Relay Positioning for Energy Efficiency and Improved Performance of
Cooperative Wireless Networks
by
Vignesh Vellimalaip Sivakumar
A thesis submitted to the Graduate Faculty of
Auburn University
in partial fulfillment of the
requirements for the Degree of
Master of Science
Auburn, Alabama
May 03, 2014
Keywords: Greedy Algorithm, approximation algorithm, 2-approximation, Receiver
Diversity, Transmitter Zero Forcing
Copyright 2014 by Vignesh Vellimalaip Sivakumar
Approved by
Prathima Agrawal, Chair, Ginn Distinguished Professor of Electrical and Computer
Engineering
Shiwen Mao, McWane Associate Professor of Electrical and Computer Engineering
Chwan-Hwa Wu, Professor of Electrical and Computer Engineering
Abstract
Cooperative communications in wireless networks have gained much interest due to their
ability to mitigate the effect of fading in wireless networks by achieving spatial diversity. One
of the techniques used in cooperative communication systems, is by relaying data through
relay nodes. The number of base stations (BS) in a network is small, so many users who are
far from them require more power to transmit data. One issue is to find where to position a
limited number of available relay nodes (RN) to reduce energy consumption of user nodes.
Two ideas are proposed in this thesis as solutions to the above problem. First, we use
a greedy algorithm to determine the position of the relay nodes. In this method, relays
are placed at half way distance between the farthest user and the base station. Second,
we use an approximation algorithm for positioning the relay nodes. In this method, relays
are positioned at near optimal locations in an iterative manner. The algorithm tries to
position the relay nodes at the periphery of the base station?s coverage area. We compare
both the algorithms in terms of average energy consumption, average number of hops for
a packet to reach the base station and average r-cover which is the coverage radius of RN.
The approximation algorithm is shown to outperform the greedy algorithm in all the above
mentioned metrics.
We then investigate the application of two capacity enhancement techniques - Receiver
Diversity (RD) and Transmitter zero forcing (TZF) - in cooperative wireless networks. The
objective is to provide an analysis for the comparison of TZF and different RD strategies
such as Maximal Ratio Combining (MRC), Equal Gain Combining (EGC) and Selective
Combining (SC). We find that there is no case of dominance for the two techniques. TZF
can be used when interference is weak while RD can be adopted when the interference is
high. There always exists a trade-off between RD and TZF in network performance.
ii
Acknowledgments
I take this opportunity to thank all those who helped me and guided me throughout
this thesis.
Most importantly, I would like to express my utmost gratitude and everlasting thanks
to my advisor, Dr.Prathima Agrawal for her invaluable advice, insight and critical reviews
throughout this research. Without her patience, support and guidance, this thesis would not
have been possible.
I consider it as a special privilege to convey my prodigious and sincere thanks to
Dr.Shiwen Mao and Dr.John Wu for serving on my advisory committee and all the advice,
guidance and support given to me for my thesis work. I also extend my special thanks to
Landis+Gyr and Wireless Engineering Research and Education Center of Auburn University
for supporting my graduate studies.
With immense pleasure and satisfaction, I express my sincere thanks to all my friends
and family members for tirelessly supporting, enduring and guiding me in their own magical
way. I also express my sincere thanks to Dr.Donglin Hu, for his support and guidance right
from the beginning of my thesis.
I also thank and praise the almighty God for giving me strength, courage, guidance,
wisdom and knowledge to complete this thesis work successfully.
iii
Table of Contents
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii
Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii
List of Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Cooperative Relay Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Transmitter Zero Forcing and Receiver Diversity . . . . . . . . . . . . . . . . 2
1.3 Objective of this Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.4 Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2 Relay Node Placement for Energy Saving in Cooperative Networks 6
2.1 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2.1 Path Loss Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2.2 Routing Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2.3 Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.3 Solutions for Relay Node Placement in Cooperative Networks . . . . . . . . 9
2.3.1 A Simple Greedy Algorithm . . . . . . . . . . . . . . . . . . . . . . . 9
2.3.2 An Approximation Algorithm with Known Optimal Radius . . . . . . 10
2.3.3 An Approximation Algorithm with Unknown Optimal Radius . . . . 12
2.4 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.5 Summary of the Chapter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
iv
3 Performance Evaluation of Transmitter Zero Forcing and Receiver
Diversity in Cooperative Wireless Networks . . . . . . . . . . . . . . . . 19
3.1 Transmitter Zero Forcing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.2 Receiver Diversity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.2.1 Selective Combining . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.2.2 Maximal Ratio Combining . . . . . . . . . . . . . . . . . . . . . . . . 21
3.2.3 Equal Gain Combining . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.3 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.4 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.4.1 Receiver Diversity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.4.2 Transmitter Zero Forcing . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.5 Analysis of Transmitter Zero Forcing and Receiver Diversity on Network
Throughput for a two relay case . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.5.1 Receiver Diversity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.5.2 Transmitter Zero Forcing . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.6 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.7 Summary of chapter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
4 Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
v
List of Figures
1.1 Simple Cooperative System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Transmitter Zero Forcing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.1 Approximation Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2 Placement of Relay Nodes using Greedy Algorithm . . . . . . . . . . . . . . . . 13
2.3 Placement of Relay Nodes using Approximation Algorithm . . . . . . . . . . . . 14
2.4 Number of Relays vs. Average r-cover . . . . . . . . . . . . . . . . . . . . . . . 15
2.5 Number of Relays vs. Average Number of Hops . . . . . . . . . . . . . . . . . . 16
2.6 Number of Relays vs. Average Energy Consumption . . . . . . . . . . . . . . . 17
3.1 The Receiver in a diversity combining system . . . . . . . . . . . . . . . . . . . 20
3.2 Receiver diversity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.3 Transmitter Zero Forcing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.4 Channel Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.5 Network Throughput vs. Distance - Two Relay Case . . . . . . . . . . . . . . . 33
3.6 Network Throughput vs. Distance - Three Relay Case . . . . . . . . . . . . . . 34
3.7 Network Throughput vs. Distance - Four Relay Case . . . . . . . . . . . . . . . 34
vi
3.8 Network Throughput vs. Transmit Power - Two Relay Case . . . . . . . . . . . 36
3.9 Network Throughput vs. Transmit Power - Three Relay Case . . . . . . . . . . 37
3.10 Network Throughput vs. Transmit Power - Four Relay Case . . . . . . . . . . . 37
vii
List of Tables
2.1 A Simple Greedy Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2 An Approximation Algorithm with Known Optimal Radius . . . . . . . . . . . 11
2.3 An Improved Algorithm with Unknown Optimal Radius . . . . . . . . . . . . . 12
3.1 Primal Dual Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.2 Comparison of RD and Transmitter Zero Forcing . . . . . . . . . . . . . . . . . 32
viii
List of Abbreviations
Auburn Auburn University
LoA List of Abbreviations
ix
Chapter 1
Introduction
Cooperative communications allow communication terminals in a network to listen and
help the information transmission of each other, by taking advantage of the broadcast nature
of wireless communication. It can be used in improving network connectivity, enhancing
power and spectral efficiency and improving communication reliability.
The basic ideas behind cooperative communication can be traced back to the ground-
breaking work of Cover and El Gamal on the information theoretic properties of the relay
channel [1]. This work analyzed the capacity of a three node network consisting of a source, a
destination, and a relay and determined the upper and lower bounds on its channel capacity.
In cooperative communication, a number of relay nodes are assigned to help in forwarding a
users transmission to its destination. Various cooperative schemes such as decode and for-
ward, amplify-and-forward, selective relaying and incremental relaying have been designed
for enhancing the performance of wireless communication networks [2] - [3].
Most recently, cooperative communication has been adopted in Long Term Evolution
(LTE) Advanced network. LTE is the globally embraced wireless communication standard
adopted by smart phones and tablets manufacturers [40].
1.1 Cooperative Relay Networks
In a cooperative relay system, sources first transmit their data to the relay nodes (RN).
Each RN then processes and forwards its received data to the destination nodes following
some cooperation protocols. With the received signal from the RNs, the destinations decode
the data from their corresponding sources.
1
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g90g286g367g258g455g3g69g381g282g286
g104g400g286g396
g100g396g258g374g400g373g349g410g410g286g282g3g94g349g336g374g258g367
Figure 1.1: Simple Cooperative System
A simple cooperative system consisting of a source, a relay and a destination is shown
in Figure 1.1. The RN is connected to the base station (BS) and functions like a BS,
but is less expensive. Users can connect directly to the BS or indirectly via a RN. By
relaying the packet from user to BS via RN, the long distance communication is broken to
short distance links. Since the energy consumption is proportional to the distance, shorter
distance communication (RN based) requires less energy than direct communication. RNs,
however, have small coverage area compared to the BS. With large number of RNs being
deployed in the network the delay for a packet to reach BS increases. As a result good
placement strategy of the RNs is required to achieve spatial diversity and to reduce energy
consumption of the terminal users.
1.2 Transmitter Zero Forcing and Receiver Diversity
Interference in traditional wireless networks has been considered harmful. Multiple
concurrent transmission techniques (e.g., zero forcing, interference alignment and distributed
MIMO) [17] - [18], are proposed in which multiple senders jointly encode signals to multiple
receivers so that interference is aligned or canceled and each receiver is able to decode its
desired information.
2
Figure 1.2: Transmitter Zero Forcing
In [31] - [32], when the number of antennas in sender and receiver are 2 as shown in
Figure 1.2. If we represent the signals corresponding to packets 1 and 2 as x1, x2 respectively,
ignoring noise, we have that the received signals at receiver antennas 1 and 2 are y1 =
h11x1 + h21x2, and y2 = h12x1 + h22x2, respectively. Here hij is a complex number whose
magnitude and phase represent signal attenuation and delay from sender antenna i to receiver
antenna j. The receiver estimates the channel H as shown in Figure 1.2. It can recover x1
and x2 by multiplying H?1, the inverse of H, with the received signal vector Y (Y = [y1y2]T
where [.]T represents vector transpose). By rewriting the received signal as
?
?? y1
y2
?
?? = H
?
?? 1
0
?
??x
1 + H
?
?? 0
1
?
??x
2 (1.1)
we can view the received signal as the sum of two scaled vectors. The decoding of each
packet, say x1, can be viewed as projecting H
bracketleftbigg
1 0
bracketrightbiggT
x1 onto a vector that is orthogonal to
the vector H
bracketleftbigg
0 1
bracketrightbiggT
carrying the interfering signal x2.
If the sender knows the channel H, the sender can multiply H?1 with X and send the
resulting signal X?. Again, ignoring noise, we can verify that the receiver antenna 1 will
receive only x1, no mixing of x2; similarly, receiver antenna 2 will receive only x2. This
technique is often called zero forcing.
3
The basic concept of receiver diversity [33], is that the receiver has more than one
version of the transmitted signal available, and each version of transmitted signal is received
through a distinct channel. When several versions of the signal, carrying the same informa-
tion, are received over multiple channels that exhibit independent fading with comparable
strengths, the chances that all the independently faded signal components experience the
same fading simultaneously are greatly reduced. There are three common technique to di-
versity combining, viz Selective Combining (SC), Maximum Ratio Combining (MRC) and
Equal Gain Combining (EGC).
Further explanation of RD and TZF can be found in chapter 3.
1.3 Objective of this Thesis
Here our objective is to reduce the energy consumption at the user node assuming the
number of relays in the system is known. First, we use a greedy algorithm to deploy the
relay nodes in the system. In this method the relays are placed at half way distance between
the farthest user and the base station. The other method proposed in this thesis - the
approximation algorithm, is a 2-approximation [15], for the center selection problem. This
algorithm tries to position the relay at the periphery of the base stations coverage area.
Next, we investigate the performance of TZF and RD in cooperative relay networks. We
formulate the problem of cellular network with multiple relay nodes and two users. Then we
derive system capacity for TZF and RD and evaluate the capacity of the system by varying
the distance between the user and relay, and also by varying the transmit power at the relays.
The main contributions of this work consist of:
? Comparison between the greedy and approximation algorithms and determine the best
algorithm for positioning the relay nodes to reduce energy consumption,
? Comparison between RD and Transmitter Zero Forcing in cooperative relay networks,
4
? Deriving a closed-form expression for influence of RD and Transmitter Zero Forcing
on network throughput
? The implementation of the proposed relay node placement algorithms and capacity
enhancement techniques using Matlab.
1.4 Organization
This work is divided into two parts. The first part discusses the relay node place-
ment strategies to reduce energy consumption for the users and the second part discusses
the comparative study of the capacity enhancement techniques applied in a cooperative re-
lay network. The related work and the introduction required for the respective topics are
discussed before the idea is presented. As a result, a separate literature review section is ne-
cessitated. A conclusion section summarizes the finding in the study of cooperative wireless
networks.
5
Chapter 2
Relay Node Placement for Energy Saving in Cooperative Networks
In cooperative communication, wireless nodes assist each other in information deliv-
ery, with the objective of gaining greater reliability and efficiency than they could obtain
individually. Cooperative communication represents another new paradigm for wireless com-
munications [16].
A number of relay nodes is integrated in the single hop cellular network [4] and [40], to
improve the performance, fairness, energy, throughput etc. These benefits make relay node
an asset to the network. The location for installing the relay node must satisfy conditions
like quality of the link to the base station, power supply, Signal to Interference plus Noise
Ratio (SINR). Finding the best relay node location in a network is an important task. It
should be noted that with increase in the number of relays the delay for the packets to arrive
at its destination in the network increases i.e, the number of hops for a packet to reach the
destination increases which increases the delay. Deploying relay nodes at the optimal position
minimizes the number of relay nodes required to effectively cover the network, improve the
performance and reduce the energy consumption for the users.
The goal is to find a set of relay node (RN) positions, so that the maximum distance
from a user to its nearest RN is minimized.
6
2.1 Literature Review
The relay node placement problem can be found in different applications like wireless
sensor networks [5], heterogeneous networks [6], wireless local area networks [7] and 802.16j
networks [8].
The cost optimal deployment of the RN and access points (AP) for wireless local area
network (WLAN) are discussed in [9]. The methodology proposed can determine and
compare the most cost efficient deployment mixes of APs and RNs. A comparison between
deployment of micro APs and RNs along with macro APs is studied. The result shows that
deploying RN is more cost efficient. In [10], location of the RNs depends on the demanded
telegraphic distribution. In the proposed method, the mobile station (MS) constructs a
database from the location pattern and teletraffic pattern. This scheme provides teletraffic
demand with higher spatial resolution which is used for RN location planning. In [11], the
relays are positioned to achieve full diversity gain and minimize error probability. The scheme
proposed in [11] places the relays based on the SINR between the source and destination.
In [6], RN placement is based on the physical distance between the nodes and BS. The
algorithm arranges the RNs to optimize connectivity at disadvantaged location and uses
both cellular and ad hoc medium resource. In [12], RN placement is dependent on link
quality and power allocation.
The algorithms proposed in this thesis are also distance based in selecting the RN
position. When the number of RNs that can be deployed in the network is predetermined,
the algorithm gives the best possible location for positioning the RNs, so that the users
energy consumption is less while minimizing the number of hops required for the packets to
reach a BS.
7
2.2 System Model
We consider a network with M base stations (BS) (indexed from 1 to M) and N end
users (indexed from 1 to N) randomly deployed within a huge area. Due to the deployment
cost of BSs, the number of BSs is very small and many devices far away from BSs require a
large amount of power to transmit data. In order to address this problem, we would place
K relay nodes to help users to deliver their data to the destination and reduce their power
consumption.
2.2.1 Path Loss Model
The complexity of signal propagation makes it difficult to obtain a single model that
characterizes path loss accurately across a range of different environments. In order to
capture the essence of signal propagation and seek a trade off between complexity and
approximation accuracy, we adopt the following simplified model for path loss [13], as a
function of distance:
PrdBm = PtdBm + ?dB?10? log10( dd
0
) (2.1)
where Pr, Pt, and d are received power, transmit power, and distance, respectively. ? is a unit
less constant that depends on the antenna characteristics and average channel attenuation,
d0 is a reference distance, and ? is the path loss exponent. ? is given by
?dB = 20log10( ?4?d
0
) (2.2)
where ? is wavelength of radio wave. Path loss exponent ?, is a function of carrier frequency,
environment, obstruction etc. Typically ranges from 2 to 8. For a free space propagation
model ? is 2 and for two ray propagation model ? is 4. To meet the Quality of Service (QoS)
requirements, we assume that the received power Pr should be greater than certain threshold.
8
Then, the transmit power Pt becomes a function of distance d. Therefore, reducing power
consumption is equivalent to reducing transmission distance.
2.2.2 Routing Model
Since our objective is to reduce transmitted power, we assume that each relay node is
connected to its nearest BS and each user is connected to its nearest BS or relay node (RN).
Denote A, R and U as the set of BSs, RNs and user nodes, respectively. Then, the BS m?
that relay node k is connected to is given by:
m? = argd(k,A) = argmin
m?A
d(k,m) (2.3)
whered(k,m) is the distance between BSmand userk. We assume the distance is symmetric:
i.e. d(k,m) = d(m,k). Similarly, the BS or RN that user n is connected to is given by:
i? = argd(n,A?R)arg min
i?A?R
d(n,i) (2.4)
2.2.3 Objective
We say that BS?s and RN?s form an r ?cover if each user is within distance at most r
from one of BS or RN which implies d(n,A?R) ? r for all users n ? U. The minimum r is
called the r ?cover of the union A and R and is denoted as r(A?R). Since the locations
of BS?s are fixed, we can simplify r(A?R) as r(R). Our objective is to select a set R of K
RN?s for which r(R) is as small as possible.
2.3 Solutions for Relay Node Placement in Cooperative Networks
2.3.1 A Simple Greedy Algorithm
Simple greedy algorithm works as follows. It places the first relay node (RN) at halfway
between the base station (BS) and its furthest user, and then keeps on adding RN?s so as
9
to reduce the r ? cover (coverage radius of RN) each time. The algorithm is presented in
table 2.1.
Table 2.1: A Simple Greedy Algorithm
1: Initialize A and U
2: Let R = ?
3: While |R| ? K
4: Find the BS-user or RN-user pair with minimum distance:
{i?} = argmini?A?R,j?U d(i,j)
5: Find i*-user pair with maximum distance:
{j?} = argmaxi?i?,j?U d(i,j)
6: Place RN c at the halfway point between i? and j? and add c to R
7: End while
It turns out that this algorithm is too simplistic to be effective. The RNs are selected
based only on the longest distance. In some cases, it can lead to very poor performance.
2.3.2 An Approximation Algorithm with Known Optimal Radius
k-center problem - Given n cities with specified distances, one wants to build k ware-
houses in different cities and minimize the maximum distance of a city to a warehouse. In
graph theory this means finding a set of k vertices for which the largest distance of any point
to its closest vertex in the k-set is minimum.
Although the k-center problem is NP complete, there is a simple 2-approximation algo-
rithm [14] - [15], that provides a near optimal solution for the k-center problem. Suppose
we know that there is a set of K optimally deployed RN?s, R?, with radius r(R?). We need
to find some set of K RN?s whose radius is not much larger than r(R?). It turns out that
finding a set R of K RN?s with covering radius at most 2r(R?) can be achieved by our
approximation algorithm in table 2.2.
10
Table 2.2: An Approximation Algorithm with Known Optimal Radius
1: Initialize A and U0 = U
2: Let R = ? and U1 = ?
3: Move users whose d(n,A) ? 2r(R?) from U0 to U1
4: While |R| < K and U0 negationslash= ?
5: Dj = mini?U1,j?U0 d(i,j)
6: {j?} = argmaxj?U0 Dj
7: {i?} = argmini?U1 d(i,j?)
8: Add i? to R
9: Move users whose d(n,i?) ? 2r(R?) from U0 to U1
10: End while
11: If U0 negationslash= ? and |R| = K
12: There is no set of K RN?s with covering radius r(R?)
13: End if
Lemma 1. Any set of RN?s, denoted by R, returned by the algorithm in table 2.2 has
covering radius r(R) ? 2r(R?)
Proof. Figure 2.1 gives us an idea of the approximation algorithm. We must show that
r(R) ? 2r(R?).
Let us assume, for the sake of contradiction, that r(R) > 2r(R?).
Let U be any site in {u0,u1,...,un,}. Let r? ? R? be the center closest to U. Similarly,
let r ? R be the center closest to r?.
Then, by the triangle inequality, we must have dist(U;R) ? dist(s;r?) + dist(r?;r).
We know that, dist(U;r?) ? r(R?) and dist(r?;r) ? r(R?).
Therefore, we must have
dist(U;R) ? 2r(R?), which implies that r(R) ? 2r(R?).
This is a contradiction, and, therefore, our assumption must be incorrect.
Hence r(R) ? 2r(R?).
11
Figure 2.1: Approximation Algorithm
2.3.3 An Approximation Algorithm with Unknown Optimal Radius
We can start with some guesses about the optimal radius. According to the design of
the algorithm in table 2.2, one of two things will happen. Either we find a set of RN?s or we
conclude that there is no solution. In the first case, we can lower our guess on the radius.
In the second case, we can raise it. This makes us to perform a binary search on the radius.
This algorithm is described in table 2.3
Table 2.3: An Improved Algorithm with Unknown Optimal Radius
1: Initialize r0 = 0 and r1 = maxi?A,j?U d(i,j)
2: While |r1 ?r0| > ?
3: Set r = (r1 + r0)/2 and run the algorithm in table 2.2
4: If there is no solution
5: r0 = r
6: Else
7: r1 = r
8: End if
9: End while
The algorithm stops when two estimates, r0 and r1, are close to each other. The solution
2r1 is a 2-approximation to the optimal radius.
12
2.4 Simulation Results
We performed simulations using MATLAB to study the performance of the proposed
algorithms. The following system model is used. We created a network area of 100x100, the
number of base stations (BS) in the network is 3 and the number of Users in the network are
100. Both Users and BSs in the network are uniform randomly distributed. The simulations
are done multiple times and the average r?cover, number of hops and energy consumption
are determined to evaluate the performance of the proposed algorithms.
0 100 200 300 400 5000
100
200
300
400
500
 
 
Base Stations
Users
Relays
Figure 2.2: Placement of Relay Nodes using Greedy Algorithm
13
0 100 200 300 400 5000
100
200
300
400
500
 
 
Base Stations
Users
Relays
Figure 2.3: Placement of Relay Nodes using Approximation Algorithm
Figure 2.2 and Figure 2.3, show the placement of the K(Number of relays) = 10 relay
nodes when greedy algorithm and approximation algorithm are used, respectively.
14
4 6 8 10110
120
130
140
150
160
170
180
190
K (Number of relays in the system)
r?Cover (meters)
 
 
Approximation Algorithm
Greedy Algorithm
Figure 2.4: Number of Relays vs. Average r-cover
In Figure 2.4, we examine the r?cover value for the two algorithms. It can be seen that
the approximation algorithm has smaller r?cover value compared to the greedy algorithm.
This is due to the near optimal positioning of the relay nodes. Smaller r?cover value means
the users need to spend less energy to send their packet to the relays. K (the number of
relays) in the system is varied from 4 to 10. It can be seen that, as the number of relays
allowed in the system increases the difference r ? cover value between the two algorithm
decreases.
15
4 5 6 7 8 9 101.5
2
2.5
3
3.5
4
K (Number of relays in the system)
Average Number of Hops
 
 
Approximation Algorithm
Greedy Algorithm
Figure 2.5: Number of Relays vs. Average Number of Hops
In Figure 2.5, we examine the average number of hops for the two algorithms for trans-
mitting a packet from a user node to a BS. It can be seen that, when approximation algorithm
is used, it takes less number of hops compared to the greedy algorithm. Less number of hops
means less time delay for a packet to reach the destination from the users. For different K
relays (K = 4 to 10 ) in the system, the average number of hops for the user is calculated and
it is evident that, for different number of relays in the system the approximation algorithm
has better performance.
16
4 5 6 7 8 9 10?15
?10
?5
0
5
10
15
20
K (Number of relays in the system)
Average energy consumption (dBm)
 
 
Approximation Algorithm ? Free Space Model
Greedy Algorithm ? Free Space Model
Approximation Algorithm?Two Ray Model
Greedy Algorithm?Two Ray Model
Figure 2.6: Number of Relays vs. Average Energy Consumption
In Figure 2.6, we examine the average energy consumption for the users in the system.
It can be seen that the approximation algorithm saves more energy compared to the greedy
algorithm. As the K (K = 4 to 10) value increases, the average energy consumption of
the user decreases. In all cases, the approximation algorithm consumes less energy. This is
because in the approximation algorithm the relays are placed at the periphery of the coverage
distance of the BS, energy consumption for the users to reach the relays is less. Whereas in
the greedy algorithm the relays are placed at half way points from the farthest user, which
may not be an optimum distance for positioning the relays. The average energy consumption
for both free space model and two ray model [13] are shown in Figure 2.6. In both the cases
the approximation algorithm performs better than the greedy algorithm.
17
2.5 Summary of the Chapter
In this chapter, we studied the positioning of relay nodes (RN) to reduce energy con-
sumption. We modeled the two relay node placement strategy i.e. greedy algorithm and
approximation algorithm. In greedy algorithm the RNs are place at halfway distance be-
tween the farthest user and base station (BS) whereas, in approximation algorithm the RNs
are placed at the periphery of the coverage distance of the BS. We compared both the al-
gorithms against various metrics such as average r ? cover, average number of hops for a
packet to reach the BS and average energy consumption at the user node. We found that
the approximation algorithm performs better than greedy algorithm in all aspects.
18
Chapter 3
Performance Evaluation of Transmitter Zero Forcing and Receiver Diversity
in Cooperative Wireless Networks
3.1 Transmitter Zero Forcing
In the communications community, novel techniques such as zero forcing [17] and
interference alignment [18] are proposed for simultaneous transmission and reception. If the
sender knows the channel state information, the sender can precode the message and send the
resulting signal to the receiver. Ignoring noise, the receiver receives only the intended message
and there is no interference from other transmitters. This technique is called Transmitter
zero forcing (TZF) [17].
Description of transmitter zero forcing is as follows [25]. Consider two transmitters
(denoted as X1 and X2 ) and two receivers (denoted as R1 and R2). Let S1 and S2 be the
signal corresponding to the packet to be sent to R1 and R2, respectively. With transmitter
zero forcing, the transmitter X1 and X2 send the compound signal C1,1S1 + C1,2S2 and
C2,1S1 + C2,2S2, respectively, to the two receivers R1 and R2 simultaneously. Where Ci,j is
the precoding matrix. If the channel noise is ignored, the received signals Y1 and Y2 can be
written as:
?
?? Y1
Y2
?
?? =
?
??H1,1 H1,2
H2,1 H2,2
?
??
T ?
??C1,1 C1,2
C2,1 C2,2
?
??
?
?? S1
S2
?
?? = HT ?C ?S (3.1)
Where Hi,j is the channel gain from transmitter Xi to receiver Tj, for all i and j.
19
From (3.1), it can be seen that both the receiver can perfectly decode their signal if the
precoding matrix C is chosen to be [HT]?1, i.e., the inverse of the channel gain matrix. With
this technique, the transmitters are able to send packets simultaneously and the interference
between the two concurrent transmission can be effectively canceled at both the receiver.
3.2 Receiver Diversity
Diversity combining [33], devotes the entire resources of the array to service a single user.
Specifically, diversity schemes enhance reliability by minimizing the channel fluctuations due
to fading. The central idea in Receiver Diversity (RD) is that different antennas receive
different versions of the same signal. The chances of all these copies being in a deep fade are
small.
g121
g121
g121
g1108g3 g75g437g410g393g437g410g3g94g349g336g374g258g367
g116g1004g910
g116g1005g910
g116g69g882g1005g910
Figure 3.1: The Receiver in a diversity combining system
20
Figure 3.1 shows the working of a receiver in a diversity combining system. Within
Receiver Diversity (RD) are three common techniques: Selective Combining(SC), Maximal
Ratio Combining (MRC) and Equal Gain Combining (EGC). For all three schemes, the goal
is to find a set of weights w, as shown in Figure 3.1. The weights are chosen to minimize
the impact of fading for a single user. The three techniques differ in how this weight vector
is chosen.
3.2.1 Selective Combining
Selective Combining (SC), is one of the simplest diversity techniques. The signals are
not weighted and the receiver simply picks the signal with the largest SNR. The overall SNR
is presented by:
?SC = max
i=1,???,M
?i (3.2)
where ?i is SNR at the i-th branch.
3.2.2 Maximal Ratio Combining
In Maximal Ratio Combining (MRC), all the branches are co-phased and individually
weighed to provide the optimal SNR at the output. The signals are co-phased prior to
summing in order to ensure all the branches are added in phase for maximum diversity gain.
The weights assigned to each branch are optimized to maximize the overall SNR, denoted
by ?MRC, which can be expressed as:
?MRC =
Msummationdisplay
i=1
?i (3.3)
where ?i is SNR at the i-th branch.
21
3.2.3 Equal Gain Combining
The signals are co-phased on each branch and then combined with equal weights. The
overall SNR is given by:
?EGC = 1M(
Msummationdisplay
i=1
??
i)2 (3.4)
where ?i is SNR at the i-th branch.
3.3 Literature Review
In [19], the design of the zero forcing precoder in a Multiple Input Multiple Output
(MIMO) system for maximizing performance under high signal-to-noise ratio (SNR) and
low SNR regime has been studied. The computation cost of finding the optimal precoder
is high. [20], focuses on the design of coordinated beam forming for zero forcing (ZF) in
static channel and [21] focuses on design of coordinated beam forming for ZF in time varying
channel for a MIMO system. In [22], the performance of Transmitter/Receive ZF in a MIMO
system is studied by deriving the upper and lower bounds of the overall outage probability,
their high signal-to-noise ratio approximations and diversity order. In [23], a modified
ZF decoder for ill conditioned MIMO channels has been proposed. The proposed decoder
overcomes the inherent noise enhancement in the zero forcing decoder by only considering
the well conditioned elements of the channel. In [24], source nodes and the relays cooperate
in choosing their precoding matrices and the filter coefficients, respectively, to perform a
cooperative zero forcing.
Receive Diversity is a well known combining scheme that has been studied extensively.
In [26], the impact of receive diversity on the error rate performance of a relay assisted co-
operative scheme has been studied. It is shown that for a destination with N antennas, the
maximum achievable diversity order under average power scaling and instantaneous power
22
scaling constraints are N+1 and 2N respectively. In [27] receive-diversity combining tech-
nique for Single Carrier - Frequency Division Multiple Access scheme (SC-FDMA), based
cooperative relay systems is proposed which was shown to provide diversity gain in multi-
path channel environment without suffering from error propagation phenomena. In [28],
the effects of phase noise on the performance of Maximum ratio combining-Orthogonal Fre-
quency Division Multiplexing (MRC-OFDM), wireless system in Rayleigh fading channel are
investigated. [29] describes the application of receive diversity in wireless sensor network
for improving field estimation while ensuring energy and spectrum efficiency. In [30], RD
for OFDM based broadband communication system is investigated. TZF and RD are two
well-known physical layer technologies. To our knowledge, research on the comparison of
TZF and RD has not been conducted yet.
3.4 System Model
In this section, we present the system models for both transmitter zero forcing and
signal combining technologies. We consider two users, denoted as user 1 and 2, are located
in a cellular network. The two users are so far away from the Base Station (BS) that they
cannot successfully receive the signals from the BS directly. We further assume M (M ? 2)
relays are deployed to help the BS deliver data to the two users. The transmission between
the BS and all relay nodes (RN) is assumed to be reliable. The channel is modeled as a
time-slotted, block-fading channel [36]. In the following section, we analyze the network
performance for two cases: receiver diversity and transmitter zero forcing.
3.4.1 Receiver Diversity
In receiver diversity, the signals from independent paths associated with multiple relays
are combined to obtain a compound signal which is a weighted sum of the co-phased fading
signals from different paths.
23
BS
User 1
User 2
Relay 1
Relay 2
BS
User 1
User 2
Relay 1
Relay 2
BS
User 1
User 2
Relay 1
Relay 2
BS
User 1
User 2
Relay 1
Relay 2
Time Slot 
1
Time Slot 
2
S1
Time Slot 
3
Time Slot 
4
S1
S2
S2
S1
S1
S2
S2
Figure 3.2: Receiver diversity
For receiver diversity, we need to use four time slots to send two packets to two users.
In Figure 3.2, the BS sends packet 1 to all relays in the first time slot, and then, user 1
receives all signals from all relays in the second time slot. Packet 2 is sent to relays and user
2 in the third and fourth time slot, respectively. The total network throughput (CRD) using
shannon capacity [37] - [38], is given by:
CRD = B4 bracketleftbiglog2(1 + ?1RD) + log2(1 + ?2RD)bracketrightbig (3.5)
24
where B is channel bandwidth, ?1RD and ?2RD are received signal-to-noise ratio (SNR) for
user 1 and 2 using receiver diversity, respectively.
3.4.2 Transmitter Zero Forcing
In Figure 3.3, the BS sends signal 1 and 2 to all relays in the first and second time
slot, respectively. Let Sj (j = 1,2) denote the signal to be transmitted to user j. In the
third time slot, relays transmit compound signals to the two users simultaneously using
transmitter zero forcing. In this way, the undesired signals are canceled at the receivers and
BS
User 1
User 2
Relay 1
Relay 2
BS
User 1
User 2
Relay 1
Relay 2
BS
User 1
User 2
Relay 1
Relay 2
Time Slot 
1
Time Slot 
2
S1
Time Slot 
3
S1
S2
S2
c11S1 + c12S2
c21S1 + c22S2
c11S1 + c
12S2
c21S1 + c22
S2
Figure 3.3: Transmitter Zero Forcing
it takes three time slot to complete the transmission. Thus, the total network throughput
25
(CTZF), is expressed as:
CTZF = B3 bracketleftbiglog2(1 +?1TZF) + log2(1 + ?2TZF)bracketrightbig. (3.6)
where ?TZF1 and ?TZF2 are received SNR for users 1 and 2 using transmitter zero forcing,
respectively.
As mentioned before, in the third time slot, relay i sends a compound signal ci,1S1+ci,2S2
to the two users, where ci,1 and ci,2 are the weights to be determined. Ignoring channel noise,
we can obtain the received signal Yj at a user j as, [25]:
Yj =
Msummationdisplay
i=1
Hi,j
2summationdisplay
n=1
ci,nSn
=
2summationdisplay
n=1
Sn
Msummationdisplay
i=1
ci,nHi,j (3.7)
where Hi,j is the channel gain from the i-th relay to user j. For user j, only signal Sj should
be decoded and the other signals should be forced to zero. The zeros-forcing constraints
[17], can be written as:
Msummationdisplay
i=1
ci,2Hi,1 = 0 and
Msummationdisplay
i=1
ci,1Hi,2 = 0 (3.8)
Usually, the transmit power of the relay is limited by a peak power Pmax. Since Sj has unit
power, the power of each transmitted signal is the sum squared of the coefficients. The peak
power constraint is given by:
c2i,1 + c2i,2 ? Pmax,i = 1,??? ,M (3.9)
Since Sj has unit power, the received SNR at user j is written as:
?TZFj = (
summationtextM
i=1 ci,jHi,j)
2
N0 ,j = 1,2 (3.10)
26
To determine the weights, we maximize the network throughput in equation (3.6) with
constraints (3.8), and (3.9). To solve the problem, we define non-negative dual variables vector? =
[?1,??? ,?M]T for the inequality constraints (3.9) and arbitrary dual variable vector? = [?1,?2]T.
The non-negative dual variables and arbitrary dual variables are the Lagrangian multipliers.
Lagrangian multiplier is a strategy to find the local maxima and minima of a function subject
to equality constraints. The Lagrangian function is [25]
L(vectorc,vector?, vector?) =
2summationdisplay
j=1
log2(1 + (
summationtextM
i=1 ci,jHi,j)
2
N0 ) +
Msummationdisplay
i=1
?i(Pmax ?c2i,1 ?c2i,2) +
?1
Msummationdisplay
i=1
ci,2Hi,1 + ?2
Msummationdisplay
i=1
ci,1Hi,2
=
2summationdisplay
j=1
Lj(vectorc,vector?,?j) +
Msummationdisplay
i=1
?iPmax (3.11)
where vectorc is a vector consisting of all weights ci,j?s and
Lj(vectorc,vector?,?j) = log2(1 + (
summationtextM
i=1 ci,jHi,j)
2
N0 )?
Msummationdisplay
i=1
(?ic2i,j ??jci,3?jHi,j) (3.12)
The primal dual algorithm is a method for solving a linear programming problem by
working with the dual and a related primal problem. Optimization problems may be viewed
from either of two perspectives, the primal problem or the dual problem. The solution to
the dual problem provides a lower bound to the solution of the primal problem. However,
in general, the optimal values of the primal and dual problems need not be equal. Their
difference is called the duality gap. The standard primal problem is generally defined as the
maximization problem [25] and [39].
27
The above problem can solved iteratively. In Step ? ? 1, for given vector vector?(?) and vector?(?),
we adopt the gradient method to maximize primal problem [25].
vectorc(? + 1) =vectorc(?) +?p
2summationdisplay
j=1
?vectorcLj(vectorc(?),vector?(?),?j(?)) (3.13)
where ?vectorcLj(vectorc(?),vector?(?),?j(?)) is the gradient of the primal problem and ?p is a small positive
step size.
The master dual problem for a given vectorc(? + 1) is:
min
vector?,vector?
L(vectorc(? + 1),vector?, vector?) (3.14)
Since the Lagrangian function is differentiable, we adopt sub-gradient method to update vector?
vector?(? + 1) = [vector?(?)??d?vector?L(vectorc(? + 1),vector?(?), vector?(?))]+ (3.15)
where ?d is a positive step size, and [?]+ denotes the projection onto the non negative axis.
Since vector? is a vector with two arbitrary numbers, we update it using gradient method
vector?(? + 1) = vector?(?)??d?vector?L(vectorc(? + 1),vector?(?), vector?(?)) (3.16)
The duality gap between primal and dual problem will be zero. The Primal-Dual algo-
rithm is presented in Table 3.1 [25], where ? is a sufficiently small threshold for convergence.
28
Table 3.1: Primal Dual Algorithm
1: Set ? = 1;vector?(1) to positive values;
2: Set vectorc(1) and vector?(1) to arbitrary values;
3: DO
4: Compute vectorc(? + 1) as in (3.13)
5: Compute vector?(? + 1) as in (3.15)
6: Compute vector?(? + 1) as in (3.16)
7: ? = ? + 1
8: WHILE (||vectorc(?)?vectorc(? ?1)|| > ?)
3.5 Analysis of Transmitter Zero Forcing and Receiver Diversity on Network
Throughput for a two relay case
To analyze receiver diversity (RD) and transmitter zero forcing (TZF), we consider a
simple case where the number of relays and the number of users is two and the channel is
considered to be symmetric. Figure 3.4, shows a simple case with two relays and two users.
Relay 1
Relay 2
User 1
User 2
H1
H2
?2H
2
?1H1
Figure 3.4: Channel Model
The channel gains from relay 1 to user 1 and from relay 2 to user 2 are denoted as H1 and
29
H2, respectively. The cross channel gains are ?1H1 and ?2H2, where 0 < ?1,?2 < 1 are
cross channel fading factors. Depending on the relation between signal parameters and the
channel parameters different signals will undergo different types of fading. Here, the fading
factor considered is flat fading [34].
3.5.1 Receiver Diversity
According to equations (3.3), (3.4) and (3.2), we can find the overall signal to noise ratio
(SNR) for all three combining schemes, namely, maximum ratio combining (MRC) ?MRCj ,
equal gain combining (EGC) ?EGCj and selective combining (SC) ?SCj , which is given by:
?MRCj = H
2
jPmax
N0 +
?2jH2jPmax
N0
= (1 + ?2j)H
2
jPmax
N0 (3.17)
?EGCj = 12(
radicalBigg
H2jPmax
N0 +
radicalBigg
?2jH2jPmax
N0 )
2
= (1 +?j)
2
2
H2jPmax
N0 (3.18)
?SCj = H
2
jPmax
N0 (3.19)
Where, j represents the user and Hj and ?j are channel gain and fading factor between
the relay and corresponding users, respectively. The following definition is used to calculate
SNR [35]. ?(SNR) = H2PN , where P, N and H are transmitted power, noise and channel
gain, respectively.
30
Then, the network throughput [37] - [38], for three combining schemes (MRC, EGC
and SC) using (3.5) can be written as:
CMRC = B4
2summationdisplay
j=1
log2(1 + (1 +?2j)H
2
jPmax
N0 )
CEGC = B4
2summationdisplay
j=1
log2(1 + (1 + ?j)
2
2
H2jPmax
N0 )
CSC = B4
2summationdisplay
j=1
log2(1 + H
2
jPmax
N0 ) (3.20)
3.5.2 Transmitter Zero Forcing
For transmitter zero forcing, the compound signals X1 and X2 transmitted by relay 1
and 2 using the precoding matrix as the inverse of the channel gain matrix, are:
X1 = K1H2S1 ??1K2H1S2
X2 = K2H1S2 ??2K1H2S1 (3.21)
where K1 and K2 are two arbitrary real numbers. S1 and S2 are the signals transmitted by
the relays 1 and 2, respectively. Assuming relay 1 and 2 use maximum power to transmit
these two signals, we have the following two equations
K21H22 + ?21K22H21 = Pmax
K22H21 + ?22K21H22 = Pmax (3.22)
Then, the received signals at user 1 and 2 using equation (3.1), denoted by Y1 and Y2, are
Y1 = (1??1?2)K1H1H2S1
Y2 = (1??1?2)K2H1H2S2 (3.23)
31
from (3.22) and (3.23), we have the SNRs [35], for two users as follows
?TZFj = (1??1?2)
2K2
jH
2
1H
2
2
N0
= (1??1?2)(1??
2
j)H
2
j
1 + ?1?2
Pmax
N0 (3.24)
where ?TZFj is received SNR at user j. The corresponding network throughput using (3.10)
is given by
CTZF = B3
2summationdisplay
j=1
log2(1 + (1??1?2)(1??
2
j)H
2
j
1 + ?1?2
Pmax
N0 ) (3.25)
Comparing (3.20) and (3.25), we can rewrite the network throughput as
C = gBB
2summationdisplay
j=1
log2(1 +gjP HjPmaxN
0
) (3.26)
where gB and gjP are coefficients of bandwidth and power, respectively. The comparison of
RD and Transmitter Zero Forcing is presented in table 3.2.
Table 3.2: Comparison of RD and Transmitter Zero Forcing
Coefficient of bandwidth (gB) Coefficient of power (gjP)
MRC 1/4 1 + ?2j
EGC 1/4 (1+?j)22
SC 1/4 1
Transmitter Zero Forcing 1/3 (1??1?2)(1??2j)1+?1?2
32
3.6 Simulation Results
We performed simulations using MATLAB to study the performance of Transmitter
Zero Forcing (TZF) and the diversity combining schemes - Maximum Ratio Combining
(MRC), Equal Gain Combining (EGC) and Selective Combining (SC). The simulations are
performed to determine network throughput by varying the distance between the user and
relay and by varying the transmitter power.
3 4 5 6 7 8 9 10 110
0.5
1
1.5
Distance from Relay to User
Ne
tw
ork
 Th
rou
gh
pu
t (M
bp
s)
Two Relay Case
 
 
MRC
EGC
SC
TZF
Figure 3.5: Network Throughput vs. Distance - Two Relay Case
33
3 4 5 6 7 8 9 10 110
0.5
1
1.5
Distance from Relay to User
Ne
tw
ork
 Th
rou
gh
pu
t (M
bp
s)
Three Relay Case
 
 
MRC
EGC
SC
TZF
Figure 3.6: Network Throughput vs. Distance - Three Relay Case
3 4 5 6 7 8 9 10 110
0.5
1
1.5
Distance from Relay to User
Ne
tw
ork
 Th
rou
gh
pu
t (M
bp
s)
Four Relay Case
 
 
MRC
EGC
SC
TZF
Figure 3.7: Network Throughput vs. Distance - Four Relay Case
34
Figure 3.5, 3.6 and 3.7 show the simulation results of a two relay, three relay and
four relay cases in the system, respectively. The number of users considered for all cases
are two and the channel gain between the users and relay depends on the distance and log
normally distributed shadowing effect. The transmitter power is taken to be 1 watt. In
Figure 3.5, 3.6 and 3.7, we demonstrate the impact of distance between user and relay on
the throughput of the schemes. The distance between the user and relays are increased from
3 to 11 meters.
As the distance between user and relay increases all throughputs are degraded. TZF
outperforms combining schemes when the distance between the user and relay are small
but is inferior to combining schemes as the distance increases. There is a cross over point
between TZF and diversity combining schemes curves when the distance between the user
and relay is 9 meters. This is because as the distance increases, the interference increases
in TZF and diversity combining schemes, but in diversity combining schemes, the receiver,
receives different versions of the same signal there by mitigating the effects of fading.
35
1 2 3 4 5 60
0.05
0.1
0.15
0.2
0.25
Transmitter power
Ne
tw
ork
 Th
rou
gh
pu
t (M
bp
s)
Two Relay Case
 
 
MRC
EGC
SC
TZF
Figure 3.8: Network Throughput vs. Transmit Power - Two Relay Case
Figure 3.8, 3.9 and 3.10 show the simulation results of a two relay, three relay and four
relay cases in the system, respectively. The number of users considered for all cases are two
and the channel gain between the users and relay depends on the distance and log normally
distributed shadowing effect. In Figure 3.8, 3.9 and 3.10, we demonstrate the impact of
transmit power on the throughput of the schemes.The transmit power is varied from 1 to 6
watts.
As the transmitter power increases the throughput of both TZF and diversity combining
schemes are increased. Diversity combining schemes outperform TZF when the transmitter
power is small. However, as the transmitter power increases TZF outperforms all the com-
bining schemes. This is because when the transmitter power is small, signal to interference
plus noise ratio (SINR) is high in TZF and diversity combining schemes, but in diversity
36
1 2 3 4 5 60
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
Transmitter Power
Ne
tw
ork
 Th
rou
gh
pu
t (M
bp
s)
Three Relay Case
 
 
MRC
EGC
SC
TZF
Figure 3.9: Network Throughput vs. Transmit Power - Three Relay Case
1 2 3 4 5 60
0.1
0.2
0.3
0.4
0.5
Transmitter Power
Ne
tw
ork
 Th
rou
gh
pu
t (M
bp
s)
Four Relay Case
 
 
MRC
EGC
SC
TZF
Figure 3.10: Network Throughput vs. Transmit Power - Four Relay Case
37
combining scheme, the receiver receives different versions of the same signal there by mit-
igating the fading. As the transmitter power increases, SINR in both TZF and diversity
combining scheme reduces and TZF clearly outperforms diversity combining schemes.
3.7 Summary of chapter
In this chapter, we studied the application of Transmitter Zero Forcing (TZF) and
Receiver Diversity (RD) techniques like, Maximum Ratio Combining (MRC), Equal Gain
Combining (EGC) and Selective Combining (SC) in cooperative cellular networks. We for-
mulated the problem of both RD and TZF in cooperative relay networks and addressed the
problem using the primal-dual algorithm. We further analyzed a simple case with two relays
and two users, and derived the closed-form formula for the influence of both RD and TZF
on network throughput. There was excellent agreement between our analytical model and
simulation results. We performed a simulation study and compared network throughput of
both TZF and RD against transmitter power and distance between user and relay, and found
that there is no case of dominance for the two strategies.
38
Chapter 4
Concluding remarks
In this thesis, initially, we studied the positioning of relay nodes (RN) to reduce energy
consumption. We modeled the two relay node placement strategy - a greedy algorithm and
an approximation algorithm. This positioning of the relay is dependent on the distance
between the users and BS. In greedy algorithm, RNs are place at halfway distance between
the farthest user and base station (BS). In approximation algorithm the RNs are placed at
the periphery of the coverage distance of the BS. We compare both the algorithms in terms
of average energy consumption, average number of hops for a packet to reach the base station
(BS) and average r-cover which is the coverage radius of RN. The approximation algorithm
is shown to outperform the greedy algorithm in all the above mentioned metrics. The results
provide us an insight into positioning of the relays in a cooperative wireless network to reduce
energy consumption of the users.
Second, we studied the application of Transmitter Zero Forcing (TZF) and Receiver
Diversity (RD) like, Maximum Ratio Combining (MRC), Equal Gain Combining (EGC)
and Selective Combining (SC), to cooperative cellular networks. We analyzed a simple
case with two relays and two users, and derived the closed-form formula for the influence
of both RD and TZF on network throughput. There was excellent agreement between our
analytical model and simulation results. We formulated the problem of both RD and TZF in
cooperative relay networks and addressed the problem using the primal-dual algorithm. We
compared network throughput of both TZF and RD against transmitter power and distance
between user and relay. In the simulation study, cross points with TZF and RD were found,
indicating that there was no case of dominance for the two strategies. We conclude that
39
TZF can be used when interference is weak while RD can be adopted when the interference
is high.
40
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