Throughput Analysis for Adaptive Transmission Cognitive Radio by Pablo Betancur, Date 05-2010

7/29/2019 Throughput Analysis for Adaptive Transmission Cognitive Radio by Pablo Betancur, Date 05-2010

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THROUGHPUT ANALYSIS FOR ADAPTIVE TRANSMISSION

COGNITIVE RADIO

Thesis

Submitted in partial fulfillment of the Requirements forThe Master Degree in Communication and Information

Engineering

M.Sc. Candidate: Juan Pablo Betancur Agudelo

Major : Communication and Information Systems

Supervisor : Dai-ming Qu

Huazhong University of Science and Technology

Wuhan, Hubei 430074, P. R. China

25th May, 2010


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I

OFDM

BS

BS

BS

CRDSA802.16WiMAX

OFDM


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ABSTRACT

Through this project is presented an adaptive transmission scheme for cognitive radionetworks. The proposed scheme perform adaptive modulation using OFDM in order to choosethe most bandwidth-efficient signal constellation that can be used for the current channelcondition.

In the scheme, the secondary base station (BS) sense the spectrum applying cognitive radiocapabilities, choosing the optimal band for the transmission and estimating the distance to the

primary user. By knowing the distance for the primary user and according to the interferencetemperature concept the secondary BS could calculate the allowable transmit power for non-harmful interference over the licensed network.

As both primary and secondary networks are sharing the same band for transmit datasimultaneously, we have found that the throughput of the secondary user is influenced negativelyby the interference caused by the primary base station (BS). Latter the secondary networkpresent an elliptical contour map where the primary transmitter is non-centric positioned on itand the axes of the ellipse will change on function of the interference levels caused by theprimary BS.

Hence, the throughput of the secondary network will depend on the currents channel conditionschannel capacity and SINR, due to the parameters interference level, received signal power,transmitted signal power and adaptive modulation.

Keywords:Adaptive Transmission, Cognitive Radio (CR), Dynamic Spectrum Access (DSA),802.16 (WiMax), OFDM (Orthogonal Frequency-Division Multiplexing).


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TABLE OF CONTENTS

......IAbstract......II

Table of Contents.....III

List of Figures.....V

List of Tables....VII

PrefaceVIII

1 INTRODUCTION ..... (1)

1.1 Overview of the thesis work.. (1)

1.2 Motivation of this thesis .... (2)

1.3 Background.... (3)

1.4 Survey of related works.. (7)

1.5 Organization of the thesis work... (14)

2 BASICS OF DIGITAL COMMUNICATIONS..... (15)

2.1 Digital Modulations...... (15)

2.2. AWGN Channel...... (23)

2.3 Path Loss...... (24)

2.4 SNR and SINR..... (26)

2.5 Error Probability ...... (29)

2.6 Channel Coding.... (33)


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IV

3 COGNITIVE RADIO, OFDM AND ADAPTIVE TRANSMISSION..... (37)

3.1 Multi-Carrier modulation and adaptive data rate..... (37)

3.2 OFDM (Orthogonal Frequency Division Multiplexing) . (40)

3.3 The System Model... (46)

3.4 Adaptive Modulation ... (47)

3.5 Setup OFDM, Secondary Network...... (50)

4 SYSTEM SIMULATION AND RESULT ANALYSIS......... (55)

4.1 The system model based on 802.16..... (55)

4.2 Link Budget 802.16 Primary Network...... (56)

4.3 Link Budget, Secondary Network.... (57)

4.4 System performance, Secondary BS.... (59)

4.5 Spectrum Sensing and optimal band selection..... (60)

4.6 Allowed transmit power, secondary BS... (62)

4.7 Interference... (66)

4.8 System performance, Secondary MS... (70)

5 CONCLUSIONS AND FUTURE WORK...... (73)

Acknowledgment...... (75)

References......... (76)

Appendix....... (80)


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V

LIST OF FIGURES

Figure 1.1 Spectrum Hole Concept in Dynamic Spectrum Access....................................... (3)

Figure 1.2 Transmission scenario and environment for the CR systems.............................. (5)

Figure 1.3 Dynamic Spectrum access models............................... (6)

Figure 1.4 Spectrum sharing Overlay Waveform.......................... (8)

Figure 1.5 Spectrum sharing Underlay Waveform............................ (9)

Figure 1.6 Overlay-Underlay sharing waveform............................. (10)

Figure 1.7 Interference Temperature Model................................ (11)

Figure 1.8 Transmission system model................................ (13)

Figure 1.9 Transmission scenario and environment for the CR systems......... (13)

Figure 2.1 Signal Space diagram for M-ary ASK signals............ (17)

Figure 2.2 Signal Space diagram for M-ary PSK signals................................. (19)

Figure 2.3 Signal Space diagram for M-ary QAM signals .......... (20)

Figure 2.4 Nyquist banwidth and raised cosine comparison ....... (22)

Figure 2.5 Basic Modulator - demodulator without channel coding ....... (28)

Figure 2.6 RequiredEbN0

reqdand receivedEb

N0

r....... (29)

Figure 2.7 Modulator-Demodulator with channel coding ....... (34)

Figure 2.8 Coding gain ........ (36)

Figure 3.1 Comparison of effect of channel on single carrier versus multi-carrier communication.... (38)

Figure 3.2 Link adaption, higher SNR imply higher data rate ............ (39)

Figure 3.3 Per-subcarrier pulse shape (a) and spectrum (b) for basic OFDM transmission ... (40)

Figure 3.4 OFDM subcarrier spacing .......... (41)


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Figure 3.5 General block diagram for OFDM transceiver .......... (42)

Figure 3.6 Addition of a guard period to an OFDM signal ......... (42)

Figure 3.7 General System model........ (46)

Figure 3.8 RequiredEb

N0in adaptive modulation for a given target BER ......... (49)

Figure 3.9 Throughput vs. SNR to maintain a BER below a given threshold for the adaptive modulation

.......... (52)

Figure 3.10 Required SNR, data rate and channel capacity for adaptive modulation ......... (53)

Figure 3.11 Normalized channel capacity (C/W) and spectral efficiency (Throughput/W) vs. SNR...... (54)

Figure 4.1 Specific System model ....... (55)

Figure 4.2 Coverage area for the primary network based on 802.16........... (56)

Figure 4.3 Coverage areas for the secondary network at maximum power ........ (58)

Figure 4.4 Secondary network model .......... (59)

Figure 4.5 Throughput vs coverage of the secondary MS........... (60)

Figure 4.6 selection of the optimal band by the spectrum sensing mechanism....... (61)

Figure 4.7 sensing and calculation of allowed transmit power at secondary BS..... (62)

Figure 4.8 Allowed transmit power for different allowed interference levels. ....... (63)

Figure 4.9 Allowed transmit power at different distances for maximum interference level Rss/4.......... (64)

Figure 4.10 Throughput comparisons with different transmitted power.................................................. (65)

Figure 4.11 Secondary user in presence of interference caused by the primary BS................................ (66)

Figure 4.12 Secondary user interference influence at different positions around the secondary BS... (67)

Figure 4.13 Throughput analyses for different level of interference........................................................ (68)

Figure 4.14 SINR analyses for different level of interference................................................................. (68)

Figure 4.15 Elliptical contour map caused for the interference over the secondary user.... (69)

Figure 4.16 Throughput analyses for different received signal power..................................................... (71)

Figure 4.17 Throughput analyses for different transmitted power... (72)


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VII

LIST OF TABLES

Table 2.1 Equivalent BER M-ary QAM for Q(x) and erfc(x).......... (32)

Table 3.1 Comparison of effect single carrier versus multi-carrier communication ....... (38)

Table 3.2 OFDM PHY parameters 802.11a (WiFi), 5 GHz U-NII band......... (44)

Table 3.3 OFDM PHY data ratesROFDM in Mb/s for 802.11a ... (45)

Table 3.4 OFDM PHY parameters 802.16(WiMax)........ (45)

Table 3.5 OFDM PHY data ratesROFDM in Mb/s for 802.16.......... (45)

Table 3.6 Required SNR to maintain a BER below a given threshold........ (48)

Table 3.7 Required SNR to maintain a BER below a given threshold........ (48)

Table 3.8 RequiredEb

N0in adaptive modulation for target BER < 106........... (49)

Table 3.9 OFDM PHY parameters 802.16....... (50)

Table 3.10 OFDM PHY data rates 802.16 in Mb/s...... (51)

Table 3.11 Data rate and Receiver SNR Assumptions......... (51)

Table 4.1 Sample Link for a Wimax System (802.16) from [63] table 2.8 and simulation results..... (57)

Table 4.2 SNR and maximum distance attainable for adaptive modulation........ (59)

Table 4.3 Elliptical contour map bound for each modulation scheme. ....... (69)


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VIII

PREFACE

Frequency spectrum is a limited resource for wireless communications and it is becoming

congested by the required accommodation of the diverse types of air interface used in next

generation wireless networks. For this reason the FCC (Federal Communications Commission)

initiated a new spectrum paradigm, which will be more flexible to allow secondary users

(Cognitive Radio user or unlicensed user) to access the spectrum as long as the primary users (or

Licensed user) are not interfered with, this new spectrum licensing paradigm will improve the

utilization of the frequency spectrum and enhance the performance of wireless systems.

Cognitive radio based on dynamic spectrum access has emerged as a new design model fornext generation wireless networks. Cognitive radio aims at maximizing the utilization of the

limited radio bandwidth while accommodating the increasing number of services and

applications in wireless networks.

As the development of dynamic spectrum access-based cognitive radio technology has to deal

with technical and practical considerations there is place for research new approaches in the next

generation wireless networks.

The main idea of this project is to improve the underlay sharing method of the dynamic

spectrum access-based in cognitive radio technology by using adaptive modulation throughOFDM (Orthogonal Frequency division multiplexing) and increase the attainable throughput of

the secondary user by changing the modulation scheme providing a higher data rate of the

system.

The project is divided in five chapters: Chapter 1 (Introduction), Chapter 2 (Digital

Modulations and Channel Coding), Chapter 3 (Adaptive Transmission), Chapter 4 (System

Simulation and results analysis) and Chapter 5 (Conclusions).

Chapter 1, Introduction, provide an introduction to the cognitive radio network, and basic

concepts in dynamic Spectrum access, Sharing methods, channel capacity and temperature

interference model. Chapter 2, Digital Modulations and Channel Coding, provides the generalconcepts of digital modulations, channel coding and path loss models needed in the adaptive

transmission. In Chapter 3, Adaptive Transmission, this chapter presents the necessary

knowledge to understand the adaptive modulation by using multi carrier modulation, the

multicarrier modulation used by the cognitive radio system is OFDM.


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Chapter 4, System simulation and result analysis, in this chapter the system considered consist

in a primary network according to the 802.16 standard, and a secondary based in 802.16 with

some modifications over the standard, applying cognitive capabilities the data rate of the system

is estimated using adaptive modulation over OFDM improving the throughput of the secondary

user.

Chapter 5, Conclusions, this chapter is dedicated for highlight the advantages of this research,

also is mentioned the future improvements of this research, in addition the key points of the

adaptive modulation used with the cognitive radio technology are summarized.

In the appendix section is added the Matlab Scripts designed and used in this project, all the

scripts include comments that help the future researchers to understand the code.


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1 INTRODUCTION

The increasing demands for wireless communication in consumer electronics applications, and

personal high-data-rate networks indicate a promising commercial potential. Throughput,

reliability, service quality, and the ever-present availability of wireless services are more and

more demanded. The number of devices based on multiple wireless standards and technologies

will therefore substantially grow in the future exciting progress but new problems will be

created with these increasingly widespread wireless communications.

These problems are the limited availability of radio spectrum and the difficult spectrum

coexistence of dissimilar radio systems in a shared spectrum. Until today, such problems couldbe neglected to a great extent because network operators have usually enjoyed the privilege of

exclusive access to their parts of the radio spectrum.

Dynamic spectrum access refers to the time-varying, flexible usage of parts of the radio

spectrum under consideration of regulatory and technical restrictions. A cognitive Radio (CR) is

a radio that can change its transmitter parameters based on interaction with the environment in

which is operates. Cognitive radios together with dynamic spectrum access attempt to overcome

the described problems.

1.1 OVERVIEW OF THE THESIS WORKThis thesis work is presented as solution for the overcoming problem in wireless

communication the limitation in the spectrum and the difficulty in spectrum sharing. The method

used through this work is easy to understand and can be easily implemented adding some

cognitive capabilities to the current terminal network devices. We use adaptive modulation with

OFDM choosing the most bandwidth-efficient modulation QPSK, 16QAM and 64QAM at

current channel conditions, additionally the system perform sensing capacities and power control

algorithm for protect the licensed user from interference.

The adaptive transmission cognitive radio is simulated with the throughput as the major

measure of the system performance. We have noted that the throughput will depend directly to

the SINR because depending on how big the SINR is, will be the higher data rate performed by

the cognitive radio user. By the way the SINR will depend on the interference power, received

signal power and channel characteristics.


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In case of the interference power is found that can influence the throughput negatively,

decreasing significantly the data rate of the system when the interferer is nearest to the secondary

user. The interference decrease the SINR value thus the constellation scheme used in the

adaptive transmission should be lower.

We analyze the throughput of the system with and without interference then we compare these

two results. Within these process we found that the secondary network will have a contour map

elliptical caused by the interference from the primary transmitter. Latter we change other

parameters as transmitted power and received signal power comparing with the initials results.

1.2 MOTIVATION OF THIS THESIS

The main purpose of the thesis work is to present the adaptive transmission in cognitive radio

networks as problem solutions of the limited available radio spectrum and the spectrum

coexistence of dissimilar radio systems in a shared spectrum. The thesis work improves the

coexistence of two different radio systems, sharing the same frequency band with high data rate

performance.

The principal idea is to share the spectrum used initially for the licensed network with the

cognitive radio network without cause harmful interference over the licensed users. The sharing

spectrum method adopted is capable to use the spectrum simultaneously for both networks

licensed and unlicensed, then within the cognitive radio capabilities for the secondary network

are included sensing of the primary transmitter and primary receiver, power control and adaptive

transmission.

1.3 BACKGROUND

It is necessary to understand clearly the cognitive radio and dynamic spectrum access as key

technologies for improve the reuse of the electromagnetic spectrum, thats why in this section is

explained the general concepts needed to understand the approach of this work.

Cognitive Radio (CR)

A cognitive Radio (CR) is a radio that can change its transmitter parameters based on

interaction with the environment in which is operates. Cognitive radio technologies have the

potential to provide a number of benefits that would result in increased access to spectrum and

also make new and improved communication services available to the public. A cognitive radio


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could negotiate cooperatively with other spectrum users to enable more efficient sharing of

spectrum [1].

The cognitive radios are radio systems that autonomously coordinate the usage of spectrum.

They identify radio spectrum when it is unused by the incumbent radio system and use thisspectrum in an intelligent way based on spectrum observation [2]. The CR (Cognitive Radio) is

defined as a wireless transmission technology combined with awareness, learning, and

adaptation capabilities [3]. Unused Spectrum is referred also as Spectrum hole or white space

[4], this concept is clarified in figure1.1.

The CR system actively recognizes the given channel environment at specific time using radio

sensors. At this time, the recognized channel information is involved in Radio Environment Map

of the CR system, and then the CR system adaptively provides the optimal transmission

parameters to the CR users in the given channel environment using learning algorithms based on

the Radio Environment Map. The CR system can improve efficiency of spectrum usage, since itreuses limited radio resources by recognizing idleness of the spectrum in time, frequency, space

and region. In addition, the CR system can provide the optimal QoS (Quality of Service) even for

various channel environments, since it is possible to adaptively adjust system parameters by the

learning algorithms and adaptation capabilities.

Figure 1.1Spectrum Hole Concept in Dynamic Spectrum Access.

Cognitive networks require a Software Adaptable Network (SAN) to implement the actual

network functionality and allow the cognitive process to adapt the network. Similarly to

cognitive radio, which depends on a Software Define Radio (SDR) to modify aspects of radiooperation (e.g. time, frequency, bandwidth, code, spatiality, waveform), a SAN depends on a

network that has one or more modifiable elements. Practically, this means that a network must be

able to modify one or several layers of the network stack in its member nodes [5].

The design principle for cognitive radio (CR) networks regards the cognitive radio users as

visitors in the spectrum they occupy [6]. This necessitates efficient spectrum management

Frequency

Time

Power

Spectrum Hole

Primary users


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functionalities to occupy idle channels without causing interference with the primary users, and

leave these channels when primary user activity is detected. The successful operation of these

principles relies on the CR users ability to be aware of their surroundings, which is

accomplished through spectrum sensing solutions [7].

The central mechanism of the cognitive network is the cognitive process [8]. This is the

process that does the actual learning and decides on the appropriate response to observed

network behavior. The cognitive capability of a cognitive radio enables real time interaction

with its environment to determine appropriate communication parameters {Power, Frequency,

Space (location), signal (coding/modulation)} [9] and adapt to the dynamic radio environment.

The cognitive radio capability can be divided in four main functions [10][7] such as:

Determine which portions of the spectrum are available Spectrum Sensing Select the best available channel Spectrum Decision Coordinate access to this channel with other users Spectrum Sharing Vacate the channel when a licensed user is detected Spectrum Mobility

About the Cognitive Radio network architecture can be classify by the operation band (Licensed

or Unlicensed band) and by the network architecture as centralized (infrastructure-based) or

distributed (infrastructure-less) [11].

The following are the basic components of primary networks [6], shown in figure 1.2:

Primary user or licensed User: A primary user has a license to operate in a certainspectrum band.

Primary base station: A primary base station is a fixed infrastructure network componentthat has a spectrum license, such as a base station transceiver system (BTS) in a cellular

system.

The basic elements of the CR network (also called secondary network or Next Generation

network) are defined as follows [6], also shown in figure 1.2:

CR user, secondary user or next generation (xG) user: A CR user has no spectrum license.Hence, additional functionalities are required to share the licensed spectrum band.

CR base station, secondary Base Station or next generation (xG) Base Station: A CR basestation is a fixed infrastructure component with CR capabilities. It provides single-hop

connection without spectrum access licenses to CR users within its transmission range

and exerts control over them.

Spectrum broker: A spectrum broker (or scheduling server) is a central network entitythat plays a role in sharing the spectrum resources among different CR networks.


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Figure 1.2Transmission scenario and environment for the CR systems*

*

This figure has been taken from [12], where Akyildiz refer the CR network as xG network.

, [12].

Dynamic Spectrum Access (DSA)

Dynamic spectrum access refers to the time-varying, flexible usage of parts of the radio spectrum

under consideration of regulatory and technical restrictions [1]. The emerging DSA technologiesmay improve communication connectivity and/or capacity are smart antenna/Multiple Input-

Multiple Output (MIMO) and Orthogonal Frequency Division Multiplexing/Access

(OFDM)/(OFDMA) and Cognitive Radio (CR) technologies [13]. According to [14] the

principal Strengths of a DSA system are Support of decentralized spectrum management,

Situation awareness, higher spectral efficiency, Learning capability, Polite coexistence and

Frequency agility.

Dynamic spectrum access (DSA) models for cognitive radio can be categorized in three

approaches [1] as shown in figure 1.3, the exclusive-use model, the shared-use model [15], and

the commons model. In the exclusive-use model, a licensed user can grant an unlicensed user theright to have exclusive access to the spectrum. In a shared-use model, an unlicensed user

accesses the spectrum opportunistically without interrupting a licensed user. In a commons

model, an unlicensed user can access the spectrum freely [16].


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Figure 1.3Dynamic Spectrum access models.

Exclusive-use model

In the exclusive-use model for spectrum access, the radio spectrum is licensed to a

user/service to be exclusively used under a certain rule. In this model, the licenser (e.g. the

government) allocates the spectrum to a licensee. However, the licensee or spectrum owner may

not fully utilize the allocated spectrum in all times and in all locations. Therefore, spectrum

access rights can be granted to cognitive radio users.

Spectrum commons model

For the spectrum commons model or Unlicensed Spectrum, all cognitive radio users have the

same right to access the radio spectrum. Also referred as Open Sharing Model in [17], this modelemploys open sharing among peer users as the basis for managing a spectral region. Advocates

of this model draw support from the phenomenal success of wireless services operating in the

unlicensed industrial, scientific, and medical (ISM) radio band or the Unlicensed National

Information Infrastructure (U-NII) bands in the US at 5 GHz [1].

Shared-use of Primary Licensed Spectrum

For the approach of this project the Shared-use of Primary Licensed Spectrum model will be

used, following [18], the spectrum owned by a licensee is shared by a non-license holder

commonly referred to as a secondary user. Such sharing takes place without the primary beingaware of secondary users; the transmissions of secondary user are expected to have minimal

impact on the operating conditions for which primary user devices are designed. This model is

attractive as it increases spectrum access and utilization and also, shows promise of co-existing

with existing spectrum management. Two possible models of such use are spectrum underlay

and spectrum overlay, these spectrum access techniques are introduced in the next section.

Dynamic Spectrum Access Models

Shared-Used of primarylicensedspectrum

Commons model(Open Sharing Models)

Exclusive-use model

Spectrum

Underlay

Spectrum

Overlay


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1.4 SURVEY OF REL ATED WORKS

In this section is explained the related work used to base the approach of the research develop in

this thesis.

Sharing Methods and Channel Capacity

Channel capacity is the tightest upper bound on the amount of informationthat can be reliably

transmitted over acommunications channel. By the noisy channel coding theorem, the channel

capacity of a given channel is the limiting information rate that can be achieved with arbitrarily

small error probability [19][20].

Information theory, developed by Claude E. Shannon during World War II, defines the notion

of channel capacity and provides a mathematical model by which one can compute it (see

equation 1.1).

For CR environments the channel capacity based in the Shannon theorem depend directly of

the spectrum shared model used, as following we explain the channel capacity for Spectrum

Shared-use Overlay, Spectrum Shared-use Underlay and Spectrum Shared Overlay/Underlay.

Spectrum Shared-use Overlay

Agree with [16] in the case of spectrum overlay, a primary user receives an exclusive right to

spectrum access. However, at a particular time or frequency, if the spectrum is not utilized by a

licensed user, it can be opportunistically [21] accessed by a secondary user. Therefore, to access

a spectrum band, a secondary user has to perform spectrum sensing to detect the activity of a

primary user in that band. If a spectrum hole is found (see figure 1.3 and figure 1.4), a secondary

user may access the spectrum.

Spectrum overlay model is shared explicitly in one of three ways opportunistic, cooperative and

mixed [22]; In the opportunistic way the spectrum is used whenever the licensee does not use it,

in the cooperative way the frequencies are allocated centrally based on real-time negotiation with

the licensee, and in the mixed way sharing is cooperative when possible and opportunistically

otherwise.
http://en.wikipedia.org/wiki/Informationhttp://en.wikipedia.org/wiki/Channel_%28communications%29http://en.wikipedia.org/wiki/Noisy-channel_coding_theoremhttp://en.wikipedia.org/wiki/Channel_%28communications%29http://en.wikipedia.org/wiki/Information_theoryhttp://en.wikipedia.org/wiki/Claude_E._Shannonhttp://en.wikipedia.org/wiki/World_War_IIhttp://en.wikipedia.org/wiki/World_War_IIhttp://en.wikipedia.org/wiki/Claude_E._Shannonhttp://en.wikipedia.org/wiki/Information_theoryhttp://en.wikipedia.org/wiki/Channel_%28communications%29http://en.wikipedia.org/wiki/Noisy-channel_coding_theoremhttp://en.wikipedia.org/wiki/Channel_%28communications%29http://en.wikipedia.org/wiki/Information


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(1.1)

(1.2)

According to Shannons channel capacity [25][26] condition given by equation 1.1, channel

capacity can be optimized by increasing the signal-to-noise ratio (S/N or SNR) and/or channel

bandwidth (W)[19].

C = w log2 1 + SNThe overlay Channel capacity can be written as equation 1.2 according to [23][24].

CCR = WukNk=1

log1 + CRkWukNk=1n0

Wuk

Nk=1

Where N is the total number of unused spectral bands in the total CR monitored bandwidth W,

Wuk is the bandwidth of the kth unused band andCRk the power spectral density of the CRtransmission in the kth unused band.

Spectrum Shared-use Underlay

In Spectrum Shared-use Underlay model the spectrum is used by a second party at the same

time as the primary licensee [22], but with the intent of causing as little interference as possible

(see figure 1.5), this is the interference avoidance concept [27].

CR Primary CR Primary CR Primary

band user1 band user2 band user3

Frequency

Figure 1.4Spectrum sharing Overlay Waveform [23][24].


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(1.3)

Ultra Wideband (UWB) [28] technologies are particularly suited for this type of spectrum

sharing because signals are spread over large swaths of spectrum and the signal strength isaround the RF noise level (this allows a UWB signal to operate on occupied spectrum with a

very low power output, and not cause any interference). This model relies on measuring the

ambient noise and the interference caused in the operating range and maintaining it under a

predefined threshold [27] or the temperature interference limit [29].

In resume spectrum underlay allows unlicensed secondary users to simultaneously operate in

primary user bands but under strict transmit power constraints [21]. The channel capacity of

underlay transmission treated in [23][24] is given by equation 1.3:

CUWB = W log1 + UWB Wn0W + Pi WPiMi=1 wheren0 is the additive Gaussian noise power spectral density, UWB is the average power

spectral density of the UWB transmission, M is the total number of primary users operating

within total bandwidth W, Pi is the narrow band average power spectral density of the ithprimary user andWPi is the corresponding bandwidth of ith primary user.

Spectrum Shared Overlay/Underlay

In cognitive radio techniques, frequency agile transmitters target unused spectrum holes and

transmit power within these unused regions In this context, unused spectrum has been allocated

but is not currently being used whereas underused spectrum is allocated and being used but not

to its full capacity[27]. Similarly, there are currently two enabling CR waveforms, including an

overlay waveform and an underlay waveform. An overlay waveform only operates in unused

spectral regions while avoiding interference to primary assigned users. An underlay waveform is

Frequency

Primary Primary Primary

user1 user2 user3Underlay

Signal

Noise Floor

Figure 1.5Spectrum sharing Underlay Waveform.


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(1.4)

spectrally coincident with primary assigned users and induces minimum tolerable interference

[30][31].

The research in [25], [27], [30], [31] and [32] trend suggests that a hybrid technique

combining overlay/underlay concepts can be employed to maximize spectral efficiency by usingboth white and gray spectral regions. The benefits of both overlay waveform and underlay

waveform are exploited in the hybrid overlay/underlay (both the unused spectrum holes and

underused spectrum bands) to improve the channel capacity and BER performance of the

secondary user.

Finally the Simulations of the hybrid overlay/underlay waveform have proven its superior

performance over both conventional overlay and underlay waveforms. The hybrid

overlay/underlay waveform is shown in figure 1.6.

The channel capacity for the hybrid Overlay/Underlay transmission treated in [23][24] is given

by equation 1.4:

Chybrid = W log1 + CR1kWukNk=1 + CR2iWPiMi=1n0W + Pi WPiMi=1

Where

CR1k is the CR transmitted power spectral density in the kth unused band, and

CR2i

is the CR transmitted power spectral density in the ith underused band. The following constraintsare imposed to maximize overall channel capacity while minimizing mutual interference

between CR users and other primary users:

CR2i Ii,iCR1k k,k

Frequency

CR Primary CR Primary CR Primary

band user1 band user2 band user3

CR band CR band CR band

Figure 1.6Overlay-Underlay sharing waveform.


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CR1kWukNk=1

+CR2iWPiMi=1

Swhere Ii is the interference tolerance level in the ith used band,k is the maximum allowedtransmitted power spectral density (e.g., FCC mandated interference temperature) in the kthunused band, and S is the total transmit power of the cognitive user across all unused and

underused frequency bands.

Interference Temperature Model

The Interference Temperature model is the concept introduced by the FCC (Federal

Communications Commission) in [2] and [33] to effectively manage the limited spectrum

resources, and it is used for quantifying all the interference factors generated in the radiofrequency.

Figure 1.7 Interference Temperature Model [62].

Kolodzy has mentioned in [34] that the central role of the spectrum management is theinterference management, and then the Interference Temperature is introduced as metric for

Cognitive radio networks.

Threshold Set by

Unlicensed User

P2

P1

Frequency

Power

dB

Noise Floor

Allowable Interference


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According with [29] and [35] the concept of interference temperature is identical that the noise

temperature concept it is a measure of the power and bandwidth occupied by interference.

Interference Temperature is specified in Kelvin and is defined as

TI(fc , W) =PI(fc , W)

K W

WherePI(fc , W) is the average interference power in Watts centered at fc, covering bandwidthW

measured in Hertz. Boltzmann's constant K = 1.38 1023 Joules per Kelvin degree. By usingthe PSD (Power Spectral Density) S(f) of the interference on the considered bands, theTI can be

equivalently expressed as

TI(fc , W) =1

W2K S(f)dffc +W/2

fc

W/2

The fundamental premise of the generalized model is that we have no a priori knowledge of

our signal environment, and consequently have no way of distinguishing licensed signals from

interference and noise. Under these assumptions, the interference temperature model can be

expressed as

TI(fc , W) +MfPt

K W TL(fc)

WhereTL(fc) is the given interference temperature limit. Note that Pt denotes the transmission

power of the CR user, and Mf which is a fractional value between 0 and 1, represents a

multiplicative attenuation due to fading and path loss between the CR transmitter and theincumbent users receiver.

The signal to interference plus noise ratio for the interference temperature is defined in [3] and

[36] as

= TL(fc) TI(fc , W)Mf TI(fc , W)

Where Ls is the path loss factor between the cognitive radio user and the primary user.

(1.5)

(1.6)

(1.8)

(1.7)


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13

Adaptive Transmission Scheme

According to [1][3] the author present an adaptive transmission scheme for CR systems based

on interference temperature measure [39]. The adaptive transmission method guarantees the

maximum throughput of the secondary users through power constraints [40] and adaptivemodulation to minimize the interference to primary user. The adaptive transmission power

methods [40] takes the premise that using interference temperature model [12], cognitive radios

operating in licensed frequency bands would be capable of measuring the current interference

environment, and adjusting their transmission characteristics as power [38] in such a way that

their transmission avoids raising the interference temperature over regulatory limit [2].

Figure 1.8Transmission system model

The scheme presented [1][3], estimates the distance between a secondary user and the

incumbent primary user using the Interference Temperature (IT)[39] information measuredthrough the spectrum sensing procedure. Then, the secondary user determines the transmit power

constraint [36] which does not cause any interference to the licensed user. At this point the

secondary user maximizes the throughput using adaptive modulation (see figure 1.8). Choi and

Lee realize in [20] a similar analysis for potential coexisting cognitive radio in the ISM band for

technologies such as Zigbee, Bluetooth and WLAN.

Figure 1.9Transmission scenario and environment for the CR systems.

Primary

UserCR

CR

CR

QPSK

16QAM

64QAM

Primary

User CRTx

d1 d2

CRRx


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14

The basic cognitive radio transmission scenario and environment is shown in Figure 1.9.

Where the fc and B denote the carrier frequency and the bandwidth commonly used by the

cognitive radio user and the licensed user. The distance (d1) between the licensed user and the

secondary user are estimated by the interference temperature model considering a channelenvironment with distance based Path Loss factor and the Additive White Gaussian Noise

(AWGN) without the multipath fading. The distance d2 is the distance from the secondary user

and the respective destination node, d1>d2.

1.5 ORGANIZATION OF THE THESIS WORK

The thesis work is distributed sequentially starting from the general background and basics

knowledge necessary for understand the main idea of the key technologies cognitive radio and

dynamic spectrum access. As next is required to understand the digital modulations, OFDM andadaptive transmission concepts that will be used in the system model.

When all the theory and technical knowledge is completed, we follow with some basic setups

and simulation of this technical knowledge, before the simulation and analysis results chapter it

is necessary to setup parameters of OFDM and adaptive transmission. We base our work in the

standard 802.16 for the primary network and the cognitive radio network.

We calculate the corresponding data rate for each modulation scheme and the relation SNR

distance for perform higher throughput and increase the efficiency of the spectrum. As the

adaptive transmission is performed, we added to the system cognitive capabilities that allow the

both network work in the same spectrum at the same time.

Next to this work we found that the interference caused from the primary BS over the

secondary user will have great influence in to the secondary user performance or throughput. The

interference decreases considerably the data rate given for the secondary user depending on the

position of it. Analyzing different possible position for the secondary user its found that the

contour map for the secondary network its not circular as usually is expected for the adaptive

transmission system. The interference influence over the throughput give a result of elliptical

contour map and the secondary base station is non-centric positioned on it.

Additionally the performance of the system decrease as the SINR at the secondary userdecrease, and that can be caused by three different reasons: increasing the interference level,

decreasing the received signal or decreasing the transmit power. As last we conclude the

research work done and we suggest the future work of this approach. The analysis done here is

for only one cell, as the 802.16 is a cellular based system for future work can be improve by

simulate all the system.


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15

2 BASICS OF DIGITAL COMMUNICATIONS

This chapter is dedicated to introduce the principal concepts used in the research for adaptive

transmission in underlay cognitive radio networks. The concepts treated are digital modulations,

AWGN channel, path loss and channel coding.

Digital modulation is the process by which digital symbols are transformed in to waveforms

that are compatible with the characteristics of the channel. Our project is based in adaptive

transmission using QPSK, 16QAM and 64 QAM modulations then is essential to have a clear

view of these concepts.

The Adaptive modulation use channel coding in order to obtain a higher spectral efficiency,

channel coding refers to the class of signal transformation designed to improve communications

performance by enabling the transmitted signals to better with-stand the effects of various

channel impairments, such noise, interference and fading.

In this chapter we consider the performance of the digital modulation techniques over AWGN

channels, with performance criteria of interest the error probability or Bit Error Rate (BER). The

system is simulated under AWGN channel then characteristics of the channel as noise, path loss,

signal-to-noise power ratio (SNR), and signal to noise plus interference radio (SINR) are

introduced.

2.1 DIGITAL MODULATION

Digital modulation is the process by which digital symbols are transformed in to waveforms that

are compatible with the characteristics of the channel [37].

Pulse Amplitude Modulation (M-ary PAM)

In digital pulse amplitude modulation (M-ary PAM) or Phase shift Keying (M-ary ASK), the M

signal waveforms are represented as

() = ReAm g(t)ej2fc t, m = 1, 2 , . , M, 0 t T= Am g(t)cos 2fct

(2.1)


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16

WhereAm denote the set of M possible amplitudes corresponding to = 2 possible k-bit blocksof symbols. The signal amplitudesAm take the discrete values (levels)

Am = (2m 1M)d, m = 1,2, MWhere 2d is the distance between adjacent signal amplitudes. The waveform g(t) is a real-valued

signal pulse.

The MPAM signals have energies

m = 2

(t)dt

0

=1

22 g2(t)dt = 120 2 g

Whereg denote the energy in the pulse g(t). Clearly, these signals are one-dimensional, and,hence are represented by the general form

(

) =

(

)

Where f(t) is defined as the unti-energy signal waveform given as

() = 2g g(t) cos2fctAnd

= Amg2 = 1,2, The minimum distance between constellation adjacent points is = d2g . Thecorresponding signal space diagrams form M=2, M=4 and M=8 are shown below.

(2.2)

(2.3)

(2.4)

(2.5)


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17

Figure 2.1Signal Space diagram for M-ary ASK signals.

Phase Shift Keying (M-ary PSK)

In digital phase modulation or phase-shift keying (M-ary PSK), the M signal waveforms are

represented as

() = Re g(t)ej2(m1)M ej2fc t , m = 1, 2 , . , M, 0 t T= g(t)cos 2fc t + 2

M(m 1)

= g(t) cos2M

(m 1) cos2fct g(t) sin 2M

(m 1) sin2fct

Where g(t) is the signal pulse shape and = 2(m 1)/M, m =1,2,M, are the M possiblephases of the carrier that convey the transmitted information.

2d

M=2 Symbols k= 1 bits

0 1

2d

M= 4 Symbols k= 2 bits

00 01 11 10

000 001 011 010 110 111 101 100

M= 8 Symbols k= 3 bits

2d

(2.6)


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18

The energy of the MPSK signal waveform is

=

2 (t)dt

0

=1

2 g2(t)dt = 1

2

0

gFurthermore, the signal waveforms may be represented as a linear combination of two

orthonormal signal waveforms [37],1() and2() as following

(

) =

11(

) +

22(

)

Where

1() = 2g g(t) cos2fct2() = 2g g(t) sin 2fct

And the two dimensional vectors

= [

1,

2] are given by

= g2 cos 2M (m 1) ,g2 sin 2M (m 1) , = 1,2 . .Signal Space diagrams for M=2 also called Binary PSK (BPSK), M=4 also called Quadrature

PSK (QPSK) and M=8 or 8PSK are shown below [38].

The minimum distance between constellation adjacent points is dmin =2gsin(/M), where2g is typically a function of the signal energy. For M = 2k or 10log2M = k, wherekarethe need bits for transmit M symbols PSK. Usually these bits are coded in gray coding, note that

between the nearest constellation point only change one bit.

(2.8)

(2.7)

2.9


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19

Figure 2.2Signal Space diagram for M-ary PSK signals.

Quadrature Amplitude Modulation (M-ary QAM)

For M-ary QAM, the information bits are encoded in both the amplitude and phase of the

transmitted signal. Thus, whereas both MPAM and MPSK have one degree of freedom in which

to encode the information bits (amplitude or phase), MQAM has two degrees of freedom. As a

result, MQAM is more spectrally-efficient than MPAM and MPSK, in that it can encode the

most number of bits per symbol for a given average energy [38].

The transmitted signal is given by

() = ReAm ejm g(t)ej2fc t, m = 1, 2 , . , M, 0 t T= ReAm (cos m + j sin m ) g(t)ej2fc t

() = Am cos m g(t)cos2fct Am sin m g(t)sin2fct= Amc g(t)cos2fct Ams g(t)sin2fct

01


BPSK


QPSK

00

01

11

10


8PSK

000

001011

010

110

111

101

100

(2.10)


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20

WhereAmc = Am cos m and Ams = Am sin m , Amc andAms are the information-bearing signalamplitudes of the quadrature carriers and g(t) is the signal pulse.

Alternatively, the QAM signal waveforms may be expressed as

() = ReAm ejm g(t)ej2fc t, m = 1, 2 , . , M, 0 t T= Am g(t)cos(2fct + m )

WhereAm = Amc2 + Ams2 and m = tan1(Ams /Amc ). From this expression, it is clear thatthe QAM signal waveforms may be viewed as combined amplitude and phase modulation [39] as

show in figure 2.3.

Figure 2.3Signal Space diagram for M-ary QAM signals.

64QAM

16QAM

QPSK

(2.11)


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21

The QAM signal waveforms may be represented as linear combination of two orthonormal

signal waveforms [25][37] :

(

) =

11(

) +

22(

)

Where

1() = 2g g(t) cos2fct2() = 2g g(t) sin 2fct

And the two dimensional vectors = [1, 2] are given bySm = Amcg2 , Amsg2 , m = 1,2 . . M

Where theg is the energy of the signal pulse g(t). The Euclidian distance between any pair ofsignal vectors is

= m n= g2 [(Amc Anc )2 + (Ams Ans )2]

In special case where the signal amplitudes take the set of discrete values {(2m 1M)d,m=1,2,M , the signal space diagram is rectangular, in the rectangular QAM the minimum

distance between adjacent points is = d2g

M-ary Signals

For signaling schemes that process k bits at time, the signaling is called M-ary. Each symbol

in an M-ary alphabet can be related to a unique sequence of k bits, where

= 2 102 = [ /]

(2.12)

(2.13)

(2.14)


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22

And where M is the size of the alphabet. In the case of digital transmission, the term symbol is

refers to the member of the M-ary alphabet that is transmitted during each symbol duration ,since one of M symbols or waveforms is transmitted during each symbol duration

, the data

rate R can be expressed as

= 2 = /The effective duration of each bit is:

= 1We can define then the Symbol rate as

= 1 = 2 /The bandwidth W and the Symbol rate are related by

= 12

(1 + ) = 12 (1 + ) []

Where is the Roll Off factor with values between 0 1 , for = 0 is called thenyquist bandwidth which is the minimum bandwidth required for the transmission using a

perfect rectangular shape for the pulse, and for

= 1 is called Raised cosine as shown in the

figure 2.4. The formula can have variation if Double Side Band (DSB) signals are considered[26], in that case = (1 + ). This is not our case, and then we will consider the firstequation.

Figure 2.4Nyquist banwidth and raised cosine comparison [37].

(2.15)

(2.16)

(2.17)

(2.18)


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23

In general we will consider = 1 raised cosine, and no ISI (Inter Symbol Interference) then thebandwidth W is:

=

2.2. AWGN CHANNEL

As next we consider the performance of the digital modulation techniques over AWGN

channels, with performance criteria of interest the error probability or Bit Error Rate (BER). In

order to understand the AWGN channel we introduce concepts as noise, path loss, signal-to-

noise power ratio (SNR), energy-per-bit ( ) and energy per-symbol ( ). Following thissequence we describe the error probability on AWGN channels for different modulation

techniques as parameterized by these energy metrics.

Noise

Every communication system have error performance degradation from the transmitted signal

to the received signal, then the important task of the detector is to retrieve the bit stream from the

received waveform as error free as possible. The two main causes for the error performance

degradation are the effect of the filtering at the transmitter, channel, and receiver described as

Intersymbol interference (ISI) [37].

Moreover the other cause of the error performance degradation is the electrical noise and the

interference produced by a variety of sources, such as galaxy and atmospheric noise, switching

transients, intermodulation noise, as well as interference signals from other sources.

With proper precautions, much of the noise and interference entering a receiver can be reduced

in intensity or even eliminated. However, there is one noise source that cannot be eliminated, and

that is noise caused by thermal motion electrons in any conducting media.

The primary spectral characteristic of the thermal noise in communication systems, is that

two-sided power spectral density

(

) =

02

is flat for all frequencies of interest. When the

noise power is characterized by such a constant-power spectral density, we refer to it at white

noise. Since the thermal noise is present in all telecommunication systems and is the

predominant noise source for many systems, the thermal noise characteristic (additive, white,

and Gaussian, givin rise the name AWGN) are most often used to model to the noise in the

detection process and in the design of receivers. Whenever a channel is designated as an channel

(2.19)

(2.19)


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24

(with no other impairments specified), we are in effect being told its impairments are limited to

the degradation caused by this unavoidable thermal noise.

The thermal noise is define as

= 0 []Where is the bandwidth of the system and0 is defined as

0 = With is Temperature in Kelvin and Botlzmanns constant = 1.38 1023 [/] [/]For some case maybe be consider the noise figure NF of the antenna at the receiver an rewrite

the noise equation in dB as[40]

= 10 log10(0) + 2.3 PATH LOSS

The achievable signal coverage for a given transmission power determine the maximum

distance for communicate source and destination in a wireless system. There are different

modeling for the path loss calculation, most of them are characterized by a distance-power-

gradient[41] calculations, free-space path loss or empirical path Loss models, some of these

modeling are Two-Ray model, Local Mean Received Power, The Okumura Model[42], Hata

Model, long distance path loss model[43] and simplified path loss.

Free space propagation model

For free space propagation model the received power is define as [44]:

= 4 Where is the transmitted power, and are the antenna gain of the tranmiter and

receiver respectively, is the Path loss exponent, is the wave length of the transmitted signaland is the distance between the transmitter and receiver. The equation ####is also called theFriss transmission equation

(2.21)

(2.20)

(2.22)


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25

Then the path loss is define as

=

4

Expressing the equation 2.22 in dB

= + + We will omit the sub index dB. Thus,

Ls = 10 log10 4

+ 10 log10(d)

Accurate path loss models can be obtained from complex analytical models or empiricalmeasurements when tight system specifications must be met or the best locations for base

stations or access point layouts must be determined. Then the Path loss simplified model [3][36]

(or long distance model in [43]) can be expressed as

Ls = L0 + 10 log10 dd0And

L0 = 20 log10 4d0Whered0 is reference distance with value 1 m.

COST321 Hata Model

The Hata model is widely used for cellular networks in the 800MHz/900MHz band. As PCS

deployments begin in the 1,800MHz/1,900MHz band, the Hata model was modified by the

European COST (Cooperation in the field of Scientific and Research) group, and the extended

pathloss model is often referred to as the COST-231 Hata model. This model is valid for the

following range of parameters [45]:

150MHz f 2000MHz 30m hb 200m 1m hm 10m

(2.23)

(2.24)

(2.25)

(2.26)

(2.26)


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26

1km d 20kmThe median path loss for the COST-231 Hata model is given by

Ls = 46.3 + 33.9 log10f 13.82 log10hb + (44.9 6.55 log10hb)log10d a(hm ) + CFThe MS antenna-Correction factor, a(hm ) is given by

a(hm ) = (1.11 log10f 0.7)hm (1.56 log10f 0.8)For urban and suburban areas, the correction factor CF is 3dB and 0 dB, respectively. The

WiMAX (802.16 standard) forum recommends using this COST-231 Hata model for system

simulations and network planning of macrocellular systems in both urban and suburban areas for

mobility applications. The WiMAX Forum also recommends adding a 10dB fade margin to the

median path loss to account for shadowing [45].

2.4 SNR and SINR

In an AWGN channel the modulated signal () = Reu(t) ej2fc t has noise n(t) added to itprior to reception. The noise n(t) is a white Gaussian random process with mean zero and power

spectral density N0/2. The received signal is thus r(t) =s(t) +n(t) as in the approach followed by

[3].

We define the received signal-to-noise power ratio (SNR) as the ratio of the received signal

power Pr to the power of the noise within the bandwidth of the transmitted signal s(t).

The received power Pr is determined by the transmitted power and the path loss, shadowing,

and multipath fading. The noise power is determined by the bandwidth of the transmitted signal

and the spectral properties of n(t).

(2.27)

(2.28)


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27

Specifically, if the bandwidth of the complex envelope u(t) of s(t) is W then the bandwidth of the

transmitted signal s(t) is 2W. Since the noise n(t) has uniform power spectral density02

, the total

noise power within the bandwidth 2W is

= 02 2 = 0So the received SNR is given by

= 0In systems with interference, we often use the received signal-to-interference-plus-noise power

ratio (SINR) in place of SNR for calculating error probability. If the interference statistics

approximate those of Gaussian noise then this is a reasonable approximation. The received SINRis given by [40]

= 0 + Whereis the average power of the interference.The SNR is often expressed in terms of the signal energy per bitor per symbol as

=

0

=

0=

0

Then we know that = 1 then [47] = 0

0 is called SNR per symbol. Then for M-ary modulation we have0

0 =

0

2 0 is called the bit energy per noise power spectral density (or SNR per bit) and it is a importantparameter for the specific error probability of the modulation.

0 is the SNR per bit measured atthe receiver.

(2.32)

(2.30)

(2.31)

(2.29)

(2.33)


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28

Changing the equation 2.33 as [40] we have SNR equal to

=

0

= 10

10

2

+

0

Another approach presented in [37] is

0 = 0 = 0

That using the data rate

=

1

[bit/s] and symbol rate

=

1

[Symbol/s] we obtain that

0 = 0 = 0 Lets illustrate our system by a diagram for clarify the idea.

Figure 2.5Basic Modulator - demodulator without channel coding.

M-ary

Modulator / = 2 /Input

M-ary

Demodulator

SNR

0 = 0 = 0

= 2

Output

(2.34)

(2.35)

(2.36)


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29

In figure 2.5 the Basic Modulator - demodulator is illustrated, the modulator receives a

waveform during each interval . The signal is transmitted through AWGN channel and then theprobability that the demodulator makes a symbol error

(Symbol Error Probability).

2.5 ERROR PROBABILITY

The bit error probability (BER, also called Bit error Rate) is related to the probability thatthe demodulator makes a bit error and it is related with the symbol error probability for M-arysystems as

= 2

Where PE is function ofEs

N0, thenPE EsN0 andPb (BER) is function of EbN0, thenPb EbN0

These error probabilities are depending of the digital modulation used by the systems.

Required vs. received

We need to differentiate between required0

and the actual or received 0, see figure.

Figure 2.6RequiredEbN0

reqdand receivedEb

N0

r

0 0 0

(

)

1

2103

105

(2.37)


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30

The required0 is corresponding to the necessary 0 at the receiver for determinate BER

and digital modulation, thats mean if the received

0

is less than the

0

the transmit

cannot be, actually for design the modulator-demodulator link [37] is necessary to achieve The

required0 +2dB , in other words0 0 + 2

This is the condition of the modulation at given BER.

Error Probability for M-ary PSK

The symbol error probability and the bit error probability (BER) of the M-ary PSKmodulation is given by [25], [26]

= 2 2 0 sin =2 20 2 sin

2

For BPSK, M=2, then we have

= 2 2 0 = 2 20

For QPSK, M=4, then we have

= 2 0 = 20

(2.38)

(2.39)

(2.40)

(2.41)


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31

Error Probability for M-ary QAM

According to [46], [47] for high SNR the BER for Rectangular M-ary QAM can be

approximated to

PE 4M 1M Q 3(M 1) EsN0 and Pb 4M 1Mlog2 M Q 3log2 M(M 1) EbN0

For 4QAM, M=4 then

2 0 20Then we can say that QPSK and 4QAM are equivalent modulations.

For 16QAM, M=16

PE

3Q

1

5

Es

N0

and Pb

3

4Q

4

5

Eb

N0

For 64QAM

PE 72 Q 363 EsN0 and Pb 712 Q 1863 EbN0

(2.42)

(2.43)

(2.44)

(2.45)


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32

The Complementary Error Function Q(x) or erfc(x)

The Complementary Error FunctionQ(x) or co-error function has a equivalent function erfc(x),

since we are using MatLab for the simulation is necessary to find the relationship between these

two functions completely equivalent.

() = 2 2() = 1

2 2

Then changing Q(x) by erfc(x) we have

Table 2.1Equivalent BER M-ary QAM for Q(x) and erfc(x)

Modulation Pb(Q(x)) (erfc(x))M-QAM

Pb 4M 1Mlog2 M Q 3log2 M(M 1) EbN0 2 1 log2 3log2 2( 1)0QPSK,

4QAM 20 12 016QAM

Pb 34 Q 45 EbN0 38 25 064QAM

Pb 712 Q 1863 EbN0 724 erfc 963 0

(2.46)


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33

2.6 CHANNEL CODING

Channel coding refers to the class of signal transformation designed to improve

communications performance by enabling the transmitted signals to better with-stand the effects

of various channel impairments, such noise, interference and fading [37].

Coding allows bit errors introduced by transmission of a modulated signal through a wireless

channel to be either detected or corrected by a decoder in the receiver. Coding can be considered

as the embedding of signal constellation points in a higher dimensional signaling space than is

needed for communications.

Data rate for coding channel

We have introduced in last section the data rateR without channel coding for M-ary signals as

R = Rs log2 M bits/s

A binary block code generates a block of n coded bits from l information bits. We call this an

(n, l) binary block code. The coded bits are also called codeword symbols.

For coding channel we have the coding rateRc is define as [49]

Rc =data bits

coded bits=

l

n

The coding rateRc is given in {information bits per codeword symbol} with Rc 1.If we assume that codeword symbols are transmitted across the channel at a rate of Rs

symbols/second, then the data rateR for M-ary signals associated with an (n, l) block code is

R = RcRs log2 M bits/s

or

Rs =R

Rc

log2

Msymbols/s

Thus we see that block coding reduces the data rate compared to what we obtain with uncoded

modulation by the code rate Rc (this is true for using a channel with the constant

bandwidth,Rs = W ).

(2.47)

(2.48)

(2.49)


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34

SNR for coding channel

Since the encoding transformation has replaced l data bits withn channel bits (coded bits),

then the ratio channel-bit energy to noise power spectral density, 0, is computed bydecrementing the value of

0 by the factor Rc = ln.0 = Rc 0Also, since each transmission symbol is made up of log2 M channel bits, then the SNR

0 is0 = log2 M 0 = Rc log2 M 0Expanding this result to the received power over the noise power spectral density

0 = 0 = 0 Rc = 0 In order two explain clearly the concept of the coding channel we can see the next figure,

where the block coding has been included, and how the block code change our original system

(modulation without channel coding, see figure 2.5).

Figure 2.7Modulator-Demodulator with channel coding.

Encoder

M-ary

Modulator / = 2 /Input

/

DecoderM-ary

Demodulator

SNR

0 = 0 = 0 Rc = 2Output

= ()

(2.50)

(2.51)

(2.52)


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35

The error probability

As shown in the figure 2.7 the symbol error probability PE (after demodulator block) for

determinate M-ary system may be

PE = F EsN0It is necessary to remember that for coding channel

0 = Rc log2 M 0Now that decoder block is present in the system, then the designated channel-bit-error

probabilityis given as PE

log2 MPE 1

This step is necessary because when coding is used the system error performance doesnt only

depend on the performance of the demodulator; it also depends on the performance of the

decoder.

The final output decoded bit error probability Pb (BER) depends on the particular code, the

decoder and the channel-bit-error probabilityby the following approximation [37], [46]Pb 1n j nj pcj (1 pc)nj

n

j=t+1

Where n is the channel bits (coded bits) and t is the largest number of channel bits that the code

can correct within each block of n bits.

Coding gain ()Coding gain in AWGN is defined as the amount that the SNR can be reduced under the

coding technique for a given Pb (see figure 2.8). Coding gain can be described as measure of the

reduction in the requiredEb

N0

that needs to be provided, due the error performance properties of

the channel coding. Coding gain is a function of the modulation type and the bit errorprobability.() = EbN0uncoded () EbN0coded ()

(2.53)

(2.54)

(2.55)

(2.56)


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36

Figure 2.8Coding gain.

There are different coding methods mentioned in [34], [37], [26], [44], [48] and [19] as linear

block codes, convolutional codes, concatenated codes and turbo coding; for adaptive

transmission [43][48][50][51] is considered convolutional codes for achieve error-performance

improvements without expansion of signal bandwidth. A example of convolutional codes used is

the Trellis coding that is perfectly designed for band limited channel employs larger signals

alphabets as M-ary PAM, PSK or QAM, the coding gain for trellis coding varying between 3dB

to 6dB [19].

()

104

106

102

1

2


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NOTICE:

Chapter 3, Chapter 4, Chapter 5,References and further are deleted

intentionally.

Documents

Throughput Analysis for Adaptive Transmission Cognitive Radio by Pablo Betancur, Date 05-2010