Contents
Abstract
1
1 Introduction
1
1.1
1.2
1.3
Introduction to cooperative relay networks . . . . . . . . . . . . . . . . . . .
1
1.1.1
The relay protocols . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4
1.1.2
Advantages of Cooperative Diversity Relaying Networks . . . . . . .
5
Introduction to Network Coding . . . . . . . . . . . . . . . . . . . . . . . . .
7
1.2.1
Non-Binary and Binary Network Coding . . . . . . . . . . . . . . . .
8
1.2.2
Advantages of Network Coding . . . . . . . . . . . . . . . . . . . . .
9
1.2.3
Weaknesses of Network Coding . . . . . . . . . . . . . . . . . . . . .
11
Cooperative Diversity Relaying Networks using network coding . . . . . . . .
13
2 System models
15
2.1
Traditional Relay Multiple-Wireless Networks . . . . . . . . . . . . . . . . .
16
2.2
Single Relay Networks using Network Coding . . . . . . . . . . . . . . . . .
20
2.3
Multiple-Relay Networks using Network Coding . . . . . . . . . . . . . . . .
22
3 Outage Probability Calculations
24
3.1
Mutual Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
24
3.2
Outage Probability Definition . . . . . . . . . . . . . . . . . . . . . . . . . .
25
3.3
Outage Probability of Multiple-Relay Networks . . . . . . . . . . . . . . . .
27
3.3.1
Traditional Decode-and-Forward relaying . . . . . . . . . . . . . . . .
27
3.3.2
Selection Decode-and-Forward relaying . . . . . . . . . . . . . . . . .
29
3.4
Outage Probability of Single Relay Networks using Network coding . . . . .
32
3.5
Outage Probability of Multiple-Relay Networks using Network Coding . . . .
36
Conclusions and Future Works
42
iii
Bibliography
43
iv
List of Figures
1.1
Frequency Diversity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2
1.2
Space Diversity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2
1.3
Cooperative relay network . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6
1.4
An example of Network Coding . . . . . . . . . . . . . . . . . . . . . . . . .
7
1.5
An example of Non-linear Network Coding . . . . . . . . . . . . . . . . . . .
8
1.6
An example of linear Network Coding . . . . . . . . . . . . . . . . . . . . . .
9
1.7
The butterfly network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10
1.8
The weakness of Network Coding . . . . . . . . . . . . . . . . . . . . . . . .
12
2.1
A traditional single relay network . . . . . . . . . . . . . . . . . . . . . . . .
19
2.2
A traditional multiple-relay network . . . . . . . . . . . . . . . . . . . . . . .
19
2.3
Network coding in single relay network . . . . . . . . . . . . . . . . . . . . .
20
2.4
Multiple-relay network using network coding . . . . . . . . . . . . . . . . . .
22
3.1
The direct link between the input and the output . . . . . . . . . . . . . . .
25
3.2
Outage probability of a direct link . . . . . . . . . . . . . . . . . . . . . . . .
27
3.3
Outage Probability of fixed and selection DF relay . . . . . . . . . . . . . . .
32
3.4
The degraded system model of a single relay network based on NC . . . . . .
34
3.5
The degraded system model of a single relay network based on NC . . . . . .
35
3.6
Outage probability of the single relay network with and without network coding 36
3.7
Link s1 r1 is in outage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
39
3.8
Outage probability of relay networks with different scenarios . . . . . . . . .
41
v
Abstract
In communication, Cooperative Diversity Relaying refers to devices communicating with one another with the help of relays in order to increase the
performance of the network. However, in one timeslot, the relay only transmits the signal of one source. Therefore, Network Coding is introduced to
improve the throughput of the network. Combining Cooperative Relay Network and Network Coding should be studied to achieve significant benefits
and overcome some weakness. In this thesis, we consider the effect of Network Coding on Cooperative Relay Network. We propose to use Selection
Decode-and-Forward instead of Traditional Decode-and-Forward protocol at
the relay. We also use the instantaneous channel gains to calculate the outage
probability of the proposal system model.
The rest of the thesis is organized as follows. In Chapter II, the system
model of a multiple-relay network is described. The outage probability is
calculated in Chapter III. Finally, the conclusions and the future works are
drawn in Section IV.
Chapter 1
Introduction
1.1
Introduction to cooperative relay networks
The sharp increase in the number of mobile subscribers which needs large
bandwidth for multimedia applications anywhere and anytime requires the
network service providers to optimize and develop the current technologies in
order to ensure that the Quality of Services (QoS) is always satisfied. Diversity
scheme are used to improve the reliability of a message signal by transmitting
multiple version of the same signal over different communication channels.
Because of time-varying channel conditions, the diversity plays an important
role in combating fading and co-channel interference. Diversity techniques
are divided into the following types: time diversity, frequency diversity, space
diversity, polarization diversity, muiltiuser diversity! [1] .
• Time diversity: The transmitter sends the same data at different time
instants or a redundant error correcting code is added into the messages
before transmitting. Repetition coding is one of the most popular types
of time diversity.
1
• Frequency diversity: The signal transmitted by using different frequency
channels on a single antenna. At the destination, it requires the number
of receivers as the number of frequencies used at the transmitter. It
therefore requires more spectrum usage.
Transmitter
1
Transmitted
signal
antenna
Receiver 1
Recovered
signal
antenna
Transmitter
2
Receiver 2
Figure 1.1: Frequency Diversity
• Spatial diversity. The signal is transmitted over different path by using
several antennas at the transmitter in order to allow multiusers to share
a spectrum and avoid co-channel interference.
Figure 1.2: Space Diversity
• Polarization diversity: The same messages are transmitted and received
by using antennas with different polarization. A diversity combining technique designed to combine the multiple received signals at the destination
is used in this case.
2
• Multiuser diversity: In this technique, the transmitter and receiver rely
on the quality of the link between the transmitter and each receiver in
order to selects the best partner.
In recent years, MIMO (multi-input multi-output) technology based on
spatial diversity and spatial diversity has attracted attention in wireless communication because it greatly improves the reliability, the throughput and the
transmission rate without additional bandwidth nor requiring higher transmitter power. However, this technique requires both the transmitter and the
receiver to have multi-antennas, and all channels must be independent. In
practice, users do not often achieve full-rank MIMO because they either do
not have multiple-antennas installed on a small-size devices, or the propagation environment cannot support MIMO, for example, there is not enough
scattering. Even if the users have enough antennas, full-rank MIMO is not
guaranteed because the links between several antenna elements are often correlated.
To overcome the limitations in diversity gain MIMO, a new communication
paradigm which uses an intermediate node to generate independent channel
between the user and the base station was introduced. The intermediate
node often called relay node receives the signal transmitted from the user
and forward it to the base station. And this paradigm is called Cooperative
Diversity Relaying Network.
3
1.1.1
The relay protocols
A key aspect of the cooperative communication process is the processing of
the signal received from the source node carried out by the relay. These different processing schemes depend on the protocols of the relays which can be
generally categorized into fixed relaying schemes, selection relaying protocol
(adaptive relaying schemes) and incremental relaying protocol.
In Fixed relaying protocols, the relay either amplifies what it receives, or
fully decodes, re-encodes, and re-transmits the source message. These fixed
relaying options are called amplify-and-forward (AF) and decode-and-forward
(DF), respectively. Amplify and Forward is the protocol in which the relay
receives the signal form the source and amplifies it before forwarding to the
destination. While, Decode-and-Forward relay decodes and re-encodes the
received message before sends it to the destination. Note that the decoded
signal at the relay may be incorrect. If an incorrect signal is forwarded to
the destination, the decoding at the destination is meaningless [2]. Therefore,
sometimes the relay must be silent because it can not detect the presence of
the signal or the signal quality is not good enough for the relay to decode
fully the messages.
Selection relaying (SR) protocol is designed to overcome the shortcomings of
DF relaying when the measured SNR at the relay falls below a threshold that
the relay becomes unable to decode the message, the source simply continues
its direct transmission to the destination using repetition coding or other more
powerful codes.
In incremental relaying (IR) protocol, the relay only transmits upon a neg4
ative feedback from the destination. Fixed relaying makes inefficient use of
relay channel resources when operating at high rates because the relays repeat
all the time, and under good transmission conditions this is un-necessarily.
In IR networks, the destination sends a one-bit ACK to the source and the
relay if it can successfully decode message from the source, otherwise it sends
a NACK to signal it fails to decode the message. Only when the relay receives a NACK and if it is able to decode the source message, it will forward
the message to the destination by employing AF relaying. The destination
receiver then uses maximum ratio combining (MRC) of the signal from the
source and the relay to build up its receive SNR until it can successfully
decode the message. This is equivalent to using the well known repetition
coding technique to combat deep fading situations.
1.1.2
Advantages of Cooperative Diversity Relaying Networks
Cooperative Diversity Relaying refers to devices communicating with one
another with the help of relays in order to increase the performance of the
network [3]. Thereby, the relay channel can be considered as an auxiliary
channel to the direct channel between the source and destination.
Figure 1.3 shows a network model using M relays. The operation of this
model can be divided into M + 1 time slots. In the first time slot, the source
sends its messages to the relays and the destination using the broadcast
method. The relay i relies on the defined protocol to receive and process
the source message before retransmitting it to the destination in timeslot i.
The presence of the signal is decided at the destination by comparing the
5
measured SNR with a threshold.
R1
R2
Direct link
S
Broadcast
mode
RM
D
Broadcast
mode
Figure 1.3: Cooperative relay network
The operation of each relay is independent of the others, so that there is no
correlation among all channels. We will show that the diversity gain and the
robustness of this system model is increased significantly. It is clear that the
destination can not decode a source’s messages if and only if all links connecting the M relays and that source to the destination are in outage. Assuming
that the outage probabilities of these links are the same, and denoted by p.
Then the probability of system outage event is pout = pM +1 .
In [4], the diversity gain is defined as
D,
− log P
SN R→∞ log SN R
lim
(1.1)
in which P is the outage probability, SN R is the signal to noise ratio. Then
D=
− log P M +1
≈M +1
SN R→∞ log SN R
lim
(1.2)
Equation 1.2 indicates that the user can guarantee the maximum diversity
which is equal the number of the relays plus the direct link, i.e being the
minimum cut at each source. It means that the limitation of MIMO technique
6
has been overcome.
However, in cooperative relay network shown in figure 1.3, we are able to
use one or more relays, but in one timeslot, the relay only transmits the signal
of one source.
1.2
Introduction to Network Coding
As discussed in the previous section, in a typical network, information is
transmitted from the source node to each destination node through a chain of
intermediate nodes by a method known as store-and-forward. In this method,
the intermediate node only processes and transmits a unique signal at one
time without overlapping, thus slow down the through. In order to increase
the throughput of the network, network coding technique was introduced
in [5] and then further developed in [6], as a new paradigm which exploits the
characteristics of the broadcast communication channel to combine several
input signals into one output signal at the intermediate node.
Figure 1.4: An example of Network Coding
In figure 1.4, both N1 and N2 want to send their signal to node N4 using
7
broadcast mode. When network coding is applied, the intermediate node will
combine these signals into an output before retransmitting to the destination. The question are how the intermediate node combine them and how
the destination node detect the received messages. When we study on the
protocol of the intermediate node, we can divide network coding into binary
and non-binary network coding.
1.2.1
Non-Binary and Binary Network Coding
In binary network coding showed in figure 1.5, the intermediate node uses
XOR operator to consolidate the received messages transmitted form sources.
Because XOR operator is only used to add two binary bits, the input data
S1
x1
R
S2
x1 x2
D
x2
Figure 1.5: An example of Non-linear Network Coding
must be in binary form. It means that the data must be decoded over GF (2)
and it only supports two sources. The main benefit of non-linear network
coding is simple and can be easily implemented by a hardware. However, it is
sub-optimal [7]. It means that, the diversity order of system does not change
8
when we increase the number of relays.
In non-binary network coding, each intermediate node uses a linear equation to combine the inputs and the destination uses the system of linear
equation to decode the received messages. Figure 1.6 is an example of linear
network coding with two sources and one relay. a1 and a2 are elements of
GF (2q ); x1 and x2 are decoded over GF (2q ). One drawback of using network
S1
x1
R
S2
a1 x1 a2 x2
D
x2
Figure 1.6: An example of linear Network Coding
coding over non-binary fields may be higher complexity, since computations
in large finite fields are more complex than over the binary field. Therefore, it
also causes worse transmission delay and more bandwidth consumption. [8].
So that, in general case, we cannot conclude which better linear or non-linear
network coding. In this thesis, we only concentrate on binary network coding.
1.2.2
Advantages of Network Coding
Increasing throughput achieved by increasing the efficiency of packet transmission is the most well-know benefit of network coding. To prove this point,
9
we consider a typical model of network coding which is called the butterfly
network (see Figure 1.7) [9].
S
b1
1
b1
b2
S
b1
b2
1
2
b1
b2
3
b1
2
3
b1 b 2
b1
b2
b1 b2
4
b2
4
D2
D1
b2
D1
b1 b2
(a)
D2
(b)
Figure 1.7: The butterfly network
In this network, the source node S wants to send its signal in the form bits
b1 and b2 to two destination nodes D1 and D2 over different output channels
by using multi-cast mode. Figure 1.7a indicate that b1 is sent on channel
(s, 1) and b2 is sent on channel (s, 2). The received signal at the intermediate
nodes 1 and 2 are b1 and b2 , respectively. In turn, node 1 (or 2) broadcast
their signal to destination D1 and node 3 ( or D2 and node 3) by using two
channels (1, D1 ) and (1, 3) (or (2, D2 ) and (2, 3)). Now, we consider the input
and output of the node 3. There are two input channels but only one output
channel (3,4). Normally, node 3 has to choose either b1 or b2 to send to
the node 4. Suppose the b1 is sent to the node 4 by using link (3, 4) as in
10
Figure 1.7a. To complete the transmission, the node 4 broadcast b1 to the
destination D1 and D2 . Finally, at the node D2 , both b1 and b2 are received.
While, at node D1 , two copies of b1 are received, therefore the problem is that
b2 cannot be recovered.
(b1 ⊕ b2 ) ⊕ b1 = (b1 ⊕ b1 ) ⊕ b2 = b2
However, if network coding is applied at node 3 as shown in 1.7b, this
problem may be solved. In Figure 1.7b, node 3 receives both b1 and b2 then
combines them into a unique signal by using modulo 2 addition before retransmitting it to node 4. Then, the signal at the destination D1 are b1 ⊕ b2
and b1 . In order to recover b2 , we add b1 ⊕ b2 and b1 by using module 2
operator. It is similar to recover b1 at the destination D2 .
This network model illustrates an important point: If network coding is not
applied at node 3, in order to send both b1 and b2 to D1 and D2 , we must use
more capacity at channel (3, 4) or more timeslot. So that, we may conclude
that network coding can increase throughput for broadcast network.
1.2.3
Weaknesses of Network Coding
The main issue of using network coding is that if a transmission error
occurs, it could affect the detecting and coding at the intermediate node,
and the destination node could receive useless information [10]. Considering
the scenario shown in Figure 1.7, the channel between the source S and the
intermediate node 2 is faded. It mean that node 2 is unable to decode the
received messages successfully. Then, it could send incorrect messages to
11
node 3 and the destination D2 . Therefore, combing and encoding the signals
transmitted from node 1 and node 2 at node 3 is incorrect even when the
channels s − 1 and 1 − 3 are perfect. After several transmission phases, there
are two messages at the destination D1 : b1 (correct or incorrect) and b1 ⊕ b2
(incorrect). It means that b1 is detected by using incorrect messages.
b1
S
1
b2
b2
2
3
b1
1b1 2b2
b2
4
D1
1b1 2b2
D2
Error dectection
Figure 1.8: The weakness of Network Coding
Besides, synchronization and transmission delay among the incoming data
streams at the input of the intermediate node or destination node are also
significant issues that need to be considered when network coding is applied.
The transmitted data can not be recovered until all the necessary information
is received. These are not big problems for non-real time services (e.g data
and voice transmission), but they are should be considered carefully for real
12
time services (e.g video transmission,...).
1.3
Cooperative Diversity Relaying Networks
using network coding
As discussion above, both cooperative diversity relaying and network coding have advantages and weaknesses thus combining cooperative relaying with
channel coding should be studied to achieve significant benefits and overcome
some drawbacks. In an NC-based network, a source node sends messages to a
destination node via a number of relay nodes whereby an intermediate node
first encodes the messages received from its input nodes into a new message
and then sends this message to its output nodes. By decoding its inputs, the
destination node can recover the original messages sent by the source node.
The most common example of NC-based network model is two-source onerelay topology, as shown in Figure 2.3. In this topology, two sources transmit
their signals to the relay and the destination using broadcast technique. Then,
the relay combines its received signals into a unique signal and sends it to
destination. The traditional Decode-and-Forward (DF) protocol is often used
at the relay which decodes the messages from its input nodes before sending
them to its output nodes. Often, the links between the sources and relay
are assumed to be error-free so that the relay decodes the received messages
successfully [3, 11–13]. In [14], taking into account of link errors, the relay
is assumed to perform DF without error checking and the network codes are
designed for error correction.
In this thesis, instead of using DF relaying as in [14], we propose to use
13
selection DF relaying at the relay. The selection DF relaying protocol is
designed to overcome the shortcomings of DF relaying when the measured
SNR at the relay falls below a threshold such that the relay becomes unable to
decode the messages, the source simply continues its direct transmission to the
destination using repetition coding [15]. In addition, we use Maximum Ratio
Combining (MRC) at the destination. Finally, we analyze the performance of
the proposed scheme in terms of outage probability by using the instantaneous
channel gains. The analysis is based on a newly developed method for exact
calculation of the outage probability [16].
14
Chapter 2
System models
In theory, the relay node can operate in both time-division (TD) and
frequency-division (FD). If the frequency-mode method is applied, the bandwidth W is divided into a bandwidth of αW where the relay node listens and
(1 − α)W where the relay transmits. The destination node pays attention the
whole bandwidth W. Similarly, if the time-division mode is applied, then for
a given time window D, in the relay-receive phase, the relay uses a fraction of
time αD to received the messages from its source and uses the remaining time
(1 − α)D of the window to send the received messages to its destination. It
is clear that from an information-theoretic point of view, there is no different
between TD mode and FD mode for the fixed channel gain case. In fading
channels, however, the TD mode has more benefit than the FD mode because
can be adjusted to the instantaneous channel conditions, whereas α is often
fixed in the FD mode [17]. So, in this thesis, we only deal with the relays
operating in the TD mode.
In fixed DF relaying, the relay decodes the received message from the source
and sends it to the destination. The decoded message at the relay can be
15
correct or incorrect. If an incorrect signal is transmitted to the destination,
the decoding at the destination is meaningless. It is clear that the diversity
order of this scheme is only one, because the performance of the system is
limited by the worst of the source−relay and source−destination links.
Selection relaying (SR) protocol is designed to overcome the shortcomings of
DF relaying when the measured SNR at the relay falls below a threshold that
the relay becomes unable to decode the message, the source simply continues
its direct transmission to the destination using repetition coding or other more
powerful codes.
In this thesis, we only consider the relay using selection Decode-and-Forward
protocol in Time-Division mode.
2.1
Traditional Relay Multiple-Wireless Networks
In this section, we will discuss about end-to-end signal of the selection
Decode-and-Forward relay. Relaying is assumed to operate in the time division mode having two phases (two time slots): the relay-receive phase and
the relay-transmit phase.
In phase 1 called the relay-receive phase, the sources S1 , S2 transmit the
N -symbol message to both the destination D and the relays R1 ,R2 , i.e, the
broadcast mode is applied. We assume that the transmitted power of each
relay is constant, then the received signals at the relay R1 ,R2 and destination
16
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