AN INVESTIGATION OF ADAPTIVE CONTROL
TECHNIQUES IN OFDM WIRELESS
MODULATION
By
KRISHNAVENI RAMASAMY
Bachelor ofEngineering
Coimbatore Institute OfTechnology
India
1999
Submitted to the Faculty of the
Graduate College of the
Oklahoma State University
in partial fulfillment of
the requirements for
the Degree of
MASTEROF SCIENCE
December, 2002
AN INVESTIGATION OF ADAPTIVE CONTROL
TECHNIQUES IN OFDM WIRELESS
MODULATION
Thesis Approved:
_~_~A.6~
De~htiraduate College
11
ACKNOWLEDGEMENTS
Firstly my sincere thanks are to my advisor Dr. Jong-Moon Chung for his
patience, critical suggestions, inspiration, effective guidance, and diligence in helping me
through the struggles and without whose help this would have not been possible. I would
also like to thank my committee member Dr. Guoliang Fan for the support in the
completion ofmy thesis.
My sincere thanks are also to the Advanced Communication Systems Engineering
Laboratory (ACSEL) & Oklahoma Communication Laboratory for Networking and
Bioengineering (OCLNB) at the Oklahoma State University for supporting me with the
most advanced resources which helped me to achieve my goals efficiently. My gratitude
to the OFDM research group for providing vital information in the OFDM area and
assisting me with the computer simulations.
My special thanks are to Dr. Ramakumar for serving on my thesis committee and
providing much guidance throughout my career at the Oklahoma State University.
Finally, I would like to thank my father, Professor Ramasamy Ellapanaidu,
mother, sister, and my brother for their moral support and enthusiasm that I regard most
important.
111
Dedicated to
My dear father,
Prof. Ramasamy Ellapanaidu
"In the time we have it is surely our duty to do all the good we
can to all the people we can in all the ways we can."
-William Barclay (1907-1978, Scottish Theologian, Religious Writer, Broadcaster)
v
TABLE OF CONTENTS
Chapter Page
I. Introduction 1
II. Applications of OFDM Systems
2.l.Wireless Broadband Communications ..4
2.2. Present and Future Communication Systems 5
2.3. MAC Protocols 6
III. Technical Review of Single-Carrier & Multi-Carrier Systems
3.1. Single-carrier, Multicarrier, and OFDM Channel Model.. 8
3.2. OFDM System Representation 15
IV. Adaptive Rate, Adaptive Power Modulation Systems
4.1. Spectral Efficiency of Adaptive M-QAM for continuous rate
Adaptation 32
4.2. Optimal Power Adaptation .37
4.3. Spectral Efficiency of Adaptive M-QAM for discrete rate
Adaptation 43
4.4. Constant power, Adaptive rate and constant rate, Adaptive power
systems 45
4.5. BER performance results of the continuous and discrete rate
adaptation 48
4.6. Observations 49
V. Adaptive Modulation for OFDM system and Macroscopic Diversity Techniques
5.1. Adaptive OFDM 50
5.2. Modulation Parameters in case of Adaptive Modulation
of Subcarriers 51
5.3. Signaling & Blind Detection 54
5.4. Macroscopic diversity 56
VI. Conclusions & Future Research 66
VI
Appendix-A. Matlab Codes 68
References 72
Vll
CHAPTERl
INTRODUCTION
Orthogonal Frequency Division Multiplexing (OFDM) is subject to fading and
frequency errors, which reduce its usefulness in wireless mobile communication
channels. This thesis deals with analyzing the frequency and phase errors and applying
adaptive modulation to improve the overall throughput and bit error rate (BER)
performance of the OFDM system using adaptive modulation.
Wireless mobile radio channels are subject to both slow and fast fading. Fast
fading is caused by the reflected and diffracted signals arriving at the receiver at different
times and reducing the signal strength. Goldsmith and Chung [4.1] introduced an
adaptive rate and adaptive power modulation control mechanism for capacity
improvement at a constant BER performance. Keller and Hanzo [5.3] ] introduced an
adaptive rate modulation scheme in which OFDM systems are adaptively switched
between BPSK1
, QPSK2
, 16-QAM3 modulations. In this thesis we implement adaptive
rate and adaptive power modulation in OFDM systems and apply diversity techniques to
further improve the performance. The research also extends the Goldsmith model [4.1] of
the adaptive M-QAM approximation technique to reduce the fading and shadowing
effects.
1 BPSK - Binary Phase Shift Keying
2QPSK - Quadrature Phase Shift Keying
316-QAM - 16-Quadrature Amplitude Modulation
1
The organization of this thesis is as follows. Chapter 2 gives an introduction to the
application ofOFDM systems. Chapter 3 provides the background information on OFDM
and its synchronization technologies. In addition the general definitions of components
used in the system model followed by a discussion of channel and effective
synchronization procedures are summarized. Adaptive modulation, another key area in
improving signal reception of a single carrier system, is discussed in Chapter 4.
Additionally, in Chapter 4 the application of variable-rate and variable-power adaptive
systems in general and the analysis of their performance when applied to an OFDM
systems is investigated in Chapter 5. Following this the shadowed fading channel model
is analyzed. To improve the performance due to shadowing effects the macroscopic
diversity technique is implemented along with the adaptive system. The results and
observations documented in this thesis were generated using Matlab and Mathematica
programs by employing Monte Carlo simulations. Chapter 6 summarizes the conclusion
of the research and presents areas for future research.
2
CHAPTER 2
APPLICATIONS OF OFDM SYSTEMS
In this chapter we review the applications and features of practical Orthogonal
Frequency Division Multiplexing (OFDM) systems that have been implemented by
industry.
OFDM was initially used only in military applications due to its implementation
difficulties. Now, it has found new implementations in systems such as IEEE802.lla as
well as in the new European satellite-based digital audio/video/terrestrial broadcasting
systems [2.1]. In addition, the OFDM-time division multiple access (TDMA) structure
has found new applications in wireless Asynchronous Transfer Mode (WATM) providing
Broadband Integrated Services Digital Network (B-ISDN) services to mobile users [2.1].
OFDM is considered as one of the cornerstone technologies for next generation wireless
systems. New products with higher data rates are now possible through OFDM
technology, such as, wireless local area network (WLAN) systems including IEEE
802.11a, European Telecommunications Standards Institute Broadband Radio Access
Networks (ETSI BRAN), and new emerging wireless broadband multimedia applications.
3
2.1. Wireless Broadband Communications
The demand for wireless (mobile) communications as well as Internet/multimedia
communications is growing exponentially. While the current systems are primarily
designed to provide either voice or multi-media communications, future mobile
communication and wireless LAN technology aims at integrating both voice and data
services. The next generation Wireless Broadband Multimedia Communications System
(WBMCS) aims at a high information rate which requires a careful selection of
modulation techniques. One of the emerging wireless broadband networks are the
wireless LANs with new systems running in frequency bands above 3GHz.
The frequency bands for wireless broadband communications is as shown in
Fig. 2.1. The wireless broadband air access interface channel will demand a relatively
large frequency band greater than 2 Mbps, which is easier to accomplish at higher
frequencies. Both Europe and the United States have reserved frequency bands for
Mobile Broadband Systems (MBSs). Some wireless indoor applications use Orthogonal
Frequency Division Multiple Access (OFDMA) in an unlicensed 60 GHz frequency band
in support of 155 Mbps data rates. OFDM is used in WATM networks as well with burst
transmission. The various projects in the Advanced Communication Technologies and
Services (ACTS) program and the parameters used are listed below [2.1]:
4
Project WAND AWACS SAMBA MEDIAN
FEC Complementary Reed- Reed-Solomon Reed-Solomon
coding SolomonIBCH (55/71)
Radio access TDMA/TDD TDMA/TDD TDMAlFDD TDMA/TDD
TDMAslotsize IATMcell 8ATMc/burst 2ATMc/burst IATMc/OFDM
ATM services CBR, VBR, UBR CBR, VBR, UBR CBR, VBR, CBR, VBR, UBR
UBR
Frequency 5 GHz 19GHz 40GHz 61.2 GHz
Radio bit rate 20 Mbps 70 Mbps 82 Mbps 155 Mbps
Modulation OFDM,16 OQPSKlcoherent OQPSK OFDM, 512 carrier,
carriers, 8 PSK detection DQPSK
Radio-cell size 20-50 m 50-100 m l200m, 6000m 10m
Target Indoor In/Outdoor In/Outdoor Indoor
Environment
Table 2.1. Projects in ACTS
The demand for video/voice and data communication over the Internet on mobile
phones and Personal Digital Assistant (PDA) are increasing day by day. The application
ISM
EUur~ c=J1 I~~~~~LAN D v.tAAMBS
~I ---0 v.tAAMBS
Jap n .LI-_-_M-_BS-_-_- L..-v.tAAMBS---J
2.40-2.4835 5.15-5.25 5.47-5.825 10-16 17.1-17.3 59-S4
Fig.2.1.Frequency band for wireless broadband conYllunications.
of broadband Internet access on mobile phones is one objective of the research
application of this thesis.
2.2. Present and Future Communication System
The third generation (3G) Communication technologies are based on both voice
and data communications over mobile telephones at higher data rates at the range of upto
2 Mbps. Wireless Broadband Multimedia Communications Systems (WBMS) technology
5
is based on integrated services wireless (mobile) communications and
Internet/multimedia with an information rate ranging from 2 Mbps to 54 Mbps
(IEEE 802.IIg/aIb and HIPERLAN systems using frequency bands in the 2 to 60 GHz
ranges).
The selection of the modulation and multiplexing technique is critical in
determining the performance and efficiency of the system, which led to the research of
this thesis on OFDM technology.
2.3. Medium Access Layer Protocols (MAC)
Communications become more difficult when different users share a common
transmission medium. Without a protocol to provide coordination and control, all the
devices may attempt to transmit simultaneously and the transmission collisions will result
in a very low user throughput.
Two possible types of MAC protocols are: I) Static Allocation Protocols and 2)
Dynamic Allocation Protocols.
6
MAC Protocols
I
r I
Static Protocol Dynamic Protocol
1 I
I FDM I I TOM I I ALOHA I I CSMA/CD l
Flg.2.3. Comparing some of the static and dynamic MAC protocols.
Static Allocation protocols include Time Division Multiplexing (TDM) and
Frequency Division Multiplexing (FDM) where every user is given a fixed timeslot or
frequency band to be used temporarily, and hence the implementation is simpler. Static
protocols are most beneficial only when all the users have equal amounts of data to send
and are constantly transmitting, thus consuming all of the available bandwidth. Imagine a
system with N slices of bandwidth and only M users transmit. In this case, the difference
(N-M) slices of bandwidth is not utilized. The situation becomes worse when all the users
do not require the same amount of bandwidth. The Dynamic Allocation Protocol assigns
bandwidth on an as-needed basis, which is a better topology in the case of the non-uniform
transmission data rate and user characteristics. Random access protocols, which
are s part of the dynamic allocation protocols, include ALOHA, Slotted ALOHA and
Carrier Sense Multiple Access with Collision Detection (CSMAlCD) MAC techniques.
The Slotted ALOHA Protocol gives an efficient means of access for OFDM techniques.
7
CHAPTER 3
TECHNICAL REVIEW OF SINGLE-CARRIER AND MULTICARRIER
SYSTEMS
In this chapter the mathematical structure of OFDM systems and channel
performance characteristics are presented.
This chapter is divided into the following sections. In the first section, a
comparison of single-carrier and multicarrier systems in terms of BER performance and
channel characteristics are studied. Further, we analyze the performance of these systems
in a Gaussian and non-Gaussian environment. The basic OFDM system is modeled in this
chapter. Four main criteria are used to assess the performance of the OFDM system; they
are: tolerance to multipath delay spread, peak power clipping, channel noise, and time
synchronization errors. Further, the OFDM mathematical representation model with the
fading characteristics is also studied. The probability of failure of frequency
synchronization, which is a main criterion in determining the orthogonality of the system,
is also calculated.
3.1. Single-Carrier, Multi-Carrier and OFDM Channel Model
Selection of the modulation technique employed in wireless systems plays an
important role in determining system cost and efficiency. Some of the recent equipment
manufacturers are using OFDM in place of Single-Carrier systems (SC) due to the reason
that OFDM has a higher efficiency than SC systems. The use of OFDM is advantageous
8
(3.1)
because it removes the intersymbol interference (lSI) if the delay spread is less than the
guard band. IEEE802.11a WLANs OFDM is used with an 800 ns of cyclic prefix to
eliminate the multipath delay spread. Although research is going on in this field, most of
the papers in the literature do not give analytical comparisons of different systems. In this
section, SC to multicarrier modulation and OFDM modulation techniques in Gaussian
and Rayleigh channels are analyzed.
1) Statistical Models for Multipath Fading channels
The communication environment under study is a multipath fading channel. The
transmitted signal, when transmitted, depending on the propagation area and multipath
profile, will arrive at the receiver at different times. These signals sometimes may add up
or sometimes become nullified. When the signal is nullified it is said that fading has
occurred.
2) Single carrier systems
In a single carrier system with the carrier frequency represented by Ie' the
transmitted signal s(t) can be represented as [3.1]
set) =Relsl (t)ej21ifct j
Here, sl (t) represents the complex form of the transmitted signal. The received signal
with the attenuation factor and the phase shift due to fading is given by,
r(t) ~ Re{[:~>" (t)e -J'.,'.0' SI (t) }J'';'' }
9
n
The equivalent lowpass channel is represented as
n
n
= Lan (t)cos 27ifJn (t) - /Lan(t)sin 27ifctn (t)
n n
=Xl (t) + X 2 (t),
where Xt(t) and X 2 (t) are two zero-mean Gaussian random variables. The amplitude
and phase of the received signal are given by, Ra(t) =~XI (t)2 + X 2(t)2 and
OCt) =tan-t(X2 (t)/ XI(t)), respectively [3.4].
The Rayleigh distribution is mostly used as a channel distribution model for
multipath fading in mobile channels. The power distribution is closely related to a chi-square
distribution given by Ra = X I
2 + X; where XI and X 2 are two zero-mean Gaussian
random variables with variance 0'2. Since the result is a chi-square distribution with two
degrees of freedom, the general probability density function can be reperesented as [3.4]
2
2r n-l -r-f
(r) - e 20-
2 VCr)
R - 2n/2 O'nf(n / 2)
The probability density function for the same are given by
r 2
fR(r)=_r_
2
e 20-
2
, r>O (n=2,f(n-2)=(n-2)!=1,for n>O)
(5
10
(3.2)
1 f o(8) =-, -TC::5 8::5TC
2TC
(3.3)
The graph below shows the probability density function of the Gaussian and Rayleigh
density of a single carrier system.
Gaussian and Rayleigh probability density functions
0.7 r---.-------.------,-----,.---,.--------,
0.6
0.5
c:
o ·S
,igii 0.4
'ii
~'"' 0.3
.'0" e
c..
0.2
0.'
~3=--_-'-2------J-''-----'-0----1'---2.L.--....:.::::::=l3
Rayleigh/Gaussian variable r,X
Fig.3.l. Probability Distribution Function of a SC system.
Probability of error: The probability of bit error for a BPSK system in an AWGN channel
is given by the equation (3.4), (based on a signal-to-noise ratio represented by Eb ). The
No
noise is assumed to follow the Gaussian distribution function with variance a of No /2 .
11
(3.4)
To find the communication system probability of bit error in a Rayleigh fading channel
[3.1], the probability of error is integrated over the Rayleigh distribution function as
shown below:
00
Pbr = JPbCrb)!Yb (Yb)dYb
o
Yb
Pbr =ler!C~ [~]e Yb
o Yb
Probability of bit error rate in AWGN and Rayleigh Fading Channel
10° ~-~---r---r---r-----,.--.,---,-----.
• Rayleigh BER(BPSK)
10
01 ...... ~~ • AWGN BER(BPSK)
.".. ................
...................................................
..........................................
100e L-_-l-_~__.l...---l.--..L._--1__=-_-::'::-_---J
o 5 10 15 20 25 30 35 40
Average SNR per bit
Fig.3.2. Performance ofBER on a single-carrier Rayleigh fading channel.
12
(3.5)
where J" (1)) is the prohahility function of the SNR, which IS [;Je~;; where
rb denotes the average SNR.
The performance graph of the single carrier BPSK signal in a fading channel (Fig.3.2)
shows that fading introduces a significantly higher BER compared to AWGN channels.
From Fig.3.2, we observe that for a bit error rate of 0.01 approximately a 25dB gain in
the signal to noise ratio is required for the system to perform equivalently in Rayleigh
fading channels.
3) Single-Carrier and Multicarrier M-QAM systems
Performance of M-QAM in a non-Gaussian environment: The performance of most
of the M-QAM digital communication systems is based on a Gaussian environment. But,
in actual situations, the noise model must also include various man-made interference
factors, as well as shadowing and multipath fading effects. Non-Gaussian noise can be
characterized as large impulses occurring at the detection interval.
The transmitted signal is given by:
OQ
St(t) = :L(Ak + jBk)a(t-kT),
k~-",
where aCt) is the low-pass shaping pulse and T is the symbol duration. (Ak + jBk )
corresponds to the complex symbol transmitted during the k th symbol interval.
13
Noise model: The noise model is represented by two factors: the AWGN noise no(t) and
the impulse noise np (t) . Combining the two factors together we obtain
(3.6)
where nOt (f) is the complex envelope of no (t) and np/t) is the complex envelope of
np(t). At the receiver, the noise vector n is defined by two complex random variables as
shown in (3.7).
In our model, we take the analysis with these impulse noise terms following a Rayleigh
distribution in the fading environment.
The probability distribution function and hence the probability ofBER is given by [3.1],
(3.7)
Let 0'2 represent the impulsive noise variance and let 0'2 =(NO /2) represent the two-np
no
sided Gaussian noise variance. The modulus of the real and imaginary components of the
14
non-Gaussian random variable is represented as r =~X 2 + y2 , and r is the distribution
parameter.
a 2
The term p =~ is the factor that determines the ratio of the impulsive noise power
a 2
np
and Gaussian power, which plays an important role in the performance analysis of single-carrier
M-QAM systems. The first-order approximations and the quasi-Gaussian
approximations of the AWGN channel are compared with the results from the Rayleigh
distribution in Fig.3.3.
Nc=2r=no. of subcarriers
....•.\.~
.'..:., r-1o
Awmt.i r-9
:.f
1o·a L-_-J-_---l__...J......_-:::------:::'::-_~-__:::':_-_:'
o 5 10 15 20 25 30 35 40
SNR/bit
Fig.3.3. Performance of Rayleigh fading system.
3.2. OFDM System Representation
1) Mathematical Representation of OFDM Systems
In case of multipath signal propagation, different signals arrive at different times. This
leads to a delay spread of the channel, which causes intersymbol interference (ISI).
15
OFDM is an orthogonal multiplexing technique used to eliminate lSI by using guard
bands. This section gives an introduction to the multicarrier modulation implemented in
the OFDM system using Fast Fourier Transform (FFT) and Inverse Fast Fourier
Transform (IFFT).
Multicarrier modulation (MCM) reduces the interference effects induced on
single-carrier systems. The analysis is the same as the previous section with the white
noise characterized by the Gaussian distribution and the impulsive noise characterized by
Rayleigh distribution. All the sub-carriers exhibit the same modulation level M.
MCM is a parallel transmission technique where the bit stream to be transmitted
is divided into equal length symbols applying Nc number of carriers. Using the IFFT
modulator, the received sample rk , in terms of transmitted sample and noise factor nk , is
given by
N -I - j210lk
The received sample after FFT is given by ~! rke~
vNc n;O
The probability distribution function of the noise random variable is given by,
The M-QAMlMCM technique has a similar effect to the SC-QAM except that the
distribution parameter ris replaced by the multiplicative term of the number of
16
subcarriers Nc ' The equation below represents the probability of error for a multicarrier
system.
P 4 -]N ~(yNc)k 1 [ 1 ] e = e C LJ (l--)Pk (l--)Pk
k=O k! JM JM
where the term Pk is given by
P - 1 er cl 3 Ea)
k -"2 1< 2(M -1) er~ ,
2 2 k 2 erk =erG +--er[.
yNc
The term eri is based on two noise variance factors, erb =er 2 and er 2 =er 2 . no [nfJ
In case of a multicarrier system, increasing the number of carriers decreases the
er 2
impulsive component p = ;0. In case of low p, the performance reaches AWGN as
a
nfJ
the number of carriers increase. When P» yNc ' the noise is highly impulsive. This
shows that with an increase in number of carriers, the Gaussian BER performance can be
closely approached by the multicarrier system. The structure of an OFDM system is
provided in Fig.3.4.
17
Modulation
Base Station
Data for
M-oAM/MPSK
user1 Modulation
Mapping on Modulation
8ubcarriers IFFT
(TDMA) ••
Ch
a
n
n
e
I
FFT
N _I - 21Dlk
1 c - I '"Ice Nc
l--__-' .[ii; n=O
•
Demodulation
for k =0 Nc - 1
MQAM/MPSK
~----1 Demodulation
Demapping 1<;::-----1 Demodulation
Mobile Station
Data for
sern
Data for
u er 1
Da a for
user 2
Fig.3.4. OFDM System Model
a) Serial to Parallel Conversion: In the system shown in Fig.3.4, the input serial data
stream is formatted into the word size required for transmission, e.g., 2bit/word for
QPSK, 1bit/word for BPSK and shifted into a parallel format. The data are then
transmitted in parallel by assigning each data word to one carrier in the transmission.
b) Modulation of Data: The modulation techniques commonly used in OFDM are either
M-QAM (Quadrature Amplitude Modulation with M number of constellations) or M-PSK
(Phase Shift Keying) systems. The data to be transmitted on each carrier are differentially
encoded with previous symbols then mapped into a PSK or QAM format. Since
differential encoding requires an initial phase reference an extra symbol is added at the
start for this purpose. The data on each symbol are then mapped to a phase angle based
on the modulation method. For example, in QPSK the phase angles used are 45°, 135°,
18
c) Inverse Fast Fourier Transform: After the required spectrum is worked out, an
inverse fast Fourier transform (lFFT) is used to find the corresponding time waveform.
The guard period is then added to the start of each symbol.
d) Guard Period: The guard period is a cyclic extension of the symbol to be transmitted.
This is to allow for symbol timing to be easily recovered by envelope detection and helps
avoid interchannel interference (leI). After the guard period has been added, the symbols
are then converted back to a serial time waveform. This becomes the baseband signal for
the OFDM transmission system.
e) Channel: The transmitted signal then passes through the radio channel. This radio
channel is modeled as a scatter communication channel. The receiver is designed with the
multitude of reflected and delayed signal components. These signals tend to reinforce or
cancel each other. This results in fading. This channel model is characterized by a
lognormally shadowed Rayleigh fading model (described later in this chapter)
undergoing mutipath delay spread shadowing. A feedback link is also available which
informs the receiver about the channel conditions and hence make some changes in the
transmission parameters of the signal.
t) Receiver: The receiver basically does the reverse operation of the transmitter. After
demodulating the signal from the transmission band, the guard period is removed from
the data/voice symbol. The FFT of each symbol is then taken to find the original
transmitted signal. The phase angle of each transmission carrier is then evaluated and
19
converted back to the data word by demodulating the received phase. The data words are
then combined back to the same word size as the original data.
2) Application of Rayleigh fading characteristics on an OFDM system
Orthogonal frequency division multiplexing uses guard intervals to eliminate the
intersyrnbol interference between data blocks. But, since the channel undergoes time
variations, there is a loss of subchannel orthogonality. If the bandwidth of the channel is
larger than the coherence bandwidth, then the channel is a non-frequency selective fading
channel. If Tm is the delay spread of the channel, then the coherence bandwidth for the
channel is tenned as 1/Tm =Bd' In case of frequency selective channel, the effective
bandwidth of the channel is less than the coherence bandwidth.
The same procedure applied to calculate the destruction introduced due to a single
carrier system is also employed in multicarrier OFDM systems which can be denoted as
follows:
Let the received signal be given as
The Rayleigh fading envelope of ro is given by,
2
'0
f () ro -2"2 0
R ro =-2e cr ,ro >
a
20
(3.8)
Similarly, the Rayleigh faded envelope for sample r,v_l can be written as,
2
-rN--!-
f ( ) rN I 2 2 0
R rN -1 =-Te CT , rN-1 > .
a
The joint probability function of the two sample points can be represented by the
density equation,
Substituting from (1), the probability density function (PDF) of a becomes,
The overall bit error rate for the BPSK modulated OFDM signal is given by,
OC) 2
Pbr =f erfc( 1-2:-a_E~S-)fa (a)da
o CTp +No /2
(3.9)
where No /2 represents the Gaussian noise density, a; gives the leI noise power, and
a 2Es is the effective signal strength after fading.
21
3) OFDM Frame Synchronization
Synchronization is an important factor of OFDM modulation. Since the OFDM
system performance is highly dependent onOOO maintaining the orthogonality of the
carriers, avoiding intercarrier interference (ICI) and intersymbol interference (lSI)
becomes an important factor. The receiver needs to know the exact position of the
subcarriers in order for the system to be in synchronization with the transmitter. The
synchronization error as a result may lead to two types of effects: frequency offset or
phase error. The frequency and phase jitter introduced in the system leads to the
displacement of the subcarriers being separated by exact intervals thus causing ICI and
lSI.
Comparison of single-carrier Systems and multicarrier Systems in terms of
interference: For single carrier systems, phase noise and frequency offsets introduce
degradation to the performance. The sensitivity of phase noise and frequency offset has a
greater effect on multicarrier systems than single-carrier systems, which is one of the
disadvantages of OFDM relative to single-carrier systems.
Degradation in multicarrier systems (OFDM): This section discusses the degradation
introduced due to phase noise and frequency offset.
An OFDM signal consists of N sinusoids (bins), which are orthogonal and are
spaced T seconds apart. The effect of frequency offset and phase error in terms of the
variance of the noise terms is calculated as [3.2]
22
0"; =E~ 812 ]+ IIE~ l k - m 1
2
]
m=O
,»,~k
In (3.10), the tenn E~ 812 J results from the additional noise component, whereas
(3.10)
N-l [ ] L E~ I k-m 1
2 represents the interbin interference noise variance caused due to other
m=O
m'l=k
bins interfering with the k th bin.
As E~ 1m 1
2Jdecreases with increasing m, we can approximate 0"; as
0-,7 ~ E~ " 1
2]+ ~AI I k-m 1
2 ~ J:\1m 1
2
]- E1J
m",k
where E1 = E[llo1
2
] . Let T represent the symbol duration. When there exists a
. I sin(1r!1jT)
frequency offset gIVen by !1f ,then 10 1= .
1r!1jT
I E~ 1m [2 ]- E} =1- E}
m=-oo
where E6 is the power of the useful component. Therefore, the variance of other noise
terms is given by
0"2 =E} - E6 + 1- E1 =1- E; .
v
23
(3.11)
Sensitivity of Signal to Noise Ratio due to Frequency offset: The OFDM symbols use
FFT technique for frequency modulation techniques. The frequency carriers of this
OFDM symbol should be an integer number of cycles in the FFT interval. The effect of
frequency offset introduces the carriers to be no longer an integer multiple of FFT
interval. Hence, ICI is introduced into the system thus reducing the SNR.
The detailed calculation are discussed below. The following BER sensitivity of
OFDM systems to Carrier Frequency Offset and Weiner Phase Noise leads to finding the
probability of failure of synchronization. Let I be the number of the OFDM symbol with
k number of subcarriers. The resulting OFDM signal can be written as (without noise
and static frequency offset),
where Tu is the OFDM symbol period, H, k is the transfer function for the Rayleigh
frequency selective fading channel with a maximum dispersion of r max ~ /1 represented
by the equation,
2Jrr !5....
H"k ='~"hi (t)e 'r.u
The FFT signal output for the symbol can be written as,
N-I
r/,k =a/,klO + La"nlk-n + n/,k
n=O
n*k
24
where Eo = E~ 10 I] contributes for the useful component of the signal and 8 is the noise
component. The degradation can be defined as the SNR without phase error and
frequency offset to the SNR with the influence of error.
SNR
Wlt}101I1 - freqllency-offset
SNR
with - freqllency-offset
SNR E s
without- frequency-offset 1
Degradation No = ----------=--'--- =-----
SNR E6 E6 without - frequency-offset
i~ +a; l+a;(~~)
Taking the logarithm on both sides we get,
which corresponds to the degradation caused due to frequency offset.
Noise power due to static frequency errors a; is derived from equation (3.11) as
With the static frequency, the receiver is phase rotated which in tum leads to leI.
10 2 Es Dfreq =:--(NJr/1jT) -
31nl0 No
DMe -_ -10- NJrI..AJ. ifT)2 -Es
freq - 3ln 10 ( No
25
(3.13)
(3.14a)
(3.14b)
The equation (3 .14a) represents the degradation introduced in case of single-carrier
systems and the equation (3 .14b) gives the degradation of a multicarrier system where N
represents the number of subcarriers in the system.
The graph below shows the degradation introduced due to frequency offset based on the
equation (3. 14a).
...
...
Effect of Frequency Offset
...
...
...
...
...
1
-4 -3.8 -3.6 -3.4 -3.2 ·3 -2.8 -2.6 -2.4 -2.2 -2
Normalized Linewidth/Subcarrier Spacing
Fig.3.5. Effect of Degradation due to Frequency Offset
Sensitivity to Phase Error: Phase Offset in an OFDM system leads to two effects. The
first effect is that a phase offset leads to a random phase error and in such cases the
oscillator linewidth is much smaller than the OFDM symbol rate leading to correlation
from symbol to symbol. The amount of degradation compared to the original signal
strength is calculated as follows. Sensitivity to phase noise is given by [3.2]
D == _11_4JZ:fJT~
phase 6ln 10 No
26
(3.14)
This is derived from [3.2] as indicated below:
From equation (3.11) and according to experimental results it is proved that the variance
(72 in case of phase noise is given by,
phase-noise
1 2 E1 = 1- -(4trf3T) = EO
6
2 1
(7 =- (4trflT).
phase-noise 6
We obtain the degradation due to phase noise as,
D ~~(47Z:1?T)2~
freq - 61n 10 fJ.L No
(3.16)
Impact of Symbol Timing Error: At the receiver, the guard interval is removed and
then Fast Fourier Transform is processed to the OFDM symbol. In order to identify the
exact occurrence of the OFDM symbol, there should not be any timing offset. The
introduction of timing offset in an OFDM signal leads to the disturbance of the subcarrier
symbol defined by
j2tr'!.£ N - n
f',k=e N NE"a/kH'k+nn(l,k). G
(3.17)
The noise power due to the timing offset can be calculated by the autocorrelation of the
symbols given by,
27
2
=~(n& - ;,)- ~2 (n~ _2n~i +;, )
=~dC. __1_dC.2
N I N 2 I'
h T. were dc. =n --.!.....
I & T
4) Probability of failure of frequency synchronization
The noise terms (thermal noise distribution a1 along with other noise terms a~ror(l,k»
of the signal can be represented as a~ + a;rror(l,k) . Hence, the signal-to-noise ratio can
be given by
£6 SNR=--~--
a 2 + a 2
N error(/,k)
where I is the number of the OFDM symbol and k is number of subcarriers.
The resulting OFDM reveived signal can be written as (with noise due to frequency offset
and phase error) can be given by Zt,k [3.3]
28
The average power of the channel noise is given by the factor N[ ,k, whereas
n!if (l, k), n phaseoffset (l, k) constitute the noise variance due to frequency and phase offset
error and its sum is given (J2
error(/,k)
The Probability of failure of symbol synchronization is determined by the condition,
(J2 < -.!...a2 where K is a constant depending on channel conditions.
error(l ,k) K N
Time and frequency synchronization is a critical performance measure of OFDM
systems. Various synchronization procedures are followed to reduce the above
synchronization error. In this thesis, we assume that we have perfect synchronization
between the transmitter and receiver.
In order to improve the overall performance of the OFDM system, OFDM
Adaptive modulation is employed to improve the optimization of the power transmission
and effective modulation techniques (which is discussed in the coming chapters).
29
CHAPTER 4
ADAPTIVE RATE, ADAPTIVE POWER MODULATION SYSTEM
In this chapter, we discuss the bit error rate performance and spectral efficiency of
an adaptive rate and adaptive power system which was presented in Goldsmith and
Chung [4.1].
Adaptive modulation is one of the key areas of research currently under
investigation to maximize the capacity and performance of wireless systems. The mobile
channels under investigation suffer from deep fades due to multipath signals arriving at
the receiver. Choosing the highest modulation scheme that will give the best BER could
maximize the spectral efficiency of these communication channels. Using adaptive
modulation, the carrier modulation is matched to SNR, maximizing the overall spectral
efficiency (in bps/Hz) of the channel. A Time Division Duplex Channel (TDD) (feedback
channel) is used in order to appropriately determine channel conditions during the next
time slot for the transmitter to select the required modulation levels for its subcarriers.
High-speed wireless communication applications require a system with high
spectral efficiency. In a non-adaptive system, it is required that the system be designed
for worst or average channel conditions. Since the wireless channel characteristics are
dynamic, in case the channel quality gets worse, the channel capacity will not be utilized
effectively. When the channel is estimated and the information is transmitted back to the
transmitter, the power and transmission rate can be adapted to make best use of the
30
channel conditions and hence produce a better system performance compared to fixed
wireless systems. In [4.1], the spectral efficiency of variable-rate and variable power
adaptive systems applying M-QAM is studied showing that the adaptive system results in
an improved performance.
The analysis is carried out for two types of systems - continuous and discrete. An
ideal adaptation system is the continuous rate adaptation using infinite modulation levels.
The discrete rate adaptation is the one that can be implemented in a practical system. It
takes finite levels of modulation index changes. The following sections describe these
two types of adaptations and their spectral efficiency in an M-QAM system.
4.1. Spectral Efficiency of Adaptive MQAM for continuous rate adaptation
In order to analyze adaptive modulation techniques using optimal power and rate
adaptation, the BER equation for M-QAM in [4.1] has to be approximated to a more
differentiable form as given below in this section.
The following adaptation analysis is done for single-carrier modulation. Let
M represent the number of constellation levels with M = 2k , where k gives the number
of bits/symbol used in the modulation.
E
With Gaussian noise of NO' let ;v represents the average signal to noise ratio.
o
From Proakis [2.1], the probability of BER can be calculated as follows,
(4.1)
31
Assuming Gray-bit mapping, Substituting M = 2k in (4.1), the probability of bit-error
rate can be obtained by the equation, Pb = ~ PM , resulting in
:-1[l-l(l-( 1 3 Eav J2]] 2(1- --)erfc( ----
k .[;k 2k -1 NO
2(1 1.5 Eav J ::: - (1- --)erfc( ----) .
k .[;k 2k -1 NO
Since this function cannot be easily differentiated, the above BER equation is converted
to a more easily differentiable fonn based on [4.1]. The difference of this approximation
is found to be within 1dB (Fig.4.1) [4.1]. The following approximation is carried out for
k ~ 2 and BER :s; 10- 3 .
[
-1.6 * SNR]
BERM - QAM ::: O.2exp 2k -1
32
(4.2)
Hi
10.2
10·'
cr
UJ
CD
1O.e
1O.e
1O.'D
0 5 10
•
•
•
15 20
SNR(dB)
25
·.0.0
·0
"fJ.
~
+J
iO
<0
"·0•o•o
35
Fig.4.I. BER for M-QAM
Now, the BER approximation can be defined, where k is found from the above equation
and compared with the Shannon capacity limit. The spectral efficiency is plotted (Fig.4.2)
and compared for different BER requirements (10-3 and 10-6
). Taking logarithm on both
sides of equation (4.2), we obtain the following derivations:
o
10
_...J..- __~ ~ __..-.o....--_~_ _ ~____ J
15 20 25 30 35 40
A>erage SNR(dB)
FigA.2. Maximum spectral efficiency for continuous rate adaptation.
33
BERMQAM {- 1.6 •SNR]
'" ex
0.2 2k -I
{
BERMQAM 1 ) =In({ex-1.6 *SNR]J
0.2 2k -I
( ) [
-1.6*SNR]
In SBERMQAM = 2k -1 .
Based on the results we can see that
2k -1- [ -1.6 *SNR ]
- lr;(SBERMQAM )
2k =1+[ -1.6 *SNR ] lr;(sBERMQAM ) .
From the above equation we obtain,
( [
- 1.6 * SNR ]J k = log 2 1+
In(SBERMQAM ) . (4.3)
Based on equation (4.3) the spectral efficiency is plotted out in figA.2. It is evident from
the three curves that the BER performance is achieved at the expense of spectral
efficiency, ie., to achieve a BER of 10.6 the spectral efficiency has to be much lower
(about 1.5bps/Hz) compared to the BER of 10-3 requirements, at a fixed SNR.
The approximation of the bit-error-rate for different channel conditions r can be
obtained from equation (4.4). The coefficients CI =O.2,C2 =-1.6,c3 =1,c4 =1 [4.1] were
substituted to provide general access to the equation (4.4).
[
-C2SNR(Y)]
BER(y) ~ cl exp c k( )
2 3 r -C4
34
(4.4)
Let S denote the total transmitted signal power, then the instantaneous value of
the received SNR can be represented by the equation SNRCy) =y S~) , where SCy) is the
S
instantaneous value of the power. Here SCy) is the adapted transmit power for received
y.
To obtain the instantaneous bit-error-rate equation, the average BER is equated to
the instantaneous BER as given below: BER =BERCy)
- [--C2 SNR CY)] BER =BERCy) ~ cl exp c k( )
2 3 r - C4
Taking natural logarithm of the above equation yields
which can be reorganized in the form of
- c 2 SNR (y)
In BER
C1
And correspondingly,
35
- c2 SNR (y)
+ c4
BER
In--
cl
- C1 SNR (y) - + c
BER 4
In--
k(y) ~ _--=-- c, .....::e..
C3
(4.5)
Number of modulation bits (k(r») for M-QAM: The continuous levels of modulation
and the discrete levels used in the adaptive rate system are shown in the following figures
Fig.4.3, 4.4, 4.5, 4.6. No transmission occurs when the channel condition is below the
desired SNR level. In this case, no modulation bit is employed. In Figs. 4.4-4.6, the
adaptation threshold value is assumed to be 5 dB for Rayleigh channel for a BER of 10.3
.
Based on the continuous level, the adaptation system takes infinite continuous switching
levels, whereas the discrete adaptation system takes finite switching levels based on the
target BER conditions for the data system. For the case shown below, the switching
levels in case of discrete adaptation comprise of key) =0, 2, 4, 6, 8, 10, and 12. The
number of degrees of freedom is assumed based on implementation considerations.
36
'2 12
fO fO ~
.~ 8
~
.! ~ B
16
5 ..
~ ./ l 6
i !
~ , ~
i
.,. ,
,/ i Z z
./
00 10 '5 20 15 II :l5 <0 00 10 ,5 20 25 Xl 35 <0 S~db)
SNR{db'
FigA.3. Continuous rate average BER. FigAA. Continuous rate instantaneous BER.
°0L..-----'-.--:'::10----,5':-----2O-'----"-25--'l:l---:35"------'.a
SNR(db)
Fig.4.5. Discrete rate average BER.
4.2. Optimal Power Adaptation:
00'-----'---:...-'-,0--'.5.....- .~..... -...2..5--l:l'------'-35--l40
SNR(db)
FigA.6. Discrete rate instantaneous BER.
1) Continuous rate adaptation: Since there are two variables to be optimized-
(transmitter power and adaptation rate), we introduce two Lagrange variables - (AI and
,.1.2). The Lagrange equation for the instantaneous BER is given in terms of power and
rate by,
37
ao ao ao ao
J(8(y),k(y)) = jk(y)p(r)dy +Al fBER:y)k(r)p(y)dy -BER fk(y)p(Y)dY +..1,2 jS(y)p(r)dy - S
o 0 0 0
Since for instantaneous BER, BER(y)=BER, the above equation can be reduced to one
Lagrange variable,
I r-C2SNR(y)
og2 + C4
l In BER
J(S(y» =1 Cl
o C3
<Xl
p(y)dy +}., jS(y)P(y)dy - S
o
SNR(y) = Y S~)
S
Performing optimal power condition, ~=0 for S(y) ~ O,k(y) ~ 0, the equation for the
as(y)
power becomes
S(y) 1 1
-=-=-
S c3 (In 2)}"S yK
S(y) 1 1
--=--=----
S yoK yK (4.6)
where K gives the power loss when a non-adaptive QAM is used for modulation. It is
given by the equation,
K=
(
BER)
C4 ln ~
The power adaptation equation is a water filling equation, which means that more power
is used when the channel quality is good. The cutoff fade depth is given by Yo below
which 8(y) = O. The above equation is plotted as shown in the figure 4.7.
38
'4
1
---- -~"
I
'"2
~ 08 ~
I I
Q. 0"61
OA
0"2
.~.;-~
.' .........
oL-: ..__
o 5 10 '5 20
SNR(dB)
-~ - --........ _--- - _._-
25 30 35 40
. S(y)
FlgA.7. -=- for MQAM
S
In adaptive OFDM CAOFDM) systems, depending on the channel conditions the
modulation parameters are varied. The channel threshold SNR value above which
transmission takes place is given by Yo. For the conditions above, S(y) = 0 for y < Yo.
The term JCYI'Y2' YN'SCY)) is the Langrange multiplier equation for the variables,
adaptive rate and adaptive power. It is given by
J(y, .y,•.......¥N.S(y»= ""~}}><y)dy+A,[""~}'j<BEJ{y)- BE~P(Y)dY]+"'[lS(y)p(y)dY-S]
The optimal power and rate adaptations are obtained from solving the following
conditions:
aJCn,Y2,·······¥N,S(y))
a5(y)
- a L 14Yi+1 a [Yi+l J f P(Y)dy +At - L 14 fCBEl(y) - BE19P(Y)dy
a5(y) OgsN-l Yi a5(y) QgsN-I Yi
39
+ A2 ~fa:>fs(r)p(r)dr - s] as(r)
Yo
[ ]
r ] a y;+\ a:> '"'
=O+Al aSC) I ki JCBERCr)pCr)dr- O +A2l J-o-SCr)pCr)dr-O
r O$i:SN-l a5Cy) y; Yo
_ II 1 " aBERCy) , 1 - V+/i-l'" "t'1\.2·
I a5Cr)
In summary, we obtain,
Subsft1ufmg BER MQAM "" 0.2 exp [-16'..SNRJ'm the equatI.On (4.7),we get,
ll-l
To simplify (4.8), we substitute 2k
; -1 = fCk i ) in which we obtain,
Taking a logarithm on both sides we obtain,
40
(4.7)
(4.8)
Si(Y)
-1.6 *Y--- ['U'(k')] ___--'S'---- = In '':1 I
f(k i ) 3.2*ki y
Si5!) =IO[ )[(kj )5 ] f(k i )
S -3.2 *kiy -1.6* Y (4.9)
2) Discrete Rate, Instantaneous HER: In case of discrete rate analysis, ki takes discrete
values for the regions defined by [yi ,Yi+1)' These rate region boundaries are determined
by the average power and BER constraint. Assuming an instantaneous BER for analysis,
we have, the average BER = BER(y) , which becomes
BER
[
- CZSNR(Y)]
~ C\ exp k()
2c3 r - C4 '
based on
SNR(y) = Y S~) .
S
Substituting, 2k ; -1 = f(ki ) we obtain,
S~) =_ f(k j ) IO(BER J.
S Cz Cl
3) Constant rate, Instantaneous HER:
41
(4.1 0)
Sj(Y)
-1.6*y-_- [U(k') ]
___.....:S'-- = In ":1 I
f(k j ) 3.2*ki y
Si!!) =In[ Af(ki )5 ] f(ki )
S -3.2*ki y -1.6*y (4.9)
2) Discrete Rate, Instantaneous BER: In case of discrete rate analysis, kj takes discrete
values for the regions defined by [r j ,Yi +1)' These rate region boundaries are determined
by the average power and BER constraint. Assuming an instantaneous BER for analysis,
we have, the average BER = BER(y) , which becomes
- [-C2 SNR BER ~ CI exp c k( ) (Y)]
2 3 r - C4 '
based on
SNR(y) =Y S~) .
S
Substituting, 2k; -1 = f(ki ) we obtain,
s~) =_ f (k i ) In(BER ) .
S C2 cl
3) Constant rate, Instantaneous BER:
41
(4.10)
The spectral efficiency of the modulation scheme is defined as the average data rate per
unit bandwidth (RIB). Since the rate is kept constant, k can be taken outside the
integration and hence the equation becomes,
00
~ =k fp(y)dy
Yo
which we apply
2k -1 = f(k),
and obtain
S~) =In[ Jf(k)S] I(k)
S cl c2 * ky - c2 *Y
18
16
1.4
1.2
Q , ~i
08
Cl.
0.6
0.4
..........
0.2 .~ .._,.;
0'0 15 20 25 :D 35 40
Average SNR(dB)
Fig.4.8. Power ratio for Adaptive M-QAM systems.
42
(4.11)
25 :Jl
A".rage SNR(d8)
35 40
Fig.4.9. Power ratio for constant rate, adaptive power systems.
4.3. Spectral Efficiency of Adaptive M-QAM for discrete rate adaptation:
1) Discrete Rate and Average Bit Error Rate: In case of discrete rate adaptive modulation,
k takes discrete values within 0 ~ k ~ N -I. From the equation of spectral efficiency,
( [
- 1.6 * SNR ] J Spectra/Efficiency = log2 1+ ( -) M represents the number of signal
In 5BERM _QAM M
constellations given by 2k and the discrete boundaries of M are considered to be within
6 regions given by M =0, 2, 4, 16, 64, and 256.
With the discrete constellation sizes at appropriate region boundaries the suboptimal
spectral efficiency is selected as shown in the figure figA.10. It is found from the graphs
below that the continuous rate modulation yields the highest spectral efficiency while the
discrete rate system also yields a close efficient spectral performance.
43
14 r-----r------.------r-----r---r---~
°1O':---1"=5---::'2Q:------::25':---:J):'-::----:'35:-----'40Average
SNR(dB)
FigA.I0. Spectral Efficiency for Variable rate, Variable power M-QAM systems.
12 r----.,.-----,-----,------,----,.------,
°10l----:'15:---20::':---~25:'-::---~lJ:'::----:35:'::----'40
Avarage SNR(db)
FigA.ll. Spectral Efficiency for M-QAM systems with constant transmit power.
44
20 25 7() 35 40
Average SNR(db)
15
o'-_---'-__--'-__.J...-._~_____'__ ______'
10
Fig.4.12. Spectral Efficiency for constant rate M-QAM systems.
Fig.4.10. shows the spectral efficiency achieved on a variable rate, variable power
adaptation system for continuous and discrete systems.
4.4. Constant power, Adaptive Rate and Constant Rate, Adaptive Power Systems
Constant Power, Instantaneous BER: The same analysis is also carried out for a single
adaptation system - for both the variable rate and the variable power adaptive system.
Fig.4.2 and fig.4.3 gives the resulting spectral efficiency achieved with the single variable
adaptive system. With the restriction of either constant power or rate with or without
thresholds, the adaptive system is further analyzed for the possible loss of spectral
efficiency.
45
Constant Power Instantaneous BER: From (4.2),
-czSNR(y)
log z ---==--=B=£=R='-- + C4
In--
key) ~ _--=-__c,__--=
C3
Substituting, SNR(r) =y S~) , we obtain,
S
-czy S~)
S +c
BER 4
In--
k(y) ~ _--=--__c,____=_
C3
The Lagrange equation for the instantaneous BER is given by,
C() 00 00 00
JCSCY),kCy» = JkCy)pCy)dy +A, JBEM:y)kCy)pCy)dy -BERJkCy)p(Y)dY +~ JSCy)pCy)dy - S.
o 0 0 0
Since for the instantaneous BER, B£R(y) =B£R, the above equation is reduced to one
Lagrange variable given by
CJJ CJJ
J(k(y» = fk(y)p(Y)dY + A fS(y)p(y)dy - S
o 0
This is possible due to the constant power condition. The Lagrange equation with two
variables of adaptive rate and adaptive power can be reduced to a single variable for
adaptive rate only.
Differentiating w.r.t. rate and given a constant power of 8(y) =S, we have
S
=---
S CJJ
fp(Y)dY
Yo
46
Yo
Therefore,
-C2Y OCJ
fp(y)dy
key) ~ --=-------=-
The spectral efficiency for a constant rate system can be given by
00
~ = fk(y)p(y)dy
Yo
OCJ
= f--=------------=:. p(y)dy
C3
With p(y) as an exponential distribution function and with a zero threshold value, the
above equation can be reduced to
-C2Y -----==== + C4
BER
OCJ 10--
R
B
= f_-=-_C--"l__-=-p(Y)dY
c3
10
The results of equation (4.12) is plotted in FigA.1l.
47
(4.12)
4.5. BER performance results of the continuous and discrete rate adaptation
systems
To obtain the perfonnance of the variable-rate and variable-power systems, for the
continuous adaptive rate case we apply equations (4.3) and (4.2) to obtain Fig.4.13, and
for discrete k adaptive case we apply (4.3) with discrete levels into the Matlab program
provided in Appendix A (program 8.m) to obtain the resuits in Fig.4. 14.
10.2 ,---_--,-__---.-__..,--__.---_--,-__-,
:~:::::::!~~~~r,.,"'
...." : " Target 8ER=10'6
............::::::::::::::::i::::::::::::::::::::~::::::::::::: :::::::::::
10.4L-_..........__--'-__-'--_~'___----'-__-'
10 15 20 25 30 35 40
Average SNR(dBl
Fig.4.l3. BER for continuous rate adaptive modulation.
48
\..
".~
5 10
\/et.~ER=1.~.~
. " ....
\~ ....
"\
.....
'\
15 20 25
SNR(db)
30 35
\ ....
\
\
40
FigA.14. BER for discrete rate adaptive modulation.
4.6. Observations
The numerical results plotted in this chapter are for a BER of 10.3 and 10.6
Rayleigh fading results and taking into consideration only a flat fading distribution [4.1].
The BER approximations and the Lagrange expressions are carried out for single-carrier
modulation. The spectral efficiency figures shown in FigA.2, FigA.l 0, and Fig.4.11 show
that there is not much of a difference in the spectral efficiency obtained for the
continuous rate and discrete rate adaptation technologies. This means that discrete rate
adaptation can be processed without much of a spectral loss. The optimal BER adaptation
curve is shown in Fig.4.13 and FigA.14 for the constrained average BER of 10.3
.
This system model applying adaptive rate and adaptive power control has been
applied for OFDM modulation in this chapter. Further, in the following chapter, the
numerical analysis is extended to also include lognormal fading systems (shadowing
effects) and also investigate the system features of macroscopic diversity combining.
49
CHAPTERS
ADAPTIVE MODULATION FOR OFDM SYSTEM AND
MACROSCOPIC DIVERSITY TECHNIQUES
In this chapter the adaptive rate and adaptive power modulation, and HER
approximation model (by Chung and Goldsmith [4.1]) is combined with an OFDM
system. The signaling and detection techniques and their probability of false alarm are
also calculated. In the second part of this chapter, the macroscopic diversity techniques
are combined with the developed adaptive OFDM.
In [5.7], Steele and Webb introduced the adaptive M-QAM for burst-by-burst
adaptation for QAM modulation. In this research, the adaptive rate and adaptive power
M-QAM multicarrier modulation technique is considered on an OFDM-TDMA channel
for mobile communication systems. The mobile channel suffers from flat fading. The
OFDM system with the help of adaptive modulation reduces the BER and improves the
performance with the efficient use of the bandwidth. The investigation is further extended
to the analysis of the signaling and detection of the modulation technique using pilot
carriers.
5.1. Adaptive OFDM
Since fixed OFDM transmission systems are not well suited for varying channel
conditions, adaptive OFDM modems are investigated as a mean to improve the
performance. OFDM transmitter parameter adaptation is an action of the transmitter in
50
response to time varying channel conditions. It is only suitable for duplex communication
because the transmission parameter depends on some fonn of signaling and channel
estimation. To improve the perfonnance of an OFOM system, subcarrier modulation
modes can be adapted to the channel conditions. For subcarners exhibiting low SNR
levels, low modulation levels are used, whereas the subcarriers with a high SNR can be
set for a higher multilevel modulation scheme.
The thesis is based on an OFOM system with N data symbols Sn' where n
ranges from 0 to N-I. These symbols are multiplexed over N subcarriers. The time-domain
samples sn are generated by the inverse fast Fourier transfonn (IFFT) and
transmitted over the channel after the cyclic prefix is inserted. On the receiver side, the
OFDM time-domain samples are subject to the removal of cyclic extension followed by
the fast Fourier transform (FFT) to receive the data symbols Rn • The received data
symbols can be expressed as [5.1]
(5.1)
where n is the AWGN sample. n
The following procedures are to be followed for an adaptive OFOM system.
a) Channel Quality Estimation: In order to execute the adaptive modulation
techniques, the transmitter and receiver should have knowledge of the channel
conditions. There are two types of channel quality estimation known as open-loop
adaptation and closed-loop adaptation. In case of open-loop adaptation (a TOO system),
51
where the channel is duplex, each station can estimate the quality of the channel by the
use of received OFDM symbols. In case of the closed-loop adaptation (an FDD system)
where the channel is not reciprocal, the receiver explicitly invokes the remote transmitter
as to which modem mode to adapt to for the next active time slot. In our analysis, the
system assumes open-loop adaptation.
b) Determination of Modulation Parameters for the subcarriers: This is performed
by the method described in section 5.2 below using pilot symbol detection.
5.2. Modulation Parameters in case of Adaptive Modulation of subcarriers
For a higher throughput, a higher proportion of low-quality OFDM subcarriers
have to be used for the transmission of inherently vulnerable high-order modem modes,
transmitting several bits per subcarrier. Many researchers have demonstrated adaptive
subcarrier selection and the results show BER performance improvements ([5.1], [5.2],
[5.3]).
There are various kinds of adaptivity that can be applied to an OFDM system.
Two types of systems are looked into in the current research. The first one is based on
subcarrier-by-subcarrier basis and the second type is the subband adaptive modulation. In
this thesis, to reduce the system complexity, the OFDM modulation is not applied on a
subcarrier-to-subcarrier basis but instead it is divided into subbands consisting of a set of
subcarriers and this subband is assigned a single modulation level according to the
channel conditions.
The modulation of the subcarriers is allocated block by block. Consider an N-subcarrier
(say 512 subcarriers) OFDM system with K number of users in a WLAN
52
system with a carrier frequency of 60 GHz. Consider the different types of modulations
applied to the system as M n where n is 0, I, 2, 3, 4, 5, and 6 depending on the various
modulation schemes as: no modulation, BPSK, QPSK, 8-PSK, 16-QAM, 64-QAM.
The average modulation level M is given by,
This section discusses two issues. First, Keller and Hanzo's adaptive algorithm [5.3] is
studied and second, based on [4.1], adaptive rate and adaptive power OFDM system BER
performance results are compared with the results from the model applied in [5.3].
Choice of the Modulation Scheme: There are three schemes suggested by the
researchers for the selection of the modulation scheme [5.3]. In this thesis, we analyze the
performance of the Fixed Threshold Adaptation Algorithm.
Fixed Threshold Adaptation Algorithm: This adaptation algorithm is assumed for a
constant instantaneous SNR over all of the symbols in a subband. If the subband is larger
than the coherence bandwidth, then this algorithm will not hold good leading to a penalty
of throughput due to the frequency selective channel with the channel quality varying for
different subcarriers. When the SNR of the switching level I" falls in the range given by
the table 5.1, then the corresponding modulation level M n is selected as the modulation
level for that subband.
53
Switching Levels:
odB to 3.31 dB
No modulation
3.31 dB to 6,8 dB
BPSK, M 2, k-1
6.8 dB to 11 dB
QPSK, M=4, k=2
> 11 dB
16-QAM, M-16, k-4
Table 5.1. Adaptive Modulation Look-Up Table
Proposed system:
a) The following BER approximation system was used in [4.1] for an M-QAM system,
and in this chapter it has been applied with a variable rate and variable power AOFDM
system applying Hanzo's BER estimator adaptation algorithm. A Performance analysis
of the two systems in a Rayleigh fading channel is given in Fig.5.l.
.. ......·...-...7...·..--...'..-----...--.......·..~..,..·,·....--·--·.......--...
Adaptive rate. adaptive powsr algorithm
Instantaneous 8ER with
Subband 8ER Estimator Algorithm
fo,r 16S8 1e'2 target 8ER ... .. ...
100
10'1
10'2 .. ... .. lr
W ....~............-
lD
10,3
10"
10 15 20 25 :IJ
Average SNR(d8)
35 40
Fig.5.l. BER performance of the proposed OFDM system.
Fig.5.1. resulted by taking into account the channel conditions and its
corresponding SNR of [4.3].
54
3
-0E2
~
Q;
c..
.~ , .Q
o
Q;
~ 0
Z
.-------- .........""
..-/"
constant Ira~ pOWl!r system
\/'
,fl
.(-r'
,~'/
.~/"\vanable rate variable power system
/:.'
.-::~/
......
. , I
-2Oc---5'---'"'-O--'"'-5--20-'---25-'---3:)-'---35-'--------'40
Average SNR(d8)
Fig.5.2. Throughput perfonnance of the proposed OFDM system.
From Fig.5.l, it is found that the BER perfonnance for the proposed system is
almost a steady BER perfonnance curve compared to the rapidly varying BER
perfonnance of a constant transmitter power system. Fig.5.2. shows the throughput
efficiency of the two systems. Based on the results of Fig.5.2., it is evident that there is
not much of a tradeoff in throughput between the two systems for a given BER of 10-3
.
5.3. Signaling and Blind Detection
The receiver needs to have knowledge of the modulation scheme used for the
different subbands. This is achieved by the use of Pilot Symbol Aided Modulation
techniques.
a) Signaling: The simplest way of signaling is just replacing one data symbol by a
signaling symbol of a known modulation. Coherent phase detection is perfonned at the
receiver and an error free detection is assumed.
55
While transmitting data on the channel, one of the data symbols are replaced by
M-PSK symbol, where M is the number of the modulation scheme. When employing one
symbol for signaling, the signaling error probability is given by the above equation. In
[5.3], the signaling symbol is QPSK modulated. The detection error probability when
using one symbol for detection is given by
(5.2)
where ps(r) gives the detection error probability function and r is the average channel
SNR. The signaling error probability in case of Ns signaling symbols can be expressed
as [5.3]
(5.3)
The results of equation (5.3) is shown in Fig.5.3.
56
, ,
\,/NS=4
10·f)~,-~''--_---11_~-'-'''';'''_--'-'~_.LI__,'--_-1'_----',
o 5 10 15 20 25 )J 35 40
Average channel SNRldB]
Fig.5.3. Probability of erroneous detection of existing system.
..... •.•... .•..
tp~8\
10-C L..-_--"-_---'::----_--'--_-'-_----::':_----,-'--_--"-_-' o 5 10 15 20 25 30 35 40
Averaga channel SNRldBI
Fig.5A. Probability of erroneous detection of proposed system.
Applying the HER approximation from [4.1], we get
[
-1.6 *SNR] BER :::; O.2exp
M-QAM 2k -l'
57
Ps (y) = 1- (1- BERM_QAM )2 . (5.4)
The results of the equation (5.4) is plotted in Fig.S.4. From Fig.5.3 and Fig.S.4, it is
evident that the The proposed adaptive system of using the BER approximation given
below yields a lower detection error compared to the existing system.
5.4. Macroscopic diversity
Diversity is known to be an effective method of reducing the deleterious effects of
the fading in radio channels. Diversity techniques can be used to reduce the signal
variability. The concept behind space diversity is relatively simple. If one signal
undergoes a deep fade at a particular point of time, another independent signal
component detected at a distance location may have a strong signal. This technique when
combined with adaptive modulation system could yield an improved BER performance.
There are various types of diversity used in communication systems operating
over fading channels. They are: Space Diversity, Frequency Diversity, Time Diversity,
Polarization Diversity, and Multipath Diversity.
Whatever the diversity technique employed is, the receiver has to process the
diversity signals obtained in a fashion that maximizes the power efficiency of the system.
There are several possible diversity reception methods employed in communication
receivers. The most common techniques are: Selection Diversity, Equal Gain Combining
(EGC), and Maximal Ratio Combining (MRC).
The aim of this section is to study the improvement achieved by the use of
Macroscopic Selection Diversity on adaptive rate and adaptive power systems (modeled
in Chapter 4) thus reducing the overall BER of the system. Space diversity is achieved by
58
placing different base stations separated large enough so that the resultant components at
each base station (i.e., the fast (Rayleigh) and slow (lognonnal) fading components) are
independent. Macroscopic diversity is then performed on the mean of each system and
the BER perfonnance is analyzed. In this section, the probability of BER of non-macroscopic
and macroscopic diversity systems (analysis is done with three base station
for one mobile system) are compared and the results are plotted using Matlab via Monte
Carlo simulations.
a) Radio Channel model
The channel model considered in this chapter is a mobile radio channel model.
The radio channel is characterized by multipath propagation of the signal due to
diffraction and scattering from buildings. The received signal is characterized by fast
fading, superimposed by the slow fading due to the shadowing effects. The fast fading
envelope is modeled as a Rayleigh distribution while the slow fading is characterized as a
lognonnal component with a standard deviation in the range of 9-12dB.
b) Probability of non-macroscopic diversity techniques
The PDF of the lognormal density function including the multipath and
shadowing effects is given using the approximation method of [5.8], which results in the
form of
10 [ (lOloglOy-m )2J p(y) = ~2 xexp -----2---
yO' loge 10" LJr 20'
with mean m and standard deviation a .
59
(5.5)
The probability of bit error using adaptive rate and adaptive power M-QAM
modulation is given by
[
-1.6· Y ]
PBER(M-QAM) =O.2exp .
2k(y) -1
The BER approximation of the lognormal and Rayleigh fading channel is implemented
by applying the BER equation from [4.1] and integrating over the PDF distribution given
in equation (5.5), which results in
<IJ
P'n-BER(M-QAMl = JPBER(M-QAM) (y)p(y)dy .
o
2k(Yl_J_1 -1.6*y 1
-lJ{SBERM _ QAM)
2klyl -( +I -1.6 *y 1
- lIn(SBERM - QAM)
60
(5.6)
The results of equation (5.6) are plotted out in Fig.5.5 .
....... .......
•..,."..,,, / Rayleigh mOd~i·~f·G·oiaSifllttr.8nd..CbJdQ.L ..
............" .." , ..
--..~ -- .........................
............
.................
'"'''''''' Rayleigh 8. lognormal model applying ····".., 1 Goldsmith and Chung approximation
. .
15 20 25 :IJ
Average SNR(dB)
35 40
Fig.5.5. BER performance graph.
The effect of the lognormal shadowing is included with the adaptive rate and
adaptive power BER approximation [5.8] for the required BER of 10-3
. Based on the
Fig.5.5, it can be clearly observed that there is a large BER loss in case where shadowing
effects are included in the radio channel model.
The following section proposes macroscopic diversity combining system that will
be applied with the adaptive OFDM system to reduce this degradation in the BER
performance due to the shadowing effects.
c) Probability of m-branch macroscopic diversity techniques
Assume 3 base stations each separated from the mobile station at equal distance. In this
case, the mobile station is assumed to receive the same strength of signals. Therefore, the
61
assumption applied in the simulation is ml =m2 =m3 = OdB and 0"1 = 0"2 = 0"3 = 9dB for
the three base station signals.
Fig.5.6. Three base stations at equal distance.
The probability of bit error of the m-branch macroscopic diversity system is given by
[5.8]
00
P,,,-BER(M -QAM) = fPBER(M -QAM) (r)Pm (r)dr
o
where PBER(M-QAM) == 0.2 exp[ - 1.6 *Y ] is used from [4.1] and k(y) is given by
i<Y) -1
( [
-1.6 * SNR ]J key) =log2 1+
In(SBERM
_
QAM
) •
(5.7)
(5.8)
The PDF of the m branch macroscopic diversity system IS given by the following
approximation,
62
P (r) - 10m [ (lOIOglOr-mj)2ll- (1010glOr-mjj\]m-1
m - - x exp - Jx P , (5.9)
raj loge 10.JZJr Zal aj
h ( 10 loglOr - m.J' . were P aj I IS the cumulative nonnal distribution function with mean
mj == ml == m2 == m3 == OdB and standard deviation aj == al == a2 == a3 == 9dB.
Substituting equations (5.8) and (5.9) in (5.7) and integrating the resulting equation via
Monte Carlo simulation, the final solution results in Fig.5.?
10.
2 r----,...----.-------,------,---,.----,
...••..• non·macroscopic, mullipOith and shadowing
10.
3
:liGOldSmilh's BER approximation
.......
cr uu
[D
'"- ...
'" ....".,,:;;..,. 7~a'c;:ii~copic..M:7.3, multipath and shadowin h Goldsmith's i3f:R"aPProltimOitiolL.
•.<:::::::::::::::................ non· macroscopic, multipalh o~~.. " .. ··..···....·· ····::::::~~:~~~/~h~.aEfLappr.Q.~ma.!!!! ..
.........
..............•.
10.
5 ':---~---=----::'::-----::'=-----:.J.---....J
10 15 20 25 30 35 40
Average SNR(dB)
Fig.5.? BER perfonnance results in macroscopic diversity system.
Comparing Fig.5.5. and Fig.5.?, it is found that when multiple antennas are used
(macroscopic technique) in a radio channel (with both multipath and shadowing),
significant improvements in the BER perfonnance can be obtained.
63
In most cases, the base stations may not be equally spaced from the mobile
station. In this case, the signal received by the nearest base station is more likely to be
stronger.
a) Case (i): Let the mean of the received signal from first base station be ml, the
second-m2 and the third-m3. In the first case, the mobile station is assumed to be
close to one base station compared to the other two stations. In this case, we have,
m\>m2=m3.
Base Station 2
m3
Base Station1
dio lower
Fig.5.8. Three base stations at equal distances.
b) Case (ii): Another possible case could be when the mobile station is closer to two
of the base stations i.e., m2 and m3 than it is to the other one (m(). In this case, we
have, m2=m3> ml as the condition.
64
10.
2 r---.-----,----.------.----.....-----,
10.
3
•··•·•·•••·•..~...•..•.•..••..._nln-macroscoPic with shadowing and multipath fading
"'-.
..........
10 15 20 25 30
Average SNR(dB)
35 40
Fig.5.9. BER perfonnance for unequal macroscopic diversity.
The perfonnance of the M-branch macroscopic diversity technique is plotted in
Fig.5.9. For a BER of 2x10·4 an improvement of around 20dB in SNR is achieved by
using the 3-branch macrodiversity combining system. With the increase in the number of
macrodiversity combining branches, the BER perfonnance reaches an upper bound
constant value.
65
CHAPTER 6
CONCLUSIONS & FUTURE RESEARCH
Two conclusions are derived from this research. First, based on the research in
Chapters 3 and 4, adaptive rate and adaptive power control when applied to OFDM
systems yields a better BER perfonnance with no reduction in the throughput of the
system (Fig.5.1, 5.2, 5.3, 5.4). Secondly, by applying adaptive rate and power control the
signaling and detection error rate is significantly reduced compared to the conventional
system with a smaller number of symbols used for signaling.
The deleterious effects of multipath propagation and shadowing are dominant
terms that are used to characterize mobile radio channels. The fast fading term is
approximated using a Rayleigh fading distribution. In this thesis, the fast fading
component is reduced by using the adaptive rate and adaptive power modulation
incorporated applying the methods proposed in [4.1]. Slow fading follows a lognormal
distribution. This thesis considers both Rayleigh and log-normal fading in mobile
channels and attempts to provide a solution of using adaptive modulation with
macroscopic diversity. The macroscopic diversity model proposed by Turkmani [5.8] is
applied to the OFDM system to reduce the probability of bit error rate (BER). This is
made possible by approximating a composite Rayleigh plus lognormal distribution by a
simplified lognormal distribution (Fig.5.5, 5.6, and 5.7). The performance of the
66
macroscopic diversity systems with equal distant base stations provided a significant
SNR gain for the BER ranges of 10-3 and 10-6.
With the Monte Carlo integration and matlab simulation, the following two main
observations are reached in this thesis. With the application of OFDM adaptive rate and
adaptive power control, for a constraint BER of IxlO-3, a gain of25 dB in SNR (Fig.5.!)
is achieved without coding for a Rayleigh fading system. Further, for a particular SNR
value (say 25 dB in Fig.5A), the BER approximation used for signal detection reduces
the detection rate by (== 1/10) times compared to the existing system. The second
important conclusion reached is the SNR gain of around 20 dB (for a BER lxlO-4 in
Fig.5.9) obtained by using macroscopic diversity systems. All these conclusions obtained
are based on the restrictions described in Chapter 5.
OFDM is likely to find a range of further attractive applications in wireless and
wireline communications. Some of the future research topics are summarized in the
following.
a) Coding Modes: This thesis is limited to considering the performance and simulation
for non-coded systems. Future research including error control coding can be included
with the adaptive modulation system.
b) MIMO/OFDM: OFDM with adaptive modulation can also be applied to MultipleInput
Multiple-Output (MIMO) systems. The same procedure of analyzing constant rate
and power to adaptive rate and power techniques in terms of the BER performance can be
carried out. Further, the performance of the system can be improved by using selection
diversity as well as other more advance space diversity combining techniques.
67
APPENDIX A
Matlab Codes
The programs in this appendix are the matlab codes used to plot the figures from
Chapter 2 to Chapter 5. The Matlab version used to simulate the codes in this appendix is
Matlab 6.5.
1) Program l.m
IIThis code leads to the generation of Fig.2.1. Effect of Degradation due to Frequency
110ffs et
i = -1 *4;j = -1 *2; k=l;
for beta = i: 0.2:j
degrad (k) = beta + 21.3863; Iidegradation equation
deg = degrad (k);
xlabel ('Normalized Linewidth/Subcarrier Spacing'); //label, title & legends
ylabel ('Degradation (db)');
title ('Effect of Frequency Offset');
semilogy (beta, deg,'*'); hold on;
k = k + 1;
end
2) Program 2.m
II Fig.2.l. Probability Distribution Function of a SC system.
x = -3:0.1:3;
p = raylpdf (x, 1); IIRayleigh Distribution pdf.
y = normpdf (x,O, 1); IIGaussian Distribution pdf
plot (x, p,'-');
hold on;
plot (x, y) .
xlabel ('Rayleigh/Gaussian variable r,x'); Illabel, title & legends
ylabel ('Probability distri~ution'); ., . ., .
title ('Gaussian and RayleIgh probability denSity functIOns),
text (-1 ,0.4,'Rayleigh distribution--Single carrier system');
text (-1.5,0.25,'Gaussian distribution');
68
3) Program 3.m
IIFig.3.1. BER for MQAM
for SNR=0:0.5:40
BER=(1-0.5)*erfc (sqrt (1.5*(10"'(SNR/lO))/3)); IIM=4(signal constellations)
BERI=0.5*(1-0.25)*erfc (sqrt (1.5* 1OI\(SNR/ 10)/15)); IIM= 16(signal constellations)
BER2=0.25*(1-0.2)*erfc (sqrt (1.5* 101\(SNR/IO)/63)); IIM=64(signal constellations)
BER3=0.2*(1-0.11)*erfc (sqrt (1.5* 1OI\(SNR/ 10)/255));IIM=256(signal constellations)
BERa=0.2*exp (-1.6*(101\(SNRlI0))/3); IIAdaptive MQAM , k=2
BERla=0.2*exp(-1.6*(101\(SNR/lO))/15); IIAdaptive MQAM , k=4
BER2a=0.2*exp(-1.6*(1 OI\(SNR/I 0))/63); IIAdaptive MQAM , k=8
BER3a=0.2*exp(-1.6*(1 OI\(SNR/I 0))/255); IIAdaptive MQAM , k=16
hold on;
plot (SNR, BER,'*'); plot(SNR,BERl ,'*');plot(SNR,BER2,'*');plot(SNR,BER3,'*');
plot (SNR,BERa,'o');plot(SNR,BERla,'o');plot(SNR,BER2a,'o');plot(SNR,BER3a,'o');
xlabel('SNR(db)');ylabel('BER');
text(2,0.75,'*- \rightarrow Standard Fonnula','FontSize',10);
text(2,0.5,'o- \rightarrow Approximation','FontSize', 10);
end
4) Program 4.m
II The following codes are for the key) for MQAM: Fig.3.3.Continuous rate Average
IIBER, Fig.3.4.Continuous rate Instantaneous BER, Fig.3.5.Discrete rate Average BER,
IlFig.3.6.Discrete rate Instantaneous BER
for SNR = 0:0.1 :30
n = log2 (1 +«lOl\(SNR/I 0)))); IICapacity equation.
m = log2 (I +«101\(SNR/lO))/(101\(5.8/1 0))));
plot (SNR,m,'--');
plot (SNR,n,'--');
hold on;
end
5) Program 5.m
for SNR=O: 1:30
nl=log2(1+«(1 OI\(SNRll 0))))-0.5;
ml=log2(1+«1 Q/\(SNRlI 0))/(1 01\(5.8/1 0))))-0.5;
plot(SNR,ml,'--');
plot(SNR,n1,'--');
hold on
end
6) Program 6.m
for SNR=0:O.2:40
if(SNR<5)
k=O;
kl=O;
69
else
k=(1I1)*((Iog2(IO""((SNR-5)110»)/(10AO.005» IIContinuous case with threshold
//value of 5dB.
~~~(I/l )*((Iog2(I OA((SNR-5)/ I0»)/( IOAO.00005»;
plot(SNR"k '_I).,
plot(SNR,kl,'-'); "
hold on;
end
xlabel('SNR(db)');
ylabel('Number ofbits for modulation-MQ~M');
7) Program 7.m
for SNR=O:O.I: 14 k=O;plot(SNR,k,'-') hold on; end
for SNR=14:0.1:18 k=2;plot(SNR,k,'-') hold on; end
for SNR=18:0.1 :22 k=4;plot(SNR,k,'-'); hold on; end
for SNR=22:0.1 :27 k=6;plot(SNR,k,'-'); hold on; end
for SNR=27:0.1 :32 k=8;plot(SNR,k,'-'); hold on; end
for SNR=32:0.1 :37 k=lO;plot(SNR,k,'-'); hold on; end
for SNR=37:0.1:40 k=12;plot(SNR,k,'-'); hold on; end
for k=0:0.1:2 SNR=14;plot(SNR,k,I_'); hold on; end
fork=2:0.1:4 SNR=18;plot(SNR k 1_'); hold on; end
for k=4:0.1:6 SNR=22;plot(SNR'k',,-,); hold on; end
for k=6:0.1:8 SNR=27;plot(SNR'k',,-,); hold on; end
for k=8:0.l: 10 SNR=32;plot(SNR'k'i'-'); hold on; end
for k=IO:0.1: 12 SNR=37;plot(SNR:k:"-'); hold on; end
xlabel('SNR(db)'); ylabel('Number of bits :for modulation-MQAM');
8) Program 8.m
for SNR=0:0.1:8 k=O; plot(SNR,k,'-'); hold o:m; end
for SNR=8:0.1: 14 k=2; plot(SNR,k,'-'); holdJ on; end
for SNR=14:0.1:21 k=4; plot(SNR,k,'-'); holld on; end
for SNR=21:0.1:27 k=6; plot(SNR,k,'-'); holld on; end
for SNR=27:0.1 :32 k=8; plot(SNR,k,'-'); hol.ld on; end
for SNR=32:0.1 :38 k=10; plot(SNR,k,'-'); h&ld on; end
for SNR=38:0.1:40 k=12; plot(SNR,k,'-'); h&ld on; end
for k=0:0.1:2 SNR=8; plot(SNR,k,'-'); hold ePn; end
for k=2:0.l:4 SNR=14; plot(SNR,k,'-'); hold' on; end
for k=4:0.l:6 SNR=21; plot(SNR,k,'-'); hold' on; end
for k=6:0.1:8 SNR=27; plot(SNR,k,'-'); hold' on; end
for k=8:0.1: 10 SNR=32; plot(SNR,k,'-'); holJd on; end
for k=IO:0.1: 12 SNR=38; plot(SNR,k,'-'); hcPld on; en~ ,
xlabel(lSNR(db)'); ylabelCNumbef of bits foff modulatlOn-MQAM);
forSNR=0:0.1:14 k=O; BER=(0.02*((2Ak)-I: »/((lOA(SNR/lO»*k); plot(SNR,BER,'-');
hold on; end
-po
end
end
end
end
SNR=14;plot(SNR,BER,'-');hold on;
SNR=18;plot(SNR,BER,'-');hold on;
SNR=22;plot(SNR,BER,'-');hold on;
SNR=27,'plot(SNR"BER,'-')'hold on',
forSNR=14:0.1: 18 k=2;BER=(0.02*«2/\k)-1 ))/«IO/\(SNRlIO))*k);plot(SNR,BER,'-');
hold on; end
forSNR=18:0.1 :22 k=4;BER=(0.02*«2/\k)-1 ))/« IO/\(SNRlIO))*k);plot(SNR,BER,'-');
hold on; end
forSNR=22:0.1 :27k=6;BER=(0.02*«2/\k)-1 ))/« IO/\(SNR/I O))*k);plot(SNR,BER,'-');
hold on; end
for SNR=27:0.1 :32 k=8; BER=(0.02*«2/\k)-1 ))/« 1O/\(SNR/I O))*k);plot(SNR,BER,'-');
hold on; end
for SNR=32:0.1 :37k=10;BER=(0.02*«2/\k)-1 ))/« IO/\(SNR/I O))*k);plot(SNR,BER,'-');
hold on; end
for SNR=37:0.1 :40k=12;BER=(0.02*«2/\k)-1 ))/« 1O/\(SNR/l O))*k);plot(SNR,BER,'-');
hold on; end
for BER=0.0005:0.0001 :0.001
for BER=0.0005:0.0001 :0.001
for BER=0.0005:0.0001 :0.001
for BER=0.0005:0.0001 :0.001
9) Program 9.m
for BER=0.0005:0.000 1:0.001 SNR=32;plot(SNR,BER,'-');hold on; end
for BER=0.0005:0.0001 :0.001 SNR=37;plot(SNR,BER,'-');hold on; end
xlabel('SNR(db)'); ylabel('BER');
10) Program 1O.m
for SNR=14:0.1:18 k=2; x=IO/\(SNR/IO); y=(2/\k)-I;
C=-log«O.OI *y)/(0.2*x))*(y/( 1.6*x));plot(SNR,C,'-') hold on end
for C=0:0.05:0.38 SNR=14; plot(SNR,C,'-'); hold on end
for SNR=18:0.1:22 k=4; x=10/\(SNR/IO); y=(2/\k)-I;
C=-log«O.OI *y)/(0.2*x))*(y/(l.6*x));plot(SNR,C,'-') hold on end
for C=0.2:0.05:0.7 SNR=18; plot(SNR,C,'-'); hold on end
for SNR=22:0.1:27 k=6; x=10/\(SNR/I0); y=(2/\k)-I;
C=-log«O.O1*y)/(0.2*x))*(y/( 1.6*x));plot(SNR,C,'-') hold on end
for C=0.4:0.05:0.9 SNR=22; plot(SNR,C,'-'); hold on end
for SNR=27:0.1:32 k=8; x=IO/\(SNR/IO); y=(2/\k)-I;
C=-log«O.OI *y)/(0.2*x))*(y/(1.6*x)); plot(SNR,C,'-') hold on end
for C=0.5:0.05: 1.1 SNR=27; plot(SNR,C,'-'); hold on end
for SNR=32:0.1:37 k=10; x=IO/\(SNR/IO); y=(2/\k)-I;
C=-log«O.OI *y)/(0.2*x))*(y/(l.6*x)); plot(SNR,C,'-') hold on end
for C=0.6:0.05: 1.3 SNR=32; plot(SNR,C,'-'); hold on end
forSNR=37:0.1:40 k=12; x=10/\(SNR/I0); y=(2/\k)-I;
C=-log«O.OI *y)/(0.2*x))*(y/(1.6*x)); plot(SNR,C,'-') hold on end
for C=0.6:0.05: 1.6 SNR=37; plot(SNR,C,'-'); hold on end
xlabel('Average SNR(dB)');
ylabel('Power ratio');
71
REFERENCE
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[3.3] V. K. Dubley and L. Wan, "Bit error probability of OFOM system over frequency
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[4.1] S.T. Chung and A. J. Goldsmith, "Degrees of Freedom in Adaptive Modulation: A
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72
[5.2] T. Keller, T. H. Lewis, and L. Hanzo, "Adaptive Redundant Residue Number
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73
VITA
Krishnaveni Ramasamy
Candidate for the Degree of
Master of Science
Thesis: AN INVESTIGATION OF ADAPTNE CONTROL TECHNIQUE IN
OFDM WIRELESS MODULATION
Major Field: Electrical Engineering
Biographical:
Personal Data: Born in Coimbatore, India on May 27th 1978.
Education: Received a Bachelor of Science in Electrical Engineering from
Coimbatore Institute Of Technology, Coimbatore in August 1999. Completed the
requirements for the Master of Science degree with a major in Electrical
Engineering at Oklahoma State University in December, 2002.
Experience:
1) Employed by Oklahoma State University, School of Electrical and
Computer Engineering as a research assistant, August 2000 to May 2002.
2) Employed by Oklahoma State University, School of Electrical and
Computer Engineering as a teaching assistant, January 2000 to May 2002.
3) Worked as an Intern in TechtroIInc., Pawnee, OK, May 2002 to July 2002.
THE MOST IMPORTANT CO-LEADER SKILLS
AND TRAITS ON EXTENDED OUTDOOR
EXPEDITIONS AS PERCEIVED
BY LEADERS
By
CHRISTEL RILLING
Bachelor of Science (Agriculture)
University of Guelph
Guelph, Ontario
1990
Submitted to the Faculty of the
Graduate College of the
Oklahoma State University
in partial fulfillment for
the Degree of
MASTER OF SCIENCE
December, 2002