Error Rate Performance of Multi-Hop Communication Systems Over Nakagami-m Fading Channel

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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

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To our parents, family, siblings, friends and teachers

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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 Single Input 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 a MMR system, communication between the source node and destination node is achieved through an intermediate node (i.e., Relay Station). It is widely accepted that multi-hop relaying communication can provide higher capacity and can reduce the interference in BWANs. Such claims though have not been quantified. Quantication of such claims is an essential step to justify a better opportunity for wide deployment 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 transmission. Binary Phase Shift Keying (BPSK) has been employed as the modulation technique and Additive White 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 their BER, 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 Gracious and the Wise, whose help and support are unbounded and gave us patience and ability to reach this stage of knowledge.

We would like to thank Prof. Sven Nordebo for his supervision, valuable time and advices and support during this thesis work. We would also like to thank the Swedish Government for giving us an opportunity to 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 Sweden and providing a home away from home. Thanks to Mr. Ishtiaq Ahmad for his invaluable help and suggestions. Last but not the least, it wouldn’t have been possible without the countless prayers and love of our parents, grand parents and siblings. We are thankful to all our family for their support and encouragement.

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List of Figures

2.1 Single-Hop Network Topology . . . 11

2.2 Multi-Hop Network Topology . . . 11

2.3 Stationary Relay Stations . . . 13

2.4 Mobile Relay Stations . . . 13

2.5 Relay in a network . . . 14

3.1 Doppler Effect. . . 17

4.1 Rayleigh Fading: BER vs SNR for single and dual hop systems . . . 25

4.2 Rician Fading: BER vs SNR for single and dual hop systems . . . 25

4.3 Nakagami Fading: BER vs SNR for single and dual hop systems . . . 26

4.4 Nakagami Fading: BER vs SNR for five hops . . . 26

4.5 Nakagami for different m. . . 27

4.6 Varying Gain . . . 27

5.1 SISO System . . . 29

5.2 SIMO System . . . 29

5.3 MISO Systems . . . 30

5.4 MIMO Systems . . . 30

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CHAPTER 1 INTRODUCTION

The era of wireless communications started when the first generation (1G) of wireless cellular systems was launched in the early 1980s. These systems utilized analogue air interface and supported voice applications only. With the higher user demand for cellular services and the increased need for better quality of service (QoS), the second generation (2G) of wireless cellular systems was introduced. 2G utilized digital air interface, providing higher bandwidth and better voice quality. In addition to supporting voice applications, 2G had the capability to support limited data applications. The capabilities of supporting higher bandwidths and better voice quality have led to the tremendous popularity of 2G wireless cellular systems, 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 growth of the Internet have resulted in an increased demand for wireless data services any time and anywhere using any wireless device. This has motivated the development of the third generation (3G) wireless cellular systems for better QoS and a higher capacity support. One of the 3G systems is Universal Mobile Telecommunications 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 to offer new data services.

The increased demand for supporting new applications with a higher data rate, led to the need for data rates beyond what is supported by current 3G wireless systems. To fulfil the support for such 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 has been 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 LTE system supports data rates greater than 100 Mbps, and efficiently utilize the spectrum using an OFDM system. Another BWANs is the Worldwide Interoperability for Microwave Access (WiMAX), which has been standardized by the IEEE 802.16 group [5]. WiMAX is a BWANs that has the capability to support data rate up to 70 Mbps.

BWANs such as LTE and WiMAX have gained tremendous attention lately for leveraging the support of a wide range of applications with different Quality of Service (QoS) requirements. Despite the support for such range of applications, satisfying the different QoS requirements while maximizing the network capacity and extending the network coverage are still major issues in these networks. Mobile Multi-hop relaying (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 these wireless networks. The emerging MMR extension enhances the conventional BWANs to enable support of multi-hop communication between a mobile station (MS) and a base station (BS) through intermediate relay 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 bandwidth limitations, it is mostly impractical and sometimes expensive to increase the bandwidth. in that case there 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 certain media. The fading, attenuation can vary with time, geographical location and/or radio frequency so it is 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 affects the wave propagation. There are different fading models that can be used to estimate the fading over a channel, 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 systems over Nakagami-m fading channel. In multi-hop communication systems the transmitter (usually Base Station) and the receiver (Mobile Station) does not have a direct connection. They are connected through a Relay Station (RS) which helps in the transmission from MS to BS and vice versa. The relay station has 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-advanced and WiMAX to extend the coverage area and control the power issues. In this thesis the objectives are to;

• Provide an expression for the end to end Signal to Noise Ratio (SNR) of a two-hop and multi-hop relay networks.

• The capacity of the above system will also be analysed and presented.

1.2 Thesis Organization

This thesis is divided into different chapters. Chapter1is the introduction and gives an overview of the whole report. Chapter2 is about Multi-hop networks, gives an insight into the background and related work that has been carried out on multi-hop communication systems. Chapter3is about different fading channels which were considered during this study, namely, Rayleigh, Rician and Nakagami. Chapter4 includes the discussion and presentation of the results. Chapter5is the conclusion drawn from the thesis and 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. The reason being that there is a high demand for high data transfer, online interactive games and a very high quality of service is required by the users. These requirements can only be fulfilled by high data transfer which in turn requires high bandwidths. However, as soon as high frequency is used, it gives rise to other problems for example high attenuation, deviation of the transmitted signals and distortion. The rate 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. One of the many solutions will be discussed in the upcoming sections i.e., the use of Relay Networks (Relayed transmission).

Multi-hop transmission is a combination of short links to cover a long distance communication network using many intermediate relaying terminals in between the transmitter and the receiver. There are many benefits of using relayed transmissions, the most important is that the transmit power required by both, the transmitter and receiver, reduces by a great amount and it ultimately improves the battery life. Dual-hop transmission was first come across in the bent pipe satellites where the main idea was to relay uplink carrier into downlink. This concept has also become famous in wireless communication systems in the recent years [17].

The most common performance assessment criterion for a digital system in literature is bit error rate (BER). Average BER is the ratio of erroneous bits at the receiver, on average. It is a function of the fading model of the channel and the types of receivers employed. Moreover, average BER is also a function of the type of modulation used at the transmitter. This performance criterion is used to assess the performance of non-regenerative multi-hop communication system (See more in Chapter4).

2.2 Single & Multi-Hop Systems

This section covers two types of hops namely single and multi-hop along with introduction of RSs to achieve multi hoping with different modulation techniques. Rather than having a direct single hop communication between base station and mobile terminal, the transmission is spread out on several relay 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 operation to 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 figure2.1, 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 or terminated at the end users (i.e., Mobile Station (MS)) that are in the direct transmission range of the BS. Regardless of whether the communication is between two MSs that are directly associated with the BS, 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 illustrated in figure 2.2a and figure 2.2b. In both figures, the solid arrowed lines are used to connect the network entities that are one hop away from each other, and thus can directly communicate with each other. Meanwhile, dotted arrowed lines represent the possible communication between two network entities 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 figure2.2aare probably able to receive from and transmit to the network entities which are more than one hop away from them directly, 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 figure2.2acan be engaged in direct transmission with not only BS, but also RS2 and RS3. Meanwhile, MS3 can only establish a direct communication with RS3 in figure2.2b.

2.3 Relay Station

Relays are part of a communication network that are dedicated to storing, amplifying and forwarding data received from the BS to the user devices, and vice versa. Unlike the BS, they are not connected to a wired line network through a back-haul connection. They rely on wireless transmission to communicate to the BS. Relays, at times, need additional power but still they are cheaper than installing a BS due to their limited functionality. Deploying relays can really help improve performance for MS that are on the edge of the cell and are affected by fading and they also have the potential to solve the coverage problem for high data rates in macro-cells. Cellular-relay networks could be such that the relay-to-user links use a different spectrum than base-to-user links [15]. For example, the relays could communicate to 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 to the 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 placement of 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 because the base has to transmit to the relay using the same spectrum. The other reason to expect performance gains is multiple simultaneous transmissions that are possible within the cell by using relays. The simultaneously 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 desired improved performance.

The relay station is connected to the base station on one side and to a group of mobile stations on the other. The connection to the base station, where the relay acts more or less as a subscriber/mobile station, is called the relay link, while the connection to the mobiles, where the relay acts as a simple base station, 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 illustrated in figure 2.3a, where a mobile terminal (MS) is far from the nearest base station. In a conventional cellular network MS is required to increase transmit power to reach BS and the same applies for the base station. In a multi-hop system the transmission takes place at a lower power level by allowing MS to communicate with a neighbouring relay station (RS), which then relays the signal further to the base station. Naturally, there could be more than one relay-mode relay terminal involved in the communication link. There is an upper limit on the number of relays that can be used with a single base station and hence limits the range of a particular base station, the limit is set by the latency allowed within a certain cellular environment.

On many occasions there is no line-of-sight between a mobile terminal and the base station. A typical situation in an urban environment would be a base station located around the corner of a building as shown in figure2.3b. The signal attenuation over such a propagation path may be very high, demanding much larger transmission power than would be necessary for covering the mere distance. In multi-hop systems such a case may be dealt with much greater efficiency. A relay terminal located at the corner has a line-of-sight to both communicating parties and it can relay the signal with much lower loss in the propagation path.

2.3.2 Mobile Relay Stations

Mobile Relay Station (MRS) is a relay station that is intended to function while in motion. MRS mobility is constrained by the same limits as a Mobile Station (MS) in IEEE 802.16e-2005. Relays may be 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 bus that provides service to passengers on board. As the MRS moves within an area, it will have to perform handover 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 by Multi-Hop

Figure 2.3: Stationary Relay Stations

time the group of mobile stations it supports will also change dynamically over time. The physical layer mode used in each cell is determined by the base station that serves it. As the propagation environment differs from cell to cell (e.g. urban, suburban, rural), different base stations may require different physical layer modes. While simple terminals, supporting only the mandatory modes, are still backwards compatible with all base stations, they need to be able to support the advanced modes in order 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 into two main categories, namely, regenerative or non-regenerative systems.

1. In regenerative systems, the relay fully decodes the signal that went through the preceding hop and retransmits 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 while risking 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, amplified and 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 is time sensitive, such as voice and live video.

Non-regenerative relay systems can in turn be classified into two sub categories namely (i) Channel State Information (CSI)-assisted and (ii) blind relays. Non-regenerative systems with CSI-assisted relays use instantaneous CSI of the preceding hop to control the gain introduced by the relay and as a result fix the power of the retransmitted signal. In contrast, systems with blind relays do not need any kind of 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 transmitted power depends on the power of the received signal at the relay station. If the received signal power is more, after amplification the transmit power will be higher. These blind relays do not perform as well as the CSI-assisted relays, however their low complexity relative to other relays make them a suitable choice 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 which comprises of a base station (BS), relay station (RS) and a mobile station (MS). The scenario can be seen in figure2.5, where the BS is communicating with a MS through a RS. The BS is transmitting a message signal m(t) with an average power, P_avg, if β₁ and B₂ represent the fading amplitude of the channels between 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 n_p₁ 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 is dependent on the relay being used in the system. Some relays have a fix amplification and others have variable amplifications depending on the power of the received signal. If a high power signal is received the amplification performed at the relay is adapted according to that, in order to avoid saturation of the relay. In this work, fixed relays are used and so when the signal is received at the BS, it has the following form,

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 AWGN signal with power np₂ at the input of BS. Signal to noise ratio (SNR) at the BS can be written as [17]

SN R =

Pavgβ₁² n_p1

β₂² n_p2 β₂²

n_p2 +_γ2n¹_p1

. (2.3)

It is evident from the above equation that the choice of gain, γ, will effect the SNR. A fixed gain has been suggested in [16] which is used in this thesis work. Gain is the ratio of the transmit power of the relay to the input power at the relay terminal and is given below

γ =

s P_T

Pavgβ₁²+ np₁

, (2.4)

where PT is the power of the transmitted signal at the output of the relay. There can be other gains that maybe used, for example, when using regenerative systems as mentioned earlier. However, in this thesis the above gain has been used for the relays so that the result can be compared with the previous literature and also to compare different fading channel models. It is important to mention that, the choice of an optimal gain is important because SNR is highly dependant on the choice of gain and SNR effects the BER (explained in Chapter4).

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 systems by 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 in the MMR enhanced infrastructure. However, the BS has to be modified to allow communication with RS and to be able to support traffic from multiple RSs. To achieve the best possible results the placement of 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 multipath propagation or shadowing, the problem can be taken care of by using relay systems and allow the MS to have full functionality. Relayed transmissions may also be used to extend the coverage area by extending the range at the edge of the cell which also allows a better indoor coverage. Another example of an interesting 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 are still 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 important concern.

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CHAPTER 3 FADING CHANNELS

3.1 Introduction

In wireless communication radio waves propagate from the transmitting station to the receiver station while 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 station is 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 scattering from different structures in the surrounding environment. Therefore, signals arrive at the receiver via 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 random amplitudes and phases combine either constructively or destructively, mostly the later case. This causes noticeable 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 to local multipath propagation. Whereas, long-term variation in the mean signal level is called large-scale fading [10]. The latter effect is due to the travel of the signals over long distances that can cause a lot of variations in the overall path between the transmitter and the receiver. Large-scale fading is also known as shadowing, because this usually occurs when the MS moves into the shadow of taller objects such as buildings and hills. Due to multipath, a moving receiver can sometimes experience several fades in a very short period of time. In the worst case scenario the MS may stop at a location where the signal is in 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 when they travel from a transmitter to a receiver. One of the important aspects of the path between transmitter and receiver is fading. Therefore, different channel fading models have been introduced which helps in estimating 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 and ultimately one can find which channel model best fits the real time communication scenarios. Some of the 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

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3.4. RAYLEIGH FADING CHAPTER 3. FADING CHANNELS

Figure 3.1: Angle of arrival α

n

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 is transmitted from the antenna and before its reception on the receiving antenna. A direct ray, travels directly from the transmitter to the receiver. It is usually (not always) the strongest signal of all the signals that reach at the receiving antenna. The other signals (rays) arrive at the receiving antenna through indirect paths (after going through reflections, refractions, diffractions). Even though these rays find a way to the reach the receiver but they arrive with different angles and time delays. They also take more time in reaching the receiver and usually have a weaker power than the direct signals. Depending on 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, for example, by an equalizer

Besides the multipath propagation, Doppler effect also has a negative effect on the transmission characteristics of the mobile radio channel. Due to the movement of the transmitter/receiver there is a frequency shift in each of the partial waves. The angle of arrival αn, is defined by the direction of arrival of the nth incident wave and the direction of motion of the mobile unit [18] as shown in Figure3.1. αn

determines the Doppler frequency (frequency shift) of the nth incident wave according to the relation

fn= fmax cos αn , (3.1)

where f_max is the maximum Doppler frequency related to the speed of the mobile unit v, the speed of light c_◦, and the carrier frequency f_◦ [18] by the equation

fmax= v

c_◦f_◦. (3.2)

Multipath propagation, with the movement of transmitter or receiver, leads to rigorous and random fluctuations 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 models can help in modelling the important statistical properties of real world communication systems and can also give an idea of the signal amplitudes of the transmitted signals that can be expected at the receiver side. 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 statistical models 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. Rayleigh fading is one of the model for estimating the effect of propagation environment on a radio signal. It states 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 environment exist as well. If there is a strong line of sight component of the signal at the receiver, Rician fading (to be discussed shortly) may be more applicable.

The mobile station antenna does not always receive the transmitted signal over LOS. It receives a number of reflected, diffracted and scattered waves as a result of multipath propagation. As a result the phases are random and ultimately, the received power also becomes a random variable. The transmitted signal with a frequency fcmay reach the receiver via a number of paths, the jthpath having an amplitude Aj, and a phase φj [10]. If we assume that there is no direct path or line-of sight (LOS) component, the received signal m(t) can be expressed as

m(t) =

N

X

j=1

Ajcos(fc+ φj) , (3.3)

where N is the number of paths. The phase φj depends on varying path lengths, changing by 2π when the 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 receiver and there is no LOS between the transmitter and the receiver, Rayleigh fading is used to estimate the channel performance. Its probability density function (pdf) is

P R(r) = 2r

Ω exp^−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 used to simulate high frequency communication for example, ionospheric communications. Unfortunately, it does 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 can be a useful model for that scenario. In such situations there is no LOS between the transmitter and the 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 frequency communication such as ionospheric and tropospheric signal propagation the particles in the atmosphere also act as scatterers which can be approximated by Rayleigh fading. Rayleigh fading is a small scale effect. There are different properties of the environment for example path loss and shadowing which are superimposed by fading. The speed with which the channel fades is affected by how fast the receiver and/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 can be 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 Rayleigh distribution is given by

R =p

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 = px²+ y², where x and y are independent normal random variables.

• If R ∼ Rayleigh(1), then R²has 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 signal due to the multipath effect. This is mostly common in urban areas where it is difficult to establish a LOS between the transmitting station and the receiver. However if there are some open areas, the direct signal may reach the receiver with some attenuation. In such case, when there is a strong direct component 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 between the transmitter and the receiver along with the multipath waves that arrive at the receiver. The probability distribution function can be written as

p(r) = r σ²exp

−r²+ A² 2σ²

J_◦ rA σ²

, r ≥ 0 , (3.8)

where J_◦() is the 0^thorder modified Bessel function of the first kind [21].

J_◦(z) =

∞

X

n=0

z²ⁿ

2²ⁿn!n! f or 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. 3.3can be written as

m(t) =

N −1

X

j=1

A_jcos(f_c+ ω_djt + φ_j) + A cos(f_ct + ω_dt) , (3.10)

where the constant A is the strength of the direct component, ω_dis the Doppler shift along the LOS path, and ωdj are the Doppler shifts along the indirect paths. The probability density function is given in [11].

Rician distribution is mostly described by the Rician factor K, which is defined as the ratio between the power of the direct path and the power of the indirect paths [21]. The value of K can be expressed in 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 becomes Rayleigh 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+ Y² 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]. Rayleigh distribution failed to estimate the channel behaviour over long distances and high frequencies, this was was first observed by Nakagami. He also, suggested a parametric gamma distribution based density function, to describe the experimental data he obtained. Later it was also shown by different researchers using real life data that was best explained by the model provided by Nakagami rather then other models like Rayleigh and Rician. Nakagami also provides best fit to the mobile communication channel data and other deep space communications [12].

Unlike the Rician distribution, Nakagami distribution does not assume a LOS conditions between the transmitter and the receiver, it uses a parametric gamma distribution-based density function to describe the experimental data and get approximate distribution, the PDF of Nakagami distribution is

f (r) = 2m^mr^2m−1 Ω^mΓ(m) exp

−mr² Ω

, m ≥1

2 : r ≥ 0 , (3.12)

where m is Nakagami scale parameter (fading parameter), it describes the fading degree of the propagation media due to scattering and multipath interference processes. When m → ∞ Nakagami fading channel becomes a non-fading channel. and Ω is the average power of multipath scatter field, Γ(m) is the gamma function [12]. The parameters m and Ω can be estimated as following:

m = E²[X²] V ar[X] , and

Ω = 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. For m > 1, the fluctuations of the signal strength reduce compared to Rayleigh fading and with higher values of 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 random variable from a gamma distribution. Let Y ∼ Gamma(k, θ), then it is possible to get a random variable X ∼ 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 following settings. Let 2m be an integer, then nakagami distribution f (y; m, Ω) can be generated with the parameter k set to 2m and then following it by the scaling transformation. This can be checked by performing the following transformation on the pdf of a Chi-distribution as below [23]:

y =p

(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 reducing the effects of fading channels. Some of them are discussed below in detail. Equalization may fix most of distortion caused by the channel but it may not amplify a signal that is going through a very deep fade. At times when the fading is deep it can be very difficult sometimes, even impossible, to recollect the transmitted signal. To avoid losing the data due to deep fading diversity combining can be be employed.

3.7.1 Diversity

The concept of diversity combing suggests that if more than one transmitting/receiving antennas are used for reception/transmission of the signal, the probability that deep fades will occur on all the antennas at 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 effect of deep fades to a great amount, which ultimately improves the reception quality. There are different methods 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 the signals is then used for reception.

2. Scanning Diversity: In this technique the signals are compared to a threshold value, when one is found that signal is then used for reception regardless of its power compared to other signals. However, if the power of the signal drops below the threshold value the scanning process is 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 then added together. Before that it must be assured that they have the same phase in order to get constructive addition. The signals can also be delayed to make sure that they have the same phase.

3.7.2 Channel Coding

After using equalization and different diversity techniques to reduce loss or corruption of data, there still may be bits that contain errors. Channel coding is the next step that can be taken, it helps in reducing the probability of errors in the data. Redundant bits are added to the data which can help in detecting errors in the receiver and also correct them at times. The higher the number of redundant bits the higher the 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. Redundancy bits are added to each block of data. The redundancy allow error detection and sometimes it can correct 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. At the receiver the data is divided by the same polynomial used in the encoder. If the result after division is 0, there are no errors. If the result is non-zero, errors have occurred and the result can be used to locate the location of error.

3. Turbo Codes: Multiple convolution encoders and decoders along with interleaving (spreading the bits so that bits with errors are separated from each other ) are used. Shannon channel capacity limit is almost reached with turbo coding, that is why it has advantage over other coding techniques .

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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 communication systems, for example, OPNET, LabView and Matlab just to name a few. In this thesis work 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 into what steps were carried out to perform the required simulations. Different channels (mentioned in Chapter3) 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 explanation of these distributions can be found in sections 3.4, 3.5 and 3.6, respectively. The following subsections will describe how these channel distributions were generated based on their description in theory.

4.2.1 Rayleigh Distribution

There are different ways of generating Rayleigh distributions in Matlab, the method used in this work is given below, which on comparison with other standard methods as mentioned in Section 3.4showed the same result. A snippet of the code is shown below,

sigma = s q r t ( 1 0 . 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 channel fading, respectively. Sigma represents the noise variance and SNR is predefined with its value between 0 and 45 increasing with a step size of 2.5. nr data bits are the number of bits that are to be transmitted which 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. The difference is on their usage, Rician distribution is used for estimation when there is direct path between the 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 channel fading and similarly different fading can be generated for different hops.

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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 . ˆ 2 + 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 factor here can take different values which can represent different kinds of distributions depending on the environment 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 p a r a m e t e r

h1 = [ 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 and m = 0 generates Rayleigh and Rician distributions respectively. Choosing other values for m will give different distributions.

4.3 Important Concept for Simulation

Multi-hop systems mean, when there is no LOS between the transmitter and the receiver. A relay is installed which amplify and forward the signal that it receives from the transmitter/receiver. Assume that MS is transmitting a signal m(t) which has an average power Pavg. The received signal at the RS can be written as

RRS(t) = β1m(t) + N1(t) , (4.1)

where β₁is the fading amplitude of the channel between MS and the relay station (RS) and N₁(t) is an Additive White Gaussian Noise (AWGN) with a power n_p₁ at the input of the RS. As described earlier there are two main types of relays; Regenerative Relays, received signal is decoded and then forwarded to 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 signal and noise are multiplied by the gain of the relay, G, at Relay Station (RS) and then retransmitted to terminal of the Base station (BS). The received signal at the BS can be written as

R_{M S}(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 with power np₂ at the input of the BS. Non-regenerative relays introduce fixed gain to the received signal regardless of the fading amplitude on the first hop. A gain of

G =

s PT

P_avgβ₁²+ n_p₁ , (4.3)

is used in this simulation for comparison reasons. Where Pavgβ₁²+ 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 retransmit the 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 the code will be discussed.

%N o i s e a d d i t i o n y1 = h1 .∗ x + n1 ;

%R e c e i v e r

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4.5. DISCUSSION OF RESULTS CHAPTER 4. SIMULATION RESULTS

r 1=y1 . / h1 ;

r 1 = r e a l ( r 1 ) >0;

% c o u n t i n g t h e e r r o r s

noEr1 ( : , k ) = sum ( i n p = r 1 ) ;

%R e c e i v e d S i g n a l Power a t t h e Relay s i g n a l p o w e r 1 = mean ( abs ( h1 .∗ x ) . ˆ 2 )

%N o i s e Power a t t h e Relay

n o i s e p o w e r 1 = mean ( abs ( ( n1 ) ) . ˆ 2 )

%Average SNR a t 1 s t HOP

SNR1( k , : ) = 10∗ log10 ( s i g na l po we r1 / noise power1 ) ;

The code above shows how the signal was transmitted and received at the relay station. The data was 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. Number of errors are calculated by comparing the transmitted and the received data. Signal and Noise power are calculated which then help in calculating the signal to noise ratio for the system. As a result BER versus 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 SNR plot.

• Number of bits, SNR has already been defined in the program. The default value for SNR is 0 to 45 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 previously using 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) is applied 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-hop in a multi-hop relay network adopting BPSK modulation over Rayleigh, Rician and Nakagami fading channels. 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 Rayleigh fading channel is considered. Figure 4.1shows 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 at the destination for two hop system as compared to the single hop. This is because the relay type is amplify-and-forward, hence it amplifies the signal as well as noise received from the first channel. So at the destination, an increase in BER is observed as compared to the single hop. The effect of fading is clear from the graph as the curve for two-hop spreads away from that of single hop. Two hops systems improve the performance (even though the average BER increases) since the overall range of the system is extended by adding a repeater.

As described for Rayleigh distribution the BER versus SNR graph of Rician fading shows almost the same results as can be seen in Figure4.2. Even though it is clear that the BER for Rician fading is higher as seen from the curve for the two hop system. It is further away from the single hop curve.

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0 5 10 15 20 25 30 35

10⁻⁴ 10⁻³ 10⁻² 10⁻¹ 10⁰

BER Performance of Two−Hop System over Rayleigh Fading Channel

Average SNR per hop

Bit Error Rate

BER Theory BER One−Hop BER Two−Hops

Figure 4.1: Rayleigh Fading: BER vs SNR for single and dual hop systems

0 5 10 15 20 25 30 35

10⁻⁴ 10⁻³ 10⁻² 10⁻¹ 10⁰

BER Performance of Two−Hop System over Rician Fading Channel

End−to−End SNR

Bit Error Rate

BER One−Hop BER 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 Figure 4.3. Even here, it is visible that the BER decreases as SNR increases. After the addition of the second hop it is evident from the graph that at the second hop the BER has increased. The simulation was started with one hop and then more hops were added with the same SNR to see the effect of addition of hops in to the system. Addition of each hop means extending the coverage area by the same amount provided physical conditions remain the same. As shown in Figure4.4that the rate with which increase in BER occur is not the same, that is to say that the rate with which the BER increases after the addition of successive hops has a diminishing effect. This is an interesting result considering the fact that the same 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 Nakagami distribution. Another important factor in Nakagami channel modelling is the m parameter. Different values of m were checked and the changes in corresponding graphs are presented in Figure4.5aand4.5b.

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0 5 10 15 20 25 30 35

10⁻⁴ 10⁻³ 10⁻² 10⁻¹ 10⁰

BER Performance of Two−Hop System over Nakagami Fading Channel

End−to−End SNR

Bit Error Rate

BER One−Hop BER Two−Hops

Figure 4.3: Nakagami Fading: BER vs SNR for single and dual hop systems

0 5 10 15 20 25 30 35

10⁻⁴ 10⁻³ 10⁻² 10⁻¹ 10⁰

BER Performance of Multi−Hop System over Nakagami Fading Channel

End−to−End SNR

Bit Error Rate

BER One−Hop BER Two−Hops BER Three−Hops BER Four−Hops BER 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 varying the gain of relay can be seen. It is evident from the graphs that as soon as we increase the gain of the relay the BER decreases. The error rate after the addition of hops decreases too. It leads to the conclusion that the optimum choice of relay gain is important. However, increasing the gain can not be economical at times, therefore a trade-off between gain selection and BER has to be made in order to design a network.

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4.6. CONCLUSION CHAPTER 4. SIMULATION RESULTS

0 5 10 15 20 25 30 35

10⁻⁴ 10⁻³ 10⁻² 10⁻¹ 10⁰

End−to−End SNR

Bit Error Rate

BER One−Hop BER Two−Hops BER Three−Hops BER Four−Hops BER Five−Hops

(a) For m = 1.5

0 5 10 15 20 25 30 35

10⁻⁴ 10⁻³ 10⁻² 10⁻¹ 10⁰

End−to−End SNR

Bit Error Rate

(b) For m = 3.5

Figure 4.5: Nakagami-m fading for different m values

0 5 10 15 20 25 30 35

10⁻⁴ 10⁻³ 10⁻² 10⁻¹ 10⁰

End−to−End SNR

Bit Error Rate

(a) 10 times increase in gain

0 5 10 15 20 25 30 35

10⁻⁴ 10⁻³ 10⁻² 10⁻¹ 10⁰

End−to−End SNR

Bit Error Rate

(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 versus signal to noise ratio. Numerical results showed that relaying technology is useful and the fading effects are reduced to a considerable level. However, it is also concluded that increasing the number of hops can be a reason for more erroneous data. When more hops were added to the system it was deduced that each hop extends the coverage area by the same amount provided other conditions remain identical at the cost of increasing the BER. There has to be a trade off between what is required and what is achieved. Increase in BER is not a big problem and can be taken care of by using different coding techniques or using diversity techniques. Another option to decrease the BER is to increase the gain of the relays being used. It is clear from the analysis that increasing the number of hops has a diminishing effect on the lowering of system performance.

It can be deduced that using complicated modulating techniques or increasing the power of the transmitter to increase the coverage area is not a good option as it is expensive and makes the system more complex. Rather, it is a good idea to implement multi-hop relay networks. This concept applies to cellular networks and wireless networks. It helps in overcoming obstacles and improves the capacity by decreasing the distance. They also help decrease the cost since they are much cheaper than installing a 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 wireless communication links which can support applications like voice, video, web browsing etc. To fulfil these demands the service providers have to go through tough challenges due to the fact that they have to use high frequency bands which gives rise to more attenuation, multipath phenomenon and other hurdles which ultimately causes performance degradation. Usually the medium is shared so there is a high level of interference as well. There are other challenges for high speed wireless applications which include the limited bandwidth, hardware complexity and cost of the systems [8].

To overcome these problems the simple approach that comes to mind is to use higher modulation schemes to improve the bandwidth efficiency. Another option can be to increase the bandwidth. In most of the cases somehow, these methods are not reliable. The most effective technique for a reliable high 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 to improve communication performance. It is important to mention here that the terms input and output refer to the radio channel carrying the signal, not to the devices having antennas. Wireless communication has been able to perform better due to the implementation of MIMO technology, which significantly increases the data rate, extends the coverage without the need for additional bandwidth or extra transmit power.

Several diversity techniques are also used to provide more robust communication even over varying channels. The main objective of the diversity is to provide different faded replicas for the receiver of the transmitted signal and with the hope that at least one of these multiple replicas could be received correctly. 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 for each fading channel and different distributions. The channels between the transmitter and the receiver were varied. Rayleigh, Rician and Nakagami fading models were used to compare the effects on bit error rate. It was concluded that, bit error rate increased with the addition of each hop. However, addition of hops a diminishing effect on the degradation of the system performance.

Chapter2gives a basic idea of the multi-hop systems and introduce the different kinds of relays that can be used in multi-hop networks. Bit error rate can be reduced by different techniques which were discussed in Chapter3. Simulation results have been discussed in Chapter 4. All the simulations were

Error Rate Performance of Multi-Hop Communication Systems Over Nakagami-m Fading Channel

Degree project