1

CHAPTER 1

INTRODUCTION

As the field of wireless communication grows, profound interest

has been created in improving the wireless network performance in terms of

spectral efficiency, link reliability and data rate. Multiple Input Multiple

Output (MIMO) technology provides all these benefits as it combats fading

and interference (Mehrzad Biguesh and Alex B.Gershman 2006, Yijia Fan

and John Thomson 2007). However, the main drawback of MIMO technology

is that placement of multiple antennas into a small mobile terminal which

faces the practical difficulty of size limit (Vahid Tarokh et al 1998, Feifei Gao

et al 2008). In order to overcome this drawback, communications using

devices referred to as relays are employed in wireless communication

networks (Van der Meulen 1968, Thomas Cover and Abbas A.El Gamal

1979). Relays are actively studied and considered in the standardization

process of next generation mobile broadband wireless communication

standards such as Third Generation Partnership Project (3GPP), Long Term

Evolution-Advanced (LTE-A), Institute of Electrical and Electronics

Engineers (IEEE) 802.16j multi-hop relay and IEEE 802.16m advanced air

interface for Fourth Generation (4G) working groups (Yang Yang et al 2009).

1.1 EVOLUTION OF WIRELESS RELAY NETWORK

Wireless relay network is a type of collaborative communications

(Yang Yang et al 2009) in which a Relay Station (RS) helps to forward user

information from neighboring Mobile Station (MS) to a local Base Station

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(BS) (3GPP TR 36.814 V1.2.1). Primarily, in a cellular wireless network,

relays act as repeaters (Jun Ma et al 2011) in forwarding the information from

source node to destination node when there is no direct line of sight path

between them. Basically, a wireless network with relays or virtual antennas is

an arrangement of spatially dispersed nodes placed between source node and

destination node intended for expanding communication range or increasing

communication rate. The concept of using relays in communication systems

was proposed by Van der Meulen in 1971 and was referred as 3 terminal

communication systems (Van der Meulen 1971). Later, it was coined as

Wireless Relay Network (WRN) by Michael Gastpar and Martin Vetterli in

2002 (Michael Gastpar and Martin Vetterli 2002). However, the first

computer based WRN was constructed in the early 1970s by Norman

Abramson (Norman Abramson 1970, Scott Guthery 1997). Figure 1.1 shows

a Wireless Relay Network.

Figure 1.1 Wireless Relay Network

The principle of operation of a wireless relay network is that it

transmits the data in two phases namely phase I and phase II. In phase I, the

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source node transmits an information signal to relay node through a broadcast

channel. The relay node receives the signal and performs signal processing

tasks referred as relaying strategies (Alireza Shahan Behbahani et al 2008). In

phase II, the processed signal from the relay node is forwarded to the

destination node. In this form of WRN scenario, spatial diversity or antenna

diversity is obtained, as the information signal from the source node reaches

the destination node by passing through two independent fading paths.

Usually spatial diversity techniques provide an additional diversity gain

without incurring an expenditure of transmission time or bandwidth (Rohit U

Nabar et al 2004). By virtue of this form of operation, a WRN gains attention

and it is considered as an effective means to compensate signal fading due to

multipath propagation and shadowing. Signal fading is compensated through

exploitation of spatial diversity provided by the relay nodes in WRN. Also,

WRN attains prominence due to efficient use of power resources yielding

reduced power levels in increasing the battery life of a Wireless Sensor

Network (WSN) (Bo Wang et al 2006).

Currently, WRN is used for realizing long-range communication,

by deployment of relay nodes at intermediate locations along the longer

ranges when direct line of sight path is in deep fade (Himal A.Suraweera and

Jean Armstrong 2007). It also provides flexibility to meet temporary

communication demands under certain scenarios, due to the non requirement

of a fixed infrastructure (Jun Ma et al 2009, Jun Ma et al 2011). Further,

WRN boosts signal strength in coverage holes, in thick buildings, in

underground tunnels or on the cell edges (Chan-Byoung Chae et al 2008, Jun

Ma et al 2011), as they are easier, faster, cheaper to deploy, posses reduced

terminal radiation and longer battery life (John Boyer et al 2004).

As the relay nodes in WRN play an instrumental role in providing

these advantages, three major factors govern its successful operation. They

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are i) consideration of the relay nodes, ii) relay network topology and iii)

relaying strategy or relaying protocols (Feifei Gao et al 2008, Alireza Shahan

Behbahani et al 2008).

1.2 RELAY NODE CONSIDERATION

The first major factor in improving the performance of WRN is the

selection of suitable scenario to place the relay nodes. In general, there are

two possible scenarios of considering relay nodes. In the first scenario, the

relay nodes can be obtained from a telecommunication agency and in the

second, it can be obtained by cooperating terminals of other users. The second

scenario is referred to as Cooperative Communication (Andrew Sendonaris

et al 2003, Feifei Gao et al 2008).

Cooperative Communication is a form of communication by which

each user acts as a relay for a certain period, has its own information to

transmit and provides coordination between the source node and one or more

relay nodes thereby resulting in spatial diversity (Andrew Sendonaris et al

2003). This is an innovative manner of realizing spatial diversity gain in a

distributed fashion, which is also referred as cooperative diversity or

cooperation diversity (Nicholas Laneman et al 2004). Ultimately, this

enhances reliability, power efficiency, spectral efficiency and data rate in

comparison to MIMO communications.

WRN also allows mobile terminals to act as relays and participate

in information transmission when they are neither the initial source node nor

the final destination node. This aspect of a relay node or mobile terminal in a

WRN makes it suitable for extending the signal and service coverage of a BS

in a cellular network, Wireless Local Area Networks (WLAN), ad-hoc and

hybrid Networks (John Boyer et al 2004). However, cooperative

communication is a promising technique for next generation cellular wireless

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system and is considered by several task groups in the family of IEEE 802.16,

mainly in IEEE 802.16j and IEEE 802.16m standards (Sebastien Simoens et

al 2010, Kamran Ettimad and Max Riegel 2010).

International MobileTelecommunications -2000 IMT-2000

IEEE 802.16e, IEEE 802.16j IEEE 802.16m

Wideband Code Division Multiple Access (W-CDMA) Worldwide interoperabilityHigh Speed Downlink Packet Access (HSDPA) for Microwave accessHigh Speed uplink Access (HSPUA) (WiMAX)High Speed Packet Access Plus (HSPUA+)Long Term Evolution (LTE)Long Term Evolution Advanced (LTE-A)- 3GPPCode Division Multiple Access (CDMA) 2000 1xUltra Mobile Broadband (UMB) -3GPP2

High Speed Wireless Access Services

Figure 1.2 High Speed Wireless Access Services

Wireless systems to achieve high speed wireless access services are

classified into two categories, as shown in Figure 1.2. They are International

Mobile Telecommunications-Advanced (IMT-A) which is the name defined

by the International Telecommunication Union (ITU) for 4G mobile wireless

broadband communication system and Worldwide interoperability for

Microwave Access (WiMAX) which was approved to become a 3G standard

in the ITU IMT-2000 (Yang Yang et al 2009, Ian F Akyilidiz et al 2010,

Yongming et al 2010) standards family for transmission of data through

wireless communication.

IEEE launched 802.16j working group to develop relay based

multi-hop techniques for WiMAX standards. IEEE 802.16j is a Mobile Multi-

hop Relay (MMR) standard for WiMAX networks created by IEEE in March

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2006 (IEEE standard/Part16/2009). It mainly intended to enhance the

performance of IEEE 802.16e with the use of relay station (Yang Yang et al

2009). The main objectives of introducing IEEE 802.16j (Vasken Genc et al

2008) are to extend the coverage area, enhance throughput and system

capacity, saving battery life of source node and minimizing relay node

complexity. Primarily, there are two working groups which contributed to the

development of IEEE 802.16j standard (IEEE 802.16j/D9 2009). The first

group IEEE 802.16 working group on broadband wireless (David Soldani and

S.Dixit 2008) access standard supports the development of broadband

Wireless Metropolitan Area Network (WMAN) and the second group is the

WiMAX (Chackchai So-In et al 2009), forum which certifies and promotes

broadband wireless products.

Generally two types of relays are defined in IEEE 802.16j task

group namely Type-I (Non-Transparency) and Type-II (Transparency) (Yang

Yang et al 2009).

1.2.1 Type-I (Non-Transparency)

Type-I relays are used to establish communication between local

BS and MS located far away from the BS. A relay link is established between

a MS and a RS and an access link between BS and RS. The access from the

MS to the BS takes place through the relay station(s). The Type-I relay station

transmits common reference signals and control information of the BS to the

MS in order to communicate with the MS and connect the same to the BS.

This process allows to increase capacity and improve the service coverage, as

the remote mobile station units are connected to the base station through the

Type-I relay station (Yang Yang et al 2009, 3GPP TR 36.814, V1.2.1).

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1.2.2 Type-II (Transparency)

If the MS is within the vicinity of the BS, then Type-II relays are

used. In this case, the RS does not transmit common reference signal or

control information to the MS. The local MS service quality and the link

capacity is improved by connecting the MS to the BS via the relay station in

presence of a direct communication link between the BS and MS. The overall

capacity of the system is improved by achieving multipath diversity and

transmission gains of the local mobile station (Yang Yang et al 2009).

1.3 RELAY NETWORK TOPOLOGY

In a WRN, one of the significant factors to be considered for

improving the network performance is network topology (Younsun Kim et al

2008). There are two types of relay transmission topologies namely

i) Serial Relay Transmission Topology

ii) Parallel Relay Transmission Topology

1.3.1 Serial Relay Transmission Topology

Serial relay transmission is used for long distance communication

and range-extension in regions having shadows. In serial relay topology,

signal propagates from one relay to another relay and the channels of

neighboring hop are orthogonal to avoid any interference. The advantage of

this topology is that it provides power gain. However, the drawback of serial

relay transmission is that it suffers from multi-path fading. In outdoors and

non-line of sight communication, signal wavelength is large and installation

of multiple antennas is not possible.

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1.3.2 Parallel Relay Transmission Topology

Parallel relay transmission is employed in WRN to increase

robustness against multi-path fading (Helmut Bolcskei et al 2006). In this

topology, the signal propagates through multiple relays in the same hop(Wael

Jafar et al 2010) and the destination node combines the signals received with

the help of various combining schemes. The advantage of this scheme is that

it provides power gain and diversity gain. A typical WRN topology is shown

in Figure 1.3. The topologies are described as follows

i) A single antenna source node, a single antenna relay node and

a single antenna destination node.

ii) A single antenna source node, multiple relay nodes with

single antenna and a single antenna destination node.

iii) A source node with multiple antennas, a relay node with

multiple antennas and a destination node with multiple

antennas.

iv) Multiple source nodes with single antenna relay node with

multiple antennas and multiple destination nodes with single

antennas.

v) Multiple source nodes with multiple antennas, multiple relay

nodes with multiple antennas and multiple destination nodes

with multiple antennas.

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Figure 1.3 WRN Network Topology

1.4 RELAYING STRATEGY

The third factor which facilitates the WRN performance is the

relaying strategy or relaying protocols. There are two major classifications of

relaying strategy namely Non-Regenerative relaying strategy and

Regenerative relaying strategy as (Xiaojun Tang and Yingbo Hua 2007, Olga-

Munoz Mediana et al 2007) shown in Figure 1.4. Non-regenerative relaying

strategy (Ronghong Mo et al 2010) mainly comprises of Amplify and

Forward (AF) and Compress and Forward (CF) relaying strategies.

Regenerative relaying strategy comprises of Decode and Forward (DF), and

Demodulate and Forward (DMF) relaying strategies (Alireza Shahan

Behbahani et al 2008).

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Figure 1.4 WRN Relaying strategy

1.4.1 Amplify and Forward Relaying Strategy

In AF relaying strategy as shown in Figure.1.5, the signal

broadcasted from the source node is received by the relay node and the relay

node sends a scaled version of it to the destination node. Mainly, the relay

node performs a linear signal processing task (or) an amplification operation

on the transmitted signal (Feifei Gao et al 2008). AF relaying strategy uses

varying gain or constant gain to limit the transmit power at the relay node.

Varying-gain relaying scheme (Mazen Omar Hassna and Mohammed Slim-

Alouini 2004) is based on the knowledge of the instantaneous source to relay

channel coefficients at the corresponding relays and maintains constant

transmit power at the relays. Whereas, constant gain relaying scheme reduces

system complexity and maintains long-term average transmit power at each

relay. Fixed gain relaying scheme is less complex as it does not require the

knowledge of the fading channel realization (and hence channel estimation) at

the relay node (Foroogh.S.Tabataba et al 2011). Functionally, AF relays

Non-Regenerative relaying strategy Regenerative relayingstrategy

Amplify and Forward Compress and Forward Decode and Forward Demodulate and Forward

Relaying strategy

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resemble traditional analog relays. The main advantages of AF relaying

strategy are

Its inherent simplicity (Woraniti Limpakoom et al 2009),

Lower computational complexity in terms of less processing

burden (load) on the relay (Mazen Omar Hassna and

Mohammed Slim-Alouini 2004, Chirag S. Patel and Gordon

L. Stuber 2007),

Energy saving in power limited systems (Woraniti

Limpakoom et al 2009).

Very short delay as it only amplifies the signal (Rui Zhang

et al 2009).

The drawback of AF relaying strategy is

Noise accumulation along the transmission path when the

channel is in deep fade (Karim G.Seddik et al 2007).

In general, AF relaying strategy is suitable in applications where

high complexity is not acceptable. When AF relaying strategy is applied to a

wireless relay network, it is referred to as Amplify and Forward Wireless

Relay Network (AFWRN) (Shashibhushan Borade et al 2007). AFWRN

relays operate in half-duplex or full duplex mode. In half duplex mode,

communication is supported in both directions, but only one direction at a

time. Typically, when a destination node receives a signal from the source

node, the destination node must wait till the source node to stop transmitting

the signal before it replies. A full duplex relay is practically realizable because

it transmits and receives at the same time but it is hardly implementable in

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reality (Rui Zhang et al 2009). An example of the half-duplex system is a

walkie-talkie. There are several benefits of using half-duplex over full-duplex.

The most important one is its lower implementation complexity, whereas for a

full-duplex system, simultaneous transmission and reception of signals

requires precise design for the component.

Figure 1.5 Amplify and Forward Wireless Relaying Strategy

1.4.2 Compress and Forward Relaying Strategy

A CF or estimate and forward or observe and forward or quantize

and forward relaying strategy quantizes the received signal. More precisely,

the relay employs source coding with side information at the destination node.

This scheme is also known as Wyner Ziv coding (Sebastien Simoens et al

2010). The CF relaying strategy is efficient in cases where source node to

relay node and source node to destination node channels are of comparable

quality, and relay node to destination node channel is also good.

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1.4.3 Decode and Forward Relaying Strategy

A DF is an example of regenerative relaying strategy in which the

relay node first verifies the correctness of the information sent from the

source node by decoding all the information. Then it re-encodes the

information and forwards it to the destination node as shown in Figure 1.6. If

DF is employed in WRN, it is referred to as Decode and Forward Wireless

Relay Network (DFWRN). In DFWRN, channel estimation is similar to that

in a traditional point to point system. Since relays are geographically

distributed and different relays come from different mobile terminals, the

individual power constraint for each relay needs to be considered (Feifei Gao

et al 2008a). The advantage of this DF relay strategy is that it involves

decoding and encoding of information bits at relay nodes. However, the

drawbacks of DF relaying strategy are

Longer propagation delay, higher delay tolerance causing

security problems (Yongming Huang et al 2010) and

increased computational complexity due to decoding and

encoding.

Suffers from error propagation (Karim G. Seddik et al 2007)

Highly non trivial and the complexity increases significantly

as the number of relay node grows (Bo Wang et al 2006).

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Figure 1.6 Decode and Forward Wireless Relaying Strategy

1.4.4 Demodulate and Forward Relaying strategy

In Demodulate and Forward (DMF) relaying strategy, the relay

demodulates each received symbol individually, remodulates and retransmits

them to the destination node (Alireza Shahan Behbahani et al 2008).

Demodulate and Forward relaying strategy is an alternative to decode and

forward relaying strategy to reduce receiver power consumption due to

channel decoding at the relay as well as to minimize the overall delay at the

destination node.

Among the various relaying strategies, AF is found highly suitable

for parallel relay networks due to its ability to pass on soft information

(Krishna Srikanth Gomadam and Syed Ali Jaffar 2009). It is also used for

adhoc wireless systems in which high implementation complexity for

encoding and decoding is rarely acceptable (Yanwu Ding et al 2009). Due to

the advantages offered by AF relaying strategy, this thesis mainly pertains to

amplify and forward wireless relay networks and its performance analysis. In

addition a small section on DFWRN is also dealt herein this thesis.

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1.5 SYSTEM MODEL FOR THREE TERMINAL AFWRN

Consider an AFWRN with three terminals namely a source node, a

relay node and a destination node as shown in Figure 1.7 with single antenna

in each of the nodes (Yu Bi and Yanwu Ding 2012).

Figure 1.7 Three Terminal AFWRN

As shown in Figure 1.7, a source node communicates with a

destination node directly and also with the help of a relay node. The AFWRN

assumes perfect synchronization among the nodes, employs half-duplex

transmissions with an orthogonal transmit scheme in non overlapping time

slots. In AFWRN, information data transfer between the source node to

destination node is accomplished in two phases namely phase I and phase II.

In phase I, signal is transmitted from the source node to the destination node

and also to the relay node as the channel is a broadcast channel. The received

signal at the destination node (Woraniti Limpakom et al 2009) is given as

dssdsd nxfy (1.1)

where sdf is the Channel Impulse Response (CIR) or Channel State

Information (CSI) between the source node and the destination node, sx is the

transmitted signal and dn is the noise at the destination node. Similarly, the

received signal at the relay node (Woraniti Limpakom et al 2009) is

represented as

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rssrsr nxgy (1.2)

where srg is the CSI between the source node and the relay node sx is the

transmitted signal and rn is the noise at the relay node. During phase II, the

received signal at the relay node sry is amplified by and forwarded to the

destination node. The received signal at the destination node is expressed as

rd rd sr dy h y n (1.3)

where rdh is the CSI between the relay node and the destination node and is

the amplifying gain (Yu Bi and Yanwu Ding 2012). The gain is chosen

such that it satisfies the power constraint at the relay and it is given as

22Ssr

r

PgP (1.4)

where SP is the source node power, rP is the relay node power and 2 is the

noise variance. The CSI defined by srsd gf , and rdh represent the effects of

path-loss, shadowing and frequency non-selective fading. The terms rn and

dn capture the effects of receiver noise and interference at relay node and

destination node respectively. These terms are modeled as mutually

independent, circularly symmetric, complex Additive White Gaussian Noise

(AWGN) with zero mean and variance 2 ( Woraniti Limpakom et al 2009).

1.6 SYSTEM MODEL FOR THREE TERMINAL MIMO AFWRN

Consider a three terminal MIMO AFWRN equipped with SN

antennas at the source node ,S relN antennas at the relay node R and DN

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antennas at the destination node D as shown in Figure 1.8

Figure 1.8 Three Terminal MIMO AFWRN

The MIMO channel matrix between the source node and the relay

node is represented as G and from the relay node to the destination node as

H respectively (Kyoung-Jae Lee et al 2010). It is assumed that the elements

of channel matrices are Independent Identically Distributed (IID) and

experience Rayleigh flat fading as assumed in 3 terminal Single Input Single

Output (SISO) AFWRN system. MIMO channel matrices are represented

mathematically by Srel NNCG and relD NNCH and its entries are assumed to

be circularly symmetric complex Gaussian random variables with zero mean

and unit variance.

In phase I, the source node transmits a 1SN data signal vector s

through the MIMO channel ,G to the relay node and the received signal

vector 1relN at the relay node (Kyoung-Jae Lee et al 2010) is given as

RR nGsy (1.5)

where Rn is the 1relN AWGN vector at the relay node. In phase II, at the

relay node R , the 1relN received signal vector Ry is multiplied by an

relrel NN amplifying matrix F and the signal is forwarded to the destination

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node. The amplifying matrix is defined as PF , where is the fixed

amplifying gain at the relay node and P is an relrel NN unitary Precoding

matrix and it is usually a diagonal matrix or permutation of a diagonal matrix.

The 1DN received signal vector at the destination node in a 3 terminal

MIMO AFWRN system (Kyoung-Jae Lee et al 2010) is represented as

DeRD nHFnHFGsy (1.6)

where Den is the 1DN noise vector at the destination node. Let HFGW

be the SD NN overall channel matrix between the source node and the

destination node and DeRD nHFnn be the 1DN overall noise vector at

the destination node. Then, Equation (1.6) is represented as

DD nWsy (1.7)

1.7 CHANNEL ESTIMATION FOR AF WIRELESS RELAY

NETWORK

Channel estimation in an AFWRN (Tao Cui et al 2007, Feifei Gao

et al 2008) is a technique of estimating the wireless channel coefficients or

CSI between a transmitter or source node and a receiver or a destination node.

The wireless channel in an AFWRN normally contributes to undesirable

effects of time dispersion, attenuation in magnitude and reduction in phase in

the signal. These undesirable effects have to be eliminated, before data

detection in an AFWRN in case if linear modulation schemes are to be

applied at the source node for data transmission.

Channel estimation in an AFWRN is carried out using estimators

which are based on estimation theory. Estimation theory forms the basis for

many signal processing applications intended for extracting information.

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Extracting information ultimately implies estimation of the values of a group

of parameters. The estimates are usually obtained from a mathematical

operator named as Estimator. Mathematically, an estimator may be thought of

as a rule that assigns a value to the estimation parameter of interest for each

realization of the observed signal (Steven M. Kay 1993).

The parameters of interest in a group can be Deterministic or

Random but are unknown. Estimation of parameters in a group can be

classified into two types namely Classical estimation and Bayesian

estimation. Estimation of Deterministic parameters in a group is referred as

Classical estimation and estimation of Random parameters in a group is

referred to as Bayesian estimation. The classical estimation approaches are

Cramer-Rao Lower bound (CRLB), Rao-Blackwell-Lehman-Scheffe, Best

Linear Unbiased Estimator (BLUE), Maximum Likelihood (ML) estimator,

Least Squares (LS) estimator and Method of Moments (MOM). The

Bayesian estimation approaches are Minimum Mean Square Error (MMSE)

estimator, Maximum APosteriori Estimator (MAP), Linear Minimum Mean

Square Error (LMMSE) estimator (Steven M. Kay 1993).

In addition to the above classification based on the parameter of

interest, basically, an estimator can be classified into two types based on the

property it satisfies. An unbiased estimator is defined as the one that on an

average the estimator yields true value of the unknown parameter. Unbiased

estimators tend to have a symmetric Probability Density Function (PDF)

centered about the true value of the parameter. Within this class of unbiased

estimators, the estimator with minimum variance exists. In general, a

Minimum Variance Unbiased (MVU) estimator does not exist although

several methods are available to find them and those methods rely on Cramer-

Rao Lower bound and the concept of a sufficient statistic. If a minimum

variance unbiased estimator does not exist, or if the previous approaches fail,

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a constraint is placed on the estimator to be linear in data. This results in an

easily implementable estimator. On the other hand, a biased estimator is the

one that is characterized by a systematic error, which presumably should not

be present (Steven M. Kay 1993) and its performance is always very poor.

Performance of any estimator obtained will be critically dependent

on the PDF assumptions and estimators in general need to be optimal. In

searching for optimal estimators an optimality criterion needs to be adopted.

A natural one is the Mean Square Error (MSE) (Steven M. Kay 1993) which

measures the average mean squared deviation of the estimator from the true

value. Unfortunately, adoption of this natural criterion leads to unrealizable

estimators, which implies that it cannot be written as a sole function of data.

Figure 1.9 Block Diagram of Wireless Communication System

As shown in Figure 1.9, the technique of channel estimation

actually forms an estimate of the amplitude and phase shift of the wireless

channel with the aid of the estimation algorithms and training data signal or

the pilot signal. This is essential to eliminate the effect of the wireless channel

and thereby makes data detection more efficient in an AFWRN. Hence,

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channel estimation attains significance as an important tool for determining

receiver performance in an AFWRN. Channel estimation technique in an

AFWRN (Aris S. Lalos et al 2008) depends mainly on the pilot signal energy,

channel estimation algorithms, and the environment conditions. CSI for an

AFWRN can be obtained through three techniques:

Training based channel estimation technique

Blind channel estimation technique

Semi-blind channel estimation technique

In training based channel estimation technique for AFWRN,

training data signals or pilot signals that are known a priori to the destination

node are transmitted into the wireless channel from the source node. The

commonly employed training data signals (Feifei Gao et al 2008, Oomke

Weikert and Udo Zolzer 2007) are presented in the Table 1.1.

Table 1.1 Training Data signals

Training Data Sequence Mathematical DescriptionAll one vector sequence 11..111N1 is an 1N vector

with onesZadoff Chu sequence – It is ageneralized chirp like polyphasesequence. The elements of thissequence have same magnitude inboth time and frequency domain toreduce Peak to Average Power Ratio(PAPR) problem

oddisNNnN

qnQnj

evenisNNnN

qnQnj

e

enx

;1....2,01;)21(

;1....2,01;)2(

)(

where q and Q are integers in whichQ is relatively prime to N

Perfect Root of Unity (PRUS)sequence - It is constructed for anylength N using Frank-Zadoff Chusequences.

;1,...01;)1(

;1,...01;2

)(NkoddwithNfor

NkQkj

NkwithevenNforN

Qkj

e

enx

where Q is a natural number greaterthan zero and co-prime to N

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Blind channel estimation technique is carried out by evaluating the

statistical information of the channel and it does not rely on the knowledge of

the transmitted signal. A well known class of blind estimation algorithms is

the decision directed or decision feedback algorithms. These algorithms rely

on the demodulated and detected sequence at the receiver to reconstruct the

transmitted signal. Blind channel estimation has its advantage in that it has no

overhead loss. But, it is only applicable to slowly time-varying channels due

to its need for a long data record. The major drawback of the blind channel

estimation technique is that a decision or bit error at the receiver will cause

the construction of an incorrect transmitted signal. On the whole, the decision

error introduces a bias in the channel estimate thereby making it less accurate.

Semi-blind channel technique is a hybrid of blind and training

techniques, which utilizes pilots and other natural constraints to perform

channel estimation. The techniques commonly used for estimating the

channel coefficients in a an AFWRN are Least Squares (LS) estimator,

Minimum Mean Square Error (MMSE) estimator, Best Linear Unbiased

Estimator (BLUE) and Maximum Likelihood (ML) estimator. Also other

variants of LS estimators namely Scaled LS, Sequential LS, Ordered LS,

Weighted LS. Further, Relaxed Minimum Mean Square Error (REMMSE)

estimators and Maximum APosteriori (MAP) estimators also exist (Mehrzad

Biguesh and Alex B. Gershman 2006, Steven M. Kay 1993). This thesis

focuses mainly only on the general forms of estimators and not into its

variants.

1.7.1 Least Squares Estimator

LS is an estimator with no optimality property associated with it

and does not constrain it to be linear in data. The method of LS dates back to

1795 when Gauss used the method to study planetary motions (Steven M.

Kay 1993). LS estimator minimizes the squared difference between the

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received signal and the assumed data or noiseless data. The advantage of LS

estimator is that it is easy to implement The drawback of LS estimator is that

it reduces signal error and does not reduce channel estimation error since it

makes probabilistic assumptions only on the data for the signal model which

is assumed (Steven M. Kay 1993,Mehrzad Biguesh and Alex B. Gershman

2006).

1.7.2 Minimum Mean Square Error Estimator

It is an optimal estimator defined to be the one which minimizes

mean square error when averaged over all the realizations of the estimation

parameter of interest and the received signal. The estimator which minimizes

the Bayesian MSE is called as Minimum Mean Square Error (MMSE)

estimator. MMSE estimator is the mean of the posterior Probability Density

Function (Steven M. Kay 1993). The advantage of MMSE estimator is that it

produces the minimum mean square error through minimization of Bayesian

MSE. The drawback of MMSE estimator is that it is based on conditional

PDF and integration of it is complex for increased number of observation

samples.

1.7.3 Best Linear Unbiased Estimator

Best Linear Unbiased Estimator (BLUE) is an estimator obtained

by restricting the estimator to be linear in data and finding the linear estimator

that is unbiased and has minimum variance characteristics. This estimator

referred to as BLUE is Best Linear Unbiased Estimation according to (Steven

M. Kay 1993) is determined only with the knowledge of only the first and

second moments of the probability density function. The first moment is the

mean and the second moment is the spread from the mean. It does not require

the complete knowledge of PDF and hence it is employed for practical

implementations (Steven M. Kay 1993, Mehrzad Biguesh and Alex B.

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Gershman 2004). Also, BLUE posses the minimum variance among the

family of unbiased estimators making it a Minimum Variance Unbiased

(MVU) estimator. The advantage of BLUE is that it has minimum variance

characteristics. The drawback of BLUE is that it is a suboptimal estimator.

1.7.4 Maximum Likelihood Estimator

Maximum Likelihood (ML) estimator is defined as the value of the

estimation parameter which maximizes the likelihood function or PDF

(Steven M. Kay 1993). ML has asymptotic properties of being unbiased,

achieves CRLB and has a Gaussian PDF. The advantage of ML estimator is

that it is the optimal estimator as it is based on the PDF. The drawback of ML

estimator is that it is an intensive search algorithm.

In general, the channel estimation techniques use two estimation

theoretic performance metrics, namely MSE and CRLB. The first metric MSE

depends on the specified channel estimation algorithm employed at the

receiver. MSE defines the expectation of the squared value for the difference

between the estimated value and the true value of the estimation parameter of

interest. Second metric, CRLB sets a lower bound on the MSE of the channel

estimator. Also, it allows to place a lower bound on the performance of an

unbiased estimator and at worst, acts a benchmark against which the

performance of any unbiased estimator can be compared. On par with MSE of

the channel estimation, the expression for CRLB is independent of specific

channel estimation technique employed at the receiver (Steven M. Kay 1993).

1.8 PERFORMANCE METRICS FOR AFWRN

The metrics for analyzing the performance of AFWRN are ergodic

capacity, Bit Error Rate (BER) and outage probability.

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1.8.1 Ergodic Capacity

Ergodic capacity is an important metric for analyzing AFWRN

performance as it specifies the ability to maintain long term constant bit rates

(Shin Jin et al 2010). Ergodic capacity refers to averaging the randomness of

the channel gain over time (Bo Wang et al 2004). It attains an important

metric as it yields an information (Thomas M. Cover and Thomas 1991)

theoretic bound (Bhuvan Modi et al 2012) on the achievable rate for reliable

communication over fading channels. But, ergodic capacity is generally

difficult to obtain (Shin Jin et al 2011). Ergodic capacity (Bo Wang et al

2005) analysis with Perfect CSI and Imperfect CSI provides an insight into

the maximum capacity (Anders Høst Madsen 2002, Gerhard Kramer et al

2003) that can be reached.

1.8.2 Bit Error Rate

Bit Error Rate is an important performance metric which analyzes

the performance of AFWRN for any specified modulation scheme. BER is

defined as the rate at which errors occur in an AFWRN when a set of

information bits are transmitted (Seungyoup Han et al 2009). The definition

of BER is defined by a simple formula

BER = number of errors / total number of bits sent

In practical situations, the wireless channel suffers from severe

fade, and ultimately degrades the overall AFWRN system performance. As a

result, proper receiver structure is to be designed to improve system

performance (Feifei Gao et al 2008, Yindi Jing and Babak Hassibi 2004).

1.8.3 Outage Probability

Outage Probability (David Tse and Pramod Viswanath 2005) is an

important metric to analyze the performance of AFWRN in slow fading

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channels. It arises when the channel is so poor and that no scheme can

communicate reliably at a fixed data rate. The largest rate of reliable

communication at a certain outage probability is called outage capacity. An

AFWRN system is said to be in outage if the received Signal to Noise Ratio

(SNR) falls below a specific threshold SNR

1.9 RESEARCH ISSUES IN AFWRN

1.9.1 Channel Estimation

Channel estimation is one of the major issues in an AFWRN. It

attains significance as it is essential for signal detection in wireless relay

networks in order to carry out phase alignment which is required in coherent

relaying. Another important feature of channel estimation is that the

performance of a good receiver is based on impact of the channel. Generally,

channel state information is considered to be perfect or its availability is

known to destination node in an AFWRN. When perfect CSI assumption is

made at the destination node, each of the source node present in an AFWRN

completely subtracts/cancels out its own data at the broadcasting phase. Also,

channel uncertainty, due to channel estimation errors, prevents the users from

subtracting/canceling out completely their own data. This leads into self

interference and consequently system performance degradation. Moreover, in

practical environments, CSI is not available and has to be estimated.

In an AFWRN, individual channel coefficients between source

node to relay node and relay node to destination node need not be estimated

and only the overall channel coefficients needs to be estimated (Feifei Gao

et al 2008). This is because estimating the source node to the relay node and

relay node to the destination node channel coefficients has several drawbacks.

The first drawback is that the relay node must inform the destination node of

the estimate of the source node to the relay node channel, which consumes

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bandwidth efficiency and consumes additional transmitting power. The

second drawback is that the transmission of channel estimate will suffer from

further distortions (Feifei Gao et al 2008).When channel coefficients are

estimated it results in errors and delays which deteriorate the potential

performance improvement of AFWRN. Hence, selection of the estimation

algorithm which reduces estimation error to a minimal value needs to be

considered.

1.9.2 Synchronization

Synchronization is another issue in AFWRN as the receiver has to

determine when there is a signal to demodulate and where the packets start in

order to interpret the received signal. When there is no data transmission, it is

important that the receiver is able to enter into a mode where power can be

saved. However, as soon as transmission starts the receiver has to achieve

synchronization in a very short time to prevent the loss of data.

1.9.3 Power Allocation

In AFWRN transmission power is the primary resource as it is

shared by many relay nodes and it ultimately plays a role in its lifetime and

scalability (Tony Q.S. Quek et al 2010). In AFWRN, relay terminals

cooperate with each other for data transmission, making power control of the

source terminal and power allocation issues too complicated. Hence, to

overcome complications, and to maximize AFWRN throughput, best relay

node selection with uniform power distribution between the source node and

the relay nodes needs to be considered (Jun Cai et al 2006). Under uniform

power allocation, threshold based sufficient and necessary conditions have to

be derived to facilitate the search of feasible relay node so that better network

throughput in terms of average mutual information can be achieved from user

relaying over direct transmission. With the help of the derived conditions,

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searching time for the best relay node from a set of available relay nodes can

be reduced. From the selected relay node, an analytical expression, optimal

power allocation can be developed. Moreover, to minimize symbol error rate

for overall transmission, optimal power allocation schemes can be employed.

Generally, optimal power and power allocation schemes are obtained using

Convex Programming (Feifei Gao et al 2008) so that signal to noise ratio can

be maximized at the destination node even with partial availability of CSI.

1.9.4 Information Exchange/Forward/Backward

Information exchange in an AFWRN plays an important role in

implementing any resource optimization process. This is mandatory for

amplify and forward wireless relay networks employing coherent modulation

and demodulation techniques. The information is transmitted from the source

node to relay node and relay node to the destination node in the forward

direction. In backward direction information bits are sent in as feedback from

the destination node to the relay node which is useful for applications like

Beamforming.

Beamforming is a spatial filtering or a signal processing technique

used in sensor arrays for directional signal transmission or reception. This is

achieved by combining elements in a phased array in such a way that signals

at particular angles experience constructive interference while others

experience destructive interference. Beamforming can be used at both the

transmitting and receiving ends in order to achieve spatial selectivity. The

improvement compared with omni-directional reception/transmission is

known as the receive/transmit gain. During transmission, a beamformer

controls the phase and relative amplitude of the signal at each transmitter, in

order to create a pattern of constructive and destructive interference in the

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wavefront. While receiving, information from different sensors is combined

in a way where the expected pattern of radiation is preferentially observed.

In the receive beamformer, the signal from each antenna is

amplified by different weights. Generally different weighting patterns are

used to achieve the desired sensitivity patterns. A main lobe is produced

together with nulls and side lobes. Moreover, controlling the main lobe width

(the beam) and the side lobe levels, the position of a null can be controlled.

This is useful to ignore noise in one particular direction, while listening for

events in other directions. A similar result can be obtained on transmission.

Beamforming techniques are broadly divided into two categories,

namely conventional beamforming and adaptive beamforming. Conventional

beamformers use a fixed set of weightings and time-delays (or phasing) to

combine the signals from the sensors in the array. Primarily, it uses the

information about the location of the sensors in space and the wave directions

of interest. In contrast, adaptive beamforming techniques generally combine

this information with properties of the signals actually received by the array,

mainly to improve rejection of unwanted signals from other directions. This

process may be carried out in either time or in frequency domain.

Adaptive beamformers automatically adapt its response to different

situations. A criterion has to be set up to allow the adaptation to proceed such

as minimizing the total noise output. Because of the variation of noise with

frequency, in wide band systems it may be desirable to carry out the process

in the frequency domain. Adaptive beamforming has the characteristics of

interference signal minimization.

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1.9.5 Interference Management

Interference arises in an AFWRN due to the broadcast nature of the

relay nodes, presence of multiple of relay nodes and multiple source nodes.

Generally, the broadcast nature in an AFWRN exposes the relays to common

interferers which results in correlated noise at the nodes (Krishna Srikanth

Gomadam and Syed Ali Jafar 2006) which is a significant drawback for

successful operation of AFWRN. Such common interference is minimized by

careful selection of relay gains so that they add out of phase. Existence of

multiple relays in a network naturally creates a multiuser scenario and

multiple sources, can produce interference among data streams. Interference

management is therefore closely related to resource optimization problems as

well as multiple access techniques in relaying systems.

Other issues of AFWRN such as level of relay mobility, time and

frequency synchronization require careful examinations but are not dealt with

this thesis. This thesis addresses only channel estimation issue and ergodic

capacity, BER metrics as they govern the successful operation of an AFWRN.

In this thesis, it is assumed that the nodes have perfect synchronization and no

interference among them.

1.10 SCOPE OF THE THESIS

Among the research issues of AFWRN, this thesis addresses the

issue of estimating the channel coefficients of WRN, since the knowledge of

channel state information plays an important role in signal detection. This

thesis analyses BLUE based channel estimation technique and the

conventional channel estimation techniques namely LS estimator and MMSE

estimator for SISO AFWRN and MIMO AFWRN. This thesis also addresses

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the effect of channel estimation error on ergodic capacity and BER

performance of AFWRN.

1.10.1 Objectives

1. To develop a channel estimation technique for AFWRN

which provides minimal estimation error.

2. To analyze the performance of the proposed channel

estimation technique and compare its MSE performance with

the existing estimation methods for both SISO AFWRN and

MIMO AFWRN.

3. To analyze ergodic capacity and BER performances of

AFWRN with Imperfect CSI and analyze the impact of the

proposed channel estimation technique on these performance

metrics for SISO AFWRN and MIMO AFWRN.

4. To apply the proposed channel estimation technique in the

various practical system models of SISO AFWRN and MIMO

AFWRN and analyze the performance.

1.11 ORGANIZATION OF THE THESIS

In Chapter 2, a new method using the concept of BLUE is proposed

for estimating the overall channel coefficients of SISO AFWRN. Analytical

expression for MSE of the proposed technique is also derived. The MSE

performance of the proposed technique is analyzed and compared with CRLB

and other existing methods. In Chapter 3, the proposed technique is extended

for estimating the overall channel coefficients for MIMO AFWRN. The MSE

performance is also analyzed and compared with existing techniques.

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Chapter 4, presents ergodic capacity and BER analysis of AFWRN with

Imperfect CSI in SISO and MIMO environments. In Chapter 5, the proposed

channel estimation technique is applied for a relay assisted multi user

downlink transmission system. Though, this thesis is mainly concerned with

AFWRN, using BLUE, channel estimation for DFWRN using BLUE is also

mathematically portrayed for analysis. Chapter 6, concludes the thesis, with a

note on future work.