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ENERGY-EFFICIENT COLLABORATIVE DATA TRANSMISSIONS IN
WIRELESS SENSOR NETWORKS
A Thesis
Submitted to the Faculty
of
Purdue University
by
Jing Feng
In Partial Fulfillment of the
Requirements for the Degree
of
Doctor of Philosophy
May 2012
Purdue University
West Lafayette, Indiana
ii
This work is dedicated to my parents and my grandma.
iii
ACKNOWLEDGMENTS
I would like to thank my adviser Professor Yung-Hsiang Lu for having taught me
how to do research, and for his constant guidance, mentorship and support. Thanks
are also due to the members of my advisory committee Professor Jung, Professor
Peroulis, and Professor Hu for reviewing my work.
I would like to extend my thanks to my friends: Guangyu Ji, Serkan Sayilir,
and colleagues in the HELPS research group: Yu-Ju Hong, Karthik Kumar, Yamini
Nimmagadda, Jibang Liu, Chencheng Wu, and Nikhil Balaji.
I would like to thank my parents for the many sacrifices they have made for me
through the years. Thanks are also due to my parents for their constant support and
understanding and to all my friends for their encouragement.
I want to thank the financial support from NSF. Any opinions, findings, and
conclusions or recommendations in this dissertation do not necessarily reflect the
views of the sponsor.
iv
TABLE OF CONTENTS
Page
LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii
ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii
1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Energy Saving and Consuming in Beamforming (Chapter 3) . . . . . 8
1.2 Transmitter Scheduling for Energy Balancing in Beamforming (Chap-ter 4) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.3 Beamforming in Multi-hop Transmissions (Chapter 5) . . . . . . . . . 13
1.4 Publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2 RELATED WORK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.1 Transmission Methods . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.1.1 Multi-hop Transmission . . . . . . . . . . . . . . . . . . . . . 18
2.1.2 Collaborative Beamforming . . . . . . . . . . . . . . . . . . . 19
2.1.3 Beamforming in Multi-hop Transmission . . . . . . . . . . . . 21
2.2 Pre-beamforming Preparation . . . . . . . . . . . . . . . . . . . . . . 22
2.2.1 Synchronization and Localization . . . . . . . . . . . . . . . . 22
2.2.2 Random Walk Algorithm for Phase Alignment . . . . . . . . . 24
2.2.3 Transmitter Selection for Phase Alignment . . . . . . . . . . . 25
2.2.4 Data Sharing in Pre-Beamforming . . . . . . . . . . . . . . . . 25
2.2.5 Deployment and Clustering . . . . . . . . . . . . . . . . . . . 26
2.3 Energy Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
v
Page
2.3.1 Energy Model 1 . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.3.2 Energy Model 2 . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.3.3 Energy Model 3 . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.4 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3 ENERGY SAVING USING COLLABORATIVE BEAMFORMING . . . . 33
3.1 Energy Overhead on Phase Alignment . . . . . . . . . . . . . . . . . 34
3.1.1 Random Walk Phase Alignment . . . . . . . . . . . . . . . . . 36
3.1.2 Energy Savings by Beamforming . . . . . . . . . . . . . . . . . 39
3.1.3 Simulation and Analysis . . . . . . . . . . . . . . . . . . . . . 40
3.2 Data Sharing in Pre-beamforming . . . . . . . . . . . . . . . . . . . . 43
3.2.1 Data Sharing Procedures . . . . . . . . . . . . . . . . . . . . . 44
3.2.2 Data Sharing Energy Overhead . . . . . . . . . . . . . . . . . 47
3.2.3 Simulation and Analysis . . . . . . . . . . . . . . . . . . . . . 49
3.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
4 TRANSMITTER SCHEDULING FOR ENERGY BALANCING IN BEAM-FORMING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
4.1 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.1.1 Steps of the Transmission System . . . . . . . . . . . . . . . . 59
4.1.2 Energy Calculation Models . . . . . . . . . . . . . . . . . . . . 65
4.2 Transmitter Scheduling Algorithms . . . . . . . . . . . . . . . . . . . 66
4.2.1 Transmitter Scheduling Algorithms for Single-Cluster Networks,Energy and Phase (EP ) . . . . . . . . . . . . . . . . . . . . . 68
4.2.2 Transmitter Scheduling Algorithms for Multi-Cluster Networks,Multi-cluster Energy and Phase (MEP) . . . . . . . . . . . . . 73
4.3 Simulation, Analysis, and Experiments . . . . . . . . . . . . . . . . . 76
4.3.1 Single Cluster Comparison . . . . . . . . . . . . . . . . . . . . 78
vi
Page
4.3.2 Network Lifetime . . . . . . . . . . . . . . . . . . . . . . . . . 88
4.3.3 Sensitivity Analysis of Single-Cluster Scheduler . . . . . . . . 90
4.3.4 Sensitivity Analysis of Multi-Cluster Scheduler . . . . . . . . . 94
4.3.5 Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
4.3.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
4.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
5 COLLABORATIVE BEAMFORMING IN MULTI-HOP TRANSMISSIONS 102
5.1 System Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
5.2 Problem Description . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
5.3 Beamforming in Multihop . . . . . . . . . . . . . . . . . . . . . . . . 106
5.4 Simulation and Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 107
5.4.1 Minimum Frequency Difference . . . . . . . . . . . . . . . . . 108
5.4.2 Energy Consumptions with Different Sweeping Frequencies . . 110
5.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
5.5.1 Frequency Separation . . . . . . . . . . . . . . . . . . . . . . . 111
5.5.2 Error Tolerance . . . . . . . . . . . . . . . . . . . . . . . . . . 111
5.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
6 CONCLUSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
LIST OF REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
vii
LIST OF TABLES
Table Page
1.1 Acronyms used in this thesis . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.1 Comparison of the proposed algorithm with existing studies. MC: MultipleClusters; DS: Data Sharing; PAR: Phase Adjustment Required; ENL:Extend Network Lifetime. . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.2 Comparison of energy models used in this dissertation. . . . . . . . . . . 27
2.3 Symbol and parameters of the energy model 2 . . . . . . . . . . . . . . . 28
2.4 Symbol and parameters of the energy model 3 . . . . . . . . . . . . . . . 30
3.1 Symbols for analyzing the energy overhead for phase alignment . . . . . 39
3.2 Symbols for analyzing the energy overhead for data sharing . . . . . . . . 50
4.1 Symbols used in Chapter 4 . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.2 Default simulation parameters for Chapter 4 . . . . . . . . . . . . . . . . 77
4.3 List of Scenarios Compared in Figure 4.5 and the Ratio of P using EP,IPP, and PP to the Upper Bound (i.e. 4522). . . . . . . . . . . . . . . . 82
4.4 Network lifetime P using EP, IPP, and PP . . . . . . . . . . . . . . . . . 86
4.5 Network lifetime for different number of sensing nodes . . . . . . . . . . 94
5.1 Symbols used in Chapter 5 . . . . . . . . . . . . . . . . . . . . . . . . . . 104
viii
LIST OF FIGURES
Figure Page
1.1 Three ways to transmit data from a sensing area to a base station. (a)Direct transmission: Single node directly transmit the data packet fromthe sensing area to the base station. (b) Multihop transmission: Data arepropagated through many hops from the sensing area to the base station.(c) Beamforming transmission: Multiple nodes transmit the same datasimultaneously towards the same base station. . . . . . . . . . . . . . . . 2
1.2 Constructive and destructive interferences of two waves. . . . . . . . . . 3
1.3 Distributed beamforming. Ten nodes are deployed in a square shaped areawith side length L. The shaded area shows the radiated wave pattern withfour selected transmitters (four antennae in bold). D is the receiver, i.e.the base station. A is a far field point. . . . . . . . . . . . . . . . . . . . 5
1.4 General structure of this dissertation. . . . . . . . . . . . . . . . . . . . . 8
1.5 Two nodes (A and B) form a transmission beam using their frequencydifference. At different time, the beam points at different directions. As-suming that the beam is rotating clockwise, at time t−∆t, the beam hasnot reached node C; at time t, the beam points the direction towards nodeC; after another ∆t, the beam moves away from the direction of node C. 14
2.1 Timing diagram to illustrate one round of sensing and transmitting oper-ations using direct or beamforming as the transmission method. Differentfrom direct transmission, beamforming requires two preparation steps, in-cluding: phase alignment and data sharing. T is the time for one roundof sensing and transmitting operations. . . . . . . . . . . . . . . . . . . . 22
3.1 Beamforming efficiency and the phase differences at the receiver for dif-ferent numbers of transmitters. For a small number of nodes N , largephase differences (> 0.3π) affect the beamforming efficiency significantlyand cause instability. A larger N stabilizes beamforming. . . . . . . . . . 36
ix
Figure Page
3.2 (a) Phase differences (unit: π) converge faster by choosing a larger stepsize. Each line shows the phase difference between one transmitter andthe first transmitter. (b) Maximum phase difference (max |φa − φ1|, 1 ≤a ≤ N) for different numbers of transmitters N . The unit for the verticalaxis is π. (c) Beamforming efficiency after iterations for different N . . . 38
3.3 Relationship between number of sensors N and minimum data size bmin.Each line represents different beamforming performance e. The datashown in this figure is the average of 10 convergence tests. . . . . . . . . 42
3.4 Relationship between beamforming performance e and minimum data sizebmin. Each line represents different number of sensors N . The data shownin this figure is the average of 10 convergence tests. . . . . . . . . . . . . 42
3.5 Time for one round of transmission. T1 is the time for sharing data amongall the transmitters and T2 is the time for beamforming transmission. Sens-ing is performed simultaneously with communication and transmission.Data collected in kth round is shared and transmitted in the k+ 1th round. 43
3.6 Four steps for data sharing in T1. . . . . . . . . . . . . . . . . . . . . . . 45
3.7 Compared with direct transmission, beamforming always saves energy oneach transmitter. The distance to the base station d is 50000 meters. Theenergy consumption in this figure is the average of 20 random deployments. 51
3.8 Energy consumed over the network when using direct transmission andbeamforming transmission respectively. The distance to the base stationis fixed to be d=50000 meters. The energy consumption in this figure isaveraged by 20 random deployments. . . . . . . . . . . . . . . . . . . . . 53
3.9 Energy consumed on data sharing has little affect on the number of suc-cessful beamforming transmissions. Distance to the base station d= 50000meters and the deployment radius is ρ=100 meters. . . . . . . . . . . . . 56
4.1 General steps of the proposed system. Beamforming transmitter schedul-ing is the main focus of this chapter. . . . . . . . . . . . . . . . . . . . . 59
4.2 Sensing and transmission are divided into rounds: T1 is the time for sharingdata among the transmitters and T2 is the time for beamforming trans-mission. Sensing is performed simultaneously with communication andtransmission. Data collected in kth round is shared and transmitted in thek + 1th round. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
4.3 General flow of the proposed scheduling algorithm. . . . . . . . . . . . . 67
x
Figure Page
4.4 When the distance to the base station is farther than 3000m, beamformingachieves more transmissions than direct and multi-hop. . . . . . . . . . . 81
4.5 Number of beamforming transmissions increases with higher percentagesof energy exhausted nodes, ξ. Compared with PP, EP achieves 118% moretransmissions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
4.6 Network lifetime, P , increases as higher percentages of energy exhaustednodes, ξ. N = 100, L = 100 m, and d = 3000m. . . . . . . . . . . . . . . 85
4.7 Both Multi-cluster schedulers achieve more beamforming transmissionsthan single-cluster scheduler when L increases. The network lifetime inthis figure is averaged by 10 random deployments with N = 100 node foreach deployment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
4.8 Maximum number of beamforming transmissions with different γ. . . . . 90
4.9 For 100 nodes, phase uncertainties are randomly generated. Beamformingefficiency is averaged by 50 trials. (a) Beamforming efficiency vs phaseuncertainty. (b) With the raised threshold, more transmissions becomesuccessful. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
4.10 I adopt an existing phase estimation method [20] to reduce the phase un-certainties. (a) The phase uncertainty reduces as the number of transmis-sions for phase estimation increases, i.e. more packets exchanges betweenthe master node and each beamforming transmitter. (b) The networklifetime is reduced due to energy consumption on phase estimation. . . . 93
4.11 With 100 nodes deployed in area A = 10002meter2, the number of beam-forming transmissions with the number of clusters C increases from 1 to25. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
4.12 Transmitter setup in the outdoor experiments. . . . . . . . . . . . . . . . 96
4.13 Receiving antenna in outdoor experiments. . . . . . . . . . . . . . . . . . 96
4.14 (a)-(b) Transmitters’ locations (i.e. black dots) in a circle of radius =3.5λ. White dots indicates the nodes that are not transmitting. (c)-(d)Simulated radiation patterns, signal strength in each angle is normalizedto the maximum signal strength. (e)-(f) Measurements compared withsimulations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
5.1 A sample deployment with N = 50 nodes. . . . . . . . . . . . . . . . . . 103
xi
Figure Page
5.2 The required minimum data rate Rsb decreases as the transmission dis-tance increases. Regardless of the data rate Rsn, the transmission dis-tance needs to be longer than 155m for sweeping beam with two nodes toconsume no more energy than traditional single node transmission. . . . 109
5.3 The energy consumption difference using sweeping beam and single node,with different transmission distance when Rsn = Rsb. . . . . . . . . . . . 110
5.4 Energy consumption difference using sweeping beam and single node, whenRsb 6= Rsn. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
xii
ABSTRACT
Feng, Jing Ph.D., Purdue University, May, 2012. Energy-Efficient Collaborative DataTransmissions in Wireless Sensor Networks. Major Professor: Yung-Hsiang Lu.
Wireless sensor networks provide great potential for environment monitoring and
military missions. In many applications, sensor nodes need to be deployed far away
from the base station, where the data are collected, stored, and analyzed. Long dis-
tance transmissions are often required in wireless sensor networks and they consume
significant amounts of energy. Collaborative beamforming achieve long distance, yet
low energy consuming, transmissions by means of multiple simultaneous nodes trans-
mitting the same data to the same receiver. However, each type of collaborative trans-
mission introduces some energy overhead due to additional steps. This dissertation
presents several techniques in achieving energy-efficient collaborative transmissions in
wireless sensor networks. It addresses the following questions: (1) whether collabora-
tive transmissions save energy, and what are the determining key factors, (2) how to
perform collaborative transmissions in order to prolong the network lifetime, and (3)
how to perform collaborative transmissions to extend the transmission distance. The
first question is addressed by studying the various steps in achieving collaborative
beamforming transmissions using different approaches. This dissertation analyzes
the factors that affect the energy savings for beamforming transmissions. The second
question is addressed by proposing an energy-efficient transmitter scheduling algo-
rithm to balance the energy consumption over the network, hence prolonging the
network lifetime. Finally, the third question is addressed by proposing a method
to use beamforming in multi-hop transmissions to extend the transmission distance
between hops.
1
1. INTRODUCTION
Wireless sensor networks (WSNs) [1–3] provide great potential for studying environ-
ment monitoring and military missions. WSNs are used in many applications, such as
habitat monitoring, environment observation, and health condition tracking. Sensor
nodes are deployed in an area of interest to collect and transmit data to a base sta-
tion, where the data are stored and analyzed [4, 5]. Several common characteristics
are often seen in wireless sensor network applications: (1) large numbers of nodes
are densely deployed in the sensing area, in order to accurately monitor and model
the sensed phenomena; (2) nodes usually have limited supporting facilities, including
power supply, and have limited computational capabilities; (3) nodes may fail due
to lack of power or physical damage. In order to provide a stable and long-lasting
wireless sensor monitoring system, the nodes need to be effectively managed.
Among all the functions that are performed on sensor nodes, wireless communi-
cation over long distance is a major energy consumer [6]. In some applications, data
are sent directly from the sensing area to the base station, i.e. direct transmission.
An illustration of direct transmission is shown in Figure 1.1(a). When the distance
from the sensing area to the base station is long, a single transmitter may not be
able to directly send the data, or it may consume too much energy. Many studies
have been devoted in reducing energy consumed for wireless communication by using
energy-efficient routing algorithms [7, 8]. These routing algorithms suggest that the
data can be sent through multiple hops. As illustrated in Figure 1.1(b), the data
collected by a sensor node that is far away from the base station is first forwarded to
a relay node that is closer to the base station. Then the relay node sends the data to
the base station. The data forwarding technique can be extended to more hops when
the distance to the base station is even farther. By transmitting through multiple
2
1
Base Station
Wireless Sensor Network
Sensor Node
(a) Direct Transmission
1
Base Station
Wireless Sensor Network
Sensor Node
Relay Node
(b) Multihop Transmission
Wireless Sensor Network
Sensor Node
1
Base Station
(c) Beamforming Transmission
Fig. 1.1. Three ways to transmit data from a sensing area to a basestation. (a) Direct transmission: Single node directly transmit thedata packet from the sensing area to the base station. (b) Multihoptransmission: Data are propagated through many hops from the sens-ing area to the base station. (c) Beamforming transmission: Multiplenodes transmit the same data simultaneously towards the same basestation.
3
Fig. 1.2. Constructive and destructive interferences of two waves.
4
hops, the distance between every two hops is shorter than that in direct transmission.
Therefore, less energy is consumed on each relay node. However, in some applica-
tions, the distance between even two hops can also be too far for a single node to
transmit, for example, sending the data that are collected by a sensor on the ground
to a satellite. In these cases, collaborative transmission (Figure 1.1(c)) can be used.
Collaborative transmissions use the concept from electromagnetic wave interferences:
adding two waves that have zero phase differences doubles the amplitude; adding two
waves that are 180 out of phase results in cancellation of the waveform. An example
of electromagnetic wave interferences is shown in Figure (1.2). As shown in Equation
1.1, by controlling the arrival phase of the signals (i.e. ∆φi) from N transmitters, the
signal strength in a particular direction can be enhanced.
r(t) = <(∑N
i=1 ej(2πft+∆φi))
=∑N
i=1 cos(2πft+ ∆φi)(1.1)
Many existing studies propose to use cooperative communication (CC) [9–11] and
collaborative beamforming [12–16] to save transmission energy. Among CC tech-
niques, multiple-input/multiple-output (MIMO) uses multiple antennae at both the
transmitters and the receivers to improve signal strength. However, sensor nodes are
usually small and each node can have only one antenna; multiple antennae may be
too costly. Therefore, traditional MIMO cannot be directly applied to wireless sensor
networks. Miller et al. [10] propose a new CC technique: the receiver detects the
signal based on the distortion of the radiation pattern due to multiple paths. Their
method does not improve signal strength in the direction of the receiver. Collab-
orative beamforming uses multiple transmitters to form antenna arrays and create
highly directional signals for transmission or reception, as illustrated in Figure 1.1(c).
Figure 1.3 shows an example of beamforming with four transmitters. The main beam
of the radiation pattern points at the direction of D (i.e. the intended receiver). At
point A, the signal strength is much weaker than the signal strength at point D. This
is because the waves from all transmitters have different phases at this point.
5
Fig. 1.3. Distributed beamforming. Ten nodes are deployed in asquare shaped area with side length L. The shaded area shows theradiated wave pattern with four selected transmitters (four antennaein bold). D is the receiver, i.e. the base station. A is a far field point.
6
Previous studies [12–16] show that collaborative beamforming can be used in
sensor networks to improve the directivity of electromagnetic waves. Collaborative
beamforming enhances the signal strength in a particular direction by properly align-
ing the phases of the signals from multiple transmitters at the receiver. Collaborative
beamforming can be adopted for four reasons. First, to reach a receiver too far for
an individual transmitter. If the receiver is beyond the range of a single transmitter,
beamforming allows signals to travel farther by enhancing the signal strength. As
seen in Figure 1.3, the signal strength is enhanced at point D. Second, to balance
the energy consumption over the network among all nodes. By sending data through
the same distance using beamforming, the transmission energy is spread over multiple
nodes, and each node can use much lower power to transmit. The transmission energy
on individual transmitters is then balanced over multiple transmitters. This prevents
some of the nodes from running out of energy much faster than the others. Third,
to improve data security. Beamforming may reduce, or completely eliminate, signals
in undesired directions. As shown in Figure 1.3, point A and point D have roughly
the same distance to the center of the deployment. However, due to the interfer-
ences of the signals, signals are canceled at the direction of point A, while the signal
strength at point D is enhanced. Fourth, to reduce latency in data dissemination.
Using multi-hop transmission, the data need to be propagated through many hops
until they reach the base station, and the latency in data dissemination depends on
the number of hops. Using beamforming, this latency can be greatly reduced.
In order to achieve energy-efficient beamforming transmissions in a resource con-
strained wireless sensor network, the following questions are important.
• Does collaborative beamforming save energy under all conditions? What are
the key determining factors to save energy using beamforming?
• How to schedule the transmitters in beamforming to achieve more transmissions,
i.e. extend the network lifetime?
7
• How to use beamforming to extend the transmission distance? Can beamform-
ing be applied to improve other existing transmission techniques?
This dissertation addresses the above questions as follows. In Chapter 3, I address
the first question by studying the procedures in achieving collaborative beamforming
transmissions using different approaches, e.g. phase adjustment to align the phases
of the signals arrived at the base station, data sharing among the transmitters and
sensing nodes in pre-beamforming. I find that minimal amounts of data need to be
transmitted with beamforming in order to compensate for the energy consumed on
phase alignment using a random walk algorithm. Data sharing among the transmit-
ters and sensing nodes requires that the distance among the sensor nodes be relatively
short compared with the distance to the base station in order for beamforming to save
energy. In Chapter 4, I address the second question by proposing an energy-efficient
transmitter scheduling algorithm to balance the energy consumption over the net-
work, hence prolonging the network lifetime. The network lifetime is defined as the
total number of successful beamforming transmissions towards the receiver before
all nodes are energy-exhausted. My scheduling method is adaptive to the size of
the deployment area. For a network within a small deployment area, My scheduling
algorithm extends the network lifetime by at least 50% compared with an existing
algorithm. For a network within a large deployment area, the distances between the
transmitters needs to be considered in reducing the energy consumption overhead.
Hence, the nodes are divided into clusters based on their geographical locations, and
clusters perform beamforming transmissions in turns. The results show that the
network lifetime is tripled when the size of the deployment area is considered when
scheduling the transmitters. In Chapter 5, I address the third question by proposing
a method to use beamforming in multi-hop transmissions to extend the distance be-
tween hops. Considering frequency skew, periodic re-configuration is often required
in scheduling to achieve accurate time and phase synchronizations. In this chapter,
the differences between two nodes’ frequency skews is used to form high strength
signal. This method does not require any knowledge of phase offsets and does not
8
Co
llab
ora
tive
B
eam
form
ing
Energy consumption and saving analysis for beamforming
Transmitter scheduling algorithm to balance the energy consumption
Phase alignment
Data sharing
Small networks: Energy and Phase (EP)
Large networks: Multi-cluster Energy and Phase (MEP)
Beamforming in multi-hop transmission to extend distance between hops
(Chapter 3)
(Chapter 4)
(Chapter 5)
Fig. 1.4. General structure of this dissertation.
require frequency synchronization. Figure 1.4 shows the structure of this dissertation.
The following subsections provide an overview of the three parts. Table 1.1 lists the
acronyms used in this thesis.
1.1 Energy Saving and Consuming in Beamforming (Chapter 3)
Compared with a single transmitter, collaborative beamforming spreads the long
distance transmission energy over multiple transmitters. This saves energy and bal-
ances the battery lifetime on individual nodes because each transmitter can use lower
power to transmit. However, successful beamforming depends on proper coordination
of phases among the participating sensor nodes. As shown in Figure 1.2, in order to
create constructive interference at the receiver, the signals need to be in phase. In
most of the applications, sensor nodes are randomly deployed in the sensing area and
each one is driven by it’s own crystal (i.e. clock). The signals from all nodes arrive at
9
Table 1.1Acronyms used in this thesis
Definition Acronym
Wireless Sensor Network WSN
Multiple-Input/Multiple-Output MIMO
Cooperative Communication CC
Collaborative Beamforming CB
Energy and Phase transmitter scheduler EP
Multi-cluster Energy and Phase transmitter scheduler MEP
Phase Partition transmitter scheduler PP
Improved Phase Partition transmitter scheduler IPP
Time-of-arrival TOA
Phase Lock Loop PLL
Sensor Cluster Head SCH
Beamforming Cluster Head BCH
Power-Cost Progress routing algorithm PCP
10
the receiver at different phases. Therefore, phase alignment is required. Phase align-
ment can be achieved in two ways: (1) the location information of the transmitters
and the receiver are not known a priori, and a random walk algorithm is used to ad-
just the transmitting phases [13,17]; (2) the location information is known, and nodes
are selected based on the phase differences. No phase adjustment is required [18].
When multiple sensing nodes are used for monitoring and beamforming is adopted
for transmission, all transmitters must have the same data so that the transmitters can
emit the same waves. As a result, communication (called “data sharing”) is required
among the sensing nodes and the transmitters, because (1) the sensing nodes and
transmitters are selected based on different criteria. The sensing nodes are selected to
accurately monitor the sensed phenomena, but the transmitters are selected to create
strong signals to reach the receiver. Hence, the sensing nodes and the transmitters
may be different. (2) Even when the sensing nodes are the same as the transmitters,
data sharing is still necessary because two sensing nodes may have different measured
data and the transmitters must have the same data before beamforming. The energy
for data sharing can potentially abate the energy saved by beamforming. In order to
prolong network lifetime, it is important to conserve energy for data sharing.
Even though beamforming has the potential benefit of saving energy, no existing
study has been devoted to the analysis of the energy overhead before beamforming.
This dissertation first analyzes the parameters and conditions to answer whether
beamforming saves or consumes energy. Transmitters may save energy in the beam-
forming stage; in the pre-beamforming stage, energy is consumed on phase align-
ment and data sharing. I consider these two energy-consuming operations in the
pre-beamforming stages one at a time.
Considering phase alignment, I show the minimum data that need to be transmit-
ted to compensate the energy consumed for phase alignment using the random walk
algorithm proposed by Bucklew et al. in [13]. I suggest that by relaxing the conver-
gence requirement, the transmitters can determine their phases an order-of-magnitude
faster and save energy in pre-beamforming preparation. My analysis shows that the
11
number of nodes and the amount of data are two critical factors for determining
whether beamforming can save energy: the minimum amount of data needs to be
sent using beamforming in order to compensate the energy consumed for phase align-
ment.
With the transmitters selected using phase partition method [18], I analyze the
energy consumed for data sharing by first presenting the procedures for data sharing
when multiple sensing nodes and transmitters are used. I analyze the energy con-
sumed for data sharing among different numbers of sensing nodes and transmitters,
and the impact on beamforming transmissions. (1) I show how data can be shared
among the transmitters when there are multiple sensing nodes and transmitters in
each round. (2) In each round, nodes are categorized into four types of roles as:
transmitter, master node, sensing node, and all other nodes that are not transmitting
or sensing. I examine the energy consumed for each type of nodes in data sharing. (3)
I compare the energy consumed by direct transmission and beamforming to achieve
the same number of transmissions.
1.2 Transmitter Scheduling for Energy Balancing in Beamforming (Chap-
ter 4)
Knowing the conditions and key factors for beamforming to save energy, the next
issue addressed in this dissertation is how to prolong the network lifetime while using
beamforming. In Chapter 4, we show how this may be achieved using an efficient
scheduling algorithm.
Beamforming efficiency depends on the phase differences between the electromag-
netic waves [19]. The efficiency is 100% when phase differences are zero. Assuming
each transmitter uses the same power and has free-space attenuation, N transmitters
increase the power at the receiver by N2 times and the transmission range by N times
farther. Alternatively, each transmitter can reduce its power to 1/N2. However, in
practice phase differences may occur from several sources, such as frequency offsets,
12
transmitter locations, and phase offsets. In [20], Sayilir et al. show that phase dif-
ferences can be estimated using two-way signal exchanges. Beamforming efficiency
is higher when the transmitters with smaller phase differences are chosen [18]. To
achieve better efficiency, the nodes with small phase differences are always used and
these nodes will deplete their energy much faster than the others. When the nodes
deplete their energy, coverage holes may occur. Coverage holes are the areas that
are not monitored because sensor nodes run out of energy. To prevent coverage holes
and extend the network lifetime, energy consumption should be balanced among the
nodes.
In Chapter 4, I propose a beamforming transmitter scheduling algorithm that pro-
longs the network lifetime by balancing the energy consumption over the network. The
proposed scheduling algorithm selects the transmitters in each round from N avail-
able nodes. Based on the analysis in Chapter 3, I find that the transmitters should
be closer to each other in order to reduce the energy overhead in pre-beamforming.
Hence, I propose an adaptive beamforming transmitter scheduling algorithm that
considers the size of the sensing area relative to the distance from the base station. I
divide networks into two types: small network and large network. For a small network,
all nodes can directly communicate with each other and beamforming transmitters
are scheduled based on the phase differences and remaining energy of the nodes. I call
this scheduling algorithm, “energy and phase”, i.e. EP. When the size of the sensing
area is large, I divide the nodes into clusters and choose one cluster to perform beam-
forming transmission at a time. In order to balance the energy consumption over the
network, the available clusters have to take turns being the beamforming cluster. I call
this transmitter scheduling algorithm for large sensing areas, “multi-cluster energy
and phase”, i.e. MEP. I evaluate two methods of selecting the beamforming clusters:
(1) to balance the numbers of beamforming transmissions among the clusters, and
(2) to minimize the energy consumed on data sharing. The number of transmissions
to a distant base station is different when using direct, multi-hop, and beamforming
transmissions. I show the conditions for beamforming to save energy, compared with
13
direct transmission and multi-hop transmissions. The simulation results show that
the single cluster scheduling algorithm can extend the network lifetime by more than
50% compared with an existing transmitter scheduling algorithm [18]. MEP extends
the network lifetime by three times compared with EP when the size of the sensing
area increases from 104m2 to 106m2. I conducted outdoor experiments and show that
beamforming can enhance the signal strength in the intended direction by selecting
the transmitters. Through the experiments, I observe several factors affecting the
performance of transmissions that were not shown in simulations.
1.3 Beamforming in Multi-hop Transmissions (Chapter 5)
In this chapter, I show an application of collaborative beamforming to improve
multi-hop transmissions. I examine how beamforming can be used to extend the
hop distance in multi-hop transmissions and analyze the energy consumption of the
proposed method.
Multi-hop transmission forwards data from the sensing area to the base station
using relay nodes. Energy consumption for each transmission increases quadratically
as the transmission distance increases. Using more relay hops shortens the distance
between hops L, and reduces the energy consumed for each transmission. However,
using smaller L means more hops, and this could incur more overhead by means of
an additional reception and transmission for each hop, thus potentially increasing the
energy consumption. Wang et al. [21] discuss a method to compute the optimal value
of L between every two hops considering the overall energy consumption. Unfortu-
nately, there may be many problems trying to achieve a desired value for L. There
are limits of the maximum distance that each node can transmit [22]. Relay nodes
need to be deployed within the distance that other nodes can reach. Moreover, in
some scenarios, relay nodes at certain distances may not be available, due to many
reasons such as: (1) Some regions are difficult to deploy relay nodes. For example, if
the deployment area involves rivers and mountains, nodes may need to be deployed
14
farther away from each other. (2) The deployment area has several specific sub-areas
that require dense deployments of nodes for monitoring. If these sub-areas are far
apart, there is a need for a larger number of nodes, leading to a reduction in the
number of relay nodes. In these scenarios, extending the distance between every two
hops is important. In Chapter 5, I present a method that uses beamforming to extend
the distance between every two hops in multi-hop transmissions.
(a) time = t−∆t (b) time = t (c) time = t+ ∆t
Fig. 1.5. Two nodes (A and B) form a transmission beam using theirfrequency difference. At different time, the beam points at differentdirections. Assuming that the beam is rotating clockwise, at timet−∆t, the beam has not reached node C; at time t, the beam pointsthe direction towards node C; after another ∆t, the beam moves awayfrom the direction of node C.
In beamforming, to achieve perfect phase alignment at an intended location is
challenging, due to high accuracy required in time and frequency synchronization,
and precise localization. When nodes are randomly deployed in the sensing area,
the distance from each node to the base station may be different. As a result, the
signals from all nodes may arrive at the base station with different phases, even when
the nodes transmit simultaneously. These phase differences are also time-varying
because the transmitting frequency of each node is slightly different. This frequency
difference is referred to frequency drift or frequency skew. A typical frequency skew
is around ± 20ppm of the carrier frequency. When the carrier frequency is high,
periodic frequency synchronization among the nodes becomes challenging [23].
In Chapter 5, I propose a method that does not require the knowledge of the
node phase offset. Using this method, a transmission beam is formed based on the
15
frequency differences among the transmitting nodes. An example illustrates my idea
in Figure 1.5. Two nodes, A and B transmit with frequencies fc + fA and fc + fB,
respectively. Using these two nodes to transmit simultaneously, a beam with four-
time-higher signal strength (i.e. peak power) is formed based on the frequency skew,
∆f = |fA − fB|. At each time t, the main lobe points in different directions. The
beam sweeps in the 2-D plane with a speed equal to 1/∆f . Without the knowledge
of the phase offset, where the beam is pointing cannot be controlled. To ensure the
data is received by the next relay node, a lower data rate needs to be used: A and
B transmit the same data for a longer period. Hence, the energy consumption for
using beamforming may be higher, but this method can transmit data farther and
require fewer hops. For applications that are not timing-sensitive, this method can
be adopted in multi-hop to extend the hopping distance. In Chapter 5, I analyze the
energy consumption for this method and I discuss a few potential solutions to reduce
the energy consumption.
1.4 Publications
• [19] Jing Feng, Yung-Hsiang Lu, Byunghoo Jung, and Dimitrios Peroulis, ”En-
ergy Efficient Collaborative Beamforming in Wireless Sensor Networks”, Inter-
national Symposium on Circuits and Systems 2009.
• [24] Jing Feng, Yamini Nimmagadda, Yung-Hsiang Lu, Byunghoo Jung, Dim-
itrios Peroulis, and Y. Charlie Hu, ”Analysis of Energy Consumption on Data
Sharing in Beamforming for Wireless Sensor Networks”, International Confer-
ence on Computer Communications and Networks 2010.
• [25] Jing Feng, Che-Wei Chang, Serkan Sayilir, Yung-Hsiang Lu, Byunghoo
Jung, Dimitrios Peroulis, and Y. Charlie Hu, ”Energy-Efficient Transmission
for Beamforming in Wireless Sensor Networks”, IEEE Communications Society
Conference on Sensor, Mesh and Ad Hoc Communications and Networks 2010.
16
• [26] Karthik Kumar, Jing Feng, Yamini Nimmagadda, and Yung-Hsiang Lu,
”Resource Allocation for Real-Time Tasks using Cloud Computing”, Interna-
tional Conference on Computer Communication Networks, 2011 Workshop on
Grid and P2P Systems and Applications.
• [27] Jing Feng, Yung-Hsiang Lu, Byunghoo Jung, Dimitrios Peroulis, and
Y. Charlie Hu, ”Energy-Efficient Data Dissemination in Wireless Sensor Net-
works”, ACM Transactions on Sensor Networks, to appear.
• [28] Jing Feng, Serkan Sayilir, Yung-Hsiang Lu, Byunghoo Jung, Dimitrios
Peroulis, and Y. Charlie Hu, ”Reaching Farther: Beamforming in Multihop
Transmissions”, submitted to IEEE GLOBECOM 2012
17
2. RELATED WORK
In WSNs, data dissemination is the process of transmitting the collected data from
the sensing area to the base station. This dissertation focus on energy-efficient data
dissemination using collaborative beamforming in WSNs. This chapter presents some
existing studies regarding energy-efficient transmissions in wireless sensor networks.
Section 2.1 provides existing studies on multi-hop and beamforming transmissions
for wireless sensor networks. Section 2.2 provides backgrounds and existing studies
on pre-beamforming requirements, including synchronization and localization, phase
alignment, and data sharing. To analyze the energy consumption for beamforming,
three energy models used in this dissertation are introduced in Section 2.3. A simple
energy model which considers only the size of the transmitted data packets is first
used to analyze the factors in energy saving and consuming using beamforming. More
detailed energy models are adopted when I study how to schedule the transmitters
to prolong the network lifetime. Section 2.4 summarize the contributions of this
dissertation.
2.1 Transmission Methods
Many studies have been conducted on data dissemination in wireless sensor net-
works. Data dissemination is the process of transmitting the collected data from the
sensing area to the base station. It can be achieved in three different ways, as illus-
trated in Figure 1.1: (1) direct transmission from the sensing area to the base station
with increased transmit power, (2) hop-by-hop data forwarding with relay nodes from
the sensing area to the base station, and (3) collaborative beamforming with multiple
transmitters, transmitting from the sensing area directly towards the base station
at the same time. In a free space model [29], the energy consumption quadratically
18
increases as the transmission distance increases. When the distance from the sensing
area to the base station is long, direct transmission consumes too much energy.
2.1.1 Multi-hop Transmission
With limited energy, each transmitter has a maximum range. When the distance
from the sensing area to the base station is much longer than this range, multi-hop
transmissions may be used. Relay nodes are deployed between the sensing area and
the base station. Many studies suggest how to deploy relay nodes and determine
routes to prolong the network lifetime [30–36].
Some researchers focus on balancing energy consumption and maximizing the
network lifetime. In [34], the authors study the problem of deploying a minimum
number of relay nodes in the sensing field in order to balance power consumption
among all sensing nodes and relay nodes. In [32], the authors present two routing
algorithms to prolong the network lifetime by lowering the transmission power of
individual nodes and assigning edge weights based on remaining energy of sending
nodes. In [33], the authors propose a scheduling algorithm to maximize network
lifetime in surveillance systems. The sensors are scheduled to watch targets and
forward the sensed data to the base station. Vidhyapriya et al. [35] present an efficient
routing algorithm based on both the energy available in the nodes and quality of the
link.
Several other researchers focus on reducing the total energy consumption when
routing the data from the data source to the base station. Xing et al. [37] use
greedy geographic routing protocols to find shorter routes. Hua et al. [30] propose a
routing algorithm to maximize the network lifetime using data aggregation. Kuruvila
et al. [31] suggest that a localized power and cost aware routing algorithm can be
computed using Dijkstra’s single source shortest weighted path algorithm. They
propose several heuristic algorithms to choose the data forwarding hops. In [31],
Power-Cost Progress (PCP) is an energy-efficient routing algorithm where the relay
19
node is chosen based on two parameters: the remaining energy and the power used to
make a portion of the progress in distance. This method is adopted in this dissertation
for data forwarding among the cluster heads.
Multihop transmission techniques are usually considered in many wireless sensor
networks. However, multihop transmission fails when there are no relay nodes avail-
able, such as forwarding the data collected from the ground to a satellite. In such
scenarios, other transmission techniques, such as collaborative beamforming, need to
be considered.
2.1.2 Collaborative Beamforming
Using collaborative beamforming to enhance energy efficiency for wireless sensor
networks has been studied in [14,16, 38–46]. In general, these studies can be divided
into two categories: (1) analysis of beamforming characteristics and performance, and
(2) algorithms to achieve beamforming.
(1) Analysis of beamforming characteristics and performance:
Several studies analyze the characteristics of beamforming under different deploy-
ment conditions. In [16], the authors analyze the characteristics of beamforming
patterns when nodes are uniformly distributed. Ahmed et al. [39] show that beam-
forming performances can be improved when nodes are deployed with a Gaussian
distribution. Zarifi et al. [40,41] derive an average beam pattern expression for trans-
mitters located on a ring with arbitrary inner and outer radii, and show that the
width of the average beam pattern main lobe continuously decreases when increasing
the ring’s inner radius from zero to a value close to the ring’s outer radius. They also
show that by choosing the nodes from the narrow ring adjacent to the inner side of the
disc boundary, the network energy waste is reduced. In [42], the authors investigate
the relationship between the bit error rate of beamforming and phase errors, examine
the effects of the phase errors on the beamforming performance for various numbers
20
Table 2.1Comparison of the proposed algorithm with existing studies. MC:Multiple Clusters; DS: Data Sharing; PAR: Phase Adjustment Re-quired; ENL: Extend Network Lifetime.
Paper MC DS PAR ENL
[39] No Yes Yes No
[16] No No Yes No
[40,41] No No Yes Yes
[17] No No Yes No
[18] No No No No
[43] No No Yes No
This dissertation Yes Yes No Yes
of nodes and different levels of transmitting power, and derive two distinct formulas
to approximate error probability.
(2) Algorithms to achieve beamforming:
The signal strengths or transmission ranges can be increased using beamforming
with the potential benefits of saving energy. However, due to various reasons, such as
different distances and phase offsets, signals from collaborating transmitters may have
different phases. Existing research suggests that beamforming generally be achieved
generally in two different ways:
• If the phase differences of the nodes are unknown, transmitters adjust the phases
based on feedback signals. Mudumbai et al. [17] propose a mechanism for
achieving beamforming phase adjustment based on feedback signals from the
base station. Tushar et al. [43] propose an improved feedback system to achieve
phase adjustment using many iterations. In each iteration, the transmitters
adjust their phases based on a 3-bit feedback signal.
21
• If the phase differences are known, transmitters are selected based on their
phase differences. In [20], the authors present a phase difference and frequency
offset estimation technique using a modified maximum likelihood phase estima-
tor. The phase differences can be obtained by the control center when each
transmitter sends a carrier signal to the control center. Chang et al. [18] pro-
pose an algorithm, phase partition (PP), to achieve beamforming by dividing
transmitters into several groups based on their phase differences. Each round of
beamforming uses only one group. PP does not balance energy because it does
not consider the remaining energy in each node and the signal strength at the
receiver. In Chapter 4, I consider an improved phase partition method (IPP)
with multiple transmit power levels in order to reduce excessive signal strength
at the receiver.
2.1.3 Beamforming in Multi-hop Transmission
Combining beamforming and multihop to achieve energy efficient transmissions
in wireless sensor networks has recently become the focus of many researchers. Sh-
pungin et al. [47] suggest to divide the nodes into clusters and use beamforming to
transmit data from one cluster to another. In [47], the authors assume that the nodes
are pre-synchronized, and the cluster head calculates the phase offsets or selects some
nodes to form a beam pointing in the intended direction (e.g. next hop). How-
ever, it is challenging to achieve accurate synchronization in WSNs at a high carrier
frequency [19].
Bletsas et al. [48] present a method to automatically form transmission beams
using the frequency drifts of the given nodes. According to their analysis, the proba-
bility of beam forming decreases exponentially as the number of nodes increases. For
three nodes, the probability of forming a beam is less than 10%, when the frequency
drift of the nodes are uniformly randomly distributed. In Chapter 5, I use two nodes
22
Fig. 2.1. Timing diagram to illustrate one round of sensing and trans-mitting operations using direct or beamforming as the transmissionmethod. Different from direct transmission, beamforming requirestwo preparation steps, including: phase alignment and data sharing.T is the time for one round of sensing and transmitting operations.
at each hop to form a transmission beam and I present a method for the receiver to
detect the signal.
2.2 Pre-beamforming Preparation
Even though beamforming has the potential benefits of saving energy, several
preparation steps are required before beamforming can be applied. As shown in
Figure 2.1, data sharing and phase alignment are required before the data can be
transmitted to the base station using beamforming. In this section, I show existing
studies on these pre-beamforming steps.
2.2.1 Synchronization and Localization
Using beamforming to transmit data with multiple transmitters requires localiza-
tion, time and frequency synchronization among the transmitters. Localization, time
and frequency synchronization are highly correlated since they share many aspects
in common in wireless sensor networks. For example, to achieve π/6 accuracy of a
23
carrier frequency f , the wave needs to be accurately adjusted with an error less than
λ12
= c12f
; λ is the wavelength and c = 3 × 108 is the speed of light. For a carrier
frequency of f = 900 MHz, the transmitters’ clocks must be synchronized within 1.1
ns and the location error cannot exceed 2.8 cm.
In many applications, nodes are randomly deployed in the sensing area. Commu-
nications among the nodes are usually used to estimate the relative locations of the
nodes. Time-of-arrival (TOA) is the commonly used metric to calculate the relative
distance between every two nodes. Since each node is driven by its own clock, time
synchronization is required to perform an accurate localization using TOA. To syn-
chronize two nodes in time, frequency synchronization is used to cancel frequency drift
and offset. Yan et al. [49] propose a localization method using maximum likelihood
estimation based on TOA measurements. Yan and Fan also introduce a two-stage
method to synchronize frequency by canceling the frequency drift. In [50], the au-
thors propose two iterative algorithms to estimate the node locations: the Taylor
series-based least squares method and the sequential quadratic programming opti-
mization method. In [50], the authors propose a method to reduce frequency drift by
computing the differential TOAs of two adjacent transmissions between the same pair
of nodes. Another recent work [51] jointly estimates the frequency offset, frequency
drift, and the location of the nodes using synchronous anchors. The uncertainties of
the anchor positions and clock parameters are analyzed using a total least-squares
estimator. The existing work presented show techniques for improvement in the re-
duction of both localization and synchronization errors. Simulation in [50] shows that
the frequency drift can be reduced from 5ppm to 0.01ppm.
To avoid periodically re-synchronizing the transmitting frequency, Sayilir et al. [20,
23] suggest allowing the base station to broadcast a pioneer signal, and the beamform-
ing transmitters using phase lock loops (PLLs), to generate a beamforming transmis-
sion frequency according to this pioneer signal. In [20], the authors present a method
to synchronize the phase offsets by two-way message exchanges between each stan-
24
dard node and a master node in the sensing area. I examine the energy consumption
using the phase estimation communications in Section 4.3.3.
2.2.2 Random Walk Algorithm for Phase Alignment
When the locations of the nodes and the receiver are unknown, one of the methods
to achieve phase alignment is to adjust the phases of the transmitted signals from
all transmitters iteratively, based on a feedback signal from the receiver. Bucklew et
al. [13] propose a random walk algorithm to examine the sum of the electromagnetic
waves at the receiver without synchronizing or localizing the transmitters. This phase
alignment method is used in analyzing the energy consumption overhead in Section
3.1. Suppose there are s stationary transmitters and one receiver. Let φi,j ∈ (−π, π]
be the phase of the carrier signal from transmitter i at iteration j, 1 ≤ i ≤ s. At each
iteration, each transmitter randomly shifts the phase by a small amount µγi,j. Here µ
is the step size and γi,j is a random variable of normal distribution with zero mean and
variance of two. At each iteration, the ith transmitter sends the same data (i.e. same
electromagnetic waveforms) with two different carrier phases. In the first iteration,
each transmitter sends with phase φi,j and followed by phase φi,j +µγi,j. The receiver
sends feedback to all transmitters to inform them which signal is stronger. In the
next iteration, φi,j+1 is φi,j − µγi,j if the first is stronger, or φi,j + µγi,j if the second
is stronger. Bucklew’s method requires two transmissions and one reception at each
sensor node for each iteration. After n iterations, each node has to transmit 2n times
and receive n feedback. I suggest a simple improvement: the receiver remembers the
strength of the stronger signal in each iteration. Starting from the second iteration,
the receiver informs the transmitters whether the current signal is stronger than the
previous signal. This can reduce the number of transmissions at each sensor node
from 2n to n + 1 times. The value of µ is chosen based on the accuracy in required
phase differences and the total number of transmitters. Larger µ is chosen for smaller
set of transmitters or less accuracy in phase differences; and vice versa.
25
2.2.3 Transmitter Selection for Phase Alignment
If the location information of the transmitters and the receiver is known, phase
alignment can be neglected by selecting the beamforming transmitters. Without
iteratively adjusting the phases based on the receiver’s feedback to achieve phase
alignment, Chang et al. [18] propose a transmitter scheduling method, phase partition
(PP). PP assumes the location and initial phase offsets of the nodes are known. The
collaborating transmitters are selected based on their phase differences. PP divides
transmitters into several groups based on their phases. Each round of beamforming
uses only one group. The maximum phase difference among the nodes in the same
group depends on the total number of groups. PP does not consider the remaining
energy in each node and the signal strength at the receiver; the method is not energy-
efficient in achieving long network lifetime in three cases. First, too many transmitters
are assigned to the same group and the received signal strength is much higher than
necessary. Second, the transmitters in the same group have different amounts of
energy, if they are deployed at different times. When the group is selected to transmit,
the nodes with less energy will deplete their energy sooner and create coverage holes.
Third, the transmitters are assigned into groups based on their phases. As a result,
the numbers of nodes in different group can be different.
2.2.4 Data Sharing in Pre-Beamforming
Beamforming requires the same data to be sent from all collaborating transmit-
ters at the same time. Hence, data sharing is required before beamforming can be
performed. Data can be shared among all nodes using flooding, such as in [52]. In
some applications, the raw data can represent more information than the aggregated
data. However, in some other applications, the receiver is interested in knowing ag-
gregated information, such as the aggregated average, variance, humidity, and max or
min temperature. In these cases, flooding should not be used [53], since data flooding
can be energy-consuming when there are many sensors and transmitters. Aggrega-
26
tion may be performed in two ways: (1) the raw data is sent to the receiver, and
aggregation is handled by the application layer, or (2) the raw data is aggregated
and sent to the receiver. Often, (2) is more energy efficient when compared with (1),
especially in scenarios where the aggregation involves only simple computations such
as the average or median. Some researchers [54, 55] propose different methods for
data compression and aggregation in order to reduce the amount of data that need
to be sent to the base station.
2.2.5 Deployment and Clustering
Energy-efficient network topologies reduce energy consumption due to data for-
warding, and as a result, prolongs network lifetime [56]. Clustering is one such
method. When the deployment area is large, nodes are divided into clusters, and
data are gathered at each cluster head before forwarded to the base station. Clus-
tering can support data aggregation and reduce the amount of data that need to
be transmitted through the network. In [56], the authors classify several clustering
approaches based on the parameters used for electing cluster heads and determining
the sensors in each cluster. Cluster heads may be decided based on IDs [57], loca-
tions [58], and remaining energy [59] of the nodes. In Chapter 4, I divide nodes into
clusters based on their physical locations, and the cluster heads are selected among
the beamforming transmitters based on the remaining energy of the nodes.
2.3 Energy Models
I adopted three energy models in this dissertation. I start with a simple energy
model that considers only the size of the transmitted data packets to analyze the
minimum amount of data that need to be transmitted to compensate the energy
consumed on phase alignment. Then I adopt a more complex energy model which
considers both transmitted data size and the transmission distance. The parameters
27
Table 2.2Comparison of energy models used in this dissertation.
Energy Model Considering parameters
Energy model 1 [60] Size of transmitting data, fixed transmission distance and
fixed transmitting power
Energy model 2 [29] Size of transmitting data, transmitting power can be ad-
justed based on transmitting distance
Energy model 3 [21] Size of transmitting data, transmitting power can be ad-
justed based on transmitting distance, parameters are ex-
tracted based on physical measurements on a commercial
transceiver circuit
in the second energy model are to achieve an acceptable signal to noise ratio. Finally,
I use an energy model with the parameters that are extracted from a commercial
sensor node. Compared with the second energy model, the third energy model is
more detailed. Table 2.2 shows the difference between the three energy models.
2.3.1 Energy Model 1
Feeney et al. [60] model the energy for transmission and reception in wireless
sensor networks. The energy consumed on point-to-point send Etx and broadcast
receive Erx as shown in the following:
Etx = (1.9 · b+ 420)µJ
Erx = (0.5 · b+ 56)µJ,(2.1)
here, b is the number of bytes in each data packet, including data and overhead.
28
Table 2.3Symbol and parameters of the energy model 2
Parameter Symbol Value
Packet size b bytes
Free space path-loss exponent β 2
Energy consumed on radio circuitry εe 50nJ/bit
Energy consumed on radio amplifier εa 100pJ/bit
Transmission distance d meter
2.3.2 Energy Model 2
In order to compare the energy consumed using different types of transmissions, I
need an energy model that shows the energy consumed on each hardware component,
including the radio amplifier. Perillo et al. [29] presented a more complex energy
model which considers both the size of the transmitted data packet and the trans-
mission distance, as shown in equation (2.2). Etx(b, d) is the energy consumed by one
node for transmitting b bits of data through distance d meters; Erx(b) is the energy
consumed by one node for receiving b bits of data. Here, εe is the energy dissipated
for running the transceiver circuitry for transmission or reception of one bit and εa
is the energy dissipated on the power amplifier. In this model, εe = 50nJ/bit and
εa= 100pJ/bit/m2 are constants to achieve an acceptable signal to noise ratio. The
path loss is expressed by β, and β=2 to represent free-space transmissions. Table 2.3
defines the symbols and lists the values used for this energy model.
Etx(b, d) = εe × b+ εa × b× dβ
Erx(b) = εe × b(2.2)
29
2.3.3 Energy Model 3
To more accurately model the energy consumption, I adopt the third energy model
that is proposed by Wang et al. [21]. The parameters of this energy model are
extracted from a sensor node, CC1000 [61].
PT (d) = PT0 + ε×dβη
PR = PR0.(2.3)
PT (d) is the power for transmitting data through distance d. PR is the power con-
sumed for receiving one packet; η is called the drain efficiency, i.e. the ratio of RF
output power to DC input power; ε is a constant determined by the characteristics of
the antennas and the minimum receiving power required by the receiver; and R is the
data rate. Based on this energy model, the energy consumed on transmissions and
receptions in beamforming are shown in Equations (2.4). Table 2.4 lists the parame-
ters that are used in this energy model [21]. I use b1 to represent the control packets
that are used in data sharing communications and b2 is the data packet that needs to
be transmitted to the base station. Control packets include information such as the
IDs and remaining energy of nodes. The energy consumed on transmitting b bytes
of data through distance d is Ec(b, d). Using beamforming with M transmitters, the
signal can be enhanced by Gm. Therefore, to transmit b bytes of data to distance
d using beamforming, each transmitter consumes Etx(b, d,Gm), where Gm ≥ 1 and
Etx(b, d,Gm) ≤ Ec(b, d). Erx(b) is the energy consumed on one transmitter receiving
b bits of data. To reduce collisions and to compensate the packet drops due to channel
instability, the receiver is usually turned on for a longer period of time than it needs
to receive the data. This network idle listening time typically consumes 50-100% of
the energy for receiving [62]. Here, I use 80% idle listening time in receiving each data
packet. I found that the idle listening time has little effect on the estimated number
of transmissions. When the distance to the receiver is farther than 150m, the energy
consumed on transmitting a data packet dominates.
30
Table 2.4Symbol and parameters of the energy model 3
Parameter Symbol Value Unit
Power consumed on transmitting circuitry PT0 15.9 mW
Power consumed on receiving circuitry PR0 22.2 mW
Energy consumed on one node to transmit b bytes
through distance d
Ec(b, d) mJ
Energy consumed on one node to transmit b bytes
through distance d using beamfomring
Etx(b, d,Gm) mJ
Energy consumed on receiving b bytes Erx(b) mJ
Drain efficiency η 15.7 %
Antenna characteristic ε 0.0005 mW/m2
Free Space path-loss exponent β 2
Data rate R 76.8 kbps
Control Packet b1 19 bytes
Data packet b2 133 bytes
Transmission distance d meters
Number of transmitters M
Signal gain required at receiver Gm dB
Transmission frequency f 2.4 GHz
Ec(b, d) = PT (d)× bR
Etx(b, d,Gm) = Ec(b,d√Gm
)
Erx(b) = 10.2×RR × b
(2.4)
31
2.4 Contributions
Figure 1.4 shows the structure of this dissertation. There are three main chapters
in this dissertation.
In Chapter 3, I analyze the energy savings of wireless sensor networks using
beamforming and have the following three contributions. First, I demonstrate that
beamforming may save energy even though the transmitters have large phase errors.
Second, I show that adding transmitters requires more iterations to converge in pre-
beamforming preparation. Meanwhile, each transmitter can use a lower power level.
There is a trade-off between beamforming efficiency and the energy needed to achieve
the efficiency. Third, I show that whether beamforming can actually save energy de-
pends on the amount of information to transmit (b) and the number of transmitters
(s). This study shows that the number of transmitters and the amount of data are
important factors determining whether beamforming is worthwhile. The minimum
transmitted data size can be decided based on the total number of nodes and the
selected beamforming efficiency.
Chapter 4 focuses on how to achieve beamforming in order to extend the network
lifetime (i.e. send more data to a distant base station). This chapter has the following
three contributions. First, I propose a beamforming transmitter scheduling algorithm
that prolongs the network lifetime by considering the remaining energy of the nodes,
the phase differences, and the size of the sensing area relative to the distance to the
base station. I show that by considering the distance among the transmitters and
sensing nodes, the algorithm can further increase the network lifetime. Second, I show
the conditions for beamforming to save energy, compared with direct transmission and
multi-hop. The simulations show that beamforming achieves more transmissions,
when the base station is far away from the sensing area and the initial energy of the
nodes is non-uniform. Third, I conducted outdoor experiments with 20 randomly
deployed transmitters. I show that by selecting the transmitters based on their phase
differences, beamforming can enhance the signal strength in the intended direction.
32
Chapter 5 has the following two contributions. First, I present a method to com-
bine beamforming in multihop transmissions. This method uses beamforming to
extend the transmission range between hops. Without frequency or phase synchro-
nizations, the frequency drifts of the nodes are used to form transmission beams.
Second, I analyze the energy consumption of this proposed method and compare it
with the standard single node multihop transmissions. I show that the transmission
frequency and the distance between every two hops are the key factors for saving
energy.
33
3. ENERGY SAVING USING COLLABORATIVE
BEAMFORMING
From Chapter 1 and 2, it can be seen that even though beamforming may reduce the
energy consumption for long distance transmissions, several steps (Figure 2.1) are re-
quired before beamforming can be applied, in the pre-beamforming stage as described
in Section 2.2. The pre-beamforming stage consumes additional energy, because they
require communications either among the nodes or between the nodes and the re-
ceiver. In this chapter, I analyze the conditions when using beamforming can save
energy. As shown in Figure 2.1, phase alignment and data sharing are the two energy
consuming preparation steps before beamforming transmission can be achieved. In
this chapter, I first analyze the energy overhead for phase alignment. I consider two
scenarios regarding the location information of the nodes and the receiver. First, the
location information of the nodes and the receiver is not known a priori, and a ran-
dom walk algorithm is used to adjust the transmitting phases. Second, the location
information is known, and then nodes are selected based on the phase differences
using a transmitter scheduling algorithm without phase adjustment. In Section 3.1, I
consider the first scenario and analyze the energy overhead for aligning the phases at
the receiver. Through this analysis, I compute the minimum amount of data needed
to be sent using beamforming in order to compensate the energy required for the
phase alignment. For the second scenario, by adopting the phase partition method
proposed by Chang et al. in [18], the energy consumed for phase alignment can be
omitted. However, data sharing is still required. A procedure for data sharing among
multiple sensing nodes and transmitters is presented in Section 3.2. With the beam-
forming transmitters selected using phase partition, I show that the energy consumed
for data sharing has negligible affect on network lifetime, as long as the sensing area
34
is small. Compared with direct transmission, the condition for saving energy with
beamforming is that the distance to the receiver has to be relatively large compared
with the radius of the deployment area.
3.1 Energy Overhead on Phase Alignment
As shown in Figure 2.1, beamforming is divided into two stages, preparation (i.e.
phase alignment and data sharing) and operation (i.e. beamforming transmission).
In this section, I focus on the energy overhead in phase alignment and I assume that
the data are already shared with the transmitters. In this section, we assume the
phase alignment is achieved using the random walk algorithm [13], which has been
explained in Section 2.2.2. We assume that N sensor nodes are randomly deployed;
each sensor node is capable of transmitting data at different phases and power levels.
At the highest power level, a single transmitter can generate signals reachable at the
receiver with the lowest acceptable signal-to-noise ratio, but beamforming allows the
transmitters to reduce the power levels and save energy on each transmission. We
assume that the transmitters are close to each other, and the receiver is sufficiently far
away from the transmitters. Thus, the wave magnitudes are approximately the same
at the receiver, and the energy used for inter-transmitter communication is ignored.
We assume that the phase alignment preparation is a one-time overhead because
the transmitters and the receiver are stationary, and clock drifting is ignored. The
question is how much data need to be transmitted using beamforming so that the
energy overhead on phase alignment can be compensated.
In this section, I use the first energy model from Section 2.3.1 to analyze the energy
consumption in phase alignment and the energy saving in beamforming transmissions.
Since the distances between the nodes and the receiver is fixed, I only consider the
size of the transmitted data and the number of communications. We assume that the
transmitters use control packets of 25 bytes each for pre-beamforming coordination;
the feedback packets from the receiver are 18 bytes each. Both packet types include
35
a 16 byte preamble. After beamforming is ready, data packets of 36 bytes each are
sent to the base station. This is a typical packet size for Mica2 [63], but the actual
size depends on the applications. Considering the first scenario, where the location
information of the nodes and the receiver are not known a priori, transmitters adjust
their transmitting phases based on changes in signal strength reported by the feedback
mechanism. After a number of adjustments (i.e. iterations), the phase differences of
the signals from all transmitters will converge to a small enough range, and the signal
strength will be high enough for the receiver to retrieve the data.
Example: Suppose there are 5 sensor nodes. After 30 iterations, they achieve
80% efficiency of beamforming. Efficiency (e) is defined as the ratio of achieved
signal strength and the highest possible signal strength. In other words, when the 5
nodes send the data together, the signal strength at the receiver is 4 times higher.
Thus, each node needs to transmit at only 1/4th of the power level compared with a
transmission using only one transmitter. Based on Equation (3.1), in each iteration,
each node consumes 1.9 · 25 + 420 + 0.5 · 18 + 56 = 532.5µJ . The energy overhead in
preparation is 30 · 532.5 + 1.9 · 25 + 420 = 16442.5µJ .
Etx = (1.9 · b+ 420)µJ
Erx = (0.5 · b+ 56)µJ,(3.1)
Without beamforming, each sensor has to consume 1.9 ·36 + 420µJ per packet for
b/36 packets. With beamforming each sensor consumes (1.9 · 36 + 420)/4 · (b/36) +
16442.5µJ . For beamforming to save energy, for transmitting b bytes of data, the
energy consumed on direct transmitting should be more than the energy consumed
on beamforming, including phase alignment. Hence, the following condition must be
true
(1.9 · 36 + 420) · b36> 1.9·36+420
4· b
36+ 16442.5
⇒ 34(1.9 · 36 + 420) · b
36> 16442.5
⇒ b > 1616.
(3.2)
36
Fig. 3.1. Beamforming efficiency and the phase differences at thereceiver for different numbers of transmitters. For a small numberof nodes N , large phase differences (> 0.3π) affect the beamformingefficiency significantly and cause instability. A larger N stabilizesbeamforming.
If the sensor network transmits more than d1616/36e = 45 packets, beamforming
saves energy.
3.1.1 Random Walk Phase Alignment
Using random walk phase alignment algorithm as described in Section 2.2.2, in
the ideal scenario, the phase difference is zero for waves arriving at the receiver to
achieve 100% efficiency. If the transmitters are allowed to have phase differences,
the efficiency is lower but convergence is faster. Without loss of generality, I use the
first transmitter’s phase as the reference, φ1 = 0. Figure 3.1 shows the efficiency
at different phases. The horizontal axis shows the largest allowed phase difference,
namely max |φa−φ1| for transmitter a and the first transmitter, 1 ≤ a ≤ N . At π/6,
all transmitters are allowed to have a phase difference between [−π/6, π/6]. Within
this interval, the phase difference is randomly distributed. At this phase difference,
the efficiency is 95%. Efficiency can be computed using the following formula.
37
e =1
s·N∑i=1
cos(ωt+ φi). (3.3)
High efficiency provides high directivity in beamforming. This is because the
received signals are constructed at the receiver and destructed in the other directions.
In [13], Bucklew et al. suggest to use a small step size to converge the phase
differences to near zero. Using a small step size, the convergence is slower (i.e. more
iterations) but the final phase differences can be converged into a smaller range.
With the step size µ set to be 0.0005, for N = 10 transmitters, the phase error at the
receiver is nearly zero after 30,000 iterations [13]. Since two transmissions and one
reception are required for each iteration in Bucklew’s method, the energy consumed
on phase alignment is 3 · 104 · (2 · (1.9 · 25 + 420) + 0.42 · 18 + 56) = 29.96J.
As shown in Figure 3.1, beamforming can increase the received signal strength
even when the phase differences are greater than zero. Zero phase difference is not
necessary for achieving beamforming, and it has too much energy overhead. When the
maximum phase difference is π/3, beamforming can achieve 70% efficiency. Since the
goal is not zero phase difference, I propose to relax the phase difference requirement for
faster convergence. The step size µ can also be enlarged without causing instability.
Convergence can be much faster with a larger phase difference and a larger step size.
Figure 3.2(a) shows the convergence of the phase differences for 10 transmitters and
µ = 0.05. After 70 iterations, the differences are within π/3. After 100 iterations,
the differences are within π/5.
When there are more transmitters, beamforming may increase the signal strength.
However, more iterations are needed to converge and achieve acceptable efficiency.
Figure 3.2(b) shows the maximum phase differences for different numbers of trans-
mitters (N). When there are more than 100 transmitters, the phase difference remains
nearly unchanged after 200 iterations. Figure 3.2(c) shows the relationship between
the efficiency and the number of iterations. As the two figures indicate, the phase
38
(a)
(b)
(c)
Fig. 3.2. (a) Phase differences (unit: π) converge faster by choosinga larger step size. Each line shows the phase difference between onetransmitter and the first transmitter. (b) Maximum phase difference(max |φa − φ1|, 1 ≤ a ≤ N) for different numbers of transmitters N .The unit for the vertical axis is π. (c) Beamforming efficiency afteriterations for different N .
39
Table 3.1Symbols for analyzing the energy overhead for phase alignment
Parameter Symbol Unit
Number of nodes N
Data packet b bytes
Minimum number of data to compensate energy overhead bmin bytes
Step size µ
Angular velocity ω
Beamforming efficiency e
Phase difference of node i φi rad
Maximum transmitting power of one node Pm W
Energy consumed for one direct transmission using PM Em J
Energy consumed in pre-beamforming Ep J
Energy saved by beamforming Esaving J
differences remain high. Hence, the step size has to be decreased even more when the
number of sensor nodes (N) is large.
3.1.2 Energy Savings by Beamforming
After the preparation stage, the transmitters enter the operation stage and use
beamforming to send data. Suppose Pm is the maximum power level for one trans-
mitter. With beamforming, the signal strength increases by N · e times and each
transmitter can use a lower power level Pm/(N · e). Em is the energy that single
sensor needs to transmit one byte at power Pm. With beamforming each transmitter
needs to use only Em/(N · e) for sending one byte. Suppose b is the number of bytes
to send, the energy consumption for each node in the operation stage is
40
Em · b without beamforming
Em · b · 1N ·e with beamforming.
(3.4)
The energy saved by beamforming is
Esaving = Em · b(1−1
N · e). (3.5)
Let Ep be the energy for pre-beamforming preparation. Beamforming can save
energy if
Em · b > Ep + Em · b1
N · e(3.6)
bmin =Ep
Em · 1(1− 1
N·e )
. (3.7)
Here, bmin is the minimum data size required to transmit using beamforming to
balance the preparation overhead.
3.1.3 Simulation and Analysis
In this section, I use simulations to show how the minimum size of transmitted
data bmin changes when the total number of nodes N changes. Figure 3.3 and Figure
3.4 show the minimum size of data bmin needed to transmit for beamforming to
save energy when the number of sensor nodes N is given. In Fig 3.3, the x-axis
shows the number of transmitters, and the y-axis shows the corresponding bmin; each
line represents a selected beamforming efficiency. In Figure 3.4, the x-axis shows
beamforming efficiency from 30% to 90%, and each line means a different number of
N , from 10 to 70. As mentioned in section 3.1.1, for a larger amount of transmitters, a
smaller step size is required. Figures 3.3 and 3.4 use step size µ = 0.04 for converging
the phase in pre-beamforming stage. This is because we cannot achieve e=90% with
µ = 0.05 when N > 60.
41
We examine two scenarios: (1) With a required minimum beamforming efficiency,
Figure 3.3 tells how many nodes are needed for transmitting b bytes of data. For
efficiency lower than e=60%, bmin is approximately 4000 bytes. For applications that
require high beamforming efficiency (e=90%), the minimum data size increases to
13000 bytes for a group of 70 nodes. This is because a higher beamforming efficiency
requires more iterations in phase alignment and consumes more energy, therefore,
it requires more data to be transmitted to the base station to compensate for this
additional energy overhead. Even though a higher beamforming efficiency can save
more energy in the beamforming stage compared with the energy consumed for phase
alignment, the increase in beamforming efficiency is not sufficient. However, high
beamforming efficiency may be required in some applications, for example, in military
applications when the sensing area is close to the enemy territories, the security of
the transmission is important, and the transmission needs high directivity. To create
a high directivity beam, the phase differences of the transmitters have to be small.
In other words, it requires a high beamforming efficiency. The number of sensors
can be decided by the size of the transmitted data. (2) Given the total number of
nodes, Figure 3.4 indicates how the beamforming efficiency e affects the minimum
data size bmin. For a fixed number of transmitters N , higher efficiency e requires
more iterations in pre-beamforming preparation and a larger bmin to compensate this
overhead. For a large number of N , the minimum amount of data required increases
as e increases. For applications, where the efficiency is not required to be high, there
is a trade off between e and bmin.
Using random walk phase alignment, the minimum data size bmin increases as the
number of the nodes increases, as can be seen in Figure 3.4. The energy consumption
is big when the number of beamforming transmitters is large. Chang et al. propose
that if the location information of the nodes and the receiver is known a priori, phase
adjustment is no longer required [18]. Hence, the energy consumed on phase alignment
can be eliminated. However, the transmitting data still need to be shared among
the sensing nodes and the transmitters. In the next section, I analyze the energy
42
Fig. 3.3. Relationship between number of sensors N and minimumdata size bmin. Each line represents different beamforming perfor-mance e. The data shown in this figure is the average of 10 conver-gence tests.
Fig. 3.4. Relationship between beamforming performance e and min-imum data size bmin. Each line represents different number of sensorsN . The data shown in this figure is the average of 10 convergencetests.
consumed for data sharing in pre-beamforming preparation, and I show how the
energy consumed by data sharing affects the network lifetime when the beamforming
transmitters are selected using phase partition.
43
Fig. 3.5. Time for one round of transmission. T1 is the time for sharingdata among all the transmitters and T2 is the time for beamformingtransmission. Sensing is performed simultaneously with communi-cation and transmission. Data collected in kth round is shared andtransmitted in the k + 1th round.
3.2 Data Sharing in Pre-beamforming
In this section, I consider the second scenario of phase alignment, where the loca-
tion information of transmitters and receiver are known, and beamforming transmit-
ters are scheduled based on their phase differences using phase partition, as described
in Section 2.2.3. In a circular sensing area of radius ρ meters, N sensor nodes are
randomly deployed, and nodes can communicate with each other directly. The signal
from node i has a phase difference φi at the base station, due to its phase offset
and distance from the base station. We assume the phase differences are uniformly
distributed in [−π, π] and N nodes are divided into H groups based on their phase
differences. The number of transmitters N in each group may be different, but on
average M = N/H. Each beamforming transmission is assigned to one group of
nodes. The groups transmit to the base station in turns. Beamforming scheduling is
performed offline, and the transmission schedule is shared with all nodes. We assume
all nodes are synchronized and can perform simple computations, such as averaging,
counting, and multiplication. Each node has an initial energy ei, and it is randomly
distributed in range (0, emax] for reasons such as different times of deployments. Fig-
ure 3.5 is modified from Figure 2.1 by removing the phase alignment procedure, and
assuming that the sensing and transmission can be performed simultaneously. Since
44
sensing data is not the focus of this dissertation, I assume that sensing takes the
same amount of time as transmission, and the data collected by the sensing nodes
in the current round will be shared and transmitted to the base station in the next
round. There are M transmitters and S sensing nodes in each round. The number
of transmitters, M , affects the beamforming transmission distance. Collaborative
beamforming using M transmitters with no phase difference can extend the trans-
mission distance by M times [64]. For a base station located farther away, M needs
to be larger. Hence, either more nodes are deployed, or nodes are divided into fewer
groups. The size of S depends on the accuracy that is required by the application.
Sensing nodes and transmitters may be different in each round since they are selected
based on different criteria, i.e. S 6= M . In this dissertation, I assume the numbers
of sensing nodes are the same for all rounds. Each round of communication and
transmission takes time T , T = T1 + T2. Here T1 is the time for data sharing among
all transmitters and T2 is the time for one beamforming transmission. During the
data sharing period T1, control packets b1 are used for information exchanges, such
as electing the master node and exchanging the remaining energy level of nodes. A
control packet contains the ID and remaining energy for the nodes, and an ACK. The
data packets containing monitored events are called b2, and the control packets for
communication among the nodes are called b1. The size of b2 is larger than the size
of b1.
3.2.1 Data Sharing Procedures
Data sharing in beamforming is necessary because the data sent by all transmitters
need to be the same to create constructive interference of the electromagnetic waves
at the receiver. Data sharing is necessary even when the sensing nodes are the same
as the transmitters, since sensing nodes provide localized measurements, and two
sensing nodes from two different locations may have different measurements.
45
T 1
T 1−1 T 1−2 T 1−3 T 1−4 2T
Fig. 3.6. Four steps for data sharing in T1.
S sensing nodes and M transmitters are used in each round. For S sensing nodes
to broadcast their own data packet one after another, it requires S transmissions.
Since there are M transmitters, each transmitter receives one data packet from one
sensing node. Therefore, it requires S ×M receptions of data packets. It is energy-
efficient to elect a master node to gather the data from the sensing nodes, and then
multicast to all transmitters. The data from these sensing nodes are aggregated at
the master node; the final data packet is of the same size as a single data packet from
one sensing node. The S×M receptions of data packets in the previous approach can
be reduced to S +M receptions of data packet, one transmission of data packet, and
M control packets. For the master node to gather the data from S sensing nodes,
S receptions of data packets are required. M receptions and one transmission are
required for the master node to broadcast the final data packet to the transmitters.
M control packets are used to elect the master node among the transmitters, and
this is explained later in this section. In this approach, data sharing with multiple
sensing nodes and transmitters can be achieved in four steps, as shown in Figure 3.6.
Figure 3.6 illustrates the detailed steps in the data sharing T1 time, as in Figure 3.5.
• T1−1 Election for the master node in this group. Multiple sensing nodes are
used in each round. For all transmitters to have the same information, a master
node gathers the data from all sensing nodes, then forwards the data to the
transmitters. The master node is elected among the transmitters to reduce the
amount of communication. Each transmitter multicasts its ID and remaining
energy to the other transmitters. Thus, every transmitter knows the remaining
energy of the other transmitters in the same group. The transmitters know
46
which node has the highest remaining energy, i.e. the master node. Since
transmitters are scheduled in advance, every node knows its own group.
• T1−2 Share the master node’s ID with sensing nodes and select the sensing
nodes for the next round. In time T1−1, the master node is elected among
the transmitters by exchanging their own remaining energy. To save energy
consumed over the network, nodes other than transmitters do not participate in
the communication in T1−1. However, as mentioned earlier, the sensing nodes
may not be the transmitters in the same round. In order to know where to
forward their data packets, the sensing nodes also need to know which node is
the master node. In T1−2, the master node broadcasts its ID to all other nodes.
In the case that sensing nodes are not pre-scheduled, the master node can also
assign the sensing nodes for the next round. It is more energy-efficient for the
sensing nodes to receive one control packet with the master node ID than to
receive several control packets from all transmitters with their remaining energy.
• T1−3 Sensing nodes forward their data to the master node.
• T1−4 Master node multicasts the final data for beamforming. The final data will
be transmitted to the base station.
To reduce the communication in data sharing, this master node election procedure
in T1−1 does not need to be performed in every round. In T1−1, transmitters exchange
their remaining energy using control packets. Based on this message exchange, every
transmitter knows the remaining energy of the master node and the other transmitters
from the same group. Based on the master node’s remaining energy, transmitters
can estimate the number of rounds that the master node can perform before it is
energy-exhausted. This number is the lower bound for how often the master node
needs to be elected. For example, after exchanging the remaining energy information
among the transmitters, the master node has 4.5J more than the transmitter with
the second highest remaining energy. If there are five transmitters in this group, each
47
transmission and reception of a data packet consumes 0.5J and 0.2J, respectively.
The master election procedure in T1−1 can be skipped 4.5/(0.2× 5 + 0.5) = 3 times.
This is because all transmitters are scheduled based on their phase differences using
phase partition, the fact that the nodes are stationary, and that the grouping has
not changed. For each round of data sharing, the master node collects one data
packet from each transmitter in the same group, and then sends the finalized data
packet to all other transmitters. This data collection and broadcasting consumes
0.2× 5 + 0.5 = 1.5J. Hence, the same master node will be elected 4.5/1.5 = 3 times.
3.2.2 Data Sharing Energy Overhead
There are four types of nodes in each round of sensing and transmission: beam-
forming transmitters, a master node, sensing nodes, and the other nodes in the de-
ployment area that are not transmitters or sensing nodes. A master node is one of the
transmitters. Transmitters are scheduled based on the phase differences, and sensing
nodes are selected based on the application. Without loss of generality, I examine
the energy consumption on transmitters and sensing nodes separately. However, a
transmitter can also be a sensing node, and vice versa. In this section, I analyze the
energy consumed on each type of node. We examine the amount of transmissions and
receptions performed on each type of node in one round. If a sensing node is also a
transmitter, the energy consumed on that node is the sum of the energy consumed
on a transmitter and a sensing node. The master node is one special node among the
transmitters and the energy consumed on a master is more than a normal transmitter.
The symbols are listed in Table 3.2.
1. Transmitter: Multicast one control packet containing its remaining energy to
the other transmitters and receive N-1 control packets from other transmitters in
T1−1. Receive one control packet containing master node’s ID in T1−2. Receive
final data packet from the master node in T1−4.
48
ect = etx(b1, ρ) + erx(b1)×M + erx(b2) (3.8)
2. Master node: Multicast one control packet containing its remaining energy to
the other transmitters and receive N-1 control packets containing the remaining
energy from other transmitters in T1−1. Broadcast one control packet to confirm
that it is the master node and the selected sensing nodes for the next round in
T1−2. Receive S data packets from sensing nodes in T1−3. Multicast the final
data to the other transmitters in T1−4.
ecc = etx(b1, ρ) + erx(b1)× (M − 1) + etx(b1, ρ) + erx(b2)× S + etx(b2, ρ)
(3.9)
3. Sensing node: Receive one control packet from the master node in T1−2 and
send a data packet to the master node in T1−3.
ecs = erx(b1) + etx(b2, ρ) (3.10)
4. All other nodes (i.e. nodes that are not sensing or transmitting): Receive one
control packet from the master node in T1−2.
eco = erx(b1). (3.11)
According to the derivation, the total energy consumed on data sharing in each
round is the sum of the energy consumed on all types of nodes. Based on these
equations, in Section 3.2.3, I analyze the conditions for beamforming to save energy
compared with direct transmission, and show how the energy consumed on data
sharing affects the network lifetime.
49
3.2.3 Simulation and Analysis
In this section, I analyze the energy saved using beamforming, and how the energy
consumed on data sharing affects the maximum number of beamforming transmis-
sions. The second energy model in Section 2.3.2 is used in this section. This model is
used because the transmission distance for data sharing as well as sending data to the
receiver are different, thus the transmission distance need to be considered in the sim-
ulation. In this section, I show that (1) by using beamforming, the energy consumed
on each transmitter is much less than the energy consumed in direct transmission; (2)
for the same number of transmissions, whether beamforming saves energy over the
network depends on the radius of the deployment and the number of transmitters;
(3) the number of successful beamforming transmissions reduces when more sensing
nodes are used; (4) energy consumed on data sharing has very little effect on network
lifetime when the deployment area is relatively small, compared with the distance
from the receiver.
I use the following parameters in the simulation. N=100 nodes are deployed in a
circle of radius ρ=100 meters, the base station is at d =50000 meters. Sensor nodes
are divided into H=6 groups based on their phase differences. The typical data packet
for Mica2 is 36 bytes [63]. In this chapter, I assume each data packet and control
packet contain two bytes of header. The data packet b2 is 25 bytes, and the control
packet for data sharing communication b1 is 4 bytes. The actual size of the data
packet and control packet depends on the application. I assume the maximum energy
carried by one node emax is 1000 J, as suggested in [29]. The parameters and values
used in the simulation are listed in table 3.2.
Energy Saved On Each Transmitter by Using Beamforming
A data packet b2 can be transmitted from the sensing area to the distant base sta-
tion in two ways. (1) The data packet can be directly transmitted to the base station
50
Table 3.2Symbols for analyzing the energy overhead for data sharing
Parameter Symbol Value
Number of total deployed nodes N 100
Number of sensing nodes S 10-100
Number of transmitters in each round M average 16
Number of transmission groups H 6
Deployment radius ρ 100m
Distance to base station d 50000m
Control packet b1 4 bytes
Data packet b2 25 bytes
Beamforming efficiency e
Node energy (maximum) emax 1000J
Data sharing energy per transmitter ect J
Data sharing energy per sensing node ecs J
Data sharing energy Per master node ecc J
Data sharing energy per node other than transmitters or
sensing Nodes
eco J
Energy consumption for one direct transmission ed J
Energy consumption for one beamforming transmission eb J
51
Fig. 3.7. Compared with direct transmission, beamforming alwayssaves energy on each transmitter. The distance to the base station dis 50000 meters. The energy consumption in this figure is the averageof 20 random deployments.
52
using one transmitter with high power, where the energy consumed on each transmit-
ter is ed = etx(b2, d). (2) The data packet can also be transmitted using beamforming
with M transmitters, and each transmitter can use lower transmit power. Assuming
100 nodes are divided into H groups, there are M = 100/H transmitters in each
group, and the phase differences of the nodes in the same group are in the range of [0,
2π/H]. In beamforming transmissions, M transmitters with a beamforming efficiency
e can extend the transmission range by M × e times. Hence, the transmission energy
consumed on each transmitter in beamforming is eb = etx(b2,dM ·e). Beamforming re-
quires inter-communication among the transmitters, and the distance between every
two collaborating nodes affects the total energy overhead for beamforming. In Sec-
tion 3.2.1, I show that during each round of transmission, each transmitter consumes
energy ect for data sharing. Therefore, the total energy consumed on one transmit-
ter in one round is eb + ect. As shown in Figure 3.7, using direct transmission, one
transmitter consumes 500J to transmit a b2 data packet from the origin to the base
station. Compared with direct transmissions, beamforming consumes less energy on
each transmitter even when the deployment radius is large, e.g. ρ=10000 meters.
The number of transmitters in each group also affects the amount of communi-
cation in data sharing. More transmitters require more communication, but for the
transmissions to the base station, each transmitter can use lower power. In Figure
3.7, when ρ increases, the total energy consumption for beamforming increases. The
energy consumed on one transmitter in beamforming is the sum of the energy con-
sumed on data sharing ect and the energy consumed on the transmission to the base
station eb. When M is larger, ect is larger, since more communication is required for
sharing the data. However, when M is larger, eb is lower, since each transmitter can
use lower transmit power. Point A in Figure 3.7 shows that using more transmitters,
when ρ is smaller, the total energy consumption is lower. This is because the energy
consumed on a beamforming transmission dominates. As ρ increases, ect increases.
The total energy consumption is larger when using more transmitters. This is shown
as point B in Figure 3.7.
53
Fig. 3.8. Energy consumed over the network when using direct trans-mission and beamforming transmission respectively. The distance tothe base station is fixed to be d=50000 meters. The energy consump-tion in this figure is averaged by 20 random deployments.
Energy Saved by Beamforming Over The Network
Different from direct transmissions, beamforming requires collaboration between
multiple transmitters in each round, and communication needs to be performed among
multiple nodes to share data in pre-beamforming. Hence, beamforming requires addi-
tional energy consumption overhead. In beamforming, nodes other than transmitters
also consumes energy for data sharing; in direct transmission, communication among
the nodes is not required.
In this section, I compare the energy consumption for 100 transmissions using di-
rect transmission and beamforming transmission respectively. Whether beamforming
saves energy depends on the deployment radius ρ and the number of transmitters.
One node with high transmission power is used in direct transmission. Figure 3.8
shows the total energy consumed over the network using direct and beamforming
transmissions respectively. When the deployment radius is large, ρ >10000 meters,
energy consumed on beamforming transmissions is higher than the energy consumed
on direct transmissions. As the deployment radius becomes smaller, the energy for
data sharing reduces, and the energy consumed on the transmissions to the base sta-
54
tion dominates. In Figure 3.8, the energy consumed on direct transmissions is not a
constant with the change of deployment radius, but the fluctuation is small. This is
because the nodes are randomly deployed in the circle. The distance from each node
to the base station may be different, but the average distance is constant.
The amounts of data sharing communication also depend on the number of trans-
mitters. Figure 3.8 shows the comparison of the energy consumed using beamforming
when the 100 nodes are divided into 10, 5, and 3 groups. When the total number
of nodes is fixed, fewer groups indicate that each group has more nodes, and the
phase differences of the nodes in the same group has a wider range. For example,
when H=3, the phase differences are in the range of [0, 2π/3]; when H=10, the phase
differences are in the range of [0, π/5]. The transmission distance enhanced by beam-
forming is proportional to M × e, where e = E[∑M
i=1 cosφi]. For a smaller H, the
increase in M and the decrease in e are not linearly related. Figure 3.8 shows that
larger M requires more communication in data sharing, and it has an earlier energy
turn-over point. An energy turn-over point is the point when the energy consumed
for beamforming is less than the energy consumed on direct transmissions.
Network Lifetime
For a deployment with the values listed in Table 5.1, Figure 3.9 shows the number
of successful beamforming transmissions in three cases: (i) when the energy consumed
due to data sharing is not considered, (ii) when 10 sensing nodes are used in each
round, and (iii) when 40 sensing nodes are used in each round. Energy consumed
by data sharing exists in all beamforming transmission scenarios. The beamforming
case (i) is used as a reference to show the number of successful beamforming trans-
missions without considering the energy consumed on data sharing for beamforming.
In the three cases that use beamforming for transmissions, the same transmitters are
selected. When using beamforming with a required number of sensing nodes in each
round, e.g. 10 or 40, a transmission will fail when there are insufficient transmitters
55
or sensing nodes, i.e. too many nodes are energy-exhausted. Without considering the
energy consumed on data sharing, the number of successful beamforming transmis-
sions increases as more nodes are energy-exhausted. Transmission fails when there
are (i) not enough transmitters, (ii) or the phase differences of the transmitters are
too large to create a strong enough signal to reach the base station. With 10 sens-
ing nodes in each round, a transmission also will fail when there are fewer than 10
nodes possessing non-zero remaining energy. The number of successful transmissions
show almost no reduction for the case when 10 sensing nodes are used in each round.
When the number of sensing nodes is increased to 40, the number of successful trans-
missions saturates when more than 60 nodes are energy-exhausted. The number of
successful transmissions drops about 2-3 % compared with the case where 60 nodes
are energy-exhausted and no data sharing is considered. According to this figure,
when the deployment radius is much smaller compared with the distance to the base
station, i.e. 100m:50000m, the energy consumed on long distance transmissions dom-
inates, and the energy consumed on data sharing has negligible effect on the network
lifetime. In this figure, I also compare the number of successful transmissions at the
receiver using direct transmission, i.e. a single node directly transmitting the data to
the base station with an increased transmit power. Direct transmission can transmit
much less data than beamforming.
3.3 Summary
In this chapter, I analyze the energy savings of wireless sensor networks using
beamforming and show that: (1) Beamforming may save energy even though the
transmitters have large phase errors. (2) Adding transmitters requires more itera-
tions to converge in pre-beamforming preparation. Meanwhile, each transmitter can
use a lower power level. There is a trade-off between beamforming’s efficiency and
the energy needed to achieve the efficiency. (3) Whether beamforming can actually
save energy depends on the amount of information to transmit (b) and the number of
56
Fig. 3.9. Energy consumed on data sharing has little affect on thenumber of successful beamforming transmissions. Distance to thebase station d= 50000 meters and the deployment radius is ρ=100meters.
57
transmitters (s). The number of transmitters and the amount of data are important
factors determining whether beamforming is worthwhile. The minimum transmit-
ted data size can be decided based on the total number of nodes and the selected
beamforming efficiency.
58
4. TRANSMITTER SCHEDULING FOR ENERGY
BALANCING IN BEAMFORMING
In Chapter 3, I analyzed the conditions for collaborative beamforming transmissions
to save energy. Based on these analyses, besides saving energy on the transmissions
to prolong the network lifetime, balancing the energy consumption among the trans-
mitters is another important issue. The existing transmitter scheduling algorithm
eliminates the energy consumption in phase alignment, however, grouping the trans-
mitters differently will directly affect the network lifetime. In this chapter, I show
the conditions when the existing transmitter scheduling algorithm fails in balanc-
ing the energy consumption, and the network lifetime reduces. Hence, I propose an
algorithm that schedules beamforming transmitters based on their relative phase dif-
ferences and remaining energy. The proposed algorithm prolongs the network lifetime
by at least 50% compared with the existing transmitter scheduling algorithm. Based
on the analysis in Chapter 3, for beamforming to save energy, the distance to the
receiver has to be relatively large compared with the radius of the deployment area.
When the deployment area increases, using the proposed algorithm, the network life-
time decreases quickly since too much energy is consumed on data sharing. Hence,
I extend the proposed scheduling algorithm to adapt to the size of the sensing area.
The simulation results show that when considering the size of the sensing area, the
network lifetime can be tripled. Section 4.1 explains the system model that is used
in this chapter. Section 4.2 proposes the adaptive transmitter scheduling algorithm
for different sizes of deployment area. Section 4.3 compares the number of success-
ful data transmissions to the base station that is using the proposed beamforming
scheduling algorithm with direct and multi-hop transmission techniques, and existing
beamforming scheduling algorithms.
59
Deployment
Transmitter scheduling Data sharing Beamforming
(1)
(2)
(4)
Focus of this chapter
Transmissions
Sensing node selection
(3)
Fig. 4.1. General steps of the proposed system. Beamforming trans-mitter scheduling is the main focus of this chapter.
4.1 System Model
This section explains the system model that includes the steps of the transmission
system, and the equations for calculating the energy consumption.
4.1.1 Steps of the Transmission System
Figure 4.1 shows the general structure of the transmission system, including: (1)
deployment of the nodes, (2) sensing node selection, (3) transmitter scheduling, and
(4) transmissions including data sharing among sensing nodes and transmitters, and
beamforming transmissions to send the data to the base station. The sensing nodes
and the transmitters are selected based on different criteria. Sensing nodes are se-
lected based on applications, and the transmitters are selected based on the distance
to the base station as well as the phase differences of the transmitting signals. (1) and
(2) are application specific. In this chapter, I assume a given deployment as explained
in the following subsections. (3) and (4) are more general. (3) is the focus of this
chapter. The proposed transmitter scheduling algorithm can be combined with any
other deployment and sensing node selection scheme. One round of sensing and
transmission is defined as the time from the sensors collecting data to the time the
data have been received by the base station. The assumptions and setup for each
step is explained in the following.
60
Deployment of the nodes
N nodes are deployed in an L× L square sensing area. All nodes have the same
sensing and transmitting ability. Each node has the following parameters: (i) a phase
offset ϕi, (ii) energy ei, 0 < ei ≤ Emax, where Emax is the maximum energy contained
in one node, and (iii) location (xi, yi). The receiver at (xd, yd) is far away from the
nodes.
All nodes are time and frequency synchronized. All antennae are omni-directional.
The phase offsets, energy, and locations of nodes are known by a control center, where
the transmission schedule can be computed offline and broadcast to all nodes. When
each transmitter sends a carrier signal to the control center, the phase differences
and frequency offsets can be obtained by the control center using a modified maxi-
mum likelihood phase estimator, as presented in [20]. Several existing studies [65,66]
suggest that the remaining energy of the transmitters can be estimated based on the
number of transmissions. The location of the nodes can be obtained from the time
of the deployment, or the received signal strength of a beacon message that is sent
from each node to the control center [67,68].
Sensing node selection
In each round, among all N nodes, S number of nodes are sensing. S is a constant
for each round, but the actual sensing nodes for different rounds may be different.
A sensing node’s selection scheme is determined based on the applications. In this
chapter, I assume that 5% of the total available nodes are sensing for each round, and
the sensing nodes for all rounds are randomly selected before scheduling beamforming
transmitters. The selected sensing nodes are stored in a look-up table and shared with
all nodes. Section 4.3.3 will examine the impact on the number of sensing nodes that
are selected for each round.
61
Fig. 4.2. Sensing and transmission are divided into rounds: T1 isthe time for sharing data among the transmitters and T2 is the timefor beamforming transmission. Sensing is performed simultaneouslywith communication and transmission. Data collected in kth round isshared and transmitted in the k + 1th round.
Transmitter scheduling
In each round, among all N nodes, M nodes are scheduled as beamforming trans-
mitters. M is determined by the transmitter scheduler based on a signal strength
threshold at the receiver (i.e. Gm). Gm is the signal gain that is enhanced by M
transmitters. Gm = M2 × e, where e is called beamforming efficiency. Beamforming
efficiency depends on the phase differences and e ≤ 100%. Selecting transmitters is
the focus of this chapter, and the details of the proposed algorithm are presented in
Section 4.2.
Transmissions
As mentioned in Section 3.2, transmissions contain two steps: data sharing and
beamforming. I assume that sensing is performed simultaneously with data sharing
and beamforming transmissions, i.e. the data collected by the sensing nodes in the
current round will be shared and transmitted to the base station in the next round.
An example is shown in Figure 4.2. Each round of data sharing and transmission takes
time T , T = T1 +T2. Here T1 is the duration for data sharing among all transmitters,
and T2 is the time for one beamforming transmission. Sensing is performed once
in time duration T . Since the number of sensing nodes is fixed for each round,
62
and the beamforming transmitters are scheduled before transmissions, I assume all
transmissions are scheduled using Time Division Multiple Access. The operation
details are as follows.
• Data sharing
S sensing nodes and M transmitters are used in each round. In order to re-
duce the energy consumed due to data sharing, I assume that the data from
all sensing nodes are first aggregated at a master node, and then broadcast
to the beamforming transmitters. How to aggregate data to obtain the same
information as raw data is not a focus of this chapter, thus I assume the data
aggregation at the master node is performed by averaging the data from all
sensing nodes. The data that are sent to the base station are of the same size as
the data collected by one sensing node. In other words, let the data collected by
one sensing node be b bytes, and there are S sensing nodes in each round. The
data from S sensing nodes are averaged at the cluster head in each round. This
aggregated data sent to the base station have size b bytes. Since beamforming
transmitters are scheduled and the sensing nodes for each round are selected
offline, the data sharing procedure can be achieved in two steps. First, data are
sent from each sensing node to the master node for the current round. Master
node for each round is determined by the transmitter schedule. To avoid chan-
nel contention, sensing nodes forward their data to the master node one-by-one
according to the order of their ID number. Then, after aggregating the data,
the master node sends the final data to the transmitters. The final data will be
transmitted to the base station.
Nodes are divided into multiple clusters when the sensing area is large to avoid
long distance direct transmissions. Data sharing is performed in the following
three steps. First, cluster head in each cluster collects the data from the sensing
nodes in the same cluster. Second, one of the clusters is chosen as the beam-
forming cluster, and all other cluster heads forward their aggregated data to the
63
Table 4.1Symbols used in Chapter 4
Symbol Section Definition Unit
L 4.1.1 Deployment side length m
A 4.2.2 Size of sensing area=L2 m2
C 4.2.2 Number of clusters
Emax 4.1.1 Maximum energy contained in one node J
ei 4.1.1 Remaining energy in node i J
Ec(b, d) 4.1.2 Energy consumed to transmit b bits through d J
Etx(b, d,Gm) 4.1.2 Energy consumed to transmit b bits through d
with beamforming power gain Gm
J
Erx(b) 4.1.2 Energy consumed on one node receiving b bits J
Ga 4.1.1 Gain of antenna arrays dB
Gm 4.1.1 Signal gain threshold for transmitter selection dB
G 4.3.1 Signal gain required by the receiver dB
(xd, yd) 4.1.1 Base station location in Cartesian coordinates m
(xi, yi) 4.1.1 Location of node i in Cartesian coordinates m
P 4.1.1 Network lifetime
ϕi 4.1.1 Phase offset of node i rad
∆ϕi 4.1.1 Phase difference of signal from node i, at receiver rad
αik 4.1.1 Transmission coefficient for node i in round k
T 4.1.1 Time for one round of sensing and transmission s
T1 4.1.1 Time for one round of data sharing s
T2 4.1.1 Time for one round of beamforming transmission s
ξ 4.2.1 Energy-exhausted nodes (0 ≤ ξ ≤ 100) %
γ 4.2.1 Rotating degree rad
EP 4.2.1 Single-cluster beamforming scheduler
MEP 4.2.2 Multi-cluster beamforming scheduler
64
cluster head of this beamforming cluster using multi-hop transmission. Third,
the cluster head of this beamforming cluster aggregates the data and sends to
the beamforming transmitters.
• Beamforming
The phase difference of the electromagnetic waves from each node at a receiver,
∆ϕi, can be computed as the sum of the phase offset and the phase differences
caused by distance to the base station.
∆ϕi = ϕi +2π
λ
√(xi − xd)2 + (yi − yd)2, (4.1)
∆ϕi ∈ [−π, π]. For each round of beamforming transmission, the signal at the
receiver, r(t), is:
r(t) = <(N∑i=1
αik · ej(2πft+∆ϕi)), (4.2)
where < is the real part; αik is the transmission coefficient, and αik = 1 when the
ith node transmits in the kth round. If the ith node does not participate in this
transmission, αik = 0. Hence, in kth beamforming transmission (k = 1, ..., P ),
the potential signal gain Ga at the receiver’s location can be expressed as:
Ga = |N∑i=1
αik · ej(∆ϕi)|2. (4.3)
To extend network lifetime while balancing energy consumption, the following
conditions need to be satisfied. First, the total energy consumption does not
exceed the initial energy carried by each node. Second, the energy consumption
is balanced among all nodes.
65
4.1.2 Energy Calculation Models
Ec(b, d) = PT (d)× bR
Etx(b, d,Gm) = Ec(b,d√Gm
)
Erx(b) = 10.2×RR × b
(4.4)
This section shows the energy consumption of each transmission based on the size
of the data and the transmission distance, shown as in equation (4.4). This is the
energy model introduced in Section 2.3.2. A typical node has a transmission range
of 100 − 300m [69]. However, in order to examine the energy consumed on different
types of transmissions (e.g. direct and multi-hop transmissions), when the receiver
is far away from the sensing area, I assume that nodes can increase their transmit
power to reach any distance.
Based on the energy model in equation (2.3), the energy consumed by one trans-
mitter transmitting b bits of data through distance d, Ec(b, d), is the transmitting
power PT (d) times the transmission time. The transmission time is the size of the
data, b, divided by the data rate, R. Using beamforming with M transmitters, the
signal can be enhanced by Gm times. Therefore, to transmit b bits of data to dis-
tance d using beamforming, each transmitter consumes Etx(b, d,Gm). For Gm ≥ 1,
Etx(b, d,Gm) ≤ Ec(b, d). Erx(b) is the energy consumed by one transmitter receiving
b bits of data. To reduce collisions and to compensate the packet drops due to chan-
nel instability, the receiver is usually turned on for a longer period of time than the
time it needs to receive the data. This network idle listening time typically consumes
50-100% of the energy for receiving [62]. Here, I assume 80% idle listening time in
receiving each data packet. Through the simulations, I found that when the distance
to the receiver is farther than 150m, the energy consumed on transmitting a data
packet dominates. The idle listening time has little effect on the estimated number
of transmissions.
66
The network lifetime is the maximum number of successful beamforming trans-
missions achieved before there are insufficient transmitters or sensing nodes. I assume
the size of the data in each beamforming transmission is the same. Table 4.1 lists the
symbols used in this chapter. For simplicity, this chapter does not consider near-field
interference or multipath propagation.
4.2 Transmitter Scheduling Algorithms
In this section, I show two transmitter scheduling algorithms for sensor networks
of different sizes. A sensor network can have a side length from tens of meters to
thousands of meters based on the applications [70]. When the size of the sensing area
increases, the network lifetime can reduce significantly if the beamforming transmit-
ters are selected without considering the distance among them. This is because large
amount of energy is consumed due to data sharing before beamforming transmissions.
In this section, I explain the transmitter scheduling algorithm that considers the size
of the deployment area. As shown in Figure 4.3, when the sensing area has side length
L ≤ 100m (≈ 800λ), and all nodes belong to one cluster, then beamforming transmit-
ters are scheduled based on the remaining energy and phase differences of the nodes.
I call this single cluster transmitter scheduling algorithm, Energy and Phase (EP),
and it is explained in Section 4.2.1. For a sensing area with side length L > 100m,
the nodes are divided into clusters based on their geological locations. The proposed
algorithm, multiple cluster energy and phase (MEP), schedules the transmitters for
each cluster independently. For each round of beamforming transmission, one cluster
is selected. Selecting a transmission cluster is discussed in Section 4.2.2.
67
Sensor Deployment
Single Cluster
Multiple Clusters
Deployment side length > 100 meters
No
Yes
Schedule using Energy and Phase (EP)
For each cluster, schedule using EP
Divide nodes into clusters
Select one cluster for each round of Beamforming transmission
Perform Beamformingtransmission based on schedule
MEP
Fig. 4.3. General flow of the proposed scheduling algorithm.
68
4.2.1 Transmitter Scheduling Algorithms for Single-Cluster Networks,
Energy and Phase (EP )
In a single-cluster network, nodes communicate with each other directly. In this
section, I first show that to achieve the maximum number of transmissions, exhaus-
tively searching for the best scheduling has very high computation complexity. I
present a heuristic method to schedule the transmitters based on the remaining en-
ergy and their phase differences.
Beamforming Transmitters Scheduling: Exhaustive Search
We want to find a schedule α to balance the energy consumption over the network,
and maximize the network lifetime P . Here α is an N × P matrix, αik is either 0
or 1, with i representing the ith node, i=1,...,N , and k indicates the current round
of transmission, k=1,...,P . The network lifetime P is the number of transmissions
achieved before ξ% nodes are energy-exhausted. Four conditions to achieve this can
be formulated as:
1. The maximum radiation intensity is in the receiver’s direction. Directivity of
an antenna array is defined as the ratio of the radiation intensity of the antenna
array in a given direction to the radiation intensity averaged over all direc-
tions [71]. Directivity Dk(θd, φd) needs to be the maximum, i.e. the main lobe
points to the receiver.
Dk(θd, φd) = max(Dk(θ, φ))
= max( 4π·Uk(θd,φd)∫ 2π0
∫ π0 Uk(θ,φ) sin θdθdφ
).(4.5)
where Uk(θ, φ) = U0(θ, φ)|N∑i=1
αik · ej(∆ϕi(θ,φ))|2
2. The total energy consumed on each transmitter is no greater than its initial
energy.
69
p∑k=1
(αik · Eik) ≤ Ei, ∀i, 1 ≤ i ≤ N. (4.6)
3. For each round, the signal strength at the receiver, Ga(θd, φd) is at least Gm
times stronger than the signal transmitted by a single transmitter.
Ga(θd, φd) ≥ Gm. (4.7)
4. After k rounds of transmissions, no more than ξ% of nodes are energy ex-
hausted, i.e. 1-ξ% of nodes have enough remaining energy for at least one more
transmission.N∑i=1
σ(Ei − Eik −p∑
k=1
αik · Eik) > (1− ξ%) ·N, (4.8)
where σ(v) is the sign function:
σ(v) =
1, v ≥ 0
0, v < 0.(4.9)
Given the total number of nodes N and the number of beamforming transmissions
P , transmission coefficient αik is required to be 0 or 1 for all i = 1......N, k = 1......P .
There are 2NP potential schedules for N nodes with P rounds of transmissions. The
verification of each potential schedule with Equations (4.5), (4.7), and (4.9) require
a computational complexity of O(Np). Hence, the total computational complexity to
find the optimal schedule is O(2NP ). Additionally, the network lifetime P varies based
on different schedules. The exhaustive search can start with an arbitrary number P ,
but this search may take many iterations until P saturates. Hence, the exhaustive
search for scheduling beamforming transmitters is not practical.
Single-cluster Transmitter Scheduling: Energy-Phase
In this section, I present a heuristic method to schedule the transmitters based
on the remaining energy and their phase differences. Algorithm 2 shows how the
transmitters are scheduled for each round of beamforming.
70
Algorithm 1: Pseudo-code for single cluster scheduling algorithm EP
Input: number of nodes N , nodes’ locations in 2-D plane
S(X,Y ) = (x1, y1), (x2, y2), . . . , (xN , yN), phase offsets
SΦ = φ1, φ2, . . . , φN , and remaining energy SE = e1, e2, . . . , eN ; the
receiver’s location (xd, yd); the minimum signal gain for selection Gm;
rotating degree γ = π/3; percentage of energy exhausted nodes ξ;
energy consumed on one node for one beamforming transmissions Etx
Output: number of beamforming transmissions (k), transmission schedule
matrix (α), and a list of cluster heads for all beamforming
transmissions (H)
Set k = 0, H[ ] = 0, αik = 0 for i = 1 . . . N ,DL[N ] = 0;
/* DL records the index of the energy-exhausted nodes */
/* Calculate the phase difference for all nodes */
for i = 1 : N do
∆ϕi = φi + 2πλ·√
(xi − xd)2 + (yi − yd)2
71
Algorithm 2: Pseudo-code for single cluster scheduling algorithm EP (cont.)
while 1 docount ← 0 ;
for i = 1 : N do
/* Count the number of energy-exhausted nodes */
if ei < Etx then DL[i] = 1, count+ +
if count ≥ ξ ·N thenreturn k, α, H
elseαik ← 0 for all i = 1 . . . N ;
/* Calculate the Energy-Phase product for all nodes */
foreach ei ∈ E do
(epi ∈ Sep)← ei · cos(∆ϕi + γ · k)
B ← sort Sep in descending order
Ga ← 0 i← 1;
while | Ga |2< Gm and i <= N do
/* Select nodes to provide strong enough signal strength */
q ← B[i];
if DL[q] 6= 1 then
Ga+= ej(∆ϕq);
αqk = 1;
i+ +;
if | Ga |2≥ Gm then
H[k]← 0, k + +;
foreach ei ∈ E do
if αik = 1 thenei = ei − Etx;
if ei > eH[k] then H[k] = i;
else if (i− 1) == N thenreturn k, α,H
72
A desirable algorithm should achieve more transmissions before nodes become
energy-exhausted. To prevent the nodes with low remaining energy from being
energy-exhausted, the nodes with higher remaining energy should be selected first.
Meanwhile, the phase differences of transmitters are important. Two signals are can-
celed when they have 180 degrees phase difference. Therefore, the nodes cannot be
chosen based only on their remaining energy. Equation (4.3) shows that smaller phase
differences provide a larger gain. The algorithm chooses the nodes to participate in
each transmission by giving higher priorities to the nodes with (i) more remaining
energy, and (ii) smaller phase differences relative to a reference phase at the receiver.
Equation (4.10) expresses the relationship between the selected nodes and the corre-
sponding signal gain at the receiver in the kth transmission from Equation (4.3):
Ga = |N∑i=1
αik cos(∆ϕi) + jN∑i=1
αik sin(∆ϕi)|2
=N∑i=1
N∑h=1
αik · αhk · cos(∆ϕi −∆ϕh).(4.10)
Here αik and αhk ( 1 ≤ i, h ≤ N, 1 ≤ k ≤ P ) are the transmission coefficients, and
∆ϕi −∆ϕh ∈ [−π, π] is the phase difference. Equation (4.10) shows that the gain of
the antenna array is related to the phase differences among the selected transmitters.
For the kth round, the nodes are sorted with their products of the remaining energy
ei and cos(∆ϕi+γ ·k) in descending order to determine their priorities. Here γ ·k is the
reference phase at the receiver, and γ is the rotating degree. The remaining energy
of a node, ei, is always a non-negative number, and cos(∆ϕi + γ · k) is in the range
of [-1,1]. The product ei · cos ∆ϕi is positive when −π/2 < ∆ϕi < π/2. As a result,
a transmitter is never selected when ∆ϕi is outside the range [−π/2, π/2]. However,
from Equation (4.10), Ga is determined by the relative phase differences between the
selected transmitters, not the absolute values of phases. To avoid repetitively using
the same nodes for transmissions, I rotate the reference phase by γ degrees after each
transmission. The value of γ has little effect on the overall beamforming as shown in
Section 4.3.3.
73
Nodes are selected one by one based on the product ei · cos(∆ϕi+γ ·k). After one
node is selected, Ga is calculated with all currently selected nodes. If Ga ≥ Gm, the
currently selected nodes are assigned to transmit for this round. These selected nodes
have their transmission coefficient αik=1. The round number k is creased by 1 and the
number of energy-exhausted nodes are recomputed. If this number is smaller than ξ%,
I calculate the products with their updated remaining energy, and select the nodes
for the next round of transmission. If the number of energy exhausted nodes is equal
to or larger than ξ%, the scheduler stops and returns the current k as the network
lifetime. The scheduling algorithm terminates if Ga < Gm even when all nodes with
remaining energy are selected. This means no more beamforming transmissions can
be achieved, even though some nodes have energy left. Their phase differences are
too large to create a strong enough signal in the direction of the receiver.
4.2.2 Transmitter Scheduling Algorithms for Multi-Cluster Networks,
Multi-cluster Energy and Phase (MEP)
Beamforming saves energy by allowing each transmitter to use much lower power
to transmit to a distant base station, as shown in Equation (4.4). When the transmit-
ters are located far away from each other, data sharing consumes significant amounts
of energy, and the number of beamforming transmissions reduces. For example,
N = 100 with ei ∈ (0, 1000]J are randomly deployed in an area of A. The nodes
need to transmit data to a receiver at 5000m away. When A changes from 100× 100
m2 to 1000×1000 m2, using Energy-and-Phase algorithm (EP), the number of beam-
forming transmissions reduces from approximately 95000 to 12000. This reduction
is due to the following two reasons. First, beamforming transmitters are far away
from each other. In EP, transmitters are selected among all available nodes based
on their phase differences and remaining energy. When the sensing area is large,
two nodes located on the opposite corners of the sensing area may be in-phase and
carry high remaining energy. However, selecting these two transmitters for the same
74
round of beamforming requires long distance communications in data sharing, and it
consumes large amounts of energy. Second, transmitters may be far away from the
sensing nodes. If the selected transmitters are close to each other but far away from
the sensing nodes, the sensing nodes will consume large amounts of energy sending
data back to the transmitters.
In order to reduce the energy consumed due to data sharing, and prolong the
network lifetime, I design a scheduling algorithm such that the transmitters are close
to each other and the energy consumed for sending the data from the sensors to the
transmitters is both reduced and balanced over the network.
Based on the location of the nodes, the algorithm divides them into multiple
clusters if the side length of the sensing area is larger than 100m. In multi-cluster
transmitter scheduling, there are three main steps, as shown in Figure 4.3. (1) Divide
nodes into clusters, i.e. clustering. (2) Schedule the transmitters for the nodes in each
cluster using Energy-and-Phase algorithm (EP). This step is the same as in single
cluster transmitter scheduling. (3) For each round of beamforming, one cluster is
selected to perform the transmission.
Once the beamforming cluster is selected, data sharing for multi-cluster networks
is achieved in the following three steps. First, data from each sensing node is gathered
at its own cluster head. The cluster heads that collect data directly from the sensing
nodes are called Sensor Cluster Heads (SCHs). The SCHs form a subset of the
cluster heads. SCHs are used to gather the data because the sensing nodes are closer
to its cluster head than to the sensing nodes in other clusters; the data from multiple
sensors can be aggregated at each cluster head before sharing with other cluster heads.
Second, one beamforming cluster is selected and the SCHs send the data to the cluster
head of the beamforming cluster, i.e. the Beamforming Cluster Head (BCH). To avoid
long distance direct transmissions, the SCHs send the data to the BCH hop-by-hop
using other cluster heads as the relay nodes. Among the cluster heads, data are
forwarded using the Power-Cost Progress (PCP) routing algorithm in [31]; it chooses
the neighbor node to forward the packet based on both the remaining energy and the
75
power used to make a portion of the progress in distance. The energy consumed due
to forwarding the packet among the cluster heads using the PCP routing algorithm
is considered in the simulation. Third, BCH aggregates the data from SCHs, sends
it to the beamforming transmitters in the same cluster, and initiates a beamforming
transmission.
In the following, I show the details of steps (1) and (3). Step (2) is explained in
Section 4.2.1. In (3), I propose two methods to select the beamforming cluster to
either reduce or balance the energy consumption in data sharing.
Clustering
The deployment area A is equally divided into C clusters. Since the deployment
area is a square with side length L, L is divided into√C along each side. Hence, each
cluster has an area Ac = L2/C. In each cluster, there is only one cluster head; the
cluster head is determined based on the beamforming transmitter schedule. It can
be different for different rounds. Several factors need to be considered in deciding C.
First, the number of transmitters in each cluster needs to be large enough to reach
the base station. Assuming the nodes are uniformly deployed, C should be small
to allow more nodes in each cluster. Second, the energy consumed for data sharing
communications should be reduced. Beamforming transmitters are selected from the
nodes in the same cluster; therefore, the nodes should be close to each other, and C
should be large.
Select Transmitting Clusters for Beamforming Transmissions
In this section, I introduce two methods for choosing the beamforming clusters and
I show that these two methods perform differently in terms of (1) energy balancing
(Multi-cluster Energy Balancing) and (2) maximizing the number of beamforming
transmissions (Multi-cluster Energy Saving).
76
Method 1 (Multi-cluster Energy Balancing): The beamforming cluster is selected
from the clusters that contain the sensing nodes. The BCH is the SCH with the high-
est energy among all SCHs. If the sensing nodes have a uniform-random distribution
in the sensing area, these nodes may fall into each cluster with equal chance. There-
fore, selecting the SCH with high remaining energy will naturally balance the energy
consumption over the network. However, the performance of this method degrades
when the SCHs are far from each other, since the data need to be transmitted long
distances.
Method 2 (Multi-cluster Energy Saving): The beamforming cluster is at the geo-
metric center of all SCH clusters. Using this method, the energy consumed due to
data sharing is reduced. Compared with the previous approach, this method reduces
the long distance data forwarding when the SCHs are far from each other. However,
using this approach, the clusters located on the edge or corner of the deployment
area have lower probabilities to be selected as the beamforming cluster. As a re-
sult, some nodes are energy-exhausted earlier than the others. Therefore, the energy
consumption is not balanced among the whole network.
Comparing the two methods, Multi-cluster Energy Balancing is better for energy
balancing, and Multi-cluster Energy Saving consumes less energy in each round of data
sharing. Based on applications, the beamforming cluster can be chosen differently to
balance or to reduce the energy consumption. It is hard to find one general approach
that consumes minimum energy in all cases. In this chapter, I consider the above two
methods and show simulation results comparing these two approaches in Sections
4.3.2 and 4.3.4.
4.3 Simulation, Analysis, and Experiments
In this section, I evaluate the algorithms using MATLAB simulations, and I show
the conditions for beamforming to save energy. (1) In Section 4.3.1, I show that
when the sensing area is far from the base station and the initial energy of the nodes
77
Table 4.2Default simulation parameters for Chapter 4
Symbol Definition Value
N Number of nodes 100
S Number of sensing nodes in each round 5
L Side length of deployment area 50m
A Size of deployment area L× L m2
Rd Distance to base station 5000m
ei Remaining energy of node i (0,1000]J
b Data packet 133 bytes
Gm Signal gain for selection 20 dB
G Gain of the signal strength at the receiver 1 dB
is uniformly distributed, beamforming achieves more transmissions than direct and
multi-hop transmissions. (2) In Section 4.3.2, I show that when the deployment
area increases, the number of beamforming transmissions reduces due to large en-
ergy consumption from data sharing. By dividing nodes into clusters and scheduling
beamforming transmissions using the nodes in the same cluster, the method extends
network lifetime. (3) In Section 4.3.3, I perform sensitivity analysis on the single clus-
ter beamforming scheduling algorithm for the rotation degree, phase uncertainties,
and the number of sensing nodes. (4) In Section 4.3.4, I analyze how the cluster size
and the beamforming cluster selection method affects the performance of the multi-
cluster scheduling algorithm. (5) In Section 4.3.5, I show the results from our outdoor
experiments. (6) In Section 4.3.6, I discuss a few practical issues when applying the
proposed method in large-scale sensor network.
Table 4.2 lists the default parameters used in this section. Different parameter
values that are used in each specific simulation are explained in each subsection.
78
4.3.1 Single Cluster Comparison
A scenario in which N = 100 nodes are used to collect data from a sensing area
of A = 50 × 50 m2 is considered. The sensed data are sent to a base station at Rd
meters away from the center of the sensing area, and each node carries energy ei.
In this section, I show the following analysis. First, I show the conditions neces-
sary for beamforming to achieve more transmissions than both direct and multi-hop
while using the same number of nodes. Then I show the number of transmissions
achieved using the proposed algorithm compared with one of the existing transmitter
scheduling algorithms.
Direct, Multi-hop, and Beamforming Transmissions
I first compare beamforming transmissions with direct and multi-hop transmis-
sions. In this section, I show the effects of transmission distance by varying Rd from
1000 to 5000m. Among the nodes that are deployed in the sensing area, five nodes
are selected as sensing nodes in each round. For all three transmission techniques,
the data collected by all sensing nodes are first aggregated, and the final data sent
to the base station have the same size. One round of transmission is considered as a
process from the time when the data are collected by the sensing nodes to the time
the aggregated data is successfully received by the base station. The N = 100 nodes
are deployed in the following three different ways.
1. Direct transmissions
N nodes are uniformly deployed in the sensing area. The data from all sensing
nodes are first collected by one node. This node aggregates the data, and then
sends the data directly to the base station using high power. In the simulation,
I choose to use the node with the highest remaining energy to both collect and
send data to the base station for each round.
2. Multi-hop transmissions
79
Among N = 100 nodes, 68 nodes are deployed in the sensing area, and 32 nodes
are deployed as relay nodes with equal distance between every two intermediate
hops. The reason that I select 32 nodes as relay nodes is as follows. For
multi-hop transmissions, the optimal distance between two adjacent hops is
d0 = β
√(PT0+PR0)×η
(1−21−β)ε[21]. Based on the energy model in Section 2.3.3, d0 is
approximately 155m. To reach a base station at 5000m away, 5000155≈ 32 hops
are required. To make a fair comparison, for Rd < 5000m, the same 32 nodes
are deployed with fewer hops, and the same hopping distance (i.e. 155m) is
used. For each simulation with different Rd, the relay nodes are deployed at
each hop such that the total energy of nodes at each hop is as balanced as
possible.
In each round of transmission, the data from all sensing nodes are first collected
and aggregated by the node with the highest remaining energy in the sensing
area. The aggregated data are then sent to the base station through relay nodes.
At each intermediate hop, the node with the highest remaining energy is used
to forward the data to the next hop in order to prolong the network lifetime.
3. Beamforming transmissions
Using EP , more than one transmitter should be selected for each round. In
this simulation, I set Gm = 20 when selecting the transmitters. The energy
consumed on each transmitter is divided by 10Gm/10. For each round, the sens-
ing nodes forward their data to the cluster head that is scheduled for the current
round, then the cluster head aggregates the data and broadcasts the aggregated
data to the other beamforming transmitters. Finally, the beamforming trans-
mitters send the aggregated data to the base station.
Figure 4.4 shows how the distance to the base station affects the number of trans-
missions with the use of three different methods where Rd = 1000, 2000, 3000, 4000,
and 5000m. Since the energy consumed due to a transmission increases quadratically
as the distance increases, using direct transmission, the number of transmissions re-
80
duces quadratically. Using multi-hop, every two intermediate hops are 155m away.
Since the total number of the relay nodes is fixed for all distances Rd, when Rd in-
creases, fewer nodes are deployed at each hop. Data can no longer be forwarded to the
base station once the nodes on one of these hops are energy-exhausted. Beamforming
uses multiple transmitters to create directional transmissions towards the receiver.
The energy consumed due to long distance transmissions is spread over multiple
transmitters. Hence, for large Rd, beamforming achieves more transmissions than
both direct transmission and multi-hop. However, because beamforming efficiency
e < 100%, due to both the phase differences of the transmitters and the fact that
data sharing consumes energy, beamforming achieves fewer transmissions when Rd is
less than 3000m. Using beamforming, the number of transmissions also reduces as Rd
increases. In Figure 4.4, the number of transmissions reduce by 16% (i.e. from 103540
to 93560). This is because the number of beamforming transmissions is affected by
multiple factors. If the number of transmitters is fixed, the energy consumed by each
transmitter increases quadratically as the transmission distance increases. However,
the scheduling algorithm selects the number of transmitters based on the distance,
i.e. more transmitters are selected for a longer distance. If the transmitted signals
are in-phase, the signal gain is enhanced quadratically with the number of transmit-
ters. Non-zero phase differences among the transmitters cause more transmitters to
be selected. Selecting more transmitters requires more transmissions on data sharing
and consumes more energy for each round.
Energy Phase Compared with Existing Work
In this section, I compare the proposed algorithm with the phase partition (PP)
algorithm, described in Section 2.1.2. I also introduce an improved phase partition
method (IPP) that assumes each node can use a lower transmit power to avoid the
over-transmitted power at the receiver. The network lifetime using EP is compared
with both the existing work phase partition (PP) and the improved phase partition
81
Fig. 4.4. When the distance to the base station is farther than 3000m,beamforming achieves more transmissions than direct and multi-hop.
Fig. 4.5. Number of beamforming transmissions increases with higherpercentages of energy exhausted nodes, ξ. Compared with PP, EPachieves 118% more transmissions.
82
Table 4.3List of Scenarios Compared in Figure 4.5 and the Ratio of P usingEP, IPP, and PP to the Upper Bound (i.e. 4522).
Algorithm P for ξ = 100 Ratio to the upper bound (i.e. 4522)
EP 3891 86%
IPP 2359 52%
PP 1782 39%
method (IPP). Compared with PP, IPP uses the same grouping technique, but it
allows multiple transmit power levels. Using IPP, the signal strength at the receiver
is estimated based on the number of transmitters, and the transmitters can adjust
their transmitting power accordingly. Hence, transmission coefficient, αik, of each
transmitter is a discrete number in range [0,1]. For example, if all nodes transmit
using Pmax, and the signal strength at the receiver is 4 times higher than G, then
each node reduces its transmission power level to Pmax4
. The over transmitted power
at the receiver can be reduced, and the energy is saved for later transmissions; there-
fore, network lifetime can be extended. In this chapter, to reduce the algorithm’s
complexity, it is assumed that using IPP, the transmission coefficients for the nodes
in the same group are adjusted to the same level, even though the remaining energy
of each node in the same group may not be the same. More details are explained in
Section 4.3.1.
For N = 100 nodes, I show the number of transmissions using following three
scheduling algorithms: EP, PP, or IPP with 8 power levels. The receiver is at a
far-field point on the x-axis (xd = 5000m, yd = 0). The receiver requires a minimum
signal gain, G, to be 20dB, i.e. the gain of radiated power at the receiver to be 100
times higher than using an individual transmitter. I use γ = 2π/6 in EP, 6 groups in
PP and IPP in comparisons. For PP with 6 groups, each group has about 100/6 ≈
16 nodes. The expected signal gain at the receiver is 162 × e ≈ 22 dB. Hence, I set
G = 20 dB for EP. All other parameters are the same as in Table 4.3.
83
A performance upper bound of the scheduling algorithm can be obtained by as-
suming that the phase differences of all signals at the receiver are zero. A math-
ematical equation for calculating the upper bound on the number of beamforming
transmissions is shown in Equation (4.11). For N = 100 nodes, if the energy of each
node is uniformly distributed in the range (0,1000]J, the expected sum of the total
energy contained in all nodes is 500× 100 = 50000J. If all nodes have zero phase dif-
ference, to achieve a minimum signal gain G = 20 dB at the receiver, 10 transmitters
are required (M = 10). If the size of the sensing area is L×L, the longest distance for
data sharing among the nodes is the diagonal of the sensing area√
2L. The distance
from the sensing area to the base station is Rd. The energy consumed by each round
includes the following: (1) 5×Etx(b,√
2L), S = 5 sensing nodes send their own data to
the cluster head; (2) 5×Erx(b)+Etx(b,√
2L), the cluster head collects one data packet
from each sensing node and sends one aggregated data packet to the beamforming
transmitters; and (3) M = 10 transmitters consume 10 × (Erx(b) + Etx(b, Rd,GmG
)),
each beamforming transmitter receives one data packet from the cluster head and
sends it to the base station collaboratively.
Emean ·N10× (Erx(b) + Etx(b, Rd,
GmG
)) + 5× Erx(b) + Etx(b,√
2L) + 5× Etx(b,√
2L)= 4522
(4.11)
Figure 4.5 shows the number of successful beamforming transmissions (i.e. Ga ≥
Gm) versus the percentage of energy-exhausted nodes. A better algorithm can provide
a longer network lifetime for a given ξ. Table 4.3 lists the network lifetime at ξ% =
100% using three scheduling algorithm and the ratio to the upper bound of P . The
simulation results show that in all scenarios, EP achieves nearly 90% network lifetime
compared with the upper bound. Compared with PP and IPP, EP extends the
network lifetime by 118% and 56%.
84
Improved PP with Multiple Power Levels (IPP)
In this section, I improve phase partition by assuming each node can use a lower
transmit power to avoid over-transmitted power at the receiver. The network lifetime
using this improved phase partition method (IPP ) is then compared with PP and
EP . By allowing multiple transmitting power levels, the normalized transmitting
power (i.e. transmission coefficient, αik) of each transmitter is a discrete number
in range [0,1]. CC1000 RF transceiver [22] is commonly used in MICAz and other
popular nodes. CC1000 offers eight discrete RF power levels. Hence, αik is discrete
in [0, 1] with evenly divided eight levels. Improved PP (IPP ) calculates the total
phase difference of the transmitted signal from each node at the receiver, and then
groups nodes based on their phase differences. IPP estimates the signal strength at
the receiver based on the number of nodes that still have energy for transmissions
in the currently selected group, and adjust the transmit power. For example, if all
nodes transmit using Pmax, and the signal strength at the receiver is 4 times higher
than Gm, then each node reduces its transmission power level to Pmax2
. The over
transmitted power at the receiver can be reduced, and the energy is saved for later
transmissions; therefore, network lifetime can be extended. To reduce the algorithm’s
complexity, I assume that using IPP , the transmission coefficients for the nodes in
the same group are adjusted to the same level, even though the remaining energy of
each node in the same group may not be the same.
Network Lifetime
For N=100 nodes, I consider six scenarios with two factors: (1) scheduling algo-
rithm, EP , PP , or IPP with eight power levels; (2) distribution of initial energy Ei,
Ei = Emax for all nodes or Ei is uniformly random distributed in range (0, Emax].
All scenarios are listed in Table 4.4. The receiver is at a far-field point on the x-
axis, Rd = 3000m. At each round, 5% of the total available nodes are sensing, i.e.
S = N × 5%. The receiver requires the minimum signal gain, Gm, to be 20dB, i.e.
85
Fig. 4.6. Network lifetime, P , increases as higher percentages of en-ergy exhausted nodes, ξ. N = 100, L = 100 m, and d = 3000m.
86
Table 4.4Network lifetime P using EP, IPP, and PP
Cases Algorithm Ei (J) P for η = 100
A1 EP Emax 22442
A2 IPP Emax 22117
A3 PP Emax 14865
B1 EP (0, Emax] 10929
B2 IPP (0, Emax] 6920
B3 PP (0, Emax] 5575
the gain of radiated power at the receiver will be 100 times higher than using an
individual transmitter. Since the radiation power is proportional to the square of the
amplitude of the radio wave, Gm = 20dB requires 10 transmitters if they have no
phase difference. I use γ = 2π/6 in EP , six groups in PP and IPP in comparisons.
Figures 4.6 shows the number of successful beamforming transmissions (i.e. Ga ≥
Gm) versus the percentage of battery-exhausted nodes. A better algorithm can pro-
vide a longer network lifetime for a given ξ. In Figure 4.6, the six lines from the top
to the bottom show the network lifetime P with ξ changes in scenarios A1-A3 and
B1-B3. From this figure, we see that EP extends the network lifetime by at least
50% compared with PP . This is because phase partition divides transmitters into
groups without considering their remaining energy. Transmitters in the same group
participate the same number of transmissions. However, their initial energy may be
different, e.g. in scenarios B3. Since nodes in the same group carry different amounts
of initial energy, after some rounds of transmission, nodes with low initial energy be-
come energy-exhausted. In B3, the number of energy-exhausted transmitters grows as
the number of transmissions increases for ξ% ≤ 50%. When ξ% > 50%, P saturates.
This is because after many transmissions, too many nodes become energy-exhausted
in some groups, and the signals from these groups are too weak for the receiver.
When this happens, P becomes a constant as ξ increases. When the initial carried
87
energy for all nodes is the same, this problem does not occur. As shown in scenarios
A3, Ei = 1000J, using PP , all sensor nodes deplete their energy almost at the same
time. However, if the number of nodes in a group is more than necessary, the signal
strength at the receiver is higher than the requirement and energy is wasted. The
network lifetime can be further extend by reducing over-transmitted power.
Compared with PP , IPP reduces the over-transmitted power. With a small
enough step-size (e.g. 1/8 in these simulations), the gain of the signal at the receiver
can be adjusted to meet the required signal gain. In Figure 4.6, IPP prolongs the
network lifetime by 49% in scenarios A2 compared with PP . In scenarios B2, using
IPP , nodes in the same group may not have the same amount of initial energy, but
the same number of transmissions are assigned to these nodes. As k increases, nodes
with low initial energy become energy-exhausted. This means that the number of
available nodes in some groups is too small to achieve beamforming transmissions
and reach the receiver, even though some nodes still have large amounts of remaining
energy. Therefore, IPP cannot significantly extend network lifetime when the initial
energy in each node is random.
Different from PP and IPP , EP gives higher priorities to the nodes with more
remaining energy, and the energy consumption is balanced among all nodes. There-
fore, regardless of the condition of initial carried energy, all nodes start to deplete
their energy at approximately the same time. In scenarios B1, the initial energy in
all nodes is between 0 and 1000J; in scenarios A1, Ei = 1000J for all nodes. EP
schedules transmissions to the nodes with higher remaining energy. As a result, the
network lifetime is almost a constant as the number of energy-exhausted nodes in-
creases. Compared to PP , EP (scenario A1) has larger P ’s because EP reduces the
over-transmitted power by using only the necessary number of transmitters. Since
IPP reduces the transmitting power, it achieves the same network lifetime as EP .
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4.3.2 Network Lifetime
In Section 4.2.2, I show that as the deployment area increases, the energy con-
sumed due to data sharing increases. In this section, I show that multi-cluster schedul-
ing algorithm achieve more transmissions than single cluster scheduling algorithm
when the deployment area is large. When the receiver is located at Rd = 5000m, the
deployment side length is changed from L = 100m to 1000m. Figure 4.7 shows the
number of beamforming transmissions when L = 100, 300, 500, and 1000m, respec-
tively. The deployment area is equally divided into four clusters, C = 2 × 2 = 4 for
multi-cluster transmitter scheduling algorithm.
In Figure 4.7, we can see that when the deployment area is small, single-cluster
scheduler performs better than multi-cluster scheduler. As L increases, the number
of beamforming transmissions using single-cluster scheduler decreases rapidly, and
both multi-cluster schedulers achieve more transmissions than single-cluster sched-
uler. Using both multi-cluster schedulers, nodes are divided into clusters, so the
phase differences between the selected transmitters are usually larger compared with
selecting the transmitters using single-cluster scheduler. This is because transmitters
selected using multi-cluster schedulers for each round are restricted to the nodes that
are in the same cluster. When L increases, single-cluster scheduler consumes more
energy due to data sharing because the transmitters are far away from each other.
Using both multi-cluster schedulers, selected transmitters are closer to each other.
Thus, less energy is consumed due to sending the data to the transmitters. The
number of transmissions achieved using multi-cluster energy balancing scheduler is
less than using multi-cluster energy saving scheduler in Figure 4.7. This is because
multi-cluster energy saving scheduler choose the geometric center cluster as the data
gathering cluster. Therefore, the energy consumed due to data forwarding is less than
in multi-cluster energy balancing scheduler.
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Fig. 4.7. Both Multi-cluster schedulers achieve more beamformingtransmissions than single-cluster scheduler when L increases. Thenetwork lifetime in this figure is averaged by 10 random deploymentswith N = 100 node for each deployment.
90
Fig. 4.8. Maximum number of beamforming transmissions with different γ.
4.3.3 Sensitivity Analysis of Single-Cluster Scheduler
This section analyzes the effects of the following parameters: (1) rotating degree
γ, (2) phase uncertainties, and (3) the impact on the number of sensing nodes to the
number of beamforming transmissions, i.e. network lifetime.
Rotating Degree γ
Section 4.2.1 uses γ to rotate the reference phase after each transmission so that
nodes with different phases take turns to send data. Since cosine is a periodic function
for every 2π, and symmetric within 2π, I select γ in the range of (0, π]. Figure 4.8
shows the network lifetime when γ = π/50, π/20, π/10, π/5, π/3, and π/2. When γ is
too large (e.g. π/2), the network lifetime is shortened. For example, when γ = π, the
network lifetime reduces by 36%, compared with γ = π/50. This shows that γ cannot
be too big. When γ = π/50, π/20, π/10, π/5, or π/3, the number of beamforming
transmissions has little variation. The simulation suggests that the value of γ has
little effect on the energy distribution as long as γ is less than π/3.
91
(a)
(b)
Fig. 4.9. For 100 nodes, phase uncertainties are randomly generated.Beamforming efficiency is averaged by 50 trials. (a) Beamformingefficiency vs phase uncertainty. (b) With the raised threshold, moretransmissions become successful.
Phase Uncertainty
So far, it is assumed that the location and the phase offset of each node is known.
Arrival phases of the transmitted signals at the receiver are estimated based on both
the distance from the transmitter to the receiver and the initial phase offsets. This
section examines the situation when the phase of each node is uncertain. Phase uncer-
tainties can be caused by several factors, such as (1) the location uncertainty, and (2)
time and frequency synchronization error. The uncertainty makes the actual trans-
mitted signal phase different from the estimation and may reduce signal strength.
92
To compensate the uncertainties, I adjust the estimation based on beamforming effi-
ciency. The efficiency is the ratio of the estimated achieved signal strength, and the
highest possible signal strength when the maximum phase uncertainty of all nodes
is known [19]. Figure 4.9(a) shows both amplitude and power when phases are un-
certain. At point A, the maximum phase uncertainty is π/3 (i.e. all 100 nodes have
phase uncertainties in the range of [0, π/3]). The actual transmitted signal strength
at this point is roughly 67% compared with the signal strength when the phases have
no uncertainty.
In Figure 4.9(b), the top line shows the maximum number of transmissions when
there is no phase uncertainty. The bottom line is the number of transmissions that
can be successfully received when the estimated phase is uncertain. As the phase
uncertainty increases, the total number of successful transmissions decreases. When
the phase uncertainty is greater than 2.7 rad, there is almost no successful transmis-
sion. To compensate for the phase uncertainties, I adjust the transmitter selecting
threshold Gm based on beamforming efficiency. According to Figure 4.9(a), the signal
strength at the receiver would be e · Gm, where e is the corresponding beamforming
efficiency for the given phase uncertainty. The threshold on selecting nodes for each
round of transmission is raised from Gm to Gm/e so that more nodes are selected in
each transmission. With the raised threshold, the number of successful transmissions
increases, as shown in Figure 4.9(b).
When the phase uncertainties are large, communications among transmitters can
be used to estimate the phase differences. Adopting the phase estimation method
in [20], the phase differences between each transmitter and the base station can be
estimated by the following procedures. First, the base station sends beacon messages
to specify the carrier frequency. Second, the master node exchanges synchronization
packets with each transmitter. Finally, the base station sends another message using
beamforming frequency, and all transmitters retrieve their own phase differences.
If the frequency is assumed to be synchronized among all the nodes and the base
station, Figure 4.10(a) shows the relationship between the number of synchronization
93
(a) (b)
Fig. 4.10. I adopt an existing phase estimation method [20] to re-duce the phase uncertainties. (a) The phase uncertainty reduces asthe number of transmissions for phase estimation increases, i.e. morepackets exchanges between the master node and each beamformingtransmitter. (b) The network lifetime is reduced due to energy con-sumption on phase estimation.
packets and the reduced phase uncertainties. Adopting this phase estimation method,
Figure 4.10(b) shows how the number of synchronization communications affects the
network lifetime. According to simulation, we can see that the energy consumed on
phase estimation has negligible effect on network lifetime.
Number of Sensing Nodes
In the previous sections, I assume the number of sensing nodes are 5%, and in this
section, I examine how the number of sensing nodes affect the number of beamforming
transmissions. Considering the same deployment setting as in Table 4.2, Table 4.5
shows the network lifetime P (i.e. maximum number of beamforming transmissions)
using EP when the number of sensing nodes S changes from 5% to 30%. When
more sensing nodes are used in each round, the network lifetime reduces. This is
because when using more sensing nodes, more raw data are collected at each round.
Hence, more transmissions are required for data sharing between the sensing nodes
and the transmitters. However, since the side length of the deployment area (i.e.
L = 50m) is small compared to the distance to the base station (i.e. Rd = 5000m),
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Table 4.5Network lifetime for different number of sensing nodes
S P Reduction Compared with S = 5%
5% 151924 0
10% 151767 0.1%
15% 151435 0.3%
20% 151210 0.5%
25% 151061 0.6%
30% 150878 0.7%
the energy consumed by data sharing has little effect on the number of beamforming
transmissions. As we seen in Table 4.5, the network lifetime reduces by less than 1%
when the number of sensing nodes increases from 5% (i.e. S/N = 5/100) to 30%.
4.3.4 Sensitivity Analysis of Multi-Cluster Scheduler
In this section, I analyze the performance of two multi-cluster schedulers respect-
ing to different number of the clusters.
As I mentioned in Section 4.2.2, the cluster size has to be chosen based on the
size of the sensing area and the total number of nodes. To study how cluster size
affects the number of beamforming transmissions, I consider the following deployment.
Assuming that 100 nodes are deployed in an area of A = 10002m2 with the receiver
located 5000 m away. Figure 4.11 shows the maximum number of beamforming
transmissions when the same deployment is divided into different number of clusters.
In Figure 4.11, for the same deployment, the number of transmissions increases
when C increases from 1 to 4 (i.e. 2 × 2). When the distances between the nodes
in the same cluster are shorter, less energy is consumed on gathering the data from
the sensing nodes to the cluster heads. When C further increases, i.e C=4 × 4 or
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Fig. 4.11. With 100 nodes deployed in area A = 10002meter2, thenumber of beamforming transmissions with the number of clusters Cincreases from 1 to 25.
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Fig. 4.12. Transmitter setup in the outdoor experiments.
Fig. 4.13. Receiving antenna in outdoor experiments.
5 × 5, each cluster contains too few nodes to form beamforming transmissions and
the number of transmissions drops rapidly.
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4.3.5 Validation
We designed a testbed and performed outdoor experiments with 20 randomly
deployed transmitters. Figure 4.12 and 4.13 show the setup of the transmitters and
the receiver in the outdoor experiments. The transmitters are divided into four groups
based on their locations; nodes in the same group have maximum phase difference less
than π/4. Figure 4.14 shows the selected transmitters in each group. Since the node
locations are random, the number of the nodes in each group may be different. Based
on their locations, groups one to four have 3, 7, 5, and 5 nodes respectively. Figure
4.14 show the deployments and radiation patterns of all groups. The measurements
match the theoretical prediction of the radiation pattern and validate our simulator.
These experiments were conducted in an empty soccer field. We use 27MHz as the
carrier frequency (λ ≈11m). All antennae are connected to the same signal source
through grounded coaxial cables. This setup ensures that the signal into each cable
is in phase and has the same frequency. We measured the radiation patterns and
compared them with the simulation results. The received power was measured and
recorded by a power spectrum analyzer. The transmitters are approximately 90m
away from the receiver.
Figure 4.14(a) and 4.14(b) show the transmitter locations in group one and two.
Figure 4.14(c) and 4.14(d) show the expected radiation patterns for each group. In
the experiments, we measured the signal strength only in the second quadrant (φd =
[π/2, π]), shown as in Figure 4.14(e) and 4.14(f). For each group, we measure the
signal strength at 11 locations using a power spectrum analyzer. In these figures,
the data show similar radiation patterns as the simulations. For example, in Figure
4.14(e), simulation shows three nulls at 120◦, 140◦, and 170◦, with the highest peak
point at 90◦. Our measurement shows two nulls at around 120◦ and 140◦ with the
highest peak at 90◦. We missed the null at 170◦ because of the errors in the location
of the sample points. In Figures 4.14(f), our measured radiation pattern also show
the same number of peaks and nulls with a few degrees shift. The error may arise
98
radius = 3.5 λorigin (0,0)
(a)
radius = 3.5 λorigin (0,0)
(b)
-20dB
-10dB
0dB
30
210
60
240
90
270
120
300
150
330
180 0
(c)
-40dB
-20dB
0dB
30
210
60
240
90
270
120
300
150
330
180 0
(d)
(e) (f)
Fig. 4.14. (a)-(b) Transmitters’ locations (i.e. black dots) in a cir-cle of radius = 3.5λ. White dots indicates the nodes that are nottransmitting. (c)-(d) Simulated radiation patterns, signal strengthin each angle is normalized to the maximum signal strength. (e)-(f)Measurements compared with simulations.
due to the following reasons. (1) The locations of the transmitters and the receiver
are not precise. The maximum error in distance is 0.5m. (2) Another possibility is
that the radiated signal from each transmitter has a small phase difference.
99
Setting up an outdoor experiment to validate the simulations is not trivial. There
are several factors we discovered. (1) The receiver needs to be far away from the
transmitters and the signal source to eliminate near field interference. The frequency
we used in this experiment is 27MHz, a reserved ISM radio band. The wavelength
is about 11.1m; hence, we choose 90m to be the distance from the signal source to
the receiver, i.e. approximately eight times of the wavelength. (2) Transmitters are
randomly distributed in the circle, but in order to avoid the interference of the trans-
mitters, every two transmitters can not be placed closer than 1/4 of the wavelength.
(3) Our experiments were conducted on an open field to eliminate the interference
caused by metals, humans, and cables. A country road is about 10m aways from one
of the sample points. We found that whenever a car on the road was passing through,
our received signal was enhanced due to reflection. We also found that with a human
standing close to the receiving antenna, the signal was enhanced by roughly 2dB. The
receiving signals were distorted when we were initially using several long power cables
to power the receiver, even though the cables were coated with plastic rubber and
laid on the ground. To eliminate the above interferences, we used a digital camera
with automatic delay function to capture the signal strength when there is no human
or car close to the receiving antenna. We removed the power cables and used an
uninterruptible power supply for the receiving antenna and transmitters separately.
4.3.6 Discussion
In Section 4.2, I propose a method to schedule beamforming transmitters to extend
network lifetime. In the above sections, I use a network with 100 nodes as an example
to analyze the performance of the scheduling algorithm. For a larger scale sensor
network, the following practical issues will need to be considered:
1. Finding the optimal number of transmitters to achieve the most energy effi-
cient beamforming transmissions. If all nodes are deployed in a small area,
the scheduling algorithm selects transmitters with higher remaining energy and
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smaller phase differences. When a lager number of nodes are deployed, more
nodes with high energy and small phase offsets are available at each round
of scheduling. The number of nodes selected for each round of beamforming
should be optimized. This is because selecting more nodes with small phase
differences to transmit to same distance consumes less energy on each transmit-
ter. However, when more nodes are selected, more energy is consumed on data
sharing.
2. Reduce the energy consumed on data forwarding among clusters. If nodes
are deployed in a large area, significant amounts of energy may be consumed
on forwarding the data from each sensing cluster to the beamforming cluster.
Selecting sensing nodes and scheduling beamforming transmitters need to be
combined to ensure that the transmitters are close to the sensing nodes.
3. Re-schedule the transmitters to exclude the faulty nodes. As the number of
nodes increases, fault tolerance will become an important consideration for
beamforming. The proposed technique selects just the sufficient number of
nodes to achieve the required signal strength at the receiver (while accounting
for uncertainties in phase), in order to save power and extend network lifetime.
For large scale networks, this work would need to incorporate fault tolerance
by using probabilistic models that account for a certain threshold in terms of
node failures. These models would need to account for failures based on a com-
bination of metrics, including the spatial location of the nodes, the probability
of failures at the node and cluster level, and potentially, real-time metrics that
can dynamically increase or decrease these probabilities.
4.4 Summary
In this chapter, I propose a beamforming transmitter scheduling algorithm to
prolong the network lifetime. The proposed algorithm schedules the transmitters
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based on the nodes’ phase offsets, remaining energy, and locations. By reducing the
energy consumed on data sharing, the proposed scheduling algorithm further prolongs
the network lifetime. I also show that beamforming achieves more transmissions than
direct and multi-hop transmissions, when the receiver is far away from the sensing
area. We perform outdoor experiments and show that signal strength can be enhanced
by properly selecting the beamforming transmitters.
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5. COLLABORATIVE BEAMFORMING IN MULTI-HOP
TRANSMISSIONS
Multi-hop transmission and collaborative beamforming are the most commonly con-
sidered transmission methods in wireless sensor networks. Beamforming outperforms
other transmission methods by extending the transmission range while consuming
less energy. In this chapter, I discuss an application of collaborative beamforming in
multi-hop transmission to extend the transmission range between hops.
Existing research on multi-hop transmissions focuses on finding and locating relay
nodes to reduce the overall transmission distance or energy consumption, and balance
the workload to extend network lifetime. Wang et al. [21] show the optimal distance
between every two hops, while considering the overall energy consumption. Current
circuit design limits the maximum distance that each node can transmit [22]. Relay
nodes need to be deployed, within the range that one node can reach in multi-hop
transmissions. However, in some scenarios, relay nodes at certain distances may not
be available, due to many reasons. (1) Due to complex terrain, some regions in the
deployment area make relay node placement difficult. For example, if the deployment
area involves rivers and mountains, nodes may need to be deployed farther away
from each other. (2) The deployment location contains some regions that would be
ideal for placing nodes in a more condensed fashion. For example, there exist several
regions of dense deployment, but they are far apart. More nodes would like to be
deployed closely in these regions, and fewer nodes can be used as relay nodes. In
these scenarios, extending the distance between every two hops is important. In this
chapter, I present a method that uses beamforming to extend the distance between
every two hops in multi-hop transmissions.
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Fig. 5.1. A sample deployment with N = 50 nodes.
Section 5.1 explains the setup of our system. Section 5.2 describes the problem
that is solved in this chapter in details. Section 5.3 explains the procedure of our
proposed transmission method. Section 5.4 analyzes energy consumption and shows
the simulation results. Finally, in Section 5.5, I discuss potential solutions to reduce
the energy consumption.
5.1 System Setup
In this chapter, I assume that N nodes are randomly deployed in a sensing area
with side length L meters, and the base station is located outside the sensing area.
An example with N = 50 is shown in Figure 5.1. The data collected by the nodes in
the sensing area need to be sent to the base station. To reduce energy consumption
when the deployment area is large, data are sent from the sensing nodes to the base
station through multiple hops. All antennae are omni-directional.
We assume that each node has a maximum transmission range determined by
the maximum power for transmission. Typically, a node has a transmission range of
100− 300m [22]. Nodes can adjust their transmit power based on the desired range.
We assume that each symbol contains Q bits, and the channel is stationary.
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Table 5.1Symbols used in Chapter 5
Parameter Symbol Unit
Frequency drift of node i fi kHz
Frequency difference ∆f kHz
Number of symbol in each data packet Q bits
Symbol duration Ts ms
Additive noise ω
Phase offset of node i φi rad
Single node transmission data rate Rsn kbps
Sweeping beam transmission data rate Rsb kbps
Energy consumed at each hop using single node Esn mJ
Energy consumed at each hop using sweeping beam Esb mJ
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5.2 Problem Description
Equation (5.1) shows the baseband signal at the receiver, when two nodes (i.e.
Node A and B) transmit simultaneously. Here, q ∈ [1...Q] represents the symbol in the
data packet that is transmitted, hi denotes the complex channel gain from transmitter
i ∈ A,B to the receiver, Ts is the symbol duration, φi denotes the phase offset of node
i, and ω is the additive noise at the receiver. The average power of the additive noise
per symbol is E[ω[q]ω[q]∗] = N0. Frequency drift for each node i is represented using
fi, where fi has a mean E[fi] = 0, a standard deviation σ =√
E[f 2i ] = fc · 20ppm,
and fc is the carrier frequency.
r[q] =
A,B∑i
hie{j2πqTsfi+φi}x[q] + ω[q]
= x[q] + ω[q]
(5.1)
Equation (5.2) shows the signal strength at the receiver for symbol q.
|x[q]|2 = |hA|2 + |hB|2
+2|hA||hB|cos(2πqTsfA + φA − 2πqTsfB − φB)(5.2)
Let φi ≡ 2πqTsfi + φi and |hA| = |hB|, as derived in [48]. The condition for two
signals from two nodes to be aligned at the receiver can be derived as:
Pr(x[q] = 2a) = Pr(cos(φA − φB) = a) (5.3)
Here, 0 < a ≤ 1 is defined as the alignment degree of the two signals. For two
transmitters, if φA 6= φB, the condition for the signal to be in-phase at the next hop
(a = 1) is fA 6= fB.
We know that with two nodes, if the frequency drifts are different, the beam will
be formed. However, without knowledge of the phase offsets, the location of the
beam at any time instance will be unknown. Hence, to ensure that the beam can be
detected by the receiving node at the next hop, each bit needs to be transmitted for
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a duration equal to the full circle sweep time of a beam. In the following section, I
explain our method in detail and I compare the energy consumption for our method
with one using a single node at each hop.
5.3 Beamforming in Multihop
When two transmitting nodes have different frequency drift, the transmission
beam forms and rotates in a 2D plan. Since the beam is rotating, the time dura-
tion that a beam stays in one direction may be too short for the receiver to decode
the symbol. However, the receiver can detect each bit based on the signal strength
(i.e. peak power) of the rotating beam. In other words, at the receiver, each bit is
determined based on whether a high enough signal is detected within a time frame
(i.e. time for the beam to sweep a full circle). Let us call the time for the beam to
rotate a full circle as rotation duration. If a high bit (i.e. bit “1”) is transmitted, the
receiver would detect a high beam sweeping through within one rotation duration.
On the other hand, if a low bit (i.e. bit “0”) is transmitted, the receiver would not be
able to detect a beam in the same time duration. Hence, based on the existence of a
high beam within a time frame, the transmitted bit can be detected at the receiver.
This time frame can be determined based on the frequency difference between the
two transmitters. In Section 5.4.1, I discuss more about the frequency differences.
Equation (5.2) in Section 5.2 shows the signal strength at the receiver with two
transmitters, A and B. When fA = fB and φA 6= φB, the phase difference of the
two transmitted signals is constant over time. If the phase and frequency offsets are
different by ∆f = fB − fA and φ = φB − φA, the two waves become in-phase after
φ2π∆f
seconds, and the in-phase transmission appears every 1∆f
seconds.
When the beam is pointing in the intended direction (i.e. towards the base sta-
tion), the distance to the next hop can be extended by two times with two nodes.
Hence, when sending the data to the same base station, fewer hops can be used, and
less energy may be consumed. However, the transmission bit rate cannot be higher
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than the beam sweeping frequency, a longer transmission time is required, and more
energy may be consumed. In the following, I analyze the energy consumption for this
method in detail. We use the energy consumed on multi-hop transmissions with a
single node at each hop (i.e. single node transmission) as the base line in the com-
parison, although the bit detection method I used in this chapter is different from the
method used in a single node transmission.
Based on the energy model in Section 2.3.3, energy consumed on one transmitter
sending b bytes of data to distance d (i.e. to the next hop) without using sweeping
beam method can be expressed as equation (5.4).
Esn(d) = (PT (d) + PR) · b
Rsn
(5.4)
To transmit the same distance d using sweeping beam method with two nodes,
the total energy is expressed in equation (5.5). Due to constraints such as signal-
noise-ratio and transceiver circuit design limitations, Rsn is the data rate for single
node multi-hop transmission. As I mentioned earlier, using sweeping beam, the data
rate needs to be low enough so that the beam sweeps at least one full circle for each
bit. Hence, the data rate for sweeping beam is Rsb = min(Rsn,∆f).
Esb(d) =2 · (PT (d/2) + PR) · b
Rsb
(5.5)
The energy consumption difference, Esb(d) − Esn(d) with different parameters is
simulated and analyzed in the following sections.
5.4 Simulation and Analysis
In this section, I analyze the energy consumption with different sweeping frequen-
cies (∆f) and data rate (Rsn). The simulation results show (1) the minimum required
sweeping frequency for our proposed method to save energy compared with a single
node transmission, (2) the energy consumption for different bit rates, when the sweep-
ing frequency is the same as the single node bit rate (i.e. ∆f = Rsn), and (3) the
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energy consumption for different sweeping frequencies, when the sweeping frequency
is less than the single node bit rate (i.e. ∆f = Rsn). Using multi-hop transmis-
sions with single node at each hop (i.e. single node transmission), the symbol rate
Ts = 1/Rsb.
5.4.1 Minimum Frequency Difference
Rsb
Rsn
=2(PT (d/2) + PR)
PT (d) + PR(5.6)
Based on equations (5.4) and (5.5), we can find the minimum frequency difference
∆fmin for beamforming to consume the same amount of energy as a single node
transmission, i.e. Esb(d) = Esn(d). This is derived as in equation (5.6). Figure 5.2
shows the ratio of the minimum required data rate (Rsb) over the single node data rate
(Rsn) for different transmission distances. Here the transmission distance refers to
the distance between every two hops in single node multi-hop transmission (i.e. d in
equations (5.4) and (5.5)). Using sweeping beam, data cannot be sent with a data rate
higher than Rsn, i.e. Rsb ≤ Rsn. In Figure 5.2, it can be seen that for any data rate
(Rsb), the minimum distance to the next hop needs to be 155 meters for beamforming
to consume the same amount of energy. According to Figure 5.2, for beamforming to
save energy, a higher frequency is required when there is a shorter distance between
hops. This is because, compared with using a single node to transmit d meters, the
sweeping beam enhance the signal strength with the use of constructive interference.
Figure 5.3 shows the energy consumption difference (Esb(d) − Esn(d)) for trans-
mitting one data packet (i.e. 133 bytes) at one hop using single node and sweeping
beam, respectively. When the sweeping frequency is the same as the original data
rate (i.e. Rsb = ∆f and ∆f = Rsn), the energy consumption difference is larger with
a lower data rate. Since Rsb ≤ Rsn is always required, this figure shows the maximum
energy saving that can be achieved using sweeping beam compared with transmitting
using a single node at each hop, for a given Rsn. From this figure, it can be seen that
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Fig. 5.2. The required minimum data rate Rsb decreases as the trans-mission distance increases. Regardless of the data rate Rsn, the trans-mission distance needs to be longer than 155m for sweeping beamwith two nodes to consume no more energy than traditional singlenode transmission.
110
Fig. 5.3. The energy consumption difference using sweeping beam andsingle node, with different transmission distance when Rsn = Rsb.
Fig. 5.4. Energy consumption difference using sweeping beam andsingle node, when Rsb 6= Rsn.
when Rsn is low, using the beam with high sweeping frequency saves more energy
and this requires better receiver.
5.4.2 Energy Consumptions with Different Sweeping Frequencies
When Rsb 6= Rsn (i.e. ∆f 6= Rsn), Figure 5.4 shows how the energy saving
(Esb(d)−Esn(d)) varies with different sweeping frequencies. In this simulation, data
rate for single node transmission Rsn = 76kbps is used. This is the data rate proposed
in the third energy model [21] in Section 2.3.2. The frequency skew is ±20ppm of
111
the carrier frequency. For example, if two nodes transmit at 2.4GHz, the maximum
frequency difference ∆f is 96kHz. With a different carrier frequency and a frequency
skew present, the frequency difference between two transmitters can be different.
With a lower sweeping frequency, more energy is consumed by the proposed method.
For example, the energy saving with ∆f = 50kHz is less than the energy saving
with ∆f = 60kHz at d = 400m. Hence, to reduce the energy consumption, a higher
sweeping frequency is desired. However, the sweeping frequency does not need to be
higher than Rsn. When ∆f ≥ Rsn, the data rate for sweeping beam is bounded by
Rsn and no more energy can be saved with the use of a higher frequency difference.
Hence, the sweeping frequency needs to be close to Rsn to save energy.
5.5 Discussion
5.5.1 Frequency Separation
Section 5.4.2 shows that with a larger ∆f between the two transmitters at the
same hop, less energy is consumed. Typical sensor nodes have frequency drift in the
range of ±20 ppm of the carrier frequency. For any pair of nodes, the frequency
difference caused by frequency drift fall in the range of 0 to 40ppm of the carrier
frequency. For example, for a carrier frequency that equals 2.4GHz, the maximum
frequency difference between two nodes is 96kHz. Using a higher carrier frequency
can increase the maximum frequency difference. Another way to ensure the frequency
difference between two transmitting nodes is to assign different carrier frequencies to
the collaborating nodes. For example, two nodes transmit at 2.405GHz and 2.410GHz,
respectively.
5.5.2 Error Tolerance
In Section 5.3, I suggest that the receiver can determine each transmitted bit
based on the existence of a beam in a time frame. However, the receiver may miss a
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signal if only one beam signal is used to determine each bit in a time frame due to
additive noise and other possible interferences. Hence, more high beam signals in the
same time frame could be used for detecting each bit. This implies that the frequency
drift needs to be much higher. Re-writing equation (5.5) for k beams to be detected
for each bit, to reduce the energy consumption, the sweeping frequency needs to be
k times higher, since Rsb = min(R,∆f/k).
5.6 Summary
In this chapter, I present a method to combine beamforming in multi-hop trans-
missions. My method uses beamforming to extend the transmission range between
hops. To address the practical challenges in achieving beamforming, i.e. frequency
synchronization and phase knowledge, the proposed method uses frequency drifts of
the nodes to form transmission beam. The proposed method requires a new mod-
ulation scheme and a sensitive receiver. In this chapter, I also analyze the energy
consumption of this proposed method and compare it with the standard single node
multi-hop transmissions.
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6. CONCLUSION
In this dissertation, I analyze the energy consumption overhead in pre-beamforming
preparations. I show that a minimum amount of data need to be sent using beamform-
ing to compensate for the energy consumed on phase alignment that uses a random
walk algorithm. The minimum transmitted data size can be decided based on the
total number of nodes and the selected beamforming efficiency. Using the transmit-
ter selection method, the energy consumption overhead on aligning the phases can be
eliminated, but the energy consumption for data sharing still exist. I presented the
procedures for data sharing when multiple sensing nodes and transmitters are used
in each round of beamforming. I show that beamforming saves energy across the
network when compared to direct transmissions, if the base station is far away. This
saving even takes into account the data sharing energy overhead. Energy consumed
on data sharing has negligible effect on the network lifetime of beamforming, when
the transmitters are close to each other.
I present a beamforming transmitter scheduling algorithm that is adaptive to the
size of the deployment area. For a network within a small sensing area, I propose
to schedule the transmitters based on their phase differences and remaining energy.
Compared to existing work, the proposed algorithm in this dissertation prolongs
the network lifetime by 60%, even in the worst case. When the size of the sensing
area increases, the distance between the transmitters needs to be considered, since a
huge amount of energy will be consumed by data sharing if the transmitters are far
away. We show that network lifetime can be enhanced by dividing the nodes into
clusters and selecting one cluster at a time to perform each round of beamforming
transmission. By reducing the energy consumed for data sharing, the scheduling
algorithm triples the network lifetime compared with the single-cluster scheduling
114
algorithm. I also show beamforming achieves more transmissions than direct and
multi-hop transmissions, when the receiver is far away from the sensing area. I
performed outdoor experiments and show that signal strength can be enhanced by
selecting the beamforming transmitters.
I also present a method to apply beamforming to multi-hop transmissions. This
method uses beamforming to extends the transmission range between hops. Without
frequency or phase synchronizations, the frequency drifts of the nodes are used to
form the transmission beam. I analyze the energy consumption of this proposed
method and compare it with the standard single node multi-hop transmission. I find
the energy consumption using sweeping beam is related to the data rate in single node
transmission and the frequency difference between two beamforming transmitters. I
find that when the data rate in the single node transmission is low, using sweep beam
with high sweeping frequency, more energy is saved.
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115
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