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ADSL System Enhancement with Multiuser Detection A Thesis Presented to The Faculty of the Division of Graduate Studies By Liang C. Chu In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy in Electrical and Computer Engineering School of Electrical and Computer Engineering Georgia Institute of Technology Atlanta Georgia 30332 July 2001

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Page 1: ADSL System Enhancement with Multiuser Detection

ADSL System Enhancement with Multiuser Detection

A Thesis Presented to

The Faculty of the Division of Graduate Studies

By

Liang C. Chu

In Partial Fulfillment of the Requirements for the Degree of

Doctor of Philosophy in Electrical and Computer Engineering

School of Electrical and Computer Engineering

Georgia Institute of Technology

Atlanta Georgia 30332

July 2001

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ACKNOWLEDGEMENTS

There are a number of people that should be recognized for their help and assistance

during my thesis work. First of all I want to express my sincere gratitude to my thesis

advisor professor Martin A. Brooke, who has given me the opportunity to complete my

Ph.D. study at school of Electrical and Computer Engineering in Georgia Institute of

Technology. I really appreciate the time for his advising and it is very rewarding and

inspiring to discuss questions with professor Brooke. I also want to thank professor Nikil

Jayant and professor John Copeland, who have taken an active part in advising and

guiding me in my research and education.

Furthermore, I gratefully acknowledge professor Donald L. Schilling, who always

encourages my study during these years, since I was studying in my Master’s degree with

him at the City College of New York, CUNY. Also, I would like to thank professor

Russell M. Mersereau and professor Zhong L. Wang for their supporting to serve in my

thesis committee, and all my colleagues at school of Electrical and Computer

Engineering, Georgia Tech.

Finally, and most importantly, I sincerely thank my wife, Dr. Jing Li, who help and

support me in my graduate study at Georgia Tech during these years, and deeply love and

care about me always. Also, I greatly thank my parents, Mr. Hsun C. Chu, Ms. Sai Y.

Feng, and my bother, Dr. Liang T. Chu, for their continuing care and encouragement all

the times in my life. I would like to show my great appreciation to my families for their

constant help, support and encouragement.

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ADSL System Enhancement with Multiuser Detection

Approved:

Dr. Martin A. Brooke, Chairman

Dr. John A. Copeland

Dr. Nikil Jayant

Date Approved

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Table of the Contents

Chapter One: Introduction 1

Chapter Two: Background 5

2. Problem on the DSL Spectral Compatibility with Crosstalk 5

2.1. Current Crosstalk Model and Distribution 6

2.1.1 NEXT and FEXT Modeling 8

2.1.2 Crosstalk Noise Distribution 10

2.2 Spectral Compatibility between Asymmetric and Symmetric DSL Systems 10

2.2.1 Symmetric DSL Systems 11

2.2.2 Studies on Crosstalk Noise between ADSL and SDSL 11

2.2.3 Current Deployment Plan and Proposed Enhancement 15

Chapter Three: DMT-ADSL Channel Modulation and Characteristics 16

3. Multiuser Multitone Modulation System and ADSL 16

3.1 Overview of Discrete Multitone 17

3.2. Analysis of Discrete Multitone 22

3.2.1 Channel Gap Analysis 22

3.2.2 Margin of the DMT 23

3.2.3 Performance Calculation 25

3.2.4 Bit-loading and DMT-ADSL System 26

Chapter Four: Channel Model and Multiuser Transmission 32

4.1 Twisted Wire Pairs Characteristics 32

4.1.1 Electrical Characteristics of Twisted-pair Wires 33

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4.1.2 Telephone Channel 35

4.2. Multiuser Transmission System 37

4.2.1 Basic on Multiuser Detection 37

4.2.2 Optimum Multiuser Detection 38

4.2.2.1 Linear Multiuser Detection in AWGA Channel 42

Chapter Five: ADSL System Enhancement 45

5.1. Multiuser Detection on DMT-ADSL System 45

5.1.1 Theoretic Bounds on DMT-ADSL Channel 49

5.1.2 Spectral Distribution on the Multiuser Channel Capacity 49

5.1.3 Examples on Capacity Bound Analysis 58

5.2. Joint Maximum-likelihood Sequence Estimation (JMLSE) 60

5.2.1 DSL Co-channel Signal Model 60

5.2.2 MLSE Receiver Design 62

5.2.3 T/2-spaced MLSE Receiver 69

5.2.4 Analyzing MLSE Receiver Structures 72

5.2.5 Reduced Complexity Receiver Structures 76

5.3.6 Joint MLSE for DMT-ADSL Receiver 78

5.3 Preliminary Performance Studies 81

Chapter Six: Low Complexity Enhancement on ADSL Receiver 85

6.1 Tone-zeroing Method 85

6.2. Low Complexity Joint MLSE 90

6.2.1 Multi-stage JVA 90

6.2.2 Multi-stage JVA with Feedback 95

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6.2.3 Practical Enhanced ADSL Receiver 98

6.2.4 Example and Comparison 101

Chapter Seven: Performance Evaluations and Simulation Results on Enhanced ADSL

Receivers 104

7.1 Test Environment 105

7.2 Test Channel Conditions 105

7.3 Loop Characteristics 106

7.4 Capacity Improvement 107

7.5 Reach Improvement 107

7.6 Disturber Scenarios 107

7.7 Co-channel Transfer Functions 110

7.8 Simulation Results 110

Chapter Eight: Conclusions 115

Chapter Nine: Recommendations 117

Reference 119

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LIST OF FIGURES

Figure Page

2.1.1 Near-end Crosstalk (NEXT) 7

2.1.2 Far-end Crosstalk (FEXT) 7

2.1.3 NEXT Power Sum Losses for 25 Pairs of PIC Cable Binder Group 9

2.2.2.1 PSD of 2B1Q SDSL at 1168, 1552 and 2320 kbps 13

2.2.2.2 Downstream ADSL Bit Rate with 1552 & 2320 kbps SDSL NEXT 14

3.1.1 Basic Multitone Modulation Transmission 18

3.1.2 Illustration of Frequency Bands for Multitone Transmission System 19

3.2.4.1 DMT Bit-Loading Concept 29

3.2.4.2 DMT-ADSL Frequency Spectrum 31

4.1.1.1 Transmission Line Segment 34

4.1.2.1 Basic Multiuser Transmission System 38

5.1.1 ADSL Channel Model with k-l Crosstalk Signals 48

5.1.2.1 TPC Attenuation Function with Difference Length 50

5.1.2.2 Channel Attenuation and NEXT Coupling Characteristic 50

5.1.2.3 Channel Capacity – Single vs. Multiuser Channels 56

5.2.1.1 Co-channel System Model 61

5.2.4.1 Basic Receiver Structure 77

5.2.4.2 Sophisticated Receiver Structure 77

5.2.4.3 Carrier Recovery in the Noise-free AWGN Channel 78

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5.2.5.1 Joint ML Sequence Detection between Adjacent Pair 80

5.3.1 BER for ADSL System with Single-user Detector and JMLSE 83

5.3.2 ADSL System with SDSL Crosstalk on Single-user Detector and JMLSE 84

6.1.1 Joint ML Crosstalk Signal Canceller with Tone Zeroing 87

6.1.2 Margin on DMT-ADSL with Tone-zeroing Crosstalk Noise Cancellation 88

6.2.1.1 Two-stage JVA (without Feedback Section) 92

6.2.1.2 Single-user MLSE Computational Flow Structure 94

6.2.2.1 Two-stage JVA (with Feedback Section) 95

6.2.4.1 Desired Channel Performance with Three Methods 103

7.3.1 Testing Loops 106

7.6.1 Scatter Plot of Downstream ADSL Throughput with Mixed SDSL Crosstalk 108

7.8.1 Rate-reach Curves for Test Loop #1 111

7.8.2 Rate-reach Curves for Test Loop #2 112

7.8.3 Rate-reach Curves for Test Loop #3 113

9.1 Channel Attenuation and NEXT Characteristic 118

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LIST OF TABLES

Table Page

4.1.2.1 Worst-case Measurement for Telephone Channels 36

7.6.1 Disturber Scenarios 109

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Summary

In this thesis, a new approach on mitigating the cochannel interference (CCI), also

called crosstalk, in the Asymmetric Digital Subscriber Line (ADSL) transmission system

has been studied. This implementation ensures the spectral compatibility in the DMT-

ADSL system together with other DSL services in a same binder cable.

The major part of this thesis concerns a modified technique for high-speed

communication over the ADSL telephone network. Discrete Multitone (DMT)-ADSL

has been standardized in American National Standards Institute (ANSI) [1]. It offers bit

rate up to 8 Mbps downstream and 1 Mbps upstream, depending on the deployment

coverage ranges. A modified method based on multiuser detection is presented herein,

which can mitigate the crosstalk interference in DMT-ADSL receiver.

An important issue for ADSL is the problem with crosstalk, which is a major threat in

ADSL receiver with other DSL services in a same binder. The performance on the

mitigation of ADSL channel crosstalk impairment is the most important criteria for

guaranteeing the Quality of Service (QoS) in an ADSL system. The essential issue of this

thesis on optimizing the ADSL system transmission throughput is to modify its channel

transceiver design. Treating an ADSL channel as a multiple-input and single-output

(MISO) system with desired ADSL signal and cochannel interference signals is just like a

multiuser communication channel model. Our modified ADSL multiuser detection can

greatly outperform the currently deployed single-user receiver with either increasing

transmission data rates, or extending deployment rages in impairment environments.

Joint Maximum Likelihood Sequence Estimation (JMLSE) gives very good performance

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in our proposed model, but known as a computationally complex technique. The last part

of this thesis deals with low complexity multiuser detection to balance the ADSL system

performance and computational complexity with a reasonable VLSI capability, which can

be implemented in a sub-optimum solution.

With these approaches to the mitigation of ADSL impairments, the performance of

the ADSL system is greatly enhanced; for example, the ADSL service can be either

extended more than 2-kft from the current limit, or has more than 30% transmission data

rate improvement, depending on the cost requirement. Under these circumstances, the

capacity of the network is utilized to a near sub-optimum solution.

[1]Asymmetric Digital Subscriber Line (ADSL) Metallic Interface, ANSI Standard T.413-

1995, ANSI, New York.

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CHAPTER ONE

INTRODUCTION

This thesis deals with an enhancement approach on the DMT-ADSL twisted-pair

wires communication system. Our implementation ensures the spectral compatibility

between different DSL systems in a same binder cable. Therefore, the capacity of the

DMT-ADSL telephone network to support fast Internet access can be better utilized than

current solutions.

Today, an increasing number of people use the telephone access network for digital

data communication. Even if the speed of an analog modem has increased to 54 kbps, it

is still frustratingly slow for the next generation fast Internet multimedia services. High-

speed access to Internet service with various kinds of multimedia content has become an

emerging technology that is needed by all telecommunications end users. One of the best

solutions is Digital Subscriber Lines (DSL) access, which is targeted for residential users,

and has recently received much attention by many telephone companies. The

architecture of DSL systems allows telephone companies to use existing twisted-pair

infrastructures for their next-generation broadband access networks. The sheer inertia of

the worldwide installed copper base means that it could take many years for access

networks to migrate from copper to fiber. A combination of the existing copper

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infrastructure and digital subscriber line transmission technologies means that a new era

of universal broadband access can now begin at a fraction of the cost and in a fraction of

the time required for optical access networks. Even with fiber optical network, the DSL

technologies will still exist in the last-mile access transmission. Over the past ten years,

DSL technologies have been developed and use larger parts of the available TCP

bandwidth. Normally, xDSL use 1 to 15 MHz bandwidth. To be able to use this large

bandwidth, the telephone lines interface in the center office (CO) and customer premise

end (CPE) need to be exchanged when employing xDSL techniques.

However, there is a serious threat to this vision of the future: a variety of impairments

in the access systems. The reason is when trying to reach higher bit rates, there is no

problem on the channel capacity of the twisted copper pair (TCP), but rather high

frequency digital signal interfaces between the lines inside a same telephone binder. As

we know that the telephone access networks were originally built for analog voice

communication, carrying voice-band signals up to 4 kHz in the frequency bandwidth and

not for digital data communication. It is relatively simple to design transmission systems

that work well in simulations and some specific laboratory tests, but more difficult to

deliver useful capacity when subjected to the hostile environment of the real network.

The uncontrolled deployment of such advanced transmission systems in multipair cables

can result in server degradation due to cochannel interference. This interference is a

linear coupling among multiple channels, also called crosstalk [1]. Even though this

problem has been studied in the past [2], [3],[4], [5], solutions for real-world DSL

services deployment are not currently available. Even low data rate implementation, such

as ISDN service, can significantly pollute the copper network. The current DSL systems

Page 14: ADSL System Enhancement with Multiuser Detection

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are modeled as single-user channel models and crosstalk is treated as white Gaussian

noise [6]. This approach is usually conservative, as the true crosstalk signal distributions

are bounded in amplitude. However, the Gaussian assumption reduces the attainable

channel capacity, but hold for the case of current practical interests [6]. It is well known

that the spectral compatibility has become a major issue for all DSL services, especially

in the transmission of symmetric and asymmetric services in the same binder group [7],

[8], [9], [10]. It is likely that as the DSL services reach significant penetration, their

crosstalk between different services will become an important factor to the success of

DSL services.

The objective of this thesis research is to understand the spectral compatibility issues

for various DSL variants [11], in order to determine a more accurate DMT-ADSL

channel model and implement with digital signal processing techniques that realize the

true broadband potential of the existing copper access network. Currently, a study [12]

has demonstrated that crosstalk effects on VDSL might be mitigated; essentially, treated

crosstalk is not exactly Gaussian. The drawback of this approach is computational

complexity in realization. It is well known to us on accurate models for the case of a

single type of crosstalk, where all crosstalk signals have the same power spectral density.

The model is called the 1% worst-case crosstalk power-sum. It is described that no more

than 1% of all pairs in all binders can receiver more crosstalk than this model [13].

However, crosstalk from multiple different types of DSL services is a relatively new area

of study. In this thesis, we focus on a study of the DMT-ADSL system enhancement

coupling with the SDSL services in a same binder cable. Our studies can apply to any

cases of DSL application, where coexists asymmetric and symmetric services. A

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proposed multiuser channel model has been derived, and the enhancement on the DMT-

ADSL receiver is introduced to mitigate crosstalk from the SDSL services. Some

important simplification algorithms, such as tone zeroing [14], and multi-stage joint

maximum-likelihood detection for multiuser DMT-ADSL are derived, which can largely

reduce the multiuser DMT-ADSL receiver complexity. Our proposed sub-optimal

approach, multi-stage JMLSE with feedback section has a reasonable computational

complexity, and also improves Signal-to-Noise-Ratio (SNR) about 8 dB at a Bit-Error

Rate (BER) of 10-7 in the DMT-ADSL channel. This enhancement gives us a core

method on either increasing signal constellation sizes of each DMT sub-channel, or

extending the deployment ranges with a fixed transmission rate, or compensating on a

poor BER channel in achieving better throughput.

In the following sections of this thesis, the origin of the spectral compatibility

problem and its current solutions are covered; a new approach technique for mitigation

on crosstalk interference is presented; and simulation procedures and results are

addressed. Finally, discussions and conclusion of this thesis are presented.

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CHAPTER TWO

BACKGROUND

2. Problem of DSL Spectral Compatibility with Crosstalk

Digital subscriber line technology provides transport of high-bit rate digital

information over telephone lines. High-speed digital transmission via telephone lines

requires advanced signal processing to overcome transmission impairments resulting

from crosstalk noise from the signals present on the other wires in the same binder, radio

noise, and impulse noise. Fortunately, amateur radio signals are narrowband and

transmission methods attempt to notch the relatively few and narrow bands occupied by

this noise, which avoids the noise rather than transmitting through it. Impulse noise is

nonstationary crosstalk from temporary electromagnetic events in the vicinity of phone

lines. The effects are temporary and typically at much lower frequencies. The channel-

coding algorithm in ADSL overcomes this effect [15]. As increasing number of DSL

services are deployed, the concern is that assumptions made in the design of modem

equipment for one type of service will lead to errors in another type of modem

equipment, which also share the cable. This is the crosstalk noise. Crosstalk can be the

biggest noise impairment in a twisted pair and substantially reduces DSL performance

when it cannot be circumvented. In this thesis, we focus on the ADSL receiver

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enhancement design to mitigate the crosstalk from the other DSL services (mainly

targeting on SDSL service). In general, this approach can be applied to any other DSL

systems, such as VDSL, with their related channel characteristics.

2.1 Current Crosstalk Model and Distribution

The primary impairment to sending digital information through the twisted-pair loop

is crosstalk noise from similar digital services of adjacent loops. In the current situation,

DSL transmission is treated as a single-user channel with crosstalk noise as loose

Gaussian distribution [6]. The crosstalk noise can be categorized into two types.

Crosstalk to a receiver from a neighboring transmitter is called near-end crosstalk

(NEXT), as shown in Fig. 2.1.1, and crosstalk to a receiver from a transmitter at the

opposite end is called far-end crosstalk (FEXT), as shown in Fig. 2.1.2.

Page 18: ADSL System Enhancement with Multiuser Detection

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Fig. 2.1.1: Near-end Crosstalk (NEXT)

Fig. 2.1.2: Far-end Crosstalk (FEXT)

FEXT

Same Binder Group

Transmit

Receive

NEXT

Same Binder Group

Transmit

Receive

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2.1.1 NEXT and FEXT Modeling

In the case of the NEXT model, it uses Unger’s NEXT model [16], which states, as

expected, 1% worst-case power sum crosstalk as a function of frequency [17]. NEXT is

dependent on frequency as well as on the relative location of the pairs in the binder

group. Thus, to find the crosstalk noise from a contributing circuit into another twisted

pair in a 50-pair binder, the power spectral density (psd) on any line in the binder is

modeled by

),(10)49

( _5.1136 fSfNS contxtalkn ⋅⋅⋅= − (2.1.1.1)

where N is the number of crosstalk-contributing circuits in the binder, Sxtalk_cont is the psd

of crosstalk-contributing circuits.

FEXT is usually characterized in terms of 1% worst-power sum loss from all signals

on other pairs in the binder group [17]. FEXT is less severe than NEXT because the

FEXT noise is attenuated by traversing the full length of the cable.

Measurement study on a number of pairwise coupling transfer functions in a 50-pair

binder cable by C. Valenti [17] has been shown in Fig. 2.1.3. There are two interesting

issues as shown in Fig. 2.1.3. First, it shows that the NEXT increases as f1.5 with

frequency, but with significant variation in coupling with frequency.

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Fig. 2.1.3: NEXT Power Sum Losses for 25 Pairs of PIC Cable Binder Group

Note: Power Sum Loss is expressed as −−−−10 10log ( )Power Sum Transfer Function

NEXT POWER SUM LOSS(dB)1000 FT, 24 AWG PIC

0

10

20

30

40

50

60

70

0.1 1 10 100FREQUENCY(MHz) 1% Case

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Second, at any given frequency, only few other pairs may contribute significantly to

crosstalk, but over all frequencies, many wire lines contribute randomly. As a practical

convenience, many telecommunication engineers who work on DSL, average the

coupling over many pairs. They assume that the sum of many coupling functions is

constant. Therefore, as shown in Eq. (2.1.1.1), this constant has been determined by

ANSI as 136 10)49

( −⋅N in a 50-pair binder.

2.1.2 Crosstalk Noise Distribution

It has been widely used that in the time-domain, crosstalk noise at the DSL receivers

is treated as a Gaussian distribution [6]. Obviously, this statement is not true for single

crosstalk interference, because of the highly-frequency-dependent nature of the crosstalk.

When summed over all frequencies from different contributors on different lines, the

central limit theorem of statistics loosely applies to this statement. Practically, it has been

validated that this does hold for the case of practical interest [6]. The drawback of such

an analysis may strongly depend on the size error between a Gaussian distribution and its

true distribution. When background thermal noise is small, this error can actually be

large with respect to such noise.

2.2 Spectral Compatibility between Asymmetric and Symmetric DSL Systems

Determining spectral compatibility between new and existing DSL services is a

significant challenge. Recently, a number of studies have been conducted on spectral

compatibility between DSL systems [18], [19], [20], [21]. Spectral compatibility has

become a major issue for all DSL systems, especially with respect to transmission of

Page 22: ADSL System Enhancement with Multiuser Detection

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asymmetric and symmetric services in the same binder group. When DSL deployment

reaches significant penetration, crosstalk between the various DSL services will become

the dominant performance-limiting factor to QoS of DSL systems. The spectral

compatibility of the ADSL service with the deployment of SDSL services is the main

focus of this thesis.

2.2.1 Symmetric DSL Systems

In 1996, ETSI has made the single-pair HDSL (early version of SDSL) in standard.

This service transmits a full E1 payload on a single copper pair with a variable line rate

up to 2320 kbps [22]. The technique that enables this superior performance of a single-

pair SDSL service, uses the same 2B1Q modulation, (as in HDSL, and ISDN), but with a

modified maximum likelihood detection on its receiver. There is no error correction

coding in SDSL systems.

SDSL transmits the same data rate in the upstream and downstream directions and

same transmit PSD in the upstream and downstream directions. It is bi-directional and

echo-canceled system. 2B1Q SDSL transmits a 4-level baseband pulse amplitude

modulation signals. 2B1Q SDSL systems operating at different bit rates have different

transmit PSDs. More detailed information about SDSL can be found in [22], [23], [24].

2.2.2 Studies on Crosstalk Noise between ADSL and SDSL

The spectral compatibility of high-rate SDSL services with the ADSL service in the

same binder is studied herein. We focus on SDSL services interfere ADSL service,

because of the following two reasons. First, The SDAL services are high in demand for

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the future deployment and run on a single twisted pair telephone line together with ADSL

service in a same binder. Second, the PSDs of SDSL services, shown in Fig. 2.2.2.1, are

overlapped in most areas with ADSL PSD, which is from DC to 1.104MHz.

Spectral compatibility results are calculated for same-binder NEXT with the standard

Unger 1% NEXT model. The maximum achievable bit-rate of T1.413 full-rate DMT

ADSL in the presence of NEXT from SDSL systems was calculated. The DMT tones are

separated by 4.3125 kHz, and the received SNR of each tone was calculated. The

maximum bit-rate that each tone can carry with a 6dB SNR margin was found and then

summed across all tones to get the total achievable T1.413 bit rate. The average transmit

power of downstream ADSL is -40 dBm/Hz, and the average transmit power of upstream

ADSL is -38 dBm/Hz, within the passband. T1.413 ADSL is assumed to have trellis

coding gain of 3dB and 2dB ripple, and is FDD with non-overlapping upstream and

downstream spectra. Downstream T1.413 ADSL is assumed to transmit from 160 kHz to

1104 kHz, and upstream T1.413 ADSL transmits from 26 kHz to 138 kHz. The pilot

tones carry no data. A maximum of 12 bits per Hz can be transmitted by any tone in the

T1.413 simulations here, allowing a maximum constellation size of 4096 points. ADSL

bit rates are rounded down to the nearest integer multiple of 32 kbps. Cyclic prefix

redundancy (6.66%) and a minimal 32 kbps EOC redundancy was removed before

presenting the bit rates here.

Achievable downstream ADSL bit rates in the presence of SDSL crosstalk is obtained

as a function of loop length and SDSL data transmission rates. The simulation studies

have shown that high rate, such as 1552 and 2320 kbps SDSL NEXT, largely reduces the

ADSL downstream transmission data rates below its required minimum target rate, which

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is 6 Mbps (low bound) up to 9 kft and 1.5.Mbps (low bound) between 9 to 18 kft. The

results are shown in Fig. 2.2.2.2. It is obvious that the higher the data rate of the SDSL

transmission, the poorer the performance of the ADSL achievable rate. The degradation

of the ADSL achievable rates can also be caused by the other DSL services in a same

binder with the similar manner. Therefore, it is necessary for us to modify the ADSL

system to suppressing crosstalk noise from the SDSL services (also to the other DSL

services) to utilize its optimal capacity at reasonable cost. (Meanwhile, the preliminary

enhancement studies on the SDSL systems can be found in [25], [26].)

Fig. 2.2.2.1: PSD of 2B1Q SDSL at 1168, 1552 and 2320 kbps

1168, 1552 and 2320 kbps SDSL

-110

-100

-90

-80

-70

-60

-50

-40

-30

0 400000 800000 1200000 1600000 2000000

Frequency (Hz)

PSD

(dB

m/H

z)

1168 kbps1552 kbps2320 kbps

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Fig. 2.2.2.2: Downstream ADSL Bit Rate with 1552 & 2320 kbps SDSL NEXT.

6 8 10 12 14 16 18

1000

2000

3000

4000

5000

6000

7000

8000

26-AWG Loop Length in kft

Dow

nstre

am B

it R

ate

in k

bps

DMT-ADSL System with 24-SDSL Crosstalk

1552 kbps SDSL crosstalk

2320 kbps SDSL Crosstalk

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2.2.3 Current Deployment Plan and Proposed Enhancement

For the telephone companies deploying the ADSL and SDSL services in their loops,

they use a so-called loop plan, which is basically testing and estimating of their

deployment loops with limitation on the coverage and numbers of the customer

subscribers. Therefore, the ADSL achievable rates degradation resulting from the

crosstalk can be loosely controlled with various DSL services in the same binder groups.

The drawbacks of this method are inconvenience for deployment management; limit on

the transmission data rate; not rejecting out-of-band signal (crosstalk) by receivers, and

trading off the loop coverage and subscriber numbers.

Our studies on the crosstalk characteristics show that the crosstalk channel

characteristics change very slowly over the time and can be modeled as static. Moreover,

the type of crosstalk on each line, say on ADSL service line, does not change, as there are

fixed DSL services in the same binder from the CO to CPE sides. Therefore, mitigating

the crosstalk between DSL systems, we use a technique to enhance the ADSL receiver

that “filters” the crosstalk noise. Without loss generality, this approach can be applied to

the other DSL systems as well.

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CHAPTER THREE

DMT-ADSL CHANNEL MODULATION AND CHARACTERISTICS

3. Discrete Multitone Modulation System and ADSL

Discrete Multitone (DMT) is a common form of multicarrier modulation. It has been

introduced by IBM [27] to take advantage of digital signal processing and the FFT. It

was later refined to a very high-performance form [28], [29]. That later form is used in

the most recent multicarrier voiceband modems, such as ADSL [30]. DMT is a method

to approximate the channel complex filters by simpler operations, which are to exploit the

knowledge of the channel information matrices, tend to discrete Fourier transforms

(DFT) algorithm [31]. It is similar to orthogonal frequency division multiplexing

(OFDM), which is widely used in wireless communications systems. A DMT system

transmits data in parallel over narrowband channels. The subchannels carry a different

number of bits, depending on their SNR. A DMT system transmits data using a two-

dimensional QAM on each channel.

DMT-ADSL has been standardized by ANSI [15]. Herein, we only focus our study

in DMT-ADSL. We are going to have an overview on DMT system first, before landing

on the details of the DMT-ADSL system.

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3.1 Overview of Discrete Multitone

The principle of multitone transmission is by using two or more coordinated passband

(like QAM) signals to carry a single bit stream over the communication channel. The

passband signal are independently demodulated in the receiver and then remultiplexed

into the original bit stream. The motivation for multitone is that if the bandwidth of each

the sub-channel (tone) is sufficiently narrow, then no ISI occurs on any sub-channel. The

individual passband signals may carry data equally or unequally. Usually, the passband

signals with largest channel output SNR carry a proportionately larger fraction of the

digital information.

Fig. 3.1.1 shows the simplest multitone system to understand. N QAM (or like)

modulators, along with possibly one DC/baseband PAM modulator, transmit N+1

subsymbol components nX , n = 0, 1, …, N, where 2/NN = and N is assumed to be

even number. 0X and NX are real one-dimensional subsymbols while nX , n = 1, 2, … ,

N-1 can be two-dimensional complex subsymbols. Each subsymbol represents one of

nb2 messages that can be transmitted on sub-channel n. The carrier frequencies for the

corresponding sub-channels are Tnfn = , where T is the symbol period. The baseband-

equivalent basis functions are )(1Ttsinc

Tn ⋅=ϕ , n∀ . The entire transmitted signal can

be viewed as N+1 independent transmission sub-channels as indicated by the frequency

band of Fig. 3.1.2.

Page 29: ADSL System Enhancement with Multiuser Detection

18

Fig. 3.1.1 Basic Multitone Modulation Transmission

)(0 tϕ

)(1 tϕ

)(1 tN −ϕ

)(tNϕ

)(0 t−ϕ

)(1 t−ϕ

)(1 tN −−ϕ

)( tN −ϕ

h(t)

+

+

+

+ +

+

+

+

phase split

.

.

.

NN 2=

.

.

.

X0

X1

XN-1

XN

tfje 12π

tfj Ne 12 −π

tfj Ne π2

n(t)

tfje 12π−

tfj Ne 12 −− π

tfj Ne π2−

Y0

Y1

YN-1

YN nnnn NXHY +⋅=

real part

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19

Fig. 3.1.2: Illustration of Frequency Bands for Multitone Transmission System

)( fX

X0 X1 X2 XN-1 XN

)( fH nnn XHY ⋅≈

)( fY

Y0 Y1 Y2 YN-1

Input

. . .

. . .

Output

Page 31: ADSL System Enhancement with Multiuser Detection

20

The multitone-modulated signal is transmitted over an ISI/AWGN channel with the

corresponding demodulator structure also shown in Fig. 3.1.1. First quadrature

decoupling with a phase splitter and then baseband demodulating with a matched-

filter/sampler combination separately demodulates each sub-channel. With this particular

ideal choice of basis functions, the channel output basis function )(, tnpϕ is an

orthonormal basis set. Each sub-channel may have ISI, bit as ∞→N , this ISI vanishes.

Thus, symbol-by-symbol detection independently applied to each sub-channel

implements an overall maximum-likelihood (ML) detector. No equalizer (nor Viterbi

detector) is necessary to implement the maximum-likelihood detector with large N.

Therefore, ML detection is more easily achieved with multitone modulation on an ISI

channel than it is on a single QAM or PAM signal, the latter of which would require

sequence detection with the Viterbi algorithm for a large number of states. Equalization

is also unnecessary if the bandwidth of each tone is sufficiently narrow to make the ISI

on that sub-channel negligible.

Multitone modulation typically uses a value for N that ensures that the pulse response

of the ISI channel appears almost constant at )()/( fHHTnH n =≡ for

TTnf 2/1|/| <− . In practice, this means that the symbol period T greatly exceeds the

length of the channel pulse response. The scaled matched filters simply become the

bandpass filters ntTjnnp eTtsincTtt )/2(

, )/(/1)()( πϕϕ ⋅== and the sampled outputs

become

nnnn NXHY +⋅≈ (3.1.1)

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21

The accuracy of this approximation becomes increasing exact as ∞→N . Fig. 3.1.2

illustrates the scaling of nH at the channel output on each of the sub-channels. Each sub-

channel scales the input nX by the pulse-response gain nH .

Each sub-channel in the multitone system carriers nb bits per symbol. The total

number of bits carried by the multitone system is then

∑=

=N

nnbb

0

(3.1.2)

and the corresponding data rate is then

∑=

==N

nnR

TbR

0

(3.1.3)

where TbR nn /≡ . Thus, the aggregate data rate R is divided, possibly unequally, among

the sub-channels.

With sufficiently larger N , an optimum ML detector is easily implemented as N+1

simple symbol-by-symbol detectors. This detector need not search all combinations of

bm 2= possible transmit symbols. Each sub-channel is symbol-by-symbol detected.

The reason for this ML detector is so easily constructed is because of the choice of the

basis function: multitone basis functions are generically well suited to transmission over

ISI channels.

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22

3.2. Analysis of Discrete Multitone

The multitone transmission system is construed as N subchannels (tones). The most

importance is performance analysis and optimization of performance for the entire set of

subchannels.

3.2.1. Channel Gap Analysis

The probability of error for a multicarrier system is the average of the probabilities of

error on each sub-channel.

We assume that the probability of subsymbol error to be equal on all sub-channels

and to be equal to 7102/ −=eP . We also assume that the gap Γ , is a constant value for

all the sub-channels, which is defined for any coded QAM system as

)(8.9 dBcm γγ −+=Γ (3.2.1.1)

where mγ is the margin and cγ is the coding gain.

We derive for an individual thi sub-channel that having

2

22

2

2min,

4||

43

i

ii

i

i dHdδδ

==Γ (3.2.1.2)

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23

For any sub-channel, we have

)1(log2 Γ+= i

iSNRb (3.2.1.3)

as the maximum number of bits per symbol that can be carried on that sub-channel with

margin mγ and coding gain cγ . The quantity iSNR is computed by

2

2

2||

i

iii

HSNRδ

ε= (3.2.1.4)

in this thesis, we assume that εε =i , a constant value on the sub-channels used and zero

on else. This is called on/off energy distribution. In practice, a better solution on the

energy distribution, which is called “water-pouring” can be found in [32]. Moreover, in a

DMT system, the sub-channels carry a different number of bits, depending on their

respective iSNR , this is referred to as a bit-loading algorithm. Several techniques on how

to perform bit-loading in a DMT system has been studied [33], [34], [35], [36] and [59].

3.2.2. Margin of the DMT

The total number of bits that is transported in one symbol is the sum of the number of

bits on each of the sub-channels, that is

)1(log1

21

∑∑== Γ

+==N

i

iN

ii

SNRbb (3.2.2.1)

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24

Therefore, the data rate is

TbR = (3.2.2.2)

Eq. (3.2.2.1) can also be derived as

)]1([log1

2 ∏= Γ

+=N

i

iSNRb (3.2.2.3)

We can define an average SNR as

}1)]1({[1

1

−Γ

+Γ= ∏=

NN

i

iSNRSNR (3.2.2.4)

Therefore, Eq.(3.2.1.1) can be written as

)1(log2 Γ+⋅= SNRNb (3.2.2.5)

From Eq. (3.2.2.5), it permits direct computation of a margin for a multicarrier system

with fixed data rate and probability of error. Normally, the “-1” term in Eq. (3.2.2.4) can

be ignored, and the average SNR becomes the geometric average

∏−

≈N

i

NiSNRSNR

1

1

)]([ (3.2.2.6)

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25

The definition of margin, mγ , for transmission on an AWGN subchannel with a given

SNR, a given number of bits per dimension b, and a given coding-scheme/target-Pe with

gap Γ is the amount by which the SNR can be reduced and still maintain a probability of

error at or below that target Pe [37].

We may compute the margin of the DMT with Eq. (3.2.2.5) as

dBSNRc

Nbm ]8.9)

12(log10[ 10 −+

−= γγ (3.2.2.7)

3.2.3. Performance Calculation

The procedure to analyze the multicarrier system is summarized in [37] as:

1. From the power budget, compute a preliminary subsymbol energy allocation

according to N

PTi == εε .

2. Compute the sub-channel SNR’s according to

2

2||

i

ii

HSNRδ

ε= (3.2.3.1)

3. Compute the number of bits that can be transmitted on each sub-channel with

given margin and given error correction code

)1(log2 Γ+= i

iSNRb (3.2.3.2)

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26

4. For those sub-channels with 5.0<ib , reset 0=iε and reallocate their energy to

the other sub-channels equally. Then, we need re-compute ib .

5. Compute b by summing the ib , and then compute the maximum data rate R = b/T.

A margin can be computed using any number of used sub-channels. For data rates

considerably below theoretical optimums, the number of used sub-channels often

decreases with respect to the bandwidth used for the maximum data rate. The bandwidth

with the best margin is used for a target rate, which is lower than maximum data rate.

3.2.4 Bit-loading and DMT-ADSL System

In this subsection, we review the concept on the DMT-ADSL system characteristics.

Fig. 3.2.4.1, illustrates the concept of the bit-loading algorithm in the DMT-ADSL

system. Bit-loading is a technique that is used for multicarrier systems (DMT in this

thesis) operating on a stationary channel [33]. A stationary channel makes it possible to

measure the SNR on each subchannel and assign individual numbers of transmitted bits.

A subchannel with high SNR transmitted more bits than a subchannel with low SNR.

Fig. 3.2.4.1 shows a schematic picture of SNR and how the numbers of bits on each

subchannel vary accordingly.

When performing bit loading, one usually optimizes for either high data rate, or low

average transmitting energy, or low error probability. Typically two of these are kept in

constant, and the third parameter is the goal for the optimization. The parameter is

optimized depending on the system, its environment, and its application.

Page 38: ADSL System Enhancement with Multiuser Detection

27

In a multi-system environment, where there are several DSL systems transmitting in

the same binder, the problem is complicated, since this kind of system experience

crosstalk. The level of crosstalk is proportional to the transmitting power in the systems,

as shown in Eq.(2.1.1.1). It is therefore desirable to have an equal transmission power in

all systems, to obtain equal distribution. In a multi-system environment, the average

transmitting power is usually fixed, and the optimization is for either high data rate or

low BER.

There are several techniques for bit loading in DMT systems and some of these are

described [33], [38], [39], [40]. As mentioned earlier, there are several parameters that

one can optimize for. Most algorithms optimize for high data rate or low BER.

Given a certain data rate and energy constraint, the algorithm to achieve minimal

BER is to assign one bit at a time to the subchannels. The algorithm calculates the

energy cost to send one bit more on each subchannel. The subchannel with smallest

energy cost then assigned the bit. This procedure is repeated until a desired bit rate is

obtained. In [38], it has shown that complexity of this algorithm is proportional to the

number of subchannels and the number of bits transmitted in a DMT frame. It also

suggests a suboptimal algorithm of low complexity.

An algorithm that maintains an equal bit-error probability over all subchannels, given

a data rate and an energy constraint, is presented in [39].

A suboptimal way of performing bit loading to achieve a high data rate, while

maintaining a constant BER across all subchannels is shown in [40]. In this algorithm,

the bit-loading are calculated by

Page 39: ADSL System Enhancement with Multiuser Detection

28

CKgEb

k

dkkk 222 log)1

23

(log −+=δ

γ (3.2.4.1)

where bk is the number of bits carried on subcarrier k, Ek is the average symbol

transmission energy, gk is the channel attenuation, and 2kδ is the noise variance. The

coding gain is denoted dγ and the constellation expansion factor, due to coding is

denoted C. To obtain a desired symbol error rate of Pe, the design constant K is chosen to

21 )]([e

e

NPQK −= (3.2.4.2)

where Ne is the number of nearest neighbors.

Expression Eq. (3.2.4.1) can be viewed as the union bound for a QAM constellation,

with some modification for coding, where K is the SNR required obtaining an error

probability Pe. The channel SNR, 223

k

dkk

KgEδ

γ, is divided by the SNR required to transmit

one bit. The number of bits needed in the coding, log2C is subtracted to get the number

of bits carried by subchannel k.

Finally, to handle the situation where the numbers of transmitting systems vary one

can either do the bit loading for a worst case or employ adaptive bit loading. In [38], it

has presented such an adaptive algorithm, which called bit-swap algorithm, designed for

the case when a fixed data rate is specified. For detailed information on the bit-loading

for DMT-ADSL system, it can be found in [41], [42].

Page 40: ADSL System Enhancement with Multiuser Detection

29

The ANSI T1.413 and ITU g.dmt ADSL system are standardized in the DMT system

[15]. The standards of the characteristic of the DMT-ADSL system are addressed in the

rest of the section.

Fig. 3.2.4.1: DMT Bit-Loading Concept.

Bits/channel

Frequency Frequency Frequency

Crosstalk

AM Attenuation

Page 41: ADSL System Enhancement with Multiuser Detection

30

As shown in Fig. 3.2.4.2, the DMT-ADSL system has two traffic channels. One is

downstream transmission, which signals from CO to CPEs side; the revised traffic is

called upstream transmission. They occupy different bandwidths. In a downstream

transmission, the system employs a sampling rate of 2.208 MHz, a block size of 512

(FFT) with conjugate symmetry, meaning 256 tones (subchannels) from 0 to 1.104MHz.

The actual downstream symbol rate is 4 kHz and the width of a tone is 4.3125 kHz. The

average downstream psd is –40 dBm/Hz. The upstream transmission employs a sampling

rate of 276 kHz, a block size 64, with conjugate symmetry, meaning 32 tones from 0 to

138 kHz. The symbol rate for the upstream transmission is 4 kHz and the width of the

tone remains 4.3125 kHz. The average upstream psd is –38 dBm/Hz. The detailed state

of the DMT-ADSL system can be found in [15], [43].

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31

Fig. 3.2.4.2: DMT-ADSL Frequency Spectrum

Frequency in kHz

1104 240 138 30 4

Upstream Channel Downstream Channel

POTS

14

# of Bits

0

Page 43: ADSL System Enhancement with Multiuser Detection

32

CHAPTER FOUR

CHANNEL MODEL AND MULTIUSER TRANSMISSION

The investigation of crosstalk testing results [17], in Fig. 3, shows that the crosstalk

coupling function generally increases as f1.5 with frequency, but with significant (about

10 to 20 dB) variation in coupling with frequency. At any given frequency, only a few

other pairs may contribute significantly to crosstalk. Over all frequencies range, many

lines contribute crosstalk affect. Plus, the crosstalk psd is significantly high than the

background psd of AWGN. Otherwise, the crosstalk would not dominate the effect on

DSLs. With these conditions, we propose multiuser detection [44] for the DMT-ADSL

receiver that significantly outperforms the single-user detection, which treats crosstalk as

a Gaussian distribution. In the following section 4 and 5, we derive the twisted-pair

channel model and introduce the multiuser transmission systems.

4.1 Twisted Wire Pairs Characteristics

Twisted wire pairs are the dominating cable type in telephone access networks that

are built for point-to-point two-way communication. The copper wire pair does not

change its physical behavior significantly with time and is considered a stationary

channel [55]. This makes it possible to use a technique called bit loading [33], as shown

in section 3.2.4. for DMT transmission system, which also makes good use of the

Page 44: ADSL System Enhancement with Multiuser Detection

33

spectrally shaped channel. Since DMT with bit loading makes efficient use of available

bandwidth, it has become a good candidate for DSL systems.

The characteristics of the wire pair channel have been studied in number of the papers

[45], [55], [11]. In this thesis, twisted pair cable transfer function is derived from lab

measurements using an HP 89410A spectrum analyzer. The transfer function can be

modeled as

dRCfatt

efdH −⋅= 1010),( (4.1.1)

where d is the cable length, att is the maximum attenuation, and RC is the cable constant.

The corresponding impulse response is given by

<

>=−

0 0

0 4

10),(4

310

2

t

tet

RCtdh

tRCdatt

π (4.1.2)

This model is often used when DSL systems are analyzed [54], [46].

As DSL services carry on the telephone network, we discuss the characteristics of the

telephone channel in the following subsection.

4.1.1 Electrical Characteristics of Twisted-pair Wires

The details of twisted-pair wire line electrical characteristics can be found in [47] and

[48]. According to standard transmission line theory, a wire line can be thought of as a

succession of many small sections of the kind shown in Fig. 4.1.1. The inductance and

Page 45: ADSL System Enhancement with Multiuser Detection

34

capacitance of the line section are given in L and C per unit length, and the line

dissipation losses are R1 ohms per unit length down the line and R2 ohms per unit length

across the line. For any sections, the characteristic impendence, defined as the ratio of

voltage to current, is

LjRLjRZ

ωω

++

=2

10 and fπω 2= (4.1.1.1)

Fig. 4.1.1.1: Transmission Line Segment

Another wire line parameter, called propagation constant is defined as

))(( 21 CjRLjR ωωγ ++= (4.1.1.2)

+

_

V

I

dy

R2 dy

L dy

C dy

R1 dy

Page 46: ADSL System Enhancement with Multiuser Detection

35

If a voltage )( ωjV or a current )( ωjI enters the telephone line, it can be decayed

along the line as )exp()( yjV γω − or )exp()( yjI γω − . In particular, amplitudes decay as

)( ye α− , where α is the real part of γ , called the attenuation constant. Normally, it is

expressed as

ey 10log20α (dB/length) (4.1.1.3)

The wave velocity along the line is βω / , where β is the imaginary part of γ .

We need stress that all these parameters depend on the frequency. In particular R is

approximately f , because of the skin effect in conductors.

4.1.2 Telephone Channel

The telephone is an analog medium with a certain character, roughly speaking as a

linear channel with a voice passband of 300 to 3300 Hz initially. There are many kinds

of actual physical telephone channels, due to several telephone network connections in

the world. In fact, it is necessary to define the telephone channel statistically, because no

fixed definition is practical. Extensive studies of the telephone network have been made

in different parts of the world. In North America, the telephone channel has been studied

in [49], and [50]. In Table 4.1.2.1, we summarize some of its main conclusions.

Page 47: ADSL System Enhancement with Multiuser Detection

36

Table 4.1.2.1 Worst-case Measurement for Telephone Channels

Attenuation, end to end, at 1 kHz 27 dB

SNR, with special weighting 20 dB

Frequency offset 3 Hz

Peak-to-peak phase jitter, 20-300 Hz 13o

Phase jumps greater than 20o 1/per minute

Noise impulses, 4 dB below mean signal or

higher

4/per minute

Delay 50 ms

Different wire line definitions need be pointed out here for a better understanding on

the telephone loops. The term on leased line refers to a connection that is permanently

allocated to a customer, rather than dialed at each use. A connection is entirely within a

local switching area, called central office, has a much better behavior than a toll wire line,

called a local loop. In a local loop, sometimes, there are a simple wire pair and have

quite a wide bandwidth.

The sources of noise in the telephone channel are digital quantization noise, thermal

noise in detectors, crosstalk between adjacent lines, impulse, etc. Both thermal and

quantization noise can be viewed as a Gaussian noise. Therefore, the telephone channel

is normally treated as a Gaussian channel.

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37

4.2 Multiuser Transmission System

The fundamental limit of multiuser detection is to mitigate the interference among

different modulated signals, called crosstalk. We focus our study in telephone cables.

4.2.1 Basic on Multiuser Detection

The basic model for a multiuser channel and transmission system is shown in Fig.

4.2.1.1, where L different data symbols, xl, l = 1, 2,…,L, share a channel with joint

probability distribution XYp . The channel input can be considered to be one large vector

X of dimension ∑=

=L

llxx NN

1, and the output vector is of dimension N. The set of users

can be viewed as a single user with a larger signal set and a corresponding larger number

of possible messages to be transmitted. Optimum detection of the entire set will be

addressed in the late of this section. However, a receiver observing Y may not desire all

the messages, and likely is attempting to attempting to detect messages from one user.

In the most general form, the multiuser channel is described by the conditional

probability distribution YXp . Normally, many channels fit in the linear AWGN model,

that is

NXY += H (4.2.1.1)

where N is a vector of uncorrelated additive Gaussian noise values that each have

variance 2

oN per dimension.

Page 49: ADSL System Enhancement with Multiuser Detection

38

Fig. 4.1.2.1: Basic Multiuser Transmission System

4.2.2 Optimum Multiuser Detection

The optimum detector for a multiuser channel is a generalization form of the

optimum single-user channel detector. The set of all possible multiuser channel inputs

will be denoted CX, and contain || XCM = possible distinct N-dimensional symbols,

which may be a large number that typically grows exponentially with L, the number of

users. CX is a signal constellation, equivalently a code, for the set of all users. The

details of the optimum multiuser detection have been addressed in [52], and [51]. We

review some topics related to our research works.

multiuser channel

XYp

.

.

.

x1

x2

xL

X Y

Page 50: ADSL System Enhancement with Multiuser Detection

39

Theorem 4.2.2.1 (Optimum Multiuser Detection) The Probability of multiuser

symbol error is minimum when the detector selects XX C∈ˆ to maximize YXp and is

known as the maximum a posteriori multiuser detector. When all possible multiple-

user input symbol values are equally likely, this optimum detector simplifies to

maximization of the conditional probability YXp over the choice for XX C∈ˆ , and is

called the maximum likelihood multiuser detector [51].

The probability of error for such a system reflects the likelihood that any of the users

may been incorrectly detected

i

M

iicce pPPP ⋅−=−= ∑

=1/11 (4.2.2.1)

where Pc/i is the probability that the ith possible multiuser message set is correctly

received.

The users are often modeled as being independent in their choice of transmit message so

that

∏=

=L

llPP

1

)(XX (4.2.2.2)

A MAP decoder simplifies to a ML decoder, when each of the users is distributed

uniformly and independently.

Page 51: ADSL System Enhancement with Multiuser Detection

40

The ML decoder for the AWGN channel has a probability of error that is

)2

( min

δdQNP ee ≤ (4.2.2.3)

where the number of nearest neighbors, Ne, now includes all mutiuser-symbol values in

the calculation and similarly the minimum distance is over the entire set of all multiuser

symbol values. The co-channel interference in multiuser channel is defined in the

following [51].

Definition 4.2.2.1 (Co-channel Interference Free Channel) A co-channel

interference free multiuser channel (IFC) has a conditional probability distribution

that satisfies

∏=

=L

lxy ll

pp1

/XY (4.2.2.4)

This is the channel probability distribution factor into independent terms for each of

the users. When the channel is not IFC, it is called co-channel interference (CCI)

channel.

With this definition, a lemma trivially follows

Page 52: ADSL System Enhancement with Multiuser Detection

41

Theorem 4.2.2.2 (Independent Detection (ID)) The optimum decoder for the IFC is

equivalent to a set of independent optimum decoders for each individual user.

Independent detection means that we can use a separate receiver for each user,

potentially then enormously simplifying the detector implementation. Such systems are

the norm in early multiuser transmission designs, but the assumption of an IFC may not

be true especially when users are not well coordinated or channels are not completely

known during design.

The probability of being correct on the IFC channel is

∏=

−=L

llce PP

1,1 (4.2.2.5)

from which one notes that the overall probability of error can never be less than the

probability of error for any one of the users

lee PP ,≥ l∀ (4.2.2.6)

a result that also holds true for any multiuser channel, ID or not because maximization of

the probability distribution Y/lxP is the minimum-probability of error detector for the

symbol xl given the observation Y.

The individual user probability distribution can be computed directly from the overall

conditional distribution according to

Page 53: ADSL System Enhancement with Multiuser Detection

42

)/(// lxx xdPP

ll

XX

YXY ∫= (4.2.2.7)

where the integral for any specific value of xl is simply the set of values for X/xl with xl

held constant at the specific value, and it can be computed from known quantities, such

as

Y

XXY

YX P

PPP

⋅= (4.2.2.8)

Equivalently, the individual ML detector for xl given Y uses this distribution

)/(//

/ lxx

x xdPPPl

l

lXX

X XYY ⋅⋅= ∫ (4.2.2.9)

Next, we will review the linear multiuser detection with AWGN channel [51], [52],

which is the communication channel for the telephone transmission system.

4.2.2.1 Linear Multiuser Detection in AWGN Channel

The linear multiuser AWGN channel has been described in Eq. (4.2.1.1) as

NXY += H (4.2.1.1)

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43

In this channel, when desired input xl = 0 on the set of values for X/xl, in this case, the

channel output contains all the contributions from the other users, except xl. The

probability of error is as in Eq. (4.2.2.3), when all the other users are simultaneously

detected.

For detection of desired input user xl, it may be that the overall minimum distance is

too small. That is a single fixed value for xl may corresponding to the two multiuser

codewords that determine the overall dmin. This can be defined as,

)(min 'min, ''

XXXX

−=≠∧≠

Hdll xxl (4.2.2.1.1)

It is easy to see that,

minmin, dd l ≥ (4.2.2.1.2)

with the equality if and only if any codewords in CX corresponding to the overall dmin also

corresponding to different values for the lth desired users symbol contribution. That has,

minmin,min dd ll= (4.2.2.1.3)

This illustrates how it is possible for a detector extracting a single user to have better

performance on one that extracts all other users. However, there is always at least one

user that has a ld min, that is no longer than the dmin of the overall detector.

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44

Symbol sequences can be handled as the following

)()()()( DDDHD NXY += (4.2.2.1.4)

where all the vector or matrix D-transforms are defined by sampling finding the D

transform of each element and D corresponding to a delay of a symbol period.

Page 56: ADSL System Enhancement with Multiuser Detection

45

CHAPTER FIVE

ADSL SYSTEM ENHANCEMENT

5.1 Multiuser Detection on DMT-ADSL System

Last section, we reviewed the concept of multiuser detection [51], [52], where

optimum linear detectors and structures for telephone transmission channel has been

investigated. This method is very successfully used in the wireless network to combat

cochannel signals with employing frequency reuse where one or more secondary signals

from nearby cells can interfere with the desired signal. It has also been studied in the

VDSL system; together with the Home-Phone LANs (HPL) [53] and showing very little

degradation from the HPL crosstalk with multiuser detection, while large degradation

with a single-user detector.

This thesis employs multiuser detection for the DMT-ADSL system to mitigate

crosstalk from SDSL systems in the same binder. The goal of this thesis is to apply this

approach and algorithm to all DSL systems to suppress crosstalk between their services

in the same binder. The ADSL multi-access channel model can be derived in Fig. 5.1.1,

in a binder group with k pairs of wire lines. The transmitted ADSL signals are denoted as

x1 and the crosstalk data signals are xk, where K = 2,3,…,k, (can be various DSL signals in

this proposal assuming all with the SDSL). The ADSL channel transfer function is

Page 57: ADSL System Enhancement with Multiuser Detection

46

represented as Hc(f), and the attenuation characteristic of the ADSL channel is

approximated by

,|)(| 2 fc efH α−= (5.1.1)

where 0llm=α , l = length of the channel in fleet, l0 = a reference length, f in kHz, and m

= a constant of the physical channel = 1.158, as in Ref. [54]. The spectral distribution of

the NEXT interference coupling to the ADSL line channel is as in Eq. (5.1.1). A key

issue, which differs from the Gaussian model, is that each crosstalking data signal

undergoes filtering by a crosstalk coupling function before effectively being added at the

channel output to the AWGN. With multiuser detection, our proposal will ensure the

performance of telephone systems employing the ADSL loops in the presence of the

SDSL crosstalk.

At the receiver side, the received output is then

)()()()(1

inixihir k

K

kk +∗= ∑

=

(5.1.2)

where xk is the transmitted signals, hk is the channel impulse response when k=1, and

together with crosstalk coupling function when k>1, n is AWGN, and K-1 is the total

number of the crosstalk signals in a binder.

The best detector for the multiuser channel is a joint maximum-likelihood detector.

This kind of detector is complex, but theoretically provides bounding of improvement

Page 58: ADSL System Enhancement with Multiuser Detection

47

from a multiuser detector. Based on ADSL and SDSL environment studies, a sub-

optimal solution has been introduced to reduce the computational complexity.

Page 59: ADSL System Enhancement with Multiuser Detection

48

Fig. 5.1.1: ADSL Channel Model with k-1 Crosstalk Signals

Noise, σσσσ2

+

+ ADSL Receiver ADSL Channel

Crosstalk Filtering

Crosstalk Filtering

Transmit1 (x1)

Transmit2 (x2)

Transmitk (xk)

R

x

y

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49

5.1.1 Theoretic Bounds on Multiuser DMT-ADSL Channel

The maximum possible capacities for the individual users in multiuser transmission

system help provide bounds and goals that guide the design. We have investigated a

sophisticated and more convincing theoretic argument on the achievable performance

bounds by using the multiuse DMT-ADSL channel with the SDSL crosstalk noise. It

shows that data rate of the DMT-ADSL system, which is modeled as a multiuser channel

together with the SDSL crosstalk, is higher than the data rate as the single-user channel

that modeled the crosstalk as Gaussian noise with the same PSD. The later Gaussian

modeling is what is being used today in projections that the SDSL crosstalk defeats the

DMT-ADSL transmission, but is grossly pessimistic inaccurately modeling the SDSL

crosstalk

5.1.2 Spectral Distribution on the Multiuser Channel Capacity

The spectral distribution in twisted pair channels is not distributed linearly within the

width of the frequency band. The reason is that the signal amplitude attenuates as the

frequency and loop length increase, and thus for the voice band, the useful spectrum of

the TPC is located at low frequencies, as discussed in [55]. Fig. 5.1.2.1 shows a typical

TPC attenuation characteristic at low frequencies, which is from DC to 3300Hz with the

difference measurement point from the center office (CO). Fig. 5.1.2.2 shows a typical

attenuation characteristic of a TPC, which is up to 1500 kHz, and also shows the NEXT

attenuation (or the channel transfer function) from low frequencies to high frequencies.

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50

0 500 1000 1500 2000 2500 3000 3500-300

-250

-200

-150

-100

-50

0

Frequency in Hz

TPC

Atte

nuat

ion

in d

B600 feet from CO

6000 feet from CO

18000 feet from CO

Fig. 5.1.2.1: TPC Attenuation Function with Difference Length

Fig.5.1.2.2: Channel Attenuation and NEXT Coupling Characteristic

0 500 1000 1500-90

-80

-70

-60

-50

-40

-30

-20

-10

0

Frequency in kHz

Gai

n in

dB

analytic channel model, in Eq.(2)

squared crosstalk coupling function

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51

Based on Fig. 5.1.2.2, we can see that at higher frequencies, there is higher attenuation

and higher NEXT crosstalk coupling, which results in smaller the SNR and the channel

capacity per unit spectrum decreases in TPC. We derive these issues in the following and

also address a comparison on channel capacity performance with our multiuser channel

model to current single-user channel, treating crosstalk as Gaussian distribution.

For the DMT-ADSL system shown in Fig.5.1.1, basic information theory can be used

to determine a maximum data rate between the set of channel inputs containing desired

DMT-ADSL signal and crosstalk signals, {x: (x1, x2,…,xk)} and the channel output y,

which is called mutual information [56]. This mutual information can be represented as

)/()();( yHHyI xxx −= (5.1.2.1)

where H(x) is called the entropy of the source x and defined as

∑=

−=k

iii xpxpH

12 )(log)()(x (bits/outcome) (5.1.2.2)

and H(x/y) is called the conditional entropy of x, which defined as

∑−=x

x )/(log)/()/( 2 yxpyxpyH (5.1.2.3)

The mutual information can be viewed as the reduction in the uncertainty in x, on the

average, if y is known. Hence, the mutual information is a function of the crosstalk

signal contributions, which are often given and not necessarily alterable by optimization,

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52

for example using a coding scheme. Therefore, the Shannon’s paper [58] is an assertion

of the channel capacity on our study. Shannon asserted that there was a largest measure

of information that a given noisy channel can carry with vanishing small error

probability; it is called the channel capacity, which is

),(max)(

OXICXp

= (bits/channel used) (5.1.2.4)

Therefore, C is the largest possible mutual information between the input source, X,

and the output O. The capacity, C is the largest measure of information that can be

learned about X through this channel. In the following, we derive the capacity for the

conventional single-user and our proposed multiuser ADSL channel models.

Fig. 5.1.2.2 illustrates the channel transfer function, and NEXT coupling transfer

function, denoted by )( fHc , and )( fH NEXT , respectively. We assume that the channel

can be characterized as a linear time-invariant system. In DMT system, we can divide

the transmission bandwidth B of the channel onto K narrow frequency sub-channels

(bins); each of width W Hz and assume that the channel, noise and the crosstalk

characteristic vary slowly enough with frequency that they can be approximated as

constant over each bin.

In the conventional single-user ADSL receiver, it is a fact that at higher frequencies,

there is higher attenuation and higher NEXT results in smaller the SNR and the channel

capacity per unit spectrum decreases. The reason is we sum all the crosstalk

interferences and background noise (Gaussian distribution) to get the total Gaussian

noise. Consider the case of two neighboring lines carrying an ADSL service (desired

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53

channel) and a SDSL service (crosstalk channel), under the Gaussian channel

assumption, we can write the single-user ADSL receiver capacity as

dffPfHfN

fPfHCerferenceNEXTo

desiredc

PPusergle

erferencedesired

])(|)(|)(

)(|)(|1[logint

2

2

02sin sup

int,+

+= ∫∞

− (5.1.2.5)

The supermum is taken over all possible )( fPdesired and )(int fP erference satisfying:

,0)( ≥fPdesired ,0)(int ≥fP erference f∀ (5.1.2.6)

and the average power constraints for the two directions

,)(20

max_∫∞

≤ desireddesired PdffP ∫∞

≤0

max_intint )(2 erferenceerference PdffP (5.1.2.7)

The denominator of Eq. (5.1.2.5) is dominated usually by the lager NEXT,

)(|)(| int2 fPfH erferenceNEXT . This NEXT is much lager than background noise, which

usually in –140 dBm/Hz.

In our enhanced multiuser ADSL receiver shown in Fig. 5.1.1, we use a joint ML

detector, which is the best detector for the optimal solution. The objective of the JMLSE

is based on the single output available in a single ADSL, it selects over all possible

crosstalk channel inputs and main desired channel inputs (herein, as ADSL channel

inputs) that particular set of input, which minimizes the distance from the received single

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54

channel output. In another word, JMLSE decode the desired vector 1x , and possible the

interfering signal vectors kxx ,...,2=Kx , based on received signal R. The signal

component KK xH ⋅ is treated as an interfering signal matrix, which prevents the

decoding of the desired signal 1x . Rather than treating this interfering signal as a

background Gaussian noise, the JMLSE can significantly improve performance by jointly

detecting the desired signal vector 1x with crosstalk signals. Thus, we can write the

ADSL channel capacity as

dffN

fPfHCo

desiredc

Pmultiuser

desired

])(

)(|)(|1[log2

02sup += ∫

(5.1.2.8)

Obviously, we can conclude that Eq. (5.1.2.8) has much higher throughput that Eq.

(5.1.2.5).

Shown in Fig. 5.1.1, multi-user access channel capacity considers the problem where the

received signal Y consists of a superposition of signals iX , received with power iP and

bandwidth B , in the presence of additive white Gaussian noise N with sample power n

NXYi

i += ∑ (5.1.2.9)

As an example, consider the two user case, NXXY ++= 21 , and assume without loss of

generality that is 1X the signal of interest and 2X is an interfere. An intuitively

straightforward way to deal with this case is to think of 2X as another noise term and

Page 66: ADSL System Enhancement with Multiuser Detection

55

lump it into N. This "single user" approach does not take advantage of the structure of the

interfering term and results in a significant penalty in the achievable capacity. It can be

shown [56], and [57]) that in this case the achievable capacity for user 1 is

+

+=nBP

PBC2

1*1 1log (5.1.2.10)

and similarly for user 2

+

+=nBP

PBC1

2*2 1log (5.1.2.11)

In Figure 4 below, the achievable capacity region is depicted in the square formed by the

dotted lines. If however, 1X and 2X are considered jointly, then the achievable capacity

is given by

+≤

nBPBR i

i 1log ,

+

+≤+nB

PPBRR 2121 1log (5.1.2.12)

which is depicted in Figure 5.1.2.3 below by convex hull formed by the solid lines.

Notice the considerable capacity improvement when the interference structure is taken

into account.

Page 67: ADSL System Enhancement with Multiuser Detection

56

+=

nBPBC i

i 1log (5.1.2.13)

Figure 5.1.2.3: Channel Capacity – Single vs. Multiuser Channels

An alternate, we can derive the same conclusion of a better performance in

multiuser DMT-ADSL model using [14]. As shown in Fig. 5.1.1, the signal y represents

the sum of all the data signals and R is the signal at the ADSL receiver. The mutual

information I(x, y) cannot exceed the mutual information between the aggregate data

signal R and the channel output y, I(R, y) [58] ,[59]. Also, if each user has data rate Ri, i

= 1,2,…K, then we have

Rate (User 1)

Multiuser

Single User

C1

C1*

C2 C2*

Rate (User 2)

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57

` ),(1

RIRL

ii X≤∑

=

(5.1.2.14)

Now, we start with: ),(),( yRIyI ≤x , with equality if R↔x is a one-to-one

mapping. The mapping is one-to-one in all but degenerate cases when the discrete

distribution of x is considered. The case of the mapping being close to singular, not one-

to-one, is accommodated tacitly in the following analysis by the assumption attached to

the level of the power spectral density of the AWGN that is added to R from y. This later

mutual information is between a single channel input and a signal channel output and is

easily computed for an ADSL channel. The number attached to I(R, y) strongly depends

on the level of AWGN, which does not include crosstalk signal impairments. This level

can be very low for an ADSL and is often determined by receiver thermal noise or

analog-to-digital converter quantization levels, which are often controllable by design.

Any larger noise is likely to be crosstalk, and it spans a substantial bandwidth. If it is a

crosstalk signal, then this proposal will distinguish it from the noise.

Computing the mutual information I(R, y) for an ADSL system is straightforward.

This number will be high, often an order of magnitude more or higher than data rates

normally projected for an ADSL. This large value is because the AWGN is small

compared with the crosstalk signals.

The achievable data rate for the desired channel, i =1, is then bounded by the

achievable limit [60]

.),(),(2

1 ∑=

−≤K

ii yxIyRIR (5.1.2.15)

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58

The limit in Eq. (5.2.1.10) can be a much larger number than the data rate based on

Gaussian crosstalk assumptions. The sum of data rates subtracted on the right can be a

much smaller number than might be initially computed by summing the data rates of all

crosstalk signals. The smaller number will occur because of the frequency-selective

crosstalk coupling function in Fig. 5.1.1 The effective data rate or information of a highly

bandlimited random process is essentially zero when its power spectral density is less

than the AWGN level [61].

5.1.3 Examples on Capacity Bound Analysis

As an example, assume that we are interested in the pairwise crosstalk interference from

an adjacent neighboring the SDSL has psd of –38dBm/Hz to the desired DMT-ADSL

system. Each DMT-ADSL tone has a bandwidth of 4.3125 kHz. The center frequency of

the downstream DMT-ADSL is 690 kHz. The SDSL crosstalk coupling function to the

ADSL channel can be calculated with 10-9f1.5 [54]. A psd of –38 dBm/Hz SDSL

transmitted energy will have a psd of –86.8 dBm/Hz at the ADSL receiver. As we know,

the background white noise is –140 dBm/Hz in the commonly used case. The mutual

information of a SDSL crosstalk on the ADSL circuit line is

.5.78)101(log3125.4

)101(log)(68.814

2

10/)___(2_,2

kbpskHz

BWyxI signalcouplingpsdawgnpsdtoneeach

=+=

+=−

This means, it is possible to sufficiently detect a 1552 kbps SDSL signal with 20 tones in

the worst case with the right code. Moreover, though it is a pairwise result, this capacity

is very closed to an ADSL line in a binder group with many wire lines together, because

Page 70: ADSL System Enhancement with Multiuser Detection

59

our study [62] has also shown that the major dominant effect of the crosstalk is from an

adjacent neighboring pair DSL service in the same binder group. Therefore, -86.8

dBm/Hz is quite closed to the total 50-pair crosstalk degradation in the binder, but only 2

or 3 dBm worse than that [62].

Assume that a maximum instantaneous data rate of 2320 kbps SDSL signal is coupling

with an ADSL system; thus, the maximum mutual information from the SDSL signal into

the ADSL line is limited to 2320 kbps. An ADSL signal has an average attenuation of

about 43 dB in its downstream bandwidth, with psd of –40dB/Hz. Therefore, it should

have a residual capacity of

.21)101(log104.1

2320),(),(10/)]140()4340([

2

1

MbpsMHzkbpsyRIyxI

=+=

−=−−+−

In theoretic bound, there is enough room for the ADSL signal to transmit much faster

than the current limit. Though additional SDSL and other DSL signals would reduce this

21 Mbps rate a bit, it will always be possible to detect the ADSL signal even with some

large impractical interference signal levels, which may never exist in DSL line channel.

Finally, if the SDSL crosstalk coupling were modeled as a white Gaussian noise with the

same psd, the ADSL data rate then becomes

,330)101(log104.1 868.82 kbpsMHzRADSL =+= −

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60

which is almost a complete loss. Therefore, it is too pessimistic to model the crosstalk as

a white Gaussian noise, as currently used.

5.2 Joint Maximum-likelihood Sequence Estimation (JMLSE)

This technique is based on maximum-likelihood sequence estimation (MLSE) [63],

[64]. Since the cochannel signals are jointly recovered, this kind of method is referred to

as joint maximum-likelihood estimation (JMLSE) [65].

5.2.1 DSL Co-channel Signal Model

A general multi-access UTP channel model is shown in Fig.5.1.1. As our study

shows, the adjacent neighboring pair has the dominating contribution on the NEXT

interference [62]. The block of N pairs wire line channel model can be illustrated in as

Fig. 5.2.1.1. The transmitted low-pass equivalent waveforms can be represented by

NmkTtgkdtxk

mm ,...2,1),()()( ∑∞

−∞=

=−= (5.2.1.1)

where T is the symbol duration, {d1(k)} is the primary source symbol and {dm(k)},m =

2,3,…,N, is interference source symbols, and g(t) is the shaping function.

DSL systems use twisted-pair copper cable as their transmission media. The

transfer function of the twisted-pair copper cable can be modeled as [66], [67]

,10),( 10max_

dRCfatten

efdH −= (5.2.1.2)

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61

where d is the cable length, max_atten is the maximum attenuation, and RC is the cable

constant.

The corresponding impulse response is given by

<

>=−

0 0

0 4

10),(4

310

2

t

tet

RCtdh

tRCdatt

π (5.2.1.3)

Fig. 5.2.1.1: Co-channel System Model

The discrete measurement samples of the received signal r(t) at the output of the T/2-

spaced sampler in Fig. 8 are given by

T/2 Sampler

+

Ν(t) Primary Channel

CrosstalkChannel

h1(t)

h2(t) g(t)

g(t) d1(k)

d2(k)

x1(t)

x2(t)

R E C r(t)

g(t) hN(t) dN(t) xN(t)

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62

1,...,1,0),2/(

)2/()2/(1 0

,

−=++

+=+ ∑∑= =

NjjTkTN

djTkThjTkTrN

m

L

nmnm

m

(5.2.1.4)

where the noise sequences {N(kT+jT/2)} are assumed to be independent, white and

Gaussian with zero mean and equal variance. The reasons on choosing the 2/T -spaced

Joint MLSE are to eliminate the whitening matched filter, and also less sensitive to

sampling time offsets.

As an example on each adjacent pair line, the delay spreads of the primary and secondary

channels are TL1 and TL2 . The )1(2 +mL channel coefficients { )2/(, jTkTh nm + }

represent the convolution of the frequency selective channels with the transmit filter g(t),

sampled at T/2 second. The goal for our proposed receiver is to accurately recover the

sequences {d1(k)} and {d2(k)}, given reliable estimates of the channel impulse response

)(1 kh and )(2 kh , where )](),...,(),([)( ,1,0, khkhkhkhmLmmmm = . Here, we assume the UTP

channel is a Gaussian channel, which has mutually uncorrelated, white Gaussian

background noise, with zero mean and equal likely spectral density, 2/2δ .

As the JMLSE is based on the technique of MLSE, we are going to review the MLSE

receiver in the following sub-sections. This helps us on better understanding how

JMLSE works on ADSL receiver enhancement.

5.2.2 MLSE Receiver Design

The maximum-likelihood sequence estimator [68], [69], [70] has shown the best

performance among all the equalizers and detectors, which called an “optimal” receiver

in the communication systems.

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63

The optimum receiver selects the most probable transmitted sequence, using all

available information fully. The a posteriori probability is the probability that the symbol

sequence, {α } was transmitted, given that r(t) was received, as

( ) { } ( )( )trp tr αα (5.2.2.1)

The statistically optimum receiver computes a posteriori probabilities for all

transmitted sequences, and then chooses the sequence with the greatest a posteriori

probability. This receiver structure is called maximum a posteriori probability (MAP).

Using Bayes theorem, the a posteriori probability can be rearranged as

( ) { } ( )( ) ( ) { } ( )( )( ) ( )( )

( ) ( ){ }( ) { }( )( ) ( )( )trp

ptrp

trptrp

trptr

tr

tr

trtr

αααα ααα

α ==,, (5.2.2.2)

Ultimately the probability expression is used for decision-making, so the

denominator, ( ) ( )( )trp tr , can be discarded, since it is common for all hypothesised

sequences. A goal of communications is maximizing the information rate, so source

coding (e.g. Huffman coding, arithmetic coding) is often employed. The symbol

sequence is approximately white, with equiprobable symbols. Accordingly, maximizing

the a posteriori probabilities is equivalent to maximizing the conditional probabilities,

( ) ( ){ }( )αα trp tr (5.2.2.3)

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64

for all symbol sequences. This is an MLSE structure, and is optimal when the symbols

are equiprobable. As written, the conditional probabilities are computed at the end of

transmission, whereas a recursive algorithm to compute the conditional probabilities is

preferred since transmission may never stop.

A continuous time version of the derivation in [71] is used. The transmission interval

begins at tB sec and ends at tE sec. These times may be finite or infinite. The received

signal in the ith symbol interval is defined as,

+≤≤

=otherwise

TitiTtrtri 0

)1( )()( (5.2.2.4)

The signal up to time (i+1)T is the history of ri(t)

( ) ( ) ( ) +<≤

=otherwise

TitttrtR B

i 01

(5.2.2.5)

so the conditional probability can be expanded by repeated application of Bayes theorem,

as

( ) ( ){ }( ) ( ) ( ) ( ) { }( )

∏=

−=Tt

TtiiiRtrtr

E

Bii

Rtrptrp αα αα ,1, (5.2.2.6)

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65

Since the logarithm function is one-to-one and monotonic, choosing the transmitted

sequence with maximum log-likelihood is equivalent to choosing the transmitted

sequence with maximum conditional probability. The log-likelihood is defined as

( ) ( ){ }( ) ( ) ( ) { }( )

∑=

=Tt

TtiiiRtrtr

E

Bii

Rtrptrp αα αα ,lnln , (5.2.2.7)

where the product has been reduced to a sum. The sequence with the largest log-

likelihood function or metric is the maximum likelihood sequence, and it is selected by

the receiver. The sequence of complex phases, {β}, can reconstruct the symbol

sequence, {α}, so it is sufficient for a receiver to maximize the log-likelihood over {β}

instead, where the revised metric equals

( ) ( ){ }( ) ( ) ( ) { }( )

∑=

=Tt

TtiiiRtrtr

E

Biri

Rtrptrp ββ ββ ,lnln , (5.2.2.8)

With linear modulations, the information phase, β k does not arrive at the receiver

until t = kT+ξF, so the partial sum, ( ) ( ) { }( ) ∑

=

1

, ,lnk

TtiiiRtr

Bii

Rtrp ββ , depends on the

transmitted sequence only up to β (k-1). At the kth symbol interval, there are

1+− Ttk BM distinct metrics, and in general this number grows exponentially with the

transmission duration. Thus choosing the ML sequence involves searching for the best

metric through an ever-expanding tree.

Page 77: ADSL System Enhancement with Multiuser Detection

66

The kth log-likelihood, ( ) ( ) { }( )ββ ,ln , ikRtr Rtrpii

, at the kth symbol period is labeled the

branch metric. The running total of branch metrics, from TtB to k, is labeled the path

metric. A sequence of transmitted symbols is called a path, since it defines the branches

taken through the tree.

In hardware implementations of Viterbi algorithm, the log-likelihood,

( ) ( ) { }( )ββ ,ln , ikRtr Rtrpii

are usually converted to bit metrics as,

])|([log)|( brparM ji

ji

ji

ji += ββ (5.2.2.9)

where a and b are chosen such that the bit metrics are small positive integers that can be

easily manipulated by digital logic circuits. Therefore, the path metric for }{β is

computed as,

∑=

=k

Tti

ji

ji

B

rMM]/[

)|()|( ββr (5.2.2.10)

Thus, the code word }{β that maximizes β)|(trp also maximizes )|( βrM .

"Per-Sequence-Processing" is the reason for the exponentially increasing complexity.

In the general communications problem, the optimal receiver structure has no a priori

knowledge of the channel. However, knowledge of the channel and other parameters is

necessary to compute the branch metrics, and these are progressively estimated. The

estimation is normally data-dependent, since the transmitted signal must be de-

convoluted from the received signal before the channel is revealed. Thus the estimated

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67

channel and the branch metric depend on the whole symbol sequence history. The

number of branch metrics increases exponentially in time.

Furthermore, the log-likelihood of equation (5.2.2.8) is difficult or impossible to

compute when all random processes are considered. The transmitter carrier oscillator, the

receiver carrier oscillator, the transmitter symbol rate oscillator and the receiver symbol

rate oscillator all introduce random phase noise. The multipath channel has a random

number of paths, with a randomly time-varying path attenuations, delays, and arrival

angles. The receiver’s motion is random. When all the individual pdfs are known, it is

mathematically prohibitive to construct the joint pdf. When the pdfs are not known, it is

impossible.

Thus the MLSE receiver structure is not implementable, except when a simple

statistical model can describe the communication system and either the transmission

interval is short or the tree search simplifies to a trellis search. Trellis searches arise

when no data-dependent quantities need to be computed and the branch metric is a

function of a finite number of code states and transmitted symbols.

One example is the transmission of uncoded data through a time-invariant channel

corrupted by white noise, when the channel, the carrier’s frequency and phase, the

symbol rate oscillator’s frequency and phase, and the beginning of transmission are

completely known [72], [73]. The received pulse shape extends over L symbol periods.

The branch metric is a function of the hypothesis vector, ( ){ }iLi ββ K,1+− . There are only

a finite number, ML, of hypothesis vectors, which can be mapped to the ML branches of

an ML-1 state trellis. At the ith symbol period, the trellis’ state is controlled by the first L-1

symbols, ( ) ( ){ }11 , −+− iLi ββ K . The last symbol, βi, specifies which of the M branches are

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68

selected. There are M paths arriving at each state in the (i+1)th symbol period [72] and

[73] demonstrate that the path metric can be constructed as the sum of independent

branch metrics. Accordingly, the exhaustive comparison required to compute the

maximum likelihood sequence can be performed iteratively, before the end of

transmission. Since a path’s metric beyond the ith symbol period is independent from its

path metric before the ith symbol period, it is sufficient for each state to retain only the

path with the best metric from the M arriving paths. Thus each symbol period, the MLSE

receiver extends ML-1 surviving paths in ML ways, one for each hypothesis vector.

Immediately, these paths are pruned back to the best ML-1 surviving paths. This is the

Viterbi algorithm [72]. Ideally, the algorithm makes no decisions until the end of

transmission ("ideal Viterbi"); however, the path histories require linearly increasing

storage, and the decisions are delayed too long. In practice, the decision delay is

truncated to some fixed value.

Herein, we choose a fractionally spaced MLSE for enhanced DMT-ADSL receiver.

It is addressed in the following sub-section. The ideal fractionally spaced MLSE receiver

has the same performance as the conventional MLSE receiver. We derive an equivalent

receiver that does not implement the matched filter, but instead uses a fixed analog filter

that is matched to the pulse shaping filter. A noise-whitening filter having a fixed

structure that does not depend on the unknown channel is used to whiten the T/2-spaced

noise samples. A Viterbi algorithm then operates on the T/2-spaced received sequence at

the output of the noise-whitening filter.

In conclusion, we summarize the Viterbi algorithm implementation processing.

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69

The Viterbi decoding process begins with building the accumulated error metric for

some number of received channel symbol pairs, and the history of what states preceded

the states at each time instant t with the smallest accumulated error metric. Once this

information is built up, the Viterbi decoder is ready to recreate the sequence of bits that

were input to the channel. The detail steps are in the following.

Accomplishment steps

(1) Select the state having the smallest accumulated error metric and save the state

number of that state.

(2) Iteratively perform the following step until the beginning of the trellis is reached:

Working backward through the state history table, for the selected state, select a new

state, which is listed in the state history table as being the predecessor to that state. Save

the state number of each selected state. This second step is called traceback.

(3) Work forward through the list of selected states saved in the previous steps. Look up

what best estimated input bit corresponds to a transition from each predecessor state to its

successor state.

5.2.3 T/2-spaced MLSE Receiver

It is known to us that the optimum receiver filter, given the received signal r(t), is a

filter matched to h(t) [72]. In Ref. [72], it showed that a matched filter followed by a

symbol-rate sampler gives sufficient statistic to estimate the transmitted sequence {βl}.

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70

In conventional MLSE receiver, the T-spaced samples at the output of the matched filter

must be obtained at the correct timing phase.

The signal at the output of the matched filter is

∑ +−=l

lMF tvkTtxtr )()()( β (5.2.3.1)

where )()()( * ththtx −∗= , and v(t) is the response of the receiver filter to the white noise

signal n(t).

In the receiver of Eq. (5.2.3.1), the signal rMF(t) is sampled with rate 2/T. The overall

channel impulse response and the sampler can be represented by a discrete time T/2-

spaced transversal filter with coefficients

),,...,,,,...,,( )2(2

)2(12

)2(1

)2(0

)2(1

)2(12

)2(2

)2(LLLL xxxxxxx −−+−−=x . (5.2.3.2)

In Eq. (5.2.3.2), we assume that the samples are obtained at the correct timing phase, i.e.

)2/()2( lTxxl = and *)2()2( )( ll xx −= , where )2()(⋅ indicates rate 2/T sampling.

The T/2-spaced noise samples at the output of the matched filter have the autocorrelation

)2(0

* ][21

mnnm xNvvE −= (5.2.3.3)

The z-transform of x(2), denoted as X(2)(z), has 4L roots and can be factored as

)/1()()( **)2( zzz VVX = (5.2.3.4)

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71

where V(z) and V*(1/z*) are polynomials of degree 2L having conjugate reciprocal roots.

The T/2-spaced correlated noise samples are now whitened using a filter that has a

transfer function 1/V*(1/z*). Once again, V*(1/z*) is chosen such that all its roots are

insider the unit circle. The output of the noise-whitening filter is

)2(2

0

)2()2(l

L

iilil Ivy η+= ∑

=− (5.2.3.5)

where { )2(lη } is a T/2-spaced white Gaussian noise sequence with variance

02)2( ]|[|

21 NE l =η and the {vk} are the coefficients of a T/2-spaced discrete-time

transversal filter having a transfer function V(z). The sequence { )2(β } is the

corresponding T/2-spaced symbol sequence given by

==

=,...,, l,...,,ll

l 531 , 0420 , 2/)2( β

β (5.2.3.6)

Then, we have

∑ ∑= =

===L

i

L

iii xxgv

2

00

0

)2(0

22 |||| (5.2.3.7)

Notice that the samples )2(2ly and )2(

12 +ly correspond to the lth received baud where

∑=

− +=L

ililil vy

0

)2(22

)2(2 ηβ

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72

∑=

+−++ +=L

ililil vy

0

)2(1212

)2(12 ηβ (5.2.3.8)

Note that )2(2ly is not necessarily equal to yk due to the fact that different noise-whitening

filter is used to whiten the T/2-spaced noise samples.

Maximum likelihood sequence estimation can be applied to the T/2-spaced received

samples in a very similar to that described in Ref. [72]. The Viterbi decoder searches for

the most likely path in the trellis based on the T/2-spaced received sequence. However,

two samples are fed to the Viterbi decoder for every baud, and a branch metric for each

transition in trellis is evaluated. For each transition into the state )(1

ils + , the samples )2(

2ly

and )2(12 +ly are used by the Viterbi algorithm to evaluate the following branch metric

|)()(|)( 2

1

)(210

)2(21 ∑

=−++ +→−=→

L

m

jlmlm

il

jlll

il

jll svssvyss ββγ

∑=

−+++ +→−+L

m

jlmlm

il

jlll svssvy

1

2)(1211

)2(12 |)()(| ββ

(5.2.3.9)

We can easily see that T/2-spaced MLSE receiver has the same number of the states

as the conventional MLSE receiver, but required twice the number of computations.

5.2.4 Analyzing MLSE Receiver Structures

The BER of linear receiver structures is relatively straightforward to compute, since

symbols are processed independently and so their errors are independent too. However,

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73

this is not the case for non-linear receiver structures, since consecutive errors are not

usually independent.

The exact BER can be computed as follows. Given a transmitted sequence, the joint

pdf of all hypothesized sequences’ path metrics is calculated. This can be viewed

geometrically as a density function in a multidimensional space. Each hypothesized

sequence is assigned its own (positive only) axis. All the path metrics at the end of

transmission can be written as a coordinate vector, specifying a point in this

multidimensional space. The value of the density function at this point expresses the

likelihood of computing that set of path metrics.

The space can be divided into decision regions. Points within the same decision

region share the same largest path metric, and so detect the same maximum likelihood

sequence. In fact, a hypothesized sequence’s decision region encloses the points closer to

its axis than any other.

When the ML sequence is detected instead of the transmitted sequence, there are a

number of bit errors, unless the ML sequence is the transmitted sequence. This number,

divided by the total number of bits in the transmitted sequence, weights each region of

the joint pdf. Then the bit error rate due to the transmitted sequence is calculated by

repeatedly integrating over all the weighted joint pdf’s dimensions. The overall BER is

then this quantity, averaged across all transmitted sequences.

Clearly, this exact method has little value since it is difficult to compute. The number

of path metrics is increasing exponentially with the transmission length, so the jointly pdf

gets very complicated and the number of integrations gets very large.

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74

Forney’s union bound technique is more straightforward to compute [72]. The

probability that the sequence with the largest path metric that is not the transmitted

sequence can be upper bounded by the probability that any error sequence has a larger

path metric than the transmitted sequence’s path metric. Thus a joint pdf is not needed,

only the pdf of the path metric difference, for all possible transmitted and error

sequences.

Furthermore, there is no need to compute the pdf over the whole transmission

interval. An error sequence follows the same states as the transmitted sequence until the

first error. Errors follow until the two sequences merge at a common state again. This

sequence of errors is called an error event. Any useful communications system has a low

BER, so the error events are normally short compared to the mean time between them.

Accordingly, they can be considered independent, so their probability can be calculated

by only considering the pdf of the path metric difference in the vicinity of the error event.

We point out some notations before our further discussions. The actual transmitted

sequence is denoted by {β u,v}. Potential error events are written as {β u,v,w}. The

superscript u denotes the length of the error event under consideration. The superscript v

enumerates each distinct transmitted sequence in the vicinity of the length u error event.

Each transmitted sequence can be confused with several others, so the error sequences are

enumerated by a further index, w. When an error occurs, the ML sequence is one of the

error sequences, {β u,v,w}.

The probability that the sequence, {β u,v}, is transmitted is labeled by ( )P u vβ , . The

probability that an error sequence has a better metric than the transmitted sequence (the

pairwise probability of error) is denoted by ( )P u v u v wβ β, , ,→ . In general, the pairwise

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75

probability of error depends on the correct symbols in the vicinity of the error event as

well as the actual erroneous symbols. The number of bit errors that arise from the error

event is written ( )e u v u v wβ β, , ,→ .

An upper bound on the BER can be deduced from a union bound over all error

events. Since this is an infinite sum, it must be truncated. The truncated bound is a

credible upper bound if at least the dominant error events are considered; the bound is

tight if these error events are relatively disjoint.

Thus the BER bound is the union bound of the dominant error events, averaged

across the transmitted sequences in the vicinity of the error event,

( ) ( ) ( )∑ →→<wvu

wvuvuwvuvuvu

MePPBER

,, 2

,,,,,,,

logβββββ (5.2.4.1)

The form of an error sequence is {β u,v,w} = ( ){ }β θ εu v u v w u v wj, , , , ,exp + , where the

sequences {ε u,v,w} and {θ u,v,w} specify the particular error sequence, and are constrained

so that {β u,v,w} is also an allowed sequence. For an error event extending from the ith to

the (i+u-1)th symbol period, ε kru v w, , is zero for k < i and for k > i+u-1. When the data is not

encoded rotationally-invariantly, θkru v w, , is always zero; otherwise θkr

u v w, , is zero for k < i+u

and it is constant for k ≥ i+u. This remaining phase offset allows the error event to end

when phase lock between transmitter and receiver is lost (cycle slip), since the

rotationally invariant code prevents further bit errors. By constraining {θ u,v,w} to be zero

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76

until the end of the error event, the sequences, {ε u,v,w} and {θ u,v,w}, uniquely describe an

error event. Therefore the error sequence can be written as

( ) ( ) ( ) ( ) ( ) ( )( ){ }KKK ,exp,,,,, ,,,1

,1

,,,,1

,2

wvuui

vuuiui

vuui

wvui

vui

vui

vui j ++−+−+−− ++ θβεβεβββ (5.2.4.2)

5.2.5 Reduced Complexity Receiver Structures

Since the complexity of the MLSE receiver increases exponentially in time and the

necessary log-likelihood cannot easily be computed, reduced complexity systems are

employed. In a basic receiver with linear detection, carrier frequency, carrier phase,

channel estimation, channel equalization and symbol timing are acquired by separate sub-

systems, as in figure 5.2.5.1. The symbol-rate oscillators at transmitter and receiver are

assumed to be sufficiently precise and stable that the symbol rate is known a priori at the

receiver. The more sophisticated scheme of figure 5.2.5.2 uses a fractionally spaced

equalizer for joint carrier phase recovery, symbol timing estimation and channel

equalization. The carrier recovery structure in an AWGN telephone channel is shown in

Fig. 5.2.5.3.

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77

Figure 5.2.5.1: Basic Receiver Structure

Figure 5.2.5.2: Sophisticated Receiver Structure

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78

Many successful algorithms exist for each of these tasks, for the channels of our

interest, namely the AWGN channel. Through, the performance of many of these

algorithms degrades substantially in the fast fading wireless channel, but not in the

telephone wireline DSL channel, which we study herein. Some of these difficulties can

be further studied to motivate the development of new receiver structures, explicitly

designed for the fast channels. Simple received signal models are used for illustrative

purposes, since the same or worse problems appear when more sophisticated signaling

formats and channel models are used.

Figure 5.2.5.3: Carrier Recovery an AWGN Channel

5.2.6 Joint MLSE for DMT-ADSL Receiver

Jointly ML receiver detects both desired ADSL signals as well as crosstalk data

signals, which showed in Fig.5.1.1. This technique has been proved an optimal receiver

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79

for communication channels with co-channel interference in many wireless applications

[74], [75], and [76]. The principle of JMLSE on ADSL channel is by selecting over all

main desired channel inputs and all possible crosstalk interference channel inputs, that

finding a particular set of inputs that minimize the distance from the received single

channel output. We notice here that JMLSE across all the channels, which including

main channels and crosstalk channels. This detector is very complex, but theoretically

allows bounding of improvement from multiuser detectors.

The structure of the optimal JMLSE is a straightforward extension of the single

channel MLSE. As in a adjacent pair case, if L1+1 and L2+1 are the channel impulse

response lengths of the two co-channel signals, then the JMLSE selects the ith joint

symbol sequence { ki

ki xx 2,1, , } that maximizes the metric

),|(),|( ,2,1,2,1k

jk

jkk

ik

ik xxrpxxrp ≥ (5.2.6.1)

for all ij ≠ where )}1(),...,1(),({ rkrkrr k −= is the received sequence. The JMLSE can

be implemented using a joint Viterbi algorithm.

For the joint demodulation of two cochannel signals, the objective of JMLSE, which

can be illustrated in Fig. 5.2.6.1, is to determine the pair of sequences { kj

ki xx 2,1, , } that

minimizes the sum of squared errors defined by the error sequence kjie , . When the

channel has a finite impulse response (FIR), that Viterbi algorithm (VA) is a practical

way of implementing optimal single-user MLSE, as shown in [64]. The VA for JMLSE

is implemented in a method very similar to that of the single-channel VA. A joint state

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80

],[ 21 ,12,

,11,

,1 Lki

Lki

Lki ssS −−− = is defined by appending the primary )( 1,1

1,Lk

is − and secondary

)( 2,12,

Lkis − states. Therefore, the received metric is equal to

( ) ( ){ }( ) ( ) ( ) { }( )

∑=

−−−− =

Tt

Tti

LkiiiSRtr

LkiStr

E

B

Lkiii

Lki

SRtrpStrp ,1,

,1 ,lnln ,1,1 (5.2.6.2)

Observe that in this case, each joint state at time k-1 can have transition to M2 states at

time k and can be reached by the same number of states from time k-2. The number of

states required to implement the optimal joint VA is 21 LLM + . For high-order signal

constellation, for example 64-QAM, the computational complexity will be very high on

joint VA.

Fig. 5.2.6.1: Joint ML Sequence Detection between Adjacent Pair

+

rk

Primary Channel Estimate

Secondary Channel Estimate

+

kix 1,

kjir ,ˆ

-

kjie ,

kjx ,2

f1(k)

f2(k)

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81

JMLSE for the SDSL crosstalk interference on the ADSL channel model are derived

in this thesis. The basic concept is that all the possible transmitted signals of both DMT-

ADSL and SDSL crosstalk are searched and that group of signals that best matches the

received signals over a given symbol period is found. JMLSE is the optimum detector

for a narrowband DMT-ADSL channel with relatively small AWGN. As an example

shown in Fig. 5.2.6.1, for the joint detection of two cochannel signals (desired ADSL and

SDSL crosstalk interference), the objective of JMLSE is to determine the pair of

sequences (ADSL signal and SDSL crosstalk) that minimizes the sum of the squared

error defined by the error likelihood sequence. The squared minimum distance for

JMLSD is used to allow accurate projection of the performance of the ADSL system.

When the channel is a finite impulse response, the joint Viterbi algorithm for JMLSE is

implemented with a method similar to the standard VA, as we have derived in the above.

5.3 Preliminary Performance Studies

In the same binder group, the spectral compatibility study here is a SDSL disturber

NEXT into a T1.413 full rate DMT-ADSL system [15]. The DMT-ADSL system has a

channel coding inside, which makes the SNR gap at a very low level; we have chosen a

gap of 4 dB in our simulation. As an example, assume that both ADSL and SDSL

channels are FIR, with a total channel memory of 2L = 8. The performance of the

optimal 256282 ==LM states in JMLSE is required to implement a joint VA. That is, a

associated trellis diagram has 256 nodes at each stages. Notice here, that the complexity

if the JMLSE exponentially increases with the length of the channel impulse response.

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82

Fig.5.3.1, shows that the bit error rate (BER) v.s. the channel SNR on multiuser and

single-user scenarios for the DMT-ADSL receiver. For the single-user receiver, the SNR

is 21.5 dB with BER of 10-7, and it just needs 18.3 dB with multiuser detection. The

JMLSE performs better than the conventional ADSL receiver does by more than 3 dB in

SNR.

In a DSL system, it is designed conservatively to ensure that a prescribed probability

of errors occurs. The margin of a design at a given performance level, which we use

here, is the amount of additional SNR in excess of the minimum required for a given

code with a gap (= 4 in our example) [15]. The margin can be represented as

,)12( 2arg −⋅Γ

=binm

SNRγ (5.3.1)

where Γ = ( ),( CPeΓ , which is a function of a chosen probability of symbol error Pe and

the line code, C.) is the gap, and b is the achievable bit rate on the ADSL system, which

is,

).1(log21

2 Γ+= SNRb (5.3.2)

It has also been shown that the modified ADSL receiver can outperform the conventional

receiver much better in the margin, as in Fig. 5.3.2.

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83

Fig.5.3.1: BER for ADSL System with Single-user Detector and JMLSE

17 17.5 18 18.5 19 19.5 20 20.5 21 21.5 2210-16

10-14

10-12

10-10

10-8

10-6

10-4

10-2

SNR in dB

BER

Bit Error Rate for ADSL

single-user detector

multiuser via JMLSE

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84

Fig.5.3.2: ADSL System with SDSL Crosstalk on Single-user Detector and JMLSE

4 6 8 10 12 14 16 18-30

-25

-20

-15

-10

-5

0

5

10

15

20

ADSL Service Length in kft

Mar

gins

in d

B

JMLSE

Single-user Detector with SDSL Crosstalk

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85

CHAPTER SIX

LOW COMPLEXITY ENHANCEMENT ON ADSL RECEIVER

JMLSE is an “optimal,” but has a high computational complexity for any DSL

channels. This approach estimates the channels of both the desired signal (ADSL signal

here) and the cochannel interference, and then uses a vector-JMLSE equalizer to jointly

demodulate the desired signal and crosstalk. The full search for the minimum distance

requires approximately equal to (number of sub-channel)∗ (set size of crosstalk)2

computations. Therefore, the complexity increases exponentially with the sum of the

channel lengths of the desired signal and the crosstalk. We use some simplification

methods to reduce the complexity of JMLSE. The technique we proposed is sort of

having feedback session between the primary and secondary sequence estimators.

Meanwhile, we also review an alternative method, called Tone-Zeroing [77], [81] for

complexity reduction. Our comments with this method have also been discussed after the

reviewing.

6.1 Tone-Zeroing Method

Using the loading algorithm [78], [79] in DMT system together with the studies on

ADSL and SDSL spectral compatibility results, a sub-optimum solution on ADSL

receiver enhancement and modified deployment plan will be proposed.

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86

With the property of DMT system, a proposed scheme for the SDSL and the DMT-

ADSL joint detection minimum distance improvement is to zero a few tones in the DMT-

ADSL transmission that correspond to the largest instance of the SDSL crosstalk noise.

After FFT output, the crosstalk detector is used to find out the crosstalk look-up table. It

can be realizes as, the DMT-ADSL receiver decides initially the SDSL crosstalk

sequence by using the tone zeroed for the DMT on corresponding sub-channels. In

another word, by using tone zeroing, it can eliminate various crosstalk error event

sequences from consideration. Simulation result has shown that it reduces the

complexity and also largely mitigating the crosstalk noise on DMT-ADSL system. For

some case, less than 5 tone zeroed, it can improve more than 10 dB in margin, comparing

to single-user ADSL solution.

Communications theory allows accurate projection of the performance through

the calculation of the squared-minimum distance for the joint ML detector [72], [80] as,

,|)()(|0

2''

},{},(

2min min

0''

∑=≠

−−−==

N

nnininnn

XXCCXXHd

ninin CC (6.6.1)

The expression in Eq.(6.1.1) for jointly detection minimum distance can be increased

in value by zeroing DMT-ADSL signal on tones where the SDSL crosstalk signals are

large. As we have discussed in the previous section, the number of the tone being zeroed

is depended on the coupling DSL data rate, the ADSL transmitting throughput and its

bandwidth. In fact, in very high bit rate DSL (VDSL), just a few zeroed tones lead to a

dramatic improvement in minimum distance [81]. The choice of setting tones to zero

depends on knowledge of where crosstalk signals have the largest energy, but generally

the band of any crosstalk is known, if the various of DSL systems are co-located in a

Telco CO. Loading algorithms in DMT allow for various tones to be easily zeroed and

Page 98: ADSL System Enhancement with Multiuser Detection

87

thus unused [59]. For example, in DMT-VDSL, it may be wise to zero tones in the 7 –

7.3 MHz transmission band because of radio emissions [81].

The receiver for this prototype can be derived in Fig.6.1.1 and is considerably

simplified, but slightly more performance loss, with respect to JMLSE. The receiver

decides initially the crosstalk sequence Ci by using only the tones zeroed for DMT-ADSL

system. Upon detecting the crosstalk signal, the proper crosstalk coupling function is

applied and the entire crosstalk interference on the remaining tone is reconstructed and

subtracted, leaving only desired DSL signals and background noise. This is like “Echo-

Cancellation” type method on crosstalk noise suppression at DMT-ADSL receiver. In

another word, the DMT-ADSL system seems “orthogonal” to the crosstalk signals on

these “heavy crosstalk affected tones”. If the data rate of the crosstalk signal is low and

the SNR is excellent, only a few tones are necessary to create a detection error probability

below 10-7.

Fig. 6.1.1: Joint ML Crosstalk Signal Canceller with Tone Zeroing

y FFT

Crosstalk Detector

Crosstalk Table

+ DMT Decoder

Y

Ci -

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88

We use the same example of the SDSL coupling to the DMT-ADSL channel, in

section 5.3, and assume that the DSL channel is static and constant on crosstalk profile

table. By zeroing about 20 tones to build up a NEXT cancellation table, we can get

about 10 dB in margin near 18kft, shown in Fig. 6.1.2. Therefore, there is a large

potential for us to delivery a high bit rate, with crosstalk profile table modifications on

receiver.

Fig. 6.1.2: Margin on DMT-ADSL with Tone-zeroing Crosstalk Noise Cancellation

4 6 8 10 12 14 16 18-30

-25

-20

-15

-10

-5

0

5

10

15

20

ADSL Service Length in kft

Mar

gins

in d

B

JMLSE

Single-user Detector with SDSL Crosstalk

Tone-zeroing

Page 100: ADSL System Enhancement with Multiuser Detection

89

Surely, this method has an advantage of mitigate the NEXT and complexity

reduction (comparing with JMLSE) with asymmetric and symmetric services coexist.

The key issue for the tone zeroing is necessity of accurate modeling of noise (crosstalk),

as described in [77]. Since the feedback section is using some kind of adaptive filter

technique. The adaptive filter coefficient is largely depends on frequency components

with high power. If a frequency band making NEXT noise has small power, it can not be

modeled correctly due to high power frequency component until sufficient number of

coefficient are used [77]. Therefore, the tone zeroing modeling works well for high

frequency power noise component. If so, in a common case of the telephone channel,

many kinds of random noises often occur in any selected frequency band, it is very likely

to make an error decision on the cancellation table and induce error propagation.

As described in the above, tone zeroing technique has a deterministic co-channel

signals profiles assumption (crosstalk table), which may lead error propagation, due to

the random source signal transmissions and various random noises in any selected

frequency band on DMT-ADSL channel. Therefore, very frequently crosstalk table

tracking and updating are needed in order to make accuracy crosstalk signals estimation.

This processing makes the receiver frequently adaptive to random channels and may

more complexes to realize in practical loops. But, we still believe that tone zeroing is a

good technique on reducing computational complexity to achieve a better throughput. It

performs a better solution for less complicated loops, especially in DMT version DSL

solutions.

The simplified technique that we use in this thesis is a multi-stage joint MLSE for

ADSL receiver. This method is a sub-optimal to the ideal joint MLSE estimator,

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90

provides an excellent way to trade a sub-optimal performance for reducing complexity.

This approach can apply to both DMT and non-DMT versions of DSL solutions in the

same manner.

6.2 Low Complexity Joint MLSE

6.2.1 Multi-stage JVA

The structure of the Joint MLSE, as derived in the previous section is a

straightforward extension of the single channel VA. The drawback for Joint MLSE is the

large computational complexity, due to the exponential increasing on the transition states.

In the Fig.5.2.5.1, as an example of only one co-channel interference case, for a M-ary

symbol alphabet, the JVA requires 21 LLM + states, with M2 transition leaving (and

entering) every state.

In order to reduce the complexity of JMLSE (or JVA), we introduce a multi-stage

JVA method. Using the same example in Fig.5.2.5.1, we can describe a two-stage

JMLSE scheme in Fig.6.2.1.1, which can be extended, to N stages on N co-channel

interference case, without loss generality. As a first step, the complexity reduction can be

attempted by employing a two-stage JVA having only 21 LL MM + states by

implementing a successive interference cancellation approach [52]. For N co-channel

interferences case, this computational complexity is reduced largely comparison with

JMLSE, and its ratio can be derived as

N

N

LLL

LLL

MMMMR +++

+++= ...21

21 ... (6.2.1.1)

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91

As an example, assumption on all equal tap length, L, the Eq. (5.2.1) can be further

simplified as

)1( NLLN

L

MNM

MNR −⋅ ⋅=⋅= (6.2.1.2)

In Eq. (6.2.1.2), it is always true to have N > 1 in any telephone binders, thus, L(1-N) <0.

It is obvious to us that R is always (much) smaller than one. Therefore, multi-stage joint

MLSE reduces the computational complexity largely comparison with ideal joint MLSE.

This multi-stage VA technique is very similar to conventional VA receiver (section

5.2.2), instead having multi-stage inputs and outputs. The primary (strong) signal r1(k) is

estimated using low delay decisions from a single-channel VA, and )(ˆ)( 1 krkr − is

forwarded to the second VA section to estimate the co-channel signal. This structure that

we use it here, as a category of JVA, through it likes a feed-forward multi-stage single

channel VA detectors. We name this as multi-stage JVA (MS-JVA). The major

advantage for this structure is largely reducing the complexity on optimal JVA as shown

in Fig. 6.2.1.1. Its computational complexity is in a similar range of a single-channel

VA, with just a scale-increasing factor by N (N is the total number of UTPs in a binder,

assuming the same length, L, for all the channels.).

Page 103: ADSL System Enhancement with Multiuser Detection

92

Fig. 6.2.1.1: Two-stage JVA (without Feedback Section)

The trade-off on mitigation of the crosstalk with this method is relatively poor

performance comparing to the optimal JVA at a low signal-to-crosstalk ratios (SCRs)

channel condition. The reason for this is while the secondary section receives a relatively

CCI free signal sequence, the primary section is sensitive to the un-cancelled secondary

signal.

In practice, a viable reduced-complexity single-user MLSE receiver can retain fewer

survivor sequences, one for each combination of the latest S ≤ W hypothesized symbols.

The choice for S is a trade-off between complexity and performance [82]. Fig. 6.2.1.2

VA 1LM states

VA 2LM states +

+

_

1L

r(k)

)(ˆ11 Lkd −

)(ˆ22 Lkd −

)(ˆ1 kd

)(ˆ)( 11 krkr −

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93

shows the single-user MLSE receiver computational flow structure for unknown channels

when the signal’s second order statistics are known.

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Fig. 6.2.1.2: Single-user MLSE Computational flow structure

Page 106: ADSL System Enhancement with Multiuser Detection

95

Fig. 6.2.2.1: Two-stage JVA (with Feedback Section)

6.2.2 Multi-stage JVA with Feedback

Achieving the better performance and complexity reduction on the ADSL receiver,

we introduce a multi-stage JVA with feedback section (w/FB), shown in Fig. 6.2.2.1. A

similar structure has been used by [83] on a two-stage JMAPSD detector. Hence, we use

multi-stage JVA, instead of JMAPS. The reason is that it is preferable using JVA due to

tolerate longer decoding delays, because the complexity of JMAPSD grows exponentially

with the decoding delay, while it is essentially linear for the [83]. This characteristic of

JVA fits the need of the ADSL receiver, which widely used in real-time multimedia

applications. As shown in Fig. 6.2.2.1, where at time k, the low delay causal decisions

from the secondary, namely )}(ˆ),...,1(ˆ{ 2,2,2 Lkdkd ii −− , are used to cancel a portion of

VA 1LM states

VA 2LM states + +

+

_

)(ˆ2 kf

)1(1̂ −kf

+ _

r(k)

)(ˆ11 Lkd −

)(ˆ22 Lkd −

)(ˆ 2,2 kd Lk)(ˆ 1,

1 kd Lk

)1(2̂ +kr

)(1 ks )(2 ks

)(1̂ kr

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96

the cochannel signal r2(k) from the input to the primary VA section. This structure just

has an additional L2 tap filter on computational complexity comparing to the MS-JVA.

The performance on MS-JVA-w/FB is considerably better than MS-JVA, as the MS-

JVA-w/FB can cancel the secondary energy corresponding to the previous estimated

symbol )(ˆ2 jkd − , where j = 1,2,…,L2.

A suboptimal multi-stage JMLSE rule to make a decision on the (k-L)th symbol, at

time k, is )()(ˆ LkdLkd n −=− , where

Lkn

Lk dd ,,ˆ = , )]|(max[ , kLkni

rdpArgn = (6.2.2.1)

In each single stage channel, the MLSE metrics are updated independently like derived in

section (5.2.2). It is shown in Eq. (5.2.2.8)

( ) ( ){ }( ) ( ) ( ) ( ) { }( )

∑=

−−=

Tt

TtiiiRtrtr

E

Bii

Rtrptrp ββ ββ ,lnln 1,1 (6.2.2.2)

In a similar to [83], the overall two-stage JVA is summarized in the following two

steps. This algorithm can be easily applied to N stage JVA with a similar extension.

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97

Two-stage JVA Algorithm

Step 1: 1st JVA stage

(1): Determine 1st. input )(ˆ)()( 21 krkrks −=

(2): Update 1st JVA metrics with Eq. (6.2.2.2)

(3): Compute 1st decisions with Eq. (6.2.2.1)

(4): Compute total estimate of 1st. signal

∑=

−−=+1

0max,1,11 )(ˆ)1()1(ˆ

L

ll lkdkfkr

Step 2: 2nd. JVA stage

(1): Determine 2nd input )(ˆ)()( 21 krkrks −=

(2): Update 2nd JVA metrics with Eq. (6.2.2.2)

(3): Compute 2nd decisions with Eq. (6.2.2.1)

(4): Compute total estimate of 2nd signal

∑=

−+=+2

0max,2,22 )1(ˆ)()1(ˆ

L

ll lkdkfkr

Step 3: Return to step 1 for a new sequence.

Page 109: ADSL System Enhancement with Multiuser Detection

98

This MS-JVA-W/FB employs only an additional 2L tap filter in comparison with MS-

JVA. For large ADSL channel sequences, it has the same computational complexity as

the MS-JVA. Our studies have shown that the MS-JVA-w/FB has considerably better

performance than the MS-JVA. Further more, this enhancement and reasonable

complexity are exactly suitable for our proposed DMT-ADSL receiver with crosstalk

environments, which normally above 10 dB in SCR [15].

Therefore, we choose MS-JVA-W/FB for the enhanced DMT-ADSL receiver.

Moreover, a T/2-spaced MLSE algorithm is used for this proposed receiver. In the next

sub-section, a practical T/2-spaced MLSE receiver is described, which has a great

advantage than conventional MLSE receiver for unknown channels.

6.2.3 Practical Enhanced ADSL Receiver

In Fig. 6.2.3.1, it shows the block diagram of a practical ADSL channel system.

Fig. 6.2.3.1: Practical ADSL Channel System

+ {βl}

g(t) Channel c(t) g*(t)

Sampling rate 2/T

T/2-spaced noise-whitening filter

T/2-spaced MLSE

}ˆ{ lβ

n(t)

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99

Since rate 2/T sampling satisfies the sampling theorem, the two systems can be

represented by the T/2-spaced discrete-time signals. Let G(2)(z), C(2)(z) and H(2)(z) be the

z-transform of the T/2-spaced discrete-time signals that correspond to g(t), c(t) and h(t),

respectively, where g(t) is the shaping function, c(t) is the impulse response of the

telephone channel function, and )()()( tctgth ∗= . The z-transform of the autocorrelation

function of the noise samples at the output of the receiver filter )()( )2(0

* zXNtg g= ,

where **)2()2()2( ))/1()(()( zgzgzX g = . Using the factorization

**)2()2()2( ))/1()(()( zVzVzX ggg = , (6.2.3.1)

the noise can be whitened by using a filter with transfer function **)2( ))/1(( zVg . The z-

transform of the overall response at the output of the noise-whitening filter is

**)2(**)2()2()2()2( ))/1(/())/1()(()()( zVzGzCzGzV geq =

)()( )2()2( zVzC g= . (6.2.3.2)

On the other hand, we have

)()()( )2()2()2( zCzGzH = (6.2.3.4)

and

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100

**)2()2(**)2()2()2( ))/1()(())/1()(()( zCzCzGzGzX = (6.2.3.5)

Let

**)2()2(**)2()2( ))/1()(())/1()(( zVzVzCzC cc= (6.2.3.6)

be a factorization of C(2)(z)(C(2)(1/z*))* such that **)2( ))/1(( zVc has a minimum phase.

Using Eq. (6.2.3.1), Eq. (6.2.3.5) and Eq. (6.2.3.6), we have

**)2()2(**)2()2()2( ))/1()(())/1()(()( zVzVzVzVzX ccgg= . (6.2.3.7)

The transfer function of the noise-whitening filter must be chosen as

)))/1(())/1(/((1 **)2(**)2( zVzV cg . Therefore, the overall transfer function at the output of

the noise whitening filter, is equality to conventional one, V(z), which is given by

)()()( )2()2( zVzVzV cg= . (6.2.3.8)

The equivalent response )()2( zVeq in Eq. (6.2.3.2) has the same amplitude as V(z), but

different phase. Also,

)())/1()(( )2(**)2()2( zXzVzV eqeq = (6.2.3.9)

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101

Therefore, the distance between sequences of channel outputs using the system in

T/2-spaced MLSE channel is the same as in the conventional MLSE channel, that

implements the matched filter, and they have the same performance. The advantage of

the T/2-spaced system is that the noise-whitening filter does not depend on the unknown

channel and has a fixed structure. The unknown overall channel can be estimated after

the noise-whitening filter and the MS-JVA-W/FB is then implemented using the

combined metric in Eq. (5.2.3.9). Although the number of computational needed in this

practical receiver is about twice as the conventional receiver [72], the latter one cannot be

implemented for unknown channels. Moreover, for unknown channels the conventional

MLSE implemented with a matched filter has poor performance when the matched filter

is implemented using an inaccurate channel estimate.

6.2.4 Example and Comparison

We consider adjacent pair wire line co-channel interference as an example. Assume

that the channel has PAM modulation with desired channel memory of two symbols. The

trellis for VA in the desired channel section has two parallel transitions. The computer

simulation performances on the symbol error rate vs. channel signal-to-noise ratio for

ideal JMLSE, multi-stage JMLSE with feedback section and without feedback section

have been studied. As we mentioned in section 6.2.2, the SCR is normally above 10dB in

most of the DSL channels, we have chosen SCR = 10 dB in our simulation studies. The

results are shown in Fig. 6.2.4.1. From Fig. 6.2.4.1, we can see that MS-JMSE W/FB

outperform MS-JMLS WO/FB significantly when SCR is 10 dB or better. This approach

is a sub-optimal solution to ideal JMLSE with slightly degradation, but has about 90%

Page 113: ADSL System Enhancement with Multiuser Detection

102

saving in computational complexity. Therefore, multi-stage JMLSE with feedback

section is our solution for ADSL receiver enhancement.

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103

Fig. 6.2.4.1: Desired Channel Performance with Three Methods

4 6 8 10 12 14 16 18 20 2210-4

10-3

10-2

10-1

100

Signal-to-Noise Ratio

Sym

bol E

rror R

ate

* : MS-JMLSE-W/FBo : Ideal-JMLSE

+ : MS-JMLSE-WO/FB

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104

CHAPTER SEVEN

PERFORMANCE EVALUATIONS AND SIMULATION RESULTS ON

ENHANCED ADSL RECEIVER

In current DMT-ADSL receiver, channel noise is lumped together and accommodated

by reach and rate restrictions as well as margin limits. No attempt is currently made to

take advantage of the structure of the interferers. This “single user” approach ignores the

underlying sources of noise in environments where spectral interference occurs.

However, channel capacity is inherently higher in communications channels that employ

multiuser receivers to distinguish and address discrete noise sources to effect higher

performance (e.g., rates, reach and margin), as derived in section 3.2. JMLSE technique

described here takes advantage of such principles to compensate crosstalk noise and

enable higher loop plant utilization.

The multiuser detector is completely compatible with existing DMT-ADSL standards

and is designed to be integrated into commercial DMT-ADSL transceiver chipsets with

modest computational impact. The multiuser detector technique can be inherently single-

ended and relies on input available in the DMT-ADSL network.

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105

7.1 Test Environment

The ADSL noise compensator has been tested on simulated DSL disturbers, with a

significant margin gain demonstrated. For the purposes of this thesis, examples are

shown which illustrate this impact when the compensator is implemented in a DMT-

ADSL CPE receiver, subject to foreign NEXT (major threat, hence from the SDSL

services and some other DSL services) in realistic deployment scenarios.

7.2 Test Channel Conditions

The ADSL receiver crosstalk compensation is single-ended, which is present at the

receive side of the ADSL link. The victim DSL service is DMT-ADSL. Disturber that

we investigate here is 2B1Q SDSL NEXT, HDSL NEXT and ISDN NEXT. Because in

the frequency band between 25 to 138 KHz, HDSL and/or ISDN services result in similar

and even slightly higher NEXT PSD level than ADSL. Therefore, in our crosstalk

simulation study, though we focus mainly on SDSL NEXT, but also with other types of

the above services. Moreover, considering the UTP binder segregation in real world is

not feasible [84], we will expect that all interfering sources to be in different types of

services. Meanwhile, the ADSL self-NEXT will not be considered as a disturber due to

the practical condition that ADSL is installed almost exclusively in FDM mode.

SNR improvement through recovery of margin depends on the particular loop

characteristics and disturber scenario. For this reason, the JMLSE receiver results are

stated in terms of margin recovery for specific scenarios, each of which include a main

channel specification, set of co-channel transfer functions, and a selected disturber set.

Three cases are shown that represent impaired DMT-ADSL loops, which are chosen from

Page 117: ADSL System Enhancement with Multiuser Detection

106

G996.1 [85]. For each of these cases, the expected multiuser DMT-ADSL receivers’

performance improvement is stated in terms of margin recovery (SNR gain), bit rate

improvement, and loop reach.

For all scenarios described in this thesis, a UTP background AWGN level of –140

dBm/Hz is assumed.

7.3 Loop Characteristics

We choose three representative ADSL test loops for our simulation studies, which are

studied in [85]. They are shown in Fig. 7.3.1.

Fig. 7.3.1: Testing Loops

ATU - R ATU - C

ATU - R ATU - C

ATU - R ATU - C

18000 ft 26 AWG

6000 ft 26 AWG

1500 ft 26 AWG

3000 ft 26 AWG

9000 ft 26 AWG

2000 ft 24 AWG

500 ft 24 AWG

500 ft 24 AWG

1500 ft 26 AWG

1500 ft 26 AWG

1500 ft 26 AWG

1500 ft 26 AWG

1500 ft 26 AWG

Test Loop #3

Test Loop #1

Test Loop #2

ATU - R ATU-C

ATU - R ATU- C

ATU - R ATU-C

26 AWG

6000 ft 26 AWG

1500 ft 26 AWG

3000 ft

9000 ft 26 AWG

2000 ft 24 AWG

500 ft 24 AWG

500 ft 24 AWG

1500 ft 1500 ft 26 AWG

1500 ft 26 AWG

1500 ft 26 AWG

1500 ft 26 AWG

Page 118: ADSL System Enhancement with Multiuser Detection

107

7.4 Capacity Improvement

To estimate capacity improvement (achievable transmission data rates) with enhanced

multiuser detection DMT-ADSL receiver, the margin is held at 6 dB and the bit loading

algorithm uses the improvement in SNR to calculate the maximum downstream ADSL

capacity.

7.5 Reach Improvement

To estimate reach improvement with enhanced multiuser detection DMT-ADSL

receiver, the margin is held at 6 dB, and the loop is extended until the simulation results

in a bit rate equivalent to the impaired bit rate.

7.6 Disturber Scenarios

The main focus on the spectrum management standard of this thesis limits the

maximum SDSL bit rate on a given loop length to assure spectral compatibility with

ADSL. As shown in Fig. 2.2.2.2, limit based on maximum SDSL bit rates is that

crosstalk from lower bit rates is always less damaging than crosstalk from higher bit

rates. This is not always obvious to all the practical cases, especially considering that

there may be mixed crosstalk from a number of lower bit rates, such as lower rate SDSL.

Our simulation results below show how the random SDSL bit rates and lower rate DSL

services implicit to downstream ANSI DMT-ADSL throughput.

To start, simulations run with randomly generated SDSL bit rates uniformly

distributed between 160 kbps and 2320 kbps. Each simulation has three clumps of SDSL

disturbers, and each clump has the same randomly generated bit rate. The total number of

Page 119: ADSL System Enhancement with Multiuser Detection

108

SDSL disturbers is uniformly distributed, and the number of disturbers in each SDSL is

uniformly distributed with mean equal to one-third of the total number of SDSL

disturbers. Scatter plot of downstream ANSI DMT-ADSL bit rates on a 9 kft 26 AWG

loop as a function of the total number of SDSL disturbers with SDSL disturbers having

uncontrolled random bit-rates are presented in Fig. 7.6.1 [86].

Fig. 7.6.1: Scatter Plot of Downstream ADSL Throughout with Mixed SDSL Crosstalk

0100020003000400050006000700080009000

10000

0 10 20 30 40 50Total Number of SDSL NEXT

Dow

nstr

eam

AD

SL

bit r

a(k

bps)

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109

Fig. 7.6.1 shows little correlation between random SDSL bit rate disturber numbers for

downstream ANSI ADSL bit rates. Our conclusion is that controlling the gross number

of SDSL disturbers has little effect on ADSL performance, without controlling the SDSL

bit rates, which is not practical in real world at all. The real solution is to modify the

DMT-ADSL receiver to mitigate crosstalk effect on the ADSL throughout.

Tables 7.6.1 list the disturber sets used in the simulation. The disturber scenarios

illustrate interference situations that might result from a predominately residential 25

pairs UTP binder that has just a few installed symmetric services to businesses. They

reflect a situation in which there is a mix of symmetric services installed prior to the

Spectral Management Standard [87], which do not conform to its’ deployment limitations

as well as Symmetric services that do conform to the Spectral Management Standard.

Table 7.6.1 Disturber Scenarios

784 Kbps 784 Kbps 416 Kbps 160 Kbps

Fully Loaded

Test Loop #3

3 SDSL 1 HDSL 2 SDSL 1 ISDN

18 DMT-ADSL

Disturber Pairs

1.0 Mbps 784 Kbps 656 Kbps 160 Kbps

Fully Loaded

1.0 Mbps 784 Kbps 720 Kbps 160 Kbps

Fully Loaded

Test Loop #2 Test Loop #1

784 Kbps 784 Kbps 416 Kbps 160 Kbps

Fully Loaded

Disturber Pairs

1.0 Mbps 784 Kbps 656 Kbps 160 Kbps

Fully Loaded

1.0 Mbps 784 Kbps 720 Kbps 160 Kbps

Fully Loaded

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110

7.7 Co-Channel Transfer Functions

The NEXT co-channel transfer functions have been measured as the way in section

4.1 on real cable. These measured co-channels are similar to those found in the spectral

management draft standard [87]. These co-channels are used to simulate the coupling

between the DMT-ADSL and other DSL distributors.

7.8 Simulation Results

In the test simulation, each interference noise source in the disturber scenario (Table

7.6.1) is randomly assigned as cochannel input. Results are averaged due to the statistical

nature of the binder assignments. The standard deviation of the improvements is

maintained and a representative case below shows the 1σ limits of the compensation

margin improvement.

It is useful to look at multiuser detection improvements from the limiting case of

when the disturbers are installed to the same equivalent working length in an intact

binder. In this case, all disturbers are assigned similar co-channel transfer functions that

represent approximate co-location of the disturbers and DMT victim.

The results of the simulation test of the compensator for DMT-ADSL CPE receiver

are shown below in Fig. 7.8.1 through Fig. 7.8.3. In these figures, we compare three

different solutions, which are conventional (currently deployed), ideal JMLSE, and multi-

stage JMLSE with feedback section DMT-ADSL receiver.

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111

Fig. 7.8.1: Rate-reach curves for Test Loop #1

9 10 11 12 13 14 15 16 17 180

0.5

1

1.5

2

2.5

3

3.5

4

ADSL Service Length in kft

Ach

ieva

ble

Dow

nstre

am D

ata

Rat

e in

Mbp

s square : ideal JMLSEx : multi-stage JMLSEo : conventional ADSL receiver

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112

Fig. 7.8.2: Rate-reach curves Test Loop #2

9 10 11 12 13 14 15 16 17 180

0.5

1

1.5

2

2.5

3

3.5

ADSL Service Length in kft

Ach

ieva

ble

Dow

nstre

am D

ata

Rat

e in

Mbp

s

square : ideal JMLSE

x : multi-stage JMLSE

o : conventional ADSL receiver

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113

Fig. 7.8.3: Rate-reach curves for Test Loop #3

4 6 8 10 12 14 16 18 200

1

2

3

4

5

6

7

8

9

10

ADSL Service Length in kft

Ach

ieva

ble

Dow

nstre

am D

ata

Rat

e in

Mbp

s

square : ideal JMLSE

x : multi-stage JMLSE

o : conventional ADSL receiver

extensionprediction

Page 125: ADSL System Enhancement with Multiuser Detection

114

Fig. 7.8.1 through Fig. 7.8.3 shows how the margin improvement enabled by the

enhanced multiuser ADSL receiver. This modification can be used for either increasing

the capacity, which moving achievable data rate vertically from the conventional rate to

the great improved rate, or deployment limits, which moving reach limit horizontally

from the conventional deployment rage to the further extension limits.

Furthermore, Fig. 5.1.1 show that when services strictly adhere to spectral

management deployment limits, crosstalk from the other DSL services in the channel can

affect the DMT downstream rate at points significantly removed from the coupling. In

these cases, as well as those that represent legacy disturber scenarios that may exist in the

loop plant prior to the spectrum management standard [15]. The multiuser ADSL

receiver improvement in bit rate and loop reach extensions, and represents an important

performance enhancement to the DMT type DSL receivers.

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115

CHAPTER EIGHT

CONCULUSIONS

This thesis suggests that the traditional approach to DSL cochannel interference

modeling and receiver design may dramatically under-project achievable capacity level in

DMT-ADSL transmission systems. With the increasing importance of spectral

compatibility and a difficulty in surmounting the multiple problems created by the

mixture of different DSL services, the principle of multiuser detection has been used to

relieve substantially the problems created by crosstalk in ADSL system.

The use of this enhanced multiuser detection technique has a wide array of potential

benefits for spectral management and deployment in all DSL services, where interference

exists due to legacy services, and newly deployed services with heavy crosstalk noise.

This approach is a core method on improvements of either increasing transmission data

rate, or extending deployment areas, or compensating in poor BER DSL channels, based

on different requirements. In our studies, it has shown that this modified ADSL receiver

is able to achieve and sustain significantly higher data rates. Also, this enhancement on

the receivers having ability to reject the effect of interferers, the length limit on

potentially interfering services, such as SDSL services, may be relaxed without harm to

victim services (like ADSL).

Page 127: ADSL System Enhancement with Multiuser Detection

116

Our simulation results show that higher rate services can be deployable further out in

the loop plant. Therefore, this approach on the ADSL receiver gives degrees of freedom,

and great overall loop plant utilization, while preserving spectral compatibility.

Finally, our enhanced ADSL system also has acceptable computational complexity

for current VLSI capability.

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117

CHAPTER NINE

RECOMMENDATIONS

Without loss generality, using the multiuser detection receiver technique described

herein to mitigate the effects of crosstalk can be applicable across all existing and

contemplated DSL transceivers, including DMT/QAM/CAP ADSL, HSDL, SDSL and

future VDSL. The benefits vary and are significant. Further more, the techniques

contained herein are extensible to fiber and wireless.

Studies of the twisted-pair channel (TPC) model and conventional crosstalk coupling

function [55], [88] show the characteristic of the TPC attenuation and NEXT function in

Fig.9.1. It is explicit that for high data rate downstream ADSL transmission between 6 to

14 kft, JMLSD is needed to suppress the SDSL NEXT interference. Other complexity

reduction methods for joint VA decoding will be further studied for this enhanced ADSL

receiver. As it reaches further, such as above 14 kft, the NEXT will be very large and

easy to detect, and then it will be easy to cancel them. Based on the ADSL downstream

data rate threshold or noise margin, a switched dual-mode of single-user and multiuser

DMT-ADSL receiver could be used for simplicity and less latency with QoS of the

transmission rates.

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118

Fig.9.1: Channel Attenuation and NEXT Characteristic

0 500 1000 1500-90

-80

-70

-60

-50

-40

-30

-20

-10

0

Frequency in kHz

Gai

n in

dB

analytic channel model, in Eq.(2)

squared crosstalk coupling function

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119

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BIOGRAPHY

Liang C. Chu was born in Shanghai, China at January 29, 1965. He received his M.S.

in electrical engineering at the City College of New York, CUNY, in 1990. He worked

with Science and Technology, Bell South Inc., Atlanta, GA and SCS Telecom. Inc., Port

Washington, NY. He also taught undergraduate and graduate courses in the Department

of Electrical and Computer Engineering, Manhattan College, Riverdale, NY.

His research interests include multiuser detection and communication theory, wireless

communications, broadband access technologies, and digital signal processing.

He has received Regent's Scholarship at Georgia Institute of Technology and

University Merit Fellowship at the City University of New York for his graduate studies.

He is a student member of IEEE.