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DEGREE PROGRAM IN WIRELESS COMMUNICATION ENGINEERING
MASTER’S THESIS
UNDERSTANDING THE IMPACT OF SPATIAL
REUSE ON AUTONOMOUS SENSING ORDER
CHANNEL SELECTION
Author Akmal Sultan
Supervisor Adjunct Professor (Docent) Janne Lehtomaki
Second Examiner D.Sc. (Tech.) Zaheer Khan
November, 2016
A. Sultan (2016) Understanding the Impact of Spatial Reuse on Autonomous
Sensing Order Channel Selection. University of Oulu, Department of Communica-
tions Engineering, Degree Program in Wireless Communications Engineering. Mas-
ter’s thesis, 44 p.
ABSTRACT
In wireless communication systems, there is a need to design efficient schemes in
order to overcome the problem of spectrum scarcity. One technology to address
the problem of spectrum scarcity is cognitive radio (CR), in which a network
entity is able to adapt intelligently to the environment through observation, ex-
ploration and learning.
When multiple autonomous cognitive radios are searching for spectrum oppor-
tunities, they face competition from each other in order to access the available
free channel. This will result in reduced throughput which occurs due to collision
between cognitive radios, when they try to transmit in the same channel.
The purpose of this thesis is to study a smart adaptation scheme for efficient
channel access which enable autonomous cognitive radios to improve their overall
bandwidth efficiency in a distributed cognitive radio network with the help of
spatial reuse.
An adaptive persistent strategy with efficient collision detection has been stud-
ied in this work for autonomous channel sensing order selection which enable dis-
tributed CRs to avoid collision and allow them to improve their overall system ef-
ficiency by increasing the average number of successful transmissions, especially,
when number of available channels are less than the number of CRs competing
to access these free channels.
The performance of the studied strategy is compared with random selection of
sensing orders. Simulation results are presented, which indicate that the studied
strategy with spatial reuse achieves the highest number of successful transmis-
sions in a given time slot as compared to other strategies. Simulation results are
also compared for the case with no spatial reuse and the results indicate that
it degrades the system efficiency by reducing the average number of successful
transmissions in a given time slot.
Keywords: Autonomous cognitive radios, channel sensing, distributed cognitive
radio network, opportunistic spectrum access, spatial reuse.
TABLE OF CONTENTS
ABSTRACT
TABLE OF CONTENTS
FOREWORD
LIST OF ABBREVIATIONS AND SYMBOLS
1. INTRODUCTION 7
1.1. Cognitive Radio Technology . . . . . . . . . . . . . . . . . . . . . . 7
1.1.1. Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.1.2. Benefits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.1.3. Challenges . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.2. Autonomous devices in a multichannel CRN . . . . . . . . . . . . . . 9
1.2.1. Distributed Coordination in a multichannel CRN . . . . . . . 9
1.2.2. OSA for autonomous devices in a multichannel CRN . . . . . 9
1.2.3. OSA radio rendezvous problem in multichannel cognitive ra-
dio network . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.2.4. Challenges in designing efficient OSA techniques for a multi-
channel CRN . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.2.5. Solution: an adaptive persistent strategy with efficient colli-
sion detection mechanism . . . . . . . . . . . . . . . . . . . 11
2. RELATED STUDIES 14
3. SYSTEM MODEL 16
3.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.2. Studied methods under different PU activity models . . . . . . . . . . 16
3.3. Channel Sensing & Data transmission . . . . . . . . . . . . . . . . . 16
3.3.1. Sequential Channel sensing . . . . . . . . . . . . . . . . . . 18
3.3.2. Sequential Channel Sensing Scenarios . . . . . . . . . . . . . 18
4. CHANNEL SENSING ORDER SELECTION 21
4.1. Studied Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
4.2. γ-Persistent Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . 22
4.2.1. Initialization . . . . . . . . . . . . . . . . . . . . . . . . . . 22
4.2.2. Weighted Coin Toss . . . . . . . . . . . . . . . . . . . . . . 22
4.2.3. Possible Outcomes . . . . . . . . . . . . . . . . . . . . . . . 22
4.2.4. Restart Again . . . . . . . . . . . . . . . . . . . . . . . . . . 24
4.3. Collision Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
4.3.1. Spatial Reuse . . . . . . . . . . . . . . . . . . . . . . . . . . 24
4.3.2. Proposed Efficient Collision Detection with spatial reuse . . . 24
5. PERFORMANCE ANALYSIS OF THE PROPOSED STRATEGY 27
5.1. Randomize after every collision strategy . . . . . . . . . . . . . . . . 27
5.2. Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
5.2.1. Scenario A . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
5.2.2. Scenario B . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
5.2.3. Scenario C . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
5.2.4. Scenario D . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
5.2.5. Scenario E . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
6. SUMMARY 40
7. REFERENCES 41
FOREWORD
This thesis has been written in completion of Masters in Wireless Communication En-
gineering at University of Oulu, Finland. This thesis is funded by Center for Wireless
Communication as a part of its Master’s Thesis grant program. The main theme of
this research work is to study the impact of spatial reuse on autonomous sensing order
channel selection.
In the beginning, it was very challenging for me to start my thesis but D.Sc. (Tech.)
Zaheer Khan always keep on encouraging me that I can finish it. I would like to
thank my supervisor Adjunct Professor (Docent) Janne Lehtomaki for his continuous
support, incomparable supervision and mentoring that I was able to finish my thesis.
I would also like to thank my co-supervisor D.Sc. (Tech.) Zaheer Khan for being an
amazing mentor and friend throughout my thesis.
I have also been blessed with incredible friends especially Abdul Moiz, Ikram
Ashraf and Saad Bin Liaqat who really motivated me whenever I was feeling down
or having any problem related to my thesis.
Finally, I would like to dedicate my thesis to my parents Safdar Sultan and Zaid
Akhter for being the light of my life and always supporting me in whatever I have
done in my life.
Oulu, Finland November 24, 2016
Akmal Sultan
LIST OF ABBREVIATIONS AND SYMBOLS
CR Cognitive Radio
CDR Constant Detection Rate
CRN Cognitive Radio Network
DSA Dynamic Spectrum Access
FCC Federal Communications Commission
MAC Medium Access Control
NTIA National Telecommunications and Information Administration
OSA Opportunistic Spectrum Access
OSP Optimal Stopping Problem
PUs Primary Users
RSM Radio Resource Management
RSOP Random Sensing Order Policy
SUs Secondary Users
M total number of cognitive transmitter-receiver pairs
N set of available channels
Pd,i detection probability
Pd desired target value
θi probability of PU being present in each time slot
αi PU transition probability from the state of being occupied to free
βi PU transition probability from the state of being free to occupied
iTs entire duration of the sensing stage
T − Ts time required for the data transmission stage
Ts duration of single sensing step
T entire duration of the given time slot
IP sensing order
L set of available sensing orders
SC success counter
b binary flag
γ persistence factor
Pfa probability of False alarm
p∣
∣L∣
∣-element probability vector
pi probability of detecting the ith sensing order
1. INTRODUCTION
In recent years, wireless services have been growing at a very rapid rate, yielding
a huge demand on the radio spectrum. Resource scarcity has been a very common
drawback for wireless communication systems [1, 2, 3]. Thus, there is an urgent need
for finding intelligent ways of managing the scarce spectrum resources in order to
accommodate the explosive growth of wireless services.
Federal Communications Commission (FCC) is the regulatory authority responsible
for managing the usage of radio spectrum resources. It assigns radio spectrum on long
term basis to permanent users or licensed holders which are also known as primary
users (PUs) for usually a large geographical area. Generally, the available radio spec-
trum resources are not intelligently used by the PUs because the assigned spectrum
resources are not always used by the PUs which eventually results in under utilization
of large portions of available spectrum resources. This inefficient usage of bandwidth
limited resources leads us in finding dynamic spectrum access techniques which can be
employed for users having no allocated licensed spectrum by allowing them to utilize
temporarily the unused licensed spectrum, when PUs are not active. These users are
known as secondary users (SUs).
In recent years, FCC has been searching for more reliable, comprehensive and flexi-
ble ways for the usage of available scarce spectrum resources [4] by employing cogni-
tive radio technologies [5].
The overall network performance can be improved by the deployment of smart ra-
dios (cognitive radios) which can efficiently coordinate and adopt to their environment.
Cognitive radio (CR) is considered to be a very important technology in enabling com-
munication networks to opportunistically utilize the unused spectrum which is also
known as Opportunistic Spectrum Access (OSA) [5].
In this thesis, smart adaptation and coordination methods have been studied for wire-
less communication which allows wireless devices to perform in a very effective fash-
ion to enhance the overall bandwidth efficiency of a wireless network. The introduction
of dynamic spectrum access (DSA) and radio resource management (RSM) in wireless
networks enable wireless devices to employ their available radio spectrum efficiently.
The main theme of this research work is to study a smart adaptation scheme for
efficient channel access which helps to find out a way to improve the overall bandwidth
efficiency for distributed CRs in a multichannel Cognitive radio network (CRN).
An adaptive persistent strategy with efficient collision detection and spatial reuse
has been studied in this work for autonomous channel sensing order selection. This
will enable distributed CRs to avoid collision and allow them to improve their overall
system efficiency by increasing the average number of successful transmissions, espe-
cially, when number of available channels are less than the number of CRs competing
to access these channels.
1.1. Cognitive Radio Technology
In wireless communication, spectrum scarcity is a very common issue. There has been
a lot of research going on through out the world to overcome the problem of spectrum
scarcity.Cognitive radio technology has been considered a very important technology
8
in overcoming spectrum scarcity by employing smart radios to utilize the spectrum
efficiently.
1.1.1. Definitions
The term ”cognitive radio” was used for the first time by Joseph Mitola in [6] and
ever since it has gained a great interest from a very wider section of wireless commu-
nity. Some of the most popular definitions of cognitive radio from the literature are as
follows.
• Mitola [6] defines cognitive radio as: ”A radio that employs model based rea-
soning to achieve a specified level of competence in radio-related domains.”
• Simon Haykin [7] defines cognitive radio as: ”An intelligent wireless communi-
cation system that is aware of its surrounding environment (i.e., outside world),
and uses the methodology of understanding-by-building to learn from the envi-
ronment and adapt its internal states to statistical variations in the incoming RF
stimuli by making corresponding changes in certain operating parameters (e.g.,
transmit-power, carrier frequency, and modulation strategy) in real-time, with
two primary objectives in mind: highly reliable communications whenever and
wherever needed; and efficient utilization of the radio spectrum.”
• The National Telecommunications and Information Administration (NTIA) [8]
has defined cognitive radio as:”A radio or system that senses its operational elec-
tromagnetic environment and can dynamically and autonomously adjust its radio
operating parameters to modify system operation, such as maximize throughput,
mitigate interference, facilitate interoperability, and access secondary markets.”
In this thesis, a cognitive network is defined as a group of autonomous wireless
devices which have the tendency to act intelligently in making decisions related to their
operating parameters and enhance coordination with each other efficiently in order to
achieve desired goals.
1.1.2. Benefits
Some of the common benefit of Cognitive Radios discussed in [9] are as follows:
• CR helps to achieve greater spectrum efficiency through improved access.
• Interoperability and coexistence
• CR simplifies and reduces the tasks needed to setup and use a radio.
• Enhanced interface for applications related to communication tasks.
• A CR can improve its performance based on the information known to CR re-
lated to its internal affairs.
9
1.1.3. Challenges
There are certain hurdles and complexities in designing and implementing a CR net-
work. Some of them are discussed in [10, 11, 12, 13] which are as follows:
• Sometimes CRs have to deal with or articulate complex queries which are des-
tined from one radio to another and in some cases it has to execute certain com-
mands sent by another radio.
• CRs are supposed to use frequency spectrum efficiently and this is only possible
when CRs have the ability to switch among different frequency channels with
minimum delay.
• Adaptive decision making ability of CRs require them to make use of past out-
comes in order to efficiently utilize the frequency spectrum.
1.2. Autonomous devices in a multichannel CRN
Licensed frequency spectrum is generally a scarce resource in wireless networks. CR
networks utilize this scarce resource in a very efficient manner by exploiting it oppor-
tunistically in order to access unused spectrum bands for the time period until there
is no PU activity. There are many OSA techniques in the literature but the most com-
monly used technique is sensing based OSA because it does not requires PUs to change
their structure or way of working [14].
Autonomous devices in a multichannel cognitive radio network are capable of mak-
ing decisions independently based on information related to spectrum sensing and
feedback in a wireless network. Sometimes, these autonomous devices have to deals
with lack of computational resources and information related to their surrounding en-
vironment which can eventually degrade the overall wireless system performance.
1.2.1. Distributed Coordination in a multichannel CRN
The main idea behind distributed coordination in a multichannel CRN for autonomous
devices is to build a very adaptable wireless network which enables these independent
devices to act independently and to ensure efficient utilization of resources by using
low complexity methods.
1.2.2. OSA for autonomous devices in a multichannel CRN
Periodic spectrum sensing is performed for autonomous devices in sensing based OSA
so that they can free the channel when a PU becomes active in a channel in order to
avoid interruption in PU activity [15]. Time slotted multiple access is widely utilized
for OSA in multichannel CRN when multiple frequency channels are available [16,
17, 18, 19, 20]. Autonomous devices uses first portion of each time slot for spectrum
sensing and the second portion is used for accessing the channel, if found free.
13
are certain performance degrading factors in random sensing order selection which are
discussed in chapter 5.
The likelihood of collision reduces when autonomous CRs choose those sensing
orders which allows them to avoid one another, but still there are chances that two or
more autonomous CRs will choose the same sensing order.If more then one CR finds
the channel free and they transmit in the same channel at the same then a collision will
occur. There should be an efficient collision detection mechanism which can reduce
the likelihood of collision.
Spatial reuse has been utilized in this thesis by taking advantage of the transmitting
and receiving ranges of the autonomous CR’s transmitter-receiver node pairs for effi-
cient collision detection in order to increase the overall throughout of the system which
is explained in detail in Chapter 4.
14
2. RELATED STUDIES
Recently, the problem of designing efficient channel sensing selection strategies have
gained a lot of attention. In sensing based OSA, periodic spectrum sensing is achieved
when a CR vacates the channel free as a result of PU being active in a channel [15].
A time slotted periodic sensing model is divided in two categories: Periodic sensing
for a single potentially available primary user band and Periodic sensing for a multiple
potentially available primary user bands. In case of single primary user band, single
licensed spectrum band is explored by the CRs [23]. CRs use the first portion of each
time slot for the purpose of sensing the licensed band and if it is free then the second
portion of each time slot is used for accessing the band [24].
Multiple licensed spectrum bands are explored by CRs in case of periodic sensing for
multiple potentially available primary user bands [21] and from here it can be further
divided in to single channel sensing and sequential channel sensing [23]. In single
channel sensing, the CR initially selects a channel for sensing and transmitting only
when it is free in a given time slot, apart from that it remains quite for the whole
duration of the slot. Whereas in sequential channel sensing, a CR can sense more than
one channel for the entire duration of the time slot.
Sequential channel sensing for a single user CR system has been discussed in [25,
26, 27] which utilizes the optimal stopping problem (OSP) models. In multi-user CR
systems, some initial results were reported in literature for OSP models, such as in [28]
a heuristic solution was proposed and in [17] a centralized solution for two-user system
was proposed. In this work, sequential channel sensing has been used in which two
or more autonomous CRs sense the channels sequentially for spectrum opportunities
in some sensing order. There have been several optimal policies in the literature for
the selection of channel sensing order. Optimal policies for the selection of channel
sensing order is explained in [21, 18, 29, 30]. Problem of multi-user sequential channel
sensing and access in dynamic CR networks have been studied in [30], which involves
active user set to be changed randomly from slot to slot and also there is no information
exchange among users. The goal of the users in [30] is to determine the channel order
for sensing and access, it also addresses the overlapping of channel sensing order by
introducing a generalized interference metric. A coordinator for a two-user CRN has
been used by Fan [17] to determine the optimal sensing order selection which is based
on channel availability statistics.
Impact of cooperative sensing has been considered in [31] along with the sensing of
channels in multi-channel DSA networks for decision making, whereas, we consider
channel occupancy for decision making in channel sensing. Several cooperative sens-
ing strategies, i.e., parallel, sequential, and parallel-sequential has been proposed and
compared in [31] to schedule all users to sense multiple channels in order to attain op-
timal throughput. In [32], the author has studied cooperative sensing in heterogeneous
CR network, where the number of receive antennas may be different for each SU and
have different signal processing capabilities.
A simple channel sensing order has been proposed in [20] for SUs in a distributed
CRN, where there is no prior knowledge of PU’s activity and it assumes that CRs
have the knowledge of channel gains. Whereas, we do not consider the knowledge of
channel gains in our work and we have proposed an adaptive sensing order selection
strategies for channel sensing.
15
The effect of imperfect information on the performance of the autonomous SUs has
been discussed in [14] which will access the spectrum resources opportunistically. The
results in [33] shows that the rate of convergence has been reduced due to the impact
of the imperfect information and the amount of competition between SUs and the level
of PU activity which determines this performance loss. The author in [34] analyzes the
impact of imperfect channel sensing on casual channel estimation methods in corre-
lated CR channels. We have also considered the impact of imperfect information which
includes the effect of false alarms and channel errors on making adaptation decisions.
A two stage process for allocating fungible channel sets to multiple CRs for op-
portunistic spectrum access is the topic of [35], which eliminates the possibility of
collision among CRs and allows CRs to focus more on avoiding collisions with the
primary user (PU). A learning based dynamic channel selection algorithm on the set
of channels is used in [35] whose performance is accurately estimated by the proposed
neural network, and it’s done by using the duty cycle and the complexity of the PU’s
behavior on channels.
The modelling and performance analysis of a random sensing order policy (RSOP)
has been studied in [36] for a distributed CRN. A novel markov process has been used
for modeling the behaviors of SUs and an optimization problem is defined to keep the
interference level bounded and to maximize the average throughput in [36].In addition,
two efficient algorithms are proposed which improves the performance of RSOP by
adjusting the sensing-access parameters adaptively.
Collision free schedules have been achieved in [37, 38, 39] using learning based
medium access control (MAC) methods. The transmitter in the above methods must
do sensing before transmission in order to determine available channels because these
schemes do not consider channel availability due to the presence of PUs.
Spatial reuse in wireless mesh networks has been studied in [40] to increase the
network throughput. It also optimizes the efficiency of spectrum utilization by taking
use of the interplay between spatial reuse and network coding. A joint spatial-temporal
spectrum-sensing scheme has been proposed in [41] that improves the performance of
temporal sensing by exploiting the information from spatial sensing.
16
3. SYSTEM MODEL
3.1. Introduction
In this thesis, a distributed cognitive radio network has been studied which consists
of M cognitive transmitter-receiver pairs and a set N=1,2,3,....,N of channels. The
separation distance between transmitter and receiver node in an autonomous CR is
considered to be constant and it is same for all CR pairs in a distributed CRN. CRs
can make use of the available free channels, when these channels are not occupied by
primary users. A time slotted system for both PU and CR activity is adopted and it
assumes that the primary user can only be present for the entire time slot or it remains
absent for the entire time slot.
As we know, there are always hardware constraints in designing a distributed CRN,
so it is considered that a CR can either transmit or it can only sense during any time
slot but it is not allowed to perform sensing and transmitting at the same time. Each
CR is assumed to sense only one channel at a given time.
The detection probability (Pd,i) for an autonomous CR is set to a desired target value,
(Pd,i = Pd), for all i ∈ M . According to [15], (Pd) needs to be close to 1. When the
detection probability is fixed at a constant target value, it is defined as constant detec-
tion rate (CDR) requirement [42] and the false alarm probability for an autonomous CR
varies. The effect of varying probabilities has been considered in our work, whereas
we have neglected the impact of missed detection errors for the sake of simplicity.
3.2. Studied methods under different PU activity models
We have analyzed the PU activity model as follows:
1. In a given time slot, the probability of PU being present in each time slot is θi,i ∈ N . The PU activity in this model for a given time slot is considered to be
independent of PU activity in any other time slot and it also has no dependency
of PU activity in any other channel as well. Similar channel occupancy model
for the PU activity has been adopted by [20, 16, 43].
2. In consecutive time slots, the PU utilizes correlation in channel occupancy for
this model and a two-state markov chain describes the state of each channel. A
two-state markov chain contains αi which defines the PU transition probability
for the ith channel from the state of being occupied to free, and βi which defines
the PU transition probability for the ith channel from the state of being free to
occupied. H. Su [28] has also adopted the similar PU activity model.
3.3. Channel Sensing & Data transmission
In a distributed CRN, channel sensing and data transmission using opportunistic trans-
mission is explained as follows by the help of Figure 4:
18
3.3.1. Sequential Channel sensing
When multiple autonomous CRs search for available free channels for spectrum oppor-
tunities, the following events might appear in a single sensing step from the viewpoint
of a single CR:
1. The CR arrives at a given channel and finds it free and is the only one to find it
free. The CR will transmit in that channel and it will keep control of this channel
until the remainder of the time slot.
2. The CR arrives at a given channel and finds it busy which means it is either
occupied by PU activity or any other CR activity. In that case, CR continues its
searching process in the next sensing step until it finds a free channel.
3. The CR arrives at a given channel and finds it free which means it will transmits
in that channel. In the meanwhile, another CR during the same time finds the
same channel free and it also transmits in that free channel. Ideally, a collision
will occur when both CRs will transmit in the same channel at the same time,
but in this thesis an efficient collision detection mechanism has been studied
which employs spatial reuse by taking advantage of the transmitting and receiv-
ing ranges of the transmitter-receiver node pairs of each CR in order to make
the decision whether collision will occur or not (details are presented in the next
chapter). If both the CRs are out of their transmitting and receiving ranges which
means that they won’t interrupt their data transmission, then there will be no col-
lision even if they are transmitting in the same channel, otherwise, there will be
a collision.
3.3.2. Sequential Channel Sensing Scenarios
Some times, CR thinks that the channel is busy of either PU activity or any other CR
activity but in reality it is free. It happens due to False alarms which could effect our
goal of improving overall system efficiency by increasing the number of successful
transmissions in a distributed CRN. Different sequential channel sensing scenarios has
been explained below:
1. In this channel sensing scenario, CR1 finds channel 5 free in its third sensing step
as shown in Figure 6. CR1 will keep control of the channel until the remainder
of the time slot. Whereas, CR2 and CR3 will collide with each other because
both of them finds channel 2 free in their first sensing step and also they have the
same sensing order. When two or more CRs finds the same channel free then a
collision will occur because every CR will try to transmit in the same channel.
19
Figure 6: Scenario (1)
2. In this channel sensing scenario, CR1 finds channel 4 free in its 3rd sensing step,
CR2 finds channel 1 free in its first sensing step, and CR3 finds channel 2 free
in its fourth sensing step after finding out that channel 4 and channel 1 are busy
because both of them have already been found free in the other steps as shown
in Figure 7.
Figure 7: Scenario (2)
3. In this channel sensing scenario, CR1 and CR2 will collide with each other be-
cause both of them have chosen the same PU-free channel index in their first
sensing step and both of them have found channel 3 free in their first sensing
step as depicted in Figure 8. On the other hand, CR3 finds channel 5 free in its
fourth sensing step.
20
Figure 8: Scenario (3)
4. In this channel sensing scenario, CR1 and CR2 have chosen the same sensing
order as shown in the Figure 9. Ideally, collision will occur between CR1 and
CR2 but they will not collide because CR1 has found channel 2 free in its first
sensing step and CR2 generates a false alarm in its first sensing step which avoids
collision and it finds channel 1 free in step 3. On the other hand, CR3 finds
channel 5, 2, and 1 busy because other CRs may have found them free in the
earlier steps.
Figure 9: Scenario (4)
21
4. CHANNEL SENSING ORDER SELECTION
The main goal of this research work is to study a channel sensing order selection strat-
egy with spatial reuse which will help to improve the average rate of successful trans-
missions in a distributed CRN and by successful transmission, it is meant that CR is the
only sole user to transmit in that particular channel because it has found that channel
free from any PU activity or any other CR activity.
4.1. Studied Strategy
Generally, when two or more autonomous CRs search for available free channel for
spectrum opportunities, there is usually a competition between the CRs to access the
free channel because the purpose of this competition from the CR prospective is to
become the sole user of that free channel. As a result of this competition, collisions
will occur among CRs because they simultaneously transmit in the same channel and
this will lead to an overall reduced throughput.
The main theme of this work is to find out a way to improve the average rate of
successful transmissions in a distributed CRN which means that the chances of find-
ing a channel free simultaneously for two or more CRs is reduced by adopting smart
channel sensing and efficient collision detection techniques. In this thesis, an adaptive
persistent strategy [23] has been studied for channel sensing order selection which will
help distributed CRs to avoid collision and allow them to improve the average rate of
successful transmissions.
In adaptive persistent strategy, we start with set of available sensing orders by denot-
ing it with L. The sensing order can either be chosen from the space of all permutation
of channel N or from a Latin Square as shown in Figure 10.
Figure 10: Different channel sensing order illustration. Space of all permutations for
N=4 channels is shown in (a), and a predefined Latin Square is illustrated in (b).
22
Sensing orders from a predefined Latin square (Figure 10 (b)) which is a N by Nmatrix of N channel indices and each channel index does not repeat itself in any row
or column of the matrix which means it appears only once in any row or column of
the matrix [44, 45, 23]. The sensing order of an autonomous CR can be any row of
the Latin square (Figure 10 (b)) or it can be any row of the space of all permutations
(Figure 10 (a)) depending on which strategy has been selected for channel sensing.
4.2. γ-Persistent Strategy
A γ-persistent strategy [23] with efficient collision detection has been studied in this
thesis, which make use of the successes and failures of a CR in using the current
sensing order in the prior time slots. The successes and failures of a CR in the prior
time slots can be tracked by the help of a success counter (SC) and a binary flag b.
The persistence factor of this strategy is γ, which is utilized as follows:
1. A fixed value of the persistence factor (γ ∈ (0, 1)) has been used by the au-
tonomous CR.
2. Success counter (SC) and false alarm probability is considered by the au-
tonomous CR to employ the persistence factor γ = 1 − ( 1SC−log
2(Pfa)
). This
approach also assumes that the autonomous CR has the ability to estimate its
false alarm probability.
Both these approaches will be explained in detail at the end of this chapter.
We start with γ-Persistent Strategy by letting each CR maintain a∣
∣L∣
∣-element prob-
ability vector p and we donate pi as the probability of detecting the ith sensing order
which can be taken from space of all permutation of channel indices N , or it can be
taken from a Latin Square. The step by step explanation of γ-Persistent Strategy is
given below:
4.2.1. Initialization
We begin with∣
∣L∣
∣-element probability vector p=[
1∣
∣L
∣
∣
, 1∣
∣L
∣
∣
, 1∣
∣L
∣
∣
, . . . , 1∣
∣L
∣
∣
]
and by setting
the binary flag and the success counter to b=SC=0.
4.2.2. Weighted Coin Toss
A weighted coin is tossed to choose a sensing order with pi as the probability of se-
lecting the ith sensing order. After the weighted coin toss, the channels starts sensing
sequentially in the pattern mentioned in the chosen sensing order.
4.2.3. Possible Outcomes
Following are the possible outcomes after sensing the channels sequentially:
23
1. Successful Transmission: When CR finds a channel free and in the mean while
no other PU or CR finds that channel free, the CR will transmit in that channel.
The CR updates pi and pj as pi = 1 and pj = 1, ∀j 6= i using the current sensing
order i. Thus, it will use the same sensing order to visit the channels in the next
slot and the CR sets SC=SC+1.
2. All Channels found busy: In this scenario, CR finds all channels busy which
means that in the current slot the CR using the sensing order i find all the chan-
nels occupied by either a PU or any other CR. The CR updates pi and pj as
pi = 1 and pj = 0, ∀j 6= i using the current sensing order i.Thus, it will use the
same sensing order to visit the channels in the next slot and CR then sets b=1.
3. Collision between CRs: When a CR collides with any other CR in the current
slot using sensing order i, the CR updates pi as follows:
pi =
{
1/∣
∣L∣
∣ SC=0 and b=1
γpi, otherwise
and the CR updates pj as follows
pj =
{
1/∣
∣L∣
∣ if SC=0 and b=1
γpi +1−γ∣
∣L
∣
∣
−1, otherwise
In the current slot, when a collision occurs the CR randomly selects a sensing
order in case of SC=0 and b=1; else ways the probability of selecting sensing or-
der i reduces multiplicatively as the CR evenly distributes the probability across
the other sensing orders. Now, the CR sets SC=b=0. This is further explained by
going through all the different states of the success counter and binary flag b on
experiencing the collision as follows:
When SC > 0 and b = 0 or b = 1, an autonomous CR is not sure whether the
sensing order it has selected was not selected by any other CR, whereas SC > 0
indicates that there are high chances that the CR is the only user of that sensing
order in time slot n. Once a collision occur, a CR does not change its sensing
order, whereas it continues with the same sensing order i with probability γpi,and the probability (1 − γpi) is reassigned uniformly across the other sensing
orders. This will enhance the average rate of successful transmissions because
the successful CRs will continue with the same sensing order which will directly
reduce the number of CRs randomly selecting a sensing order.
When SC = 0 and b = 0, it means that the CR was neither successful nor found
all channels busy in the current time slot using the sensing order i before expe-
riencing the collision. Thus, the probability of choosing the same sensing order
in the next time slot decreases because there is a possibility that any other CR
may have been successful in the same sensing order and it may continue with the
same sensing order, and the probability (1− γpi) is reassigned uniformly across
the other sensing orders.
When SC = 0 and b = 1, it indicates that all channel were found busy by CR t
in time slot n using the sensing order i. As CR t stays quiet because it is not
24
sure that whether CR t is the only user of sensing order in time slot n because
it may happen that any other CR have chosen the same sensing order and it is
quite possible that it may have found it free and thus transmitted or it may have
found all channels busy. Therefore, after experiencing the collision the CR t will
choose the sensing order independently and randomly with uniform probability
because SC = 0 and it cannot be sure that it is the sole user of sensing order in
time slot n.
4.2.4. Restart Again
Once any of the possible outcomes in section 4.2.3 happens, the process starts again
by returning to section 4.2.2 and the same process continues again.
4.3. Collision Detection
A collision occurs in a distributed CRN whenever CR fails to receive an acknowl-
edgment (ACK) for a transmitted data frame. As in our case, we have a common
predefined Latin Square from which the CR selects the sensing order. Two or more
CRs will only collide with each other once they try to transmit simultaneously after
choosing the same sensing order.
4.3.1. Spatial Reuse
Spatial reuse gives the freedom to use the same band which is at far off location simul-
taneously with out any interference, whereas, a collision will occur if the same band is
simultaneously used in a neighbouring location [46]. Thus, spatial reuse provides an
opportunity to SUs to use the same band simultaneously at a far off location with out
any interference.
Spatial reuse is generally achieved with careful planning of the interference parame-
ters which are set for SUs to improve the overall wireless system bandwidth efficiency.
For every configuration of the network, there exists a minimum distance which must be
separating SUs from each other in order to transmit simultaneously in the same band
[47]. As a result, maximum no of simultaneous transmissions are achieved which al-
lows to attain the maximum network throughput.
In this thesis, we have utilized spatial reuse in order to enhance the efficiency of
collision detection of the studied adaptive persistent strategy. The details are explained
in the section below.
4.3.2. Proposed Efficient Collision Detection with spatial reuse
Ideally, a collision occurs when two or more CRs transmits at the same time and they
have the same sensing order but there are various other factors which could be em-
ployed to reduce the likelihood of collisions and to improve the overall system per-
27
5. PERFORMANCE ANALYSIS OF THE PROPOSED
STRATEGY
In this chapter, we analyze the performance of our studied adaptive scheme with ef-
ficient collision detection mechanism by comparing it with a randomize after every
collision adaptive (RAND) strategy [23] with the help of numerical results in terms
of average number of successful transmissions in a network. A comparison of the
proposed strategy is also done in case when there is no utilization of spatial reuse.
In the first section, RAND strategy is discussed and in the next section simulation
results are presented for the performance analysis of the studied adaptive persistent
strategy.
5.1. Randomize after every collision strategy
In randomize after every collision strategy, adaptive randomization is utilized which is
based on feedback for CRs to reduce the likelihood of collision and thus increasing the
average number of successful transmissions in a network.
In this strategy, a CR selects independently and randomly a sensing order which
may come from the space of all permutations of N channels or from a Latin-square
with equal probability. A CR can only select the other sensing order in a time slot,
when a collision has occurred in the previous time slot, otherwise, it sticks with its
sensing order. The main motive is to reduce the likelihood of collision by randomizing
the sensing orders of CRs, only when there is a collision in the previous time slot.
5.2. Simulation results
In this section, numerical results are presented to illustrate the performance of adap-
tive persistent strategy with efficient collision detection mechanism. These results are
utilized to analyze the performance of our studied strategy in terms of average number
of successful transmission in a given time slot considering different parameters and
scenarios which are explained in detail in this section.
For simulation purposes, a distributed cognitive radio network has been consid-
ered which consists of M cognitive transmitter-receiver pairs and a set N=1,2,3,....,N
of channels. M cognitive transmitter/receiver pairs are randomly distributed over
a 150m*150m square area. The separation distance between a cognitive transmit-
ter/receiver pair is kept constant for all M cognitive transmitter/receiver pairs as ex-
plained in system model.
In adaptive persistent strategy, spatial reuse is utilized in which a collision will only
occur when two CRs finds the same channel free and the receiver of one CR falls in
the transmitting range of another CR, otherwise there will be no collision even when
two CRs are transmitting in the same channel simultaneously. We have analyzed the
impact of spatial reuse by varying the transmitting and receiving ranges of cognitive
transmitter/receiver pairs and observed its impact on the average number of successful
transmission in a given time slot. In our scenarios, we have varied the transmitting
28
and receiving ranges from 70 meters to 200 meters over a 150m*150m square area in
which M cognitive transmitter/receiver pairs are randomly distributed.
Different scenarios are considered in this section in which number of channels are
kept constant (N=16), but number of M cognitive transmitter/receiver pairs are varied
in order to determine the impact of average number of successful transmission in a
given time slot when we vary M. We are more interested in the cases when M>N in
order to determine the efficiency of our studied scheme when it has to face the problem
of spectrum scarcity (M>N).
The different scenarios are explained as follows:
5.2.1. Scenario A
In this scenario, a distributed cognitive radio network of M=16 cognitive transmit-
ter/receiver pairs and a set N=1,2,3,....,16 of channels is considered. M cognitive
transmitter/receiver pairs are randomly distributed over a 150m*150m square area.
The separation distance between a cognitive transmitter/receiver pair is kept constant
for all M cognitive transmitter/receiver pairs.
In Figure 13, for N=16 channels and M=16 cognitive transmitter/receiver pairs, the
average number of successful transmission for different strategies in a given time slot
is depicted. There are five different plots shown in Figure 13 which gives us simu-
lation results based on different transmission and reception ranges for the cognitive
transmitter/receiver pair.
It can be seen from Figure 13 that our proposed adaptive persistent strategy with
efficient collision detection achieves the highest average number of successful trans-
mission in all five different plots.
When we keep on increasing the transmission and reception ranges for the cognitive
transmitter/receiver pair over a 150m*150m square area, it will increase the probability
of collision because now there are more chances that a receiver of one CR falls in the
transmitting range of another CR due to increase in the transmission range. This will
reduce the average number of successful transmissions in a given time slot which can
be seen in Figure 13. In this case, our strategy with high persistence value γ=0.9
performs slightly better, as compared to when γ is used as a function of false alarm
probability and SC as shown in Figure 13(e). This happens due to the fact that high
persistence value allows CR to continue with its sensing order with high probability.
Efficient collision detection plays a pivotal role in increasing the average number
of successful transmission by reducing the likelihood of collision with help of spatial
reuse. Figure 14 gives us simulation results for the adaptive persistent strategy pro-
posed in [23] for the case when M=N=16. There is no spatial reuse in this case when
two CRs selects the same sensing order and they wants to transmit simultaneously.
29
(a) Range=70 meters
-
(b) Range=90 meters
(c) Range=110 meters
-
(d) Range=130 meters
(e) Range=200 meters
Figure 13: Simulation results for average number of successful transmissions in a given
time slot for different strategies when M=N=16, false alarm probability of each CR is
set to 0.2, and θk = 0,3, ∀k ∈ N
30
Figure 14: Simulation results for average number of successful transmissions in a given
time slot for different strategies when M=N=16, false alarm probability of each CR is
set to 0.2, and θk = 0,3, ∀k ∈ N
By comparing the simulation result in Figure 13 and Figure 14. It is quite clear
that our strategy has the highest average number of successful transmissions in case
when we have M=N. This happens due to the fact that spatial reuse helps to reduce
the likelihood of collision by allowing CRs to transmit in the same channel when the
receiver of one CR does not falls in the transmitting range of another CR.
5.2.2. Scenario B
In this scenario, a distributed cognitive radio network of M=20 cognitive transmit-
ter/receiver pairs and a set N=1,2,3,....,16 of channels is considered. M cognitive
transmitter/receiver pairs are randomly distributed over a 150m*150m square area.
The separation distance between a cognitive transmitter/receiver pair is kept constant
for all M cognitive transmitter/receiver pairs.
In Figure 15, for N=16 channels and M=20 cognitive transmitter/receiver pairs, the
average number of successful transmission for different strategies in a given time slot
is depicted. There are five different plots shown in Figure 15 which gives us simu-
lation results based on different transmission and reception ranges for the cognitive
transmitter/receiver pair.
31
(a) Range=70 meters
-
(b) Range=90 meters
(c) Range=110 meters
-
(d) Range=130 meters
(e) Range=200 meters
Figure 15: Simulation results for average number of successful transmissions in a given
time slot for different strategies when M=20 and N=16, false alarm probability of each
CR is set to 0.2, and θk = 0,3, ∀k ∈ N
It can be seen from Figure 15 that adaptive persistent strategy with efficient collision
detection achieves the highest average number of successful transmission in all five
different plots. In case of M>N, the likelihood of collision increases which happens
due to spectrum scarcity as we have now more CRs then number of available channels.
When we keep on increasing the transmission and reception ranges for the cognitive
transmitter/receiver pair over a 150m*150m square area, it will increase the probability
of collision because now there are more chances that a receiver of one CR falls in the
transmitting range of another CR due to increase in the transmission range.This will
32
reduce the average number of successful transmissions in a given time slot which can
be seen in Figure 15. In this case, our strategy with high persistence value γ=0.9 and
spatial reuse performs slightly better, as compared to when γ is used as a function
of false alarm probability and SC as shown in Figure 15(e). This happens due to the
fact that high persistence value allows CR to continue with its sensing order with high
probability.
Spatial reuse plays a pivotal role in increasing the average number of successful
transmission by reducing the likelihood of collision. Figure 14 gives us simulation
results for the adaptive persistent strategy proposed in [23] for the case when M =20
and N=16. There is no spatial reuse in this case when two CRs selects the same sensing
order and they wants to transmit simultaneously.
Figure 16: Simulation results for average number of successful transmissions in a given
time slot for different strategies when M=20 and N=16, false alarm probability of each
CR is set to 0.2, and θk = 0,3, ∀k ∈ N
By comparing the simulation result in Figure 15 and Figure 16. It is quite clear that
our strategy with spatial reuse is performing significantly better than the one proposed
in [23] in terms of average number of successful transmissions for the case when we
have M=20 and N=16. This happens due to the fact that spatial reuse helps to reduce
the likelihood of collision by allowing CRs to transmit in the same channel when the
receiver of one CR do not falls in the transmitting range of another CR.
33
5.2.3. Scenario C
In this scenario, a distributed cognitive radio network of M=24 cognitive transmit-
ter/receiver pairs and a set N=1,2,3,....,16 of channels is considered. M cognitive
transmitter/receiver pairs are randomly distributed over a 150m*150m square area.
The separation distance between a cognitive transmitter/receiver pair is kept constant
for all M cognitive transmitter/receiver pairs.
(a) Range=70 meters
-
(b) Range=90 meters
(c) Range=110 meters
-
(d) Range=130 meters
(e) Range=200 meters
Figure 17: Simulation results for average number of successful transmissions in a given
time slot for different strategies when M=24 and N=16, false alarm probability of each
CR is set to 0.2, and θk = 0,3, ∀k ∈ N
34
In Figure 17, for N=16 channels and M=24cognitive transmitter/receiver pairs, the
average number of successful transmission for different strategies in a given time slot
is depicted. There are five different plots shown in Figure 17 which gives us simu-
lation results based on different transmission and reception ranges for the cognitive
transmitter/receiver pair.
It can be seen from Figure 17 that adaptive persistent strategy with efficient collision
detection achieves the highest average number of successful transmissions when we
have high persistence value γ=0.9 in all five different plots. As in case of M>N, the
likelihood of collision increases which happens due to spectrum scarcity, as there are
more CRs then number of available channels.
When we keep on increasing the transmission and reception ranges for the cognitive
transmitter/receiver pair over a 150m*150m square area, it will increase the probability
of collision because now there are more chances that a receiver of one CR falls in the
transmitting range of another CR due to increase in the transmission range. This will
reduce the average number of successful transmissions in a given time slot which can
be seen in Figure 17. In this case, high persistence value γ=0.9 performs slightly
better, as compared to when γ is used as a function of false alarm probability and SC.
This happens due to the fact that high persistence value allows CR to continue with its
sensing order with high probability.
Figure 18: Simulation results for average number of successful transmissions in a given
time slot for different strategies when M=24 and N=16, false alarm probability of each
CR is set to 0.2, and θk = 0,3, ∀k ∈ N
35
Spatial reuse plays a pivotal role in increasing the average number of successful
transmissions by reducing the likelihood of collision. Figure 18 gives us simulation
results for the adaptive persistent strategy proposed in [23] for the case when M =24
and N=16. There is no spatial reuse in this case when two CRs selects the same sensing
order and they wants to transmit simultaneously.
By comparing the simulation result in Figure 17 and Figure 18. It is quite clear that
our strategy is performing significantly better than the one proposed in [23] in terms
of average number of successful transmissions for the case when we have M=24 and
N=16. This happens due to the fact that our proposed efficient collision detection helps
to reduce the likelihood of collision by allowing CRs to transmit in the same channel
when the receiver of one CR do not falls in the transmitting range of another CR.
5.2.4. Scenario D
In this scenario, a distributed cognitive radio network of M=32 cognitive transmit-
ter/receiver pairs and a set N=1,2,3,....,16 of channels is considered. M cognitive
transmitter/receiver pairs are randomly distributed over a 150m*150m square area.
The separation distance between a cognitive transmitter/receiver pair is kept constant
for all M cognitive transmitter/receiver pairs.
In Figure 19, for N=16 channels and M=32 cognitive transmitter/receiver pairs, the
average number of successful transmission for different strategies in a given time slot
is depicted. There are five different plots shown in Figure 19 which gives us simu-
lation results based on different transmission and reception ranges for the cognitive
transmitter/receiver pair.
It can be seen from Figure 19 that results are quite random because M»N in all five
different plots. This will increase the likelihood of collision and now there are more
chances a collision will occur which will result in reduce overall network throughput.
Figure 20 gives us simulation results for the adaptive persistent strategy proposed
in [23] for the case when M =32 and N=16. There is no smart and efficient collision
detection utilized in this case when two CRs selects the same sensing order and they
wants to transmit simultaneously.
36
(a) Range=70 meters
-
(b) Range=90 meters
(c) Range=110 meters
-
(d) Range=130 meters
(e) Range=200 meters
Figure 19: Simulation results for average number of successful transmissions in a given
time slot for different strategies when M=32 and N=16, false alarm probability of each
CR is set to 0.2, and θk = 0,3, ∀k ∈ N
37
Figure 20: Simulation results for average number of successful transmissions in a given
time slot for different strategies when M=32 and N=16, false alarm probability of each
CR is set to 0.2, and θk = 0,3, ∀k ∈ N
By comparing the simulation result in Figure 19 and Figure 20. It can be seen that
the simulations results are quite similar because of the randomness in the plots due to
M >> N .
5.2.5. Scenario E
In this scenario, a distributed cognitive radio network of M=16 cognitive transmit-
ter/receiver pairs and a set N=1,2,3,....,10 of channels is considered. M cognitive
transmitter/receiver pairs are randomly distributed over a 150m*150m square area.
The separation distance between a cognitive transmitter/receiver pair is kept constant
for all M cognitive transmitter/receiver pairs.
In Figure 21, for N=10 channels and M=16 cognitive transmitter/receiver pairs, it
compares average number of successful transmission achieved in timeslots, for n=200,
as a function of number of CRs for different adaptive strategies. There are six dif-
ferent plots shown in Figure 21 which gives us simulation results based on different
transmission and reception ranges for the cognitive transmitter/receiver pair.
38
(a) Caption1
-
(b) Caption 2
(c) Caption12
-
(d) Caption 22
(e) Caption 212
-
(f) Caption 212
Figure 21: Caption for this figure with two images
It can be seen from Figure 21 that adaptive persistent strategy with spatial reuse
achieves the highest average number of successful transmissions in all six different
plots.
When we keep on increasing the transmission and reception ranges for the cognitive
transmitter/receiver pair over a 150m*150m square area, it will increase the probability
of collision because now there are more chances that a receiver of one CR falls in
the transmitting range of another CR due to increase in the transmission range. This
will reduce the average number of successful transmissions in a given time slot which
can be seen in Figure 21. In case of M>N, our strategy with high persistence value
gamme=0.9 and spatial reuse performs slightly better, as compared to when gamma
39
is used as a function of false alarm probability and SC as shown in Figure 21. This
happens due to the fact that high persistence value allows CR to continue with its
sensing order with high probability.
Spatial reuse plays a pivotal role in increasing the average number of successful
transmission by reducing the likelihood of collision. Figure 14 gives us simulation
results for the adaptive persistent strategy proposed in [23] for the case when M=16
N=10. There is no spatial reuse in this case when two CRs selects the same sensing
order and they wants to transmit simultaneously.
Figure 22: Efficient Collision Detection Scenario (a)
By comparing the simulation result in Figure 21 and Figure 22. It is quite clear that
our strategy has the highest average number of successful transmissions in case when
we have M=N and M>N. This happens due to the fact that spatial reuse helps to reduce
the likelihood of collision by allowing CRs to transmit in the same channel when the
receiver of one CR do not falls in the transmitting range of another CR.
40
6. SUMMARY
Generally, when two or more autonomous CRs search for available free channel for
spectrum opportunities, there is usually a competition between the CRs to access the
free channel. The purpose of this competition from the CR prospective is to become
the sole user of that free channel. As a result of this competition, collisions will occur
among CRs because they simultaneously transmit in the same channel which will lead
to an overall reduced throughput.
The main theme of this research work is to find out a way to improve the average
rate of successful transmissions in a distributed CRN when number of available free
channels are less then the number of autonomous CRs competing to access these free
channels. This can be achieved by reducing the probability of finding a channel free
simultaneously for two or more CRs by adopting smart channel sensing and efficient
collision detection techniques.
A adaptive persistent strategy with spatial reuse has been studied in this thesis for
efficient channel access in a distributed CRN. We found out that the efficiency of the
wireless system reduces when channels are randomly accessed. An adaptive persistent
strategy with efficient spatial reuse is the answer for the reduced efficiency caused by
random selection of sensing orders.
The likelihood of collision between CRs that are transmitting in the same chan-
nel can be reduced by utilizing the transmitting and receiving ranges of the CR’s
transmitter-receiver node pair with the help of spatial reuse. Simulation results have
validated that adaptive persistent strategy with spatial reuse achieves the highest num-
ber of average successful transmissions in a given time slot as compared to RAND
strategy and also for the case when there is no spatial reuse for the adaptive persistent
strategy.
In simulation results, when we increase the transmitting and receiving ranges of
the CR’s transmitter-receiver node pair, it reduces the average number of successful
transmissions in a given time slot because now there are more chances that a transmitter
of one CR falls in the receiving range of another CR which will lead to a collision when
both CRs try to transmit at the same time. High persistence value γ=0.9 and spatial
reuse performs slightly better, as compared to when γ is used as a function of false
alarm probability and SC, for the case when probability of collision is high.
We also found out that when adaptations are employed, it will increase the average
number of successful transmissions when channel sensing orders are selected from a
predefined Latin-square. We also investigated the impact of false alarms and channels
errors on system efficiency. The average number of successful transmissions increases
even when there are false alarms and channels errors in our studied strategy.
41
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