Three Step Cooperative Mimo Relaying

Three Step Cooperative MIMO Relaying

Feasibility And Evaluation Study

CHAFIC NASSIF

Master’s Degree Project Stockholm, Sweden 2005

Three Step Cooperative MIMO Relaying

Feasibility And Evaluation Study

CHAFIC NASSIF

Master’s Degree Project March 2005 TRITA–S3–RST–0511 ISSN 1400–9137 ISRN KTH/RST/R--05/11--SE

Radio Communication Systems Laboratory Department of Signals, Sensors and Systems

Abstract The Cooperative MIMO Relaying (CMIMOR) System is a relatively new topic that researches the possibility of benefiting from the capacity gains offered by a Multiple Input Multiple Output channel despite the physical limitations of the mobile phones. This thesis investigates an enhancement to the CMIMOR network that aims for a reduction of the cost of implementation. The main goal is to study the feasibility of the proposed Three-Hop CMIMOR Network, and evaluate it with respect to its original Two-Hop CMIMOR counterpart. Both systems are presented and a comparison in terms of end to end throughput reveals that the two-hop system performs better. The problem with the Three-Hop system appears to be that the resources are not allocated in an optimized manner. To improve the performance some modifications are proposed, and the results prove that the proposed modifications produce increased capacity. The increase in capacity is especially evident when a proper allocation of bandwidth or a good relay selection criteria are applied, allowing the Three-Hop CMIMOR network to perform as well (better for some cases) as the Two-HOP CMIMOR network. Finally at the end of the study a brief cost analysis reveals that, in addition to the good performance of the proposed system, the cost with respect to throughput is less than that of the Two-Hop CMIMOR system.

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Acknowledgements Looking back over the past months that I spent working on my thesis, I realize that this has been one of the most educational experiences of my life. Not only did I gain so much knowledge in the field that I was working on, but I also learned how to manage my work, communicate my ideas to my colleagues, and above all I learned how to properly conduct a research. Along the way I accumulated many memories from the day to day working environment to the sleepless nights spent in the labs. I remember the frustration of reaching a dead end and the thrill of discovering a new solution. I remember the weariness from writing a report and the excitement from stumbling over a great result. All these memories I cherish, but most importantly I remember the people that I have been in contact with. Many of those people to whom I owe a large debt of gratitude for being there for me throughout the period of this thesis. So I would like to extend my appreciation to them, and I will start off with my advisor Bogdan Timus whom I thank for all the indispensable advice and crucial assistance that he has offered me, and for bearing with me when my time-table got somewhat hectic. I would also like to thank my examiner S. Ben Slimane for providing positive feedback and expert opinion. My sincere gratitude goes to my family (Habib, Reine, and Rami Nassif) back in Lebanon for their continuous moral support and encouragement. A special thank you also goes to Georges and Rita Khoury for providing me with a home away from home. I would also like to thank my friends both here and abroad (especially Nelly Nassar) who have been so warm hearted and supportive, and I apologize for not mentioning all their names but they know who they are. Finally I would like to say that I am grateful to the Wireless Systems department for providing me with the opportunity to come and study in the beautiful city of Stockholm and earn my Masters Degree.

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Contents 1 Introduction 1.1 Background . . . . . . . . . . . 1.1.1 MIMO . . . . . . . . . . 1.1.2 Virtual Antenna Arrays 1.2 Problem Definition . . . . . . . 1.2.1 Motivation . . . . . . . 1.2.2 Objectives . . . . . . . .

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2 System Model 2.1 System Units . . . . . . . . . . . . . . . . . . . . 2.1.1 The Macro BS . . . . . . . . . . . . . . . 2.1.2 The Acess Point . . . . . . . . . . . . . . 2.1.3 The Mobile Terminal . . . . . . . . . . . . 2.1.4 The Relays . . . . . . . . . . . . . . . . . 2.2 The Reference System Model . . . . . . . . . . . 2.2.1 General Architecture of the 2-hop System 2.2.2 Relay Activation Criteria . . . . . . . . . 2.2.3 Radio Resource Allocation . . . . . . . . . 2.2.4 Capacity Calculations . . . . . . . . . . . 2.3 The Three-Hop Model . . . . . . . . . . . . . . . 2.3.1 General Architecture of the 3-hop System 2.3.2 Relay Activation Criteria . . . . . . . . . 2.3.3 Radio Resource Allocation . . . . . . . . . 2.3.4 Capacity Calculations . . . . . . . . . . . 2.4 Modified 3-hop System . . . . . . . . . . . . . . . 2.4.1 Varying Number of Active Relays of FT . 2.4.2 Varying Bandwidth Distribution . . . . . 2.4.3 Alternate Relay Activation Algorithm . .

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3 Simulation Environment 3.1 System Layout . . . . . . . . 3.1.1 Placing the Terminal . 3.1.2 Placing the Relays . . 3.2 Path Gain Computation . . . 3.3 Interference and Noise Models 3.4 Simulation Parameters . . . .

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Contents

4 Results 4.1 Throughput of the Reference System . . . . . . 4.2 Throughput of the Proposed System . . . . . . 4.3 Modifications for the Proposed System . . . . . 4.3.1 Varying Number of Active Relays of FT 4.3.2 Varying Bandwidth Distribution . . . . 4.3.3 Alternate Relay Activation Algorithm .

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5 Cost Evaluation

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6 Conclusion

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7 Suggested Future Work 7.1 Propagation Model . . . . . . . 7.2 Multi-Cell Topology . . . . . . 7.3 Vary the Density of the Relays 7.4 Relay Activation . . . . . . . . 7.5 Bandwidth Allocation . . . . . 7.6 Regenerative Relays . . . . . .

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References A First Hop Analysis A.1 Scenario One . . . . . . . . . . . . . . . . . . A.1.1 Capacity for the First Hop . . . . . . A.1.2 Capacity for the Second & Third Hops A.2 Scenario Two . . . . . . . . . . . . . . . . . . A.2.1 Capacity for the First Hop . . . . . . A.2.2 Capacity for the Second & Third Hops A.3 Comparison of the Two Scenarios . . . . . . . B Relay Density Derivation

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List of Tables 3.1

Table of Simulation Parameters. . . . . . . . . . . . . . . . . . .

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Table of densities used within simulation. . . . . . . . . . . . . .

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5.1 5.2

Macro BS costs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . Pico BS costs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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List of Figures 1.1 1.2 1.3 1.4

Diagram of MIMO wireless transmission system. VAA Scheme suggested by Dohler. . . . . . . . . VAA groups in a Cell. . . . . . . . . . . . . . . . Three-Step Cooperative MIMO Relaying. . . . .

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Relay Distribution around Terminal with Direct Path from BS. . Example of Channel Assignment - number of active relays is 4. . The relays with best gain are activated while the other relays (faded) are inactive. . . . . . . . . . . . . . . . . . . . . . . . . . The Schematic Description of a CMIMOR architecture. . . . . . The three-hop CMIMOR scenario. . . . . . . . . . . . . . . . . .

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The Terminals are randomly but uniformly generated around the BS at a distance R. . . . . . . . . . . . . . . . . . . . . . . . . . . Normalized throughput of 2-hop system for MT 100m from BS. . Normalized throughput of 2-hop system for MT 300m (upper left), 500m (upper right), 700m (lower left), and 900m (lower right) away from BS. . . . . . . . . . . . . . . . . . . . . . . . . . Normalized throughput of the 2-hop system with respect to varying density for MT 100m away from BS and number of relays in the VAA=5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Normalized throughput of the 2-hop system with respect to varying distance of MT from BS, where number of relays in the VAA=5 and density=157.2 Relays/km2 . . . . . . . . . . . . . . . Normalized throughput of 3-hop system for MT 100m from BS. . Normalized throughput of the 3-hop system for MT at 300m (upper left), 500m (upper right), 700m (lower left), and 900m (lower right) away from AP. . . . . . . . . . . . . . . . . . . . . . . . . . Normalized throughput of the first hop, for distance between the AP and MT equal to 100m (uppermost), 300m (2nd row left), 500m (2nd row right), 700m (3rd row left), and 900m (3rd row right). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Comparison between the 2-hop and 3-hop normalized system throughputs for density=157.2 Relays/Km2 where the VAA’s are composed of 5 relays. . . . . . . . . . . . . . . . . . . . . . . . . . Comparison between the normalized throughput of the first hop and the combination of second and third hops of the 3-hop system for density=157.2 Relays/Km2 and MT at 500m away from AP. xi

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List of Figures 4.10 Normalized throughput of 3-hop system, with varying number of FT relays, where MT is 100m (uppermost), 300m (2nd row left), 500m (2nd row right), 700m (3rd row left), and 900m (3rd row right) from BS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.11 Comparison between the normalized throughput of the first hop and the combination of second and third hops of the 3-hop system for T=10, density=509.3 Relays/Km2 , and MT at 100m away from BS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.12 Normalized throughput of the 3-hop system, with improved bandwidth allocation for distance between the BS and MT equal to 100m (uppermost), 300m (2nd row left), 500m (2nd row right), 700m (3rd row left), and 900m (3rd row right). . . . . . . . . . . 4.13 Comparison between the normalized throughputs of the 2-hop system and 3-hop modified (Bandwidth Allocation) system. The number of relays in FT=5, density=75.34 Relays/Km2 , and MT at 500m away from BS. . . . . . . . . . . . . . . . . . . . . . . . 4.14 Comparison between the normalized throughputs of the 2-hop system and 3-hop modified (Bandwidth Allocation) system. The number of relays in FT=5, density=157.2 Relays/Km2 , and MT at 100m away from BS. . . . . . . . . . . . . . . . . . . . . . . . 4.15 Normalized throughput of the 3-hop system with Alternate Relay Activation Algorithm for distance between the BS and MT equal to 100m (uppermost), 300m (2nd row left), 500m (2nd row right), 700m (3rd row left), and 900m (3rd row right). . . . . . . . . . . 4.16 Comparison between the normalized throughput of the 3-hop unmodified system and 3-hop modified (Alternate Relay Activation Algorithm) system. The number of relays in FT=5, density=75.34 Relays/Km2 , and MT at 500m away from BS. . . . . 4.17 Comparison between the normalized throughputs of the 2-hop system and 3-hop modified (Alternate Relay Activation Algorithm) system. The number of relays in FT=5, density=157.2 Relays/Km2 for MT 100m (Upper) and 300m (lower left) away from AP, and density=75.34 Relays/Km2 for MT at 500m (lower right) away from BS. . . . . . . . . . . . . . . . . . . . . . . . . . A.1 Comparison between the 1st scenario (upper line) and 2nd scenario (lower line) for x varying from 1 to 43dB. Note the thick lines represent a bundle of 10 plots each that correspond to values of R varying from 1 to 10 relays per VAA. . . . . . . . . . . . . .

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List of Notations α BWhop1 BWhop2−3 BWT Chop1 Chop2−3 Co Dsf Gd Gf f Gsf Gtot I λ No nrand NR NT Pmax rµ R σsf T U

Attenuation Coefficient Bandwidth of Hop 1 Bandwidth of Hops 2 and 3 Total Bandwidth of the System Capacity of Hop 1 Capacity of Hops 2 and 3 Okumura-Hatta Coefficient Correlation Distance of Lognormal Shadow Fading Distance Based Attenuation Component Fast Fading Attenuation Component Shadow Fading Attenuation Component Overall Power attenuation of the Signal Interference Relay Density Noise Normal Distributed Random Variable Number of Active Relays Number of Transmitters Maximum Power of a Unit Average Distance of the Closest Relay to the MT Number of Channels between MT and its Relays Standard Deviation of a Lognormal Shadow Fading Component Number of Channels between Transmitter and the Relays Uniformly Distributed Variable

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List of Abbreviations AP BS CMIMOR FDMA FT MIMO MT RX SISO ST STC STTB STTC TX VAA

Access Point Base Station Cooperative MIMO Relaying Frequency Division Multiple Access First Tier Multiple Output Multiple Input Mobile Terminal Reciever Antenna Single Input Single Output Second Tier Space Time Codes Space Time Block Codes Space Time Trellis Codes Transmitter Antenna Virtual Antenna Array

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Chapter 1

Introduction Wireless communication dates back to the first human that used physical gestures to convey an idea to another human. This concept evolved in parallel with the evolution of humanity, and its need for more advanced means of interaction. From smoke signals, beacons, and heliographs (messages by mirrors), to the present radio, television, and cellular phones; the evolution process has been drastic. Numerous technological breakthroughs that were thought to be a luxury some time ago have become essential to our everyday life. A very common phenomenon that endorses the above statement is the massive outbreak of mobile phones around the world today. In Europe, for example, nearly every individual has his/her own mobile phone. Originally, voice transmission was the basic idea behind mobile phones, and then gradually other applications started appearing with the introduction of ‘data transfer’. The possibilities presented by transfering huge amounts of data were immense; however, there were certain capacity restrictions dictated principally by limits of physical resources such as the electromagnetic spectrum or the available power factors [1], and the cost involved in setting up these channels and maintaining them. Recently, the advances in technology and coding techniques have somewhat overcome the physical limitations, through increasing the spectrum efficiency, and allowed for transfer of data at approximately the channel capacity limits, yet there exists a need for even higher data rates to accommodate more demanding applications. Towards this end, Multiple Input Multiple Output (MIMO) channels were introduced; the idea was to introduce an additional resource, or extra dimension, namely ‘space’ that provides diversity. These MIMO channels promised increased capacity provided that solutions could be discovered to bypass the mobile terminal’s spatial capacity limitations. One possible solution was to shift to higher communication frequencies, which inevitably would result in limiting the transmission range, since the attenuation increases with the carrier frequency [1]. Another solution, which has recently emerged and is currently under study, is to emulate a MIMO channel through the concept of Cooperative MIMO Relaying (CMIMOR). The CMIMOR scheme basically consist of a base station that transmits, through multiple antennas, to a network of relays, which in turn act as if they were multiple antennas connected (wirelessly) to one designated receiver. The details of this plan are elaborated in the next section of this report, but the 1

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Chapter 1. Introduction

result, according to [2], is a theoretically higher capacity limit for cellular networks than the currently achievable one. The focus of this thesis is to work with the CMIMOR scheme and study the possibility of implementing it at a lower cost. That is, an adjustment to the original CMIMOR design is proposed, and the feasibility in terms of the capacity is evaluated, taking into consideration the radio resources needed for deployment. The proposed modification involves replacing the ‘Multiple Antenna Transmitting Macro Base Station’ by a Pico Base Station with a single antenna element. The Pico Base Station has a shorter range than the Macro Base Station [3] which would dictate the presence of more relays and more hops for the signal. Hence, such a modification is proposed to eliminate the huge cost of the Macro Base Station at the expense of a possible loss in system capacity. The next sections of this chapter provide a background of the relevant concepts and define the objectives. Then chapters two and three discuss the system model and the simulation environment respectively. Chapter four presents the results of the simulations, and chapter five provides a brief cost analysis. Finally, the conclusions are drawn in chapter six, and the future work are suggested in chapter seven.

1.1

Background

This section covers a general overview about Multiple Input Multiple Output (MIMO) schemes, and Virtual Antenna Arrays (VAA) or Cooperative MIMO Relays (CMIMOR).

1.1.1

MIMO

Until recently, researchers have focused mainly on improving coding techniques and devising methods to eliminate interference. Lately, however, the concept of MIMO has emerged as a possible solution for offering data rates far in excess of conventional systems [4] through the introduction of the extra dimension of space. As defined in [5], and illustrated in Figure 1.1, a MIMO system consists of a transmitting end and a receiving end both equipped with multiple antenna elements. The idea behind MIMO is that the signals are sent from the transmitter end (TX) through parallel streams over the same frequency band and time interval to the receiver end (RX). The receiver then combines the incoming signals via multiple receiver antennas to form the original data stream. Because the parallel channels exist over the same frequency and time intervals, high data rates can be achieved without the need for extra bandwidth [4]. This architecture allows the MIMO system to exploit the multipath scattering found in the environment to achieve significant gain in link capacity. Consequently, and under the theoretical assumption of uncorrelated fading, if we consider the rank of the channel coefficient matrix n = minimum (N, M), where N and M are the number of transmit and receive antennas respectively, then n parallel channels will be created effectively between (TX) and (RX), thus increasing the spectral efficiency n times [6]. This translates into a linear

1.1. Background

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Figure 1.1: Diagram of MIMO wireless transmission system.

increase in capacity relative to the increase in the n number of antennas [7]. It can also be proven, according to [8], that given a full rank matrix, deploying an unequal number of transmitter and receiver elements is a waste of resources. If the number of transmitters exceeds the number of receivers then the capacity saturates very fast. On the other hand, if the number of receivers is greater than the number of transmitters then the capacity increases logarithmically. Hence, the only solution is for the elements on both ends to be equal which as stated above will result in a linear increase of capacity. To be accurate, it must be noted here that the assumption of a full rank matrix is only a simplification. In practice it is not so common to have a full rank matrix nor can a designer of a system control the matrix such that it is rendered full. The set of coding schemes that are conventionally implemented at the MIMO (TX) antennas are called Space Time Codes (STC). These coding schemes provide both data rate maximization and diversity maximization. There are two types of STC, the Space Time Trellis Codes (STTC) and the Space Time Block Codes (STTB). The first type of codes provides a diversity benefit equal to the number of transmit antennas in addition to a coding gain that depends on the complexity - i.e. the number of states in the trellis - without any loss in bandwidth efficiency. The second type was introduced later on and it provides the same diversity gain as STTC with minimal coding gain; however, they are much simpler to decode so they are more popular [5]. For more detailed information about MIMO systems and their architecture the following references [5], [6] are recommended. It must also be noted that in this thesis no specific coding shall be considered, since the calculations are based on Shannon’s capacity calculations that no practical coder can provide us with.

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1.1.2

Chapter 1. Introduction

Virtual Antenna Arrays

The benefits of the MIMO scheme and STC codes are realizable only in the case when we have an antenna array at both the transmitter and the receiver; however, the number of antenna elements on a terminal and the fading independence between them is limited by the space constraint. To solve this problem Dohler suggested a scheme called Virtual Antenna Arrays (VAA [8]), which will be described in this section.

Figure 1.2: VAA Scheme suggested by Dohler.

Figure 1.3: VAA groups in a Cell. The existing cellular systems are designed so that a Base Station (BS) communicates with each Mobile Terminal (MT) individually; hence, the BS has total control over a cell [1]. In the VAA concept, Dohler suggests that MTs form a mutually communicating entity that emulates a real MIMO system [8]. To better understand this scheme let us consider the downlink case as an example. A base station array (refer to Figure 1.2 and Figure 1.3) consisting of several antenna elements transmits a space time encoded data stream to the associated mobile terminals which can form several independent VAA groups.

1.2. Problem Definition

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The entire data stream is received by every MT in the group. Each individual MT extracts its own information and relays further information to the other surrounding MTs. The target MT then receives more of its own information from these surrounding MTs and finally it processes the entire data stream it has received. The wired links within a traditional receiving antenna array are thus replaced by wireless links [8]. Of course this concept is easier theorized than physically applied. There are many issues that remain to be resolved, most obvious of which is the assumption that MTs are aware of each other and manage to establish intelligent synchronization and data scheduling algorithms amongst one another. Moreover, there are concerns such as distance estimation, power control, encoding, and data relaying. Dohler does not provide definitive solutions for these concerns, rather he suggests possible scenarios. For example he proposes the use of Bluetooth technology for inter-MT communications while assuming that each MT is able to process the signal it has received and regenerate it (regenerative relaying) [2]. Although, as discussed above, the VAA model is in need of many refinements that are outside the scope of my study, it still holds a lot of potential for providing higher capacity gains than the conventional systems and is worth looking into.

1.2

Problem Definition

The problem definition and the objectives of the thesis work are stated explicitly in this section. The ‘Motivation’ subsection explains the logic of the thesis topic while the second subsection relays the objectives.

1.2.1

Motivation

Technology has always suffered from trade-offs between cost and efficiency. To lower the cost one has to sacrifice some efficiency, as long as it is within certain acceptable limits. This also applies to communication systems; hence, if the difference between the capacities of two systems is small while the cost reduction is significant then the use of the system with the lower capacity may be economically sustainable. Taking the above into consideration, the thesis being proposed here was initially formulated according to the following logic: 1. A multi-antenna Macro BS provides good performance but is expensive. 2. A wireless relay (Pico BS) costs much less than a Macro BS and can act as an access point (transmitter-receiver). 3. A wireless relay doesn’t possess multiple antennas; hence, it cannot benefit from the advantages offered by the MIMO concept, unless Cooperative MIMO relaying is employed. 4. Thus, instead of deploying a new Macro BS, an existing wireless relay could be converted to a Pico BS (using CMIMOR). Then the question

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Chapter 1. Introduction would be if it is possible to achieve approximately the same performance as is attainable by the Macro BS?

Stated in one sentence, the motivation of this thesis is to: “Explore the possibility of implementing a three step MIMO communication system and evaluate its capacity gains with respect to Dohler’s (Two-Hop distributed MIMO Communication) reference system.” The way to do that is by suggesting a scheme that could reduce the cost of BSs needed to cover a certain region by replacing some Macro BSs with Pico BSs and utilizing the concept of cooperative MIMO relaying (VAA). To better understand this notion, consider a BS that needs to send a signal to a MT that is out of range. The BS would then send the signal to a wireless array of relay antennas that are perhaps located on lamp posts (in range). These relay antennas would then send the message to their neighbouring antennas and so on in a virtual MIMO channels fashion until the target MT is reached (refer to Figure 1.4).

Figure 1.4: Three-Step Cooperative MIMO Relaying. For this study, a relay antenna is transformed into an access point (AP) which will represent a Pico BS. We shall assume that the signal is transmitted from this AP and the analysis starts from the first hop until the target MT.

1.2. Problem Definition

1.2.2

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Objectives

The objectives of this thesis can now be stated explicitly in the following points: • Evaluate the 3-hop proposed system with respect to the 2-hop reference system. • Explore the optimality of the initial 3-hop system settings. • A brief comparison of the approximate expenses involved in the implemention of both the 2-hop and 3-hop systems.

Chapter 2

System Model The approach that will be adopted throughout this thesis will focus mainly on obtaining the maximum end-to-end throughput of the system as stated in the previous chapter. Therefore the assumptions and parameters of the system model shall be discussed herein. The system units are presented first. Then the reference and proposed systems are described consecutively along with the capacity calculations.

2.1

System Units

There are four system units and they are: the Macro BS, the AP, the MT, and the Relays. In this section the characteristics of each unit shall be presented and discussed.

2.1.1

The Macro BS

The Macro BS unit exists only in the 2-hop reference system and is considered to be placed at the center of the system with the rest of the units distributed all around it. It is a structure possessing multiple antenna elements that are used (in this study) for transmitting a signal to the MT and the Relays. The antennas are assumed to be omni-antennas (0dB gain, to simplify the analysis), which might not be the optimum assumption since the use of directional antennas might yield better results. The macro base station is assumed to be mounted on a high location, such as a mast, and therefore has high infrastructure costs, especially in terms of deployment [3]. The power of the Macro BS is divided equally over the number of antenna elements and these elements form a MIMO channel together with both the relays and the MT.

2.1.2

The Acess Point

The AP unit exists only in the 3-hop proposed system. It has only one antenna element (0dB gain) that is used for transmitting a signal to the first virtual antenna array composed of regenerative relays. The antenna element of the AP sends the signal to the regenerative relays via independent orthogonal channels. 9

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Chapter 2. System Model

This means that the AP is responsible for dividing the signal, distributing it over the orthogonal channels, and defining which specific part of the signal is sent by which relay in the first tier of relays. The AP is the unit that substitutes the Macro BS (of the 2-hop system) but it utilizes much less power (equal to the power consumed by the individual relays). It is expected to lead to a decrease in the deployment costs, due to the fact that it is not located on a high mast, which is the reason for the substitution. It must be noted; however, that the deployment of the AP affects the type of propagation of each connection, but this aspect is beyond the scope of the thesis.

2.1.3

The Mobile Terminal

The MT unit represents the final destination of the transmitted signal. This unit exists in both the reference system and the proposed one. It possesses one antenna element (0dB gain) for receiving the signal from the Macro BS (or AP in the 3-hop case) and the surrounding relays. The MT is placed at varying distances from the BS such that the transmitted signal is influenced by different power attenuation and noise factors. During the interval of analysis the MT is assumed to be stationary, and the study is carried out according to snapshots of the stationary terminal at different positions.

2.1.4

The Relays

The relays are assumed to have the same physical properties as the AP, that is they are not mounted on a high mast, they consume the same amount of low power, and they have one omni-directional antenna element. The relays implemented in this thesis can be divided into two types according to functionality: Regenerative and Non-Regenerative (Transparent). The difference between the two types of relays is that the regenerative relays receive a signal, process it (decode it and then re-encode it) before re-transmitting it, while the transparent relays simply amplify the received signal before re-transmitting it. In general, regenerative relaying outperforms the non-regenerative in terms of end-to-end throughput as proved in [9] for the SISO multi-hop case over flat Rayleigh fading channels. This improved performance, however, is achieved at the expense of implementing more complex systems [10], and much costlier ones. The transparent relays are found around the MT in both the 2-hop and 3hop systems (to stay consistent with reference [11]). The regenerative relays, on the other hand, are only utilized around the AP in the 3-hop case. The relays are uniformly distributed to form VAAs according to a predefined activation criteria. The relay density is denoted by λ and is measured as the number of relays available in one squared kilo meter. To give the reader a more perceptive idea of what a certain distribution of the relays means, I have related the density to the average distance of the closest relay to the terminal denoted as rµ . Thus a certain rµ corresponds to a certain λ through the following formula (refer to Appendix B for the derivation based on [12]): rµ = 0.5 ×

p

1/λ

(2.1)

2.2. The Reference System Model

11

The power of the relays is assumed to be constant and equal for both types. Each relay has one antenna element (0dB gain) that is used for receiving signals and transmitting them alternatively. The transparent relays form orthogonal SISO channels with the MT while the regenerative relays form orthogonal SISO channels with the AP. In the 3-hop case the regenerative relays and the transparent relays form the MIMO channel.

2.2

The Reference System Model

The reference system is Dohler’s ‘Two-Hop distributed MIMO Communication System’ [13], which was portrayed earlier in Figure 1.2. It is assumed that there is one transmitting Macro BS with a fixed number of antennas. The signal is sent from this BS towards a tier of relays (with a varying number of relays), that in turn amplify the signal and resend it to the destination terminal. To model this process, certain assumptions and parameters are presented in this section in detail, keeping in mind that the description also applies for the second and third hops of the proposed system - the difference is that the BS antenna elements are replaced by individual relays.

2.2.1

General Architecture of the 2-hop System

The signal is initially transmitted by the BS antenna elements towards the relays and the terminal. The terminal receives a direct transmission of the signal from the BS and an amplified one from the relays around it. Figure 2.1 shows the topology of the system with one BS and one user terminal surrounded by a pre-specified density of relays per km2 .

Figure 2.1: Relay Distribution around Terminal with Direct Path from BS. The relays around the MT are activated according to the criteria discussed in the next section. After the required number of relays is chosen, each active relay receives a signal from all the BS antenna elements, amplifies it and resends it over an independent orthogonal channel to the terminal as shown in Figure 2.2.

12

Chapter 2. System Model

Figure 2.2: Example of Channel Assignment - number of active relays is 4.

2.2.2

Relay Activation Criteria

The decision of which relays are to be chosen (activated) is done based on the channel conditions. For this system it is assumed that the relays with the best path gain to the terminal are chosen. Of course this method takes for granted that the relays are able to communicate with each other and the terminal, to calculate the individual path gains and decide upon the best of them.

Figure 2.3: The relays with best gain are activated while the other relays (faded) are inactive. As can be observed in Figure 2.3, the relays that are chosen don’t need to be the closest to the terminal since both Shadow and Rayleigh fading are taken into consideration. Moreover, it must be noted that the activated relays may not have the best path gain from the BS (since the activation criteria is the best path gain from the terminal). As for the ‘number’ of active relays and their ‘density’, these variables will be regarded as simulation parameters.

2.2. The Reference System Model

2.2.3

13

Radio Resource Allocation

The total available bandwidth of the system is set at a fixed value denoted by BWT as assumed in the previous work done in [14] and [11]. This bandwidth is divided equally into 1 + NR channels, where NR represents the number of active relays. IN other words, only 1/(1 + NR ) of the available bandwidth is used by the MIMO channel in an amplify-and-forward (non-regenerative) CMIMOR architecture.

2.2.4

Capacity Calculations

The analysis presented herein is a summary of document [15] which calculates the capacity expression for a non-regenerative CMIMOR connection. This analysis applies to both the 2-hop reference system and the combined capacity of the second and third hops of the the proposed 3-hop system. It is assumed that the downlink connection is established between a BS with T antenna elements(for the three hop case the T antenna elements are the T relays of the first VAA), through a number of R relays, to a target terminal with one antenna element, as shown in the figure 2.4 (which is extracted from [15]).

Figure 2.4: The Schematic Description of a CMIMOR architecture. The following capacity calculations are based on two assumptions. The first assumption is that the channels are Gaussian, i.e. the received signals are normally distributed. The second assumption is that the channel state matrices are assumed to be known both by the sender and the receiver. The signal model for a two hop CMIMOR connection is given by the equations 2.2 and 2.3 and exemplified in Figure 2.4, where r and y are the signals received by the R relays and the target MT respectively. x is the signal initially sent by the BS, while n

14

Chapter 2. System Model

and m represent the noise vectors. Finally H and K are the channel coefficient matrices of the MIMO channel and the R orthogonal channels respectively. r = Hx + n

(2.2)

y = AKr + m

(2.3)

A is the amplification factor that is multiplied by the signal before the relays resend it to the MT. The expression for A is depicted below (derivation is found in [15]): 2

|Aii | = Psend,i ·

2 σnn,i

T Pt X 2 |Hi,t | + T t=1

!−1 (2.4)

The capacity calculations of the system are based on the mutual information; thus, the expression for capacity is as follows: Chop2−3 = max {I (y, x)} where, I (y, x) = h (y) − h (y|x)

(2.5) (2.6)

Computation of the values of h(y) and h(y|x) lead us to the following expressions: h (y) h (y|x) Cww

i 1 h R ln (2Π) · e · det(Cyy ) 2 i 1 h R = ln (2Π) · e · det(Cww ) 2 = AKCnn K H AH + Cmm =

(2.7) (2.8)

Hence, after substituting the values above into the equation of I(y, x) and simplifying, we obtain an expression for Chop2−3 of the following form: d

Chop2−3 =

1X ln(1 + λB,i ) 2 i=1

(2.9)

The capacity is calculated in terms of (Bits/sec/Hz). λB,i is the set of eigenvalues of matrix B which is calculated to be as follows: Pt 2 −1 · [Aii Kii ]R×R · |H| · [Aii Kii ]TR×R · Cww (2.10) T Finally, equation ( 2.9 ) is multiplied by the Bandwidth of the channels to make it comparable with the calculations of the first hop capacity for the 3-hop system; hence, the unit of measurment becomes (Bits/sec). B=

2.3

The Three-Hop Model

The Three-Hop Model is the system that is proposed by this thesis and evaluated with respect to the reference 2-Hop Model. It can be viewed as an enhancement to the reference system which means that the description of the reference system applies to the second and third hops of this system.

2.3. The Three-Hop Model

2.3.1

15

General Architecture of the 3-hop System

The Macro BS and its antenna elements of the reference system are replaced by the AP and the First Tier (FT) of regenerative relays. The signal is initially transmitted by the AP towards the FT of relays through independent orthogonal channels. The reason for choosing to have these links as orthogonal channels and not let the AP simply broadcast is explained in the Appendix A. The regenerative relays receive the signal process it and then send it over the MIMO channel to both the Second Tier (ST) of relays and the MT. The terminal receives a direct transmission of the signal from the FT relays and an amplified one from the ST relays around it. Figure 2.5 shows the topology of the system with one AP, the FT and ST of relays, and one MT surrounded by a pre-specified density of relays per km2 .

Figure 2.5: The three-hop CMIMOR scenario.

2.3.2

Relay Activation Criteria

The decision of which relays are to be chosen (activated) in the FT and ST is done as in the case for the 2-hop system, i.e. depending on the channel conditions. For this system the ST relays with the best path gain to the terminal are chosen, and similarly the relays of the FT with the best path gain to the AP are activated. Of course this method is not the optimum and it takes for granted that the relays are able to communicate with each other and the terminal (or AP), to calculate the individual path gains and decide upon the best of them. The activated relays are not necessarily the closest to the terminal since both Shadow and Rayleigh fading are taken into consideration. As for the ‘number’ of active relays and their ‘density’, these variables will be regarded as simulation

16

Chapter 2. System Model

parameters to be discussed in the next chapter.

2.3.3

Radio Resource Allocation

The total available bandwidth of the system is set at a fixed value denoted by BWT . However, unlike the 2-hop case this bandwidth is divided equally into 1 + NR + NT channels, where NR represents the number of active relays in the ST, NT represents the number of active relays in the FT, and the remaining channel represents the MIMO channel.

2.3.4

Capacity Calculations

Knowing that the three-hop system utilizes regenerative relays in the FT, we can split our capacity analysis into two parts: • The capacity of the first hop. • The capacity of the second and third hops combined. Thus, we could calculate the capacity of the two separate parts and then compute the total capacity of the proposed system to be the minimum between the two capacities. Moreover, the proposed three-hop system resembles the reference system except for the addition of one extra hop in the beginning. This means that the capacity calculations for the reference system are the same as the capacity calculations for the combined second and third hops of the proposed system. Keeping the above in mind this section of the report calculates only the first hop capacity, since the capacity for the second and third hops is summarizes in section 2.2.4. Hence, from Shanon’s channel limit [16], and as explained in ( [17], p.585), we can obtain the following formula for the capacity (Bits/sec) of each individual channel of the first hop: Ct = W1 × log2 [1 + W1 =

P × Gt ] T × No W1

WT T +R+1

where, Ct = the capacity of the channel between the AP and Relay t. W1 = the bandwidth of the channels of the first hop. WT = the total bandwidth of the system. T = the number of channels in the first hop. R = the number of channels in the third hop. P = the maximum power transmitted by a relay = cst. Gt = Gt,dist(d) × Gt,shadow × Gt,Rayleigh

(2.11)

(2.12)

17

2.4. Modified 3-hop System

Thus the expression of the total capacity that could be provided by the first hop would be limited by the minimum capacity of the multiple channels as follows: Chop1 = T × min[Ct ],

t=1→T

(2.13)

Now that we have the expression for the first hop capacity, the end to end throughput of the 3-hop system can be expressed as:

where, Chops2−3

2.4

Ctotal = minimum{Chop1 , Chops2−3 } Pd = BWhop2,3 i=1 ln(1 + λB,i ) (Bits/sec).

(2.14)

Modified 3-hop System

In this section three modifications to the already discussed 3-hop system are presented. The aim of introducing these modifications is to investigate the possibility of increasing the total throughput of the system. The first modification consists of increasing the number of active relays around the AP. The second modification handles the optimization of the bandwidth distribution over the channels. The third, and last modification, implements a new algorithm for activating relays around the AP.

2.4.1

Varying Number of Active Relays of FT

One of the advantages of the 3-hop system over the reference system is that there are no physical limitations on the number of relays used in the FT. In the 3-hop system discussed in the previous section we chose this number to be equal with the Macro BS antenna elements of the 2-hop reference system. Here we make use of this advantage by varying the number of relays in the FT as well as the number of relays in the second VAA. The possible advantage offered by increasing the number of relays is to increase the efficiency of the MIMO channel provided that there are enough resources.

2.4.2

Varying Bandwidth Distribution

The unmodified 3-hop system distributes the bandwidth equally among all the channels. This, as mentioned earlier, is not the optimum resource allocation technique. The reason is that the first hop of the system will have a much greater capacity than the second and third hops combined due to the fact that the FT relays are closer to the AP than to the rest of the units of the system. Given that the system is bounded by the lowest throughput it is important that the resources be allocated in a way that would render the capacity of the first hop and the combined capacity of the second and third hops equal (to some extent). Thus, this modification considers assigning most of the bandwidth to the second and third hops such that the first hop will have a bandwidth BW1 and the second and third hops will have a bandwidth BW2,3 , where

18

Chapter 2. System Model

BW1 +BW2,3 = BWT . Then the bandwidth of each channel in the first hop will become BWhop1 = BW1 /NT and the bandwidth of each channel in the second and third hops will become BWhop2,3 = BW2,3 /(NR + 1).

2.4.3

Alternate Relay Activation Algorithm

The capacity of the second and third hops acts as the bottle-neck of the unmodified 3-hop system since the relays of the FT are usually quite far away from the relays of the ST and the MT. One way of attempting to rectify this situation is through presenting an alternate method for choosing which relays in the FT should be activated. The activation criteria for the relays of the second VAA is kept as it is so that the system remains comparable with the 2-hop reference case. The modified activation criteria consists of activating those relays (within a certain predefined area around the AP) that have the best path gain with the terminal rather than with the AP. The logic behind this modification is that the line of sight paths between the FT relays and the mobile terminal constitute a very significant impact on the capacity of the second and third hops as proved in [14] (for the 2-hop system). Another incentive is that if the relays are chosen to have a better path gain with the MT, then chances are that they will also be closer to the ST relays which will improve the capacity of the MIMO channel. Therefore, if the path gain for the direct path is optimized then the capacity should increase at the expense of an acceptable decrease in the first hop capacity.

Chapter 3

Simulation Environment The programming environment used to virtually emulate the system model (described in the previous section of this report) was Matlab. Of course, a description of the environment is necessary for comprehending how the study is carried out. Therefore, this section is dedicated to explaining the simulation environment and its parameters.

3.1

System Layout

In every simulation environment, the real life objects (such as relays) are placed in a certain setting to enable the study to focus on the required result while keeping the system as genuine as possible. The system layout herein is no exception, and in the following is a description of the chosen settings. Keeping in mind that the main interest is to calculate the capacity of only one link from the BS (or AP) to the terminal, where the BS and the AP are chosen to be placed at the origin of the system. The reference system and the proposed one have similar topologies with a few differences. Throughout this discussion the discrepancies are pointed out and explained clearly.

3.1.1

Placing the Terminal

The program uniformly generates hundreds of terminals along the circumference of multiple circles with predefined radiuses. The reason for this sort of generation is to allow each generated terminal to be subjected to a different path gain due to distance, Shadow fading, and Rayleigh fading variations. The different path gains make it possible for us to study the average throughput to terminals at a certain distance, which renders the results more realistic. Figure 3.1 shows the positions of terminals generated along a circle of radius=R.

3.1.2

Placing the Relays

It has been explained earlier that there are two types of relays: regenerative relays (forming the First VAA), and non-regenerative relays (forming the Sec19

20

Chapter 3. Simulation Environment

Figure 3.1: The Terminals are randomly but uniformly generated around the BS at a distance R. ond VAA). The regenerative relays are randomly but uniformly distributed in a circular area (with a certain predefined density) around the AP. Similarly the non-regenerative relays are randomly but uniformly distributed around the user MTs (also with a certain predefined density). For the reference system only the non-regenerative relays exist; hence, there is only one VAA whose distribution is identical to that of the relays of the second VAA of the proposed three hop system.

3.2

Path Gain Computation

The propagation model that will be adopted is based on three methods of power attenuation: distance based attenuation (Gd ), a slow fading component (Gsf ), and a fast fading component (Gf f ). We will not consider the antenna elements gain since as noted in chapter two, it is assumed to be 0dB gain. The distance attenuation model is established according to the Okumura-Hata path loss model [18]:

Loss =

69.55 + 26.16 × log (f ) − 13.82 × log (hBase ) − a(hM obile ) (3.1) +(44.9 − 6.55 × log (hBase )) × log (d)

Where, a(hM obile ) = (1.1 × log (f ) − 0.7) × hM obile − (1.56 × log (f ) − 0.8)

(3.2)

This is not the most suitable model for the system at hand; however, it is one of the most commonly used models, and it is the model that was implemented in the previous work that was done in this area [11], [14]. The slow fading component models the shadow fading effect. Shadow fading is due to the existence of major terrain obstacles such as hills, large buildings,

21

3.3. Interference and Noise Models

etc. . . obstructing the line of sight path of the signal being sent [19], and introducing a lognormal fading variable with standard deviation σsf and a spatial correlation for all extracted variables within a distance of Dsf . As for the fast fading component, it is there to represent the change of the reflectors around the relays which would result in different path losses for the signal arriving at the receiver [19]. This type of fading is modeled by means of a Rayleigh fading function such that the fast fading received by a unit from one antenna element is utterly uncorrelated with the fast fading received from the other antenna elements. Fast fading is the only factor in the propagation model that changes between the same MT and BS, since both the shadow fading and path loss are assumed fixed (due to the fact that the analysis of the system is based on snapshots). Thus, we can model the overall power attenuation of the system as the sum of the above three attenuation models (in dB): Gtot = Gd + Gsf + Gf f

3.3

(3.3)

Interference and Noise Models

The noise model that was adopted consisted of a fixed thermal noise No = −200dB. The interference component, on the other hand, was modeled as a normally distributed random function with mean −127.5dB and standard 2 deviation of σnrand = 2.5. The range of the interference component was taken from the study done by [11] where multiple cell topology was considered.

3.4

Simulation Parameters

The values of the parameters1 that were used in the simulation are listed in Table 3.1 below. It is assumed that the parameters are fixed unless otherwise indicated in the ‘Results’ section. Table 3.1: Table of Simulation Parameters. Parameter α = 3.5 Co = −38.8 T =5 BWT = 5M Hz No = −200dB I = nrand − 127.5dB 2 σnrand = 2.5 PBS = 20W Prelay = 1w σsf = 1 Dsf = 100 Omni Antennas

Significance Attenuation Coefficient Okumura-Hatta Coefficient Number of BS Antennas Total available bandwidth Fixed Noise level Interference Normal distributed variable with mean zero Power of the BS Power of indivisual relays Standard deviation of lognormal shadow fading Correlation distance of lognormal shadow fading 0dB Amplification

1 The value of the Bandwidth is assumed 5MHz only for simulation purposes. In reality BWT should be smaller since this study is assumed valid for Narrow-Band channels.

Chapter 4

Results This chapter is divided into four main sections that encompass a summary of the simulation results and the verification of these results. First, the study done on the reference system is presented, followed by the study done on the proposed system. The performance measure in both systems is the bit-rate of the throughput (in bits/sec); however, it is normalized by 106 bits to stress on the fact that the focus of this work is on the behavior of the graphs and not on the absolute values of the results. After the two systems are considered, some modifications that were made to the proposed system (to render it more efficient) are revealed. Finally, a brief insight into the approximate cost of implementing the proposed 3-hop system is presented.

4.1

Throughput of the Reference System

The 2-hop system was chosen to be the reference system since it has been studied thoroughly by [11], [14], [8]. In addition, the proposed 3-hop system has been constructed as a modification to the 2-hop case which makes the latter the most logical reference system. In this section the total throughput of the 2-hop system is studied in terms of two variables. The first variable is the number of relays in the VAA distributed around the terminal, while the second variable is the distribution density of the VAA relays. It is important to note that the focus of this section (and this thesis - as mentioned in Chapter 1) is not on optimizing the performance of the 2-hop case, but on presenting it as a valid reference system. This means that if the 2-hop case is optimized through the use of multi-cell resource management as was done in [11], then the 3-hop case will also perform better in accordance with it. Now we need to set our parameters and restrict the variables to a certain range. The first parameter to fix is the number of BS antenna elements which was set to 5. The choice of that specific number of antenna elements was based on the physical restrictions imposed on an antenna in order to have all the signals emitted experience the same shadow and distance fading with a noncorrelated fast fading component. As explained in the ‘System Model’ chapter, the bandwidth is divided by the number of relays in the VAA plus one (the direct path). The number of relays 23

24

Chapter 4. Results

is assumed to vary from zero to 10 relays. This range is logical since using more relays will consume too many resources to justify their existence. The density on the other hand was somewhat tricky to place within a certain range; thus, as explained in subsection 2.1.2, the density was defined in terms of the average distance of the closest relay to the terminal (equation: 2.1). Then in order to be consistent with the study done in [11], the range of rµ was chosen to be: 20m ≤ rµ ≤ 65m

(4.1)

Which is roughly equivalent to a density range within the following boundaries: 56.59(Relays/km2 ) ≤ λ ≤ 509.3(Relays/km2 )

(4.2)

Six specific densities have been chosen within the given range. Table 4.1 shows the chosen densities and their corresponding rµ . Table 4.1: Table of densities used within simulation. λ (Relays/km2 ) 509.3 259.8 157.2 105.2 75.34 56.59

rµ (m) 22.15 31.02 39.88 48.75 57.60 66.46

With the relevant variables discussed, the results of simulating the 2-hop reference system are presented below for five different cases. Figure 4.1 represents the first case where the throughput of the system is measured for the six different densities (discussed above) when the MT is 100m away from the BS. The horizontal axis is the number of relays in the VAA, while the vertical axis is the throughput in bits/sec. Figure 4.2 contains plots of the throughput for the six densities when the MT is 300, 500, 700, and 900 meters away from the BS respectively. As can be observed in Figure 4.1, when the Terminal is relatively close to the BS (100m away), then the total throughput of the system is proportional to the density of the relays. This means that the more we increase the density of the relays, then the better our throughput will be. Figure 4.3 shows how the throughput varies when the density of relays is increased. However, this does not apply for the other cases where the terminal is placed at a further distance from the BS. We observe from the other plots for distances larger than 100m that the different densities converge together in a bundle. This phenomenon can be explained by the fact that when the MT is far from the BS then the distance dependent path loss from the BS to the relays becomes the most prominent factor. Thus, the relays (which are activated according to the best gain to the terminal criteria) have approximately the same gain to the BS (with small variations due to shadow and fast fading) no matter how dense they are.

25

4.1. Throughput of the Reference System

18

DENSITY = 509.3 Relays/(square km) DENSITY = 259.8 Relays/(square km) DENSITY = 157.2 Relays/(square km) DENSITY = 105.2 Relays/(square km) DENSITY = 75.34 Relays/(square km) DENSITY = 56.59 Relays/(square km)

16

Throughput (Bits/sec)

14 12 10 8 6 4 2

2

4 6 8 Number of Relays in the VAA

10

Figure 4.1: Normalized throughput of 2-hop system for MT 100m from BS. DENSITY = 509.3 Relays/(square km) DENSITY = 259.8 Relays/(square km) DENSITY = 157.2 Relays/(square km) DENSITY = 105.2 Relays/(square km) DENSITY = 75.34 Relays/(square km) DENSITY = 56.59 Relays/(square km)

8

6 5 4

3 2.5 2

2

1.5

2

3

4 6 8 Number of Relays in the VAA

1

10

DENSITY = 509.3 Relays/(square km) DENSITY = 259.8 Relays/(square km) DENSITY = 157.2 Relays/(square km) DENSITY = 105.2 Relays/(square km) DENSITY = 75.34 Relays/(square km) DENSITY = 56.59 Relays/(square km)

2.5 Throughput (Bits/sec)

3.5

3

1

2

1.5

DENSITY = 509.3 Relays/(square km) DENSITY = 259.8 Relays/(square km) DENSITY = 157.2 Relays/(square km) DENSITY = 105.2 Relays/(square km) DENSITY = 75.34 Relays/(square km) DENSITY = 56.59 Relays/(square km)

4

2

1.4

4 6 8 Number of Relays in the VAA

10

DENSITY = 509.3 Relays/(square km) DENSITY = 259.8 Relays/(square km) DENSITY = 157.2 Relays/(square km) DENSITY = 105.2 Relays/(square km) DENSITY = 75.34 Relays/(square km) DENSITY = 56.59 Relays/(square km)

1.3 1.2 Throughput (Bits/sec)

Throughput (Bits/sec)

7

5 4.5

Throughput (Bits/sec)

9

1.1 1 0.9 0.8 0.7

1

0.6 0.5

2

4 6 8 Number of Relays in the VAA

10

0.5

2

4 6 8 Number of Relays in the VAA

10

Figure 4.2: Normalized throughput of 2-hop system for MT 300m (upper left), 500m (upper right), 700m (lower left), and 900m (lower right) away from BS.

26

Chapter 4. Results

Throughput (Bits/sec)

7.5

x 10

7

6.5

6

5.5

100

200 300 400 Density (Relays/Km²)

500

Figure 4.3: Normalized throughput of the 2-hop system with respect to varying density for MT 100m away from BS and number of relays in the VAA=5. Another significant trend that can be observed is that the total throughput decreases logarithmically with the increase in the number of relays. This behavior appears in the plots regardless of the distance of MT from the BS, and it is attributed to the fact that the resources needed to support more relays overweigh the benefits in performance. The solution to this problem is presented in [11] through the use of tight resource allocation among the cells. In this study it is not possible to implement resource management techniques that are typical to multi-user systems since only one cell is considered. 7

x 10

Throughput (Bits/sec)

6 5 4 3 2 1 0 100

200

300 400 500 600 700 Distance Between MT and BS (m)

800

900

Figure 4.4: Normalized throughput of the 2-hop system with respect to varying distance of MT from BS, where number of relays in the VAA=5 and density=157.2 Relays/km2 . Finally it is important to note that as the distance of the terminal from the BS increases the total throughput decreases. This behaviour is emphasized in Figure 4.4 which plots the throughput in terms of distance between MT and BS. This is expected, of course, because the path loss increases with distance.

27

4.2. Throughput of the Proposed System

4.2

Throughput of the Proposed System

The 3-hop system is the system being evaluated and in order for the comparison with the reference system to be meaningful, they have to be studied under the same circumstances. Again we are interested in the total throughput (Bits/sec) of the system in terms of the number and density of relays. In this case the number of relays in the FT is fixed to 5 so as to be compatible with the 5 BS antenna elements of the reference system, while the number of relays in the second VAA is varied between 1 and 10. As for the density of relays, both tiers are assumed to have the same density; hence, when we simulate for different density levels, this applies to both VAAs. The total bandwidth remains fixed (as in the case of the 2-hop), but now we divide it by the sum of: the number of relays in the FT, the number of relays in the second VAA, and one (the MIMO channel). The rest of the parameters are set to the same values as in the 2-hop case, and the results of this system’s simulation are depicted in Figures 4.5, and 4.6.

6.5

509.3 Relays/km² 259.8 Relays/km² 157.2 Relays/km² 105.2 Relays/km² 75.34 Relays/km² 56.59 Relays/km²

6

Throughput (Bits/sec)

5.5 5 4.5 4 3.5 3 2.5 2

1

2

3 4 5 6 7 8 Number of Relays in the Second Tier VAA

9

10

Figure 4.5: Normalized throughput of 3-hop system for MT 100m from BS. If we were to study the plots of the 3-hop case we can note some remarks to discuss and explain the behavior of the system: • The first detail to note about the 3-hop system plots is that the magnitude of the total capacity for each case is much less than the magnitude of

28

Chapter 4. Results 1.5

2.6

509.3 Relays/km² 259.8 Relays/km² 157.2 Relays/km² 105.2 Relays/km² 75.34 Relays/km² 56.59 Relays/km²

2.2

509.3 Relays/km² 259.8 Relays/km² 157.2 Relays/km² 105.2 Relays/km² 75.34 Relays/km² 56.59 Relays/km²

1.4 1.3 Throughput (Bits/sec)

Throughput (Bits/sec)

2.4

2 1.8 1.6

1.2 1.1 1 0.9 0.8 0.7

1.4

0.6

1.2 1

2

0.75

9

0.6

2

0.45

0.5 0.45 0.4

3 4 5 6 7 8 Number of Relays in the Second Tier VAA

9

10

509.3 Relays/km² 259.8 Relays/km² 157.2 Relays/km² 105.2 Relays/km² 75.34 Relays/km² 56.59 Relays/km²

0.5

0.55

0.4 0.35 0.3 0.25 0.2

0.35

0.15

0.3 0.25

1

0.55

Throughput (Bits/sec)

0.65

0.5

10

509.3 Relays/km² 259.8 Relays/km² 157.2 Relays/km² 105.2 Relays/km² 75.34 Relays/km² 56.59 Relays/km²

0.7

Throughput (Bits/sec)

3 4 5 6 7 8 Number of Relays in the Second Tier VAA

1

2

3 4 5 6 7 8 Number of Relays in the Second Tier VAA

9

10

0.1

1

2

3 4 5 6 7 8 Number of Relays in the Second Tier VAA

9

10

Figure 4.6: Normalized throughput of the 3-hop system for MT at 300m (upper left), 500m (upper right), 700m (lower left), and 900m (lower right) away from AP. the corresponding 2-hop case. To show this more explicitly, Figure 4.8 compares the throughput of the two systems for the same relay density (157.2 Relays/Km2 ) with respect to the distance between the MT and the AP (or BS). It is obvious that the 2-hop system outperforms the 3hop system and this is due to the fact that in the latter system more resources are required to establish a connection. Since we are using the same bandwidth but dividing it into more channels, then it is only natural that we have worse performance. • The second remark deals with the shape of the plots. It is obvious that the plots in the 2-hop case decrease logarithmically, while the 3-hop plots tend to rise to a maximum before starting to decrease as a function of the number of relays in the second VAA. The explanation for this phenomenon can be found in knowing two facts about the 3-hop system. The first fact is that the total capacity (as discussed before) is the minimum between the first hop capacity and the combination of the second and third hop capacities. The plots of the first hop capacity (refer to Figure 4.7) show us that it is much higher than the second and third hops combined which means that the total capacity of the system is limited by and identical to the combined capacity of the second and third hops. The second fact is that Chop2−3 is approximately the same as the capacity for the 2-hop reference system with a few discrepancies. The most major of these discrepancies is the bandwidth; hence, if we were to make the assumption that the other discrepancies are insignificant compared to the bandwidth

29

4.2. Throughput of the Proposed System

30

509.3 Relays/ km² 259.8Relays/ km² 157.2 Relays/ km² 105.2 Relays/ km² 75.34 Relays/ km² 56.59 Relays/ km²

Throughput (Bits/sec)

25 20 15 10 5 0

2

3 4 5 6 7 8 Number of Relays in the Second Tier VAA 28

30

509.3 Relays/ km² 259.8 Relays/ km² 157.2 Relays/ km² 105.2 Relays/ km² 75.34 Relays/ km² 56.59 Relays/ km²

20

24

15 10

9

10

509.3 Relays/ km² 259.8 Relays/ km² 157.2 Relays/ km² 105.2 Relays/ km² 75.34 Relays/ km² 56.59 Relays/ km²

26

Throughput (Bits/sec)

25 Throughput (Bits/sec)

1

22 20 18 16 14 12

5

10 1

2

20

9

16

1

2

20

12 10

3 4 5 6 7 8 Number of Relays in the Second Tier VAA

9

10

509.3 Relays/ km² 259.8 Relays/ km² 157.2 Relays/ km² 105.2 Relays/ km² 75.34 Relays/ km² 56.59 Relays/ km²

18

14

8

8

10

509.3Relays/ km² 259.8 Relays/ km² 157.2 Relays/ km² 105.2 Relays/ km² 75.34 Relays/ km² 56.59 Relays/ km²

18 Throughput (Bits/sec)

3 4 5 6 7 8 Number of Relays in the Second Tier VAA

Throughput (Bits/sec)

0

16 14 12 10 8

1

2

3 4 5 6 7 8 Number of Relays in the Second Tier VAA

9

10

6

1

2

3 4 5 6 7 8 Number of Relays in the Second Tier VAA

9

10

Figure 4.7: Normalized throughput of the first hop, for distance between the AP and MT equal to 100m (uppermost), 300m (2nd row left), 500m (2nd row right), 700m (3rd row left), and 900m (3rd row right).

30

Chapter 4. Results

7

x 10 2−hop 3−hop

Throughput (Bits/sec)

6 5 4 3 2 1 0 100

200

300 400 500 600 700 800 Distance between MT and BS (m)

900

Figure 4.8: Comparison between the 2-hop and 3-hop normalized system throughputs for density=157.2 Relays/Km2 where the VAA’s are composed of 5 relays.

then we can mathematically prove that the capacity of the second and third hops combined decreases logarithmically as in the 2-hop case. It only appears to rise since it is divided by a different number of channels.

• Another thing to note is that the capacity of the first hop is much higher than the capacity of the combined second and third hops. To see this fact more clearly I have plotted (as an example) both the first hop capacity and the combined second and third hops’ capacity in Figure 4.9 for the case when the MT is 500m away from the AP and the relay density is 157.2 Relays/Km2 . The explanation for this is that the relays of the FT are relatively close to the AP; thus, the path loss is not too great and the available bandwidth is more than enough to provide for a good throughput. This fact is used in the next section in order to improve the performance of the whole system.

• The final remark deals with the different densities and their behavior. At first glance it appears that the density plots contain no logical pattern and in every plot it appears as though a different density is providing the optimum performance. This is not true because these density plots represent the average of many simulations that are varying over large intervals. Therefore, these values are not statistically relevent.

31

4.3. Modifications for the Proposed System

100

Throughput (Bits/sec)

First Hop Second & Third Hops

10

1

0.1

1

2

3

4 5 6 7 8 Number of relays in Second VAA

9

10

Figure 4.9: Comparison between the normalized throughput of the first hop and the combination of second and third hops of the 3-hop system for density=157.2 Relays/Km2 and MT at 500m away from AP.

4.3

Modifications for the Proposed System

From the above results it is clear that the 3-hop system is performing much worse than the 2-hop reference system. The graphs show that the proposed system needs to be modified to render comparable throughput to the 2-hop case if it is to be considered as a possible cheaper alternative. Towards this end, three modifications on the originally proposed 3-hop system are presented and discussed in this section.

4.3.1

Varying Number of Active Relays of FT

The results depicted in Figure 4.10 portray ten plots per graph that correspond to the capacity of the system for a different number of relays in the FT. Each graph considers the terminal at a different distance from the AP, with a predefined density of the relays. The density is chosen to be the one that yielded the best throughput (refer to the plots for the respective distances) in the previous section. The remarks that can be inferred from these plots are the following: • From the graphs we can deduce that considering 5 relays in the FT is not the optimum choice; however, choosing another number does not offer much larger total capacity. • It appears that choosing to activate 10 relays yields the best results when the distance of the terminal from the AP is short. This can be explained

32

Chapter 4. Results

5 4.5

Throughput (Bits/sec)

4 3.5 T=1 T=2 T=3 T=4 T=5 T=6 T=7 T=8 T=9 T=10

3 2.5 2 1.5 1 0.5 0

1

2

3 4 5 6 7 8 Number of Relays in the Second Tier VAA

9

10

1.4

2 1.8

1.2

T=1

1.4 1.2

T=1 T=2 T=3 T=4 T=5 T=6 T=7 T=8 T=9 T=10

1 0.8 0.6 0.4 0.2 0

Throughput (Bits/sec)

Throughput (Bits/sec)

1.6

1

2

3 4 5 6 7 8 Number of Relays in the Second Tier VAA

9

T=3 T=4

0.8

T=5 0.6

T=6 T=7

0.4

T=8 T=9

0.2 0

10

T=10

1

2

3 4 5 6 7 8 Number of Relays in the Second Tier VAA

9

10

0.35

1.4 T=1 T=2 T=3 T=4 T=5 T=6 T=7 T=8 T=9 T=10

1.0 0.8

0.3

Throughput (Bits/sec)

1.2

Throughput (Bits/sec)

T=2

1.0

0.6

0.25 T=1 T=2

0.2

T=3 T=4

0.15

T=5 T=6

0.4

0.1

0.2

0.05

0

0

T=7 T=8

1

2

3 4 5 6 7 8 Number of Relays in the Second Tier VAA

9

10

T=9 T=10 1

2

3 4 5 6 7 8 Number of Relays in the Second Tier VAA

9

10

Figure 4.10: Normalized throughput of 3-hop system, with varying number of FT relays, where MT is 100m (uppermost), 300m (2nd row left), 500m (2nd row right), 700m (3rd row left), and 900m (3rd row right) from BS.

by the fact that the existence of more relays increases the probability that these relays have better gain towards the relays of the second VAA. On the other hand, this observation does not apply to the further distance cases,

33

4.3. Modifications for the Proposed System

and thus we can deduce that the the optimum number of relays is not absolute and depends on many factors such as the range of the terminal.

100

Throughput (Bits/sec)

Second &Third Hops First Hop

10

1

1

2

3 4 5 6 7 8 Number of Relays in the Second Tier VAA

9

10

Figure 4.11: Comparison between the normalized throughput of the first hop and the combination of second and third hops of the 3-hop system for T=10, density=509.3 Relays/Km2 , and MT at 100m away from BS.

• The total capacity of the system is still limited by the combined capacity of the second and third hops, while the first hop capacity is much larger. Figure 4.11 shows both the first hop capacity and the combined second and third hops capacity when the MT is at 100m from the BS.

4.3.2

Varying Bandwidth Distribution

Distributing the bandwidth equally among all the channels has been established as a sub-optimum solution to say the least. For this reason another way of distributing the bandwidth is presented here. The new distribution methodology consists of splitting the available bandwidth into two unequal parts, one for the first hop and one for the second and third hops. This split is justifiable since the first hop is separated from the rest of the system by a tier of regenerative relays. The bandwidth is not split into two equal parts since it is evident that the first hop does not require as much resources as the rest of the system. For this reason the following distribution was chosen empirically such that the majority

34

Chapter 4. Results

12

System Capacity Capacity of 2nd and 3rd hops Capacity of 1st hop

11

Throughput (Bits/sec)

10 9 8 7 6 5 4

1

3 4 5 6 7 8 Number of Relays in the Second Tier VAA 4

5

System Capacity Capacity of 2nd and 3rd hops Capacity of 1st hop

4.5 4 3.5 3 2.5

1

2

3 4 5 6 7 8 Number of Relays in the Second Tier VAA

9

3 2.5 2 1.5

0.5 1

10

2.2

2

1.3

2

9

10

1.1

1.6 1.4

Throughput (Bits/sec)

Throughput (Bits/sec)

3 4 5 6 7 8 Number of Relays in the Second Tier VAA

System Capacity Capacity of 2nd and 3rd hops Capacity of 1st hop

1.2

1.8

System Capacity Capacity of 2nd and 3rd hops Capacity of 1st hop

1.2 1 0.8

1.0 0.9 0.8 0.7

0.6

0.6

0.4 0.2

10

1

2 1.5

9

System Capacity Capacity of 2nd and 3rd hops Capacity of 1st hop

3.5

Throughput (Bits/sec)

Throughput (Bits/sec)

2

1

2

3 4 5 6 7 8 Number of Relays in the Second Tier VAA

9

10

0.5

1

2

3 4 5 6 7 8 Number of Relays in the Second Tier VAA

9

10

Figure 4.12: Normalized throughput of the 3-hop system, with improved bandwidth allocation for distance between the BS and MT equal to 100m (uppermost), 300m (2nd row left), 500m (2nd row right), 700m (3rd row left), and 900m (3rd row right).

35

4.3. Modifications for the Proposed System of the bandwidth is assigned to the second and third hops:     BWT 4BWT BWhop1 = , BWhop2,3 = 5T 5(R + 1)

(4.3)

where, T = Number of channels from AP to Active Relays in the FT, and R + 1 = Number of channels from Active Relays in the second VAA to terminal plus the MIMO channel. The capacity is also a function of the distance between the AP and the terminal; thus, the optimum division of the total bandwidth varies for the different distances.That is when the MT is at a distance of 100m from the APthe opti
4BWT T ; and BWhop2,3 = 5(R+1) mum bandwidth division could be BWhop1 = BW 5T however, when the distance is 500m (for example) then the optimum bandwidth  
6BWT T division could be BWhop1 = BW and BW = hop2,3 7T 7(R+1) . The division chosen above in equation 4.3 is only intended to provide an insight into the bandwidth optimization possibilities. The subject of optimizing the bandwidth for all the different cases requires a complete thorough study by itself and the time limitations set on this thesis allow only for a glimpse that proves how important resource optimization is for improving the performance.

3.5

Throughput (Bits/sec)

3

x 10 2−hop 3−hop

2.5 2 1.5 1 0.5

2 4 6 8 10 Number of relays of VAA (second VAA for the 3−hop system)

Figure 4.13: Comparison between the normalized throughputs of the 2-hop system and 3-hop modified (Bandwidth Allocation) system. The number of relays in FT=5, density=75.34 Relays/Km2 , and MT at 500m away from BS. The depicted graphs in Figure 4.12 represent the case where the bandwidth is divided according to equation 4.3. By observing these graphs closely, the following remarks can be inferred: • The total capacity of the system shows a notable increase and approaches the capacity provided by the 2-hop system (refer to Figure 4.13). In fact

36

Chapter 4. Results

14

x 10 2−hop 3−hop

Throughput (Bits/sec)

12

10

8

6

4

2 4 6 8 10 Number of relays in VAA (second VAA for the 3−hop system) Figure 4.14: Comparison between the normalized throughputs of the 2-hop system and 3-hop modified (Bandwidth Allocation) system. The number of relays in FT=5, density=157.2 Relays/Km2 , and MT at 100m away from BS. for some cases, such as for example the case of 7 active relays when the terminal is 100m away from the AP (refer to Figure 4.14), we notice that the capacity of the 3-hop system outperforms the 2-hop case by a slight margin. • When the Terminal is within a radius of 100 and 300 meters from the AP then the combined capacity for the second and third hops is higher than the first hop capacity especially when the number of relays in the second tier is low. • All the graphs show that the capacity of the first hop decreases to a certain extent while the bottle-neck capacity of the rest of the system increases thus raising the total capacity of the system. • The shape of the curve for the second and third hops capacity resembels that of the 2-hop system since now we divide the bandwidth by only R + 1 and not R + 1 + T . • From these results we can deduce that if the relays were to know (by some external means) the approximate distance of the target terminal then the bandwidth allocation can be optimized in such a way as to allow the 3-hop system to perform as well as the 2-hop case (perhaps better even).

4.3.3

Alternate Relay Activation Algorithm

The simulations so far have proved that the capacity of the second and third hops is indeed acting as the bottle-neck of the system (except for the case when

37

4.3. Modifications for the Proposed System

25

System Capacity 1st Hop Capacity

Throughput (Bits/sec)

20

15

10

5

0

1

16

3 4 5 6 7 8 Number of Relays in the Second Tier VAA 7

System Capacity 1st Hop Capacity

14

9

10

System Capacity 1st Hop Capacity

6 5 Throughput (Bits/sec)

Throughput (Bits/sec)

2

12 10 8

4 3 8 7 6 5

6

4 4

1

2

9

3

10

1

2

2.4

6

System Capacity 1st Hop Capacity

5.5 5 4.5 4 3.5

3 4 5 6 7 8 Number of Relays in the Second Tier VAA

9

10

System Capacity 1st Hop Capacity

2.2 Throughput (Bits/sec)

Throughput (Bits/sec)

3 4 5 6 7 8 Number of Relays in the Second Tier VAA

2 1.8 1.6

3 1.4

2.5 2

1

2

3 4 5 6 7 8 Number of Relays in the Second Tier VAA

9

10

1.2

1

2

3 4 5 6 7 8 Number of Relays in the Second Tier VAA

9

10

Figure 4.15: Normalized throughput of the 3-hop system with Alternate Relay Activation Algorithm for distance between the BS and MT equal to 100m (uppermost), 300m (2nd row left), 500m (2nd row right), 700m (3rd row left), and 900m (3rd row right).

38

Chapter 4. Results

optimized bandwidth allocation is applied). To rectify this situation the alternate activation criteria for choosing which relays in the FT should be activated is utilized. The activation criteria for the relays of the second VAA is kept as it is so that the system remains comparable with the 2-hop reference case. The modified activation criteria chooses those relays (within a certain predefined area around the AP) that have the best path gain with the terminal rather than with the AP. For the cases when the MT is at 100 and 300 meters from the AP the predefined area is taken to be of radius 450 meters with density 157.2 Relays/Km2 . Alternatively for the cases when the MT is at 500 and 700 meters from the AP the predefined area is taken to be of radius 650 meters with density 75.34 Relays/Km2 . As for the case when the MT is 900 meters away from the AP then the predefined area is taken to be of radius 750 meters with density 56.59 Relays/Km2 .

Throughput (Bits/sec)

5

x 10

4

3 Unmodified 3−hop Modified 3−hop 2

1

0

2

4 6 8 Number of relays in second VAA

10

Figure 4.16: Comparison between the normalized throughput of the 3-hop unmodified system and 3-hop modified (Alternate Relay Activation Algorithm) system. The number of relays in FT=5, density=75.34 Relays/Km2 , and MT at 500m away from BS. The simulation results for the terminal at different distances from the AP with the same densities used in section 4.3.2. are displayed in the graphs of Figure 4.15. The following comments can be made: • The increase in capacity over the unmodified 3-hop case is clear and positively drastic. It can be observed clearly in Figure 4.16 for the case of the MT being 500 meters away from the AP. • The first hop capacity is still higher than the second and third hops capacity but the difference is decreased. This is natural since the active relays of the first tier no longer have the best path gain with the AP.

39

4.3. Modifications for the Proposed System

14

x 10 2−hop 3−hop

Throughput (Bits/sec)

12 10 8 6 4 2

6

2 4 6 8 10 Number of relays in VAA (second VAA for 3−hop system) x 10 x 10 6

2−hop 3−hop

5

4

3

2

1

2 4 6 8 10 Number of relays in VAA (second VAA for 3−hop system)

Throughput (Bits/sec)

Throughput (Bits/sec)

2−hop 3−hop

5

4

3

2

1 2 4 6 8 10 Number of relays in VAA (second VAA for the 3−hop system)

Figure 4.17: Comparison between the normalized throughputs of the 2-hop system and 3-hop modified (Alternate Relay Activation Algorithm) system. The number of relays in FT=5, density=157.2 Relays/Km2 for MT 100m (Upper) and 300m (lower left) away from AP, and density=75.34 Relays/Km2 for MT at 500m (lower right) away from BS. • Compared to the 2-hop reference system, we observe that for the case when the terminal is 100 meters away from the AP, the performance is approximately the same (refer to Figure 4.17). Furthermore, for the case when the distance is 300 meters and above, the modified 3-hop system outperforms the reference system by a clear and notable margin. • The results prove that the direct path gains between the FT active relays and the terminal constitute an extremely significant parameter in the analysis and the choice of which relays to activate can radically influence the performance of the whole system.

Chapter 5

Cost Evaluation The cost evaluation presented in this chapter is a simple analysis based on the cost estimation of different types of BS [3] in a typical Wideband Code Division Multiple Access (WCDMA) system. According to [3] the cost involved in setting up a BS can be split into two major categories. The first category is the Initial Cost and this includes the price of the equipment, the cost of building the site, and the site installation costs. The second category is called the Annual Cost and it encompasses the annual operations and management (O&M) dues, the site lease, and the transmission cost. The cost involved in setting up a Macro BS is depicted in Table 5.1 and the values are in European Euro (e ). Similarly the cost involved in setting up a Pico BS is depicted in Table 5.2 and the values are also in European Euro (e ). Table 5.1: Macro BS costs. Initial Cost Equipment = 50K Building Site = 70K Site Installation = 30K Total = 150K

Annual Cost Annual O&M = 3K Site Lease = 10K Transmission = 5K Total = 18K

Table 5.2: Pico BS costs. Initial Cost Equipment = 5K Building Site = − Site Installation = 3K Total = 8K

Annual Cost Annual O&M = 1K Site Lease = 1K Transmission = 5K Total = 7K

For the sake of this analysis, the AP and each one of the relays shall be assumed to have the same cost as a Pico BS, while the BS implemented in the 2-hop reference system shall be assumed to have the same cost as the Macro BS. In order to compare the cost of the two systems we shall consider a modified 41

42

Chapter 5. Cost Evaluation

version of the 3-hop system which is the best modification scenario presented in the earlier sections. Therefore, we shall assume to have 5 active relays in the FT, and we shall activate them according to the modified activation criteria discussed in section 4.3.2. The simulation of the 3-hop system with these assumptions can be viewed in the graphs of Figure 4.17 which show that the total throughput is approximately the same as the 2-hop reference system with some positive difference in favor of the 3-hop. This means that we can achieve, to some extent, the same performance for both systems; thus, rendering them directly comparable in cost. The number of relays used in the VAA’s is irrelevant in this analysis since both systems have the same cost for the same number of relays. Consequently, calculating the initial setup cost of the AP equals 8Ke which is 142Ke less than the initial cost of setting up the Macro BS which stands at 150Ke . Now keeping in mind the initial setup cost, we proceed to calculate the Annual Cost assuming that the units of the system have a lifespan of 10 years. We also assume that the cost of the site lease increases 10% each year. Using equation 5.1 and knowing that x = 10Ke is the site lease while y = 8Ke is the sum of the annual O&M and Transmission costs for the Macro BS, then for 10 years, these costs add up to ≈ 240Ke . 9 X

x · (1.1)n + y

(5.1)

n=0

Similarly for the AP, using equation 5.1 and knowing that x = 1Ke is the site lease while y = 6Ke is the sum of the annual O&M and Transmission costs, then for 10 years, these costs add up to ≈ 76e . If we add these values to the Initial costs we would have a total cost of 390Ke for the 2-hop system and a total cost of 84Ke for the 3-hop modified system. This means that for approximately the same performance (with the modified 3-hop performing better) the three hop system will cost ≈ 306Ke less than the two hop system. It has to be noted here that the numbers used in this evaluation are not absolutely accurate, they are simply there to give the reader an insight into the cost savings that are expected to be attained from implementing the proposed system, rather than the reference system.

Chapter 6

Conclusion The objective of this work was to study the feasibility of implementing a 3-hop CMIMOR network and evaluating it with respect to the 2-hop CMIMOR system. The resources needed to implement the proposed system were discussed in detail throughout this report and the system was implemented in a Matlab environment. The results showed that the 2-hop reference system was superior in terms of total throughput to the initially proposed 3-hop system. The reason for the inferiority in performance of the latter system was the fact that more channels had been added with equally allocated resources to all channels. This allocation of resources was obviously not optimal which required the introduction of modifications on the initially proposed system. The modifications discussed herein exploited the inherent properties of the 3-hop system to give it an advantage over the reference system. The first modification was to vary the number of active relays in the first tier of relays. The goal from this modification was to increase the diversity of the received signal in the second and third hops which lead to a slight but negligible increase in system capacity as the number of active relays increased for the case where the terminal was relatively close to the Access Point. The second modification opted for an unequal distribution of the limited bandwidth between the first hop, and the combination of second and third hops. It was apparent that the first hop needed less bandwidth than the rest of the system and hence it was offered approximately one fifth of the available bandwidth. This maneuver raised the bottle-neck capacity of the second and third hops so that the total capacity became quite close to the capacity of the reference system, even overtaking it in some special cases. Last but definitely not least was the introduction of a new activation criterion for the relays of the first tier. The aim from this was to allow the relays of the first tier to have better direct path gain to the terminal and increase the combined capacity of the second and third hops, at the expense of an acceptable decrease in the capacity of the first hop. The simulation results proved that this modification did indeed increase the throughput of the system drastically, to the extent of over performing the 2-hop reference system. After the proposed modifications elevated the capacity of the 3-hop system, it was possible to compare it with the reference system in terms of cost. The straightforward study revealed that the 3-hop system is much cheaper to imple43

44

Chapter 6. Conclusion

ment than the 2-hop and if modified, as was discussed above, could provide for better total throughput too. Finally, the following points constitute a summary of the main conclusions drawn from this work: • The three-hop proposed system cannot compare to the throughput of the two-hop reference system unless it is modified. • The most significant modifications were the optimized bandwidth allocation for the channels, and the alternative algorithm for activating the relays in the first VAA. • The proposed modified 3-hop system can outperform the reference system at a lower cost of implementation per throughput.

Chapter 7

Suggested Future Work Due to time limitations, the study that has been carried out and discussed in this report does not cover all the aspects and angles of the 3-hop CMIMOR system which leaves room for more enhancements and suggestions that are conferred herein.

7.1

Propagation Model

The propagation model used in this thesis was the Okumura-Hata which does not really apply for all scenarios. In fact the Okumura-Hata model applies only for urban areas at 900 and 1800 MHz bands, flat terrain, and the antenna heights must be above roof level [18]. It was used here only because it is a very common propagation model that was implemented by most of the references. The use of another more accurate model would probably lead to more realistic results and better performance.

7.2

Multi-Cell Topology

The system here has been investigated according to the existence of one transmitter and one receiver. It would be interesting to study system in a multi-cell topology with more than one user as was done for the 2-hop reference case in [11]. This sort of study would allow for enhanced resource allocation that would surely increase the throughput of the system.

7.3

Vary the Density of the Relays

The densities of the relays in the FT and the second VAA are always assumed to be varying identically throughout this report. One suggestion would be to attempt to simulate the densities independently. This might not yield a significant increase in throughput but it is one of the variables that could be studied 45

46

Chapter 7. Suggested Future Work

more to be able to emulate the real life density distributions of the relays.

7.4

Relay Activation

The selection criteria for activating the relays plays an essential role in the performance of the system as was shown in section 4.3.3 and constitutes a complete study by itself. This thesis focuses on two possible activation criteria for the relays of the FT: best path gain from the AP and best path gain from the MT. As for the second VAA only the best path gain to the MT criterion is considered. One suggestion includes activating the relays that have best path gain to each other. That is, activate the relays of one of the VAAs first and then activate the relays of the second VAA according to the best path gains to the active relays of the first VAA. Another suggestion is to activate the relays that have the best combined path gains to the MT and to the relays of the AP. This technique would improve the capacity of the second and third hops; hence, the total throughput. The other aspect of relay activation is the decision upon the number of active relays. The question of the optimum number of relays with the available resources presents itself. One suggestion to answer this question is to check if all the activated relays at one point are contributing equally or not. If there are some activated relays that are not contributing in proportion with the rest of the relays then maybe it would be better to shut them down and resume transmission with a lower number of active relays.

7.5

Bandwidth Allocation

The issue of bandwidth allocation between the first hop, and the second and third hops is quite significant. Proper allocation could improve the performance as was shown in section 4.3.2 of this report. A good suggestion is to study how to balance the bandwidth between the two parts of the system so that no part becomes a bottle neck for the whole system.

7.6

Regenerative Relays

In this study it was assumed that the relays in the FT were regenerative while the ones in the second VAA were non-regenerative. It would be interesting to investigate the use of regenerative relays in both tiers since it should provide better throughput according to [8]. The cost of these regenerative relays could also be affordable since the current studied system proved to be much cheaper than the reference system.

References [1] Dohler M.; Lefranc E.; Aghvami H. Virtual antenna arrays for future wireless mobile communication systems. ICT2002, Beijing, China, June 2002. [2] Dohler M.; Said F.; Aghvami H.;. An overview over vaa. PREP2002, Nottingham, UK, April 2002. [3] Johansson K.; Furuskar A.; Karlsson P.; Zander J.;. Relation between base station characteristics and cost structure in cellular systems. IEEE PIMRC, 2004. [4] Ozdemir M.K.; Arvas E.; Arslan H.;. Dynamics of spatial correlation and implications on mimo systems. In Communications Magazine, IEEE, volume 42, pages S14–S19, June 2004. [5] Gesbert D.; Shafi M.; Da shan Shiu; Smith P.J.; Naguib A.;. From theory to practice: an overview of mimo space-time coded wireless systems. In Selected Areas in Communications, IEEE Journal on, volume 21, pages 281–302, April 2003. [6] Beach M.A.; McNamara D.P.; Fletcher P.N.; Karlsson P.;. Mimo-a solution for advanced wireless access? In Eleventh International Conference on (IEE Conf. Publ. No. 480), volume 1, pages 231–235, April 2001. [7] Chiurtu N.; Rimoldi B.; Telatar E.;. On the capacity of multi-antenna gaussian channels. In Information Theory,IEEE International Symposium, page 53, June 2001. [8] Dohler M. Virtual antenna array. PhD Thesis, submitted to University of London, Department of Electrical and Electronic Engineering, 2003. [9] Hasna M.O.; Alouini M.-S.;. Performance analysis of two-hop relayed transmissions over rayleigh fading channels. In IEEE 56th, Vehicular Technology Conference, volume 4, pages 1992–1996, Sept 2002. [10] Munoz O.; Agustin A.; Vidal J.;. Cellular capacity gains of cooperative mimo transmission in the downlink. In Communications, 2004 International Zurich Seminar, pages 22–26, 2004. [11] Nordmark H.;. Resource allocation for cooperative mimo relaying systems. M.Sc. Thesis, RST KTH, February 2005. 47

48

References

[12] Kendall M.G.; Moran P.A.P.;. Geometrical Probability. Charles Griffin and Co. Ltd. London, 1963. [13] Dohler M.; Gkelias A.; Aghvami H.;. A resource allocation strategy for distributed mimo multi-hop communication systems. In Communications Letters, IEEE, volume 8, pages 99–101, Feb 2004. [14] Rodriguez M.;. Cooperative mimo relaying. M.Sc. Thesis, RST KTH, January 2004. [15] Timus B.;. Capacity calculations for a non-regenerative cmimor connection. prepared within the Cooperative Antenna System(CSA) project supported by Wireless @ KTH, Stockholm , Sweden, 2004. [16] C.E. Shannon. The mathematical theory of information. University of Illinois Press, Urbana, Illinois, 1949. [17] Proakis J. G.; Salehi M.;. Communication Systems Engineering. Prentice Hall, 1994. [18] Digital mobile radio towards future generation systems. COST 231 Final Report. [19] Ahlen L.; Zander J.;. Principles of Wireless Communications. Studentlitteratur, Lund. Second edition, 1998.

Appendix A

First Hop Analysis This analysis is intended to study two different scenarios for the first hop. In the first scenario the AP is assumed to be transmitting the signal to the active relays of the FT through independent orthogonal channels, while in the second scenario the AP simply broadcasts the information over one common channel. The objective is to determine analytically which scenario provides the optimum throughput for the system.

A.1

Scenario One

The assumptions considered in this case are the following: • The AP transmits through ‘T’ independent orthogonal channels. • The signal is divided into uncorrelated equal portions and sent over to the different relays. • The second hop of the system is a MIMO channel. • The third hop of the system compromises the ‘R’ orthogonal channels from the active relays to the terminal. • The Total Bandwidth is divided equally over all the channels.

A.1.1

Capacity for the First Hop

From Shanon’s channel limit [16], and as explained in ( [17], p.585), we can obtain the following formula for the capacity of each individual channel of the first hop: C1t = W1 × log2 [1 + W1 =

P × Gt ] T × No W1

WT otal T +R+1

where,

49

(A.1) (A.2)

50

Appendix A. First Hop Analysis C1t = the capacity of the channel between the AP and Relay t. W1 = the bandwidth of the channels of the first hop. WT otal = the total bandwidth of the system (5MHz). T = the number of relays in the first tier. R = the number of relays in the second tier. P = the maximum power transmitted by a relay = cst. Gt = Gt,dist(d) × Gt,shadow × Gt,Rayleigh

Thus the expression of the total capacity that could be provided by the first hop would be limited by the minimum capacity of the multiple channels as follows: C1hop1 = T × min[C1t ],

A.1.2

t=1→T

(A.3)

Capacity for the Second & Third Hops

As derived in [15], the capacity of the second and third hops can be expressed in the following form: d

C1hops2−3 = W1 ×

1X ln(1 + λB,i ) 2 i=1

(A.4)

Where, λB,i is in terms of noise. Through simulation it will be possible to determine the bottle-neck of the system; hence, the system Capacity would be equal to: C1total = minimum{C1hop1 , C1hops2−3 }

A.2

(A.5)

Scenario Two

The assumptions considered in this case are the following: • The AP Broadcasts over one channel. • The same signal is subjected to different path loss before it is recieved by all relays. • The second hop of the system is a MIMO channel. ´ orthogonal channels from • The third hop of the system compromises the R´ the active relays to the terminal. • The Total Bandwidth is divided equally over all the channels.

A.2.1

Capacity for the First Hop

In this case we have same channel but different paths from the transmitter to the receivers; hence, each path would have a different signal to noise ratio. This means that the capacity is limited by the lowest SNR (given that the SNR is influenced by the fading coefficients):

51

A.3. Comparison of the Two Scenarios

C2t = minimum{W2 × log2 [1 + W2 =

P × Gt ]} No W2

WT otal R+2

(A.6)

(A.7)

where, C2t = the capacity of the channel between the AP and Relay t. W2 = the bandwidth of the channels of the first hop. WT otal = the total bandwidth of the system (5MHz).

A.2.2

Capacity for the Second & Third Hops

As derived in [15], the capacity of the second and third hops can be expressed in the following form: d

C2hops2−3 = W2 ×

1X ln(1 + λB,i ) 2 i=1

(A.8)

Where, λB,i is in terms of noise. Through simulation it will be possible to determine the bottle-neck of the system; hence, the system Capacity would be equal to: C2total = minimum{C2hop1 , C2hops2−3 }

A.3

(A.9)

Comparison of the Two Scenarios

If we were to set the Capacity of the first hop as the limiting factor of the system capacity in order to determine which scenario performs better, then we would have the following two inequalities: d

T × W1 × log2 [1 +

P × Gt 1X ln(1 + λB,i ) ] ≥ W1 × T × No W1 2 i=1

(A.10)

d

W2 × log2 [1 +

P × Gt 1X ] ≥ W2 × ln(1 + λB,i ) No W2 2 i=1

If we denote: d

1X ln(1 + λB,i ) 2 i=1

→

A

P × Gt ] → T ×B T × No W1 P × Gt log2 [1 + ] → C No W2

log2 [1 +

(A.11)

52

Appendix A. First Hop Analysis

Thus, equations A.10 and A.11 reduce to: T ×B ≥ A and C ≥ A respectively. ×Gt then the comparison T × B >< C Then if we assign the variable x = NPo W total becomes as follows: R+1 (A.12) )] >< log2 [1 + x(R + 1)] T By analyzing equation A.12 and running a simple simulation(refer to Figure A.1) for different values of the variables of x and R while assuming that T=5; we obtain the result that T × B has the greater capacity. This means that the first scenario, where the AP sends the signal over independent orthogonal channels, outperforms the second scenario. T × log2 [1 + x(1 +

Figure A.1: Comparison between the 1st scenario (upper line) and 2nd scenario (lower line) for x varying from 1 to 43dB. Note the thick lines represent a bundle of 10 plots each that correspond to values of R varying from 1 to 10 relays per VAA.

Appendix B

Relay Density Derivation To give a more perceptive idea of what a certain distribution of the relays means, I have related the density to the average distance of the closest relay to the terminal denoted as rµ . Thus a certain rµ corresponds to a certain λ. The derivation of the relation is initiated as follows: We assume λ is the density of relays in a certain area A. Then from the ‘Geometrical Probability’ paper by KENDALL and MORAN [12], the average distance r1 is distributed according to the following function: 2

2λπr1 · exp(−λπr1 ) ·dr1

(B.1)

To compute the average rµ of the distribution B.1 we proceed as follows: Z

∞

r1 · f (r1 )dr1

rµ = E[r1 ] =

(B.2)

0

denote :

Z

⇒ rµ

=

⇒ rµ

=

x = r1 a = πλ

∞

2

ax2 · exp(−ax ) ·dx 0 r 1 π 2× × 4 a

2×

(B.3) (B.4)

Replacing the values of a and x back into the equation results in: r rµ = 0.5 ×

1 λ

(B.5)

Hence equation B.5 is the relation between the density and the average distance of the closest relay to the mobile terminal.

53