5G Start date of the project: 1 July 2017 Duration of the project: 33 months Ref. Ares(2020)660757 - 03/02/2020
Transcript
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This project has received funding from Horizon 2020, European Union’s
Framework Programme for Research and Innovation, under grant agreement No.
761794
Deliverable D4.3 TERRANOVA’s resource management
optimisation framework for THz
networks Work Package 4 - THz Wireless Access and Resource Management
TERRANOVA Project Grant Agreement No. 761794 Call: H2020-ICT-2016-2 Topic: ICT-09-2017 - Networking research beyond 5G Start date of the project: 1 July 2017 Duration of the project: 33 months
Ref. Ares(2020)660757 - 03/02/2020
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Disclaimer This document contains material, which is the copyright of certain TERRANOVA contractors, and may not be reproduced or copied without permission. All TERRANOVA consortium partners have agreed to the full publication of this document. The commercial use of any information contained in this document may require a license from the proprietor of that information. The reproduction of this document or of parts of it requires an agreement with the proprietor of that information. The document must be referenced if used in a publication. The TERRANOVA consortium consists of the following partners.
No. Name Short Name Country
1 (Coordinator)
University of Piraeus Research Center UPRC Greece
2 Fraunhofer Gesellschaft (FhG-HHI & FhG-IAF) FhG Germany
3 Intracom Telecom ICOM Greece
4 University of Oulu UOULU Finland
5 JCP-Connect JCP-C France
6 Altice Labs ALB Portugal
7 PICAdvanced PIC Portugal
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Document Information
Project short name and number TERRANOVA (761794)
Work package WP4
Number D4.3
Title TERRANOVA’s resource management optimisation framework for THz networks
Version v1.0
Responsible unit UPRC
Involved units JCP-C, FhG, ICOM, UOULU, UPRC, ALB, PIC
Type1 R
Dissemination level2 PU
Contractual date of delivery 31.01.2020
Last update 31.01.2020
1 Types. R: Document, report (excluding the periodic and final reports); DEM: Demonstrator, pilot, prototype, plan designs; DEC: Websites, patents filing, press & media actions, videos, etc.; OTHER: Software, technical diagram, etc. 2 Dissemination levels. PU: Public, fully open, e.g. web; CO: Confidential, restricted under conditions set out in Model Grant Agreement; CI: Classified, information as referred to in Commission Decision 2001/844/EC.
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Document History
Version Date Status Authors, Reviewers Description
v0.1 06.10.2019 Draft Alexandros-Apostolos A. Boulogeorgos (UPRC)
Initial definition of the document’s structure
v0.2 18.10.2019 Draft Alexandros-Apostolos A. Boulogeorgos (UPRC),
List of Figures Figure 1: TERRANOVA RRB. ................................................................................................................... 16
Figure 2: Human blockage. ................................................................................................................... 17
Figure 3: A snapshot of the THz wireless network with un-clustered (a) and clustered (b) TAPs and
Figure 26: Running time until all requests are served .......................................................................... 48
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List of Tables Table 1: Notations ................................................................................................................................. 14
framework for THz networks,” presents the TERRANOVA radio resource management (RRM) framework as well as the caching approach, which is expected to significantly reduce the THz wireless systems latency. In particular, Section 1 discusses the motivation behind the RRM and caching design strategies in THz wireless systems as well as the scope of this deliverable. Next, Section 2 identifies the fundamental characteristics of THz wireless systems that influence the RRM and caching design strategies. In Section 3, the TERRANOVA RRM framework is presented followed by a blocking avoidance relay-based approach. Finally, Section 4 reports on the caching approach accompanied by insightful Monte Carlo simulation results. Finally, in Section 5, the main messages and findings of D4.3 are summarized, conclusions are drawn.
The main outcomes of the deliverable are:
• Identification and modelling of the particularities of the THz wireless systems, which must
be taken into account in the design of the RRM and caching;
• Quantification of the impact of blockage in directional THz wireless systems that employ
space division multiple access (SDMA);
• Formulation of a joint blockage avoidance and throughput maximation resource
allocation optimisation problem accompanied by its solution. Of note, the solution
framework, which is referred as “universal resource allocation framework”, takes into
account the impact of blockage as well as the different user equipment (UE) demands,
and after clustering UE and access points (APs), it associates each UE with one AP, which
can handle its data rate demands.
• Presentation and performance assessment of a relay-based joint beam misalignment and
blockage avoidance strategy;
• Presentation of an efficient caching system along with multiple entities and functions that
effectively reduce the usage of backhaul network resources, and significantly improve the
system performance, in the context of low delay, quick response time, and high cache hits
rates. The caching system is evaluated by defining the five cache handling scenarios in
order to show the effectiveness of each element and implemented method.
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1. INTRODUCTION
Ultra-dense wireless terahertz (THz) networks with increasing demands for high data rate transmission are of high interest for beyond the fifth generation (B5G) applications, such as three-dimensional (3D) printing, virtual reality (VR), artificial reality (AR), etc. These networks are required to countermeasure several variabilities that have their source in the THz channel particularities as well as the diverse demands of different B5G applications. Aspired by this, a great amount of research effort was devoted to analysing these particularities, defining the nature of the radio resource block (RRB) as well as presenting RRM and user association strategies. In particular, the ultra-wideband extremely directional nature of the communications links, in combination with the non-uniform user equipment (UE) spatial distribution, may lead to inefficient clustering, user association and resource allocation, when the classical minimum-distance criterion is employed. As in the case of millimetre wave (mmW) communications [1] and as proven in D4.2, THz wireless networks are noise-limited, because the high path-loss attenuates the interference. Hence, clustering, and user association metrics, designed for interference limited homogenous systems, are not well suited to THz systems [2]. On the other hand, clustering and user association should be designed to meet the dominant requirements of throughput. Likewise, due to the high channel attenuation, blockage is recognized as a fundamental cause of performance degradation. Additionally, user orientation has a substantial impact on the performance of THz links, due to the fact that directional transmission is required for mitigating the high path loss. As a consequence, transmitters (TXs) may need to employ relay strategies in order to be associated with their intended receivers (RXs).
Scanning the open technical literature, several dynamic user association schemes have been presented [3], [4], [5], [6], [7]. For example, in [3], the authors presented a load-aware cell association method and distributed algorithm for downlink heterogeneous networks, aiming to maximize the overall network throughput, whereas, in [4], the associations objective was to minimize the total power consumption. Additionally, in [5], a load balancing user association problem was presented and solved for heterogeneous networks deployments, while, in [6], the authors investigated the energy efficient user association problem in heterogeneous networks (HetNets), and formulated a network logarithmic utility maximization problem. Finally, in [7], an optimization-based framework was proposed for energy-efficient global RRM in heterogeneous wireless networks. However, none of the above presented mechanisms that take into account the particularities of the THz wireless system, and especially blockage.
1.1 Scope
Motivated by the above, the objective of this deliverable, entitled “D4.3 TERRANOVA’s resource management optimisation framework for THz networks” is to present the TERRANOVA RRM and caching strategies for wireless THz networks. In particular, after reporting the THz wireless system particularities that are expected to influence the RRM and caching designs, namely blockage, antenna misalignment and diverse user demands, we present a novel universal resource management that aims at minimizing the overall blockage probability of all the THz network users through appropriate clustering, while, at the same time, achieving network throughput maximization. In this direction, the RRM multi-objective optimization problem is formulated and it is shown that its solution is NP-hard. To break this barrier, two suboptimal problems are formulated, namely user clustering and joint user association and resource allocation. Each one of them can be simplified into a differential convex optimization problem that can be solved through an iterative algorithm, which is also provided. To quantify the performance of the proposed RRM framework, we perform Monte Carlo simulations that help deduce useful THz wireless networks design guidelines. Another useful outcome presented in this deliverable is a relay-based blockage avoidance and load balancing strategy. This strategy is suitable for THz wireless networks, in which each UE can play the role of a decode-and-forward (DF) relay. In
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more detail, assuming that the direct link is either blocked or experiences high antenna misalignment, the transmitter employs an intermediate node that decodes the received signal and forwards it to the intended receiver. A head node is pre-selected that is assumed to have perfect channel state information (CSI) for all the possible established channels, the network topology, as well as the blocker’s position. Moreover, it is capable of communicating with all the network nodes. This node uses the TERRANOVA-proposed source-relay-destination selection policy. The effectiveness of the proposed algorithm is quantified through Monte Carlo simulations and is compared against the random relay selection policy, which is considered the one of lowest complexity. Our results reveal the superiority of the proposed policy as well as the joint effect of antenna misalignment and blockage. Finally, the TERRANOVA caching architecture is reported, and its fundamental building blocks/units and algorithms are analysed. Special attention is placed on providing design guidelines that aid in the selection of the suitable parameters. Moreover, several different caching scenarios that are of much hype for THz wireless applications are presented and quantified through network system (ns)-3 simulations. Our results evaluate the average (first and last packet) delay, the wireless and wired network traffic, the cache hit ratio, as well as the cache content table size for all the defined configurations.
1.2 Structure
The structure of this deliverable is as follows:
• Section 2 is focused on presenting the particularities of THz wireless systems that TERRANOVA
RRM and caching designs are required to take into account;
• Section 3 presents the TERRANOVA RRM framework. In more detail, a universal resource
management that consists of clustering and joint user association and resource allocation
strategies;
• Section 4 reports on the caching architecture, designs, and algorithms. Moreover, it quantifies
through simulations their performance;
• Finally, Section 5 highlights the main messages and findings of D4.3 as well as the conclusions
of D4.3.
1.3 Notations
Table 1 summarizes all the notations that are used in this deliverable. Moreover, unless otherwise stated, we use lower and capital case bold letters to denote vectors and matrices, respectively.
Table 1: Notations
Symbol Description
a Scalar
a Vector
A Matrix (∙)∗ Conjugate operator
{𝑋𝑖}1𝑛 n ordered random variables
𝔼[∙] Expected value
exp(∙) Exponential function
erf(∙) Error function
𝐼𝑛(⋅) Modified Bessel function of the first kind of n-th order
𝐾0(∙) Zeroth order modified Bessel function of the second kind
𝑄(∙) Q-function
𝑄𝑢(∙,∙) Marcum Q-function
𝛤(∙) Gamma function
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𝛤(∙,∙) Upper incomplete Gamma function
𝛾(∙,∙) Lower incomplete Gamma function
𝛤(∙,∙,∙,∙) Upper extended incomplete Gamma function
𝑀𝑘,𝑚(∙) Whitaker function
𝐹𝐴(𝑎1; 𝑎2; 𝑧1, 𝑧2) Lauricella hypergeometric function
𝐻𝐴(𝑎1, 𝑎2; 𝑏1,𝑏2, 𝑏3; 𝑧) Triple hypergeometric function
𝐺𝑝,𝑞𝑚,𝑛 (𝑥|
𝑎1, 𝑎2, … , 𝑎𝑝
𝑏1, 𝑏2, … , 𝑏𝑞)
Meijer G function
𝐻𝑝,𝑞𝑚,𝑛 (𝑥|
(𝑎1, 𝑏1), (𝑎2, 𝑏2) , … , (𝑎𝑝, 𝑏𝑝)
(𝑐1, 𝑑1), (𝑐2, 𝑑2) , … , (𝑐𝑞 , 𝑑𝑞))
Fox H function
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2. THZ PARTICULARITIES THAT INFLUENCE THE RRM DESIGN
In this section, we describe the THz particularities that influence the TERRANOVA RRM design and we present the mathematical models used in the studies performed herein.
2.1 Radio resource blocks
Figure 1: TERRANOVA RRB.
An important decision in the design of the RRM layers is the definition of the RRBs, i.e., the smallest unit of the physical resources that can be allocated. In long term evolution (LTE), a RRB is defined as a portion of the time-frequency domain with certain frequency width and time duration. On the other hand, in wireless THz systems, directional transmissions enable the use of the spatial dimension [8]. As a consequence, RRBs can be defined in the time-frequency-space domain, providing the possibility of considerably improved network capacity due to resource reuse. In order to properly utilize this type of RRB, the terahertz access point (TAP) needs to group a set of terahertz user equipments (TUEs) together, which are non-distinguishable in the transmitted beam, and serve each group with one analogue or hybrid beamforming (BF) vector [9]. This indicates that an analogue BF will be used to serve only one group at a time, while hybrid BF should be employed in order to simultaneously serve multiple groups. The analogue BF partially utilizes the spatial dimension of the RRB, whereas the digital BF increases the multiplexing gain within each group.
2.2 Channel & network particularities
In this section, we describe the THz particularities that influence the TERRANOVA RRM and caching designs.
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2.2.1 Blockage
Figure 2: Human blockage.
As graphically presented in Figure 2, THz wireless systems are quite vulnerable to blockage due to higher penetration losses and reduced diffraction [10]. Even the human body can reduce the signal strength by 20 dB [11]. As a consequence, an unblocked line of sight (LOS) link is highly desirable for THz systems. Furthermore, a mobile human blocker can block the LOS path between TUE and TAP for approximately 500 ms [11]. The frequent blockages of THz LOS links and a high blockage duration can be detrimental to ultra-reliable and ultra-low latency applications. Aspired of the above, the mitigation of blockage in THz wireless system should be of high priority in the RRM designs.
2.2.2 Diverse user demands
As described in D2.2, beyond the fifth generation (B5G) wireless systems, such as the THz ones, are expected to cover a large variety of different applications. For example, most sensing systems that may be used in Industry 4.0 have low data rate demands, but the need to be able to support a massive number of devices. On the other hand, applications like virtual reality (VR) and artificial reality (AR) require data rates in the order of tens of Gbps and latency lower than 10 ms. Aspired by this, the TERRANOVA RRM approach needs to take into account the individual requirements of each TUE and optimize the THz network overall performance. Finally, note that caching strategies are also employed in the TERRANOVA approach in order to deal with the latency requirements.
3. RADIO RESOURCE MANAGEMENT
This section is focus on presenting the RRM framework. In more detail, Section 3.1 delivers the universal resource management, while Section 3.2 is devoted to present relay-based blockage avoidance and load balancing strategies.
3.1 Universal resource management
The organization of this section is as follows. Section 3.1.1 describes the network topology, while Section 3.1.2 provides the clustering approach. Finally, Section 3.1.3 presents the joint user association and resource allocation scheme.
3.1.1 Network topology
The uplink of a THz network with densely deployed terahertz cells is considered. The transmission method is time domain multiple access and all the links are utilized in the THz band. The position of the access points (APs) and the user equipment are determined through two independent Poisson
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point processes (PPPs). Note that the density of APs is assumed to be equal to λAP, while the density of UE is λUE.
The network is divided into Nc clusters, according to the approach presented in Section 3.1.2. Each cluster consists of at least one THz access point (TAP) and several THz user equipment (TUE). The clusters do not share any TAP and TUE. In each cluster, one of the TAPs is the cluster head, which is responsible for the user association and resource allocation, based on the approaches described in Sections 3.1.2 and 3.1.3.
The data rate of the k-th TAP from the l-th TUE in the m-th cluster can be obtained as
𝑅(𝑙, 𝑘, 𝑚) = log2 (1 +𝜃(𝑙, 𝑘)𝑃(𝑙, 𝑘)𝐻(𝑙, 𝑘)
𝜎2 )
where 𝑃(𝑙, 𝑘) stands for the transmission power in the l-k link, 𝐻(𝑙, 𝑘) is the path-gain of the l-k link, and 𝜎2 represents the variance of the zero-mean Gaussian noise. Finally, 𝜃(𝑙, 𝑘) is a binary random variable that denotes whether the link is LOS or not, and its cumulative density function (CDF) can be expressed as
𝐹𝜃(𝑙,𝑘)(𝑑𝑙𝑘) = (1 − 𝑃𝑜(𝑙, 𝑘)) 𝑒− 𝑎 𝑑𝑙𝑘
where 𝑑𝑙𝑘 is the transmission distance of the l-k link, 𝑃𝑜(𝑙, 𝑘) is its outage probability and 𝑎 depends on the environment and is determined by fitting the above expression to empirical data. Notice that the impact of interference in the data rate of the k-th TAP from the l-th TUE in the m-th cluster has been neglected. This assumption holds, since, as proven in D4.1, the probability of interference in THz networks in extremely low.
3.1.2 Clustering
The above described system faces one major challenge, namely blockage. We can overcome this issue with a single framework, which is clustering. In more detail, our objective is to place TUE and TAPs that have the highest LOS probability in the same cluster. In order to formulate this problem, we consider the probability of establishing a LOS link between two the k-th TAP and l-th TUE, which is provided by 𝐹𝜃(𝑙,𝑘)(𝑑𝑙𝑘). Note that as the transmission distance of the l-k link increases, both this
probability and the path gain decreases. As mentioned earlier, our objective is to maximize the LOS probability for all the links. In other words, to maximize the sum of the probabilities of utilizing LOS link. Hence, given the number of clusters, Nc, the optimization problem can be formulated as:
max𝒙,𝒚
∑ ∑ ∑ 𝑥𝑖𝑗𝑦𝑘𝑗𝐹𝜃(𝑖,𝑘)(𝑑𝑖𝑘)
𝑖∈𝑈𝑘∈𝐼𝑗∈𝐽
s.t. C1: ∑ 𝑥𝑖𝑗
𝑗∈𝐽
= 1, for each 𝑖 ∈ 𝑈
C2: ∑ 𝑦𝑘𝑗
𝑗∈𝐽
= 1, for each 𝑘 ∈ 𝐼
C3: ∑ 𝑦𝑘𝑗
𝑘∈𝐼
≥ 1, for each 𝑗 ∈ 𝐽
C4: ∑ 𝑥𝑖𝑗
𝑖∈𝑈
≥ ∑ 𝑦𝑘𝑗
𝑖∈𝐾
, for each 𝑗 ∈ 𝐽
C5: ∑ 𝑥𝑖𝑗
𝑖∈𝑈
≤ 𝑁𝑗𝑚𝑎𝑥, for each 𝑗 ∈ 𝐽
C6: 𝑥𝑖𝑗 , 𝑦𝑘𝑗 ∈ {0, 1}, for each 𝑖 ∈ 𝑈, 𝑘 ∈ 𝐼, 𝑗 ∈ 𝐽 where 𝑥𝑖𝑗 is a binary variable that describes the association between the i-th TUE and the j-th cluster,
while 𝑦𝑘𝑗 is a binary variable that indicates the association between the k-th TAP and the j-th cluster.
Moreover, 𝑁𝑗𝑚𝑎𝑥 are the maximum available timeslots in the j-th cluster. Finally, 𝐽, 𝑈 and 𝐼 respectively
stand for the set of clusters, TUE, and TAPs.
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Evidently, 𝑥𝑖𝑗𝑦𝑘𝑗 is 1 if and only if both the i-th TUE and k-th TAP belongs to the j-th cluster. The
objective function,
∑ ∑ ∑ 𝑥𝑖𝑗𝑦𝑘𝑗𝐹𝜃(𝑖,𝑘)(𝑑𝑖𝑘)
𝑖∈𝑈𝑘∈𝐼𝑗∈𝐽
reveals that the proposed optimization problem is not based on the instantaneous situation of each link, but, on the potential of a TUE-TAP pair to establish a LOS link. Constraints C1 and C2 ensure that the clusters are disjoint. Constraint C3 ensures that each cluster has at least one TAP, while C4 indicates that the number of TUE in each cluster is larger than the number of TAPs in this cluster. Likewise, C5 ensures that the number of TUE associated in the 𝑗-th cluster is lower than the number of the available timeslots.
The above clustering problem is an integer non-linear programming problem. These problems are classified as NP-hard problems and are complicated to solve. To simplify it, we first modify constraint C6 as
C6.1: 0 ≤ 𝑥𝑖𝑗 , 𝑦𝑘𝑗 ≤ 1, for each 𝑖 ∈ 𝑈, 𝑘 ∈ 𝐼, 𝑗 ∈ 𝐽
C6.2: ∑ ∑ ∑ (𝑥𝑖𝑗 − (𝑥𝑖𝑗2 ))
𝑖∈𝑈
≤ 0
𝑘∈𝐼𝑗∈𝐽
C6.3: ∑ ∑ ∑ (𝑦𝑖𝑗 − (𝑦𝑖𝑗2 ))
𝑖∈𝑈
≤ 0
𝑘∈𝐼𝑗∈𝐽
By substituting C6.1-C6.3 into C6 of the optimization problem, we can transform the optimization problem into the following
The above formulated problem is a continuous one, which is significantly more sophisticated to solve. To guarantee that the solution of x and y are integers we add two penalty factors, namely k1 and k2, which let us rewrite the optimization problem as
max𝒙,𝒚
∑ ∑ ∑ 𝑥𝑖𝑗𝑦𝑘𝑗𝐹𝜃(𝑖,𝑘)(𝑑𝑖𝑘)
𝑖∈𝑈𝑘∈𝐼𝑗∈𝐽
− 𝑘1 ∑ ∑ ∑ (𝑥𝑖𝑗 − (𝑥𝑖𝑗2 ))
𝑖∈𝑈𝑘∈𝐼𝑗∈𝐽
− 𝑘2 ∑ ∑ ∑ (𝑦𝑖𝑗 − (𝑦𝑖𝑗2 ))
𝑖∈𝑈𝑘∈𝐼𝑗∈𝐽
s.t. C1: ∑ 𝑥𝑖𝑗
𝑗∈𝐽
= 1, for each 𝑖 ∈ 𝑈
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C2: ∑ 𝑦𝑘𝑗
𝑗∈𝐽
= 1, for each 𝑘 ∈ 𝐼
C3: ∑ 𝑦𝑘𝑗
𝑘∈𝐼
≥ 1, for each 𝑗 ∈ 𝐽
C4: ∑ 𝑥𝑖𝑗
𝑖∈𝑈
≥ ∑ 𝑦𝑘𝑗
𝑖∈𝐾
, for each 𝑗 ∈ 𝐽
C5: ∑ 𝑥𝑖𝑗
𝑖∈𝑈
≤ 𝑁𝑗𝑚𝑎𝑥, for each 𝑗 ∈ 𝐽
C6.1: 0 ≤ 𝑥𝑖𝑗 , 𝑦𝑘𝑗 ≤ 1, for each 𝑖 ∈ 𝑈, 𝑘 ∈ 𝐼, 𝑗 ∈ 𝐽
which, after some straightforward mathematical manipulations of the objective function, can be equivalently expressed as
max𝒙,𝒚
∑ ∑ ∑
𝐹𝜃(𝑖,𝑘)(𝑑𝑖𝑘)
2𝑖∈𝑈𝑘∈𝐼𝑗∈𝐽
(𝑥𝑖𝑗 + 𝑦𝑖𝑗)2
+ 𝑘1𝑥𝑖𝑗2 + 𝑘2𝑦𝑘𝑗
2 − ∑ ∑ ∑𝐹𝜃(𝑖,𝑘)(𝑑𝑖𝑘)
2𝑖∈𝑈𝑘∈𝐼𝑗∈𝐽
𝑥𝑖𝑗2
−𝐹𝜃(𝑖,𝑘)(𝑑𝑖𝑘)
2𝑘1𝑥𝑖𝑗
2 − 𝑥𝑖𝑗 − 𝑘1𝑦𝑖𝑗
s.t. C1: ∑ 𝑥𝑖𝑗
𝑗∈𝐽
= 1, for each 𝑖 ∈ 𝑈
C2: ∑ 𝑦𝑘𝑗
𝑗∈𝐽
= 1, for each 𝑘 ∈ 𝐼
C3: ∑ 𝑦𝑘𝑗
𝑘∈𝐼
≥ 1, for each 𝑗 ∈ 𝐽
C4: ∑ 𝑥𝑖𝑗
𝑖∈𝑈
≥ ∑ 𝑦𝑘𝑗
𝑖∈𝐾
, for each 𝑗 ∈ 𝐽
C5: ∑ 𝑥𝑖𝑗
𝑖∈𝑈
≤ 𝑁𝑗𝑚𝑎𝑥, for each 𝑗 ∈ 𝐽
C6.1: 0 ≤ 𝑥𝑖𝑗 , 𝑦𝑘𝑗 ≤ 1, for each 𝑖 ∈ 𝑈, 𝑘 ∈ 𝐼, 𝑗 ∈ 𝐽
The terms
𝐴1(𝒙, 𝒚) = ∑ ∑ ∑𝐹𝜃(𝑖,𝑘)(𝑑𝑖𝑘)
2𝑖∈𝑈𝑘∈𝐼𝑗∈𝐽
(𝑥𝑖𝑗 + 𝑦𝑖𝑗)2
+ 𝑘1𝑥𝑖𝑗2 + 𝑘2𝑦𝑘𝑗
2
and
𝐴2(𝒙, 𝒚) = ∑ ∑ ∑𝐹𝜃(𝑖,𝑘)(𝑑𝑖𝑘)
2𝑖∈𝑈𝑘∈𝐼𝑗∈𝐽
𝑥𝑖𝑗2 +
𝐹𝜃(𝑖,𝑘)(𝑑𝑖𝑘)
2𝑘1𝑥𝑖𝑗
2 + 𝑥𝑖𝑗 + 𝑘1𝑦𝑖𝑗
are convex in respect to their variables. In other words, the objective function of the optimization problem has been expressed as the difference of two convex functions. Since the constraints of the optimization problem are also linear, the problem is a difference of two convex programming problems (DCP). This problem can be solved in an iterative manner. To transform this problem to a convex one, we employ the first order approximation of 𝐴1(𝒙, 𝒚), i.e.
�̃�1(𝒙, 𝒚) = 𝐴1(𝒙𝑙−1, 𝒚𝑙−1) + ∇𝒙𝐴1(𝒙𝑙−1, 𝒚𝑙−1) (𝒙 − 𝒙𝑙−1) + ∇𝒚𝐴1(𝒙𝑙−1, 𝒚𝑙−1) (𝒚 − 𝒚𝑙−1) where ∇𝒙 and ∇𝒚 are the gradients with respect x and y, respectively. Note that since 𝐴1(𝒙, 𝒚)is an
increasing function of x and y, the following inequality holds
𝐴1(𝒙, 𝒚) ≥ �̃�1(𝒙, 𝒚)
21
As a result, the above optimization problem can be further simplified as
min𝒙,𝒚
𝐴2(𝒙, 𝒚) − �̃�1(𝒙, 𝒚)
s.t. C1: ∑ 𝑥𝑖𝑗
𝑗∈𝐽
= 1, for each 𝑖 ∈ 𝑈
C2: ∑ 𝑦𝑘𝑗
𝑗∈𝐽
= 1, for each 𝑘 ∈ 𝐼
C3: ∑ 𝑦𝑘𝑗
𝑘∈𝐼
≥ 1, for each 𝑗 ∈ 𝐽
C4: ∑ 𝑥𝑖𝑗
𝑖∈𝑈
≥ ∑ 𝑦𝑘𝑗
𝑖∈𝐾
, for each 𝑗 ∈ 𝐽
C5: ∑ 𝑥𝑖𝑗
𝑖∈𝑈
≤ 𝑁𝑗𝑚𝑎𝑥, for each 𝑗 ∈ 𝐽
C6.1: 0 ≤ 𝑥𝑖𝑗 , 𝑦𝑘𝑗 ≤ 1, for each 𝑖 ∈ 𝑈, 𝑘 ∈ 𝐼, 𝑗 ∈ 𝐽
The above formulated problem is a convex one.
To sum up, the solution of the clustering problem can be provided by the following algorithm.
Algorithm 1: Clustering problem programming solution.
Input: ε (coverage error) Phase 1: Initialization 1: l=0 2: Choose feasible matrices 𝒙0, 𝒚0 Phase 2: Loop 3: Do 4: l = l + 1 5: Calculate �̃�1(𝒙, 𝒚) 6: Solve the convex optimization problem to achieve 𝒙𝑙 , 𝒚𝑙 7: While |(𝐴2(𝒙𝑙 , 𝒚𝑙) − �̃�1(𝒙𝑙 , 𝒚𝑙))- (𝐴2(𝒙𝑙−1, 𝒚𝑙−1) − �̃�1(𝒙𝑙−1, 𝒚𝑙−1))| ≤ 𝜀
Next, we present a number of indicative simulation results that reveal the efficiency and
limitations of the proposed approach. We consider the following insightful simulation scenario. Unless otherwise stated, we assume that the network is utilized in an area of 10 x 10 m2. The TUE density equals 1 user/m2, while the TAPs density is set to 0.1 TAPs/m2. The operation frequency is 275 GHz and standard atmospheric conditions are assumed, i.e. atmospheric temperature and relative humidity of 296 K and 50%, respectively, while the atmospheric pressure is 101325 Pa. The parameter a is assumed to be equal to 0.1 and the outage probability is evaluated according to the generalized expression provided in D3.2, assuming that all the users request the same data rate of 1 Gbps. Note that this data rate is the basic requirement of the third technical scenario, as defined in D2.2. Moreover, it is assumed that the requested bandwidth of each user is equal to 1 GHz. Note that based on our experimental results, which are presented in D6.2, THz channels are flat for such bandwidth. Finally, we assume that the transmission and reception antennas gains are 30 and 20 dBi, respectively. For the sake of simplicity, the simulation parameters are summarized in Table 2.
Table 2: Simulation parameters.
Parameter Value
Network area 10 x 10 m2
TUE density 1 user/m2
22
TAP density 0.1 TAPs/m2
Operation frequency 275 GHz
Atmospheric temperature 296 K
Relative humidity 50 %
Atmospheric pressure 101325 Pa
Blocking parameter (a) 0.1
TUE requested bandwidth 1 GHz
Transmission power 30 dBm
Transmission antenna gain 30 dBi
Reception antenna gain 20 dBi
Noise figure 10 dB
First, we consider the special case in which the number of clusters is the same as the number of the TAPs. In this scenario, each cluster will have exactly one TAP. Figure 3 presents a snapshot of the THz wireless network before and after clustering. From this figure, we observe that each cluster consists of a different number of TUEs and exactly one TAP. This indicates that the TUEs in a cluster will be associated with the cluster TAP; hence, in this scenario no TAP-TUE association method needs to be employed. Interestingly, we observe that TUEs may not be associated with the nearest TAP. This is because the blockage probability for the nearest TAP association might be higher than the one that can be achieved by associating the TUE with another TAP.
(a)
23
(b)
Figure 3: A snapshot of the THz wireless network with un-clustered (a) and clustered (b) TAPs and TUE.
Figure 4: Clustering rate vs λAP for different values of λUE.
For the same scenario, Figure 4 demonstrates the clustering rate as a function of the TAP density, for different values of TUE density. As expected, for a given λUE, as the TAP density increases, the number of TAPs also increases; hence, the clustering rate improves. Moreover, for a fixed λAP, as λUE increases, the number of TUEs that are clustered in each cluster increases; thus, the clustering rate also increases. Likewise, it is observed that with an λAP>0.4 TAPs/m2, independently of λUE, the clustering rate is higher than 90%, which is considered satisfactory. Finally, note that for λAP= 0.001 TAPs/m2, the number of TAPs equals 1 and the clustering rate equals 60%. This means that the minimum percentage of TUEs that can be served is 60%.
24
Figure 5: Clustering rate vs blockage coefficient for different values λAP.
Figure 5 depicts the clustering rate as a function of the blockage coefficient for different values of TAPs density. From this figure, we observe that, for a given TAP density, as the blockage coefficient increases, the blockage probability increases; as a consequence, the clustering rate also decreases. Likewise, for a given blockage coefficient, as the TAP density increases, the number of TAPs increases; hence, the opportunities of a TUE to be clustered also increases. As a result, the clustering rate increases. For example, for a blockage coefficient that equals 0.1 m-1, a λAP increase from 0.01 to 0.1 AP/m results to an approximately 30% clustering rate improvement.
Figure 6: Clustering rate vs λAP for different values of NJ.
Figure 6 illustrates the clustering rate as a function of the TAP density, for different values of number of clusters, assuming λUE = 2 TUEs/m2. From this figure, we observe that for a given NJ, as the TAP density increases, the number of TAPs within a cluster as well as the number of clusters increase;
25
as a result, the clustering rate also increases. Moreover, for a given λAP, as the number of clusters decreases, the number of TAPs within a cluster increases; hence, more TUEs can be served in a single cluster; consequently, the clustering rate increases.
3.1.3 Joint user association and resource allocation
By taking into account the massive number of degrees of freedom that directional communication offers, we can define dynamic cells within the clusters as a set of not necessarily collocated TUEs that are served by the same TAP. In this direction, the following attributes should be recorded by a TAP that will play the role of the cluster control unit (CCU):
• Each TUE data rate demands;
• The distance between the i-th TAP and the j-th TUE that both belong in the same cluster;
• The maximum available resources in each TAP;
• The cluster topology.
The objective of the CCU of the k-th cluster is to maximize the cluster overall throughput. In this direction, we formulate the following optimization problem:
max𝜳,𝑪
∑ 𝑟𝑖𝑗𝜓𝑖𝑗𝑐𝑖𝑗
𝑗∈𝑈,𝑖∈𝐵
,
s. t. C1: ∑ 𝑐𝑖𝑗 ≤ 1,𝑗∈𝑈 for each 𝑖 ∈ 𝐵,
C2: ∑ 𝜓𝑖𝑗 = 1𝑖∈𝐵 , for each 𝑗 ∈ 𝑈,
C3: 0 ≤ 𝑐𝑖𝑗 ≤ 𝜓𝑖𝑗, 𝜓𝑖𝑗 ∈ {0, 1}, for each 𝑖 ∈ 𝐵,
C4: 𝜓𝑖𝑗 = 0, if 𝑅𝑖𝑗 ≤ 𝑅𝑗,𝑚𝑖𝑛,
C5: 𝜓𝑖𝑗 ∈ {0, 1} where 𝑐𝑖𝑗 is the fraction of resources that the TAP i employs to serve the TUE j and rij is the data rate
of the i-j link. Likewise, 𝑅𝑗,𝑚𝑖𝑛 is the minimum required rate for the TUE j. Likewise, Ψ and C are
matrices that collect all the TUE association variables, ψij, and fraction of resources, cij, used by the TAP i to serve the TUE j. Finally, B and U are respectively the sets of TAPs and TUEs that belong to the cluster k.
In the above optimization problem, the constraint C1 ensures that the i-th TAP is not allowed to allocate more resources than the ones it has. Moreover, constraint C2 guarantees the association of the TUE j to exactly one TAP. Constraints C3 and C4 ensure a minimum acceptable QoS for every UE. Additionally, C3 ensures that every TAP i will provide a positive resource share only to its associated TUEs. Note that the solution of the optimization problem provides a long-term association policy along with proper orientation and operating beamwidths for directional wireless THz communications. This solution guarantees the optimal TUE-TAP association within the cluster as long as the inputs of the optimization problem, namely cluster topology and TUEs’ demands, are unchanged. If a TUE requires more resources, the optimization must be re-executed.
The above clustering problem is an integer non-linear programming problem. These problems are classified as NP-hard problems and are complicated to solve. A similar optimization problem was solved in D4.1 by employing a grey wolf optimizer (GWO). However, the coverage ratio of GWO is quite slow; hence, it may not be a good approach for real-time changing clusters. Motivated by this, in this deliverable, we follow a different approach. First, we relax the constraint C5 as
C5: 𝜓𝑖𝑗 ∈ [0,1] and we rewrite the optimization problem as
max𝜳,𝑪
∑ 𝑟𝑖𝑗𝜓𝑖𝑗 𝑐𝑖𝑗
𝑗∈𝑈,𝑖∈𝐵
,
s. t. C1: ∑ 𝑐𝑖𝑗 ≤ 1,𝑗∈𝑈 for each 𝑖 ∈ 𝐵,
C2: ∑ 𝜓𝑖𝑗 = 1𝑖∈𝐵 , for each 𝑗 ∈ 𝑈,
C3: 0 ≤ 𝑐𝑖𝑗 ≤ 𝜓𝑖𝑗,
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C4: 𝜓𝑖𝑗 = 0, if 𝑅𝑖𝑗 ≤ 𝑅𝑗,𝑚𝑖𝑛, C5: 0 ≤ 𝜓𝑖𝑗 ≤ 1
The above formulated problem is a continuous one, which is significantly more sophisticated to solve. To guarantee that the solution of 𝜳 is an integer, we add the penalty factor l, which lets us express the optimization problem as
max𝜳,𝑪
∑ 𝑟𝑖𝑗𝜓𝑖𝑗 𝑐𝑖𝑗
𝑗∈𝑈,𝑖∈𝐵
− 𝑙 ∑ (𝜓𝑖𝑗 − (𝜓𝑖𝑗)2
)
𝑗∈𝑈,𝑖∈𝐵
,
s. t. C1: ∑ 𝑐𝑖𝑗 ≤ 1,𝑗∈𝑈 for each 𝑖 ∈ 𝐵,
C2: ∑ 𝜓𝑖𝑗 = 1𝑖∈𝐵 , for each 𝑗 ∈ 𝑈,
C3: 0 ≤ 𝑐𝑖𝑗 ≤ 𝜓𝑖𝑗,
C4: 𝜓𝑖𝑗 = 0, if 𝑅𝑖𝑗 ≤ 𝑅𝑗,𝑚𝑖𝑛,
C5: 0 ≤ 𝜓𝑖𝑗 ≤ 1
which can be rewritten as max𝜳,𝑪
∑ 𝑟𝑖𝑗𝜓𝑖𝑗 𝑐𝑖𝑗 + 𝑙 (𝜓𝑖𝑗)2
𝑗∈𝑈,𝑖∈𝐵
− 𝑙 ∑ 𝜓𝑖𝑗
𝑗∈𝑈,𝑖∈𝐵
,
s. t. C1: ∑ 𝑐𝑖𝑗 ≤ 1,𝑗∈𝑈 for each 𝑖 ∈ 𝐵,
C2: ∑ 𝜓𝑖𝑗 = 1𝑖∈𝐵 , for each 𝑗 ∈ 𝑈,
C3: 0 ≤ 𝑐𝑖𝑗 ≤ 𝜓𝑖𝑗,
C4: 𝜓𝑖𝑗 = 0, if 𝑅𝑖𝑗 ≤ 𝑅𝑗,𝑚𝑖𝑛,
C5: 0 ≤ 𝜓𝑖𝑗 ≤ 1
Since the terms B1(𝜳, 𝑪)=∑ 𝑟𝑖𝑗𝜓𝑖𝑗 𝑐𝑖𝑗 + 𝑙 (𝜓𝑖𝑗)2
𝑗∈𝑈,𝑖∈𝐵 and B2(𝜳, 𝑪)= 𝑙 ∑ 𝜓𝑖𝑗𝑗∈𝑈,𝑖∈𝐵 are convex,
and the constraints of the optimization problem are also linear, the problem is a DCP. Hence, it can be solved by following the same approach as in Section 3.1.2 and replacing A1 with B1, and A2 with B2.
Next, we provide illustrative results that demonstrate the performance of the proposed approach. For the sake of simplicity, we assume that all the users request the same data rate that equals 1 Gbps. Furthermore, notice that the joint association and resource allocation procedure follows the clustering one. Therefore, unless otherwise stated, the same simulation parameters, which are presented in Table 2, are used.
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Figure 7: Average network throughput as a function of λAP for different values of λUE.
Figure 7 plots the average network throughput as a function of the TAP density for different values of TUE density. From this figure, we observe that for low values of TAP and UE densities, in which the clustering rate in lower than 100%, the average network throughput increases as the TAP density increases. This is due to the fact that, as shown in Figure 4, as the TAP density increases, the clustering rate also increases. Moreover, it is evident that for a medium TUE density, for which the clustering rate tends to 100%, the average network throughput depends on the efficiency of the association policy as well as the TUEs-associated TAP distance. Finally, while in the high TUE density regime the clustering rate tends to 100%, we observe that in the low and medium TAP density regime, the network is incapable of achieving the maximum possible throughput. This is because the total number of the available resources is directly connected with the number of TAPs. In other words, in these regimes, it is not the clustering rate but the number of resources/TAPs that constrains the average network throughput.
3.2 Relay-based blockage avoidance and load balancing
3.2.1 System model
A wideband THz wireless network consisting of 𝑁 user equipments (UEs) is considered. It is assumed that there is no interference between the UEs, and the transmission probability of each UE is 𝑃𝐸. Additionally, the UEs are equipped with highly directional antennas and the transceivers operate in half-duplex mode. The current topology describes a 2D network scenario, where the users are modelled as circles with radius 𝑟𝐵. Furthermore, their centres represent the UEs, whose locations are generated by a PPP with intensity λ. In order to avoid cases where two users are generated on top of each other, the minimum distance between them is set to 2𝑟𝐵.
If a user interrupts the LoS connection of a link, it is considered as a blocker, which in turn reduces the signal-to-noise-ratio (SNR) of the link to zero. On the other hand, if the beams of the TX and the RX are not perfectly aligned, the received power, and thus, the SNR are reduced. To mitigate the joint impact of blockage and antenna misalignment, another UE, whose links with the TX and RX are not
28
blocked or severely misaligned and satisfy the QoS throughput threshold, 𝐶𝑚, of the network, is set as a decode and forward relay (R) for this connection. Furthermore, the case with two maximum transmission hops is considered.
Figure 8: Example of Relaying.
In Figure 8, an intuitive example of the dual-hop relaying system topology is presented. As illustrated, one UE, namely the source (𝑆) transmits to the destination (𝐷), through an intermediate, namely the 𝑅, because the direct link is obstructed by the blocker (𝐵). The 𝑅 is selected through a set ℛ = {𝑅𝑖|𝑖 = 1, … , 𝑀} of available 𝑅s.
The baseband equivalent received signal can be expressed as 𝑦 = ℎ ∗ 𝑥 + 𝑛, (1)
where 𝑥, ℎ and 𝑛 are the complex transmitted signal, channel coefficient and additive white Gaussian noise (AWGN), respectively, for the three types of links, namely (𝑆, 𝑅𝑖), (𝑅𝑖, 𝐷) and (𝑆, 𝐷). The channel coefficient can be expressed as
ℎ = {βh𝑙 ℎ𝜑, β = 1
0, 𝛽 = 0 , (2)
where β = 0 and β = 1 denote a blocked and an unblocked link, respectively. Moreover, ℎ𝑙 stands for the deterministic path gain and ℎϕ is the antenna misalignment coefficient.
From [12] ℎ𝑙 can be obtained as
ℎ𝑙(𝑓, 𝑑) = (𝑐
4π𝑓𝑑) √𝐺𝑡𝐺𝑟 exp (−
1
2𝑘(𝑓)𝑑) , (3)
where 𝑓 stands for the carrier frequency, 𝑑 is the transmission distance, 𝑘(𝑓) is the molecular absorption coefficient, while 𝐺𝑡 and 𝐺𝑟 stand for the TX and RX antenna gains, respectively.
To accommodate the effect of misalignment fading ℎϕ, the TX beam and the RX antenna effective
area on the RX side form circular discs. Furthermore, both discs are considered on the positive 𝑥-𝑦 plane and the pointing error, ρ = |ρ| at the RX, expresses the radial distance of the transmission and reception beams. Also, without loss of generality, it assumed that ρ, is along the 𝑥-axis [13]. Then, according to [14] and [13], the antenna misalignment fading coefficient can be obtained as
ℎϕ(ρ; 𝑑) = 𝐴𝑜 exp (−2ρ2
𝑅𝑒𝑞2 ) , (4)
where 𝐴𝑜 is the fraction of the collected power by the RX at ρ = 0, 𝑅𝑒𝑞 is the equivalent TX beam
radius at the RX obtained as in [14]. Also, by assuming independent identical Gaussian distributions
29
for the horizontal and elevation displacements [13], [15], ρ follows a Rayleigh distribution and its probability density function is expressed as
𝑓ρ(ρ) =ρ
σ𝑠2 exp (−
ρ2
2σ𝑠2) , ρ ≥ 0, (5)
where σ𝑠 is the jitter standard deviation.
3.2.2 Relay Selection Strategies
In this section two relay selection strategies are discussed.
• Best relay selection strategy: The selected relay of each blocked link is the UE that offers
the highest throughput in the(𝑆, 𝑅𝑖) and (𝑅𝑖, 𝐷) links. This means that both the (𝑆, 𝑅𝑖)
and (𝑅𝑖, 𝐷) are not blocked and 𝐶𝑚 is satisfied.
• Random relay selection strategy: The 𝑅𝑖 of each 𝑆 and 𝐷 blocked link is selected randomly
with the discrete uniform distribution from among the UEs whose links with the 𝑆 and the
𝐷 are not blocked and satisfy 𝐶𝑚.
3.2.3 Performance Evaluation
In order to quantify the performance and sustainability of the potential THz wireless links in the network, the average throughput and the probability 𝑃𝐶 that a link throughput 𝐶 is below the throughput threshold 𝐶𝑚, are employed as metrics. For the THz wideband wireless communications, the capacity of a link, can be obtained as [16], [17]
C = ∫ log2(1 + �̃�(𝑓)) 𝑑𝑓B
0
, (6)
which by using (2), (3), (4), as well as the Parseval theorem can be rewritten as
γ̃(f) =Pt (
c4πfd
)2
GtGr exp(−k(f)d)
Nohϕ
2 , (7)
where Pt stands for the transmitted power spectral density (PSD), No denotes the PSD of the AWGN and B is the bandwidth. Moreover, the CDF of the capacity, PC employing eq. (6) can be obtained as
PC = Pr(C̃ ≤ Cthr), (8)
where, if the relayed link is used, �̃� = 𝑚𝑖𝑛(𝐶𝑆 − 𝑅𝑖, 𝐶𝑅𝑖−𝐷), with 𝐶𝑆−𝑅𝑖 and 𝐶𝑅𝑖−𝐷 being the
capacities of the 𝑆 − 𝑅𝑖 and 𝑅𝑖 − 𝐷 links and if the link is direct, �̃� = 𝐶𝑆−𝐷.
3.2.4 Simulation results
In this section, Monte Carlo simulations of the average throughput and 𝑃𝐶 are delivered for different values of network UE densities and levels of antenna misalignment. In what follows, standard atmospheric conditions are assumed. Moreover, the transmission bandwidth, the central frequency, 𝜃3𝑑𝐵, the network radius 𝑅𝑁, 𝐶𝑚, 𝑟𝐵 and 𝑃𝐸 are respectively set to 50 GHz, 300 GHz, 0.9𝑜, 5 m, 1 Gb/s, 0.2 m and 60 %. Furthermore, 𝜆 ∈ [0.3, 1.5] 𝑈𝐸𝑠/𝑚2 and 𝜎𝑠 ∈ {0,0.05,0.2} m. Also, note that 𝜎𝑠 =0 m is the case without antenna misalignment. Finally, the parameter 𝑔 = 𝑃𝑡𝐺𝑡𝐺𝑟/𝑁𝑜 = 100 dB is assumed, where 𝑃𝑡, 𝐺𝑡 and 𝐺𝑟 are the same and constant for all the types of links.
30
Figure 9: Average throughput vs 𝝀 for different values of 𝝈𝒔.
In Figure 9, the average throughput is depicted as a function of λ for different values of σ𝑠. It can be observed that, for a given λ, as σ𝑠 increases, the average throughput decreases. Similarly, for a fixed σ𝑠, as λ increases, the average throughput degrades. For example, as λ increases from 0.3 to 1.5 𝑈𝐸𝑠/𝑚2, the average throughput for both strategies with σ𝑠 = 0 and 0.05 m, decreases by 14.98 and 5.49 Gb/s, respectively. On the other hand, for σ𝑠 = 0.2 m, as λ increases from 0.3 to 0.7 𝑈𝐸𝑠/𝑚2 the average throughput increases by 2.66 Gb/s, while it decreases by 1.82 Gb/s as λ increases from 0.7 to 1.5 𝑈𝐸𝑠/𝑚2. For λ increasing from 0.3 to 0.7 𝑈𝐸𝑠/𝑚2, a throughput increase is observed, as more UEs function as relays than as blockers, whereas for λ increasing from 0.7 to 1.5 𝑈𝐸𝑠/𝑚2, the throughput is reduced, as more UEs function as blockers than as relays. Furthermore, as σ𝑠 increases from 0 to 0.05 m and 0.05 to 0.2 m, the average throughput with λ = 0.3 𝑈𝐸𝑠/𝑚2 decreases by 22.81 and 21.71 Gb/s, respectively. It is observed that the effect of antenna misalignment is more severe than that of blockage, and thus it is more challenging to mitigate it using relays. Moreover, the difference between “best relay” and the “random relay” strategies increases when σ𝑠 changes from 0 to 0.05 m, while it decreases when changing σ𝑠 from 0.05 to 0.2 m. For example, for λ = 0.3 𝑈𝐸𝑠/𝑚2 and σ𝑠 = 0, 0.05 and 0.2 m, the average throughput difference between the two approaches is 5.13, 9.16 and 7.1 Gb/s, respectively. The reduction in the difference between the two approaches for high values of σ𝑠 is caused by the reduction in the number of potential relays, due to severe misalignment. Thus, both approaches have to choose from a smaller pool of potential relays.
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(a)
(b)
Figure 10: 𝑷𝑪 vs target throughput for different levels of 𝛔𝒔: (a) 𝛌 = 𝟎. 𝟑 𝑼𝑬𝒔/𝒎𝟐 and (b) 𝛌 =
𝟏. 𝟓 𝑼𝑬𝒔/𝒎𝟐.
Figure 10 shows 𝑃𝐶 as a function of the target throughput for different values of λ and σ𝑠. As expected, for a fixed λ, as σ𝑠 increases, 𝑃𝐶 also increases. Furthermore, as expected, the “best relay” achieves the lowest 𝑃𝐶 for each combination of λ and σ𝑠. For example, for λ = 0.3 𝑈𝐸𝑠/𝑚2, σ𝑠 =0.05 m and target throughputs of 30 and 45 Gb/s, the 𝑃𝐶 difference between the two approaches is 0.071 and 0.069, respectively, whereas for the same parameters and σ𝑠 = 0.2 m their 𝑃𝐶 difference is 0.0432 and 0.0418, respectively. Moreover, for λ = 1.5 𝑈𝐸𝑠/𝑚2, σ𝑠 = 0.05 m, and target throughputs of 30 and 45 Gb/s, the 𝑃𝐶 difference between the two strategies is 0.082 and 0.087, respectively, whereas for the same parameters and σ𝑠 = 0.2 m their 𝑃𝐶 difference is 0.06 and 0.066, respectively. Finally, it is observed that the “best relay” performance gain with respect to the “random relay” gain decreases as σ𝑠 increases.
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3.3 SDMA
3.3.1 System model
The same system model as in Section 3.2 is assumed without misalignment and relays (Figure 11). In this sense, (2) can be rewritten as
ℎ = { βh𝑙, β = 1
0, 𝛽 = 0(9).
Furthermore, the antenna array of each UE is divided to 𝐾 subarrays. Each subarray can be used to transmit to one UE. Also, due to the half-duplex constraint, a UE can be used only as a TX or as an RX at a given time.
In Figure 11, an example of SDMA for node 𝑆 is presented. Specifically, node 𝑆 needs to transmit to nodes 𝐷2, 𝐷3, 𝐷5, 𝐷6, 𝐷7 and 𝐷8, but links 𝑆 − 𝐷2, 𝑆 − 𝐷5 and 𝑆 − 𝐷8 are blocked.
Figure 11: Example of SDMA with human blockage.
3.3.2 Transmission strategies
In this section two relay selection strategies are discussed.
• Conventional SDMA: Each TX wants to transmit to multiple RXs. The links are separated in
groups that can be realized simultaneously. Then the links are sorted in descending order
according to their capacity and the first K links are realized.
• Blockage Aware SDMA: Each TX wants to transmit to multiple RXs. The links are separated in
groups that can be realized simultaneously. Then, the links are sorted in descending order
according to their capacity. Furthermore, the blocked links are discarded. Finally, the first K
links are realized.
3.3.3 Results
In this section, Monte Carlo simulations of the CDF of the capacity, Pr(C̃ ≤ Cthr), are delivered
for different values of 𝜆 and assuming standard atmospheric conditions. The transmission bandwidth, the central frequency, the network radius 𝑅𝑁, 𝐶𝑚, 𝑟𝐵 and 𝑃𝐸 are set to 50 GHz, 300 GHz, 5 m, 1 Gb/s, 0.2 m and 60 %, respectively. Furthermore, 𝜆 ∈ [0.3,1.5] 𝑈𝐸𝑠/𝑚2 and 𝑔 = 100 dB.
In Figure 12, the CDF of the capacity is shown for 𝜆 = 0.3, 0.7 and 1.1 𝑈𝐸𝑠/𝑚2. The number of available subarrays is set to infinite, 16, 20, 24, 28, 32 and 36 and is depicted with black, blue, red, green, cyan, magenta and yellow color, respectively. It is observed that in the case of the conventional SDMA the CDF of the capacity for a certain threshold 𝐶𝑡ℎ𝑟 increases with the number of subarrays, as more blocked links are included every time. On the other hand, in the case of Blockage Aware SDMA, the probability is about the same for all numbers of available subarrays, due to the fact that the blocked links are removed from the SDMA.
4. CACHING
In general, in computing, caching consists of high-speed data layer, which stores (caches) the data and later in the future the requests will be fulfilled by quickly transmit the data from local storage instead of sending the content request to the original content storage. The primary purpose of caching is to improve the data retrieval performance and the cache stores only a subset of data. This is in contrast to databases that hold the complete data. The cache replacement method plays an important role as it updates the cache and made room for new content in the available storage to avoid out of the storage problem. The Least Recently Used caching method evicts the cache data, which have not been used for a long time, and new data referenced, which are not present in the cache. However, First in First out (FIFO) algorithm replaces the earliest stored/cached object earliest.
4.1 Social caching
Efficient caching strategy for popular content at mobile network not only alleviates the traffic explosion problem but also reduces the content access delay and energy consumption in networks. “What to cache?” has been an important research direction for the wireless networks. Popularity ranking is widely used as the basis of proactive caching. However, the popularity of the content is based on the global access of the content, which may vary depending on geographical locations, user influence, and content properties. During peak traffic period, frequent cache replacements might replace contents that have high possibility of access in future. So, only popularity-distribution-based caching may not be suitable for every caching systems. Unfortunately, besides popularity ranking, not many attributes and their influence have been taken into account in caching decisions. Therefore, we propose a new caching approach based on social connections of users.
In order to achieve that, the cache controller (CC) analyzes all the MBs request logs and marks mobile terminals with one or more common requests as socially tied. The strength of the tie is corresponding to common requests divided by all requests. After computing the social tie, the CC identifies the mobile terminal (known as the group forerunner) that initiated the largest number of common requests. The contents that are unique to the forerunner’s MoBcache (MB) are pre-fetched to the other MBs by considering the social group of mobile terminals’ MBs based on the probability proportional to the social tie among the mobile terminals.
4.2 Prefetching
Prefetching method allows to pre-emptively cache the content, before the user requests it, which is executed on-demand. The prefetching method reads the prefetch lists and sends the content URLs that are required to be prefetched at the destined MB based on the prefetching decision. After receiving the request, which contains the information about prefetched URLs from prefetch, the Cache module will check it locally whether it has the requested content locally or not. In the case content is not available locally, then there is a possibility that requests will be forwarded to high level cache nodes when hierarchical caching is deployed. Finally, if no cache node in the caching overlay has the content stored locally, the request will be forwarded to the original content source on Internet. The prefetching scheme builds on the premise that users request the content via MB. The MB stores similar content; hence, they are likely to have roughly the same preferences and are expected to
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request common content items in the future. Therefore, we consider cache contents similarity as an expression of an implicit social proximity.
Exploiting this social aspect can enhance caching operations and bring benefits both to users and network operators by two ways. First, by Proactive Scenario, where caching of the content is based on the expectation and popularity of content, i.e. that a user will request specific contents given his interests and the actions of socially close peers (this does not require physical proximity). Second, by Reactive Scenario, which is utilizing device-to-device communication for faster lookup and delivery from the caches.
• Proactive Scenario (1): CC instruct MB to pre-fetch a certain content.
1. User connects to a MB
2. MB (initial node) sends the user's info (identifier such as MAC) to CC
3. CC checks its log and try to match the new user to others with similar interest
4. if found then:
5. Identify the most popular content in that group
6. If content is unique to the initial node then instruct it to fetch that content and exit
loop
7. else move to the next popular content
8. until content list is exhausted
9. else do nothing
• Reactive Scenario (2): When the user initiates a content request
1. User requests a content from MB
2. MB connected directly to that user (initial node) check the content locally
3. if the content is cached locally then deliver it to user.
4. else forward the request to the RMB.
5. If the content is cached at another MB then fetch it and deliver it to user.
6. else fetch the content from the content server and deliver it to user.
4.3 Bloom filter
A Bloom filter is a data structure which is designed to test whether an element is present in a given set or definitely not. A Bloom filter is a probabilistic data structure where efficiency is defined in terms: False Positive (FP) matches are possible, but False Negatives (FN) are not – in other words, a query returns that elements either definitely Not in the set or Maybe in the set. The elements can be added in the set, but they are not removed (though this can be addressed with a "counting" filter). The more the elements added to the set, the larger the probability of FP. In the caching system, the Bloom Filter is used to check the list of cached objects in the MoBcache, and impact of BF in the caching system is described in the results section.
An empty Bloom filter is an array of 𝑚 bits, all set to zero. There must also be 𝑘 different hash functions defined, each of which maps or hashes some set element to one of the 𝑚 array positions, generating a uniform random distribution. Typically, 𝑘 is a constant, much smaller than 𝑚, which is proportional to the number 𝑛 of elements to be added. The precise choice of 𝑘 and the constant of proportionality of 𝑚 are determined by the intended FP rate of the filter 𝑝. To add an element, feed it to each of the 𝑘 hash functions to get 𝑘 array positions. Set the bits at all these positions to 1.
To query for an element (to test whether it is in the set), feed it to each of the 𝑘 hash functions to get 𝑘 array positions. If any of the bits at all positions is 0, the element is definitely not in the set – if it were, then all the bits would have been set to 1 when it was inserted. If all the bits are 1, then either the element is in the set, or the bits have been set to 1 during the insertion of other elements, resulting in a FP. In a simple Bloom filter, there is no way to distinguish between the two cases, but more advanced techniques can address this problem.
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Figure 13, represents the set 𝑥, 𝑦, 𝑧. The coloured arrows show the positions in the bit array where each set element is mapped. The element 𝑤 is not in the set 𝑥, 𝑦, 𝑧, because it hashes to one bit-array position containing 0.
Figure 13: An example of a Bloom filter, m = 18 and k = 3.
The hash functions used in a Bloom filter should be independent and uniformly distributed. They should also be as fast as possible (cryptographic hashes such as sha1, though widely used, therefore, are not very good choices). In addition, the requirement of designing 𝑘 different independent hash functions can be prohibitive for large 𝑘. For a good hash function with a wide output, there should be little if any correlation between different bit-fields of such a hash, so this type of hash can be used to generate multiple "different" hash functions by slicing its output into multiple bit fields. Alternatively, one can pass k different initial values known as Salt (such as 0, 1, … 𝑘 − 1) to a hash function that takes an initial value; or add (or append) these values to the key this is the adopted method in our approach.
Removing an element from this simple Bloom filter is impossible because FN are not permitted. An element mapped to 𝑘 bits and setting any one of those 𝑘 bits to zero suffices to remove the element, but it also results in removing any other elements that map onto that bit. Since there is no way of determining whether any other elements have been added that affect the bits for an element to be removed, clearing any of the bits would introduce the possibility for FNs.
4.3.1 Advantages
While risking FP, Bloom filters have a strong space advantage over other data structures for representing sets, such as self-balancing binary search trees, tries, hash tables, or simple arrays or linked lists of the entries. Most of these require storing at least the data items themselves, which can require anywhere from a small number of bits, for small integers, to an arbitrary number of bits, such as for strings. However, Bloom filters do not store the data items at all, and a separate solution must be provided for the actual storage. Bloom filters also have the unusual property that the time needed either to add items or to check whether an item is in the set is a fixed constant, 𝑂(𝑘), completely independent of the number of items already in the set. Also, the Bloom filter shines in hardware implementation because its 𝑘 lookups are independent and can be parallelized.
4.3.2 Optimal numbers of the parameters
In Bloom filter, we can modify the FP rate of the filter. A larger filter will have less FPs than a smaller one. In addition, the more hash functions we have, the slower our bloom filter becomes, and the quicker it fills up. If we have too few, however, we may suffer too many FPs.
The number of hash functions 𝑘 must be a positive integer. Putting this constraint aside, for a given 𝑚 and 𝑛, the value of 𝑘 that minimizes the FP probability as
𝑘 =𝑚
𝑛 ln 2.
The required number of bits 𝑚, given 𝑛 (the number of inserted elements) and a desired FP probability 𝑝 (and assuming the optimal value of 𝑘 is used), can be computed by substituting the optimal value of 𝑘 in the probability expression, as
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𝑚 = −𝑛 ln 𝑝
(ln 2)2.
4.3.3 Bloom filter pseudocode
The pseudo-code of Bloom filter algorithms is defined below in terms of initialization, insertion, and checking the data in the Bloom filter via Algorithms 2, 3 and 4 respectively. The name of different algorithms clearly represents its purpose of use. For example, initialization algorithm represents the first step that is performed by the Bloom Filter in order to initialize various elements and compute the required number of hash functions for the given set of values.
Algorithm 2: Initialize
1. Parameters
2. n “element count estimate”.
3. p “desired FP probability”.
4. Begin
5. Compute m “number of bits in the bloom filter”. 6. m <- ceil((n * ln(p)) / ln(1 / 2ln(2)).
7. Compute k “number of hash functions”. 8. k <- round((m / n) * ln(2)). 9. BloomFilter <- table[m bit]. 10. for each b in BloomFilter do 11. b <- 0. 12. HashFunctions <- table[k function]. 13. for each hf in HashFunctions do 14. hf <- Create Hash function with a unique Salt. 15. End
Algorithm 3: Insert
1. Parameters
2. element “data to be inserted in the bloom filter”.
3. Begin 4. for each hf in HashFunctions do 5. index <- hf(element) mod m. 6. BloomFilter[index] <- 1. 7. End
Algorithm 4: Check
1. Parameters
2. element “data to be checked in the bloom filter”. 3. Returns boolean.
4. Begin 5. for each hf in HashFunctions do 6. index <- hf(element) mod m. 7. if BloomFilter[index] = 0 then return false. 8. return true; 9. End
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4.4 Architecture
The main elements in the caching system architecture are shown in Figure 14. This caching system is consisted of MB, RMB, CC and CS. Figure 14 shows the two clusters but there could be a scenario where multiple clusters can be defined. One MBs cluster could contain one RMB, which is responsible for managing and serving all its child MBs. The child MB serves all the users available in its coverage area. There are two entities, which also communicate RMB, such as CC and CS. The CC is a server, which is responsible for analysing the user’s content request (log files) and makes prefetching decision. The CS provides the content to the end user through the child MB.
Figure 14: Network Topology.
The functions of each entities are descripted as follows: Mobile Terminal: It requests the content to the connected MB. There are multiple end-user
terminals, shown by different colours. The end-user terminals that are marked with the same colour represent the interest in the same content that helps to calculate the popularity of the content.
Child MoBCache (MB): The child MB receives the requests from the users in its coverage area and fulfils the user request either from its local storage cached or redirected to RMB. The child MB is responsible to perform the following functions: • Receive, log and respond to Mobile terminals requests. • Manage the cache content. • Create Bloom filter for current content. • Share the Bloom filter with root MB. • Receive and respond to RMB queries. • Share the requests log with the CC. • Execute pre-fetch instruction of the CC.
Root MB (RMB): The RMB is responsible for managing the child MBs in its coverage area, as all the child MBs get the communication link (e.g., Internet) from the RMB. It is responsible for the following functions: • Perform all child MB functions. • Check MB requests against the MB cluster cache using received bloom filters. • Act as an internet getaway for MB nodes. • Relay cache controller instructions to MB.
Cache controller (CC): It is a server, which analyses the log files received from the RMB and MB in order to perform the following tasks:
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• Model social ties using MB logs. • Identify popular content using MB cache. • Generate prefetching instructions for the appropriate MB.
Content Server (CS): It is a remote server that provides the content to the end users.
4.5 Caching scenarios
There can be multiple possible scenarios for caching, which reflect different possibilities of content delivery to the end-user,
• First, the content delivery to the end-user is done from caches attached directly to the MB (assuming that a user can communicate through one or more MB simultaneously). The caches attached to the end-user MB are called local caches.
• Second, the content delivery is performed by a non-local cache, which means that the content exists in the managed domain of the RMB and could also in Cache Controller (CC) but not directly in the connected MB.
• Third possibility is to retrieve the content data from the origin server/content server. • There can be other mixed possibilities based on the above three scenarios as well. To validate the effectiveness of the adopted approach, we run the same aforementioned scenarios
on the same network topology but with different cache handling strategies: • No cache at all.
• Only local cache at the MB.
• With cache at MB and RMB, but the content sharing is achieved without Bloom filters, and the
cache controller is not included.
• With cache at MB and RMB, and content sharing is achieved with Bloom filters, but the cache
controller is not included.
• With cache, and content sharing is achieved with Bloom filters; the cache controller is included.
4.6 TeraSim and Simulation setup
The proposed caching system is evaluated using the THz simulator called TeraSim [18]. It is developed in the ns3 simulator. The TeraSim has been structured by the physics of the THz band and the envisioned application scenarios. In particular, the THz band provides wireless communication devices with an unprecedentedly large bandwidth, ranging from several tens of GHz up to a few THz.
The main phenomena affecting the propagation of THz-band signals are the spreading loss and the absorption loss due to water vapour molecules [19]. The molecular absorption peaks widen up with the increasing transmission distance and consequently shrink the available bandwidth. Considering this phenomenon, THz-band communication can be categorized into two scenarios:
• Nanoscale scenario: Over short distances, usually below 1m, the THz band can be considered a single transmission window, almost 10 THz wide. In this scenario, impulse radio type communications based on the transmission of femtosecond-long pulses has been proposed [20]. As the path loss is very small at this short distance, nodes can rely on omnidirectional antennas to communicate. However, due to the very small size of the nano-devices, they might need to harvest energy from the environment to operate over extended periods of time [21], which is not a scenario in our case.
• Macroscale scenario: For longer distances, molecular absorption divides the THz band into multiple transmission windows, tens of GHz wide each. In this scenario, the transmission of ultra-broadband pulses is no longer the preferred option, but, instead, power should be focused in the different windows by utilizing (multi) carrier modulations [22]. A highly directional antenna or beamforming antenna array is needed to overcome the severe path loss in this scenario.
Figure 15 illustrates the structure of TeraSim and its association with the existing ns-3 code base. A THz-band communication network consists of ns-3 Node objects. Each Node can have one or more THzNetDevice objects that are derived from ns-3 NetDevice class. Similarly, to an NIC (Network Interface Card) implementing PHY and MAC protocol, THzNetDevice has pointers to THzMAC and
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THzPhy objects. THzMAC and THzPhy can be subclassed to create new MAC and PHY layer solutions. THzPhy uses THzSpectrumValueFactory to generate pulse for nanoscale scenario and carrier waveform for macroscale scenario. In addition, a Node uses THzNetDevice to communicate to another Node through THzChannel. THzChannel uses THzSpectrumPropagationLoss to calculate both spreading loss and absorption loss of different frequency bands. In order to accurately reproduce the real-life behaviour of energy harvesting system for nanonetwork, a THzEnergyModel is aggregated to each Node. THzNetDevice controls the THzDirectionalAntenna, which can be also configured to work as an omnidirectional antenna (e.g., for nanoscale scenarios).
Figure 15: TeraSim block diagram [18].
The ns3 THz simulator captures the capabilities of THz devices and the peculiarities of THz
channel. We shall consider the simulation scenario, where network coverage is larger than one meter
(i.e. macroscale communication networks). The simulator considers channel module, physical and link
layer. The data flow in the protocol stack is shown in the given below Figure 16.
Figure 16: ns3 simulator and Dataflow in a protocol stack.
In the context of caching system, the network simulator will emulate the communication networks in ‘network simulator 3’ (ns3), which will demonstrate the flow of data at different layer of TCP/IP
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protocol stacks in ns3. The main goal of evaluating the proposed caching system is to present the key idea about Caching as discussed in WP 4. The caching system mainly contains the remote monitoring entity, i.e. cache controller (CC), which is responsible for managing the caching at different levels and perform the prefetching action based on requirement. The RMB serves the communication connectivity and contents to MB, while MB directly serves the user terminals in its coverage area.
The evaluation process shows how the different entities communicate with each other in the proposed caching system. There are different entities/blocks in the caching system where each one will be responsible to perform the required functions. The MB will take care about Content delivery to the user, regular caching of the contents, and perform prefetching contents based on the CC directions. CC is responsible for keeping data about all caches inside the domain, processing data in order to provide the necessary directives to the MB device, cache domain management, prefetching decisions, etc.
In the simulation, we consider a Root MB, 4 MB, CC, Server and 10 Mobile terminals (see Table 3 and Figure 17). RMB has a 200 Mbps link to the server and CC, MBs are connected with 1 Gbps link to the RMB, and each MB uses THz to connect to the mobile terminals. Table 4 represents the default parameters used for THz communication. For each MB all connected mobile terminals are randomly positioned between 0 and 4 meters from it.
The simulation will start when any mobile terminal requests a content. Each terminal has 40 requests and the size of the requested content varies between 5 and 10 MiB. Between requests the terminal waits randomly between 0 to 5 seconds. The simulation stops when all terminals requests list is exhausted. Mobile terminals with the same colour have 10 common requests that occur stochastically during the simulation. In addition, each MB has a cache capacity of 40 URL with FIFO replacement policy.
Five different types of configurations are considered; in each configuration, zero or more options are activated (see Table 5), which are
• Local MB Cache: enables the MB to cache requests coming from the RMB.
• RMB Cache: enables the RMB to act as MB in addition, it searches other MBs content and
fetches the requested URL locally if found.
• Bloom Filter: enables content table sharing via bloom filters instead of plain text.
Figure 17: Network topology used in the simulation.
Table 3: Simulation setup.
No. of Root MB 1
No. of Child MB 4
No. of Mobile Terminal 10
Distance between MB & Mobile Terminal 0-4 meters
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Table 4: THz default parameters.
RTS enabled
Antenna gain 30 dB
Beamwidth 10°
Antenna turning speed 91032.04 rps
Tx power -6 dBm
Data rate 50Gbps
RF Bandwidth 40 GHz
Carrier frequency 300 GHz
Table 5: Configuration types.
Configuration
cfg-1 cfg-2 cfg-3 cfg-4 fg-5
Options
Use Local MB Cache
× ✓ ✓ ✓ ✓
Use Root MB (RMB)Cache
× ×
✓ ✓ ✓
Use Bloom filter
× × × ✓ ✓
Use Cache Controller
× × × × ✓
4.7 Simulation results
First, we assess the impact of different parameters (see Table 6) on the THz band communication, by using the TeraSim modules in ns3 simulator. The 10 distinct scenarios are executed with a variety of parameters, which are summarized in Table 7. In these scenarios, we setup one Server node and one Client node located 10 meters on the x-axis from the server. On the client, the antenna is static and oriented toward the server’s antenna while the latter uses a 360° rotating antenna. We did not shift the client node on the z-axis since TeraSim does not offer vertical beamwidth or downtilt parameters.
In the simulation, we consider four parameters (TurningSpeed, MaxGain, Beamwidth, and TxPower); where each parameter gets a value from the available three values. For every scenario, three parameters are fixed while the fourth takes different values, (see Table 7). The performance is evaluated in terms of two metrics, namely packet loss and average throughput.
Table 6: THz simulation parameters to evaluate TeraSim
Figure 18 depicts the total number of packets sent and lost for each scenario. In the first three
scenarios, we vary TxPower only, and clearly packet loss is inversely proportional to TxPower, which is expected since high transmission power translates to better signal. Scenario 4 has 100% packet loss due to the high rotation speed coupled with small beamwidth, which causes the signal to become too narrow and too fast, to establish a connection. Scenario 6 also has 100% packet loss but that is because the signal cannot cover the 10m gap due to low TxPower and antenna gain. Scenario 5 offers slightly better results compared to scenario 1, while scenario 7 offers better outcome compared to 3, which suggests that adjusting the beamwidth and antenna gain could be more efficient than increasing the TxPower. Lowering the antenna rotation speed causes the client node to spend large portion of the simulation time unconnected hence, the increase in packet loss as can be seen in scenarios 8 and 9. The effect is further amplified in scenario 10 due to the narrow beam caused by the high gain and low beamwidth.
Figure 18: Packet loss in different scenarios
For the average throughput, the results are summarized in Figure 19. For scenarios 1, 2 and 3 the throughput is directly proportional to the TxPower due to the improvement in the communication link. Scenarios 4 and 6 score no throughput since no packets are received. Scenarios 5 and 7 offer slightly better results than 1 and 3 respectively. Scenario 8 offers the highest throughput at 41Gbps followed by 9 then 10 at 23 Gbps and 20 Gbps respectively, and this can be explained by the amount of time the client spends in the server’s antenna beam. Slower rotation speed means more time; thus, the client can better utilize the link capacity, and hence the large throughput. However, slow rotation speed also means that the client node has to spend a large amount of time unconnected until the
0
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10000
15000
20000
25000
30000
35000
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45000
50000
1 2 3 4 5 6 7 8 9 10
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kets
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er
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Total packets Packets lost
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antenna makes a full rotation, which means that although this type of configuration offers high throughput, it can negatively affect real time applications, where response time has to be as low as possible.
Figure 19: Average throughput in different scenarios.
To check the validity and applicability of the proposed caching approach, we run the simulation setup shown in Figure 17. The simulation was performed 10 times for each of the 5 configurations (see Table 5).
The presented results are plotted by taking the average of obtained value in each simulation. During the simulation six parameters are measured, average delay of first and last packet, WAN
and LAN traffic and cache hit ratio at the MoBcache (MB) and Root MoBcache (RMB). Each of these attributes will be discussed further in the following paragraphs.
Average delay (First packet): For this parameter, we measure the elapsed time since the mobile terminal sends a request, until it receives the first packet of the data stream. From the user point of view, this parameter is very important to be as low as possible, since higher values will directly affect the quality of service for streaming content.
Figure 20 depicts the performance of each configuration. It is apparent that deactivating all type of caches negatively affects the delay as in cfg-1. Activating cache at MB slightly improves the delay (cfg-2) because some of the requested content is cached locally. Allowing cache at RMB (cfg-3) further reduces the delay by almost 15%, since some requests could be available locally at different MB. Adding Bloom filter bears no effect, while activating Cache Controller (cfg-5) has the most prominent effect at 33% reduction, because most of the users’ identical requests, are already pre-fetched locally to the MB, thanks to the similarity matching algorithm. Since the communication between terminals and MB uses THz, the delay for locally served requests is near zero.
0,00E+00
5,00E+09
1,00E+10
1,50E+10
2,00E+10
2,50E+10
3,00E+10
3,50E+10
4,00E+10
4,50E+10
1 2 3 4 5 6 7 8 9 10
Bit
s/se
c
Scenario
Average throughput
Average throughput
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Figure 20 Average delay (first packet) of different configurations
Average delay (Last packet): This resembles the first parameter, but we measure the elapsed time until the last packet instead of the first one. The parameter directly affects the performance when the whole requested content needs to be present before it can be processed, such as in the case in the ftp protocol. Figure 21 shows that in cfg-1 the delay is strictly governed by the backhaul and MB links speed, since the entire file must be downloaded locally and then processed. With local cache activated (cfg-2) some requested contents are served locally with the link speed of the MB, hence the slight reduction in the delay. Moreover, in cfg-3 more reduction is observed with some content transferred locally at link speed between Root MoBcache (RMB) and MB. Using the Bloom filter (cfg-4) slightly reduces the delay by lowering the congestion due to cache content sharing. With cache controller activated most of the users’ identical requests are already pre-fetched locally and served at the link speed of the MB, hence the 22% improvement in performance.
Figure 21: Average delay (last packet) of different configurations
WAN Traffic: For this parameter, we measure the ingress and egress traffic passing through the backhaul link (i.e. between the RMB and internet) , optimally the less we use the better, which we can observe in cfg-4 since some content is already cached and the content table sharing overhead is less due to bloom filter. In cfg-3 and cfg-2 traffic is slightly increased respectively, due to the use of plain text when sharing content table and deactivating the RMB cache. In cfg-1 with no caching strategy, all requests are fetched from the origin server thus the increase in traffic.
While cfg-5 had the best results in terms of delay as shown in Figure 22, when it comes to the traffic usage it has the highest amount, and this is due to the prefetching algorithm. Which will eventually instruct some MBs to pre-fetch idle content. This is content that is not sought by mobile terminals other than the request initiator, thus, the high traffic usage.
3,242 3,170
2,797 2,7972,520
0
0,5
1
1,5
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3,40 3,332,96 2,94
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Figure 22: WAN Link Usage
LAN Traffic: LAN traffic concerns the communications between MBs and RMB. In cfg-1 we observe the exact amount as WAN traffic, and that is to be expected since all requests through RMB are returned to the requesting MB. cfg-2 has the same behaviour but with less traffic, since cached contents are served directly to the mobile terminal without incurring any traffic in LAN or WAN links. For cfg-3 and cfg-4 the LAN traffic is inversely proportional to that of WAN, since some traffic is served locally from other MBs instead of the origin server. cfg-5 has the highest usage because the CC prefetching instructions are sometimes exchanged locally between MBs.
Figure 23: LAN Link Usage
Cache Hit Ratio: This parameter represents the ratio of requests served from local cache against all requests. There are two types of hits. First case when the request is found in the MB directly connected to the requesting mobile terminal. The second case is when it is at another MB and fetched through RMB.
In this simulation setup, there are 400 requests out of which 330 are unique and 70 are redundant; thus, a perfect caching strategy will yield 17.5% hit ratio. As depicted in Figure 24, the highest hit ratio of 10.15% is achieved when using cfg-5, which explains the low delay (first and last packet). cfg-3 and cfg-4 offer the same ratio of 6.04%. With cfg-2 the hit ratio reaches 1.75%, while cfg-1 offers none.
3,052,99
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Figure 24: Cache Hit Ratio in MB and RMB
Cache content table size: To illustrate the efficacy of the Bloom filter compared to plain text, we consider an example where we have an MB with cache capacity of 1000 contents. Each content is represented by 300 bytes URL, and every minute 100 URLs are added to the content cache table. For the Bloom filter, we use the following parameters:
𝑛 = 1000 𝑘 = 17
𝑝 = 0.00001 𝑚 = 2.92𝐾𝑖𝑏
In minute 0, the Bloom filter size is 2.92Kib while plaint text is 0Kib. As the time passes and cache memory is filled, the plain text size increases exponentially until it reaches minute 10 with content table saturated at size 292Kib, where it remains. Using Bloom filter the table size remains constant at 2.92Kib regardless of the content table size, which is 100 times less.
Through this example, it is clear that the Bloom filter has an advantage of being constant and predictable, regardless of the data size represented.
Figure 25: Cache content table size
0,00
1,75
0,50 0,50
3,00
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5,54 5,54
7,15
0
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%
Cache Hit Ratio
at MobCache at Root-MobCache
48
Running time: The main goal of the caching strategy is to reduce the response time for all the users, i.e. serving request as fast as possible. Figure 26 illustrates the elapsed time to serve 400 requests (330 of which are unique) with a size between 5 and 10 MiB each to 10 different users, while the number of requests is divided equally among the users.
Cfg-1 serves as a baseline, and since there is no caching strategy involved, it scores the longest running time. Cfg-2 offers some reduction, since some content is being locally served using THz communications only, while cfg-3 reduces the running time even further thanks to the RMB caching, which allows MB to share their content locally with each other, thus allowing data to be transferred at the speed of the LAN link. With cfg-4 we get the same results and Bloom filter offers no significant improvement. Cfg-5 has the most prominent effect reaching 20% reduction in running time thanks to the prefetching algorithm, which allows most of the redundant requests to be served using THz and LAN links only.
It is worth noting that the speed gain in running time is directly proportional to the number of redundant requests i.e. different users requesting the same content.
Figure 26: Running time until all requests are served
4.8 Conclusions
The THz network is emulated in ns3 simulator using the TeraSim modules. We have evaluated the TeraSim by consider the four important parameters of THz networks, which are TurningSpeed, MaxGain, Beamwidth, and TxPower. These parameters are evaluated by defining the 10 distinct scenarios, and performance metrics are observed in terms of Packet loss and Average throughput. Later, we use the TeraSim to evaluate the caching system. It is observed that by adopting an efficient caching strategy for the popular content at the mobile network greatly alleviates the traffic explosion. In addition, using social connection of the users even with limited knowledge about user contexts not only improves cache-hit ratio, but also reduces the average delay, which yields an enhanced quality of experience of the users.
147,57 140,93132,88 132,88
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5. CONCLUSIONS
This deliverable discussed the TERRANOVA RRM framework as well as the caching approach, which is expected to significantly reduce the THz wireless systems latency. In particular, after identifying the THz wireless system particularities that need to be taken into account for the RRM and caching designs, we formulated a novel joint user clustering, association and RRB allocation optimization problem, we proved that it can be simplified into a differential convex optimization problem and provided its solution, which is a low-complexity strategy that jointly minimizes the network blockage probability and maximizes the network throughput. To quantify the effectiveness of the aforementioned strategy, we delivered a number of Monte Carlo simulation results that exploit stochastic geometric approaches and revealed a number of interesting insights. Specifically, it became apparent that as the TAP density increases, the probability of establishing LoS links increases; hence, the clustering rate as well as the network throughput increases. Similarly, as the TUE density increases, the opportunities of establishing LoS links also increases; hence, the sum of the blocking probability decreases, which leads to a clustering, and network throughput increase.
Next, we presented a low-complexity relay-based blockage and misalignment avoidance strategy, in which the source node communicates with the destination node through an intermediate relay. The intermediate relay is chosen towards a set of relays that can establish blockage-free source-relay and relay-destination links and can support a minimum equivalent throughput. We evaluated the performance of this strategy through Monte Carlo simulations. As a benchmark, we considered the case in which the source node randomly selects the relay node. Our results highlighted the superiority of the proposed strategy in comparison with the random relay selection, in terms of average throughput and probability of the achievable throughput being lower than a throughput threshold for the end-to-end link.
Moreover, a blockage-aware SDMA approach was discussed, in which hybrid beamforming was employed to simultaneously serve multiple users that can establish LoS links with the BS. In order to evaluate the performance of the aforementioned approach, we performed Monte Carlo simulation and compared the results with the case in which the BS has not blockage-awareness. As expected, the blockage aware SDMA approach outperforms the blockage-unaware one in terms of probability of establishing links with throughput higher than a predetermined threshold.
A new Caching system was also presented, which consists on multiple entities and methods. The Prefetching method was implemented that pre-emptively caches the content, before the user requests it, and it is executed on-demand. The proposed new caching approach is based on social connections of users - also exploiting this collective social aspect to enhance caching operations - and bring benefits both to users and network operators, by considering two approaches such as Proactive and Reactive. The Bloom Filter algorithm is implemented, which is memory-efficient and a quick way to testing an element, whether it is present in a given set or not.
Five scenarios are defined in order to validate the effectiveness of the adopted approach on the same network topology but with different cache handling strategies. The ns3 based THz simulator is used to evaluate the proposed caching handling scenarios. It is observed that the caching strategy for the popular contents at the mobile network greatly reduces the traffic explosion. In addition, using social connection of the users with limited knowledge about user contents not only improves cache-hit ratio, but also reduces the average delay, which yields an enhanced quality of experience for the users.
50
6. REFERENCES
[1] J. Zhang, A. Beletchi, L. Yi and H. Zhuang, "Capacity performance of millimeter wave
heterogeneous networks at 28 GHz/73 GHz," in IEEE Globecom Workshops (GC Wkshps), Dec.
2014.
[2] D. Liu, L. Wang, Y. Chen, M. Elkashlan, K. K. Wong, R. Schober and L. Hanzo, "User association
in 5G networks: A survey and an outlook," IEEE Communications Surveys Tutorials, vol. 18, no.
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[3] Q. Ye, B. Rong, Y. Chen, M. Al-Shalash, C. Caramanis and J. G. Andrews, "User association for
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