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Degree project
Error Rate Performance of Multi-Hop
Communication Systems Over Nakagami-m
Fading Channel
Authors:
Hassan Sajjad
Muhammad Jamil
Date: 2012-11-12
Subject: Electrical Engineering
Level: Master Level
Course code: 5ED06E
To our parents, family, siblings, friends and
teachers
1
Science can purify religion from error and superstition. Religion
can purify science from idolatry and false absolutes.1
John Paul II, Pope
1Reston, Galileo, A Life, HarperCollins, NY, 1994, p 461
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Abstract
This work examines error rate performance of Multi-Hop communication systems, employing SingleInput Single Output (SISO) transmissions over Nakagami-m fading channel. Mobile multi-hop relaying(MMR) system has been adopted in several Broadband Wireless Access Networks (BWAN) as a cost-effective means of extending the coverage and improving the capacity of these wireless networks. In aMMR system, communication between the source node and destination node is achieved through anintermediate node (i.e., Relay Station). It is widely accepted that multi-hop relaying communicationcan provide higher capacity and can reduce the interference in BWANs. Such claims though have notbeen quantified. Quantication of such claims is an essential step to justify a better opportunity for widedeployment of relay stations.
In this thesis, Bit Error Rate (BER) of multi-hop communication systems has been analysed. Differ-ent kinds of fading channels have been used to estimate the error rate performance for wireless transmis-sion. Binary Phase Shift Keying (BPSK) has been employed as the modulation technique and AdditiveWhite Gaussian Noise (AWGN) has been used as the channel noise. The same Signal to Noise Ratio(SNR) was used to estimate the channel performance. Three channels were compared by simulating theirBER, namely, Rayleigh, Rician and Nakagami. Matlab has been used for simulation.
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Acknowledgements
In the name of Allah Almigty, the most merciful the most beneficent, the Creator, the most Graciousand the Wise, whose help and support are unbounded and gave us patience and ability to reach thisstage of knowledge.
We would like to thank Prof. Sven Nordebo for his supervision, valuable time and advices and supportduring this thesis work. We would also like to thank the Swedish Government for giving us an opportunityto study in this wonderful education system and experience Swedish life.
Thanks to all the friends whose moral support and motivation guided us through our stay in Swedenand providing a home away from home. Thanks to Mr. Ishtiaq Ahmad for his invaluable help andsuggestions. Last but not the least, it wouldn’t have been possible without the countless prayers andlove of our parents, grand parents and siblings. We are thankful to all our family for their support andencouragement.
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Contents
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1 Introduction 81.1 Thesis Contribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91.2 Thesis Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2 Multi-Hop Networks 102.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.2 Single & Multi-Hop Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2.1 Single Hop Wireless Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.2.2 Multi-Hop Wireless Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.3 Relay Station . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.3.1 Stationary Relay Station . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.3.2 Mobile Relay Stations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.4 Relayed Transmissions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.5 System and Channel Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.6 Mobile Multi-Hop Relay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3 Fading Channels 163.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163.2 Fading in Wireless Communication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163.3 Nature of Multipath Propagation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163.4 Rayleigh Fading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.4.1 Applicability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183.4.2 Generating Rayleigh Fading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183.4.3 Related Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.5 Rician Fading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193.5.1 Related Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.6 Nakagami Fading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203.6.1 Generating Nakagami Distribution . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.7 Mitigating Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213.7.1 Diversity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213.7.2 Channel Coding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
4 Simulation Results 224.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224.2 Generating Fading in Matlab . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
4.2.1 Rayleigh Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224.2.2 Rician Fading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224.2.3 Nakagami-m Fading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
4.3 Important Concept for Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234.4 Simulation Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234.5 Discussion of Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
4.5.1 Varying Gain of Relay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
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CONTENTS CONTENTS
5 Future Work 285.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285.2 Thesis Contribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285.3 Future Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295.4 Types of MIMO Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
5.4.1 SISO System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295.4.2 SIMO System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295.4.3 MISO Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295.4.4 MIMO Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
5.5 Channel Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30Bibiliogrpahy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
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List of Figures
2.1 Single-Hop Network Topology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.2 Multi-Hop Network Topology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.3 Stationary Relay Stations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.4 Mobile Relay Stations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.5 Relay in a network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.1 Doppler Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
4.1 Rayleigh Fading: BER vs SNR for single and dual hop systems . . . . . . . . . . . . . . 254.2 Rician Fading: BER vs SNR for single and dual hop systems . . . . . . . . . . . . . . . 254.3 Nakagami Fading: BER vs SNR for single and dual hop systems . . . . . . . . . . . . . 264.4 Nakagami Fading: BER vs SNR for five hops . . . . . . . . . . . . . . . . . . . . . . . . 264.5 Nakagami for different m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274.6 Varying Gain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
5.1 SISO System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295.2 SIMO System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295.3 MISO Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305.4 MIMO Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
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CHAPTER 1
INTRODUCTION
The era of wireless communications started when the first generation (1G) of wireless cellular systemswas launched in the early 1980s. These systems utilized analogue air interface and supported voice appli-cations only. With the higher user demand for cellular services and the increased need for better qualityof service (QoS), the second generation (2G) of wireless cellular systems was introduced. 2G utilizeddigital air interface, providing higher bandwidth and better voice quality. In addition to supporting voiceapplications, 2G had the capability to support limited data applications. The capabilities of supportinghigher bandwidths and better voice quality have led to the tremendous popularity of 2G wireless cellularsystems, which were successfully deployed and attracted a large number of users around the world.
The remarkable success of 2G wireless cellular systems, however, together with the continuous growthof the Internet have resulted in an increased demand for wireless data services any time and anywhereusing any wireless device. This has motivated the development of the third generation (3G) wirelesscellular systems for better QoS and a higher capacity support. One of the 3G systems is Universal MobileTelecommunications System (UMTS) that was developed by the 3rd Generation Partnership Project(3GPP) [1]. UMTS has the capability to support a transmission rate of up to 2 Mbps, consequently tooffer new data services.
The increased demand for supporting new applications with a higher data rate, led to the needfor data rates beyond what is supported by current 3G wireless systems. To fulfil the support forsuch high data rate, Broadband Wireless Access Systems (BWASs) have been developed. For example,3GPP is developing a new standardized system called Long Term Evolution (LTE) [2]. The LTE hasbeen introduced as an evolutionary step for UMTS in terms of capacity and architecture improvements,therefore it provides higher data rates, and improved coverage and spectrum efficiency [2]. The LTEsystem supports data rates greater than 100 Mbps, and efficiently utilize the spectrum using an OFDMsystem. Another BWANs is the Worldwide Interoperability for Microwave Access (WiMAX), which hasbeen standardized by the IEEE 802.16 group [5]. WiMAX is a BWANs that has the capability to supportdata rate up to 70 Mbps.
BWANs such as LTE and WiMAX have gained tremendous attention lately for leveraging the supportof a wide range of applications with different Quality of Service (QoS) requirements. Despite the supportfor such range of applications, satisfying the different QoS requirements while maximizing the networkcapacity and extending the network coverage are still major issues in these networks. Mobile Multi-hoprelaying (MMR) system has been adopted in several BWANs such as LTE-advanced (Release10) [3], [4],and WiMAX (IEEE802.16j) as a cost-effective means of extending the reach and/or capacity of thesewireless networks. The emerging MMR extension enhances the conventional BWANs to enable support ofmulti-hop communication between a mobile station (MS) and a base station (BS) through intermediaterelay stations (RSs) [6].
As mentioned above many of the applications in wireless communication require high data rate.Higher the date rate higher the required bandwidth for transmission. However, due to bandwidthlimitations, it is mostly impractical and sometimes expensive to increase the bandwidth. in that casethere is another solution to the problem, that is, using multiple transmit and receive antennas. Multiple
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1.1. THESIS CONTRIBUTION CHAPTER 1. INTRODUCTION
antennas can be used to achieve transmit diversity or Multiple-Input-Multiple-Output (MIMO) channels.More detailed explanation of MIMO will be given in the further sections.
In wireless communication, the signal can be attenuated with time while propagating over a certainmedia. The fading, attenuation can vary with time, geographical location and/or radio frequency so itis often modelled as a random process. A fading channel is a communication channel comprising fading.In wireless communication fading is mostly due to multipath propagation or shadowing which affectsthe wave propagation. There are different fading models that can be used to estimate the fading over achannel, e.g.,
• Nakagami fading
• Log-normal shadow fading
• Rayleigh fading
• Rician fading
• Weibull fading
This thesis work examines the error rate performance of multi-hop MIMO communication systemsover Nakagami-m fading channel. In multi-hop communication systems the transmitter (usually BaseStation) and the receiver (Mobile Station) does not have a direct connection. They are connected througha Relay Station (RS) which helps in the transmission from MS to BS and vice versa. The relay stationhas many advantages but also has some drawbacks which will be discussed in the coming sections.
1.1 Thesis Contribution
BWANs such as LTE and WiMAX are proposed to give high data rates and better Quality of Service(QoS) to the end users. The Mobile Multi-hop Relay (MMR) system is adopted in both LTE-advancedand WiMAX to extend the coverage area and control the power issues. In this thesis the objectives areto;
• Provide an expression for the end to end Signal to Noise Ratio (SNR) of a two-hop and multi-hoprelay networks.
• The capacity of the above system will also be analysed and presented.
1.2 Thesis Organization
This thesis is divided into different chapters. Chapter 1 is the introduction and gives an overview of thewhole report. Chapter 2 is about Multi-hop networks, gives an insight into the background and relatedwork that has been carried out on multi-hop communication systems. Chapter 3 is about different fadingchannels which were considered during this study, namely, Rayleigh, Rician and Nakagami. Chapter 4includes the discussion and presentation of the results. Chapter 5 is the conclusion drawn from the thesisand discuss possible directions for future research work.
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CHAPTER 2
MULTI-HOP NETWORKS
2.1 Introduction
In the recent years there have been many technological innovations in the field of communication. Broad-band Wireless Area Networks (BWAN), Long Term Evolution (LTE) have become very famous. Thereason being that there is a high demand for high data transfer, online interactive games and a very highquality of service is required by the users. These requirements can only be fulfilled by high data transferwhich in turn requires high bandwidths. However, as soon as high frequency is used, it gives rise toother problems for example high attenuation, deviation of the transmitted signals and distortion. Therate of attenuation is high in higher frequencies as compared to the lower frequencies. So as a result,the communication cell size is reduced and consequently it leads to the installation of more base stations(BS). There are many solutions to these problems, however a cheaper solution is usually required. Oneof the many solutions will be discussed in the upcoming sections i.e., the use of Relay Networks (Relayedtransmission).
Multi-hop transmission is a combination of short links to cover a long distance communicationnetwork using many intermediate relaying terminals in between the transmitter and the receiver. Thereare many benefits of using relayed transmissions, the most important is that the transmit power requiredby both, the transmitter and receiver, reduces by a great amount and it ultimately improves the batterylife. Dual-hop transmission was first come across in the bent pipe satellites where the main idea wasto relay uplink carrier into downlink. This concept has also become famous in wireless communicationsystems in the recent years [17].
The most common performance assessment criterion for a digital system in literature is bit errorrate (BER). Average BER is the ratio of erroneous bits at the receiver, on average. It is a function ofthe fading model of the channel and the types of receivers employed. Moreover, average BER is also afunction of the type of modulation used at the transmitter. This performance criterion is used to assessthe performance of non-regenerative multi-hop communication system (See more in Chapter 4).
2.2 Single & Multi-Hop Systems
This section covers two types of hops namely single and multi-hop along with introduction of RSs toachieve multi hoping with different modulation techniques. Rather than having a direct single hopcommunication between base station and mobile terminal, the transmission is spread out on severalrelay terminals acting as repeaters, opens the new face of technology known as Multi-hoping.
2.2.1 Single Hop Wireless Networks
Current cellular wireless network (e.g., GSM, CDMA, and IEEE 802.16) invariably confines its operationto a point-to-multipoint topology, wherein two and only two types of network entity, namely base station(BS) and mobile station (MS), can exist. As illustrated in figure 2.1, a centralized control entity (i.e.,
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2.2. SINGLE & MULTI-HOP SYSTEMS CHAPTER 2. MULTI-HOP NETWORKS
Base Station (BS)) has the sole authority to manage and coordinate the communications initiated by orterminated at the end users (i.e., Mobile Station (MS)) that are in the direct transmission range of theBS. Regardless of whether the communication is between two MSs that are directly associated with theBS, or is between an MS and an external network entity, all the traffic have to pass through the BS.
Figure 2.1: Topology for single hop point to multi-point wireless networks
2.2.2 Multi-Hop Wireless Networks
The wireless network where relays will be deployed can be divided into two distinct categories, as il-lustrated in figure 2.2a and figure 2.2b. In both figures, the solid arrowed lines are used to connectthe network entities that are one hop away from each other, and thus can directly communicate witheach other. Meanwhile, dotted arrowed lines represent the possible communication between two networkentities that logically have multiple hops in between.
(a) Topology I (b) Topology II
Figure 2.2: Different topologies for Multi-Hop Relay Wireless Network
The key difference between the two network topologies is that RSs and MSs in figure 2.2a are probablyable to receive from and transmit to the network entities which are more than one hop away from themdirectly, provided that proper modulation and coding schemes are selected. In figure 2.2b, however,radio signal propagation can only reach the stations that are one hop away from the transmitter. For
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2.3. RELAY STATION CHAPTER 2. MULTI-HOP NETWORKS
example, MS3 in figure 2.2a can be engaged in direct transmission with not only BS, but also RS2 andRS3. Meanwhile, MS3 can only establish a direct communication with RS3 in figure 2.2b.
2.3 Relay Station
Relays are part of a communication network that are dedicated to storing, amplifying and forwardingdata received from the BS to the user devices, and vice versa. Unlike the BS, they are not connected to awired line network through a back-haul connection. They rely on wireless transmission to communicateto the BS. Relays, at times, need additional power but still they are cheaper than installing a BS dueto their limited functionality. Deploying relays can really help improve performance for MS that are onthe edge of the cell and are affected by fading and they also have the potential to solve the coverageproblem for high data rates in macro-cells. Cellular-relay networks could be such that the relay-to-userlinks use a different spectrum than base-to-user links [15]. For example, the relays could communicateto the users through a wireless local area network operating on, say, the IEEE 802.11 network standard,in which case the relays are like access points and use the unlicensed band, while the BS transmits tothe relays using the cellular-network spectrum. Such a cellular relay network is proposed in [14].
Relays can improve the performance of a cellular network in two main ways. Firstly, the placementof relays in a cell reduces the propagation losses between the relay transmitters and the user terminals,which result in increasing the data rates over the link. However, some of this gain can be offset becausethe base has to transmit to the relay using the same spectrum. The other reason to expect performancegains is multiple simultaneous transmissions that are possible within the cell by using relays. Thesimultaneously transmitted signals may also interfere with each other, which can reduce the link rates.Therefore, a careful choice of which links are active during each time slot is very important for the desiredimproved performance.
The relay station is connected to the base station on one side and to a group of mobile stations onthe other. The connection to the base station, where the relay acts more or less as a subscriber/mobilestation, is called the relay link, while the connection to the mobiles, where the relay acts as a simple basestation, is called the access link. Two types of relay stations are described in the following subsections.
2.3.1 Stationary Relay Station
Multi-hop scheme allows all the mobile users as well as the base stations to reduce the transmit power.This saves battery life and also extend the range. As an example, considering the scenario illustratedin figure 2.3a, where a mobile terminal (MS) is far from the nearest base station. In a conventionalcellular network MS is required to increase transmit power to reach BS and the same applies for thebase station. In a multi-hop system the transmission takes place at a lower power level by allowingMS to communicate with a neighbouring relay station (RS), which then relays the signal further tothe base station. Naturally, there could be more than one relay-mode relay terminal involved in thecommunication link. There is an upper limit on the number of relays that can be used with a single basestation and hence limits the range of a particular base station, the limit is set by the latency allowedwithin a certain cellular environment.
On many occasions there is no line-of-sight between a mobile terminal and the base station. A typicalsituation in an urban environment would be a base station located around the corner of a building asshown in figure 2.3b. The signal attenuation over such a propagation path may be very high, demandingmuch larger transmission power than would be necessary for covering the mere distance. In multi-hopsystems such a case may be dealt with much greater efficiency. A relay terminal located at the cornerhas a line-of-sight to both communicating parties and it can relay the signal with much lower loss in thepropagation path.
2.3.2 Mobile Relay Stations
Mobile Relay Station (MRS) is a relay station that is intended to function while in motion. MRSmobility is constrained by the same limits as a Mobile Station (MS) in IEEE 802.16e-2005. Relays maybe installed nomadic (transportable, e.g. on trucks) or mobile (on buses, trains, etc.).
Figure 2.4 demonstrates the concept of a multi-hop network, including an MRS mounted on a busthat provides service to passengers on board. As the MRS moves within an area, it will have to performhandover between different base stations (when crossing from one network cell to another). At the same
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2.4. RELAYED TRANSMISSIONS CHAPTER 2. MULTI-HOP NETWORKS
(a) Reducing Transmission Distance by a Multi-Hop Communication
(b) Circumventing Shadowing byMulti-Hop
Figure 2.3: Stationary Relay Stations
time the group of mobile stations it supports will also change dynamically over time. The physicallayer mode used in each cell is determined by the base station that serves it. As the propagationenvironment differs from cell to cell (e.g. urban, suburban, rural), different base stations may requiredifferent physical layer modes. While simple terminals, supporting only the mandatory modes, are stillbackwards compatible with all base stations, they need to be able to support the advanced modes inorder to take advantage of them. The same holds for a MRS that acts as a terminal on the relay link.
Figure 2.4: Mobile Relay Stations
2.4 Classification of Relayed Transmission
Depending on the nature of complexity of the relays, relayed transmission systems can be classified intotwo main categories, namely, regenerative or non-regenerative systems.
1. In regenerative systems, the relay fully decodes the signal that went through the preceding hop andretransmits the decoded version into the next hop. This is also referred to as decode-and-forward(D&F) or digital relaying.In these systems, noise propagation from hop to hop is prevented whilerisking the probability of making an error in detecting the signal at each hop.
2. Non-regenerative systems do not perform any kind of decoding, the signal is received, amplifiedand forwarded to the next station. That is why it is sometimes referred to as amplify-and-forward(A&F) or analogue relaying. This kind of relaying is more useful when the carried information istime sensitive, such as voice and live video.
Non-regenerative relay systems can in turn be classified into two sub categories namely (i) ChannelState Information (CSI)-assisted and (ii) blind relays. Non-regenerative systems with CSI-assisted relaysuse instantaneous CSI of the preceding hop to control the gain introduced by the relay and as a resultfix the power of the retransmitted signal. In contrast, systems with blind relays do not need any kindof channel state information from the preceding hops, in these systems amplifiers are installed which
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2.5. SYSTEM AND CHANNEL MODELS CHAPTER 2. MULTI-HOP NETWORKS
amplifies the received signal with a fixed gain therefore it has a variable transmit power. The transmittedpower depends on the power of the received signal at the relay station. If the received signal power ismore, after amplification the transmit power will be higher. These blind relays do not perform as wellas the CSI-assisted relays, however their low complexity relative to other relays make them a suitablechoice from a practical point of view [7].
2.5 System and Channel Models
To briefly explain system and channel models we can take an example of a three terminal network whichcomprises of a base station (BS), relay station (RS) and a mobile station (MS). The scenario can be seenin figure 2.5, where the BS is communicating with a MS through a RS. The BS is transmitting a messagesignal m(t) with an average power, Pavg, if β1 and B2 represent the fading amplitude of the channelsbetween the BS to RS and RS to MS, respectively, then the received signal at the RS can be written as,
RRS(t) = β1m(t) +N1(t) , (2.1)
where N1(t) is an additive white Gaussian noise (AWGN) signal with a power of np1 at the input of RS.When the signal is received at the RS, it is multiplied by a certain relay gain, γ. Gain of the relay isdependent on the relay being used in the system. Some relays have a fix amplification and others havevariable amplifications depending on the power of the received signal. If a high power signal is receivedthe amplification performed at the relay is adapted according to that, in order to avoid saturation of therelay. In this work, fixed relays are used and so when the signal is received at the BS, it has the followingform,
RBS(t) = β2γ(β1m(t) +N1(t)) +N2(t) , (2.2)
where β2 is the fading amplitude of the channel between terminals RS and BS and N2(t) is an AWGNsignal with power np2 at the input of BS. Signal to noise ratio (SNR) at the BS can be written as [17]
SNR =
Pavgβ21
np1
β22
np2
β22
np2+ 1
γ2np1
. (2.3)
It is evident from the above equation that the choice of gain, γ, will effect the SNR. A fixed gain hasbeen suggested in [16] which is used in this thesis work. Gain is the ratio of the transmit power of therelay to the input power at the relay terminal and is given below
γ =
√PT
Pavgβ21 + np1
, (2.4)
where PT is the power of the transmitted signal at the output of the relay. There can be other gainsthat maybe used, for example, when using regenerative systems as mentioned earlier. However, in thisthesis the above gain has been used for the relays so that the result can be compared with the previousliterature and also to compare different fading channel models. It is important to mention that, thechoice of an optimal gain is important because SNR is highly dependant on the choice of gain and SNReffects the BER (explained in Chapter 4).
Figure 2.5: Relayed communication
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2.6. MOBILE MULTI-HOP RELAY CHAPTER 2. MULTI-HOP NETWORKS
2.6 MOBILE MULTI-HOP RELAY (MMR)
Mobile multi-hop relay (MMR) system has the ability to enhance the performance of the existing systemsby introducing the use of relay stations. The primary goals are to,
• Extend coverage area
• Enhance system capacity
• Saving battery life of SS and BS and
• Minimization of RS complexity
This new idea is backward compatible and conventional SS terminals will be able to work normally inthe MMR enhanced infrastructure. However, the BS has to be modified to allow communication with RSand to be able to support traffic from multiple RSs. To achieve the best possible results the placementof RS must be carefully chosen. Three kinds of RS are defined: fixed, nomadic and mobile.
• Fixed RS is permanently installed at a fixed location.
• Nomadic RS are fixed at a certain location for a period of time.
• Mobile RS is installed on moving vehicles such buses and trains.
In some cases SS may also act as relay station. When a MS is experiencing fading, either due to multipathpropagation or shadowing, the problem can be taken care of by using relay systems and allow the MS tohave full functionality. Relayed transmissions may also be used to extend the coverage area by extendingthe range at the edge of the cell which also allows a better indoor coverage. Another example of aninteresting usage model is to use fixed relays to provide fixed access on mobile platform such as bus,train or ferry.
Even though the systems are backward compatible and support the existing infrastructure there arestill many technical challenges and requirements. These technicalities must be taken care of when stan-dardizing for example routing, managing radio resources, power control, frequency usage consideration,the choice of antennas being used, network management and the security of RS is also and importantconcern.
Page 15 of 33
CHAPTER 3
FADING CHANNELS
3.1 Introduction
In wireless communication radio waves propagate from the transmitting station to the receiver stationwhile passing through free space. During this travel time the waves have to go through absorption,reflection, refraction, diffraction, and scattering. Ground terrain, atmosphere, buildings, bridges, hills,trees and many other things affect the waves. For these reasons the signal received at the receiver stationis not exactly as the one transmitted.
Mostly in the cellular systems, the height of the antenna is smaller that the surrounding structures.Hence, line-of-sight (LOS) communication between the transmitter and the receiver is highly impossible.In these circumstances the communication is mostly due to reflection, refraction, diffraction and scat-tering from different structures in the surrounding environment. Therefore, signals arrive at the receivervia several paths and different time delays which give rise to multipath communication.
3.2 Fading in Wireless Communication
When these signals arrive at the receiver, they have distributed amplitudes and phases. These randomamplitudes and phases combine either constructively or destructively, mostly the later case. This causesnoticeable fluctuations in the received signal amplitude. This phenomenon is called fading [10].
There are different kinds of fading, small scale fading is the fluctuation in the signal amplitude due tolocal multipath propagation. Whereas, long-term variation in the mean signal level is called large-scalefading [10]. The latter effect is due to the travel of the signals over long distances that can cause a lot ofvariations in the overall path between the transmitter and the receiver. Large-scale fading is also knownas shadowing, because this usually occurs when the MS moves into the shadow of taller objects such asbuildings and hills. Due to multipath, a moving receiver can sometimes experience several fades in avery short period of time. In the worst case scenario the MS may stop at a location where the signal isin deep fade which can be very concerning for maintaining good communication.
To fully understand wireless communication it is important to know what happens to signals whenthey travel from a transmitter to a receiver. One of the important aspects of the path between transmitterand receiver is fading. Therefore, different channel fading models have been introduced which helps inestimating the channel response between transmitters and receivers. One can find the bit error rate(BER) according to a certain signal to noise ratio (SNR), channel capacity can also be determined andultimately one can find which channel model best fits the real time communication scenarios. Some ofthe many fading channel models have been discussed in the following sections.
3.3 Nature of Multipath Propagation
When a radio signal is radiated away from a broadcast antenna it spreads out in different directions.These waves will encounter reflecting surfaces and the wave will scatter off these surfaces. As mentioned
16
3.4. RAYLEIGH FADING CHAPTER 3. FADING CHANNELS
Figure 3.1: Angle of arrival αn
of the nth incident wave illustrating the Doppler effect
earlier, in an urban environment, the waves might reflect, refract, diffract off buildings, moving trains,air planes and other objects.
Multipath propagation occurs when a radio signal takes two or more different paths after it istransmitted from the antenna and before its reception on the receiving antenna. A direct ray, travelsdirectly from the transmitter to the receiver. It is usually (not always) the strongest signal of all thesignals that reach at the receiving antenna. The other signals (rays) arrive at the receiving antennathrough indirect paths (after going through reflections, refractions, diffractions). Even though these raysfind a way to the reach the receiver but they arrive with different angles and time delays. They also takemore time in reaching the receiver and usually have a weaker power than the direct signals. Dependingon the phase of each partial wave the superposition at the receiver can be constructive or destructive.The distortion caused by the multipath phenomenon have to be compensated at the receiver side, forexample, by an equalizer
Besides the multipath propagation, Doppler effect also has a negative effect on the transmissioncharacteristics of the mobile radio channel. Due to the movement of the transmitter/receiver there is afrequency shift in each of the partial waves. The angle of arrival αn, is defined by the direction of arrivalof the nth incident wave and the direction of motion of the mobile unit [18] as shown in Figure 3.1. αndetermines the Doppler frequency (frequency shift) of the nth incident wave according to the relation
fn = fmax cosαn , (3.1)
where fmax is the maximum Doppler frequency related to the speed of the mobile unit v, the speed oflight c, and the carrier frequency f [18] by the equation
fmax =v
cf. (3.2)
Multipath propagation, with the movement of transmitter or receiver, leads to rigorous and randomfluctuations if the received signal. Depending on the speed of the receiver and the carrier frequency,fades of 30 to 40 dB below the mean value of the received signal level can occur [18].
There are different ways of modelling a communication channel which is useful. These channel modelscan help in modelling the important statistical properties of real world communication systems and canalso give an idea of the signal amplitudes of the transmitted signals that can be expected at the receiverside. The make use of different probability density functions to be able to perform these estimations.They can also give an idea of the level crossing rates and the duration of fading. Some of the statisticalmodels are explained in the following sections.
3.4 Rayleigh Fading
As mentioned in the earlier sections, when a radio wave is propagated through a communication channel,there are different factors that effect its propagation between the transmitter and the receiver. Different
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3.4. RAYLEIGH FADING CHAPTER 3. FADING CHANNELS
statistical models have been presented which help in the modelling of communication channels. Rayleighfading is one of the model for estimating the effect of propagation environment on a radio signal. Itstates that when a signal passes through a communication channel its amplitude will fade randomly,according to Rayleigh distribution [19]. Furthermore, it assumes that there is no line of sight (LOS)communication between the transmitter and the receiver and that a multipath propagation environmentexist as well. If there is a strong line of sight component of the signal at the receiver, Rician fading (tobe discussed shortly) may be more applicable.
The mobile station antenna does not always receive the transmitted signal over LOS. It receives anumber of reflected, diffracted and scattered waves as a result of multipath propagation. As a result thephases are random and ultimately, the received power also becomes a random variable. The transmittedsignal with a frequency fc may reach the receiver via a number of paths, the jth path having an amplitudeAj , and a phase φj [10]. If we assume that there is no direct path or line-of sight (LOS) component, thereceived signal m(t) can be expressed as
m(t) =
N∑j=1
Aj cos(fc + φj) , (3.3)
where N is the number of paths. The phase φj depends on varying path lengths, changing by 2π whenthe path length changes by a wavelength. Therefore, the phases are uniformly distributed over [0, 2π].
When there are a large number of scatterers in the channel that affect the signal at the receiverand there is no LOS between the transmitter and the receiver, Rayleigh fading is used to estimate thechannel performance. Its probability density function (pdf) is
PR(r) =2r
Ωexp−r/Ω, r ≥ 0 , (3.4)
where R is a random variable with Rayligh distribution and Ω is given by
Ω = E(R2). (3.5)
Rayleigh distribution is characterized by the single parameter Ω. Rayleigh fading channels are usedto simulate high frequency communication for example, ionospheric communications. Unfortunately, itdoes not simulate this sort of communication with a reliable accuracy. [12].
3.4.1 Applicability
Whenever, a communication channel has to go through many scatterers this means Rayleigh fading canbe a useful model for that scenario. In such situations there is no LOS between the transmitter andthe receiver and scatterers such as buildings, trees, dust and many other objects causes attenuation,reflection, refraction and diffraction in the transmitted signal. In long distance and high frequencycommunication such as ionospheric and tropospheric signal propagation the particles in the atmospherealso act as scatterers which can be approximated by Rayleigh fading. Rayleigh fading is a small scaleeffect. There are different properties of the environment for example path loss and shadowing which aresuperimposed by fading. The speed with which the channel fades is affected by how fast the receiverand/or transmitter are moving (Doppler effect).
3.4.2 Generating Rayleigh Fading
There are different ways of generating Rayleigh distribution from other distributions. For example,Rayleigh distribution can be generated (shown in [20]) from:
1. Exponential Distribution, Suppose X is an exponentially distributed random variable. It canbe transformed into Rayleigh distribution by the following transformation:
R =√X. (3.6)
2. Normal Distribution, Let x and y be two normally distributed random variables then Rayleighdistribution is given by
R =√x2 + y2. (3.7)
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3.5. RICIAN FADING CHAPTER 3. FADING CHANNELS
3.4.3 Related Distributions
Rayleigh distribution is also related to the following distribution as shown in [19],
• R ∼ Rayleigh(σ) is Rayleigh distributed if R =√x2 + y2, where x and y are independent normal
random variables.
• If R ∼ Rayleigh(1), then R2 has a chi-squared distribution with parameter N , degrees of freedom,equal to two (N = 2): [Q = R2] ∼ χ2(N).
• The Rice distribution is a generalization of the Rayleigh distribution.
3.5 Rician Fading
It has been seen that the signal arriving at the mobile comprises a number of copies of the original signaldue to the multipath effect. This is mostly common in urban areas where it is difficult to establisha LOS between the transmitting station and the receiver. However if there are some open areas, thedirect signal may reach the receiver with some attenuation. In such case, when there is a strong directcomponent of the signal at the receiver Rayleigh fading is no longer valid.
Rice distribution is different from Rayleigh in the sense that Rice assumes a direct LOS path be-tween the transmitter and the receiver along with the multipath waves that arrive at the receiver. Theprobability distribution function can be written as
p(r) =r
σ2exp
−r
2 +A2
2σ2
J
(rA
σ2
), r ≥ 0 , (3.8)
where J() is the 0th order modified Bessel function of the first kind [21].
J(z) =
∞∑n=0
z2n
22nn!n!for z 1. (3.9)
There are two cases in this distribution:
• If A = 0 (absence of dominant signal), p(r) becomes Rayleigh distribution.
• If A is large (dominant signal), p(r) becomes a Gaussian distribution.
In the second case, the transmitted signal given in Eq. 3.3 can be written as
m(t) =
N−1∑j=1
Aj cos(fc + ωdjt+ φj) +A cos(fct+ ωdt) , (3.10)
where the constant A is the strength of the direct component, ωd is the Doppler shift along the LOSpath, and ωdj are the Doppler shifts along the indirect paths. The probability density function is givenin [11].
Rician distribution is mostly described by the Rician factor K, which is defined as the ratio betweenthe power of the direct path and the power of the indirect paths [21]. The value of K can be expressedin decibels as
K(dB) = 10 log10
(A2
2σ2
). (3.11)
In Eq. 3.11, if A goes to zero then the direct path is eliminated and the envelope distribution becomesRayleigh with K(dB) = −∞
3.5.1 Related Distributions
Rician distribution is related to the following distributions with the parameters as described below [22]:
• R ∼ Rice(γ, ω) has a Rice Distribution if R =√X2 + Y 2 where X ∼ N(γ cos θ, ω2) and Y ∼
N(γ sin θ, ω2) are independent normal random variables and θ is any real number.
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3.6. NAKAGAMI FADING CHAPTER 3. FADING CHANNELS
• Also, if R ∼ Rice(γ, ω) comes from the following steps:
1. Generate P having Poisson distribution with parameter λ = γ2/2ω2.
2. Generate X having a chi-squared distribution with 2P + 2 degrees of freedom.
3. set R = σ√X.
• If R ∼ Rice(γ, ω) then R ∼ Rayleigh(ω) and R2 has an exponential distribution.
3.6 Nakagami Fading
Nakagami distribution has the ability to describe both Rayleigh and Rician distributions [10]. Rayleighdistribution failed to estimate the channel behaviour over long distances and high frequencies, this waswas first observed by Nakagami. He also, suggested a parametric gamma distribution based densityfunction, to describe the experimental data he obtained. Later it was also shown by different researchersusing real life data that was best explained by the model provided by Nakagami rather then other modelslike Rayleigh and Rician. Nakagami also provides best fit to the mobile communication channel dataand other deep space communications [12].
Unlike the Rician distribution, Nakagami distribution does not assume a LOS conditions between thetransmitter and the receiver, it uses a parametric gamma distribution-based density function to describethe experimental data and get approximate distribution, the PDF of Nakagami distribution is
f(r) =2mmr2m−1
ΩmΓ(m)exp
−mr
2
Ω
, m ≥ 1
2: r ≥ 0 , (3.12)
where m is Nakagami scale parameter (fading parameter), it describes the fading degree of the propa-gation media due to scattering and multipath interference processes. When m → ∞ Nakagami fadingchannel becomes a non-fading channel. and Ω is the average power of multipath scatter field, Γ(m) isthe gamma function [12]. The parameters m and Ω can be estimated as following:
m =E2[X2]
V ar[X],
andΩ = E[X2].
Rayleigh and Rician can be considered the special cases of Nakagami distribution. When m = 1,Nakagami behaves as Rayleigh distribution, with an exponentially distributed instantaneous power. Form > 1, the fluctuations of the signal strength reduce compared to Rayleigh fading and with higher valuesof m less sever channels can be modelled. For m = 0 the Nakagami acts as Rician Distribution.
3.6.1 Generating Nakagami Distribution
The nakagami distribution is related to gamma distribution. It is possible to obtain a Nakagami randomvariable from a gamma distribution. Let Y ∼ Gamma(k, θ), then it is possible to get a random variableX ∼ Nakagami(m,Ω), by setting k = m, θ = Ω/m, and taking the square root of Y :
X =√Y .
Nakagami distribution can also be generated from the chi-squared distribution with the followingsettings. Let 2m be an integer, then nakagami distribution f(y;m,Ω) can be generated with the param-eter k set to 2m and then following it by the scaling transformation. This can be checked by performingthe following transformation on the pdf of a Chi-distribution as below [23]:
y =√
(Ω/2m)x .
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3.7. MITIGATING TECHNIQUES CHAPTER 3. FADING CHANNELS
3.7 Mitigating Techniques of Fading Channels
Fading causes many problems in wireless communication systems. There are different methods of re-ducing the effects of fading channels. Some of them are discussed below in detail. Equalization mayfix most of distortion caused by the channel but it may not amplify a signal that is going through avery deep fade. At times when the fading is deep it can be very difficult sometimes, even impossible, torecollect the transmitted signal. To avoid losing the data due to deep fading diversity combining can bebe employed.
3.7.1 Diversity
The concept of diversity combing suggests that if more than one transmitting/receiving antennas are usedfor reception/transmission of the signal, the probability that deep fades will occur on all the antennasat the same time is lower than the probability that deep fades will occur on one of these antennas.Therefore, signals received from different antennas can be combined in different ways to reduce the effectof deep fades to a great amount, which ultimately improves the reception quality. There are differentmethods of combining the signals to improve the reception, given below:
1. Selective Diversity: All the signals are weighted to make sure that they have the same SNR,the signal with the highest amplitude is used for reception. This strongest signal among all thesignals is then used for reception.
2. Scanning Diversity: In this technique the signals are compared to a threshold value, whenone is found that signal is then used for reception regardless of its power compared to othersignals. However, if the power of the signal drops below the threshold value the scanning processis repeated and another signal is used for reception with its power greater than the threshold.
3. Maximal Ratio Combining (MRC): Signals are weighted according to their SNR and thenadded together. Before that it must be assured that they have the same phase in order to getconstructive addition. The signals can also be delayed to make sure that they have the samephase.
3.7.2 Channel Coding
After using equalization and different diversity techniques to reduce loss or corruption of data, there stillmay be bits that contain errors. Channel coding is the next step that can be taken, it helps in reducingthe probability of errors in the data. Redundant bits are added to the data which can help in detectingerrors in the receiver and also correct them at times. The higher the number of redundant bits the higherthe chances of detection and correction of data at the receiver.
Some of the famous channel coding techniques are given below:
1. Block Codes: These are the simplest type of codes. The data is divided into blocks. Redundancybits are added to each block of data. The redundancy allow error detection and sometimes it cancorrect the detected errors at a low level. Hamming code is one of the types of block codes.
2. Convolution Codes: In this technique, the data is convolved with a particular polynomial. Atthe receiver the data is divided by the same polynomial used in the encoder. If the result afterdivision is 0, there are no errors. If the result is non-zero, errors have occurred and the result canbe used to locate the location of error.
3. Turbo Codes: Multiple convolution encoders and decoders along with interleaving (spreadingthe bits so that bits with errors are separated from each other ) are used. Shannon channelcapacity limit is almost reached with turbo coding, that is why it has advantage over other codingtechniques .
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CHAPTER 4
SIMULATION RESULTS
4.1 Introduction
Researchers have been using different software tools to simulate the channel estimation for various com-munication systems, for example, OPNET, LabView and Matlab just to name a few. In this thesiswork Matlab was used to simulate bit error rate (BER) performance versus signal to noise ratio (SNR)for multi-hop communication systems over various fading channels. This chapter gives an insight intowhat steps were carried out to perform the required simulations. Different channels (mentioned inChapter 3) were simulated and the graphs for various calculations are presented in the sections to follow.
4.2 Generating Fading in Matlab
Three different distributions, Rayleigh, Rician and Nakagami-m, have been analysed. A detailed ex-planation of these distributions can be found in sections 3.4, 3.5 and 3.6, respectively. The followingsubsections will describe how these channel distributions were generated based on their description intheory.
4.2.1 Rayleigh Distribution
There are different ways of generating Rayleigh distributions in Matlab, the method used in this workis given below, which on comparison with other standard methods as mentioned in Section 3.4 showedthe same result. A snippet of the code is shown below,
sigma = s q r t (10.ˆ(−SNR/ 1 0 ) ) ;n1 = 1/ s q r t ( 2 ) ∗ [ randn (1 , n r d a t a b i t s ) + j ∗ randn (1 , n r d a t a b i t s ) ] ∗ sigma ;h1 = 1/ s q r t ( 2 ) ∗ [ randn (1 , n r d a t a b i t s ) + j ∗ randn (1 , n r d a t a b i t s ) ] ;
Where n1,h1 generates the channel noise (considered AWGN for this simulation) and the channelfading, respectively. Sigma represents the noise variance and SNR is predefined with its value between 0and 45 increasing with a step size of 2.5. nr data bits are the number of bits that are to be transmittedwhich are random 1’s and 0’s as Binary Phase Shift Keying (BPSK) has been used.
4.2.2 Rician Fading
As stated earlier on many occasions, Rayleigh and Rician are almost the same distributions. Thedifference is on their usage, Rician distribution is used for estimation when there is direct path betweenthe transmitter and the receiver along with other multipath waves. A snippet of the code is given below.Noise remains the same here as was generated in case of Rayleigh, for comparison purpose.
mx and my are used to shift the lower bound for the random number generator. h1 is the channelfading and similarly different fading can be generated for different hops.
22
4.3. IMPORTANT CONCEPT FOR SIMULATION CHAPTER 4. SIMULATION RESULTS
mx = 0 . 5 ;my = 0 . 5 ;sigma = 1 ;x = mx + sigma .∗ randn (1 , n r d a t a b i t s ) ;y = my + sigma .∗ randn (1 , n r d a t a b i t s ) ;h1 = s q r t ( x .ˆ2 + y . ˆ 2 ) ;
4.2.3 Nakagami-m Fading
Rician and Rayleigh can be considered as the special cases of Nakagami-m distribution. The m factorhere can take different values which can represent different kinds of distributions depending on theenvironment and the scattering conditions. The code shown below generates Nakagami distribution,which is related to Gamma distribution, generated by gamrnd().
omega=1; mu =.5; % mu= m parameterh1 = [ s q r t ( gamrnd (mu, omega . /mu, 1 , n r d a t a b i t s ) ) ] ;
mu is an important m factor, which is chosen to be 0.5 for this simulation. Choosing m = 1 andm = 0 generates Rayleigh and Rician distributions respectively. Choosing other values for m will givedifferent distributions.
4.3 Important Concept for Simulation
Multi-hop systems mean, when there is no LOS between the transmitter and the receiver. A relay isinstalled which amplify and forward the signal that it receives from the transmitter/receiver. Assumethat MS is transmitting a signal m(t) which has an average power Pavg. The received signal at the RScan be written as
RRS(t) = β1m(t) +N1(t) , (4.1)
where β1 is the fading amplitude of the channel between MS and the relay station (RS) and N1(t) is anAdditive White Gaussian Noise (AWGN) with a power np1 at the input of the RS. As described earlierthere are two main types of relays; Regenerative Relays, received signal is decoded and then forwardedto the next hop and Non-regenerative Relays, Amplifies and forwards the signal to the next hop.
A non-regenerative relay has been used for this simulation. In this kind of system, the received signaland noise are multiplied by the gain of the relay, G, at Relay Station (RS) and then retransmitted toterminal of the Base station (BS). The received signal at the BS can be written as
RMS(t) = β2G(β1s(t) +N1(t)) +N2(t) , (4.2)
where β2 is the fading amplitude of the channel between RS and the BS and N2(t) is the AWGN withpower np2 at the input of the BS. Non-regenerative relays introduce fixed gain to the received signalregardless of the fading amplitude on the first hop. A gain of
G =
√PT
Pavgβ21 + np1
, (4.3)
is used in this simulation for comparison reasons. Where Pavgβ21 + np1 is the average relay input power
after the first channel and PT is the transmit power of the relay. This kind of fixed gain will retransmitthe signal from relay to the destination.
4.4 Simulation Setup
The Matlab code shown in the box below gives the main idea of the simulation. A brief idea of thecode will be discussed.
%Noise add i t i ony1 = h1 .∗ x + n1 ;%Rece iver
Page 23 of 33
4.5. DISCUSSION OF RESULTS CHAPTER 4. SIMULATION RESULTS
r1=y1 . / h1 ;r1 = r e a l ( r1 )>0;% count ing the e r r o r snoEr1 ( : , k ) = sum( inp = r1 ) ;%Received S igna l Power at the Relays i gna l power1 = mean( abs ( h1 .∗ x ) . ˆ 2 )%Noise Power at the Relayno i se power1 = mean( abs ( ( n1 ) ) . ˆ 2 )%Average SNR at 1 s t HOPSNR1(k , : ) = 10∗ l og10 ( s i gna l power1 / no i se power1 ) ;
The code above shows how the signal was transmitted and received at the relay station. The datawas transmitted by the transmitter, channel fading and noise was added to the signal. At the receiver,the same signal was detected, dividing it by the same channel response that was added to it. Numberof errors are calculated by comparing the transmitted and the received data. Signal and Noise powerare calculated which then help in calculating the signal to noise ratio for the system. As a result BERversus SNR graph was plotted which shows the effect of adding more hops to be discussed shortly.
The following steps describe the simulation
• Main body of the program runs and asks the user to select a channel to see its BER versus SNRplot.
• Number of bits, SNR has already been defined in the program. The default value for SNR is 0 to45 with a step size of 2.5 and number of bits transmitted are 106.
• Binary Phase Shift Keying (BPSK) is used as the modulation technique.
• AWGN is used as the channel noise, channel response is also generated as described previouslyusing different distributions e.g., gamrnd(),randn().
• SNR is increased linearly (same for all fading channels).
• Transmitter transmits the data, it arrives at the RS, a fixed relay gain (given by Eq. 4.3) isapplied to it and forwarded to next hop/MS.
• Random noise and channel fading is added to the signal transmitted as shown in Eq. 4.1.
• Signal is received at the receiver after going through some changes shown by Eq. 4.2.
• Number of error bits are calculated.
• The whole procedure is done for single hop and multi hop systems.
• Graphs are generated which are discussed in the following sections.
4.5 Discussion of Results
This section gives some simulation results for bit error rate (BER) evaluation of single hop and two-hopin a multi-hop relay network adopting BPSK modulation over Rayleigh, Rician and Nakagami fadingchannels. The relays are assumed to be non-regenerative and blind.
First of all, a single hop and two-hop relayed network adopting BPSK modulation over Rayleighfading channel is considered. Figure 4.1 shows the BER versus end-to-end SNR for a single and dual-hop relay network and also presents the theoretical BER. It can be seen that the BER increases atthe destination for two hop system as compared to the single hop. This is because the relay type isamplify-and-forward, hence it amplifies the signal as well as noise received from the first channel. So atthe destination, an increase in BER is observed as compared to the single hop. The effect of fading isclear from the graph as the curve for two-hop spreads away from that of single hop. Two hops systemsimprove the performance (even though the average BER increases) since the overall range of the systemis extended by adding a repeater.
As described for Rayleigh distribution the BER versus SNR graph of Rician fading shows almostthe same results as can be seen in Figure 4.2. Even though it is clear that the BER for Rician fading ishigher as seen from the curve for the two hop system. It is further away from the single hop curve.
Page 24 of 33
4.5. DISCUSSION OF RESULTS CHAPTER 4. SIMULATION RESULTS
0 5 10 15 20 25 30 3510
−4
10−3
10−2
10−1
100
BER Performance of Two−Hop System over Rayleigh Fading Channel
Average SNR per hop
Bit
Err
or R
ate
BER TheoryBER One−HopBER Two−Hops
Figure 4.1: Rayleigh Fading: BER vs SNR for single and dual hop systems
0 5 10 15 20 25 30 3510
−4
10−3
10−2
10−1
100
BER Performance of Two−Hop System over Rician Fading Channel
End−to−End SNR
Bit
Err
or R
ate
BER One−HopBER Two−Hops
Figure 4.2: Rician Fading: BER vs SNR for single and dual hop systems
Finally, Nakagami-m fading channel with m = 0.5 was simulated and the graph can be seen in Figure4.3. Even here, it is visible that the BER decreases as SNR increases. After the addition of the secondhop it is evident from the graph that at the second hop the BER has increased. The simulation wasstarted with one hop and then more hops were added with the same SNR to see the effect of additionof hops in to the system. Addition of each hop means extending the coverage area by the same amountprovided physical conditions remain the same. As shown in Figure 4.4 that the rate with which increasein BER occur is not the same, that is to say that the rate with which the BER increases after the additionof successive hops has a diminishing effect. This is an interesting result considering the fact that thesame coverage is added each time a hop is added to the system.
This can also be concluded for Rayleigh and Rician channels as they are special cases of Nakagamidistribution. Another important factor in Nakagami channel modelling is the m parameter. Differentvalues of m were checked and the changes in corresponding graphs are presented in Figure 4.5a and 4.5b.
Page 25 of 33
4.5. DISCUSSION OF RESULTS CHAPTER 4. SIMULATION RESULTS
0 5 10 15 20 25 30 3510
−4
10−3
10−2
10−1
100
BER Performance of Two−Hop System over Nakagami Fading Channel
End−to−End SNR
Bit
Err
or R
ate
BER One−HopBER Two−Hops
Figure 4.3: Nakagami Fading: BER vs SNR for single and dual hop systems
0 5 10 15 20 25 30 3510
−4
10−3
10−2
10−1
100
BER Performance of Multi−Hop System over Nakagami Fading Channel
End−to−End SNR
Bit
Err
or R
ate
BER One−HopBER Two−HopsBER Three−HopsBER Four−HopsBER Five−Hops
Hop 1
Hop 5
Figure 4.4: Nakagami Fading: BER vs SNR for five hops
4.5.1 Varying Gain of Relay
There are different ways of decreasing the BER as discussed earlier. In figure 4.6 the effect of varyingthe gain of relay can be seen. It is evident from the graphs that as soon as we increase the gain ofthe relay the BER decreases. The error rate after the addition of hops decreases too. It leads to theconclusion that the optimum choice of relay gain is important. However, increasing the gain can not beeconomical at times, therefore a trade-off between gain selection and BER has to be made in order todesign a network.
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4.6. CONCLUSION CHAPTER 4. SIMULATION RESULTS
0 5 10 15 20 25 30 3510
−4
10−3
10−2
10−1
100
BER Performance of Multi−Hop System over Nakagami Fading Channel
End−to−End SNR
Bit
Err
or R
ate
BER One−HopBER Two−HopsBER Three−HopsBER Four−HopsBER Five−Hops
(a) For m = 1.5
0 5 10 15 20 25 30 3510
−4
10−3
10−2
10−1
100
BER Performance of Multi−Hop System over Nakagami Fading Channel
End−to−End SNR
Bit
Err
or R
ate
BER One−HopBER Two−HopsBER Three−HopsBER Four−HopsBER Five−Hops
(b) For m = 3.5
Figure 4.5: Nakagami-m fading for different m values
0 5 10 15 20 25 30 3510
−4
10−3
10−2
10−1
100
BER Performance of Multi−Hop System over Nakagami Fading Channel
End−to−End SNR
Bit
Err
or R
ate
BER One−HopBER Two−HopsBER Three−HopsBER Four−HopsBER Five−Hops
(a) 10 times increase in gain
0 5 10 15 20 25 30 3510
−4
10−3
10−2
10−1
100
BER Performance of Multi−Hop System over Nakagami Fading Channel
End−to−End SNR
Bit
Err
or R
ate
BER One−HopBER Two−HopsBER Three−HopsBER Four−HopsBER Five−Hops
(b) 50 times increase in gain
Figure 4.6: Effect of gain variation on BER
4.6 Conclusion
The performance of multi-hop systems was studied in terms of number of hops and bit error rate versussignal to noise ratio. Numerical results showed that relaying technology is useful and the fading effectsare reduced to a considerable level. However, it is also concluded that increasing the number of hopscan be a reason for more erroneous data. When more hops were added to the system it was deducedthat each hop extends the coverage area by the same amount provided other conditions remain identicalat the cost of increasing the BER. There has to be a trade off between what is required and what isachieved. Increase in BER is not a big problem and can be taken care of by using different codingtechniques or using diversity techniques. Another option to decrease the BER is to increase the gain ofthe relays being used. It is clear from the analysis that increasing the number of hops has a diminishingeffect on the lowering of system performance.
It can be deduced that using complicated modulating techniques or increasing the power of thetransmitter to increase the coverage area is not a good option as it is expensive and makes the systemmore complex. Rather, it is a good idea to implement multi-hop relay networks. This concept appliesto cellular networks and wireless networks. It helps in overcoming obstacles and improves the capacityby decreasing the distance. They also help decrease the cost since they are much cheaper than installinga complete base station.
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CHAPTER 5
FUTURE WORK
5.1 Introduction
In the modern day there is an increasing demand for high data rate, reliable and high speed wirelesscommunication links which can support applications like voice, video, web browsing etc. To fulfil thesedemands the service providers have to go through tough challenges due to the fact that they have to usehigh frequency bands which gives rise to more attenuation, multipath phenomenon and other hurdleswhich ultimately causes performance degradation. Usually the medium is shared so there is a high levelof interference as well. There are other challenges for high speed wireless applications which include thelimited bandwidth, hardware complexity and cost of the systems [8].
To overcome these problems the simple approach that comes to mind is to use higher modulationschemes to improve the bandwidth efficiency. Another option can be to increase the bandwidth. Inmost of the cases somehow, these methods are not reliable. The most effective technique for a reliablehigh speed wireless communication is to use multiple antenna systems (Multiple Input Multiple Output–MIMO). Some of the basics of MIMO systems will be discussed in the upcoming sections.
In radio communication MIMO systems use multiple antennas at the transmitter and receiver toimprove communication performance. It is important to mention here that the terms input and outputrefer to the radio channel carrying the signal, not to the devices having antennas. Wireless communicationhas been able to perform better due to the implementation of MIMO technology, which significantlyincreases the data rate, extends the coverage without the need for additional bandwidth or extra transmitpower.
Several diversity techniques are also used to provide more robust communication even over varyingchannels. The main objective of the diversity is to provide different faded replicas for the receiver ofthe transmitted signal and with the hope that at least one of these multiple replicas could be receivedcorrectly. There are different types of diversities e.g., time diversity, spatial diversity, frequency diversity,antenna diversity, modulation diversity and others [8].
5.2 Thesis Contribution
In this thesis work the effect of adding hops (relays) between transmitter and receiver has been simulated.Bit error rate of these systems has been compared with respect to a constant signal to noise ratio foreach fading channel and different distributions. The channels between the transmitter and the receiverwere varied. Rayleigh, Rician and Nakagami fading models were used to compare the effects on bit errorrate. It was concluded that, bit error rate increased with the addition of each hop. However, addition ofhops a diminishing effect on the degradation of the system performance.
Chapter 2 gives a basic idea of the multi-hop systems and introduce the different kinds of relays thatcan be used in multi-hop networks. Bit error rate can be reduced by different techniques which werediscussed in Chapter 3. Simulation results have been discussed in Chapter 4. All the simulations were
28
5.3. FUTURE CONTRIBUTIONS CHAPTER 5. FUTURE WORK
carried out for Single Input Single Output (SISO) systems.
5.3 Future Contributions
Due to time limits, only the BER was considered for simulation over different channels. There are otherperformance checking parameters for the systems and their behaviour over different channels. Capacityof the channels can be calculated numerically to judge which of the channel among the three channelsconsidered in this thesis, can best fit the data rate for real time communications. BER for MultipleInput Multiple Output (MIMO) can also be checked to see channel performance over MIMO multi-hopsystems. The increase in data rates and fading effects can be observed. Some detail of MIMO systemsis given below in order to motivate future work on this topic.
5.4 Types of MIMO Systems
There are different types of MIMO systems. The variations depend on the number of antennas beingused on the transmitter and receiver systems. Basic explanation of these different types is given in thefollowing sections.
5.4.1 Single Input Single Output–SISO
Figure 5.1 shows a standard radio system with one transmit and one receive antenna. This is called SingleInput, Single Output (SISO) in MIMO technology. These systems are easier to design and installationcosts are minimal as compared to other systems.
Figure 5.1: Single Input Single Output system
5.4.2 Single Input Multiple Output–SIMO
As the name suggests this system consists of single antenna on the transmitter side and multiple antennason the receiver side. Figure 5.2 shows a 1X2 SIMO system a simplest scenario of SIMO, with onetransmitting and two receiving antennas. This system is easy to implement and no extra coding is
Figure 5.2: Single Input Multiple Output system
needed. The receiver now sees two different faded signals and can choose the best signal hence improvingthe signal to noise ratio.
5.4.3 Multiple Input Single Output–MISO
The simplest scenario of MISO (2X1) system can be seen in figure 5.3, with two transmitting and onereceiving antenna. In this case the same data is transmitted redundantly over the two antennas. The
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5.5. CHANNEL CAPACITY CHAPTER 5. FUTURE WORK
Figure 5.3: Multiple Input Single Output system
advantage is that the multiple antennas and redundancy coding is moved to the baste station which iseasier and cheaper to implement than on the mobile user end. Space time codes are used to produceredundant signals which were introduced by Alamouti for two antennas. Space time code further improvesperformance of the system. The redundant signal is not only transmitted from different antenna but alsoat different time from the first one [8].
5.4.4 Multiple Input Multiple Output–MIMO
This is the advance system, with multiple antennas transmitting and multiple antennas receiving. Alongwith making the communication more robust it also helps in increasing the data rate. To do this, datais divided into different streams and then transmitted independently over different antennas. A 2X2MIMO system is shown in figure 5.4.
Figure 5.4: Multiple Input Multiple Output system
5.5 Channel Capacity
For years, engineers assumed that the theoretical channel capacity limits were defined by the Shannon-Hartley theorem illustrated in Eq. 5.1.
C = B log2(1 +S
N) (5.1)
As Eq. 5.1 shows, increase in SNR of the channel results in marginal gains in the channel throughput.Therefore, the most common and simple way is to increase the bandwidth in order to increase thedata rates. However, increasing the bandwidth leads to attenuation problems and an increase in thesusceptibility of the signal to multipath fading. This means that if the bandwidth is to be increased thedesigner should also look into some error reducing techniques, ways of mitigating the effects of fadingand multipath propagation. This is where relayed transmission can be of enormous help.
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BIBLIOGRAPHY
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[4] 3GPP Technical Report 36.913. “Requirements for further advancements for EUTRA (LTE-advanced)”. 2008.
[5] IEEE, Std, 802.16e-2005. “IEEE Standard for Local and metropolitan area networks, Part 16: AirInterface for Fixed and Mobile Broadband Wireless Access Systems, Amendment for Physical andMedium Access Layers for Combined Fixed and Mobile Operation in Licensed Bands”. February2006.
[6] IEEE, Std, 802.16j-2009. “IEEE Standard for Multihop Relay networks, Part 16: Air Interfacefor Fixed and Mobile Broadband Wireless Access Systems, Amendment for Physical and MediumAccess Layers for Mobile multihop Relay”. June 2009.
[7] Mazen O. Hasna, Mohamed-Slim Alouini, “Wireless communications systems and networks”,Plenum Press New York, NY, USA, pp. 443-472, ISBN:0-306-48190-1, Year of Publication: 2004.
[8] Tolga M. Duman, Ali Ghrayeb, “Coding for MIMO Communication Systems”, John Wiley & SonsLtd, 2007.
[9] M. Jankiraman, “Space-Time Codes and MIMO Systems” Artech House, (2004)
[10] Gayatri S. Prabhu and P. Mohana Shankar, “Simulation of Flat Fading Using MATLAB for Class-room Instruction”, IEEE Transactions on education, Vol. 45, NO. 1, February 2002.
[11] A. Papoulis, “Probability, Random Variables, and Stochastic Processes”, 3rd Edition, McGraw Hill,New York, 1991.
[12] Li Tang Zhu Hongbo, “Analysis and Simulation of Nakagami Fading Channel with MATLAB*”,Asia Pacific Conference on Environmental Electromagnetics, CEEM’03, pp. 490-494 Nov. 4-7,2003,Hangzhou, China.
[13] Taneli Riihonen and Risto Wichman, “Power Allocation for a Single-Frequency Fixed-Gain RelayNetwork”, The 18th Annual IEEE International Symposium on Personal, Indoor and Mobile RadioCommunications (PIMRC?07), 2007
[14] H. Wu, C. Qiao, S. De, and O. Tonguz, “Integrated cellular and ad hoc relaying systems: iCAR”,IEEE J. Sel. Areas Commun., vol. 19, no. 10, pp. 21052115, Oct. 2001.
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[15] Harish Viswanathan and Sayandev Mukherjee, “Performance of Cellular Networks With Relaysand Centralized Scheduling”, IEEE Transactions On Wireless Communications, Vol. 4, NO. 5,September 2005
[16] J. N. Laneman and G. W. Wornell, “Energy efficient antenna sharing and relaying for wirelessnetworks”, in Proc. IEEE Wireless Communications Networking Conf., pp. 712, Chicago, IL, Oct.2000.
[17] Mazen O. Hasna and Mohamed-Slim Alouini, “A Performance Study of Dual-Hop TransmissionsWith Fixed Gain Relays”, IEEE Transactions on Wireless Communications, Vol. 3, No. 6. pp.1963-1968, November 2004.
[18] Matthias Patzold, “Mobile Fading Channels”, John Wiley & Sons, Ltd. 2002, pp. 4-6.
[19] http://en.wikipedia.org/wiki/Rayleigh fading. Visited on 11-08-2012
[20] http://www1.i2r.a-star.edu.sg/ knandakumar/nrg/Tms/student/student.htm. Visited on 11-08-2012
[21] Jose M. Hernando and F. Perez-Fontan, “Introduction to Mobile Communications Engineering”,Artech House, 1999, pp. 83-85.
[22] http://en.wikipedia.org/wiki/Rice distribution. Visited on 11-09-2012.
[23] http://en.wikipedia.org/wiki/Nakagami distribution. Visited on 11-10-2012.
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