### Network Coding Strategies and

### Performance Evaluation for Bidirectional

### Relaying

### ISLAM ALYAFAWI

### Master of Science Thesis

### Stockholm, Sweden 2011

### Network Coding Strategies and

### Performance Evaluation for Bidirectional

### Relaying

### ISLAM ALYAFAWI

### Master of Science Thesis performed at

### the Radio Communication Systems Group, KTH.

### June 2011

### TRITA-ICT-EX-2011:133

### c

### Islam Alyafawi, June 2011

### Tryck: Universitetsservice AB

## Abstract

The ambitious of researchers to reach the maximum capacity of data network lead them to network coding. The simplicity of applying network coding and the improvement to achieve the maximum possible information flow in a net-work lead to apply netnet-work coding in many applications. Netnet-work coding was implemented first in wired medium, and then moved to the wireless one. Due to the special characteristics of the wireless medium and the less reliability com-pared with the wired one, this created wide research area of network coding applications for wireless systems.

In this work, the main focus will be on practical implementation problem when network coding is applied in a two way relay networks. A new proposed method of performing network coding will be presented. Our proposed method can achieve better network performance than conventional network coding. We will also provide our own method to generate the coded message. The main feature of the proposed method is to multiply the received packets together inside the relay node. The packets multiplication is at the symbol level in the complex do-main. The resulted packet will be broadcasted to both receivers. The receivers will be able to recover the other node packet by dividing the broadcasted packet with their own packets. Analytical and experimental analysis show that the pro-posed method has better performance and more robust for channel asymmetry than conventional network coding.

## Acknowledgements

Step by step to achieve my current target in Sweden. Two years of courses, projects, and labs works carried me to the tunnel end, where I can see the light to the next target. At this last step, I am carrying many thanks for all the professors, assistants, and friends who were side by side with me all this time. For this master thesis, the largest step I achieved during my master study, I am heartily thankful to my supervisor, Ben Slimane, and my advisor Jawad Manssour who encouraged, guided and supported me from the initial to the final level, enabled me to develop an understanding of the whole subject.

Lastly, I offer my regards and blessings to my Father, my mother, and my family who have been supporting and encouraging me in this study till now.

## Contents

1 Introduction 1 1.1 Related Work . . . 2 1.2 Problem statement . . . 4 1.3 Thesis Outline . . . 4 2 System model 7 2.1 What Does the node Do? . . . 72.1.1 Binary Source . . . 7

2.1.2 Convolutional Encoder/Viterbi Decoder . . . 8

2.1.3 Modulation/Demodulation . . . 9

2.2 Which network is better? . . . 10

2.2.1 SNR . . . 10

2.2.2 BER . . . 11

2.2.3 Block Error Rate (BLER) . . . 11

2.2.4 Throughput . . . 11

2.3 Channel model . . . 12

3 Network coding 15 3.1 Relaying . . . 16

3.2 Digital network coding . . . 16

3.2.1 Single Modulation, Single Rate (SMSR) . . . 17

3.2.2 Single Modulation, Multi Rate (SMMR) . . . 17

3.3 Analog network coding . . . 18

4 Symbol network coding (SNC) 21 4.1 SNC: previous work . . . 21 4.2 Proposed SNC . . . 21 5 Theoretical analysis 25 5.1 BER . . . 25 5.1.1 M -QAM BER . . . 25 5.1.2 M -PSK BER . . . 25 5.1.3 SNC constellations BER . . . 26 5.2 BLER . . . 27 5.3 Throughput performance . . . 27 vii

6 System performance and analysis 29 6.1 BER . . . 29 6.2 Updated constellations . . . 30 6.2.1 16QAM Constellation . . . 31 6.2.2 64QAM Constellation . . . 32 6.3 BLER . . . 33 6.4 Throughput . . . 36 6.4.1 Coded system . . . 36 6.4.2 Un-coded system . . . 37

7 Conclusion and future work 41 References 43 A Bit Error Rate 47 A.1 SNC (M -QAM) . . . 47

A.2 SNC (Optimized M -QAM) . . . 47

A.3 DNC (M -QAM) . . . 48

A.4 DNC/SNC (M -PSK) . . . 48

A.5 Gain . . . 48

B Block Error Rate 51 B.1 SNC (Optimized M -QAM) . . . 51 B.2 DNC (M -QAM) . . . 53 B.3 DNC/SNC (M -PSK) . . . 53 C Throughput 55 C.1 Coded system . . . 55 C.2 Un-coded system . . . 55

## List of Figures

1.1 Growth in data traffic over time . . . 2

1.2 Asymmetric two way relay network . . . 4

2.1 System model showing the packets flow from the end nodes to the relay node. . . 7

2.2 The main functions required to the node in this study: Binary source, encoder and decoder, then modulation and demodulation 8 2.3 Example of convolutional encoder with rate = 1/2 . . . 9

2.4 Example of graphical viterbi decoder with rate = 1/2 . . . 10

2.5 Transmitted 16QAM constellation . . . 10

2.6 Transmitted 16PSK constellation . . . 11

2.7 Received 16QAM constellation . . . 13

3.1 normalized power constellation: (a) QPSK modulation. (b) 16QAM modulation . . . 15

3.2 a) Two way relay network scheme with four time slots. (b) Net-work coding scheme with three time slots. (c) NetNet-work Coding scheme with two tome slots. . . 16

3.3 System model showing the packets flow inside the relay node for SMSR DNC scheme. . . 18

3.4 System model showing the packets flow inside the relay node for SMMR DNC scheme. . . 18

3.5 Analog network coding for 16QAM and QPSK constellations, it is clear that middle points are too close to each other comparing to original constellations. . . 19

4.1 Network coding with symbol multiplication scheme with three time slots. Broadcast rate are not limited by minimum modula-tion level, and can use any combinamodula-tion based on Instantaneous SNR values . . . 22

4.2 Building coded packet for symbol network coding . . . 23

4.3 normalized power constellation for QPSK multiplied with 16QAM modulations . . . 23

4.4 coded packet flow inside end nodes . . . 24

6.1 BER for theoretical and experimental results using M -QAM mod-ulation . . . 29

6.2 BER for theoretical and experimental results using M -PSK mod-ulation . . . 30

6.3 BER for 16QAM * QPSK, 16QAM, 64QAM theoretical and ex-perimental in slow fading channel as a function of normalized signal to noise ratio (SNR) . . . 30 6.4 Three parameters are used to optimize new 16QAM constellation

has better performance in multiplication case with QPSK. . . 31 6.5 The new 16QAM constellation that has the best performance

when multiply with QPSK . . . 32 6.6 BER performance for QPSK*16QAM before and after optimization 33 6.7 Define nine parameters to optimize new 64QAM constellation

that has better performance in multiplication case with QPSK. . 34 6.8 The new 64QAM constellation that has the best performance

when multiply with QPSK . . . 35 6.9 BER performance for QPSK*64QAM before and after optimization 35 6.10 Throughput comparison for symmetric coded system with 100bits/packet

and BLER threshold 10−_{1 . . . .} _{37}

6.11 Spectral efficiency CDF for symmetric coded system with 100bits/packet
and BLER threshold 10−_{1 . . . .} _{37}

6.12 Throughput comparison for asymmetric coded system with 100bits/packet
and BLER threshold 10−_{1 . . . .} _{38}

6.13 Spectral efficiency CDF for asymmetric coded system with 100bits/packet
and BLER threshold 10−_{1 . . . .} _{38}

6.14 Throughput comparison for symmetric uncoded system for BER
threshold 10−_{2 . . . .} _{39}

6.15 Spectral efficiency CDF for symmetric uncoded system with and
BER threshold 10−_{2 . . . .} _{39}

6.16 Throughput comparison for asymmetric uncoded system for BER
threshold 10−_{2 . . . .} _{39}

6.17 Spectral efficiency CDF for asymmetric uncoded system with and
BER threshold 10−_{2 . . . .} _{40}

C.1 Throughput comparison for symmetric coded system with 100bit/packet
and BLER threshold 10−_{2 . . . .} _{55}

C.2 Spectral efficiency CDF for symmetric coded system with 100bits/packet
and BLER threshold 10−_{2 . . . .} _{56}

C.3 Throughput comparison for asymmetric coded system with 100bit/packet
and BLER threshold 10−_{2 . . . .} _{56}

C.4 Spectral efficiency CDF for asymmetric coded system with 100bits/packet
and BLER threshold 10−_{2 . . . .} _{56}

C.5 Throughput comparison for symmetric uncoded system for BER
threshold 10−_{3 . . . .} _{57}

C.6 Spectral efficiency CDF for symmetric uncoded system with and
BER threshold 10−_{3 . . . .} _{57}

C.7 Throughput comparison for asymmetric uncoded system for BER
threshold 10−_{3 . . . .} _{57}

C.8 Spectral efficiency CDF for asymmetric uncoded system with and
BER threshold 10−_{3 . . . .} _{58}

### Chapter 1

## Introduction

Wireless communications is one of the most active areas of technology develop-ment, and the fastest growing division of communications industry of our time. For different applications and purposes, wireless communication has developed societies functions in different ways. This development is being driven primarily by the transformation of a medium for supporting voice telephony into a medium for supporting other services, such as transmission of videos, images, and data [1]. Thus, similar to the developments in wired line capacity in the 1990s, the demand for current wireless capacity is rising so quickly. Although there are, of course, many technical problems to be solved in wired line communications. Demands for additional wired line capacity can be fulfilled largely with the ad-dition of new private infrastructure, such as optical fiber, adad-ditional routers, switches, and so on. On the other hand, the traditional resources that have been used to add capacity to wireless systems are radio bandwidth and trans-mitter power. Unfortunately, these two resources are among the most severely limited in the deployment of modern wireless networks. Radio bandwidth is in very tight situation with regard to useful radio spectrum, In addition to the ex-tra cost on the operators for more bandwidth. The limitation of increasing the transmitter power because mobile and other portable services require the use of battery power, which is limited. These two resources are simply not growing or improving at rates that can support anticipated demands for wireless capacity [2]. Figure 1.1 depicted data traffic demands with time, it can be seen that data traffic is expected to have exponential growing in the coming few years. However, one resource that is escalating at a very rapid rate is the processing power. Moore’s Law, which asserts a doubling of processor capabilities every 18 months, has been quite accurate over the past 20 years, and its accuracy promises to continue for years to come. Given these circumstances, there has been considerable research effort in recent years aimed to enhance the wireless capacity through the deployment of new wireless technologies. A key aspect of this movement has been the development of novel signal transmission techniques as in [3], and advanced signal processing methods [4] that allow for significant increase in wireless capacity without attendant increases in bandwidth or power requirements.

One of the important wireless technologies that added a new transmission techniques concept is network coding (NC). NC is an emerging area in

Figure 1.1: Growth in data traffic over time

tion theory, its promising to have a significant impact on future design of switch-ing systems. Preliminary studies show that network codswitch-ing may increase the achievable multicast throughput by considerable amounts. Thus, deployment of network coding could help better exploit shared resources such as Internet con-nections or wireless bandwidth. Constructions of network coding have become a popular topic in recent wireless network area.

### 1.1

### Related Work

In recent years, network coding has attracted much interest in broad areas like information theory, coding theory, networking, wireless communications, cryp-tography, and computer science. For certain communication network structure, where different information sources are aiming to multicast their data to a cer-tain group of distentions, its important to calculate the maximum achieved throughput inside the network as a performance measure. NC shows that it is not optimal to illustrate information multicast as ”fluid” model in general [5], where the network capacity is the sum of all individual nodes capacities. But by deploying NC in nodes, network resources can be saved and be able to achieve higher performance than in ”fluid” model. In this section, we will give an overview of the recent developments in the field of network coding, and discuss how they can eventually lead to a new information infrastructure.

The main advantage of using network coding is to increase the overall through-put of a network [6], [7], which was first shown theoretically using linear network coding. The linear network model in [8] allows a node to apply a linear

transfor-1.1. Related Work 3

mation to a vector before passing it on. Then formulated the multicast problem and proved that linear coding suffices to achieve the optimum performance of a network, which is the max-flow from the source to each receiving node. Network coding was implemented using COPE [9]. COPE is a new architecture for wire-less mesh networks. Where in addition to forwarding packets, relay nodes mix intelligently packets from different sources to increase the information content of each transmission. COPE was the first system architecture making network coding works in the IEEE 802.11-based wireless network [10]. After COPE, researchers start studying network coding performance combined in different network layers. In [11], and [12], the main focus was to analyze the combina-tion of NC in Media Access Control (MAC) layer. While NC implantacombina-tion in the routing layer was studied in [13].

Network coding brings many challenges in the wireless medium, especially the effect of noise, fading channel, and non uniform geometry networks, where these parameters degrade the network performance. Researchers are working on different levels to solve these problems and keep the substantial improvement gained from network coding implementation exist. MIXIT in [14] exploits a ba-sic property of mesh networks. Even when no node receives a packet correctly, any given bit is likely to be received by some node correctly. Instead of insisting on forwarding only correct packets, MIXIT routers use physical layer hints to make their best guess about which bits in a corrupted packet are likely to be cor-rect and forward them to the destination. Even though this approach inevitably lets erroneous bits through, MIXIT can achieve high throughput without com-promising end-to-end reliability. The problem of noisy medium was studied in [15], if the transmission to the relay node cannot be recovered perfectly, the relay node transmit logarithm likelihood ratio (LLR) of the message to the des-tinations, which expresses how many times more likely the message are under one model than the other. NC network showed extra Throughput gain using LLR method for the same noisy channel.

There are different ways to implement NC, will be discussed in Chapter 3 and 4. The required number of time slots can be different based on the imple-mentation technique. The main focus in this work will be on NC with three time slots. When the coded packets are generated from two different packets using XOR operation, this is called NC-XOR [9]. The study in [16] used Maximum A Posterior (MAP) and Minimum Mean Square Error (MMSE) as non trivial coding operation in the relay node for noisy channel, then used joint resource channel decoder as non trivial decoder at the receivers given the proposed coding operation. While [17] research adopted hierarchical modulations to incorporate and optimize with network coding, this approach improves end-to end bit-error rate and spectral efficiency when the relay node lays in asymmetric points as compared with direct transmission and NC-XOR schemes.

Other researchers found new schemes to generate the coded packet at the relay node. In [18], the coded packet was build using different hierarchal modulation schemes from the two different modulation packets received at the relay node.

Figure 1.2: Asymmetric two way relay network

### 1.2

### Problem statement

Despite many known superiorities of NC-XOR, however, there is also practical requirement that the relay node should adjust to the lower data rate in the broadcasting stage. For the coded packet, assume the links from the relay node to the receivers do not have the same link quality (asymmetric), this can happen because of the biased location of the relay node. For example, lets assume the relay node is closer to node A than to node B as shown in Figure 1.2. This makes the averaged Signal to Noise Ratio (SNR) over A-R channel stronger than B-R channel. Consequently, node A will receive lower data rate though it has a good channel state, because it will be limited to node B rate. If the network throughput gain is bound to the channel capacity of the weakest link node, this results in overall performance degradation and canceling the substan-tial fraction of network coding gain in the symmetric cases.

To tackle the broadcast bottleneck problem of the network coding implemen-tation in wireless communication, researchers have investigated some approaches to solve the asymmetric problem in different protocol layers; the most significant one is in the physical layer where this research lays. These solutions are suc-cess to improve the network performance when the relay node has asymmetric biased, but do not give complete independent rate for independent links inside the network. In this research project, we proposed a new method that is less complex and has the highest improvement in the semmetric and asymmetric relay biased than other solutions. The main feature of the proposed solution is to overcome the data rates dependencies over the links quality, and trying to assign the maximum data rate can be achieve by each link. Networks size can vary based on different parameters, number of users, users distributions, area geography, etc. For end-to-end applications, source and distinction are the simplest network model if they can communicate directly, direct transmission (DT). If the end nodes can not communicate directly because of long trans-mission distance greater than the transtrans-mission range of both of them, another node should settle in the middle to relay data between end nodes. The simplest network model is three node, and called two way relay network (TWRN).

### 1.3

### Thesis Outline

The thesis is outlined as follows: Chapter 2 provides descriptions about dif-ferent system models. Chapter 5 gives background about network coding, and performance measures, While Chapters 3 and 4 provide show different ways to implement network coding, and our proposed method. Chapter 6 have the theo-retical and experimental results with comparison for different methods. Finally we conclude in chapter 7.

### Chapter 2

## System model

Consider a TWRN with two end nodes A, B and one relay node R, as shown in Figure 2.1.

Figure 2.1: System model showing the packets flow from the end nodes to the relay node.

Each node works on half duplex communication system, that they cannot transmit and receive simultaneously. Nodes A, B and R in the TWRN use the same averaged transmitting power and the same carrier frequency.

### 2.1

### What Does the node Do?

The main functions required inside a node for our system model is depicted in Figure 2.2. Nodes in real systems do have more functions, but these ones are sufficient for this work study and comparisons.

### 2.1.1

### Binary Source

In probability theory and statistics, a sequence or other collection of random variables is independent and identically distributed (i.i.d.) if each random

Figure 2.2: The main functions required to the node in this study: Binary source, encoder and decoder, then modulation and demodulation

able has the same probability distribution as the others and all are mutually independent [19].

The abbreviation i.i.d. is particularly common in statistics, where observa-tions in a sample are often assumed to be i.i.d. for the purposes of statistical inference. The assumption that observations are i.i.d. tends to simplify the underlying mathematics of many statistical methods. However, in practical ap-plications of statistical modeling the assumption may or may not be realistic. The generalization of exchangeable random variables is often sufficient and more easily met. The assumption is important to make sure that the destination node has no prior information from the source node, and this is mapping real model scenarios. In the classical form of the central limit theorem, this states that the probability distribution of the sum of i.i.d. variables with finite variance approaches is a normal distribution.

### 2.1.2

### Convolutional Encoder/Viterbi Decoder

Convolutional code is a type of error-correcting code in which each m-bit infor-mation symbol to be encoded is transformed into an n-bit symbol [20]. The purpose of a convolutional encoder is to take a single or multi-bit input and gen-erate a matrix of encoded outputs. Convolutional encoder is important because digital modulation in communications systems (such as wireless communication systems, etc.) noise and other external factors can alter bit sequences. By adding additional bits, this makes bit error checking more successful and allow for more accurate transfers. By transmitting a greater number of bits than the original signal we introduce a certain redundancy that can be used to determine the original signal in the presence of an error. An example of Convolutional encoder with rate = 1/2 is shown in Figure 2.3.

The Viterbi Algorithm (named after Andrew Viterbi) is a dynamic algorithm that uses certain path metrics to compute the ’most likely’ path of a transmitted

2.1. What Does the node Do? 7

sequence [21], [22]. From the ’most likely’ path, certain bit errors can be corrected to decipher the original bit sequence after it has been sent down a communicative line. A graphical example of Viterbi decoder is shown in Figure 2.4. An important feature of the Viterbi algorithm is that ties are arbitrarily solved (can be picked randomly) and still yield an original sequence. What the Viterbi algorithm can do is correctly replicate the input string at the output even in the presence of one or more errors. Obviously, with more errors introduced the likelihood of a successful decryption does go down. But the algorithm has proved to be effective.

Figure 2.3: Example of convolutional encoder with rate = 1/2

### 2.1.3

### Modulation/Demodulation

Lets the focus be on digital modulation/demodulation, Quadrature amplitude
modulation (QAM) and Phase shift keying (PSK) will be considered for study
[23]. QAM is a modulation scheme in which two sinusoidal carriers, one exactly
90 degrees out of phase with respect to the other, are used to transmit data
over a given physical channel. Because the orthogonal carriers occupy the same
frequency band and differ by a 90 degree phase shift, each can be modulated
independently, transmitted over the same frequency band, and separated by
de-modulation at the receiver. For a given available bandwidth, M -QAM enables
data transmission at twice the rate of standard pulse amplitude modulation
(M_{2}-PAM) without any degradation in the bit error rate (BER). QAM schemes
like 4-QAM (QPSK), 16-QAM and 64-QAM are used in typical wireless digital
communications specifications like IEEE802.11. The number of points in the
constellation is defined as M = 2b _{where b is the number of bits in each }

con-stellation symbol. If b = 4, 16-QAM concon-stellation will be generated as shown in Figure 2.5.

Rather than QAM modulation, where symbols may have different amplitude
in the same constellation, M -PSK modulation creates constellation with equal
amplitude for all symbols, while the required data are stored in the phase. The
phase difference between any two adducent symbols is a function of M where
M is the modulation order as 4-PSK (QPSK), 16-PSK, and 64-PSK. The phase
difference between symbols will be 2π_{M}. For high value of M , the constellation
points become so close to each other, this makes the BER threshold for M -PSK
higher than M -QAM. 16-PSK constellation is illustrated in Figure 2.6.

Figure 2.4: Example of graphical viterbi decoder with rate = 1/2

Figure 2.5: Transmitted 16QAM constellation

### 2.2

### Which network is better?

In this section, three different Performance measures will be defined, they are used to give preferences inside the network:

### 2.2.1

### SNR

The ratio between signal power and noise power is called SNR. Links quality inside wireless network are usually measured by SNR, the link that has higher value, has better quality. Noise has different source, it can come from electronic circuit as thermal noise, or from the medium as atmospheric noise, or other

2.2. Which network is better? 9

Figure 2.6: Transmitted 16PSK constellation

sources [24]. For TWRN, there are three nodes, noise may be due to unwanted signal from other nodes, SNR become called Signal to Interference and Noise Ratio (SINR). In this work, access scheme to the medium will be Time Divi-sion Multiple Access (TDMA), which means that each node has separate and complete time slot for its own transmission, SINR become equal to SNR. Due to the small values of SNR, and its not preferable to deal with long numbers, SNR is usually measure in decibel (dB).

### 2.2.2

### BER

BER is another performance measure of wireless links, its in inverse relation with SNR, where high SNR value means low BER. The ratio between the number of error bits in a packet to the full packet size is defined as BER.

### 2.2.3

### Block Error Rate (BLER)

Communication links may have low quality at some instance, and if the available SNR is not sufficient to achieve certain BER thresholds, additional bits is added to enhance the link performance, these additional bit are added by convolutional encoder. convolutional encoder does not deal with bit, but with packets [20]. The performance measure after the encoder is BLER, where BLER is defined as the ratio between number of packets have errors to the total number of packets transmitted at a certain time.

### 2.2.4

### Throughput

Throughput is the most important factor defining network performance, it is defined as the maximum amount of bit can be transmitted successfully within one time slot. Different modulation orders require different SNR thresholds for same BER limit. The maximum modulation order M that can achieve BER limit, is the one providing the maximum throughout. As a consequence,

throughput will be measured as the ratio between log2(M ) and total number of

time slots required to transmit it.

### 2.3

### Channel model

The channel model used in this work is additive white gaussian noise (AWGN) and slow fading. AWGN is a channel model in which the only impairment to communication is a linear addition of wideband or white noise with a constant spectral density (expressed as watts per hertz of bandwidth) and a Gaussian distribution of amplitude [1]. The model does not account for fading, frequency selectivity, interference, nonlinearity or dispersion. However, it produces simple and tractable mathematical models which are useful for gaining insight into the underlying behavior of a system before these other phenomena are considered. Slow fading arises when the coherence time of the channel is large relative to the delay constraint of the channel. In this regime, the amplitude and phase change imposed by the channel can be considered roughly constant over the period of use. Slow fading can be caused by events such as shadowing, where a large obstruction such as a hill or large building obscures the main signal path between the transmitter and the receiver.

The received signal over Rayleigh fading channel is in the form

yr= Hrxr+ wr (2.1)

where

• yris the received symbol in the complex domain.

• Hris complex scaling factor corresponding to Rayleigh multipath channel.

• xris the transmitted symbol in the complex domain and

• wr is the Additive White Gaussian Noise (AWGN)

Regarding the fading and the noisy channel, we used the following assump-tions to build our system:

1. The channel is flat fading - In simple terms, it means that the multipath channel has only one tap. So, the convolution operation reduces to a simple multiplication.

2. The channel is randomly varying in time - meaning each transmitted sym-bol gets multiplied by a randomly varying complex number Hr. Since H

is modeling a Rayleigh channel, the real and imaginary parts are Gaussian distributed having meanµ = 0 and varianceσ = 1/2.

3. The noise w has the Gaussian probability density function with
p(w) = √ 1
2πσ2e
−(n−µ)2
2σ2 . (2.2)
with µ = 0 and σ2_{=}N0
2

2.3. Channel model 11

4. The channel H is known at the receiver. Equalization is performed at the receiver by dividing the received symbol y by the apriority known H i.e.

ˆ yr= yr Hr = Hrxr+ wr Hr = xr+ ˆwr. (2.3)

where ˆwr=_{H}wr_{r} is the additive noise scaled by the channel coefficient.

The received symbols positions will be drifted away from the original posi-tions due to the channel effect. Figure 2.7 showing the transmitted and received constellations of 16QAM over AWGN and slow fading channel.

### Chapter 3

## Network coding

The concept of NC was first introduced by R. W. Yeung and Z. Zhang in 1999 as an alternative to relaying scheme [25]. NC is a method of optimizing the data flow in a network by transmitting coded packets, where the ”coded packet” is a composite of two or more packets. When the bits of coded packets arrive at the destination, the transmitted packet is deduced rather than directly reassembled. NC processes are divided into two parts: packets delivery from end nodes to the relay node, and broadcasting the coded packet from the relay to the end nodes. In this work, the main focus will be on the broadcasting of the coded packet from the relay node, to the end nodes, this is based on the assumption that the relay node received the end node packets correctly, or it has the prior information about their packets. As a running example for this Chapter and Chapter 4, assume both links between the relay node and the end nodes are asymmetric, they can support QPSK and 16QAM modulations as shown in Figure 3.1 (a), (b) based on their instantaneous SNR. If two symbols Si ∈

QP SK and Sj∈ 16QAM were transmitted from both end receivers with equal

energy per symbol, this means that E{|Si|2} = 1 and E{|Sj|2} = 1.

Figure 3.1: normalized power constellation: (a) QPSK modulation. (b) 16QAM modulation

Figure 3.2: a) Two way relay network scheme with four time slots. (b) Network coding scheme with three time slots. (c) Network Coding scheme with two tome slots.

### 3.1

### Relaying

Relay network is a broad network topology used in wireless networks, since the
source and destination can not communicate directly with each other, another
intermediate node settle between them to relay packets. This is called Relaying
scheme as illustrated in Figure 3.2 (a), in which nodes A and B are
exchang-ing data via the relay node. It would require four transmissions time slots to
exchange two packets in relaying scheme: node A to the relay, and the relay
*to node B, and vice versa. From the running example, the relaying scheme is*
not affected by the asymmetric links, it will use QPSK with one end node, and
16QAM with the other node in different time slots, the averaged throughput
will be (log2(4) + log2(16))/2 = 3 bit/s/Hz, throughput is divided by two as

the number of time slots is two.

### 3.2

### Digital network coding

Digital network coding (DNC) means that the relay node XORs packets in the bit level to form the coded packet. DNC technique is depicted Figure 3.2 (b), nodes A and B temporarily store their transmitted packets for later decoding. After two time slots, the relay has received the packets from both end receivers,

3.2. Digital network coding 15

encodes (XOR) and broadcasts them back to nodes A and B within one time slot. Nodes A and B each recover their packets by decoding (XOR) the received packet with the stored one. The number of transmission time slots reduces to three, one time slot less than in the relaying scheme.

Packets flow inside nodes A and B are depicted in Figure 2.1, packets in binary level will be sent to convolutional encoders to add some redundancy bits used later to reduce BER. Then convert packets from binary level to signal level by passing it through modulation block. After this, the packets are ready to be sent over independent wireless channels to the relay node.

The relay node sends the received packets one by one and in order to a reverse process inside the relay. Packets are converted from symbols to binary by passing them to the demodulation, the obtained binary packets may have some errors due to the channel condition. These errors will be corrected (if possible) by sending the packets to Viterbi decoders. After these blocks, the relay node has two packets with same binary lengths as original packets at the end nodes.

### 3.2.1

### Single Modulation, Single Rate (SMSR)

After receiving both packets at the relay node, SMSR model XOR both packets in the symbol level, and send the resultant packet to the encoder and modulation blocks in consequence as showin in Figure 3.3. The modulation order and the packet flow is chosen based on the weakest link quality in the network.

DNC performance suffers from the broadcasting rate limitation, where the rate is bound by the worse link quality. The research in [26] studied the broadcasting stage, and provided control channel algorithm from the sender to receivers and a feedback channel in the reverse direction, this algorithm showed extra gain for DNC. The study in [27] presented adaptive coding scheme that combines channel coding with network coding, which greatly reduces cod-ing/decoding complexity The scheme first designs channel codes independently for each channel, then combines them with simple network coding. [28] put forward R-Code, a network coding-based reliable broadcast protocol. R-Code established guardianward relationships between neighboring nodes that effec-tively distributes the responsibilities of reliable information delivery. Oppor-tunistic overhearing is also utilized in the research to improve the performance of R-Code protocol. Results showed that R-Code protocol can reach 100% packet delivery ratio, less transmission overhead and shorter broadcast latency.

### 3.2.2

### Single Modulation, Multi Rate (SMMR)

The research in [29] provided different solution to the asymmetric links, the network model is illustrated in Figure 3.4. In this SMMR model, the code rate for each packet will be chosen based on the instantaneous quality for each link, and will not have dependencies on the weakest link. After forming the coded packets using the convolutional encoders, both packers will be XOR in the bit level together forming one coded packet. The resultant packet will be sent to modulation block to form the coded packet, at this point, the modulation order

Figure 3.3: System model showing the packets flow inside the relay node for SMSR DNC scheme.

is limited by the weakest link quality.

From the running example, the broadcasting modulation in DNC is the one supported by the weakest link. The averaged throughput will be 2 ∗ (min{log2(4), log2(16)}) = 4 bit/s/Hz.

Figure 3.4: System model showing the packets flow inside the relay node for SMMR DNC scheme.

### 3.3

### Analog network coding

Traditionally, interference is considered harmful. Wireless networks strive to avoid scheduling multiple transmissions at the same time in order to prevent interference. Analog network coding (ANC) adopts the opposite approach; it encourages strategically picked senders to interfere. Instead of forwarding pack-ets, relays forward the interfering signals as illustrated in Figure 3.2 (c). The destinations use their own packets to cancel the interference and recover the signal destined to it. Theoretically, such an approach doubles the capacity of the relaying scheme, as the number of time slots for complete data exchange

3.3. Analog network coding 17

become two [30].

ANC has more complexity than DNC regarding synchronization between intended receivers and the relay node. This problem was discussed in [31]. Researchers in [32] found a solution for scheduling through proposed algorithm for synchronization between nodes. After receiving the interfering packets at the relay, the relay sends it to both end nodes in one time slot. If the relay use amplify and forward (AF), ANC will have double amount of noise comparing to DNC and relaying schemes, as was studied in [33]. knowing channels state information let [34] to adopt adaptive modulation techniques which jointly optimize modulations and network coding based on the channels state. [35] porposed different schemes to overcome additional noise problem, decode and forward (DF), Jointly decode and forward (JDF), denoise and forward (DNF). The numerical results showed that no scheme can achieve higher two way rate than the upper bound of DNF.

In this research, the main focus will be on relaying and DNC schemes. Anal-ysis and simulations will focus on the broadcasting stage from the relay node to intended receivers. In Chapeter 4, the proposed method will be discussed with a comparison with relaying and DNC schemes mentioned in this Chapter.

From the running example, the broadcasting modulation in ANC is the sum of both constellations E{|Si|2} + E{|Sj|2} = 2, to have unity power

constella-tion, the result will be divided by two, or equivalent to 3dB lower power than original constellation. The averaged throughput will be log2(4) + log2(16) =

6 bit/s/Hz. It required a complex system to achieve this threshold, this is due to hard synchronization, and very close points to each which yield to very high BER [23] as shown in Figure 3.5

−1 −0.5 0 0.5 1 −1 −0.5 0 0.5 1 Quadrature In−Phase

Figure 3.5: Analog network coding for 16QAM and QPSK constellations, it is clear that middle points are too close to each other comparing to original constellations.

### Chapter 4

## Symbol network coding

## (SNC)

### 4.1

### SNC: previous work

In DNC systems, the relay node receive packets from end nodes, convert them to the binary level, then operate the coding operations on them before broad-casting the coded packet to both end nodes. Due to broadbroad-casting limitation to the weakest link in the network, researches moved to apply NC on symbols instead of bits [14].

Drizzle is a new error control protocol that maximizes network throughput with the presence of errors, which takes advantage of NC at the symbol level in multichannel wireless networks [36]. Drizzle is able to outperform hybrid automatic repeat request (HARQ), which is highly optimized forward error-correcting method existing in physical-layer designs by a substantial margin. Adaptive symbol network coding (ASNC) system was designed in [37], it ap-plied dynamic block size on coded systems to solve the retransmission problems in erasure links. This is done by exploiting the relationship between block size and block error rate under the same bit error rate. Numerical and simulation results show that ASNC has better performance than conventional symbol net-work coding with fixed block size, comparison was based on averaged number of broadcasting retransmission in the network. Research in [38] studied sym-bol level network coding (SLNC) implementation in live multimedia streaming (LMS) for vehicular ad hoc networks (VANET). High data rate for LMS services in VANET is hard, yet it greatly enhanced over conventional network coding using SLNC.

### 4.2

### Proposed SNC

The proposed SNC has three time slots for complete data exchange as DNC, the first two time slots are matching with DNC, where both end nodes send their packets in two different time slots. SNC assume that these packets received correctly at the relay node, and will have main study on the broadcasting stage. DNC apply XOR operation on both packets at the bit level, while SNC multiply

both packets at the symbol level in the complex domain, the result is the coded packet to be broadcasted to both end nodes as illustrated in Figure 4.1.

Figure 4.1: Network coding with symbol multiplication scheme with three time slots. Broadcast rate are not limited by minimum modulation level, and can use any combination based on Instantaneous SNR values

SNC uses QAM modulation/demodulation with different modulation levels
(L), L ∈ {2, 4, 6}, and modulation order M = 2L_{. The coded packet is forming}

from any two different modulation orders as show in Figure 4.2, the broadcasted constellation will have the shape of multiplied constellations. As both multiplied constellation has unity power,E{|Si,j|2} = 1i, j ∈ {QP SK, 16QAM, or64QAM}

then result constellation will have also unity power E{|Si× Sj|2} = 1, this is

an advantage over ANC system, because constellation power become double for the coded packet, and it should be divided by two to get unchange constellation power. For the running example from Chapter 3, if one link supports QPSK, and the other link supports 16QAM, the result constellation will be the multi-plication of QPSK and 16QAM in the complex domain as shown in Figure 4.3. The distance between symbols in SNC coded packet, is the same as 16QAM, this is because multiplication with QPSK can be interpreted as phase rotation of the other constellation. This is an extra advantage of SNC over ANC, where BER for the coded constellation is lower in SNC scheme. After receiving the coded packet at both end nodes, each node divide it by its stored packet in the symbol level. The result packets will be sent to demodulation and decoder blocks simultaneously as illustrated in Figure 4.4. For the running example, the broadcasting modulation will not be limited by any link, and the average throughput will be log2(4) + log2(16) = 6 bit/s/Hz. SNC has some advantages

over previous schemes:

• SNC is simple model to implement.

• SNC does not require extra synchronization between nodes. • SNC is not limited by the weakest link quality.

4.2. Proposed SNC 21

• SNC has the highest possible throughput in the broadcasting stage along with ANC (6 bit/s/Hz).

Figure 4.2: Building coded packet for symbol network coding

−1 −0.5 0 0.5 1 −1 −0.5 0 0.5 1 Quadrature In−Phase

Figure 4.3: normalized power constellation for QPSK multiplied with 16QAM modulations

### Chapter 5

## Theoretical analysis

In this chapter, some derivations for four NC schemes will be considered, relay-ing, DNC using M -QAM modulation (DNCQ), DNC using M -PSK modulation

(DNCP), and SNC with the new constellation. For M -QAM and M -PSK

con-stellations, each symbol has certain number of bits L depending on the
modula-tion order M , where L = log2(M ). The averaged energy per bit is SymbolEnergy_{L} .

In this chapter, SNR (Γ )will be considered for normalized average energy per symbol.

### 5.1

### BER

The constellations will be sent over wireless channel of AWGN and slow fading as described in Section 2.3.

### 5.1.1

### M-QAM BER

Relaying scheme uses conventional M -QAM modulation, its the same used by DNCQ, therefore, their transmissions have the same BER performance.

The-oretical BER for different M -QAM modulation can be approximated as
men-tioned in [23]
Pe/DN CQ(M, Γ) =
2
log2(M )(1 −
1
√
M)erf c(k
√
Γ) − (1 −√2
M +
1
M)erf c
2_{(k}√_{Γ)}
(5.1)
where M is the modulation order, and Γ is the averaged signal to noise ratio.

### 5.1.2

### M-PSK BER

For the general M -PSK used by DNCQ there is no simple expression for the

symbol-error probability if M > 4, Theoretical BER approximation is found in [23] as Pe/DN CP(M, Γ) = 1 log2(M )erf c[ √ Γsin( π log2(M ))] (5.2) 23

### 5.1.3

### SNC constellations BER

For SNC constellations resulted from multiplication of two M -QAM constella-tions, BER equation should be updated based on the characteristics of the two multiplied constellations.

As expressed in Equation 2.1, Xr is si× sj for the multiplication case, to

retrieve si as an example, we have to divide the received symbol y by sj. The

resulted noise will be updated based on the characteristic of sjas in the following

roles: y sj = Hsi+ w sj (5.3) ˜ n = n sj = minimized if energy of sj> 1 maximized if energy of sj< 1 unchanged otherwise (5.4)

based on the above conclusion, the theoretical BER in SNC constellation is calculated as

Pe(M1, M2, Γ) =

X

M1

RM1× Pe,DN CQ(M2, EM1× Γ) (5.5)

where the EM1 means the absolute symbols power from M1 constellation,

and RM1 means the ratio of symbols have EM1 amount of power to the total

number of symbols in M1 constellation. From Equation 5.5, we conclude the

following:

• Pe(M1, M2, Γ) 6= Pe(M2, M1, Γ).

• Pe(M1, 4, Γ) = Pe/DN CQ(M1, Γ).

As an example, lets consider si ∈ QP SK and sj ∈ 16QAM, the BER

equation for QP SK alone is expressed in [23] as

Pe= 1 2(1 − s γb i γb i + 1 ) (5.6) where γb

i is the averaged SNR per bit. sj will not has instantaneous power

equal to one, but rather on average. That is because s2

j can take the following

different values (E) with the corresponding rations (R)

s2j= E = 1 ; R = 8/16 E = 0.2 ; R = 4/16 E = 1.8 ; R = 4/16

From Equation 5.3, When s2

j = 1, the network decoding operation will not

affect the BER. On the other hand when s2

5.2. BLER 25

amplified compared to when s2

j = 1 whereas when s2j = 1.8, the noise power will

be attenuated. But the BER will be dominated by the worst condition (noise is amplified).

Combining Equation 5.6 with the different values of s2

j, according to the

general Equation 5.5, SNC BER for QPSK-16QAM is given by

Pe= 1 4(1 − s γb i γb i + 1 ) +1 8(1 − s 0.2γb i 0.2γb i + 1 ) +1 8(1 − s 1.8γb i 1.8γb i + 1 ) (5.7)

### 5.2

### BLER

The main performance measure of a convolutional codes is (BLER) of the code as a function of Γ. However, free distance gives a good indication of convolutional code performance. The free distance (d) of a convolutional code is the minimum distance between two distinct valid output sequences. The correcting capability (t) of a convolutional code is the number of errors that can be corrected by the code. It can be calculated as

t = ⌊d − 1_{2} ⌋

. BLER is the number of incorrectly received data packets divided by the total number of received packets. A packet is declared incorrect if at least one bit is erroneous. The approximated value of the BLER is valid for all transmission schemes

BLER = 1 − (1 − Pe)N (5.8)

where N is the packet length, and Peis the BER.

### 5.3

### Throughput performance

For certain modulation order M supporting the weakest link in DN CQ and

DN CP networks, throughput is defined as number of bits per symbol carried in

the coded packet. And because each symbol has double amount of information with network coding at the broadcasting stage, total network throughput will be doubled.

T hroughput = 2 ∗ log2(M )

. In SNC case, modulation order is not limited by the weakest link, and the coded packet is a combination of two different modulation orders {M1, M2}.

Throughput will be

T hroughput = log2(M 1) + log2(M 2)

.

The question is, how to choose the modulation order?. For certain BER or BLER limits, the selected modulation is the higher order than can achieve certain BER/BLER for a given instantaneous Γ.

### Chapter 6

## System performance and

## analysis

In this Chapter, simulation results will be generated for BER, BLER and throughput using MATLAB. The main transmission schemes will be consid-ered is Relaying, DNCQ, DNCP and SNC.

### 6.1

### BER

After implementing the modulation/demodulation over slow fading channel model system using MATLAB, Theoretical and experimental BER results were calculated and compared together. For M -QAM constellations, Figure 6.1 show-ing a comparison between theoretical results in Equation 5.1 and simulation re-sults. It clear that theoretical and experimental results are in match with each other.

Figure 6.1: BER for theoretical and experimental results using M -QAM mod-ulation

The same comparison was made for M -PSK modulation, Figure showing theoretical results from Equation , and experimental results.

Theoretical and experimental BER results were calculated and compared together. The results shown in Figure 6.3 is an example of 16QAM when

0 5 10 15 20 25 30 35 40 100 SNR (dB) BER 4−PSK(Theory) 4−PSK(exper) 16−PSK(Theory) 16−PSK(exper) 64−PSK(Theory) 64−PSK(exper)

Figure 6.2: BER for theoretical and experimental results using M -PSK modu-lation

plied with /QPSK, 16QAM, and 64QAM/. The results prove that Equation 5.5
is perfect model for our multiplication scheme. Table A.1 in Appendix showing
all modulation orders combinations for 10−2 _{and 10}−3 _{BER thresholds.}

Tables A.1, A.3, and A.4 showing SNR thresholds for different modulation orders for SNC, DNCQ and DNCP, BER limits are {10−2, 10−3}.

0 5 10 15 20 25 30 10−4 10−3 10−2 10−1 100

BER Vs SNR for different modulation levels

SNR (dB) BER 16QAM−QPSK (theory) 16QAM−16QQAM (theory) 16QAM−64QAM (theory) 16QAM−QPSK (exper) 16QAM−16QAM (exper) 16QAM−64QAM (exper)

Figure 6.3: BER for 16QAM * QPSK, 16QAM, 64QAM theoretical and exper-imental in slow fading channel as a function of normalized signal to noise ratio (SNR)

### 6.2

### Updated constellations

As can be shown from Figure 6.3, BER thresholds for QPSK combined with 16QAM and 64QAM are higher than QPSK combined with QPSK (the same as QPSK alone). These thresholds reduce the performance of the proposed method. To improve the BER in of the multiplied constellations, new updated constellations were detected to achieve better BER performance.

6.2. Updated constellations 29

For the conventional QPSK constellation, no update can be found to improve the BER thresholds due to the following points:

• QPSK constellation points are at uniform and equal distances from each other.

• For the proposed scheme, after dividing by sj ∈ QP SK in Equation 5.4,

the noise characteristic will not change because all symbols have unity amplitude.

new 16QAM and 64QAM constellations updated were found, the following sections showing the procedure followed to get these new constellations:

### 6.2.1

### 16QAM Constellation

We refer α, β and γ to points with amplitudes√0.2, 1, and√1.8 consequently. Where the α, β and γ ranges varies between (0 − 2) of their original amplitudes as shown in Figure 6.4. α and γ are independent variables, while β is dependent on α and γ. β value is chosen to keep the constellation power unchanged before and after the updating:

Figure 6.4: Three parameters are used to optimize new 16QAM constellation has better performance in multiplication case with QPSK.

S1 = α∗ √ (2) √ (10) ; S2 = β∗ √ (10) √ (10) ; S3 = γ∗ √ (18) √ (10) ;

(α ∗ 4 ∗ S12_{) + (γ ∗ 8 ∗ S3}2_{) + (β ∗ 4 ∗ S2}2_{)}

16 = 1 (6.1)

γ = 2 − 0.1 ∗ α − 0.9 ∗ β (6.2) The values for α, β and γ, are the arguments that minimize the difference between T Snon−optand T Sopt

arg_{{α,β,γ}}min {T Snon−opt− T Sopt} (6.3)

Where T S_{non−opt}, T Sopt is the sum of SNR thresholds for QP SK and

16QAM {SNRQP SK+SN R16QAM} for certain BER threshold before and after

constellation optimization.

After extensive simulation we found the best gain occurs when α = 1.5
and γ = 1. The new constellation shape is shown in Figure 6.5. We define
constellation improvement as the difference in SNR for certain BER threshold
before and after updating. Figure 6.6 showing BER curves for QPSK*16QAM
constellations before and after optimization, also Table A.2 presenting SNR
thresholds for the updated SNC constellations, BER limits are {10−2_{, 10}−3_{}.}

Figure 6.5: The new 16QAM constellation that has the best performance when multiply with QPSK

### 6.2.2

### 64QAM Constellation

We refer {A1,...,A9} to points with amplitudes√1 42{

√

2,√10,√18,√26,√34,√50,√58,√74,√98} consequently. Where {A1,...,A9} ranges varies between (0 − 2) of their

6.3. BLER 31 0 5 10 15 20 25 10−4 10−3 10−2 10−1 100 SNR[dB] BER QPSK non−opt 16QAM non−opt QPSK opt 16QAM opt d1 d2 Gain = d1 − d2

Figure 6.6: BER performance for QPSK*16QAM before and after optimization

{A1,...,A8} to keep the constellation power unchanged before and after updat-ing, an illustration is shown in Figure 6.7.

9

X

x=1

wxAxs2x= 64 (6.4)

where wxis the number of symbols with amplitude sxas shown in Table 6.1,wx∈

{4, 8, 4, 8, 8, 12, 8, 8, 4}. Ax is the optimization parameter for sx, and s2x is the

power of symbols. A9= 64 − P8 x=1wxAxs2x 4s2 9 (6.5) The values for {A1, ..., A9}, are the arguments that minimize difference be-tween T Snon−optand T Sopt

arg_{{A1,...,A9}}min {T Snon−opt− T Sopt} (6.6)

Where T Snon−opt, T Soptis the sum of SNR thresholds for QP SK and 64QAM

{SNRQP SK+SN R64QAM} for certain BER threshold before and after

constel-lation optimization.

After extensive simulation we found the best gain occurs when {A1,...,A9} have the following values shown in Table 6.1.

The new constellation is shown in Figure 6.8. Figure 6.6 showing BER curves for QPSK*16QAM constellations before and after optimization. After updat-ing 16QAM and 64QAM constellations, we generated Table A.2 as new BER thresholds for different modulation combination. Table A.5 is showing the gains achieved by moving from the conventional to the updated constellations.

### 6.3

### BLER

In real telecom systems, data are transmitted in blocks (packets) with certain lengths. BLER is a ratio of the number of erroneous blocks to the total number of blocks received on a certain node. Extra bits added to the original data during

Table 6.1: 64QAM symbols statistics and optimization values Symbol Amplitude repetition(wx) optimization

value S1 A1∗ √ (2) √ (42) 4 A1 = 2.4 S2 A2∗ √ (10) √ (42) 8 A2 = 2.1 S3 A3∗ √ (18) √ (42) 4 A3 = 2.1 S4 A4∗ √ (26) √ (42) 8 A4 = 1 S5 A5∗ √ (34) √ (42) 8 A5 = 1 S6 A6∗ √ (50) √ (42) 12 A6 = 1 S7 A7∗ √ (58) √ (42) 8 A7 = 1.1 S8 A8∗ √ (74) √ (42) 8 A8 = 0.9 S9 A9∗ √ (98) √ (42) 4 A9 = 0.5776

Figure 6.7: Define nine parameters to optimize new 64QAM constellation that has better performance in multiplication case with QPSK.

the encoding process to help the receiver node to achieve lower BLER over the same channel. We calculated BLER for different code rates {1/3, 1/2, 2/3, and

6.3. BLER 33

Figure 6.8: The new 64QAM constellation that has the best performance when multiply with QPSK 0 5 10 15 20 25 30 10−4 10−3 10−2 10−1 100 SNR[dB] BER QPSK non−opt 64QAM non−opt QPSK opt 64QAM opt d1 d2 Gain = d1 − d2

Figure 6.9: BER performance for QPSK*64QAM before and after optimization

3/4} and different modulation orders {4, 16, and 64}. for {QAM, and M-PSK}. Tables B.2 showing the SNR thresholds for different modulation levels and different coding rate for the case of DNCQ. The block length was chosen

to be 100 bit.

After updating the constellations in SNC scheme discussed in previous sec-tion, other results in Table B.1 were found using the optimized M -QAM constel-lations. The results were obtained for different BLER thresholds with different modulation orders and different coding rates, the block length was chosen to be

100 bit also.

It can be concluded from Table B.1 that different Rate2for certain M odulation2,

will not affect the SNR thresholds for certain M odulation1and Rate1*, and vice*

*versa. For example, {Modulation*1, M odulation2} = {4, 4} with {Rate1, Rate2} =

{1/3, anyrate} will have the same SNR thresholds {3.4 dB for BLER = 10−1

and 4.9 dB for BLER = 10−2_{}. Based on this conclusion, Table B.3 }

show-ing different BLER thresholds for DNCP with different modulation orders and

coding rates, and same block length of 100 bit/block.

### 6.4

### Throughput

In this section, all the results obtained for BER and BLER were used to see the throughput performance of our proposed method comparing to DNCQ, DNCP

and Relaying transmission schemes. The experiments have the following con-figurations:

• The experiments will focus only on the broadcasting stage from the relay node to both end receivers. This is under the assumption that packets received correctly to the relay node.

• Symmetric and asymmetric models will be considered, where symmetric case is when both links connected to the relay node has the same averaged SNR {0-30 dB}. The asymmetric case on the other hand, is when one of the links has averaged SNR equal to 5 dB, and the other links has variable SNR {0-30 dB}.

• Coded and un-coded systems will be considered. Coded systems has dif-ferent rates {1/3,1/2,2/3 and 3/4}

• Links cannot support any of the modulations and rates will set to zero, without affecting the other link.

### 6.4.1

### Coded system

Starting with the coded systems, we consider symmetric and asymmetric
sce-nario with different BLER thresholds {10−1_{, 10}−_{2}. The Figures keywords are}

expressed as follow:

• Mul/Rel is the ratio between SNC and relaying models. This ratio shows the gain by moving from relaying to SNC.

• XOR/Rel is the ratio between DNCQ and relaying model. This ratio

shows the gain by moving from relaying to DNCQ.

• Mul/XOR is the ratio between SNC with QAM constellations and DNCQ

models. This ratio showing the gain by moving from DNCQ to SNC.

• Mul/P SK is the ratio between DNCQwith QAM constellation and DNCP.

This ratio shows the gain by moving from DNCP to SNC with QAM

6.4. Throughput 35

Figure 6.10 showing the symmetric scenario of coded system with BLER
threshold equal to {10−1_{}. It can be seen that our proposed method SNC}

showing better performance over DNCQand DNCP. On the other hand, Figure

6.12 showing the same coded systems model with asymmetric scenario. it can be noticed that our proposed method SNC still showing higher performance than DNCQ and DNCP methods. Symmetric and asymmetric performance for

BLER threshold {10−2_{} are shown in Figures C.1, C.3. The spectral efficiency}

distribution (bit/s/Hz) for both symmetric and asymmetric scenarios are shown in Figures 6.11 and 6.13 consequently, it can be shown than SNC has distribution over all spectral region (2-10 bit/s/Hz), while Tables ??, C.1 show summary of the coded system performance and gain.

0 5 10 15 20 25 30 35 40 45 1 1.2 1.4 1.6 1.8 2 SNR [dB]

Mean normalized relative throughput

Mul/(XOR single rate) Mul/Rel

Mul/(XOR multi rate) Mul/PSK

Figure 6.10: Throughput comparison for symmetric coded system with
100bits/packet and BLER threshold 10−_{1}

2 4 6 8 10 0 10 20 30 40 50

Sum spectral efficiency [b/s/Hz]

Percentage of performing NC

XOR single rate XOR mult rate PSK MUL

Figure 6.11: Spectral efficiency CDF for symmetric coded system with
100bits/packet and BLER threshold 10−_{1}

### 6.4.2

### Un-coded system

Regarding the un-coded systems, we compared different BER thresholds {10−2_{}.}

0 5 10 15 20 25 30 35 40 45 1 1.2 1.4 1.6 1.8 2 SNR [dB]

Mean normalized relative throughput

Mul/(XOR single rate) Mul/Rel

Mul/(XOR multi rate) Mul/PSK

Figure 6.12: Throughput comparison for asymmetric coded system with
100bits/packet and BLER threshold 10−_{1}

2 4 6 8 10 0 10 20 30 40 50 60

Sum spectral efficiency [b/s/Hz]

Percentage of performing NC

XOR single rate XOR mult rate PSK MUL

Figure 6.13: Spectral efficiency CDF for asymmetric coded system with
100bits/packet and BLER threshold 10−_{1}

can be showing than our proposed method showing better performance than DNCQ and DNCP models and over all SNR regions.

For the asymmetric model, Figure 6.16 showing the throughput performance
for the same transmission schemes. it can be noticed than the regions where
M ul/XOR and M ul/P SK are less in the asymmetric model. The spectral
ef-ficiency distribution for the symmetric and asymmetric scenarios are illustrated
in Figures 6.15 and ??. The symmetric and asymmetric performance for BER
equal to {10−_{3} are shown in Figures C.5 , C.7, and Tables ??, C.2 show }

6.4. Throughput 37 0 5 10 15 20 25 30 35 1 1.2 1.4 1.6 1.8 2 SNR [dB]

Mean normalized relative throughput

XOR/Rel Mul/Rel Mul/XOR Mul/PSK

Figure 6.14: Throughput comparison for symmetric uncoded system for BER
threshold 10−_{2}
4 6 8 10 12
0
10
20
30
40
50

Sum spectral efficiency [b/s/Hz]

Percentage

Rel Xor Psk Mul

Figure 6.15: Spectral efficiency CDF for symmetric uncoded system with and
BER threshold 10−_{2}
0 5 10 15 20 25 30 35
1
1.2
1.4
1.6
1.8
SNR [dB]

Mean normalized relative throughput

XOR/Rel Mul/Rel Mul/XOR Mul/PSK

Figure 6.16: Throughput comparison for asymmetric uncoded system for BER
threshold 10−_{2}

4 6 8 10 12 0 10 20 30 40 50 60

Sum spectral efficiency [b/s/Hz]

Percentage

Rel Xor Psk Mul

Figure 6.17: Spectral efficiency CDF for asymmetric uncoded system with and
BER threshold 10−_{2}

### Chapter 7

## Conclusion and future work

In this thesis work, we provided solution for the two way relay network in the asymmetric points to improve the system performance. We studied the conven-tional network coding models, and showed that these models performance are lower in the asymmetric points.

Conventional network coding with QAM constellations has the broadcast-ing limitation problem, where the broadcastbroadcast-ing rate is bounded by the weakest link, and this degrade the total system throughput performance. On the other hand, the conventional network coding using PSK constellation does not have the broadcasting limitation. This is due to the special characteristic of PSK con-stellation over QAM one. The result of multiplying two PSK concon-stellations is another PSK constellation. The resultant constellation can be expressed as one of the multiplied constellations with rotation phase of the other constellation. However, PSK has the problem of high SNR threshold for certain BER. This problem affects the system more for the high order PSK constellation. Constel-lation points become very close to each other at high order PSK constelConstel-lation than QAM constellation. For the specific problem we discussed in this thesis, where the relay node is more biased to one of the end nodes more than the oth-ers. The closer nodes will have higher modulation order, and the conventional PSK network coding showed lower performance.

To overcome this problem, we proposed a new method of operating network coding; we built our system model to handle different modulation orders in one coded packet. Using this technique, we don’t have the limitation problem in the conventional network coding using QAM constellation. After we generated the BER curves for the proposed method, we found that SNR thresholds become higher for the combined QAM constellation for certain BER threshold. This limited our system throughput performance, as the node required higher SNR to achieve higher throughput. In order to solve this problem, we found that the current constellation resultant from multiplying two QAM constellation to-gether is not the optimum one regarding BER thresholds. For this case, we made our own optimization problem over 16QAM and 64QAM constellation for all the combination possibilities. After extensive study, we found new 16QAM and 64QAM constellations that achieve better BER thresholds for certain SNR value than the conventional constellation. After this, we generated BER tables

for the conventional and the new constellation. The thresholds gain was cal-culated as the SNR threshold difference achieved by moving from conventional to new constellation. The maximum achieved gain was 9.8 dB when combining 64QAM*64QAM together. We found that M1-QAM*QPSK has the same BER curve as M1-QAM, because any multiplication with QPSK change the phase without affecting the shape. From this feature, we extract the BER thresholds for the conventional network coding with QAM constellation. To test our system more, we generated BER tables for PSK constellation with different modulation orders.

After this point, we moved to study coded system, as it is the one used in real
communication systems. We used Convolutional encoder and Viterbi decoder
*to switch from bits to packets and vise versa. This also helps the system to*
achieve certain BLER threshold with lower amount of SNR using the additional
bits added by the encoder. We chose 100 bits packet length to model our system.
BLER tables were generated for conventional and new QAM constellations. As
in un-coded system, we studied the BLER performance of conventional network
coding with QAM and PSK constellations.

After combining all the generated data for the coded and un-coded sys-tems, we studied the throughout system performance for the symmetric and asymmetric scenarios, and different BER and BLER thresholds. We made our focus on the broadcasting stage from the relay node to both end receivers. We found that our proposed method has better performance than both conventional network coding in the symmetric and asymmetric scenarios. The maximum achieved gains were 38.7%, 26 % and 10.7 % for the coded system compared to DNC(SMSR), DNC(SMMR) and SNC-PSK consequently.

For the future work, we will study the performance of complete two way
*relay network, from the end nodes to the relay node, and vise versa. Other*
solutions for network coding in the asymmetric two ways relay network model
will be consider. System model and data analysis will be calculated for those
models, and performance comparison will be between them and our proposed
method using different scenarios.

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