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MULTI-USER INTERFERENCE REDUCTION AND THROUGHPUT ENHANCEMENT IN
OFDM-BASED MULTICARRIER COMMUNICATION SYSTEMS
By
KYOUNGNAM SEO
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
2009
2
© 2009 Kyoungnam Seo
3
To my Parents and Family
4
ACKNOWLEDGMENTS
First of all, I would like to thank my parents who have kept encouraging and inspiring me
to pursue my dream in many ways with unconditional love. I also have to thank my lovely wife,
Juhee Kang, who willingly dedicated her dream and life to me for my dream, and brought two
precious lives, Youjee and Minhyoung. For all of this, I will always be grateful and in awe of her.
I also thank my parents-in-law for their ceaseless support and belief on me. I also thank my sister
and all the family members for their endless love for me.
I thank my academic advisor, Dr. Haniph A. Latchman for his patient guidance,
encouragement and plentiful advice until I can successfully finish my Doctoral research. I would
also like to thank the members of my PhD. committee, (Prof. Fred J. Taylor, Prof. Janise McNair,
and Prof. Norman Fitz-Coy). I am grateful for their willingness to serve on my committee and
their helpful advice
I also thank my colleagues at Laboratory for Information Systems and Tele-
communications (LIST) in ECE department. For their many helpful and friendly discussion that
always gave me a new realization I will never forget.
5
TABLE OF CONTENTS
page
ACKNOWLEDGMENTS ...............................................................................................................4
TABLE OF CONTENTS .................................................................................................................5
LIST OF TABLES ...........................................................................................................................7
LIST OF FIGURES .........................................................................................................................8
ABSTRACT ...................................................................................................................................10
CHAPTER
1 INTRODUCTION ..................................................................................................................12
Historical Background and OFDM-Based Standards .............................................................12
MC-CDMA Systems ..............................................................................................................13
Power Line Communication Systems .....................................................................................15
Impulsive Noise Mitigation in PLC Systems ..................................................................16
Spread Spectrum Scheme in PLC Networks ...................................................................17
Contribution and Organization ...............................................................................................18
2 THE PRINCIPLES OF OFDM ...............................................................................................20
Conceptual Description of OFDM ..........................................................................................20
Mathematical Description of OFDM ......................................................................................21
3 JOINT TRANSCEIVER OPTIMIZATION IN OFDM-BASED MC-CDMA SYSTEMS ...28
Introduction .............................................................................................................................28
System Model .........................................................................................................................28
Spatially Dependent Fading ............................................................................................31
Spatially Independent Fading ..........................................................................................32
Joint Optimization of Transmitter and Receiver ....................................................................34
Receiver Optimization .....................................................................................................34
Transmitter Optimization ................................................................................................39
Simulations and Comparisons ................................................................................................41
Conclusions.............................................................................................................................46
4 POWER LINE COMMUNICATIONS ..................................................................................47
PLC History and Competitions ...............................................................................................47
PLC Medium ..........................................................................................................................49
HomePlug AV PHY ...............................................................................................................50
6
5 IMPROVED IMPULSIVE NOISE DETECTION IN POWER LINE
COMMUNICATION SYSTEMS ..........................................................................................54
Introduction .............................................................................................................................54
Impulsive Noise Mitigation in Power Line Networks ............................................................54
Tighter Threshold Setting .......................................................................................................58
Simulations .............................................................................................................................60
Scenarios and Impulsive Noise Data ...............................................................................60
Primary Simulations: Parameter Setting .........................................................................65
Performance Comparison ................................................................................................67
Performance Tests in the Real Power Line Networks .....................................................69
Lab Test Results ..............................................................................................................71
Conclusions.............................................................................................................................75
6 UNIVERSAL ALGORITHM OF IMPULSIVE NOISE DETECTION IN PLC
SYSTEMS ..............................................................................................................................76
Introduction .............................................................................................................................76
Threshold Setting and Impulsive Noise Detection .................................................................77
Simulations .............................................................................................................................80
Conclusions.............................................................................................................................81
7 ADAPTIVE SUB-CARRIER ALLOCATION ALGORITHM IN SS-MC-MA-BASED
PLC SYSTEMS ......................................................................................................................82
Introduction .............................................................................................................................82
System Model .........................................................................................................................83
Power Line Channel and Bit-Loading ....................................................................................86
Subchannel Allocation Algorithm ..........................................................................................89
Simulations .............................................................................................................................91
Conclusions.............................................................................................................................95
8 CONCLUSIONS AND FUTURE RESEARCH DIRECTION ..............................................96
LIST OF REFERENCES ...............................................................................................................99
BIOGRAPHICAL SKETCH .......................................................................................................105
7
LIST OF TABLES
Table page
1-1 OFDM-based standards and products ................................................................................13
5-1 Average SNR in the case of CP length 1052 .....................................................................67
5-2 Average SNR in the case of CP length 5028 .....................................................................69
6-1 False Impulse Detection Threshold Rate (%) ....................................................................81
7-1 Proposed Subchannel Allocation Algorithm .....................................................................90
8
LIST OF FIGURES
Figure page
2-1 Comparison of the bandwidth utilization for FDM and OFDM ........................................20
2-2 Block diagram of the transmitter for the kth transmitter....................................................21
3-1 Block diagram of OFDM-based MC-CDMA system ........................................................29
3-2 Performance comparison between MC-CDMA schemes and DS-CDMA schemes
when K=10, N=10, M=2, L=0 ...........................................................................................42
3-3 Average transmit power updates with K=16, N=16, M=2, L=5 ........................................43
3-4 Performance comparison among a number of MC-CDMA system models when
K=16, N=16, L=5...............................................................................................................44
3-5 Performance comparison among the joint algorithm and existing algorithms in MC-
CDMA systems when K=16, N=16, M=2, L=5 ................................................................45
4-1 HomePlug AV Transceiver ................................................................................................51
5-1 Impulsive noise Detection Flow Chart ..............................................................................55
5-2 Windowing and averaging for 1052 CP size .....................................................................57
5-3 Averaging for 5028 CP size ...............................................................................................57
5-4 SmImp noise ......................................................................................................................61
5-5 Hair Dryer noise .................................................................................................................61
5-5 Hair Dryer noise .................................................................................................................63
5-6 Dimmer noise .....................................................................................................................63
5-7 Electrical drill noise ...........................................................................................................64
5-8 Receive signal with typical impulsive noise in power line communication ......................64
5-9 Performance comparison using various detection parameters ...........................................65
5-10 Threshold scaling factor .....................................................................................................66
5-11 PHY data rates for the short CP .........................................................................................70
5-12 Lab Test results with a Hair dryer in use ...........................................................................72
9
5-13 Lab Test results with an Electrical Drill in use ..................................................................72
5-14 Lab Test results with a Dimmer in use ..............................................................................73
5-15 Lab Test results with a Lamp in use ..................................................................................73
5-16 Lab Test results with a Yard Lamp in use .........................................................................75
6-1 Performance comparison: single impulse and a burst of impulses ....................................80
7-1 Block diagram of the adaptive SS-MC-MA system ..........................................................84
7-2 Independent channel responses of four user scenario ........................................................89
7-3 Correlated channel responses of five users regarding distance attenuation .......................92
7-4 Throughput performance comparison ................................................................................93
7-5 Throughput performance comparison along with channel attenuation ..............................94
10
Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
MULTI-USER INTERFERENCE REDUCTION AND THROUGHPUT ENHANCEMENT IN
OFDM-BASED MULTICARRIER COMMUNICATION SYSTEMS
By
Kyoungnam Seo
August 2009
Chair: Haniph A. Latchman
Major: Electrical and Computer Engineering
Orthogonal frequency division multiplexing (OFDM) uses a number of closely spaced
orthogonal sub-carriers to transmit data. OFDM-based multi-carrier modulation schemes have a
vast variety of applications in current wireless and wired communication systems, which require
high-speed data rates. The popularity of these OFDM-based schemes comes from their primary
advantage over single-carrier schemes: the ability to convert a frequency selective channel into
parallel, distinctive frequency-flat sub-channels orthogonal to each other. This results in a
simplified equalization and the elimination of inter-symbol interference (ISI) without loss of
bandwidth efficiency. This dissertation considers three OFDM-based system models—Multi-
Carrier Code Division Multiple Access (MC-CDMA), Discrete Multi-Tone (DMT) in power line
communication (PLC) systems and Spread-spectrum Multi-carrier Multiple Access (SS-MC-
MA) in PLC networks.
MC-CDMA is the combination of OFDM and a CDMA spread-spectrum technique, which
enables multi-user channel access. In MC-CDMA systems, multi-user interference (MUI) comes
from the destruction of codes’ orthogonality by the channel conversion process of OFDM. We
study MUI suppression techniques and propose a joint algorithm of minimum mean-square-error
11
(MMSE) multi-user detector and transmit power control, which results in an enhanced signal-to-
noise ratio (SNR) and reduced transmit power consumption.
In PLC systems, OFDM is combined with a bit-loading algorithm to increase throughput.
Since the number of bits to carry at each sub-carrier is assigned by the SNR level, the throughput
of the system is directly affected by impulsive noise. Our study focuses on the detection and
mitigation of impulsive noise in PLC networks. We propose a time domain impulsive noise
mitigation algorithm. This two-step iterative algorithm improves the data rate by up to 15 percent
with a small addition of one OFDM block size memory.
Finally, we consider SS-MC-MA systems that take advantage of DMT’s adaptive bit-
loading technique and CDMA’s multi-user channel access. To further increase the throughput,
we propose a dynamic sub-carrier allocation algorithm in SS-MC-MA-based PLC systems.
Systems with the proposed algorithm show the average throughput increase up to 20 percent
comparing to the conventional DMT systems and 10 percent comparing to the existing SS-MC-
MA-based PLC systems.
12
CHAPTER 1
INTRODUCTION
Historical Background and OFDM-Based Standards
OFDM-based multi-carrier modulation systems are well-suited for high data rate
multimedia services due to their ability to convert frequency-selective fading channels to distinct
flat fading channels. With this conversion, the equalization process can be much simplified.
Inter-symbol Interference (ISI) can also be easily removed by adding the guard interval.
The first OFDM scheme was proposed in 1966 [1] for dispersive fading channels. The idea
was to use parallel data streams and FDM with overlapping subchannels to avoid the use of high
speed equalization, and to combat impulsive noise and multipath distortion. The concept would
also all the full use of the available bandwidth. Since then, tremendous research efforts have
taken place in the evolution of OFDM. One of the major contributions was made by Weinstein
and Ebert [2]. In their work, the discrete Fourier transform (DFT) was employed to replace the
banks of sinusoidal generators and the demodulators, which significantly reduces the
implementation complexity of OFDM modems. This is even more simplified by using low cost
/low complexity fast Fourier transform (FFT) devices, which is one of the major advantages of
OFDM systems.
Although the concept of OFDM was proposed in 1966 [2], it did not reach sufficient
maturity for employment in standard systems until the 1990s [3]. The European digital audio
broadcast (DAB) was the first OFDM-based standard for digital broadcasting systems. Currently,
this digital multi-carrier modulation scheme is being applied in a wide variety of practical
wireless and wired communication systems and extended with multiple accesses in a 4th
generation mobile communication standard. Table 1-1 shows a summary of existing OFDM-
based standards and products.
13
Table 1-1. OFDM-based standards and products
Wired systems Wireless systems 4G mobile Comm. standards
ADSL and VDSL
Powerline Communication
Multimedia over Coax Alliance
Wireless LAN
Wireless PAN and UWB
DAB, DVB
3GPP LTE
WiMAX
WiBRO
We consider three OFDM-based system models in this work. One is the OFDM-based
MC-CDMA system where we propose a joint MUI reduction algorithm which enhances SINR
and reduces transmit power. Another is DMT in PLC systems where we propose impulsive noise
detection and a mitigation algorithm to enhance system SNR. The last is SS-MC-MA in PLC
systems where we propose a dynamic sub-carrier allocation algorithm, which significantly
increases system throughput.
MC-CDMA Systems
As a promising candidate for high data-rate wireless multimedia services, MC-CDMA
relies on FFT-based OFDM technology to convert frequency-selective fading channels into
parallel frequency-flat fading channels, thereby reducing receiver complexity [4, 5]. The
converted frequency-flat fading channels may be independent or dependent depending on the
order of the frequency-selectivity. However, even if orthogonal spreading codes are employed,
the different fading effects on each sub-carrier will eliminate the mutual orthogonality and
induce multiuser interference, especially in the uplink scenario. When users are at different
distances from the base station, the so-termed near-far effect also emerges. Hence, MC-CDMA
systems are essentially interference-limited.
To suppress interference, multiuser detectors are often employed at the receiver [6].
Multiuser detectors are temporal filters which exploit the structure of MUI. Among multiuser
detectors, the linear minimum mean-square-error (MMSE) multiuser detector is gaining
popularity by providing a good balance between complexity and performance [6]. It has also
14
been noticed that employing an antenna array at the base station helps suppress multiuser
interference by exploiting spatial diversity. A widely used method in array processing is to build
a filter which is matched to the array response of the user, combine the array observation through
the filter, and then make bit decisions for the user. A performance analysis of MC-CDMA
systems using an antenna array at the base station was presented [7, 8]. The combined
application of multiuser detection and array processing in MC-CDMA systems was also
investigated [9], where the combined approach was shown to outperform the individual ones. In
addition to these receiver processing techniques, transmitter optimization such as power control
has been shown to mitigate the near-far effect by balancing the received power of all users so
that no user creates excessive interference for others while maintaining a certain SINR
requirement, which is the deciding factor of the system's quality-of-service (QoS).
In single-carrier direct-sequence (DS-) CDMA systems, there has been a significant
amount of research on transmitter power control [10]. However, only a few investigations have
been carried out for multi-carrier systems. Several papers [11, 12, 13, 14] propose an optimum
power allocation across multiple sub-carriers while requiring a high feedback overhead of 80%.
Others (see e.g. [15, 16]) suggest power allocation across bands of sub-carriers while still others
[17, 18, 19] implement power allocation across multiple users where power control algorithms
are combined with successive interference cancelation multiuser detectors.
In this work, we investigate the joint optimization of power control, multiuser detection
and array processing in MC-CDMA systems, where power control is affected as transmitter
optimization and multiuser detection and array processing are implemented as receiver
optimization. In contrast with the algorithms [20] for DS-CDMA systems in an additive white
Gaussian noise (AWGN) channel, here we consider MC-CDMA systems in frequency-selective
15
channels. The objective of the joint algorithm is to minimize the transmit power while achieving
the target SINR without modifying the power allocation across multiple sub-carriers.
Depending on the antenna spacing, the channels between the transmitter and each element
of the receive antenna array can be either dependent or independent. Hence, our system models
are specified for both cases. It is important to note that while frequency-selectivity induces
multiuser interference in MC-CDMA systems, it also introduces multipath diversity, which can
in fact enhance system performance. We consider a decentralized linear MMSE multiuser
detector as [21] by treating other users' signals as interference and using the SINR of individual
users as the optimization criterion.
Power Line Communication Systems
Power lines, being ubiquitously deployed as a wire-line network for carrying electrical
power, are the obvious choice as the medium for communication amongst the superabundance of
home-based and personal devices. They offer the convenience of already being in place and
having outlets in almost all locations in a household for easy access. Further, devices can easily
obtain electric power if they are deployed on PLC systems, while wireless mobile devices rely on
batteries and thus have difficulty maintaining continuous power.
PLC systems, however, are not free of problems. The PLC channel is notorious for electric
noise and interference, as well as channel variability depending on the appliances that are in use
at various times. To make communication more reliable through PLC channels, our study
focuses on an impulsive noise detection algorithm. We also consider PLC systems combined
with a spread spectrum scheme, which takes advantage of multiple access and adaptive bit-
loading for high data rates.
16
Impulsive Noise Mitigation in PLC Systems
Impulsive noise is a short burst of energy consisting of either a single impulse or a series of
impulses which are non-Gaussian. Impulsive noise is present in power line networks, is highly
unpredictable, and is highly damaging to the performance of multi-carrier systems [22, 23].
Most impulsive noise mitigation algorithms operate in the time domain and require
impulse detection, identifying which time domain samples are affected by impulsive noise, and
impulse processing, operating on those time domain samples to improve overall SNR [24, 25].
Time domain impulse detection is based on the assumption that the amplitudes of impulsive
noise samples are larger than the amplitudes of the desired signal samples. When the amplitude
of an impulsive noise sample is much larger than the amplitude of a signal sample, its detection
is relatively simple and the algorithm works well. Algorithms that are based in the frequency
domain detect impulsive noise samples with a significant magnitude over a relatively large
number of time domain samples that are concentrated in a narrow frequency band [25]. This type
of algorithm requires additional FFT and IFFT steps. Some algorithms are based on decision-
directed noise estimation, which show the ability to detect impulse noise samples that are smaller
than the amplitude of a signal sample [26, 27]. These types of algorithms also require additional
FFT and IFFT, as well as an estimation of impulses based on the primary signal detection result.
Thus, because of their computational simplicity, time domain impulse mitigation algorithms are
more widely employed in current power line communication systems and will be the focus of
this chapter.
To zero in on impulsive noise locations, it is important to set a detection threshold that
works well to separate signal samples from noise samples. A simple way of setting a detection
threshold is to base it relative to the upper and lower limits of the ADC inputs (ADC rails).
Alternatively, the threshold can be chosen to be proportional to the average received power of
17
the signal. This second method typically requires more computations and memory, but can result
in superior performance. In this work, we propose two iteratively computed threshold setting
algorithms. One was developed through an exhaustive number of simulations, and the other was
obtained by the analytical study of the characteristics of impulsive noise. Both algorithms
compute a threshold that performs well in all test cases, with the added benefit of also reducing
the memory requirement compared to conventional signal envelope-based threshold setting. The
proposed simple two-step iterative algorithms require only limited additional memory of OFDM
symbol size.
Spread Spectrum Scheme in PLC Networks
Since the spread spectrum technique has been considered to be robust against interference
and able to operate multiple-access systems, the combination of OFDM multi-carrier modulation
and the spread spectrum technique have been applied in PLC systems. The performance of
power line communication systems using multi-carrier code division multiple access (MC-
CDMA) and OFDM are compared [28] with equal numbers of bits assignment for all
subchannels. MC-CDMA PLC systems are proposed as high-speed data rate communication
systems with the aid of an advanced signal processing technique [29]. The performance of MC-
CDMA systems is considered with impulsive noise [30, 31]. In contrast with prescribed systems
that consider only down-link scenarios, [32, 33] considered uplink scenarios with multi-user
detection techniques to counteract the multiple access interference. However, none of the MC-
CDMA systems consider a bit-loading scheme like that used in OFDM-based PLC systems.
As an interesting alternative to MC-CDMA, spread spectrum multi-carrier multiple-access
(SS-MC-MA) has been proposed [34, 35]. Although SS-MC-MA is a multiple access scheme
based on OFDM as MC-CDMA, it does not require a multiuser detector and takes advantage of
the spread spectrum technique. Moreover, this scheme can employ a bit-loading technique that
18
serves as the major factor in increasing systems’ data rates. PLC systems based on SS-MC-MA
schemes are proposed [36, 37], where bit-loading with the proposed multi-user dynamic
subchannel allocation algorithm is employed. Its performance in terms of data rate is compared
with the PLC systems based on the OFDM scheme. Although the proposed subchannel allocation
algorithm performs well in some circumstances, its performance in terms of data rate will be
degraded when any user has poor channel conditions. This performance degradation is caused by
the strict fairness consideration in which the algorithm always tries to allocate the subchannels,
with priority going to the user with the poorest channel condition. In this work, we propose a
dynamic channel allocation algorithm that maximizes the systems’ data rates while slightly
relaxing the fairness consideration.
Contribution and Organization
The systems considered in this work are based on OFDM-based multi-carrier modulation.
There are two main focuses in this work: to mitigate Multi-user Interference (MUI) in multi-user
multiple access environments and to achieve a very high data rate in PLC systems.
In our proposed MC-CDMA systems, we improve the SNR by reducing MUI. To do this,
we present a joint algorithm that combines a power control algorithm at the transmitter and
MMSE multiuser detection at the receiver with antenna array processing. Interestingly, the
frequency-selectivity that causes MUI also provides multipath diversity, which can help suppress
MUI. In addition to mitigating MUI, the transmitter power control also helps reduce the total
transmit power.
In PLC systems, a high data rate is achieved by bit-loading, which assigns the number of
bits by SNR on each sub-carrier. The SNR of a system can be lowered in the entire frequency
band by impulsive noise since the impulsive noise in the time domain is transformed as constant-
like noise in the frequency domain. To enhance SNR, we propose time domain impulsive noise
19
detection algorithms based on an excessive number of simulations and the characteristics of the
impulsive noises in the PLC channel. To increase the data rate, we apply the SS-MC-MA scheme.
This is a good alternative for MC-CDMA since it does not suffer from MUI but can be combined
with bit-loading. We propose an adaptive subcarrier allocation algorithm to further increase the
data rate of the PLC systems.
The remainder of this manuscript has the following organization. Chapter 2 presents a brief
overview and the mathematical derivation of the OFDM scheme. Chapter 3 describes the
proposed joint transceiver optimization algorithm of the transmitter power control and MMSE
MUD with array processing in MC-CDMA systems. In chapter 4, PLC channel characteristics
and a current physical layer specification are presented. In chapter 5, impulsive noise mitigation
algorithms in power line networks are proposed, where the detection threshold parameters are
selected empirically after a massive number of simulation work. Chapter 6 proposes an
impulsive noise detection algorithm using the statistical characteristics of impulsive noise in PLC
systems. In chapter 7, SS-MC-MA based PLC systems are described. Conclusions and a future
research direction follow.
Notation: We use lower case letters to denote scalars, lower bold case letters to denote
vectors, and bold upper case letters to denote matrices. NI represents an NN identity matrix,
N N0 represents an NN null matrix, and diag{ a } represents a diagonal matrix whose
diagonal entries are elements from the vector a . We use ,,H
and T to denote the
conjugation, Hermitian, and transposition operations, NF for an N-point FFT matrix, E for
expectation, for a convolution operator, and := for ``is defined as''.
20
CHAPTER 2
THE PRINCIPLES OF OFDM
Conceptual Description of OFDM
OFDM is a digital modulation scheme using a parallel data transmission in which a
wideband signal is split into a number of narrowband signals. In a conventional serial data
system, the symbols are transmitted sequentially, with the frequency spectrum of each data
symbol allowed to occupy the entire available bandwidth. In a parallel data transmission system,
multiple symbols are transmitted at the same time, where the data is divided among large number
of closely spaced carriers. Therefore, only a small amount of the data is carried on each carrier
and by this lowering of the bit-rate per carrier, the influence of inter-symbol interference is
significantly reduced.
Frequency bandwidth in FDM Frequency bandwidth in OFDM
Figure 2-1. Comparison of the bandwidth utilization for FDM and OFDM
When an efficient use of band width is not required, the most effective parallel system uses
FDM where the total signal frequency band is divided into multiple non-overlapping frequency
subchannels. Each subchannel is modulated with a separate symbol and the subchannels are
frequency multiplexed. In such a system, there is sufficient guard space between adjacent
subchannels to isolate them at the receiver using conventional filters. In OFDM, the total
frequency band is divided into overlapping frequency subchannels that are mutually orthogonal.
Orthogonality can be achieved by carefully selecting carrier spacing, such as letting the carrier
spacing be equal to the reciprocal of the useful symbol period. The DFT transform is used at the
21
OFDM transmitter to map an input signal onto a set of orthogonal sub-carriers. The sinusoids of
the DFT form an orthogonal basis set and a signal in the vector space of the DFT can be
represented as a linear combination of the orthogonal sinusoids. The DFT is used at the receiver
again. Since the orthogonal basis functions of the DFT are uncorrelated, the correlation
performed in the DFT for a given sub-carrier only sees energy for that corresponding sub-carrier.
This separation of signal energy is the reason that the OFDM subchannels can overlap without
causing interference. Using this method, both transmitter and receiver can be implemented using
efficient FFT techniques that reduce the number of operations form 2N in DFT, down to
logN N .
Mathematical Description of OFDM
We present the mathematical description of OFDM in this subsection in order to see how
the signal is generated and how receiver must operate. This also makes us a clear understanding
of the effects of imperfections in the transmission channel. Consider an OFDM system with N
sub-carriers where the number of transmitters and receivers are K and M, respectively.
IFFT
ks
CPInsertion
ks ks
P/S DAC
k ib
,1kb
,2kb
,kNb
i i t
Figure 2-2. Block diagram of the transmitter for the kth transmitter
The continuous-time signal at the output of the kth transmitter's digital-to-analog convertor
(DAC) can be expressed as
22
0
,k k k tr c
l
s t s l p t lT
P (2-1)
where kP represents the transmit power of the k th transmitter, ks l is the discrete-time signal
resulting from the transmitter processing, and trp t is the transmitter filter with duration cT .
The signal then propagates through a frequency-selective channel ,k m t before arriving at the
m ir m ix m iy mr n m
r t
CPremoval
FFTADC S/P
Figure 2-3. Block diagram of the receiver
m th element of the receive antenna array. Denoting the receiver filter as rxp t , we can
represent the overall channel impulse response between the k th transmitter and the m th receiver
as
, ,k m tr k m rxh t p t t p t
As in [38] the overall channel will be regarded as quasi-static. In other words, the channel
response remains invariant within the channel coherence time, but can change independently
after that. The corresponding antenna response of the signal ks t over the overall channel
,k mh t is denoted as ,k m t . Hence, the received signal at the output of the m th receiver filter
can be expressed as
, ,
1 0
,K
m k k k m c k m c m
k l
r t s l h t lT t lT t
P (2-2)
23
where the antenna response ,k m ct lT corresponds to the Tc delayed channel hk,m (t-lTc), and
m t represents the AWGN. The sampled output of the DAC operating at the chip rate 1 cT is
given by
, ,
1 0
,K
m k k m k m k m
k l
r n h l l s n l n
P (2-3)
where the summation is limited from 0 to L with L being the channel order determined by the
maximum multipath delay and the sampling period cT , , ,k m k m ch l h lT in which l is the
index of the discrete-time equivalent channel taps. ,k m l is the corresponding antenna
response to be specified in the next chapter according to the different system models, and m n
is the sampled AWGN. When 0L , adjacent symbols interfere with each other and the inter-
symbol interference (ISI) emerges.
Partitioning and converting the sampled output ( )mr n into blocks of size 1P where P is
an arbitrary integer greater than L , the input-output (I/O) relationship with ISI can be
reformulated in terms inter-block interference (IBI). Specifically, the I/O relationship of the i th
block can be expressed as
1
, ,
1
1 ,K
m k k m k k m k m
k
i i i i
r H s H s η P (2-4)
where m iη is a 1P AWGN vector, : 1 1 , 1 2 , ,T
k k k ki s i P s i P s iP s .
,k mH is a P P lower-triangular Toeplitz matrix, and 1
,k mH is a P P upper-triangular Toeplitz
matrix, which can be expressed as
24
,
,
, ,
, ,
0 0 0 0
0 0 0
:
0
0 0
k m
k m
k m k m
k m k m
h
h
h L
h L h
H
,
, ,
1
, ,
0 0 1
0
: 0
0 0 0
k m k m
k m k m
h L h
h L
H
.
In OFDM systems, the orthogonality of subchannels created by inverse FFT can be
maintained and individual subchannels can be separated by FFT at the receiver if the delay
spread is not longer than the symbol duration. The longer delay spread than the symbol duration
will cause two problems, which are ISI and inter-carrier interference (ICI). In order to solve
these problems, a guard time is introduced. It is clear that the IBI can be removed either by
padding L zeros (ZP) at the end of each block. However, ZP still does not treat ICI. To reduce
ICI, OFDM symbols are cyclically extended into the guard time in such a way that cyclic-
prefixing the last L symbols to the head of each block. Both the ZP and the CP options can be
adopted and compared by a multi-carrier transmission system [38]. With its ability of reducing
ICI, here we will focus on the CP option. The insertion of CP can be represented with the P N
CP-inserting matrix
: ,
LL N L
cp
N
0 IT
I
where :N P L . By pre-multiplying the i th information symbol block ks i with cpT , we
obtain the i th CP-inserted signal vector :k cp ki is T s , as depicted in Fig.2-2 Since k is
25
now contains the redundancy, the CP can be removed at the receiver by the P N CP-removing
matrix
: .cp N L NR 0 I
The CP insertion and removal processes can be regarded as left- and right-multiplying the
P P channel matrices ,k mH and
1
,k mH by cpR and
cpT , respectively. Since all the non-zero
elements of 1
,k mH are contained in its first L rows, the product 1
,cp k mR H turns out to be an all-
zero matrix, which removes the IBI. In addition, the product ,cp k m cpR H T is a circulant Toeplitz
matrix, which we will henceforth denote as ,k mH . As a result, the i th received signal block after
CP removal can be expressed as
1
, ,
1
,
1
,
1
1
,
K
m cp m k cp k m k cp k m k cp m
k
K
k cp k m cp k cp m
k
K
k k m k m
k
i i i i i
i i
i i
x R r R H s R H s R η
R H T s R η
H s ψ
P
P
P
(2-5)
where m iψ is an 1N AWGN vector. As we can see from Eq. (2-5), the CP insertion and
removal process converts an ISI channel into an IBI-free channel with a circulant channel matrix
[38]. The circulant channel matrix ensures removal of ICI. For notational convenience, we will
drop the block index i hereafter.
OFDM systems are implemented using a combination of FFT and IFFT blocks in practice.
At the transmitter of OFDM systems, the source symbols are treated as if they are in the
frequency domain. Thus, IFFT takes in N input source symbols at a time and converts them into
time domain data where N is the number of sub-carriers. The output of IFFT is the summation of
26
all N sinusoids which the orthogonal basis functions of IFFT. The block of N output samples
from the IFFT make up a single OFDM symbol. At the receiver, this time domain OFDM
symbol possibly corrupted by the channel will be processed by FFT, which brings it back to the
frequency domain.
One of the desirable properties of the circulant matrix is that it can be diagonalized by pre-
and post-multiplying IFFT and FFT matrices, respectively. That is,
, , , , ,diag diag 0 1 1 ,H
N k m N k m k m k m k mg g g N F H F g
where 2
, , ,0: , 0, 1
j nl
NL
k m k m k mlg n h l l e n N
. In order to exploit this property,
an N point IFFT operator is employed at the transmitter to generate the information symbol
vector : H
k N ks F b and, correspondingly, an N point FFT operator is also used at the receiver.
The n th element of the vector ,k mg is essentially the response of the channel on the n th sub-
carrier. It is obvious that the multipath channel of order L affects each sub-carrier; the channel
provides each sub-carrier with multipath diversity in the order of 1L . Multiplying mx by an
N point FFT, we obtain the signal vector at the m th receive antenna as
,
1
,
1
,
diag ,
KH
m N m k N k m N k N m
k
K
k k m k m
k
y F x F H F b F ψ
g b ξ
P
P (2-6)
where m N mξ F ψ is the AWGN vector.
Finally, we have arrived at an orthogonal frequency division multiplexing (OFDM) system
model, where the signal kb n riding on the n th sub-carrier essentially undergoes a frequency-
flat fading with channel gain ,k mg n . With all the processing in this basic OFDM scheme, we
27
see that OFDM convert the frequency selective channel in to parallel frequency flat channels and
ISI and ICI problem can be solved by employing CP processing..
28
CHAPTER 3
JOINT TRANSCEIVER OPTIMIZATION IN OFDM-BASED MC-CDMA SYSTEMS
Introduction
Multi-carrier code division multiple access (MC-CDMA) systems are well suited for high
data rate wireless multimedia services, due to their ability to convert frequency-selective fading
channels to distinct flat fading channels with low complexity fast Fourier transform (FFT)
devices. However, when multiple users are present, the performance of MC-CDMA systems is
degraded by the multiuser interference (MUI) when the channel is frequency-selective. In order
to mitigate MUI, we present a joint algorithm that combines transmit power control, antenna
array processing and multiuser detection at the receiver. Interestingly, the frequency-selectivity
that entails the MUI also provides multipath diversity which can help suppress the MUI.
Performance of the algorithm in a number of MC-CDMA system models is evaluated in terms of
the average transmit power to achieve the target signal to interference plus noise ratio (SINR).
Simulations confirm the outstanding performance of this algorithm compared with the existing
ones in MC-CDMA systems.
The reminder of the chapter is organized as follows. In the next subsection, the system
models are established. Then, we describe the receiver optimization of the joint array processing
and linear MMSE multiuser detection, assuming fixed transmit powers at all users. After that, we
present the transmitter optimization using the notion of a standard interference function with the
assumption that the receiver structure is fixed. Finally, Simulations and comparisons are
provided at the end.
System Model
Consider a multiuser system where each mobile terminal employs a single antenna due to
its size and complexity limitation, while the base station is equipped with an antenna array
29
consisting of M elements. In a K -user MC-CDMA system, the transmitter spreads the original
data stream from each user using a user-specific signature sequence onto a total of N digital
sub-carriers. In this section, we will establish the system model accounting for the multi-access
spreading, the frequency-selective channel propagation and the antenna array response. We will
also specify the system model for the cases of spatially dependent and spatially independent
fading.
k ib
Nkc ,
kd i m iyOFDM
1,kc
2,kc
Figure 3-1. Block diagram of OFDM-based MC-CDMA system
In order to accommodate multiple users, user-specific spreading is needed. Specifically,
the k th user's symbol block bk is generated by spreading the symbol dk with the spreading
sequence ck := [ck,1, ck,2, … , ck,N]T as bk = dkck, where ck,n represents the n th chip from the
signature sequence of the k th user. Substituting back into Eq. (2-6), we obtain the following I/O
relationship
,
1
diag ,K
m k k k k m m
k
d
y c g ξP (3-1)
In the special case of frequency-flat fading, we have , , , 0, 1k m k mg g n n N so that the
diagonal channel matrix ,diag k mg is simply a scaled identity matrix ,k m Ng I .
30
The I/O relationship in Eq. (3-1) can be re-written as
,
1
,K
m k k k m k m
k
d g
y c ξP (3-2)
where the mutual orthogonality of the spreading codes 1
K
k kc can be preserved. This makes the
MC-CDMA system free from multiuser interference (MUI). However, in general for frequency-
selective fading channels, the elements of ,k mg are typically different from each other. Then,
, 0: , ,diagk m L k m k mg F h α , so Eq. (3-1) can be expressed as
0: , ,
1
diag diag ,K
m k k k L k m k m m
k
d
y c F h α ξP (3-3)
where 0 : LF denotes the matrix formed by the first 1L columns of NF , the channel vector
, , , ,: 0 , 1 , ,T
k m k m k m k mh h h L h , and the antenna gain vector , , , ,: 0 , 1 , ,T
k m k m k m k m L α .
Notice that the distinct fading coefficient on each sub-carrier destroys the mutual orthogonality
among users, which gives rise to MUI. In addition, each user may experience a distinct channel
fading effect. This, together with the near-far problem induced by differing user locations, may
further aggravate the MUI.
Collecting the signals at the array consisting of M receive antenna elements, the overall
system model can be expressed as follows
1 2
1
diag ,K
M k k k k
k
d
Y y y y c G Ξ P (3-4)
Where the channel matrix ,1 ,2 ,: , , ,k k k k M
G g g g , and the noise matrix, 1 2: , , , MΞ ξ ξ ξ ,
contains the temporal and spatial AWGN samples. Depending on the relative spacing among the
elements of the receive antenna array, the channel fading coefficients can be spatially dependent
31
or independent across different elements of the antenna array. Next, we will specify the MC-
CDMA system model for these two cases.
Spatially Dependent Fading
In this subsection, we derive the complete system model employing the array of M
receive antenna elements with a spatially dependent fading channel. A spatially dependent fading
channel is assumed when the spacing among the elements of an antenna array is small such that
the channel fading coefficient corresponding to each antenna array element is identical,
, , 1,k k mh l h l m M .
When we consider a frequency-selective fading channel, the antenna response vector can
be expressed as Chap. 6 of [39]
sin1 2
, ,k l
c
dj m f
ck m l e
(3-5)
where cf is the carrier frequency, d is the distance between the elements of the receive antenna
array, 0 90k l is the direction of arrival of the k th user signal over the delay path 1, and
c is the speed of light. Thus, 2
, ,0:
j nl
NL
k m k k mlg n h l l e
. Accordingly, we can express
the I/O relationship as
,1 ,1 ,2 ,
,1 ,1 ,2 ,
0:
1
,1 ,1 ,2 ,
0:
1
0 0 0 0 0 0
0 1 0 1 1 1diag ,
0 0
diag diag
k k k k M
Kk k k k M
k k k L
k
k k k k M
K
k k k L k k
k
h
hd
h L L L L
d
Y c F Ξ
c F h A Ξ
P
P
(3-6)
where ,1 ,2 ,: , , ,k k k k M
A α α α . In this case of frequency-selective fading channel, we can
observe that the channel coefficients, ,m kg n , vary across the sub-carriers and the maximum
32
channel delay order L of the multipath channel effects allow the MC-CDMA system to exploit
multipath diversity.
When we consider a frequency-flat fading channel, the channel fading coefficient hk,m( l ) =
hk and the antenna response vector can be reformulated as
sin1 2
, .k
c
dj m f
ck m e
(3-7)
Thus, , ,:k m k k mg n h . The I/O relationship can be expressed as
,1
,2
,1 ,2 ,
1
,
1
0 0 0 ,
k
Kk
k k k k k k M
k
k N
KT
k k k k k
k
c
cd h
c
d h
Y Ξ
c α Ξ
P
P
(3-8)
where ,1 ,2 ,, , ,T
k k k k M α . The channel fading effect across all the sub-carriers is
identical. It can be stated that the system undergoes single frequency-flat fading channel across
all the sub-carriers and all the elements of an antenna array. Unlike the case of the frequency-
selective channel, the system cannot exploit the multipath diversity.
Spatially Independent Fading
In this subsection, we also derive the complete system model employing the array of M
receive antenna elements with the spatially independent fading channel such that the path from
each user to each element of an antenna array is essentially an independent fading channel,
, , ' , , 'E E E , 'k m k m k m k mh n h n h n h n m m . In order to guarantee the independence
of each channel, it is common to deploy the elements of the antenna array at a minimum distance
of half the wavelength. Due to the spatial independence of the channel coefficients, the elements
of the antenna response vector, which shows phase differences, can be set to be 1.
33
When we consider a frequency-selective fading channel, the channel coefficient
2
, 0:
j nl
NL
k m klg n h l e
. Accordingly, the channel coefficient vector can be expressed as
, 0: ,k m L k mg F h . The I/O relationship can then be expressed as
,1 ,2 ,
,1 ,2 ,
0:
1
,1 ,2 ,
0:
1
0 0 0
1 1 1diag ,
diag
k k k M
Kk k k M
k k k L
k
k k k M
K
k k k L k
k
h h h
h h hd
h L h L h L
d
Y c F Ξ
c F H Ξ
P
P
(3-9)
where ,1 ,2 ,: , , ,k k k k M
H h h h . In this case of frequency-selective fading channel, we have
temporally and spatially independent fading channels which enable the MC-CDMA system to
exploit multipath diversity of order 1L and spatial diversity of order M . In contrast with
the inherent characteristic of MC-CDMA system to exploit the multipath diversity in frequency-
selective fading channels, DS-CDMA systems may need additional processing such as a Rake
receiver to achieve the diversity. Therefore, we can achieve diversity gain more efficiently for
MC-CDMA in a frequency-selective fading channel than with DS-CDMA scheme in the same
channel.
When we consider a frequency-flat fading channel, , , , 0,k m k mh h l l L , the
channel coefficient , , ,k m k mg n h n . The I/O relationship can be expressed as
,1
,2
,1 ,2 ,
1
,
1
0 0 0 ,
k
Kk
k k k k k M
k
k N
K
k k k k
k
c
cd h h h
c
d
Y Ξ
c h Ξ
P
P
(3-10)
34
where ,1 ,2 ,: , , ,T
k k k k Mh h h h . We can observe that the channel coefficients across all the
sub-carrier are identical, and spatial independence provides the diversity of order M . We will
describe the joint optimization of the transmitter and the receiver in the next section.
Joint Optimization of Transmitter and Receiver
With the goal of minimizing the total power consumption while satisfying specified SINR
objectives, we will develop a joint optimization algorithm which combines antenna array
processing, multiuser detection (MUD), and power control. Notice that the first two operations
are carried out at the receiver, whereas the power level adjustment is made at the transmitter.
Receiver Optimization
For arbitrary transmission power levels 1
K
k kP , our goal in the receiver optimization is to
maximize the SINR of each user. Specifically, with a given observation matrix Y as in Eq. (3-
6) , user-specific filters will be constructed to maximize each user's SINR. Multiuser detectors
perform temporal filtering of the received signals by exploiting the structures in multiuser
environments. Among many multiuser detectors, we employ the MMSE multiuser detector
which is the linear filter maximizing the output SINR. Given the observation matrix Y , the
elements of m th column can be considered as a temporally received signal at the m th element
of the antenna array, and each column can be considered as the spatially separated received
signal. In order to apply the MMSE multiuser detector for the observation matrix Y , we convert
the matrix form of the observation Y into a long vector form by stacking its columns such that
1 2
1
,K
TT T T
M k k k
k
d
y y y y q ξ P (3-11)
where kq is constructed by stacking the columns of diag k kc G in Eq. (3-6) and consists of the
combined temporal-spatial received signal of the k th user which contains the channel
35
propagation effects. Likewise, the noise vector, 1 2: , , ,
TT T T
M ξ ξ ξ ξ , is also constructed in the
same manner, and has zero mean and covariance matrix 2
NM I .
Let kw denote the MUD filter coefficients vector corresponding to the k th user. Then, the
decision statistic for the k th user's symbols can be obtained as follows
H H H H
k k k k k k k j j j k
j k
z d d
w y w q w q w ξP P (3-12)
Our objective of maximizing the SINR then amounts to minimizing the mean-square-error
(MSE) of the estimate [6]; that is, the optimum filter coefficients vector kw can be obtained by
solving the following equation
2
arg min E ,H
k kd w
w w y (3-13)
assuming that the symbols kd are uncorrelated. Substituting Eq. (3-12) into Eq. (3-13), we have
the following MSE expression
22 2
2E 1H H H H
k k k k k j k j k k
j k
MSE d
w y w q w q w wP P (3-14)
It then follows that the k th user's optimum filter coefficients vector and the corresponding
MMSE are [21]:
1
2
1
KH
k k j j j NM k
j
w q q I qP P (3-15)
.1 H
k k k kMMSE w qP (3-16)
Since the matrix 2
1
K H
j j j NMj
q q IP is positive definite for all 2 0 , its inverse always
exists. This guarantees the existence of the MMSE filter coefficients vector kw . The frequency-
selectivity in MC-CDMA systems enables multipath diversity and the array of multiple receive
36
antenna provides the spatial diversity. Given multipath diversity and the receiver diversity in the
MC-CDMA systems, the MMSE MUD may be expected to benefit from those diversities, and
the expectation is confirmed later in this section and by a number of simulations described at the
end of this chapter.
From the decision statistic given in Eq. (3-12), we obtain the SINR expression of the k th
user as
2
22
H
k k k
kH H
j k j k kj k
SINR
w q
w q w w
P
P (3-17)
Substituting Eq. (3-15) into Eq. (3-17), we get the maximum SINR for the k th user:
,max
1
H
k k k
k H
k k k
SINR
w q
w q
PP
(3-18)
which is inversely proportional to the kMMSE in Eq. (3-16).
In order to see if the MMSE MUD is benefited from multipath diversity in the proposed
system, we apply the k th user's filter coefficients vector kw for the received signal. For
mathematical simplicity, we only use the received signal from the k th user :k k k kdu qP . The
k th user's receive signal output from MMSE MUD can be expressed as
1
2
1
.K
H H H
k k k k k j j j NM k
j
d
u w q q q I qP P (3-19)
Consider the system with single receive antenna. The number of users and sub-carriers are two,
and the channel is frequency selective. Then, kq is a 2 1 vector which can be expressed as
1 2
T
k k kH Hq (3-20)
37
Without loss of generality, the received signal from user 1 can be chosen for mathematical
analysis. The filter coefficient vector for user 1 can be expressed as
12
2
1 1 1
1
2 2 2
1 12 2 22 1 11 12 2 21 22
1 12 2 2
1 12 11 2 22 21 1 11 2 21
1
H
j j j NM
j
H H H H H H
D H H H H H H
w q q I q
q
P P
P P P PP
P P P P
where 2 2 2 2 22 2
1 11 2 21 1 12 2 22 1 2 11 22 21 12D H H H H H H H H P P P P PP .
Then, the output from the filter can be expressed as
2 2 221 11 1 11 12 2 11 22 21 12
H dH H H H H H
D u w
P P (3-21)
Substituting Eq. (3-21) for Eq. (3-18), we get the maximum SINR for user 1 as
2 2 22
1 11 12 2 11 22 21 12
1 2 2 2
2 21 22
H H H H H HSINR
H H
P P
P (3-22)
In case of frequency flat fading channel (L = 0), the vector the vector kq can be expressed as
,1
,2
0
0
k k
k
k k
h c
h cq (3-23)
The terms in Eq. (3-22) can be turned into
22 2
11 12 12 0 H H h (3-24)
22 2
21 22 22 0 H H h (3-25)
2
11 22 21 12 0 H H H H (3-26)
When we consider the frequency selective fading channel where the multipath delay order of
1L , the vector kq can be expressed as
38
,1
,2
0 1
0 1
k k k
k
k k k
h h c
h h cq (3-27)
The first two terms and the last two in the denominator in Eq. (3-22) can be turned into
2 22 2
11 12 1 12 0 2 1H H h h (3-28)
2 22 2
21 22 2 22 0 2 1 H H h h (3-29)
22
11 22 21 12 1 2 1 22 1 0 2 0 1H H H H h h h h (3-30)
From Eq. (3-22) through Eq. (3-30), we see that the difference in SINRs between frequency flat
and frequency selective fading channel in the system is mostly affected by the terms shown in Eq.
(3-26) and Eq. (3-30). Therefore, we can state that SINR in frequency selective case is likely
higher unless 1 2 1 21 0 0 1h h h h . Since we can assume that the channel tap coefficients
kh l are independent or have small correlation with each other, it is most likely
that 1 2 1 21 0 0 1h h h h . Consequently, we can conclude that MMSE MUD is benefited
from multipath diversity in the above case.
We consider more general case where the multipath delay order is L and the number of
sub-carriers is equal to 1L . Then, Eq. (3-21) can be turned into
2221 11 1 1 2 1 21 1 2 1
1 1 1
2 221 11 1 2 2 1 2
0 1 1
'
'
N N lH
l j jl ll l j
L L L
l l j
dH H H H H
D
dN h l h l h j h l h j
D
u wP P
P P (3-31)
Eq. (3-31) is linear addition from Eq. (3-21) due to the increment of multipath delay order L .
The last term in Eq. (3-31) 2
1 2 2 1 2
1 1
L L
l j
h l h j h l h j P , affects the SINR of the system
39
in such a way that SINR increases as L gets larger corresponding to the previous case. This
general case also confirms the system with MMSE MUD is benefit from multipath diversity. If
we substitute the multipath delay order index l or j from Eq. (3-31) for the number of elements
in receive antenna array, we can deduce that MMSE MUD also can be benefited from spatial
diversity.
Transmitter Optimization
Our goal in the transmitter optimization is to find an adaptive power control algorithm
which minimizes the average total transmit power with rapid convergence, while satisfying a
certain minimum required target SINR. Consider the following SINR-based power updating
algorithm
1SINR
P P
(3-32)
where P and 1 P represent the current and updated power levels, respectively, and
SINR and respectively denote the current SINR and the target SINR. Intuitively speaking,
the algorithm works as follows: when the current SINR is less (or more) than the target SINR,
the updated power will be increased (or decreased). However, Eq. (3-32) only works on the basis
of an individual user without the total power considerations and the minimum target SINR
constraint. Taking all these into account, we formulate the joint optimization problem such that
1
minK
k
k
P (3-33)
2
2
2such that
H H
j k j k kj k
k kH
k k
w q w w
w q
PP (3-34)
and 0, 1, 2, , ,k k K P (3-35)
40
where k is the target SINR for the k th user, and the right hand side part of Eq. (3-34) is
obtained from multiplying the inverse of kSINR shown in Eq. (3-17) by kP . Including the
iteration index , we can treat the SINR obtained by the MMSE MUD as a function of the
iteration index . For the k th user, the MMSE weighting vector kw now depends on the
instantaneous power levels of , 1,2, ,k k K P (see Eq. (3-15)).
Consequently, the maximum instantaneous SINR for the k th user at the iteration can be
expressed as
,max ,
1
H
k k k
k H
k k k
SINR
w q
w q
P
P (3-31)
where H
k w is the MMSE weighting vector at .
Let us denote the right-hand side of Eq. (3-34) as an interference function kI P , where the
1K vector 1 2: , , ,T
K P P P P , namely P contains the instantaneous
power levels at all transmitters. It turns out that kI P is a standard interference function by
satisfying the following three properties [40]:
Positivity: 0;kI P
Monotonicity: if ' , then ' ; andk kI I P P P P
Scalability: for all 1, k kI I P P .
As a result, the power control iteration in Eq. (3-34) is guaranteed to converge to the optimum
solution for the power vector.
The resulting joint power control approach is a two-step iterative algorithm. The receiver is
optimized by Eq. (3-15) with fixed transmit power in the first step, and the transmitter is
41
optimized by Eq. (3-34) in the second step with fixed receiver filter. At each iteration step of the
algorithm, the maximum interference suppression is achieved by choosing the MMSE filter
coefficients and applying the filter to the receiver. The suppression of interference then allows us
to reduce the total transmit power of the users while satisfying the minimum SINR requirements.
Compactly written, the two step receiver and transmitter optimization is given by:
1
22
21 min
MNk
H H
j k j k kj k
k kH
k k
w
w q w w
w qC
PP (3-32)
In the next section, we will evaluate the performance of the joint transceiver optimization by
simulations and comparisons with existing alternatives.
Simulations and Comparisons
In our simulations, we consider two cases of channel fading: frequency-selective and
frequency-flat fading channels. In both cases, the channel gains are Rayleigh distributed with
expected total power normalized to 1: 2
0E 1
L
klh l
, where 0L for frequency-selective
and 0L for frequency-flat. We consider quasi-static channels, where the channel gains remain
invariant within the channel coherence time, but can change independently afterwards. Users'
signature sequences are length N pseudo-random codes. The target SINR is set to be 5 (7dB) for
all users. The number of antenna array elements at the receiver is denoted by M . For all
simulations presented in this chapter, we compare the performance of the systems in terms of the
convergence rates to the target SINR or the average transmit power consumption. The number of
trials is 1000. The average SINR and the average transmit power are obtained by averaging
across all the users.
42
1 2 3 4 5 6 7 8 9 100
1
2
3
4
5
6
Iteration Index
Avera
ge S
INR
DS-dp
DS-idp
MC-dp
MC-idp
0 1 2 3 4 5 6 7 8 9 10-20
-15
-10
-5
0
5
10
15
Iteration Index
Avera
ge T
ransm
it P
ow
er
(dB
)
DS-dp
DS-idp
MC-dp
MC-idp
(a) Convergence rate to the target SINR (b) Average transmit power update
Figure 3-2. Performance comparison between MC-CDMA schemes and DS-CDMA schemes
when K=10, N=10, M=2, L=0
Test Case 1: We compare the performance of the joint power control algorithm in DS-
CDMA systems proposed in [20] and in MC-CDMA systems proposed in this chapter. We set
the number of users K = 10 and the length of the signature sequences N = 10. Since the algorithm
in [20] only applies to DS-CDMA systems in frequency-flat fading channels while our algorithm
here is tailored for MC-CDMA systems experiencing frequency-selective fading channels, we
carry out the comparison between them in frequency-flat fading channels. In both systems, we
consider two cases: i) the spatially dependent fading (dp) and ii) the spatially independent fading
(idp), thus we have four setups: DS-CDMA systems with spatially dependent fading channels
(DS-dp), DS-CDMA systems with spatially independent fading channels (DS-idp), MC-CDMA
systems with spatially dependent fading channels (MC-dp), and MC-CDMA systems with
spatially independent fading channels (MC-idp). Fig. 3-2(a) shows the convergence rates. The
MC-idp and DS-idp both take three iterations to reach the target SINR, while MC-dp and DS-dp
43
0 1 2 3 4 5 6 7 8 9 10-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
Iteration Index
Avera
ge T
ransm
it P
ow
er
(dB
)
Spatially dependent
L = 0
L = 1
L = 2
L = 3
0 1 2 3 4 5 6 7 8 9 10-10
-9
-8
-7
-6
-5
-4
-3
-2Spatially independent
Iteration Index
Avera
ge T
ransm
it P
ow
er
(dB
)
L = 0
L = 1
L = 2
L = 3
(a) Spatially dependent case with L=0,1,2,3 (b) Spatially independent case with L=0,1,2,3
Figure 3-3. Average transmit power updates with K=16, N=16, M=2, L=5
both take four iterations. Fig. 3-2(b) depicts the average transmit power required for all users to
achieve the target SINRs. Not surprisingly, the MC-CDMA and DS-CDMA systems show the
identical performance in both the SINR convergence rate and the power consumption, regardless
of the spatially dependent or independent fading. However, the systems with spatially
independent fading result in a lower total transmit powers than ones with spatially dependent
fading. This is due to the spatial diversity gain provided by the independent fading.
Test Case 2: When the channel is frequency-selective, it provides an additional multipath
diversity gain. In contrast with the power control algorithm in [20], the algorithm proposed in
this chapter can exploit multipath diversity. To see this, we test the performance of our algorithm
for MC-CDMA systems in frequency-flat (L = 0) and frequency-selective (L > 0) channels. Fig.
3-3 shows the average transmit power updates required for all users to achieve the target SINR 5.
From this simulation, it is confirmed that the joint algorithm effectively exploits the multipath
44
diversity. Furthermore, we observe that the system performance is better in the spatially
independent case than the spatially dependent case.
1 2 3 4 5 6 7 8 9 100
1
2
3
4
5
6
Iteration Index
Avera
ge S
INR
Sel-idp
Flat-idp
Sel-dp
Flat-dp
Sel-sngl
Flat-sngl
0 1 2 3 4 5 6 7 8 9 10-25
-20
-15
-10
-5
0
5
10
15
20
Iteration Index
Avera
ge T
ransm
it P
ow
er
(dB
)
Flat-sngl
Sel-sngl
Flat-dp
Flat-idp
Sel-dp
Sel-idp
(a) Convergence rate to the target SINR (b) Average transmit power update
Figure 3-4. Performance comparison among a number of MC-CDMA system models when
K=16, N=16, L=5
Test Case 3: In this simulation, we compare the system performance in a number of MC-
CDMA system models. We use the following abbreviations for simplicity: the spatially
independent (idp), spatially dependent (dp), single antenna (sngl), frequency-flat (flat) and
frequency-selective (sel). Specifically, the six setups considered here are Sel-idp, Sel -dp, Sel-
sngl, Flat-idp, Flat-dp and Flat-sngl. We set 16K , 16N , and 2M for multiple receive
antennas. In case of the frequency-selective fading channel, we set the channel order 5L . From
Fig. 3-4(a), we observe that the spatial diversity helps the convergence rate of the algorithm.
However, we can see that the frequency-selectivity does not play an important role to the
convergence rate. Fig. 3-4(b) shows the average transmit power updates required for all users to
45
achieve the target SINR 5. In this plot, we observe that both spatially diversity and the multipath
diversity help reduce the transmit power.
1 2 3 4 5 6 7 8 9 100
1
2
3
4
5
6
Iteration Index
Avera
ge S
INR
MC-jnt
MC-sngl
MC-tf
MC-mrc
0 1 2 3 4 5 6 7 8 9 10-30
-20
-10
0
10
20
30
40
50
60
70
Iteration Index
Avera
ge T
ransm
it P
ow
er
(dB
)
MC-mrc
MC-tf
MC-sngl
MC-jnt
(a) Convergence rate to the target SINR (b) Average transmit power update
Figure 3-5. Performance comparison among the joint algorithm and existing algorithms in MC-
CDMA systems when K=16, N=16, M=2, L=5
Test Case 4: In this simulation, we compare the performance of the proposed algorithm
(MC-jnt) with the performance of three existing algorithms for MC-CDMA systems. The first
algorithm, which we term MC-mrc, utilizes the conventional matched filter detector matched to
the temporal-spatial signature [7]. The second one, which we term MC-sngl, utilizes a single
receive antenna and a linear MMSE multiuser detector. The third algorithm, which we term MC-
tf, utilizes the Time-Frequency power adaptation scheme in [16]. For all algorithms, we set
16K , 16N , 2M (except for MC-sngl), and 5L . Fig. 3-5(a) shows the convergence
rates corresponding to the four algorithms. Clearly, our proposed joint algorithm (MC-jnt)
outperforms the others. In addition, the MC-mrc and MC-tf algorithms do not even converge to
the target SINR. Moreover, we observe in Fig. 3-5(b) that the MC-jnt case consumes the lowest
transmit power to achieve the target SINR; while the MC-tf and MC-mrc algorithms keep
46
increasing the average transmit power at each iteration, but can never reach the target SINR.
Although the proposed system requires an additional complexity mainly due to MMSE MUD, its
performance enhancement makes it promising solution for MUI and transmit power reduction.
Conclusions
In this chapter, we presented a joint transceiver optimization algorithm for MC-CDMA
systems. Our analysis and simulations show that this joint algorithm for MC-CDMA systems is
well suited for frequency-selective fading channels, and that both spatial diversity and multipath
diversity are exploited to enhance the MUI suppression performance. These result in an increase
of the MC-CDMA system capacity.
47
CHAPTER 4
POWER LINE COMMUNICATIONS
PLC History and Competitions
Power Line Communications (PLC) basically means any technology that enables data
transfer at narrow or broad band speeds through power lines by using advanced modulation
technology. PLC has been around for quite some time; the first remote electricity supply
metering in 1838 and the first patent on power line signaling were proposed in the United
Kingdom in 1873 [41, 42]. It has only been used for narrow band tele-remote relay applications,
public lighting and home automation. The growth of the internet accelerates the demand for the
high data rate communication services to almost every premise. If such services can be carried
over power line networks, it can provide interconnection to every home, factory and office
without any additional cost of deploying the communication medium. HomePlug 1.0, which is
the first high-speed solution for Local Area Networking in Small Office/Home Office (SOHO),
was standardized in 2001 and widely available in both North America and Europe [43, 44].
HomePlug AV [45, 46], standardized in 2005, is one of the most popular power line
communication technologies, and it supports up to 200Mbps transmission rate using power lines.
There are several technology choices for home networking. When existing wires are used,
two more options are available in addition to the PLC. The Home Phone line Networking
Alliance (HomePNA) 3.0 standard [47], using telephone lines, released in 2003 specifies data
rates up to 128 Mbps with optional extensions to 240Mbps. It also has deterministic Quality of
Service (QoS), but suffers from a limited number of available outlets in the house. Released in
2005, the Multimedia over Coax Alliance (MoCa) standard [48], using coax cables, uses 50 MHz
of bandwidth in the 850MHz to 1500MHz band. Similar to using existing telephone wiring,
48
cable outlets are typically limited to 3 or 4 in the average home and are certainly not present in
all rooms.
There are two main wireless contenders for home multimedia distribution: Ultra Wide
Band (UWB) [49, 50] and 802.11a/g/n [51]. UWB is capable of providing up to 480Mbps at
short range (3meters) and 110Mbps at 10 meters. Beyond these distances, UWB signals suffer
high attenuation; hence it is primarily useful for in-room Personal Area Networks. The 802.11
family includes over-the-air modulation techniques that use the same basic protocol. 802.11b
was the first widely accepted one, followed by 802.11g and 802.11n. 802.11n is a new multi-
streaming modulation technique that is still under draft development. It uses multiple-input
multiple-output (MIMO) and space time coding schemes. The wireless option, with the
advantage of flexibility, is certainly viable except for the fact that a dedicated wired
infrastructure connecting multiple access points is required to cover the entire home. In addition,
wireless mobile devices rely on batteries and have difficulty in maintaining continuous electric
power. The recent study shows that the present version of the HomePlug 1.0 and AV have been
shown to out-perform the traditional IEEE 802.11 a/g/n in many field tests of connectivity,
throughput and link stability [52, 53].
Power lines, being ubiquitously deployed as a wire-line network for carrying electrical
power, are then the obvious choice as the medium for communication amongst the plethora of
home-based and personal devices. They offer the convenience of already being there, and having
outlets in almost all locations in a household for easy access. Further, devices can easily obtain
electric power if they are deployed on PLC systems.
The PLC systems, however, are not free of problems. The PLC channel is notorious for
electric noise and interference, as well as channel variability depending on the appliances that are
49
in use from time to time. In the following subsections, we present the power line channel
condition and the advanced techniques used for reliable communication through power line
networks.
PLC Medium
While many have attempted to use the power line as a communication medium in the past,
it has not lived up to expectations, earning a reputation for questionable reliability. The fact is
that the power line is a difficult and noisy communications medium, characterized by several
unpredictable and strong forms of interference.
The major sources of noise on the power line are from electrical appliances, which
generate noise components that extend well into the high frequency spectrum. The appliances
connected to an outlet contribute line interference, which can be approximated as Additive White
Gaussian Noise (AWGN). In addition, the radio frequency signals also impair certain frequency
bands. Dimmer switches, motorized electrical appliances and computers, also introduce
impulsive noise.
Frequency selective fading also corrupts PLC channels, which have non-flat frequency
responses. There is an another channel impairment that the signal can be highly attenuated in
PLC channel, an average attenuation of approximately 40 dB. Because of both physical
attenuation and delay spread, the frequency response of the power line channel is variable over
frequency band. PLC channels are typically non-symmetric since the noise experienced at each
node may be highly localized due to the attenuation.
PLC systems also follow the regulatory constraints, which may be different between
countries. This unstable international regulatory environment requires that PLC systems be
flexible to adapt with changing regulations.
50
All the prescribed facts contribute PLC channels to be unstable. Therefore, it is critical that
PLC systems continually adapt to the changing channel conditions. Especially, the bit-loading
OFDM is used in PLC systems, which means that the systems determine the highest order
constellation that each carrier can support, in order to maximize the data rate.
HomePlug AV PHY
The HomePlug AV, the current PLC standard, physical layer is designed to ensure that
multiple multimedia streams can be supported simultaneously and delivered to the whole house
[54]. In order to do so, the AV PHY incorporates a number of features, which can deal with the
harsh PLC channel condition and the regulatory constraints. The AV PHY is based on OFDM
modulation, which is combined with adaptive bit loading to provide great flexibility with which
to adapt the PLC channel, allowing optimized and stable channel throughput. The bit-loaded
OFDM works in such a way that each sub-carrier with a high enough SNR to support data can be
coherently modulated up to 10 coded bits per carrier [55]. This is the major effect of the higher
maximum data rate in HomePlug AV over HomePlug 1.0. Impulsive noise is well handled in
HomePlug AV by this combination of channel adaptation and efficient retransmission scheme. In
order to satisfy different regulatory constraints throughout the world, time-domain pulse shaping
of the OFDM symbols is employed to provide flexible spectral notching [56]. In addition, the
AV PHY considers the compatibility with the previous versions of PLC standards.
PHY Protocol Data Unit (PPDU) consists of the preamble, the Frame Control (FC) and
PHY payload blocks. These HomePlug AV PHY frames uses 1155 sub-carriers in the frequency
range from 1.8 MHz to 30 MHz, where 917 sub-carriers are active and 238 sub-carriers are
turned off in the US for FCC regulation. The sub-carriers can be modulated with Phase Shift
Keying (PSK) and Quadrature Amplitude Modulation (QAM) schemes up to 10 bits per sub-
carrier depending on the SNR on each sub-carrier. The preamble block is essentially employed
51
for synchronization, and it also provides a training sequence for channel estimation and
equalization, as the preamble is an a priori known signal. The FC contains such information as
Tone Map Identifier (TMI) and length of PHY body. The TMI is an index of Tone Map, which
contains the modulation types of the OFDM symbols of the PHY body. TMI is chosen by the
receiver during channel adaptation and is sent along with the Tone Map to the transmitter. PHY
demodulate the symbols by the informed PHY body length.
Power line
384 Point
FFT
AGC
AFE
Demodulator3072 Point
FFT
AV PB
Data Out
Frame Control
Data Out
Receiver
IFFT
(372,3072)
Insert
Preamble
AFE
Cyclic Prefix,
Window &
Overlap
Mapper
Transmitter
AV Packet Body FEC
Scrambler InterleaverTurbo
Convolutional
Encoder
AV & 1.0.1
Frame Control FEC
Time
Sync
AV & 1.0.1 Frame Control
Decoder
AV Packet Body FEC
Deinterleaver DescramblerTurbo FEC
Decoder
Figure 4-1. HomePlug AV Transceiver
52
A block diagram of a HomePlug AV transceiver is shown below in Figure 4-1. Since the
purpose of this section is to briefly introduce the HomePlug AV, we only include HomePlug AV
data blocks in detail. On the transmitter side, the PHY layer receives its inputs from the Medium
Access Control (MAC) layer. Two separate processing chains are shown because of the different
error correction coding for Control Information, and HomePlug AV data.
The HomePlug AV data stream passes through a Scrambler, a Turbo FEC Encoder and a
Channel Interleaver. A Scrambler is employed for the security purpose. Turbo FEC coding is
widely known to provide performance close to theoretical channel throughput limits with
manageable complexity. The larger the block size is, the higher the coding gain can achieve.
However, the large block size on Turbo FEC causes decoding latency and computational
overhead. Interleaving is used in digital data transmission technology to protect the transmission
against burst errors such as impulse burst in PLC systems.
The outputs of both types of FEC Encoders lead into a common OFDM Modulation
structure. The coded symbols blocks are passed through the Mapper resulting in baseband
constellation symbols. Then, Inverse Fast Fourier Transform (IFFT), Preamble and Cyclic Prefix
insertion are processed. After that, windowed overlapping which eventually feeds the Analog
Front End (AFE) module that couples the signal to the Powerline medium. For windowing
process, a specifically designed pulse shape is applied to each time domain OFDM symbol,
causing reduced bandwidth occupancy of the sidelobes of each sub-carrier.
At the receiver, an AFE operates with an Automatic Gain Controller (AGC) and a time
synchronization module to feed separate control and data information recovery circuits. The
sampled data stream (which contains only HomePlug AV formatted symbols) is processed
53
through a 3072-point FFT, a demodulator with SNR estimation, a Deinterleaver followed by a
Turbo FEC decoder, and a Descrambler to recover the data stream.
HomePlug AV represents a significant advance in PLC technology even there is no
revolutionary technical advance. In order to enhance SNR performance Turbo convolutional
coding and coherent modulation are employed. Transmission is synchronized with respect to the
AC line cycle, and flexible frequency notching is achieved using OFDM symbol shaping.
Adaptive bit-loading corresponds to the significant improvement of data rate. These results
confirm that HomePlug AV is capable of supporting multiple high data rate multimedia stream.
54
CHAPTER 5
IMPROVED IMPULSIVE NOISE DETECTION IN POWER LINE COMMUNICATION
SYSTEMS
Introduction
Impulsive noise is generated by many house hold appliances that are attached to the
electrical network. Its presence is often detrimental to the performance of a power line
communication system, causing PHY throughput degradation in the order of 30-50%. The goal
of impulsive noise mitigation is to improve the SNR of the received signal by means of signal
processing tools. In this work we focus on optimizing the detection of impulsive noises. A new
method is developed for the setting of the detection threshold, that is both efficiently computed
(in an iterative manner), and performs well in various impulsive noise conditions. Once impulses
are detected they are removed from the received waveform by applying simple windowing
mechanisms. To evaluate different impulse detection algorithms we test them against real life
(impulsive) noise waveforms that have been captured on the power line. The selected algorithm
is further validated on the power line against real-time captures of impulsive noise impeded
signals.
The remainder of the chapter is organized as follows. In the beginning, we review some
conventional impulse detection and mitigation techniques and introduce some of the common
concepts in more detail. The next subsection contains the description of our new threshold-
setting algorithm for impulse detection. Then, simulation results are discussed where we also
describe the effects of some of the impulsive noise sources considered, and finally conclusions
will be following.
Impulsive Noise Mitigation in Power Line Networks
In this section, we discuss existing detection and processing methods. We also mention the
processing method we will use in this study. The algorithm for declaring the start and stop
55
sample of an impulsive noise hit is shown in Figure 5-1. In order to find the impulsive noise
starting point, a length M shift register R is employed. At first, the detection algorithm tries to
find the starting points of the impulsive noise samples.
|)(| ty NO 0)1( R
1)1( R
YE
S
(2 : ) (1: 1) at 1R M R M t
1 Start Imp NO NONRSum )(1
0)(
tt
tImap
1)( RSum
YE
S
1 Start Imp
YE
SY
ES
0
1
1)(
c
tt
tImap
NO
1
1
0)(
cc
tt
tImap
15C1 Start Imp.
0 Start Imp.
YE
S
NO
0
0startImp
)1,(zeros
c
MR
Figure 5-1. Impulsive noise Detection Flow Chart
56
At time instance t, the first element of the shift register is set to be 1 if the amplitude of the
received signal is larger than or equal to a detection threshold thre , then the register shifts. If the
sum of all the elements of the shift register are larger than N, which is the impulse starting point
threshold, then the element of the impulse map Imap(t) at that time instance is set to be 1, which is
the impulse starting point. From the impulse starting point up to fifteen samples C, if the signal is
larger than or equal to the threshold, then, the element of the impulse map at that time instance is
set to be 1. After fifteen samples from the last detected impulsive noise sample, the algorithm
tries to find the next impulse starting point.
Once the locations of impulsive noise samples are identified by the detection step, one of
several impulsive noise processing algorithms can be employed, choices include
Clipping: reduce the voltages of affected samples to a hard limit.
Blanking: replace affected samples with 0’s
Windowing: similar to blanking, but use a window shape to ramp-down and ramp-up samples
around impulses to better preserve orthogonality and not turn narrowband jammers into
broadband jammers. The overall performance of this technique is better than but more
dependent on the type of impulsive noise than Blanking. Choosing a window and window
length is another problem to solve.
Overwriting/Averaging: replace affected samples in IFFT interval with copies from the cyclic
prefix (CP).
LLR Reduction: reduce log likelihood ratios (LLR) from OFDM symbols in proportion to the
number of samples affected by impulsive noise.
Canceling: attempt to reproduce time domain waveform of impulse and subtract it from receive
waveform before demodulation.
57
In this chapter, we consider two different sizes of CP for inter-symbol interference
reduction. The first CP size is 1052, which contains the last part of the payload information. The
second CP size is 5028, which contains all the information of the payload. For 1052 CP size, our
system performs Hanning windowing and averaging with copies from the CP for jammer
mitigation, which also helps for impulsive noise mitigation. Since the length of CP is short, the
portion of the receive signal to be processed is very restricted. Therefore, we perform Hanning
windowing to mitigate the effect of the impulsive noise using the detected impulse information.
CP Payload symbol
0's
+
Payload symbol
=
Figure 5-2. Windowing and averaging for 1052 CP size
SymbolCP2CP1HW
CP2
Symbol
Zeros HW
=
Figure 5-3. Averaging for 5028 CP size
For 5028 CP size, the algorithm also uses Hanning windowing, and it performs overwriting and
averaging. Since the long CP contains all the payload symbol information, the performance
improvement using the algorithm is significant. However, employing long CP basically reduces
the effective PHY data rate by more than 50%.
58
Tighter Threshold Setting
In this section, we propose a detection threshold setting algorithm. The receive signal in
the time domain can be expressed as
( ) ( ) ( ) ( ) where [0, 1].y t h t x t n t t T (5-1)
where )(),(),( tntxth represent channel response, transmit signal and noise, respectively. T and
represent the total number of samples and the convolution operation, respectively. In order to
set a threshold, the Envelope Threshold setting method uses a peak-to-average power ratio
(PAPR) and a receive waveform average power (RWAP) information defined as
2
2
max{ ( ) }
mean{ ( ) }
s tPAPR
s t (5-2)
where )(ts represent an arbitrary time domain signal. At the first step, a rough threshold, , is
first set by multiplying known transmit waveform (TW) PAPR by computed RWAP namely
2
2
2
max{ ( ) }mean{ ( ) }
mean{ ( ) }
x ty t
x t (5-3)
This value should be located between the maximum signal envelope without noise and the
maximum receive waveform (RW) envelope defined respectively as
2
max 2
max{ ( ) }mean{[ ( ) ( )]}
mean{ ( ) }
x tS h t x t
x t (5-4)
2
max max{ ( ) }R y t (5-5)
When the threshold is smaller than maxS , the detection algorithm identifies the signal samples as
impulsive noise samples. When the threshold is larger than maxR , the algorithm does not work at
all. After a rough threshold being set, we should adjust the value using a threshold-scaling factor
such as
59
1C (5-6)
where 1C represents the threshold scaling factor. By setting the threshold-scaling factor to 1.1,
we achieve an impulse detection threshold that is 10 % higher than approximate threshold. Since
RWAP contains signal power and noise power, the threshold will be loosened (increased) when
impulsive noise power is large.
In order to make the threshold tight with respect to the envelope of the desired signal
without impulsive noise, we manipulate the Envelope Threshold method in a two-step algorithm.
In the first step, we set a threshold as a rough threshold and a threshold-scaling factor as 1.10
as follows
' 1.10 (5-7)
Then, we detect the impulsive noise samples with the rough threshold value such as
1 | ( )| '
( )0
if y t tI t
otherwise
(5-8)
We cancel the receive waveform samples at the impulsive noise detected location to zero as
0 ( ) 1
( )( )
if I t tr t
y t otherwise
(5-9)
We can then calculate a roughly impulsive noise cancelled RWAP as 2mean{ ( ) }r t . When the
average power of impulsive noise is large, we can observe two things. One is that the difference
between a rough threshold and the maxS , which can be viewed as the optimum impulsive noise
detection threshold, gets large. We want the difference to be as small as possible for better
detection. In order to do so, we have to manipulate RWAP value. The other observation is that
the difference between the original RWAP and the approximately impulsive noise cancelled
RWAP gets large where we define the difference as
60
2 2mean{ ( ) } mean{ ( ) }D y t r t (5-10)
Then, we can have a RWAP expression, which results in a tighter threshold.
2
2
2
mean{ ( ) }mean{ ( ) }
mean{ ( ) }
r tRWAP y t P D
y t (5-11)
2
2
max{ ( ) }
mean{ ( ) }
x tThreshold RWAP
x t (5-12)
where P is a constant. A proper adjustment of P allows the updated RWAP value to be as close
to maxS as possible. In the simulation section, we find that the threshold setting is good when
P equals to 3. This threshold setting algorithm results in a very good performance of impulsive
noise detection as shown in simulation results presented in the next section.
Simulations
Scenarios and Impulsive Noise Data
The performance analysis of the impulsive noise mitigation in power line networks is
evaluated using the threshold-setting algorithm proposed in this chapter. To perform a
comparatively assess of the impact of the impulse mitigation, we evaluate system performance
using the following three scenarios:
NoImpulseNoise: This represents the performance limit of the impulsive noise mitigation
algorithm. Instead of inserting noise, we only insert impulse-free Gaussian noise to the
system.
ImpulseDetection: This represents the performance of the system in which we detect impulsive
noise up to a certain threshold and mitigate it through Windowed Blanking or Blanking.
When setting the first step of the threshold, a 10% higher rough threshold is chosen to
obtain a tighter threshold. For Windowed Blanking, we use a Hanning window with a
length of thirteen; the window starting points are set at zero.
61
NoImpulseDetection: This represents the performance of the system without the impulse
detection step.
Figure 5-4. SmImp noise
Figure 5-5. Hair Dryer noise
62
The simulations use measured power line impulse responses and noise, in particular, we
use the impulsive noise captures described below and HomePlug AV-style data packets as the
signal. In order to achieve as practical an analysis as possible, sets of actual impulsive noise data
in power line networks are captured and used in the simulations. For comprehensive testing, four
typical and distinctive noise sources, SmImp, Hairdryer, Dimmer and Drill, are employed, which
represent most of the power line impulsive noise patterns. The noise we are considering can be
expressed mathematically as )()()( titgtn where )(tg and )(ti represents Gaussian and
impulsive noise, respectively. From Figure 5-4 to Figure 5-7, the four noise sources are plotted in
the time domain.
SmImp contains a large number of small amplitude impulsive noise samples. This type of
impulsive noise is present in most power line communication environments. Similar to the
additional three impulsive noise cases described in this chapter, this type of impulsive noise is
present all the other noise scenarios. However, for analytical simplicity, we assume that small
impulsive noise samples in the three other impulsive noise cases are background Gaussian noises.
Hairdryer contains a small number of large amplitude short duration (about 100 samples)
impulse samples shown in Figure 5-5. Dimmer contains a few impulsive noise samples that have
a large amplitude long duration (over 1000 samples) shown in Figure 5-6. Drill contains a large
number of large amplitude short duration impulse samples shown in Figure 5-7.
Using these four noise sources, we first separate Gaussian noise samples from impulsive
noise samples. In order to do so, we set the threshold by carefully observing the original noise
data. Any noise samples exceeding this threshold are assumed to be impulsive noise samples.
Impulsive noise samples are extracted from original noise samples. The extracted part of original
noise samples cancelled to be zeros is then filled with previous samples of the original noise. We
63
Figure 5-5. Hair Dryer noise
now have pure impulsive noise data and impulse-free Gaussian noise. By adding these two, we
have noise data for which we know the exact impulsive noise information.
Figure 5-6. Dimmer noise
64
Figure 5-7. Electrical drill noise
By completing this step in noise manipulation, we can now analyze the performance of the
impulsive noise mitigation algorithm in realistic impulsive noise environments.
Figure 5-8. Receive signal with typical impulsive noise in power line communication
65
Primary Simulations: Parameter Setting
The performance analysis of the impulsive noise mitigation in HomePlug systems with the
proposed threshold-setting algorithm is performed in these simulations. We have signal, pre-
measured channel, and noise data described in the previous section. The received signals with
four noise sources are shown in Figure 5-8.
Figure 5-9. Performance comparison using various detection parameters
Throughout the simulation, we have observed that detection performance is relatively good
when an impulse starting point threshold N is chosen to be one, the shift register length 8 and C
in figure to be 15 as shown in figure 5-9. Mitigation using Windowed Blanking was found to
perform better than other processing methods. Therefore, we set N=1 and use Windowed
Blanking for the impulse mitigation algorithm. Since we want the impulse mitigation algorithm
to be tested using a wide variety of noise conditions, we use a scaling factor for the noise part of
66
the received signal so that we can see some differences in performance of the algorithm. The
received signal can then be expressed as
),()()()( tnMtxthty
where M represents a noise scaling factor.
In order to enhance the performance of the impulse mitigation algorithm in a power line
communication system, it is crucial to properly set the impulse detection threshold. Figure 5-10
shows the independence of an average SNR on the detection threshold. As can be seen from this
plot, a particular threshold-scaling factor that produces good performances in different case of
impulsive noise scenarios, as shown in Eq. (5-7), cannot be selected. However, our proposed
tighter threshold-setting algorithm selects a very good threshold point for each impulsive noise.
The corresponding threshold scaling factors with tighter thresholds are 0.6 for Drill, 0.88 for
Hairdryer and 0.98 for Dimmer switch. These thresholds are located near the highest
performance point, shown in Figure 5-10.
Figure 5-10. Threshold scaling factor
67
Although the performance comparisons of the proposed algorithm with exist threshold-
setting methods are not included, our proposed algorithm consistently outperforms the existing
methods. Hereafter, only results using the proposed algorithm will be included.
Performance Comparison
In this performance testing, the performance of the proposed algorithm is compared with
NoImpulseNoise and NoImpulseDetection using the four prescribed impulsive noise sources.
Table 5-1 shows the performance results in the case of 1052 CP. For a simple comparison, SNR
is used as the performance criterion. In order to obtain this expression, 68 OFDM symbols are
simulated and SNR vectors are averaged for each setting. All elements of the averaged SNR
vector are again averaged to obtain a single value, which we define to be the average SNR.
Table 5-1. Average SNR in the case of CP length 1052
Hairdryer Dimmer
Noise Scaling Factor 0.4 0.8 1.2 0.4 0.8 1.2
NoImpulseDetection 19.3 13.3 9.76 15.4 9.33 5.8
ImpulseDetection 19.5 13.5 10.1 15.3 9.3 5.79
NoImpulseNoise 20.2 14.1 10.6 15.4 9.37 5.85
Drill SmImp
Noise Scaling Factor 0.4 0.8 1.2 0.4 0.8 1.2
NoImpulseDetection 12.5 6.47 2.95 22.1 16.1 12.6
ImpulseDetection 13 7.69 4.55 22.1 16.1 12.6
NoImpulseNoise 18.4 12.3 8.81 27.8 21.8 18.3
As shown in Table 5-1 we observe that the higher the amplitude of impulsive noise, the
greater the benefit when using the algorithm. Moreover, we observe that, in most cases, the
algorithm contributes to the enhancement of system performance. A detailed analysis follows.
Hairdryer shows performance results for the impulsive noise mitigation algorithm while a
hairdryer is in use. As can be seen from the noise plot, impulsive noise from Hairdryer shows a
large distinctive amplitude and a short duration. This indicates easy detection and the processing
of impulsive noise. As expected, results clearly show a performance gain using the algorithms.
68
When impulsive noise is not present, the best performance is observed. Although the locations of
impulsive noise samples are not perfectly detected, ImpulseDetection still shows good levels of
performance. As noise power increases, the algorithm shows greater gains in performance.
Drill shows performance results when an electrical drill is in use. The noise plot indicates
that impulsive noise samples of Drill are densely located and large in amplitude. Therefore, the
average SNR is very low, compared to other noise cases and NoImpulseNoise. However, the
observed improvement in performance when using the algorithm is quite large, compared to
NoImpulseDetection, where the performance difference becomes larger than the amplitude and
the density of impulsive noise samples increases.
The noise plot for Dimmer indicates that only a few impulsive noise samples have a large
amplitude and long pulse duration. Since a dimmer switch creates a small number of impulsive
noise samples, the performance degradation is small. Even the perfect detection of impulsive
noise underperforms the detection of no impulsive noise. We believe that Hanning windowing is
not well-suited for this type of impulsive noise detection. In addition, the choice of window
length also affects performance. However, the performance degradation in Dimmer is so small
that there is little difference between its performance results and no performance degradation
using the algorithm.
SmImp shows the performance of the algorithm when a large number of small amplitude
impulsive noise samples are present. As shown in the table, this type of impulsive noise severely
degrades system performance. Gaussian-type impulsive noises prevent detection through the use
of a detection algorithm. Even though these types of small impulses will most likely be detected
by chance, impulse mitigation results in performance that is almost equal to NoImpulseDetection.
Impulse mitigation is not suitable for this type of noise. Since our detection does not detect any
69
impulse samples smaller than the signal sample, impulse mitigation does not degrade the system
performance.
Table 5-2. Average SNR in the case of CP length 5028
Table 5-2 shows performance results for CP length 5028. The simulation settings are the
same as those previously listed, except for the CP length and the mitigation technique described
previously, where averaging is used. Consistent with the short CP case, the bigger the noise
scaling factor is, the clearer the benefit of using the algorithm. Unlike the short CP case,
performance results using the algorithm are better than those obtained using the NoImpulse-
Detection algorithm. Even in the case of SmImp, ImpulseDetection outperforms NoImpulse-
Detection, since the long CP contains all information for the payload of the symbol.
Performance Tests in the Real Power Line Networks
In this subsection, the system performance with real power line channels in an office
building is tested. HomePlug AV-style data packets are used as a signal, while Hairdryer,
Dimmer and Drill are used as impulsive noises. Performance results are expressed as an effective
PHY data rate (Mbps) in a steady state, showing an error-free PHY data rate.
There are two main goals for this real-time performance testing. One is to see if the
proposed algorithm helps improve the PHY data rate in real power line networks when impulsive
noise is present. The other is to check if the algorithm degrades the system performance when
Hairdryer Dimmer
Noise Scaling Factor 0.4 0.8 1.2 0.4 0.8 1.2
NoImpulseDetection 21.6 15.6 12.1 18.4 12.4 8.84
ImpulseDetection 22.2 16.6 13.1 18.4 12.4 8.87
NoImpulseNoise 23 17 13.5 18.4 12.4 8.9
Drill SmImp
Noise Scaling Factor 0.4 0.8 1.2 0.4 0.8 1.2
NoImpulseDetection 13.6 7.55 4.03 24.8 18.8 15.3
ImpulseDetection 15 10.3 7.16 24.8 18.8 15.3
NoImpulseNoise 20.9 14.8 11.3 30.8 24.8 21.3
70
there is no impulsive noise in the network. We use the three impulsive noise sources used in
previous simulations. Using the simulation results from this subsection, we can also check
whether the simulation results shown in the previous subsections are valid.
Figure 5-11. PHY data rates for the short CP
The performance results in the case of CP length 1052 are shown in Figure 5-11.
Corresponding with the results shown in Table 5-2, the algorithm helps improve the system
performance of Hairdryer and does not degrade the system performance of Dimmer. In the case
of Drill, system performance is severely degraded. With the help of the proposed algorithm,
performance enhancement is fairly large, with a reading of 20% data rate enhancement. When
there is no impulsive noise present in the network, the presence of the algorithm does not
degrade system performance. Although there is a gap between system performance,
NoImpulseNoise and ImpulseDetection, in these cases, a fairly large performance enhancement is
71
achieved using this algorithm. Moreover, the presence of the algorithm in the system does not
degrade system performance. The performance results of CP 5028 are shown in Figure 5-11. In
all cases of impulsive noise sources used during testing, performance enhancement is observed.
In spite of the enhancement, this long CP case still underperforms the short CP case in terms of
data, due to large CP overhead.
Lab Test Results
In this lab testing, we have isolated powerline channels, which are not affected by the
unpredictable and uncontrollable channel impairments. With these channel settings, we test the
exact effects of impulsive noise impairments and the performance gain using the impulse
mitigation algorithm. Another reason for this test is to see the performance enhancements in
different levels of the channel impairments. The test is done with both cases of the long CP and
the short CP. In case of the short CP, data rate is averaged by 10 received signal captures. During
one signal capture, we have four packets of the signal. Therefore, the average data rate is
obtained over forty packets of the signal. In case of the long CP, data rate is averaged by 15
received signal captures. In one signal capture, there are two signal packets, so we have average
data rate over thirty signal packets.
Figure 5-12 shows the lab testing results when a hair dryer is in use. We observe that the
performance gain using the impulse mitigation algorithm is obvious in this case. Throughout all
the attenuation level we test, the algorithm consistently improves the system performance in the
both cases of the long CP and the short CP. The performance improvement we obtain using the
algorithm is about 10 percents higher data rate on average.
The lab test results using an electrical drill are shown in Figure 5-13. Since impulsive noise
from a drill is not so consistent during the testing, we expect more variation for the performance
results. Although we observe that the results are not stable and consistent as in the case of
72
Hairdryer, we obtain good performance gains using the algorithm. At some points of the
attenuation level, we get 20 percents higher data rate and we still get about 10 percent higher
data rate at the other points using the algorithm, which are overall a better improvement than in
case of Hairdryer.
Figure 5-12. Lab Test results with a Hair dryer in use
Figure 5-13. Lab Test results with an Electrical Drill in use
73
Figure 5-14. Lab Test results with a Dimmer in use
Figure 5-15. Lab Test results with a Lamp in use
The performance results of the lab testing in case of Dimmer are shown in Figure 5-14. For
the short CP case, the system performance difference between with-algorithm and without-
algorithm is very small, which we can conclude that there is not gain or losing using the impulse
mitigation algorithm with the short CP Dimmer case. However, for the long CP, we have a large
improvement using the algorithm. We observe about 30 to 40 percent of the performance
74
improvement in terms of data rate, which is obtained by the windowing and averaging the
impulsive noise impaired signal part with the CP part of the symbol. In every case using the
algorithm, we also observe that the data rate using the short CP is much higher than one using
the long CP despite the fact that the performance improvement using the algorithm in the long
CP cases are higher.
Figure 5-15 shows the performance results when the Lamp is in use. The impulsive noise
pattern produced by the Lamp is very similar to the one of SmImp, which is characterized as
small amplitude and very high density. Therefore, we expect that the performance result of this
case is similar to SmImp. When impulsive noise from the Lamp presents, the performance
degradation is significant because the impulsive noise samples are so densely located. Since the
amplitude of impulse is smaller than the amplitude of the signal, the impulse mitigation
algorithm does not help improve the system performance in both cases of the short CP and the
long CP.
Figure 5-16 shows the performance results for the case when a Yard Lamp is turned on.
Impulsive noise from the Yard Lamp is characterized as large amplitude and large density, which
is less than Drill and more than Hairdryer. We observe that the amplitude of some impulsive
noise samples is about the same in amplitude as the signal samples at the attenuation level 15,
where the system performance with the impulse mitigation algorithm gets better than one
without the algorithm. The performance enhancement using the algorithm is about 5 to 10
percent. Although the performance improvement using the long CP is higher than the short CP,
the system with the short CP outperforms the one with the long CP in terms of data rate.
75
Figure 5-16. Lab Test results with a Yard Lamp in use
Conclusions
The proposed impulse mitigation algorithm in power line networks works well in most
cases, with performance gains of 10 to 20 percent. The additional computational burden of the
algorithm in the system is very low when used to update OFDM symbol-based thresholds.
Moreover, the algorithm does not degrade system performance when there is no impulsive noise
present in the system. This is very important, since impulsive noise may not be present for long
periods of time in power line networks. Real-time power line network testing confirms the
anticipated advantages for the proposed algorithm.
76
CHAPTER 6
UNIVERSAL ALGORITHM OF IMPULSIVE NOISE DETECTION IN PLC SYSTEMS
Introduction
Impulsive noise presented in the Power Line Communication (PLC) networks is one of the
main reasons for the degradation of the throughput performance. The goal in this work is to
optimize the detection performance of impulsive noise. In order to do so, we propose a new
impulsive noise detection threshold setting algorithm that works well in a wide variety of cases
of impulsive noise in PLC networks. A simple way of setting a detection threshold is to base it
relative to the upper and lower limits of the ADC inputs (’ADC rails’). Alternatively, the
threshold can be chosen to be proportional to the average received power of the signal. This
second method typically requires more computations and memory but can result in superior
performance. In our previous work [57], we proposed an iterative impulsive noise detection
threshold setting algorithm which outperforms the existing impulse detection alternatives. Since
the parameters are chosen by an excessive number of simulations in some particular impulsive
noise sources, the algorithm may not work well on some other impulsive noise sources. In order
to make the detection algorithm work in general, we want to derive the threshold mathematically
using the characteristics of impulsive noise in PLC systems. The characteristics of impulsive
noise in PLC systems are well studied [58, 59]. Based on these impulsive noise models, we
present the detection threshold setting algorithm.
The remainder of the chapter is organized as follows. Section 6-1 contains the description
of our new threshold setting algorithm for impulsive noise detection. In section 6-2, we present
the detection rule to declare the location of impulsive noise samples. Simulation results are
discussed in Section 6-3 where we also describe the characteristics of the impulsive noise
presented in PLC networks. Section 6-4 contains some conclusions.
77
Threshold Setting and Impulsive Noise Detection
In this section, we propose a detection threshold setting algorithm. At the receiver, the time
domain input-output relationship can be expressed as
( ) ( ) ( ) ( )y t h t x t g t i t (6-1)
where h(t), x(t), g(t), and i(t) represent channel response, transmit signal, Gaussian noise, and
impulsive noise respectively. represents the convolution operation. A single impulsive noise or
each elementary pulse inside a burst behaves as a damped sinusoid and the exponential decrease
versus time can be put in the form as te . Then, the magnitude of the impulsive noise pulse can
be expressed as
max( ) ( ) ktI t i t e (6-2)
where k represents a damping factor and max represents the peak value of the impulsive noise.
At the certain time instance T, the magnitude of the impulsive noise pulse can be expressed as
max( ) kTI T e (6-3)
So, the time instance T can be expressed as
max
1ln
T
k (6-4)
The integration of the magnitude of impulsive noise from 0 to T can be expressed as
maxmax
01
Tkt kTP e dt e
k (6-5)
Substituting T in Eq. (6-5) for Eq. (6-4), we get
max
max
1
P
k (6-6)
78
In this work, we want to find impulsive noise samples which are larger than the peak of the
desired signal. Therefore, it is crucial to set a good detection threshold which separate signal
samples from noise samples. For good detection performance, the threshold value should be as
close to the peak of the desired signal as possible since the peak of the desired signal is the ideal
detection threshold. Now, we assume that we know the ideal threshold as Ideal . From Eq. (6-6),
the damping factor k can be obtained as
max
max
1
IdealkP
(6-7)
where PI is the integration of impulsive waveform envelope that is larger than the ideal threshold.
Substituting k in Eq. (6-6) for Eq. (6-7), P can be re-expressed as
max
max
I
thre
P P (6-8)
The ideal threshold Ideal can be obtained using Eq. (6-2) as
max Idealkt
Ideal e (6-9)
where Idealt represents the time instance corresponding to the ideal threshold. Using Eq. (6-5), PI
can be expressed as
max 1
Idealkt
IP ek
(6-10)
Then, the time instance Idealt can be expressed as
max
1ln 1
IIdeal
P kt
k (6-11)
Substituting Eq. (6-11) for Eq. (6-2), the ideal threshold can be expressed as
max Ideal IP k (6-12)
79
Since the purpose of this work is to identify the impulsive noise impaired samples from the
received signal, we consider that the received signal consists of the impulsive noise impaired
samples and the other samples. A is defined as the mean of the absolute value of a waveform
envelope. Ay, Ai and Ax correspond to the received signal, impulsive noise impaired samples and
the other samples that are related as Ay = Ax + Ai. R is defined as the pick-to-average ratio of the
absolute value of the transmit signal waveform envelope. Therefore, the ideal threshold can be
expressed as Ideal xRA . When manipulating Eq. (6-8), PI can be expressed as
max
max max
1
x iI
RA RAP P P (6-13)
where Ai = PI /L and L is the block size of the impulsive noise detection process. PI now can be
expressed as
max
max
I
DLP
L DR (6-14)
The exact value of the damping factor is not known unless the ideal threshold is available as in
Eq. (6-7). Instead, substituting Ideal in Eq. (6-7) for as the alternative value, we get the
estimate of the damping factor
max
max
1
I
kP
(6-15)
Finally, the new impulsive noise detection threshold can be expressed as
maxthre IP k (6-16)
Once the threshold is set, the locations of the impulsive noise samples are identified by the
detection step. The algorithm for declaring the start and stop sample of an impulsive noise hit is
described in the previous chapter with Figure 5-1.
80
0 100 200 300 400 500 600 700 800 900 10001
1.5
2
2.5
3
3.5
4
4.5
Number of Impulse Occurence
Thre
shold
Valu
es
Impulse Detection Threshold Comparison (Single + Burst)
ROUGH
New
IDEAL
OLD
Figure 6-1. Performance comparison: single impulse and a burst of impulses
Simulations
In these simulations, we compare four threshold values: IDEAL , ROUGH , OLD , and NEW .
IDEAL and ROUGH represent the ideal threshold which is the maximum magnitude of the signal
without impulsive noise and the rough threshold which is obtained by Envelope threshold
method, respectively. OLD is a previously proposed threshold [57] and NEW is a newly
proposed threshold. We generate 1000 impulsive noises using the statistical model presented in
[59] in order to lead our test the most general manner as possible. In the simulations, we use a
combination of both classes of impulsive noises: single impulses and bursts of impulses. The
main parameters of an impulsive noise model include the pseudo frequency, inter-arrival time,
the duration of each pulse, the amplitude distribution, and the damping factor k. Except for the
amplitude distribution, which is well fitted by a normal distribution, the others are well fitted by
81
Weibull distribution. The parameters of the distributions used in the simulations are referred
from [59].
Figure 6-1 shows the performance when there is a combination of single impulses and a
burst of impulsive noise. Comparing to the ideal threshold, the rough threshold shows the huge
gap with the ideal threshold. Two threshold setting methods, OLD and NEW
, seem to show
similar performances such that OLD and NEW
are very closely valued at IDEAL. Moreover,
OLD is sometimes more closely value at IDEAL than NEW
. However, NEW is much more
desirable than OLD since it is very rare to have smaller value than IDEAL . When the obtained
threshold is smaller than IDEAL , the system falsely detects the desired signal samples as
impulsive noise ones. Table 6-1 summarizes the false detection threshold setting performance
comparison between the previously suggested algorithm and the newly proposed algorithm
where the newly proposed algorithm outperforms the previously proposed one.
Table 6-1. False Impulse Detection Threshold Rate (%)
Impulsive noise Type IDEAL NEW IDEAL OLD
Single 2.2 30.1
Burst 2.1 73
Single + Burst 1.8 51.2
Conclusions
In this paper, we propose an impulse detection threshold setting algorithm which
universally performs well in PLC systems. The algorithm not only finds a tight threshold that is
very close to the ideal threshold but it also rarely obtains a threshold value lower than the ideal
threshold. Since this simple two-step iterative algorithm requires only a limited additional
memory of OFDM symbol size, it could easily be fitted in the current PLC systems
82
CHAPTER 7
ADAPTIVE SUB-CARRIER ALLOCATION ALGORITHM IN SS-MC-MA-BASED PLC
SYSTEMS
Introduction
The idea of using power lines as a communication medium was realized in the 1980’s for
low bit rate applications such as utility control and measurement [60]. Since then, the power line
communication (PLC) technology has not been extensively used due to low data rates. The
growth of the internet accelerates the demand for high data rate communications services on
almost every premise. Due to the significant advances in signal processing and the ubiquity of
power supply grid infrastructure, PLC technology is foreseen as one of the possible candidates
for the future high data rate communication systems.
Since the power line networks are not specifically built for communication purposes, there
exist some notable barriers to use of the networks as a communication medium, such as
frequency selectivity, impulsive noise and narrow-band interference [61, 62]. These barriers
make communication through PLC channels extremely challenging. In order to cope with such a
hostile channel and achieve a high data rate, orthogonal frequency division multiplexing
(OFDM) based multi-carrier transmission schemes, which are robust and frequency efficient, are
employed in PLC communication systems. OFDM is considered to be the preferred carrier
modulation scheme for broadband power line communication systems by most researchers.
HomePlug AV, which is the most widely known broadband power line communication standard,
is also based on OFDM technique. One of the main reasons to employ OFDM is the efficient
way it deals with multipath delay spread in broadband transmission systems. The total bandwidth
is divided into parallel subchannels and bits are assigned to subchannels in proportion to each
subchannel’s SNR [63, 64]. It has some additional notable merits, such as simplified channel
equalization, and high bandwidth efficiency and flexibility in high bit rates.
83
In this chapter, adaptive spread-spectrum multi-carrier multiple-access (SS-MC-MA) is
considered, which is a combination of DMT modulation and spread spectrum technique and
frequency division multiple access. We propose an adaptive sub-carrier allocation algorithm that
attempts to maximize the total throughput of the system under power spectral density (PSD) and
finite order modulation constraints. In the simulations, it is shown that the proposed systems
outperform DMT systems and the systems with the existing channel allocation algorithm. The
performance difference is more significant when the power attenuation due to distance is taken
into account.
The remainder of the chapter is organized as follows. In the next section, the system
models are established by presenting the relationship among spread spectrum technique, OFDM,
adaptive bit-loading and frequency division multiple-access (FDMA). Then, we describe the
PLC channel characteristics and capacities, and the data rate using an adaptive bit-loading
scheme. After that, we present the sub-carrier allocation algorithm which attempts to maximize
the total throughput of the system. Finally, simulations and comparisons are provided at the end.
System Model
SS-MC-MA is an OFDM-based multi-carrier multiple-access scheme combined with
spread spectrum techniques. The adaptive SS-MC-MA system investigated in this paper
combines SS-MC-MA with an adaptive sub-carrier distribution and bit-loading technique. The
adaptive sub-carrier distribution enables an effective share of the bandwidth of the system among
the users and bit-loading brings a significant increase in the data rate by assigning the number of
bits to transmit for each sub-carrier depending on the channel condition. It is assumed that the
channel state information is known at the transmitter because of the quasi-static characteristic of
PLC channels.
84
MappingSpread
SubcarrierMapper
OFDM
DeSpreadSubcarrierDeMapper
ZFEqualizer
b
sx
sr
z z
y
C Π
H
G1
Π1
C
Figure 7-1. Block diagram of the adaptive SS-MC-MA system
The block diagram of the adaptive SS-MC-MA system is shown in Figure 7-1. We employ
a conventional OFDM scheme inserted cyclic prefix as the guard interval with perfect
synchronization assumption. The output of OFDM block can be expressed as
r Hs n (7.1)
where 1 2diag Nh h hH is the N N diagonal OFDM-converted channel matrix and n is
the 1N additive white Gaussian noise vector such that 2H
N nn I . The n-th diagonal
element of the channel matrix, nh , represent the frequency flat fading channel gain
corresponding to n-th element of the transmit symbol vector s . The input of OFDM block s can
be written as
s ΠCx (7.2)
85
The output vector of M-QAM symbol Mapper x is obtained by stacking K cluster vectors as
1 2
TT T T
K x x x x , where K is the number of clusters per OFDM block. The k-th cluster vector
of x can be expressed as ,1 ,2 ,
T
k k k k Px x x x , where P is the number of symbols per cluster.
The l-th symbol in the k-th cluster ,k px is M-QAM modulated complex-valued data where
M 2 for [2 15]m m . P complex-valued data symbols ,k px of the k-th cluster are spread
by multiplication with orthogonal Walsh-Hadamard codes of size L in such a way that ,k p px c ,
where ,1 ,2 ,
T
p p p p Lc c c c . Then, the spread symbols are superimposed with each other on L
sub-carriers. Using orthogonal Walsh-Hadamard codes for spreading the data symbols, the
maximum number of symbols we can separate for each cluster is L, where P L . The resulting
k-th cluster spread symbol vector can be expressed as
k k k s C x (7.3)
where the spreading matrix 1 2:k PC c c c and the l-th element of ks can be expressed as
, , ,1
P
k l k p p lps x c
. Combining and stacking the spread symbol vectors from all the clusters, we
obtain the vector
s C x (7.4)
where : K k C I C and 1 2
TT T T
K x x x x .
The sub-carrier mapping process assigns each element of the vector s to the corresponding
sub-carrier, which intends to maximize the system performance. In order to represent this
process, a permutation matrix Π is multiplied by the vector s in Eq. (7.2). In this mapping
process, a cluster of data is assigned to a group of subcarriers which have the same level of SNR.
The group of sub-carriers assigned for the same cluster is not restricted to be adjacent with each
other. Any cluster is assigned to only one user and multiple clusters can be assigned to each user.
86
The spreading process is done at the cluster level, so spreading is not for the user separation but
for symbol separation in each cluster.
Consider the following blocks of OFDM block in the figure 7-1 as the receiver part of the
system. The OFDM block can be viewed as a simplified channel matrix H . In order to
compensate for the channel effects, a simple zero-forcing (ZF) equalizer is employed. The ZF
equalizer, Sub-carrier Demapper and Despreader are simply inverse matrix operations of OFDM,
Sub-carrier Mapper and Spreader, respectively. Due to the inverse operation of ZF equalizer, the
receiver blocks works as an orthogonal restoring combiner and the final output can be expressed
as
1 1 1
1 2
T T T
K
y y y y C Π H r (7.5)
The k-th output cluster vector can be expressed as ,1 ,2 ,k k k k Py y y y . The p-th element of
the k-th output cluster vector ,k py can be expressed as
,
, , ,
1 ,
Lk l
k p k p p l
l k l
ny L x c
h
(7.6)
where , ,andk l k lh n represent the frequency flat fading channel gain and the white Gaussian noise
corresponding to the l-th chip in the k-th cluster, respectively. In the following section, we
present the channel characteristics and the capacity of the system.
Power Line Channel and Bit-Loading
A power line channel is a harsh and challenging communication medium since it is not
designed for communication. The frequency response of the PLC channels is not close to the
ideal such as an AWGN channel. The channel is frequency selective and slowly time varying as
electric devices are turned on and off in the PLC networks. In a PLC channel, the Signal
propagates along non-line-of-sight reflected paths between transmitter and receiver as well as a
87
direct path. This results in a multipath scenario with frequency selective fading. The attenuation
of the signal propagated on each path increases as increasing the path length and the frequency
range to use. An intensive channel measurement and modeling study is carried out in [65] where
authors show the statistical characteristics of widths, heights and numbers of the peak and notch
of the channel transfer function. Our study is based on the PLC channel models proposed in [65].
Based on the input-output relationship shown in Eq. (7.6), the capacity of k-th cluster in
system kC can be derived as
2
,
0
,
1
log 11
k p
k
k l
P
p
l S
ELC
Nh
(7.7)
Where ,k pE represents power assigned to the p-th spreading code of k-th cluster. Let us consider
block transmission by combining K clusters. The k-th subset kS of the k-th cluster belongs to uB ,
which is the set of indices k such that subsets kS belong to user u. the capacity of system C can
be expressed as
,
2,
01 1
log 11
u
k lk
k pU P
u k B p
l S
ELC
Nh
(7.8)
The capacity of the system can be obtained as following. Subchannels are grouped into clusters,
and each cluster is assigned to a specific user, where a multiple-number of clusters can be
assigned to one user. The capacity of the system is the sum of the capacities of all the user
specified clusters.
Based on the capacity expression, the throughput can be simply expressed using a convenient
quantity called the signal-to-noise ratio (SNR) gap , which is a measure of loss with respect to
88
theoretically optimum capacity. Since power spectral density (PSD) of PLC systems should not
exceed a certain level by regulation, the throughput is maximal for , andk pE E P P L .The
optimum throughput at the k-th cluster can be expressed as in [36]
,max
0
,
1log 1
1k
k ll S
L ER L
Nh
(7.9)
In order to obtain the maximum throughput using a bit-loading scheme, we have to consider
discrete modulations which constrain the throughput to be an integer number. Under PSD
constraint, and assuming the Finite Granularity (FG) of rates, the optimal loading solution to
achieve the maximal throughput is proposed in [36], where the maximal achieved throughput of
the k-th cluster is expressed as
,max ,max
,max ,max
,max
,max
2 1 1
2 1
k k
k k
R L R L
k k
R L R L
k
R L R L
L L R L
(7.10)
Corresponding to the capacity formulation of the system shown in Eq. (7.8), the
throughput of the system is the sum of the maximal throughput of all the clusters, where each
cluster is assigned to a specific user. Since the channel gain of each subchannel of each user can
be different, the throughput of the system is significantly dependent on the subchannel allocation
to the users. The maximization of the throughput can be formulated as following
,
'
'
max
for and for 'subject to
1, , for and for '
u ku
kB S
k B
k k k
u u u
R
S k S S k k
B B u B B u u
(7.11)
In the following chapter, we present the subchannel allocation algorithm achieving the balance
between the throughput and the fairness.
89
0 5 10 15 20 25 30 35 40-40
-35
-30
-25
-20
-15
-10
-5
Frequency (MHz)
Channel G
ain
(dB
)
Ch 1
Ch 2
Ch 3
Ch 4
Figure 7-2. Independent channel responses of four user scenario
Subchannel Allocation Algorithm
In this chapter, we present the subchannel allocation algorithm to maximize the throughput
of the system. The goal of the throughput maximization algorithm is to maximize each user’s
throughput while balancing the total throughput and the fairness of the system. In order to see the
advantage of this algorithm, consider the multi-user case where the signal from one user is
severely attenuated due to distance. The level of channel gain from that user will be well below
from the others. When we just try to maximize the total throughput of the system, we choose the
best subchannels which are not likely associated with the poor channel user. Therefore, the poor
channel user may not be allocated any subchannels, which prevents communication from the
poor channel user. When we just consider the fairness, we select the best subchannels from the
poor channel user with priority. This may cause dominant subchannel allocation from the poor
channel over the good channels, which cause severe degradation of the total throughput of the
system.
90
Table 7-1. Proposed Subchannel Allocation Algorithm
Subchannel Allocation Algorithm
Initialization
1 2
1
1, ,
1 2
, , , ;
, , ;
1, 2, ,
, , 0, ,0 ;
, , , ;
1; 1;
u u u uN
TT T
U
sum sum U sum
M
u
h h h
N
h h
t i B
h
H h h
h
γ
1
while
set ;
find satistying
update
find the set of exclusive subsubcarriers to each other
update
update
define , , sorted in the descending order
while
if 0 & sum( )
u
uu
u u u
TT T
U
u u
t
g i N U
H γ
g g H
,
,
, ,
find with smallest
else
find with the next smallest
end
update
update
1
end
1
end
u sum
u sum
u sum u sum u
u
u u u
u h
u h
h h g i
i i
t t
91
The proposed subchannel allocation algorithm is presented in Table 1. The algorithm
consists in finding and assigning subchannels to each user in the following method. Since the
number of bits to transmit is dependent on SNR of each subchannel, we first set the multiple
SNR ranges using the SNR range setting threshold vector γ . At the highest SNR range, the best
subchannels of the user with the smallest sum of the instantaneous SNR are selected and
assigned first, then the second lowest, and so on. The sums of SNRs assigned to each user sumh
are calculated to be used for sub-carrier allocation at the next stage. Once a sub-carrier is
assigned to a user, other users are prevented from using that sub-carrier by eliminating the sub-
carrier from the set . From the second highest SNR ranges, the best subchannels of the user
that has the smallest element of sumh at the higher SNR ranges and the lowest instantaneous SNR
at the current range are selected and assigned as described previously.
The algorithm assigns the equal number of sub-carriers to each user. If the number of sub-
carriers assigned to one user reaches that limit, an algorithm does not assign any sub-carrier to
that user any more. The algorithm ends when there is no more sub-carrier to be assigned.
After all the sub-carriers are assigned to the users, the assigned sub-carriers are sorted in
descending order and grouped as clusters. In each cluster, bits are loaded in such a way that the
maximum throughput can be achieved by Eq. (7.10). The loss of the system throughput can be
minimized, since each subchannel is competing within the same SNR range, and the user with
poor channel conditions can still communicate in the system since the poorest channel has the
priority to be selected within the same SNR range.
Simulations
In this section, simulation results are presented for the proposed adaptive sub-carrier
allocation algorithm in SS-MC-MA PLC systems. Assuming perfect synchronization at the
92
receiver and the channel state information (CSI) at the transmitter, the throughput performance
of the PLC system employing the proposed algorithm is compared with that of the adaptive LP-
DMT system as in [37] and the DMT system. We consider that the system uses the frequency
band from 0 through 37.5 MHz. The total number of sub-carriers is 1536, which makes the even
sub-carrier spacing of 24.414 KHz, and we set the length of each cluster at 16 (P = 16). We
simulate PLC channels using the channel models proposed in [65]. We assume that the signal
with -40 dBm/Hz flat PSD is transmitted through the simulated PLC channel with the white
Gaussian noise with -110 dBm/Hz noise PSD. For the bit-loading process, we allocate m bits on
each sub-carrier according to Eq. (7.10), where 2, 3, ,15m . For the target symbol error
probability of 72 10eP , the SNR gap of the uncoded QAM system can be approximated as
9.8 as in [66].
0 5 10 15 20 25 30 35 40-50
-45
-40
-35
-30
-25
-20
-15
-10
-5
Frequency (MHz)
Channel G
ain
(dB
)
Ch 1
Ch 2
Ch 3
Ch 4
Ch 5
Figure 7-3. Correlated channel responses of five users regarding distance attenuation
93
Figure 7-2 shows the PLC channel response that is generated by class 5 of the PLC
channel model proposed in [6]. We set the number of channels is 4, where each user has an
exclusively dedicated channel and each channel is independent of each other. With these given
channels, we compare the throughput performances. Case 1 in figure 7-4 shows the result where
DMT corresponds to the conventional DMT system and New Algo. represents our proposed
algorithm. Since the conventional DMT system is designated for a single user communication
system, we use the average value of the throughputs from the four user’s channels. As we can
see from case 1 in figure 7-4, the proposed algorithm outperforms the conventional DMT system
and the SS-MC-MA based LD-DMT system.
Case 1 Case 2 Case 30
50
100
150
200
250
300
350
400
450
Bit R
ate
(M
bps)
DMT
LP-DMT
New Algo.
Figure 7-4. Throughput performance comparison
Figure 7-3 shows the class 5 channel responses where the channel responses are correlated
with each other. At first, we consider the case in which four users in the network are closely
located. Therefore all the channel responses show the similar magnitudes, which can be grouped
94
by Ch1, Ch2, Ch3 and Ch4. The throughput performance comparison is shown in figure 7-4 as
case 2. For this scenario, we also see that the performance of the system with the proposed
algorithm is still better than the others.
-40 -35 -30 -25 -20 -15 -10 -5 00
50
100
150
200
250
300
350
400
Average Attenuation of the Channel (dB)
Bit
Ra
tes
(Mb
ps)
New Algo.
LP-DMT
DMT
Figure 7-5. Throughput performance comparison along with channel attenuation
From figure 7-3, we can find one more scenario where there is a notable attenuation due to
the distance difference. We also consider four-user scenario. The channels are grouped together
with Ch1, Ch2, Ch3 and Ch5. Ch5 is attenuated by 15 dB compared with the other channel
responses. For the conventional DMT system, we just obtain the average throughput over the
four channel responses as before. Interestingly, we see from case 3 in figure 7-4 that the
throughput of the LP-DMT system is lower than the conventional DMT system even though the
intention in proposing the LP-DMT system is basically to increase the throughput of PLC
systems. Due to the sub-carrier allocation rule, where the user with the smallest computed rate is
given unrestricted priority to occupy the sub-carrier, the LP-DMT achieves an even lower
95
throughput than the conventional DMT system. Since our proposed algorithm dictates that the
user with the smallest computed rate occupies the sub-carrier with priority only in the same SNR
range, the proposed algorithm does not choose the poorer subchannels from Ch. 5 without
consideration of performance degradation as in the DP-DMT system.
Figure 7-5 shows the comparison results of the throughput performances, which take into
account the attenuation due to the increase of distance and noise. We assume that the distance
between the receiver and each transmitter is different, which differentiates the average channel
gains. In order to do simulate this, we randomly assign n (dB) attenuation on each channel
where 0, 1, 10n . With the randomly attenuated channel, we test the throughput
performance by equally varying the average attenuation levels of the channels in order to see the
general performance over various attenuation levels. As we can see from the resulting plots, the
proposed algorithm performs better in terms of the total throughput over all the attenuation levels.
Conclusions
In this paper, we presented an SS-MC-MA based PLC system that maximizes the
throughput of the system. In order to increase the throughput, we propose an adaptive sub-carrier
allocation algorithm, which assigns sub-carriers to each user based on SNR information of the
channel. The algorithm groups the subchannels of all the users based on those SNR levels, then
assigns sub-carriers to the user with the lowest bit rate at each SNR range. Throughout the
simulation, we confirm that the algorithm achieves a notable increase of PLC system throughput.
96
CHAPTER 8
CONCLUSIONS AND FUTURE RESEARCH DIRECTION
Due to its robustness against channel frequency selectivity and low-complexity
implementation using FFT circuits, OFDM-based multi-carrier modulated systems are well-
suited for high data rate multimedia services. In this dissertation, we consider three OFDM-based
multi-carrier systems: MC-CDMA, DMT, and SS-MC-MA.
MC-CDMA takes advantage of user separation by using the spread-spectrum. However,
MUI emerges when the mutual orthogonality among the spreading codes is violated by the
frequency-selective channel propagation, and in the presence of the so-called near-far effect. To
mitigate MUI, we present a joint algorithm that combines transmitter power control, receiver
array processing and multiuser detection. The joint algorithm exploits both the multipath
diversity and the spatial diversity, where the former is provided by frequency selectivity and the
latter is provided by appropriate spacing among the receiver antenna array elements. These
diversity collections are realized by using a decentralized linear MMSE multiuser detector at the
receiver. The mathematical analysis of the diversity collections is described in chapter 3. In
addition to the aforementioned receiver processing technique, power control at the transmitter
has been shown to mitigate the near-far effect by balancing the received power of all users (so
that no user creates excessive interference for others) while maintaining a certain SIR
requirement. Simulations confirm the outstanding performance of the joint algorithm in MUI
suppression. In addition, we observe that the algorithm provides the best performance when the
propagation channel is frequency-selective and channel fading is independent across different
receiver antenna array elements.
The DMT scheme used in current PLC systems makes it possible to achieve data rates of
up to 200Mbps depending on the SNR level of each subcarrier. Due to its spreading in the
97
frequency domain, impulsive noise in PLC systems results in a significant decrease of the overall
data rate. To mitigate the effect of impulsive noise, we propose an impulsive noise detection
algorithm, which mainly focuses on the impulsive noise detection threshold setting. In chapter 5,
we propose a two-step iterative threshold-setting algorithm, which computes the threshold based
on the overall signal envelope. After impulsive noise processing, systems gain up to a 15 percent
performance improvement in terms of data rate. However, the threshold setting proposed in
chapter 5 is based on an excessive number of simulations on particular sources of impulsive
noise. To make a threshold setting as globally applicable as possible, we develop a threshold
setting algorithm based on the characteristics of impulsive noise in PLC systems. We compare
impulsive noise detection performance using both threshold setting methods. As expected, the
threshold setting developed for universal use outperforms the previously proposed setting in
terms of false detection rate, as shown in chapter 6. If we are allowed to access real PLC systems,
the next step of our research is to test the newly developed threshold setting against real
impulsive noise sources in real PLC networks.
We consider SS-MC-MA as a possible alternative to DMT in PLC systems due to its
ability of multiple-access, which can increase total system throughput by reducing MAC
processing. To further increase throughput, we propose an adaptive subcarrier allocation
algorithm in chapter 7. The proposed algorithm selects the best subcarriers of each user and
assigns the subcarriers to the user with the lowest SNR sum first (for fairness consideration).
Simulations show a notable increase in throughput with the proposed algorithm over the existing
alternatives. When we consider the various attenuation levels for each user due to varying
locations and propagation losses, the performance gap becomes even more significant. Consider
the case of a user whose channel attenuation is so severe that that user may not be assigned any
98
subcarriers for communication. Further research to solve this problem should be completed,
which includes applying the relay network concept to systems.
99
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BIOGRAPHICAL SKETCH
Kyoungnam Seo received his Bachelor of Science degree Tele-communication engineering
at Cheju National University, Korea in 2001 and his Master of Science in electrical and computer
engineering at the University of Florida in 2004. He is currently working toward his Ph.D.
degree in electrical and computer engineering at the University of Florida. His research interests
are in the area of signal processing, wireless and power line communications. Specifically, he is
working on impulsive noise mitigation and multiuser interference suppression in multicarrier
communication systems.
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