i

**Performance analysis of OSTBC with Hybrid Decode-Amplify **

**and Forward relay network**

**Kanoksak Wannatrong (821122-8773) **
**Mohammed Abul Hayat (820101-8754) **

**This thesis is presented as a part of degree of Master of Science in electrical engineering **

**Blekinge Institute of Technology **
**September 2012 **

iii

**Abstract **

In the last few decades, the innovation of Wireless communication has been developed very fast in order to improve the performance of communication systems. Especially, a concept of Multiple Input and Multiple Output (MIMO) is purposed to fulfill a high data rate service such as high quality video conference. However, a limitation in size and power of mobile device in the latest version of cellular system i.e. third Generation (3G) and fourth Generation (4G) causes difficulty to implement MIMO on mobile unit. Hence, Cooperative communication has been created to operate as a virtual MIMO in modern Wireless communication.

In the main purpose of this paper, the performance analysis of Hybrid Decode-Amplify and Forward (HDAF) Cooperative communication using Orthogonal Space-Time Block Code (OSTBC) is derived in term of Symbol Error Rate (SER) against Signal-to-Noise Ratio (SNR) when the system applies different type of modulation techniques. Additionally, the error performance is derived base on Moment Generating Function (MGF) of the Rayleigh fading channel. In our thesis, we only cope with the down link of the system. Assuming that multiple antennas can be equipped into a transmitter which operates as base station in cellular system, mobile unit can be equipped with only single antenna due to the size limitation which operates as relays and destination. Moreover, the receiver uses Maximum Ratio Combining (MRC) to receive the transmitted signal.

In the first step, we derive the performance of single relay system in order to show a better performance when increase the number of antennas at the transmission. In the second case, the performance of multiple relays is derived in order to express the behavior of the system when the number of relay is increased. Finally, the saturated number of relay can be investigated by the concept of relaying gain.

**Keywords: Cooperative communication, symbol error rate, moment generating function, **

iv

**Acknowledgement **

This thesis project was carried out at the Department of Electrical Engineering, Blekinge Institute of Technology, Karlskrona, SWEDEN. This thesis was done under the supervision of Maria Erman and it was started in April 2012.

We would like to express our sincere gratitude to our thesis supervisors Maria Erman, Department of Electrical Engineering, Blekinge Institute of Technology, Karlskrona-SWEDEN for her constant source of inspiration throughout the project. This project would have not been possible without their consistent advice and encouragement.

Finally we would like to thank our family members, friends for their support and help.

Karlskrona, Septermber 2012

v

**Content **

**ABSTRACT ...III**

**ACKNOWLEDGEMENT ... IV**

**CONTENT ... V**

**LIST OF FIGURES ... VI**

**SECTION 1 INTRODUCTION ... 1**1.1PROBLEM STATEMENT ... 2 1.2RESEARCH APPROACH ... 2 1.3THESIS OUTLINE... 2

**SECTION 2 BACKGROUND ... 3**2.1MULTIPATH FADING ... 3

*2.1.1 Frequency selective fading and flat fading ... 4*

*2.1.2 Slow fading and fast fading ... 5*

2.2RAYLEIGH FADING DISTRIBUTION ... 5

*Error probability in fading channel ... 6*

2.4DIVERSITY ... 8

*2.4.1 Diversity techniques ... 8*

*2.4.2 Diversity combing techniques ... 9*

*2.4.2 Transmitter diversity ... 11*

2.5MULTIPLE INPUT MULTIPLE OUTPUT ... 11

*2.5.1 The system model of MIMO ... 11*

*2.5.2 Space Time Block Coding ... 13*

*2.5.3 Decoding method ... 15*
2.6COOPERATIVE COMMUNICATION ... 16
*2.6.1 Decode-and-forward (DF) ... 17*
*2.6.2. Amplify-and-Forward (AF)... 17*
*2.6.3. Compress-and-Forward (CF) ... 18*
*2.6.4 Estimate-and-Forward (EF) ... 18*
*2.6.5 Coded Cooperation... 18*

**SECTION 3 SYSTEM MODEL ... 20 **

3.1A SINGLE RELAY MODEL... 20

*3.1.1 System model ... 20*

*3.1.2 Symbol Error Rate (SER) ... 23*

3.2MULTIPLE RELAYS MODEL ... 25

*3.2.1 System model ... 25*

*3.2.2 Symbol Error Rate ... 27*

**SECTION 4 NUMERICAL ANALYSIS ... 30 **

4.1NUMERICAL ANALYSIS OF SINGLE RELAY SYSTEM ... 30

4.2NUMERICAL ANALYSIS OF MULTIPLE RELAY SYSTEM ... 34

**SECTION 5 CONCLUSION AND FUTURE WORK... 38 **

CONCLUSION ... 38

FUTURE WORK ... 38

vi

**List of Figures **

**Figure 2.1 Multipath propagation. ... 4 **

**Figure 2.2 Diversity combiner. ... 9 **

**Figure2.3 System model of point-to-point MIMO. ... 12 **

**Figure 2.4 Alamouti space-time encoder. ... 14 **

**Figure 2.5 OSTBC space time encoder. ... 15 **

**Figure 2.6 Cooperative communication system. ... 16 **

**Figure 2.7 Decode and Forward relay mode. ... 17 **

**Figure 2.8 Amplify and Forward relay mode. ... 18 **

**Figure 2.9 Code cooperation model. ... 19 **

**Figure 3.1 System model of OSTBC with Cooperative relay with multiple antennas at transmitter. ... 21 **

**Figure 3.2 System model of OSTBC with Cooperative multiple relay with multiple antennas at transmitter. 26 **
**Figure 4.1 SER versus SNR in comparison of cooperative relay system using BPSK modulation scheme with **
**different number of transmit antennas. ... 30 **

**Figure 4.2 SER versus SNR in comparison of cooperative relay system using different kinds of M-ary phase **
**shift keying with two transmit antennas. ... 31 **

**Figure 4.3 SER versus SNR in comparison of cooperative relay system using different kinds of M-ary phase **
**shift keying with three transmit antennas. ... 32 **

**Figure 4.4 SER versus SNR in comparison of cooperative relay system using different kinds of M-ary **
**modulation scheme with two transmit antennas. ... 33 **

**Figure 4.5 SER versus SNR in comparison of cooperative N number of relays system using BPSK modulation **
**scheme with two transmit antennas. ... 34 **

**Figure 4.6 SER versus SNR of N relays system using BPSK modulation with three transmit antennas. ... 35 **

**Figure 4.7 SER versus SNR of N relays system using BPSK modulation with three transmit antennas. ... 35 **

**Figure 4.8 SER versus SNR in comparison of cooperative N number of relays system using different **
**modulation scheme with two transmit antennas. ... 36 **

1

**Section 1 Introduction **

Wireless communications have been proposed and adapted very fast in the last few decades. In present time, it was found that, new generation of wireless communications such as third generation (3G) and fourth generation (4G) can support high data rate communications and are widely used in the communication field. However, these services are not enough to fulfill ever increasing human demands due to some limitations. The limitations are caused by many parameters such as transmission power, size of mobile device, multi-path fading and noise which degrades the performance of data transmission among users. Therefore, if these limitations can be mitigated, the performance will be improved.

Multiple-Input and Multiple-Output (MIMO) communications have been proposed to overcome the limitations. MIMO exploits the idea of multiple antennas at both the transmitter and the receiver ends. When compared to the conventional Single-Input Single Output (SISO) communications, MIMO gives a better performance. For example, increasing the number of antennas at both sides can enhance the spectrum efficiency of the system [1][2]. Moreover, Maximum Ratio Combining (MRC) at the receiver can mitigate multipath fading by exploiting the Channel State Information (CSI). However, transmitter diversity is quite difficult to implement in mobile communications due to the complexity [3] with transmission in uplink mode. Therefore, Orthogonal Space-Time Block Coding (OSTBC) has been proposed as an attractive solution for MIMO systems to combat channel fading [4]. However, setting up more than one antenna on a single mobile device is impractical because of its small size, as well as the requirements of the extension of the coverage area. Therefore, Cooperative communications have been created. These systems use nodes to help other nodes receive a signal from transmitter or vice versa. The helping nodes are called relays. This kind of communication method gets rid of equipping multiple antennas on a mobile device by operating as virtual MIMO which can not only achieve a high data rate transmission but also increase the coverage area between the transmitter and the receiver [5],[6]. There are a few conventional protocols that can be used in a relay system, for example Amplify-Forward relay (AF), Decode-Forward relay (DF) and Compress-Forward relay (CF) etc. Moreover, some recent papers presented studies about applying OSTBC to Cooperative communications instead of conventional channel block coding. The result shows that OSTBC can improve the performance of Cooperative communications [7]-[10]. Recently, another type of relay system, that is Hybrid Decode-Amplify Forward (HDAF) relay, which has combined the advantages from the aforementioned AF and DF relay systems, has been investigated [11]. These papers state that a hybrid protocol can improve the performance of Cooperative communications.

2

the antenna of each relay unit as well as to have low complexity in channel coding are required to be studied. Furthermore, optimal number of relays is necessary to be considered due to the restriction in the amount of the relays in neighboring area.

**1.1 Problem statement **

In this thesis, the problem is related to OSTBC and Cooperative communication. The MIMO has some limitation i.e. size and power, so it is difficult to set up multiple antennas into a mobile device. To overcome this problem, cooperative communication is purposed to compensate the multiple antennas by using single antenna relays to operate as virtual MIMO.

**1.2 Research approach **

In this thesis, efforts have been made to extend the aforementioned works by applying multiple relays with OSTBC. Closed form expression of the Symbol Error Probability (SEP) of multiple relays using OSTBC will be derived. Optimal number of the relays to achieve the maximum performance will be calculated. This will show the minimum number of relays that the system can use and still can keep a good performance as well as low complexity.

**1.3 Thesis outline **

3

**Section 2 Background**

Signal fading is the constructive and destructive addition of a received signal which arises from multipath components occur in the wireless channel. The destructive addition of multipath components is a major cause of channel impairment. The problem of wireless communication is transmitting information via a wireless channel. This problem limits a capacity of the mobile communication. In recent year, wireless channel impairment is mitigated by MIMO system. Not only MIMO can overcome the channel impairment, but MIMO also enhance the channel capacity as well as reliability of the wireless communication [1][2][12]. The multiple antennas at both transmitter and receiver play as a dominant role in MIMO to achieve a better performance compared to a conventional SISO communication. The multiple antennas can be used to increase data rates through multiplexing or improve performance through diversity [33]. The initial propose of MIMO system was started by [1][12]. However, a limitation on size and power of a mobile communication such as cellular network make difficulty in setting up multiple antennas into a mobile device. Hence, a cooperative diversity was introduced in order to overcome these limitations [5][6].

According to the above paragraph, the important basic features of wireless communication are necessary to know as an instrument to solve this problem. This section will study about relevant topic in wireless communication.

**2.1 Multipath fading **

Signal fading is used to explain amplitude and phase fluctuations of received signal. A copy version of transmitted signal which is transmitted from a same source but arrive to a same destination in different direction and slightly different time are called multipath components. If these multipath components cause the destructive addition to a receiver, it will be called multi path fading. The multipath propagation mechanism is categorized into three types.

*Reflection happens when a transmitting electromagnetic wave bounces off an object that *

has a larger size than a wavelength of the transmitted wave. For example, the ray number1 in figure 2.1 shows a path of transmitting electromagnetic wave from a transmitter to a receiver. The property of reflected wave depends on the reflection coefficient of a reflector [32].

*Diffraction occurs when a transmitting electromagnetic wave impinge on the edge of an *

4

*Scattering occurs when a size of an obstacle or object is the same or less than a *

transmitted signal’s wavelength. The impinging signal is scattered into all direction but all scattered signal has a weaker power. For example, an object such as traffic light, lamp and leave can scatter an incoming signal as shown in figure 2.1 by the ray number3.

**Types of fading **

There are two manifestations of multipath fading that is time dispersion and frequency dispersion. These two dispersions in mobile communication channel cause four effects which depend heavily on the characteristic of a propagated signal, velocity and environment of wireless channel. The time dispersion caused by multipath components is categorized as fast fading and slow fading. The frequency dispersion caused by velocity is also categorized as frequency selective fading and frequency non selective or flat fading.

**2.1.1 Frequency selective fading and flat fading **

The multipath component leads to these two types of fading. Coherence bandwidth is statistical measurement defined by a mathematical relation of delay spread of multipath signal. Coherence bandwidth is used to measure different frequencies whether they are correlated or not when two different signal traverse via channel at the same time. If a range of frequency over which frequency correlation exceeds 0.9, coherence bandwidth can be approximated as

where is the root mean squared (rms) delay spread [32]

2.1.1.1 Frequency selective fading occurs when a bandwidth of transmitted signal is larger than the channel coherence bandwidth i.e. . Under this condition, the

5

gain of a channel is different for different spectral components of transmitted signal. This phenomenon happens in a wide band signal.

2.1.1.2 Flat or frequency non-selective fading occurs when a bandwidth of transmitted signal is narrower than the channel coherence bandwidth i.e. . In this case, the gain of a channel is constant over all spectrum components. Thus, the spectrum of a transmitted signal is still preserved. This is also called narrow band channel due to a transmitted bandwidth is narrow as compared to channel coherence bandwidth.

**2.1.2 Slow fading and fast fading **

Coherence bandwidth is an important parameter to categorize a time dispersive channel. In frequency dispersive channel, there is a parameter impacts wireless channel that is Doppler spread . Doppler spread is caused by a velocity of both mobile communication unit and environment of a channel such as traffic cars on a street. The velocity of a moving mobile unit or an environment leads to a change in time of mobile wireless channel. The time variant channel relates inversely to Doppler spread [32], that is

Where is denoted as channel coherence time which is statistical measure of time duration whether two signals are correlated or not when a same frequency signal traverse through a channel in different time.

2.1.2.1 Slow fading occurs when a coherence time changes slower than a symbol period of transmitted signal i.e. . In this condition, wireless channel is static over a particular time interval [32][33].

2.1.2.2 Fast fading occurs when a coherence time changes at rate faster than a symbol period of transmitted signal i.e. . In this case, the channel impulse response is varied within one symbol period. This distorts transmitted signal very much [32][33].

**2.2 Rayleigh Fading Distribution **

Rayleigh distribution is used to explain a statistical time varying in multipath channel. When a signal is transmitted through a wireless channel which there is no direct component arrives to a receiver. This statistical model can be represented by a complex Gaussian random variable. Two quadrature envelope components of a pass band received signal are independent and identical distribution (i.i.d.) Gaussian random variable with a zero mean and variance [32]. Therefore, the probability density function (pdf) of Rayleigh distribution is given by [30]

{

6
**Error probability in fading channel **

From the conventional probability of symbol error ( ) in Additive White Gaussian Noise (AWGN) channel, the probability of symbol error depends on a static value of SNR ( ) [33]. In fading channels, the SNR is not constant anymore but it changes randomly as result of multipath fading. Due to SNR is a random variable, it can be characterized by distribution defined as . Therefore, the average probability of symbol error ( ̅ ) can be obtained by a calculation of average over the distribution i.e.

̅ ∫ * *
In Rayleigh fading channel, is a Rayleigh distribution given in (2.3). By using some
mathematical manipulation is written as

̅ ̅ For example, the average error probability of error for BPSK is given as

̅ ∫ √ _{ ̅} ̅_{ }_{ }

̅ [ √ ̅

̅ ] ̅ * *
Note that one symbol of BPSK is equal to one bit.

For the higher modulation technique, Q-function in (2.6) makes the equation difficult for calculation. Alternative Q-function and Moment Generating function are proposed to simplify the calculation.

Consider the classical Q-function

√ ∫

( _{ )}

* *
The problem of Q-function is its integrand, because the upper bound is not infinite. This
cause the integration is more difficult. Thus, alternative representation of Q-function is
invented to solve this problem. The new from is given by [33]

∫ ( )_{ }_{ }

7

(√ ) ∫ ( )_{ }_{ }

And the probability of symbol error of M-ary Phase Shift Keying is also obtain

∫ (
)_{ }
where g= ⁄

By substituting (2.5) and (2.8) into (4), ̅ is given by

̅ ∫ ∫ ( )_{ } _{ }_{ }

By changing the position of integrand

̅ ∫ [∫ (

) _{ ] }

From the definition of MGF for a positive random variable with its distribution defined as

∫ _{ }_{ }

It can be noticed that the inner integrand is also MGF. Thus, (2.9) can be re-written as

̅ ∫

The MGF of Rayleigh fading is given by [33]

(
) (
̅
)
* *
Finally, average probability of symbol error for MPSK is given by

̅ ∫ ( ̅

)

8

**2.4 Diversity **

**2.4.1 Diversity techniques **

Diversity combining is one of the best techniques to mitigate the effects of multipath fading and improve reliability in wireless channel. Furthermore, diversity can improve a performance of transmission without increasing the transmitting power or the bandwidth [31][32]. Diversity combing exploits the truth that multiple replicas of transmitted signal independently experience the different fading channel. This cause the transmitted signals fade uncorrelated to each others. Therefore, the overall error probability of the multiple replicas of signal is lower than the error probability of any individual signal. The basic idea of diversity combing is to transmit the same signal through independent fading channels. Thus, the suitable combination of transmitted signals can decrease the effect of fading channel. Diversity techniques can be classified as follow

- Time diversity

Time diversity is achieved by transmitting the same signal in different time slots, where the time difference have to make the transmitted signal experience different uncorrelated fading channels. Hence, the time difference should be greater than the channel coherence time. Time diversity does not impact to a transmission power but it reduces the data rate because the data will be retransmitted in other time slots instead of the new ones [31]. - Frequency diversity

To achieve frequency diversity, multiple replicas of the signal are transmit by different frequencies which are necessary to be separated enough in order to make the transmitted signal fade independently [33]. Therefore, frequency separation should be more than coherence bandwidth. It can be seen that frequency diversity combining requires more bandwidth in transmission.

- Space diversity

9
**2.4.2 Diversity combing techniques **

Diversity techniques are categorized corresponding to the domain which the diversities are introduced as describe in previous subsection. In this subsection, the combing techniques are considered in order to express a complexity and performance of each technique. The key feature of diversity techniques is to coherently combine the received signal which traverses through different fading channel in order to mitigate the effect of fading. Thus, diversity techniques can be categorized corresponding to the method of combining at the receiver. According to the complexity and channel state information, the diversity combining techniques can be explained as follow [31][32].

**2.4.2.1 Maximum ratio combining **

In Maximum Ratio Combing (MRC) is a linear combining technique. From figure 2.2, the output of combiner is a sum of each branch which is weighed by either the same or different factor ( ). The multiplication factor is defined by which can remove the phase shift of branch. Thus, a co-phasing is needed at the receiver due to the phase removal requires the knowledge of signal phase on each branch and should be selected to maximize SNR at the combiner output ( ). Assuming that there are the noise power in each branch i.e. , so that the total noise power at the combiner output is

∑

* *

Hence, the total output SNR at the combiner is given by

**. . . **

X
Rx1
X
Rx2
X
Rx3
X
RxN
Output
_{ }

*branch*

10

∑_{ }

∑_{ } * *
where is the received signal at branch.

In order to obtain the distribution of , the Moment Generating Function (MGF) is considered. Assuming that branch is i.i.d. Rayleigh fading and has the same average SNR ̅. Therefore, the distribution of can be given by [33]

̅

̅ * *

**2.4.2.2 Selection combining **

Consider figure 2.2, a receive diversity system has receive antennas and Signal to Noise Ratio (SNR) equal to at each of branch. In selection combining, the output of combiner is the signal which has the highest SNR. Alternatively, the branch which has the highest SNR will be selected by the combiner. Selection combining technique needs only one branch which is used to receive a signal from the active antenna because just one antenna is used at a time. Thus, co-phasing is not required, so that this technique can be used for either coherent or non-coherent modulation scheme. The combiner output SNR is given by[32]

[ ]

**2.4.2.3 Switch combining **

In a switch combining diversity, all diversity branches are scanned and selected a branch which its SNR is above a given threshold. The output of the combiner is come from the selected branch until its SNR falls below the threshold. When SNR of an active branch drops below the threshold, the scanning process will be started again to select the other branch that its SNR is more than the threshold. This technique is same as selection combining because the output signal is received from only one active antenna. This make them do not need co-phasing at the receiver. Therefore, both two techniques can be applied in coherent and non-coherent modulations.[14][33]

**2.4.2.4 Equal Gain combining **

11

(∑

) * *

The performance of equal gain combining is close to MRC but a bit less than 1 dB of power sacrifice [33]. On the other hand, the complexity of equal gain combining is reduced significantly when compared to MRC.

** 2.4.2 Transmitter diversity **

In transmit diversity, the transmit power will be separated among the multiple antennas at the transmitter. Thus, a space, transmit power and performance processing are more concerned at the transmitter rather than the receiver. Transmit diversity can be designed as either channel gain known or unknown at transmitter.

** 2.4.2.1 Channel know at transmitter **

For this scheme, the transmitter knows a path channel gain referred as Channel State Information (CSI) by a feedback time slot from the receiver. In transmission, multiple transmit antennas will adjust the weighting factor adaptively in order to maximize power or reliability of the signal at the receiver. [15] proposed Switched diversity which is a one of examples of transmitter diversity which knows CSI. However, if the channel changes very fast and the transmitter cannot track CSI, this situation will reduce the received SNR as well as the system performance.

**2.4.2.2 Channel unknown at transmitter **

In this scheme, the transmitter broadcasts a signal without a channel knowledge i.e. CSI. The data will be processed at the signal processor of the transmitter to compensate the lack of CSI. The transmitted signal is decoupled by exploiting a signal detection scheme such as a delay diversity scheme [16][17][18]. The effective way of transmitting a signal without CSI via multiple antennas is to use space-time coding [19].

** 2.5 Multiple Input Multiple Output **

Limitation in conventional SISO wireless channel restricts a communication capacity. Hence, MIMO system has been proposed by [1][2] to overcome this limitation. The authors show that the capacity of MIMO channel grows linearly with a number of an antenna is the system. The MIMO wireless channel is generated by multiple array element antennas at both transmitter and receiver of wireless link.

**2.5.1 The system model of MIMO **

12

From a figure 2.3, * is represented a fading coefficient of each link between j th transmit *

* antenna and i th receive antenna. It can be denoted that H is a * dimension which
each its element are the channel coefficient. The transmitted signals are given by an
column matrix [ ]

*and subscript i th is represented a transmitted signal*

*from i th antenna. Thus, the transmitted signal can be written in a covariance matrix which*given by

{ }

*where superscript H denotes the Hermitian of a matrix and { } denotes as the expectation. *
According to (2.23), a transmitted power can be presented by

_{ }
**where tr(X) denotes the trace of matrix X. **

At each receiver end, there are noise described by column matrix which is denoted as and the noise power can be represented by the covariance matrix is given by

{ }

The noise covariance matrix can be defined in another way if each its element is not correlated to each others, i.e.

Encoder Decoder

13

where ** is an identity matrix has ** dimension and is a noise power in each
branch.

Therefore, the received signal vector can be derived by using simple linear calculation. The vector is given by

And the received signal covariance matrix can be represented as

The power of the received signal can be acquired the same manner as (2.24) i.e.

By using some matrix manipulation, the channel can be shown as

∑ ( )

where is a bandwidth of each sub-channel, and √ is a rank and a singular value
**decomposition of matrix respectively. Mostly, ** . According to (2.30), it is
clear that the capacity of MIMO channel grows relatively with the minimum number of
transmit or receive antennas.

**2.5.2 Space Time Block Coding **

In MIMO channel, Space-Time Block Coding (STBC) is a useful tool to approach the capacity of MIMO. STBC technique is created for using multiple antennas for signal transmission [3][4]. At a space time encoder, serial incoming bits will be mapped into parallel modulation symbols before they are transmitted by different antennas separated in proper distance and various time. This is a reason why such coding method is called space and time code. The STBC with multiple antennas which is used to transmit signal base on orthogonal design is called Orthogonal STBC (OSTBC). The OSTBC make a receiver less complexity for decoding the signal. Alamouti scheme is simple example of OSTBC to provide a transmit diversity by using two transmit and one receive antenna [20].

In figure 2.4, the group of modulated signal from modulator will be encoded by mapping them into each transmit antenna corresponding to a code matrix represented by

14

The mapped signal will be transmitted in two consecutive time slots by two transmit
antennas. In the first time slot, signal and are simultaneously broadcasted from first
antenna and second antenna, respectively. In the second time slot, the conjugate of two
signal i.e. and are also broadcasted from first antenna and second antenna
respectively. From figure 2.4, it is obvious that two columns of the matrix are mutually
orthogonal. This orthogonal property make the receiver simple and low complexity to
decode the set of coded signal by exploiting Maximum Ratio Combining (MRC) scheme with
*single receive antenna [20]. Furthermore, the authors in [20] proposed to use M receiver *
*antennas in order to approach a diversity order of 2M. The Alamouti coding can achieve a *
full diversity order by using simple decode algorithm. This coding scheme can be generated
by an arbitrary number of transmit antennas. By applying an orthogonal property, OSTBC
can get a full diversity order by transmit and receive antennas i.e. the diversity of
[4]. In figure 2.5, shows a structure of OSTBC encoder. Typically, OSTBC is given by a
**transmission matrix with dimension ** . Denoting is a number of transmission
periods for one block of coded signal. Assuming that there are points in a signal
constellation, all modulated signals in a constellation are mapped into encoded signal at
OSTBC encoder. This means that bits will be mapped into blocks by the encoder. At
the encoder output, encoded signals are generated into parallel signal with length of .
Then, these signal sequences will be transmitted simultaneously by transmit antennas
within time slots. It can be seen that there are number of coded signal transmitted in
each time slot. The ratio between a number of coded signals and transmission period is
defined as a code rate given by [3][4][19]

** The elements of transmission matrix can be generated by linear combinations of **
modulated signal and conjugated in order to make it mutually

### [

_{ }

### ]

Encoder Modulator### [

### ]

[ ] [ ]15

orthogonal for example, assuming that is the transmitted length

*from the i th transmit antenna, it can be shown that *

∑ { }

where denoted an inner product of matrix and . Not only the orthogonal transmitted matrix allow OSTBC to achieve a full diversity order, but it also help the receiver to simply decode the received signal by Maximum Likelihood (ML) decision method [19].

**2.5.3 Decoding method **

According to the simple Alamouti scheme, assume that between both ends of the system are linked by fading channel defined by fading coefficient as

_{ }

_{ }

where and are amplitude and phase of the fading channel, . At the receiver, noise is a added into two consecutive time slot. The received signals are

* *
where and are noise which is the complex Gaussian distributed with zero mean and
variance per dimension. The two combiner signals are built at the receiver by a help of
channel estimator [20]. They are given by

̃

̃ Substituting (2.34),(2.35) into (2.36),(2.37) then (2.36),(2.37) into (2.38),(2.39), resulting is

̃ OSTBC Encoder Modulator

16

̃ These combined signal corresponded to (2.40) and (2.41) are sent to the ML detector as a statistical decision rule to detect the transmitted symbols [20].

**2.6 Cooperative communication **

Wireless communication is based on a communication between a transmitter and a receiver. There are only two nodes used to contact to each other for example, mobiles unit and base station in cellular system, laptop and Bluetooth printer in Wireless Personal Area Network (WPAN) or laptop and access point in Wireless Local Area Network (WLAN). If these two nods are surrounded by others communicating nodes, they therefore will compete for the same medium i.e. carrier frequency as well as rising of interference. This downgrades the overall performance of communication system. Hence, a third party node is purposed as an assistance node to help a transmitter relays a message to a receiver or vice versa. It will be seen from [5][6] that, the third party or relay node can improve performance of the communication system significantly. This new purposed system is called Cooperative communication.

The concept behind cooperative communication is to exploit the fact that a source transmitter can broadcast messages in all directions or specific direction by using omnidirectional antenna and beamforming antenna, respectively. In broadcasting period, the neighboring third party or relay node overhear the broadcasting message and forward it to the receiver of destination. At the destination, the receiver exploits diversity technique by combining transmitted signal from both source and relay. The system model of cooperative communications with single relay is shown in figure 2.6.

The relaying protocol is used to define the way how the relay forwards broadcasted signal to the destination. The relaying protocol can be classified to various ways which will be described briefly in the subsequent sections.

Source: S Relay: R Destination: D

17
**2.6.1 Decode-and-forward (DF) **

In DF relaying, the relay decodes the transmitted signal from the source, then re-encode it before it will be forwarded to the destination [21]. The DF protocol is illustrated in figure 2.7. This process is referred as the regenerative method. Thus, DF can be alternatively called Regenerative relay. In real world transmission, the imperfect channel cause a defective decoding, the relay maybe forward the wrong version of the message to the destination. Therefore, this defectiveness reduces the system performance significantly. Moreover, decoding time of the relay limits the performance of the system. If the channel is a good condition, the relay can decoded and forward the message to the destination immediately. On the other hand, if the channel is very poor, the relay will spend more time to decode the received signal. This leads to waste of time efficiency.

**2.6.2. Amplify-and-Forward (AF) **

From figure 2.8, the relay node forwards the source’s signal to the destination by multiplying the signal with some gain. The result of signal multiplication is performed without any kind of regenerative method, so AF can be called as non-regenerative relay. Due to the signal multiplication, not only the source’s signal is amplified, but the noise also is multiplied by the gain. However, the retransmission is quite simple, so the signal processing hardware in the relay is also low complexity when compared to DF protocol [22]. For the amplifying gain, if the relay knows the channel parameter i.e. CSI is known, the relay can adjust the gain adaptively in order to achieve a better performance [2][11]. The CSI know at the relay is called CSI-assisted AF [9]. On the other hand, the semi-blind AF relay is used to refer the relay which amplifies the source’s signal with unknown CSI. It needs only the statistical parameter of the source-to-relay channel. Thus, CSI-assisted relay is more complicated to implement than the semi-blind relays.

Source Relay

Destination

18

**2.6.3. Compress-and-Forward (CF) **

In CF relaying protocol, the relay generate compressed version of the source signal by using quantization method and then forwards it to the destination. This protocol does not perform encoding or decoding the signal obtained from the source [23]. The method of compressing and quantizing the signal are the same as source coding process which convert analog to digital signal. At the destination, the receiver combines the signal received directly from the source and compressed version from the relay in order to obtain the original message.

**2.6.4 Estimate-and-Forward (EF) **

EF is similar to AF and CF in the sense that it does not perform any kind of channel coding at the relay. The relay forwards the estimated version of analog signal from the source. The estimation is performed by both scalar quantization of the signal from the source [24] and the concept of minimum mean squared uncorrelated error (MMSUE) estimate [25].

**2.6.5 Coded Cooperation **

In coded cooperation, a channel coding is integrated into relaying in order to improve the system performance [26][27]. The source’s data or user’s data is encoded by any kind of channel coding i.e. block code, convolution code or a combination of both. Then, the data is separated into different parts and each part is transmitted through a different channel in the system. In the first transmission, each user sends the first separated part of its own codeword as well as tries to decode the other part of separated codeword sent from other users. In the second transmission, if each user can decode the data from the other users, it will generate the remaining codeword of the other users and transmit the decoded data to

Source Relay

Destination

19

the destination. Otherwise, it will transmit the rest of its own codeword to the destination. Figure 2.9 is used to exemplify Coded cooperation.

At user1, the data is encoded with a block code, and the codewords are divided into two parts defined by A1 and A2, respectively. Assume that the original data can be decoded by either A1 or A2. At user2, the same encoding and dividing are done, and resulting codewords are B1 and B2. In first transmit period, user1 broadcasts the A1 to the destination as well as user2. At the same time, user2 broadcasts the B1 to both the destination and user1 in different frequency. In second transmit period, if user1 can decode B1 from user2, it will compute B2 and send it to the destination. If user1 cannot decode B1, it will transmit A2 to the destination. The behavior of user2 in transmission is identical to user1. Finally, the destination decodes the data either from User1 or User2. It can be observed that each user’s transmission performs similar way to DF with increasing in redundancy. The efficiency of Coded cooperation is higher than DF relaying.

Destination A1 A2/ B1 Period1 Period2 User 2 User 1 B1 B2/ A1 Period1 Period2

20

**Section 3 System model **

The performance analysis of Orthogonal Space Time Block Code (OSTBC) with Hybrid Decode-Amplify and Forward (HDAF) relay protocol.

**3.1 A single relay model **

Performance analysis of OSTBC with HDAF single relay is studied in this section. In the recent years, the combination between Multiple Input Multiple Output (MIMO) and Cooperative relay become an attractive research topic. For this scenario, a source and a destination are equipped with multiple antennas to communicate with each other with the help of a multiple antennas relay to transmit the signal from source to destination and vice versa. However, due to a limitation of size of cellular phone, it is difficult to equip multiple antennas on a mobile module. Therefore, the focus is on the idea of multiple antennas at the base station transmitter with a single antenna at both a receiver and a relay. The idea of this scheme can be simply explained as; the transmitter adopts OSTBC [7] to broadcasts information to both a receiver at the destination and the relay node over uncorrelated Rayleigh fading channels; if the relay node receives the information correctly, it will perform as Decode-Forward (DF) mode by re-encoding and to transmits the information to the destination. If the relay node cannot receive the information correctly, it will perform as Amplify-Forward (AF) mode by simply amplifying the signal received from the transmitter then retransmits it to the destination without performing signal regeneration; the destination combines the signal from both the source and the relay using Maximum Ratio Combining (MRC) at its receiver. Based on the PDF, the closed-form SER (Symbol Error Rate) can be investigated. Then the derivation of Moment Generating Function (MGF) of Signal-to-Noise Ratio (SNR) from both the Relay and direct transmission can be presented. It can be seen that the cooperative relay with time diversity can make the communication system more robust against fading channel. The criteria are expressed based on SNR regime.

**3.1.1 System model **

21

In the first phase, the signal vectors are received at the relay, defined as { } , and

the received signal vectors at the destination are defined as { } , are given by

(3.1)

(3.2)

respectively, where { } is the column orthogonal matrix signal transmitted from

OSTBC encoder, each signal are a linear combination of input information sequence
{ } with its conjugate { *} and K is the block length of coded signal, *

{ } denoted the source-to-relay channel and { } denoted the

source-to-destination channel at transmit antenna, { } and { } are zero mean with variance Additive White Gaussian Noise (AWGN)

vectors at a receiver of the relay and the destination respectively. In this thesis, channels are assumed to be flat-fading spatially uncorrelated Rayleigh fading channels and the large scale fading will not be considered for simple tractability.

In the second phase, it depends on an operation of the relay node during the second hop transmission as mentioned above. Therefore, the received signal vectors at the destination can be defined i.e., { } and { } for DF and AF mode, respectively,

are given by
_{ }
(3.3)
Relay
OSTBC
encoder
Source Destination
de

22

_{ }

(3.4)

where represent the relay-to-destination channel coefficient and { }_{ } are

zero mean AWGN vector with variance per dimension. For the AF mode,

*G*

is an
amplifying parameter chosen as
### √

_{‖ }

‖ (3.5)

where ‖ ‖ denotes the squared Frobenius norm.

In case of the DF mode, the information will be retransmitted to the destination during the second phase if the relay correctly decodes received signal. Therefore, the SNR at the

destination is given by

* (3.6) *

where and are the SNR of source-to-destination and relay-to-destination path,

respectively.

In case of the AF mode, the information will be forwarded to the destination by
*amplifying the received signal with the gain G. Then, the SNR * at the destination when

the relay operates as AF mode is given by

(3.7)

where is the SNR of relay-to-destination path when the relay performs as AF mode.

The received SNR per symbol from direct source-to-destination transmission is given by [7]

‖ ‖ ̅

### ‖

### ‖

(3.8)where that * is the transmit energy at the source, R is the code rate of OSTBC and *

### ̅

*is the average SNR.*

For received SNR per symbol from relay-to-destination path when the relay operates as DF is given by

23

Similarly, when apply the squaring method to decode OSTBCs expressed in [28] and some mathematic manipulation [7], the received SNR per symbol at the destination from AF relay mode is given as follow

‖ ‖ | | | | (3.10)

**3.1.2 Symbol Error Rate (SER) **

In this part, PDF statistic SNR value of system will be firstly provided in order to derive SER for the OSTBC transmission with cooperative diversity. Then, Moment Generating Function (MGF) will be expressed to simplify the performance analysis of SER.

For the PDF of SNR at direct source-to-destination transmission, SNR in (3.8) follows
the chi-square distribution of degree of freedom [7], Therefore its PDF can be
expressed as
_{ }
̅
( _{̅} )
(3.11)

From (3.9), the signal is propagated through the Rayleigh flat fading channel. Then PDF of average SNR per symbols is given by

_{ ̅}̅ (3.12)

For the CDF of SNR for OSTBC transmission in cooperative AF relay mode with multiple antennas can be expressed as [7]

_{ } _{ ̅}
̅ _{∑ }
_{ } _{ } _{ }
_{ }( √
̅ )

24
_{ } _{ ̅}
̅ _{∑ }
_{ } _{ } _{ } _{(}
̅ )
(
√
̅ )
̅ (
√
̅ )

By applying the well-know MGF approach [31], the MGF of and can be

expressed as follow;
∫ _{ ̅} ( _{ ̅} )
̅
_{ }√ _{ } [∑
( _{ )}
( _{ )}
_{ }
_{ } ]
Where ̅ , _{ } _{ } _{ } _{ } ,
, , ,
, _{ }

and ̅ ̅ which and

*are denoted as the Gauss’s hypergeometric function and the Gamma function, respectively. *
Denoting is the probability that the relay correctly decodes the symbol when the source
uses M-PSK modulation scheme to transmit information, given by

∫

̅ ̅

where .

25
∫ _{ }(
) ( )
∫ _{ }(
) ( )
Moreover, the unified MGF-based approach method of Digital communication [11] over
fading channels can be applied to calculate the performance of different kind of
modulations. Hence, the SER of a wide variety of M-ary modulations can be obtained.

**3.2 Multiple relays model **

In this section, performance analysis of OSTBC cooperative HDAF multiple relays is examined in order to attain a full diversity gain [29]. For a transmission model, the source will transmit signal to the destination via a number of relays. Each relay will operate as either DF mode or AF mode depends on some SNR threshold value set on it. If the received signal is more than the threshold value that is the relay can decode the received signal correctly, the relay will forward the signal to the destination with re-encoding the signal. On the other hand, if the relay cannot decode the received signal or the received power is below the threshold level, the relay will amplify the received signal with some gain and forward it to the destination without re-encoding the signal. In this part, it will be focus on how to combining DF protocol and AF protocol with multiple relays in order to get a better performance. Furthermore, the performance gain of HDAF over DF and AF mode will be introduced to find optimal number of the relay in the system.

**3.2.1 System model **

From the figure 3.6, the source is equipped with multiple transmit antenna, while all relays
and the destination are equipped with a single antenna. The source and the destination
*communicate over Rayleigh flat fading channel. At the N number of relay node during the *
second hop transmission, for the relays which can correctly decode the signal, they will
forward information to the destination. For the left of relays which cannot decode the
*signal, they will retransmit the signal to the destination with an amplifying parameter G. *
*Finally, the destination combines the signal from both nth number of relays and the source *
by using MRC.

*In the first phase, the signal vectors are received at each nth relay, defined as *

{ _{ }}_{ }, and the received signal vectors at the destination are defined as { } ,

are given by

(3.20)

26

*In the second phase, it depends on an operation of each nth relay node during the second *
hop transmission. Therefore, the received signal vectors at the destination can be defined
i.e., { } and { } for DF and AF mode, respectively, are given by

_{ }

(3.22)
_{ }

(3.23)

The definitions of , and ** are given as in the section 3.1. For **

{ } denote the source-to-destination channel at transmit antenna of

*each nth relay, * represents the relay-to-destination channel coefficient. , are

zero mean with variance Additive White Gaussian Noise (AWGN) vectors of noise
*between source-to-nth relay and nth relay-to- destination respectively. In this thesis *
*assumes that the channel of source-to-relay and relay-to-destination of each nth relay path *
are identical. * is an amplifying parameter for each nth relay given as*

### √

_{‖ }‖ (3.24) OSTBC encoder Source Destination de Relay1 Relay2 Relay N

27

In case of the DF mode, if some relays correctly decode the received signal, they will retransmit the received signal to the destination during the second phase. For the left of other relays which cannot decode the transmit signal from the source, they will remain silent. Therefore, the SNR at the destination of DF mode is given by

∑

where * is SNR of the nth relay-to-destination path when the relay operate as DF mode. *

*k is number of relays which can decode the received signal . *

In case of AF mode, this means that all relays cannot decode the received signal correctly. They will forward the received signal to the destination by amplifying it with each their own gain

### (

### )

. The SNR of AF mode is given by∑

Where * is SNR of the nth relay-to-destination when all relays operate as AF mode.*

**3.2.2 Symbol Error Rate **

In this section, MGF of (3.15) (3.16) and (3.17) are studied to examine SER performance of multiple relays system. According to (3.25), MGF of can be determined by [29]

∏

By substituting (3.15) and (3.16) into (3.27) MGF of is

_{̅} (

### ̅ )

(

### ̅ )

In the same manner as (3.28), MGF of can be determined by [29]

28

*As shown in (3.18) is the probability that each nth relay can decode the received signal in *
*the first phase. Assuming that source-to-nth relay path is identical. Hence, the probabilities *
( *) that k number of relays can decode the received signal and the other N-k relays cannot *
decode the signal are given by,

∫
̅ ̅
(
∫
̅ (_{ } ̅ )
)

Denote

### is

the probability that all relays fail in decoding the transmitted signal from the source, is given by (_{∫}̅ ̅ )

Therefore, HDAF protocol can be acquired by a combination of DF and AF protocol. The SER of HDAF using M-PSK modulation scheme is given by

∑ ( )
∫ _{ }(
) ( ( ))
( _{ }(
))
∫ (_{ } ) ( (_{ } ))

For a performance of DF and AF protocol with multiple relays can be calculated in the same manner as (3.34) and define as

29

∫ (_{ } ) ( (_{ } ))

After considering the behavior performance of HDAF and other two relay protocols. As
shown in [11] that HDAF scheme outperform a conventional DF and AF relay protocols.
However, there is no instrument to measure how HDAF is better than the two protocols.
This is the inspiration for [29] to deduce the performance gain that HDAF overcome the two
protocols by adapting a concept of relaying gain. As express in system model, the
*destination received the signal from both the source and N single antenna relays. Therefore, *
a diversity order of the system is equal to . By applying the relaying gain concept, the
relaying gain of HDAF when compare to DF and AF protocol can be written as

(
_{) }
(
_{) }

Where and are the performance relaying gain of HDAF compared with DF and AF

protocol respectively.

**Conclusion **

30

**Section 4 Numerical analysis **

**4.1 Numerical analysis of single relay system **

Under this part, the numerical results are be presented and considered in order to prove the performance analysis of SER derived in the previous section. This thesis is interested in multiple antenna at the transmitter and single antenna at the relay and receiver due to a size and power constraint on a mobile device. The varied number of transmit antennas and modulation schemes will be shown to consider an impact on SER of the system. All curves and figures are plotted by SER against an average SNR .

In figure 4.1, the SER performance of the BPSK modulation scheme using different number of transmit antenna are shown. It is clear that four transmit antenna give a better result when compared to two, three or a conventional single transmit antenna of HDAF relay protocol. From the curve, it can be seen that four transmit antennas improve the performance of the system at a high SNR level. Therefore, the performance can be improved if an antenna at the transmitter is increased.

31

Figure 4.2 SER versus SNR in comparison of cooperative relay system using different kinds of M-ary phase shift keying with two transmit antennas.

32

Figure 4.3 SER versus SNR in comparison of cooperative relay system using different kinds of M-ary phase shift keying with three transmit antennas.

33

Figure 4.4 SER versus SNR in comparison of cooperative relay system using different kinds of M-ary modulation scheme with two transmit antennas.

In figure 4.4 Performance of SER versus SNR is plotted. Assume there are two transmit antennas using three different 4-ary modulation schemes to transmit signal to the receiver. It is obvious that QPSK gives a better result than the others. This is because 4-AM and QAM are the modulation techniques which use different power level to transmit data while QPSK uses constant power to transmit data.

** Conclusion **

34

**4.2 Numerical analysis of multiple relay system **

In this part, a numerical analysis will be considered in order to validate the SER performance of HDAF protocol using multiple antennas and multiple relays in the system. Moreover, this part also shows how a number of relays affect the relaying gain. All curve and graph of SER performance are plotted in term of SER against SNR. The relaying gain is plot in term of relaying gain versus N numbers of relay in the system.

Figure 4.5 SER versus SNR in comparison of cooperative N number of relays system using BPSK
modulation scheme with two transmit antennas**. **

35

Figure 4.6 SER versus SNR of N relays system using BPSK modulation with three transmit antennas.

36

In figure 4.6 and figure 4.7 are the identical but the SER performance of OSTBC with HDAF cooperative using multiple relays is plotted in different scale in order to show how difference in slope of each curve is. Assume that the source is equipped with three transmit antennas and using BPSK modulation scheme in transmission. It is obvious that three transmit antennas give a better result when compare to two transmit antennas. From figure 4.7, it can be seen that a slope of four relays change more different than a slope of two and three relays. The difference of slope follows the fact that four relays give more diversity order than the others.

Figure 4.8 SER versus SNR in comparison of cooperative N number of relays system using different modulation scheme with two transmit antennas.

37

Figure 4.9 Relaying gain of HDAF relay protocol compare to AF and DF relay protocol using different number of relays.

In figure 4.9 Performance relaying gain of HDAF over AF and DF protocol is plotted. Assuming that the relay system is symmetric and channel coefficient are identical. The source communicates with all relays and the destination via Rayleigh fading by using BPSK modulation scheme. It is clear that the performance of HDAF relay overcome DF protocol and much better than AF protocol. It is noticed that the gain claim up very fast when a number of relays are increased from one to five. The gain grows slowly after six relays and saturate after around fifteen.

**Conclusion **

38

**Section 5 Conclusion and Future work **

**Conclusion **

In this thesis, the benefit of HDAF cooperative communication using multiple antennas at transmitter with single antenna at the relay and receiver are investigated. The evaluated equations of the model are implemented in MATLAB in order to observe its system performance.

The conclusion from the numerical analysis shows that the multiple antennas at the transmitter with only one antenna at the relay and the destination improve the performance of the system when compared to convention hybrid protocol. Furthermore, the multiple relay system is study by extending the knowledge from the single relay system. The result shows that the multiple relays improve the performance of HDAF significantly if a number of relays are increased.

However, the relaying gain shown that relaying gain is limited by some number of the relay. This means that even though a large number of relays are added into the system, they will not increase the performance of the HDAF in the sense that the SEP of HDAF compared to DF and AF. The required number or optimal number of the relays in HDAF system is the smallest number which makes relaying gain still approaches its maximum values.

**Future work **

Future work for this field could related to a transmit diversity. The channel known at the transmitter or CSI is interesting to study. Due to the multiple antennas can be implemented in the base station in cellular system, the antenna array can use a beam forming method by the help of CSI to operate as the smart antenna. This will enhance the performance of the system significantly.

39

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