DSpace at VNU: Vectored DSL: Potential, Implementation Issues and Challenges

Upstream Transmission The network configuration in upstream DSL transmission makes it often impossible for pre-coding to occur at the trans-mitter side; however, since the signals are al

Vectored DSL:

Potential, Implementation Issues and Challenges

Christopher Leung, Sean Huberman, Khuong Ho-Van, and Tho Le-Ngoc

Abstract—This paper investigates specific techniques suitable

for Vectored DSL, their performance, complexity and practical

implementation More specifically, various Vectored DSL

tech-niques for both upstream and downstream transmission are

discussed, including the Tomlinson-Harashima Pre-coder (THP),

Diagonalizing Pre-coder (DP), Zero-Forcing (ZF) canceller, and

Decision-Feedback (DF) canceller A thorough discussion on some

of the practical implementation aspects of Vectored DSL is

provided In particular, various implementation challenges are

discussed, including computational load, memory storage, line

management, partial crosstalk cancellation, and the effect of

imperfect channel knowledge As well, the potential gains and

challenges of combining Phantom DSL and Vectored DSL are

also discussed Illustrative examples are provided based on both

measured data and channel models to compare the various

Vectored DSL techniques and their practical implementation

challenges.

Index Terms—Digital Subscriber Line (DSL), Vectored DSL,

pre-coding, interference cancellation.

I INTRODUCTION

DIGITAL Subscriber Line (DSL) service providers are

in fierce competition with cable companies to provide

services such as multicast/unicast video, HDTV, and 3D TV

The demand for data-intensive services is on the rise In

order to support more sophisticated multimedia services and

compete with cable companies, DSL is pushing for higher

data-rates

One solution for achieving higher data-rates involves

run-ning optical fiber wire directly from the Central Office (CO) to

every Customers Premise (CP), known as Fiber-To-The-Home

(FTTH) Deploying FTTH can require costly investments

especially in buried-cable areas As such, service providers,

who have already heavily invested in DSL technology and in

their copper-wire network, wish to make use of hybrid optical

fiber and copper wire networks to meet the data-rate demands

at a lower cost

The family of hybrid optical fiber and copper wire networks

are referred to as FTTx networks The type of FTTx network

Manuscript received May 15, 2012; revised October 4, 2012 This work was

supported in part by the Natural Sciences and Engineering Research Council

of Canada and Bell Canada through the Industrial Research Chair program.

Moreover, some of the authors were funded by the Fonds qu´ebecois de la

recherche sur la nature et les technologies.

C.Leung, S Huberman and T Le-Ngoc are with the Department

of Electrical and Computer Engineering, McGill University, 3480

University Street, Montreal, Quebec, Canada, H3A 2A7 (e-mails:

christopher.leung@mail.mcgill.ca, sean.huberman@mail.mcgill.ca,

tho.le-ngoc@mcgill.ca).

K Ho-Van is with the Department of Telecommunications Engineering, Ho

Chi Minh City University of Technology, 268 Ly Thuong Kiet Street, District

10, Ho Chi Minh City, Viet Nam (e-mail: khuong.hovan@yahoo.ca).

Digital Object Identifier 10.1109/SURV.2013.011413.00098

used depends on the range of copper line lengths in the system For example, Fiber-To-The-Node (FTTN) uses optical fiber wire to transmit information from the CO to a node and then uses copper wire to transmit from the node to every CP in its distribution area In North America, FTTN loops can contain loop lengths up to 1.5 km, but FTTN loop lengths of up to 500

m are more common Similarly, Fiber-To-The-Curb (FTTC) uses optical fiber wire to transmit information from the CO to

a small DSL Access Multiplexer (DSLAM) which typically contains loop lengths of up to 500 m [1] Furthermore, Fiber-To-The-Building (FTTB) uses optical fiber wire to transmit information from the CO to a building

DSL systems transmit data to and from various CPs over bundles of copper wire encapsulated within a cable binder The interference between neighbouring lines is known as crosstalk Crosstalk is the limiting factor in the achievable data-rates of DSL systems As such, to improve the achievable data-rates, the crosstalk interference must be reduced or removed entirely There are two types of crosstalk: Near-End-Crosstalk (NEXT) and Far-End-Crosstalk (FEXT) NEXT is the crosstalk seen by neighbouring lines at the transmitter side and FEXT is the crosstalk seen by neighbouring lines at the receiver side DSL uses Frequency-Division Duplexing (FDD)

in order to remove the NEXT interference As such, the only significant form of system crosstalk is the FEXT interference Hence, higher data-rates can be achieved by minimizing or even removing the FEXT interference

Spectrum Management (SM) techniques can be employed

to achieve this goal The most basic form of SM is known

as Static SM (SSM) SSM implements static spectral masks based on a worst-case scenario assumption for all users This leads to an inefficient use of the frequency spectrum whenever the scenario is not the worst-case and consequently leads to highly sub-optimal performance

Dynamic SM (DSM) is a wide field which looks to adap-tively apply different spectral masks for each user with the in-tent of maximizing the throughput of the overall system DSM allows for a far more efficient use of the spectrum than SSM does There are three levels of DSM [2]; DSM level 1 performs spectrum balancing independently from line to line to mitigate crosstalk, DSM Level 2 performs spectrum balancing jointly across multiple lines to mitigate crosstalk, and DSM Level

3 performs signal-level coordination to remove crosstalk A detailed survey of DSM Levels 1 and 2 is provided in [3] DSM Level 3 applies Vectored DSL to effectively remove crosstalk Vectored DSL makes use of pre-coding in down-stream transmission and makes use of Multi-User Detection (MUD) interference cancellation in upstream transmission 1553-877X/13/$31.00 c 2013 IEEE

DSM Level 3 can also incorporate DSM Levels 1 and 2 in

order to mitigate any crosstalk which is not removed (e.g.,

due to imperfect channel knowledge or to crosstalk from

non-vectored lines)

In the early 21st century, a method using phantom circuitry

was proposed to transmit up to three channels worth of data

over two physical twisted-pair wires [4] The phantom circuit

can significantly increase the capacity of the system; however,

it also significantly increases the crosstalk in the system which

makes it more difficult to achieve the capacity Due to the

increased crosstalk, the phantom circuit (applied to DSL)

was abandoned, until the recent advances in Vectored DSL

technology [4]

Applying the phantom circuit to DSL technology is known

as Phantom DSL By combining Phantom DSL with the

crosstalk mitigation of Vectored DSL, the capacity gains of

Phantom DSL can be achieved without the increased crosstalk

(i.e., Vectored DSL can remove the original crosstalk, as well

as the additional crosstalk generated by the phantom process)

[5]

While Phantom DSL promises increased capacity, it also

provides some challenges from an implementation

perspec-tive More specifically, Phantom DSL requires more

sophis-ticated modems and chipsets, which are capable of

com-bining/recovering the three-channels worth of data over two

physical channels As well, the multiple-line requirement for

Phantom DSL may require infrastructure changes in locations

where consumers are only provided a single DSL line;

how-ever, it is common for two twisted-pair copper lines to service

a single dwelling, allowing for a third “virtual” pair Finally,

thus far, Phantom DSL results have only been obtained within

a lab-setting

The rest of this paper is organized as follows Section II

discusses the xDSL environment Section III presents some

downstream and upstream vectored transmission techniques

Section IV provides some numerical results to demonstrate the

performance gains of Vectored DSL Section V presents some

issues and solutions in implementing Vectored DSL Section

VI investigates the use of partial cancellation techniques, in

order to reduce the computational complexity of Vectored

DSL Section VII shows the effect of channel estimation

error on the performance of Vectored DSL Section VIII

gives an overview of Phantom DSL and summarizes some

preliminary in-lab test results Finally, Section IX provides

some concluding remarks

Notation: In this paper, non-bold variables denote scalars

(e.g.,a), lower-case bold variables denote vectors (e.g., a), and

upper-case bold variables denote matrices (e.g., A) [A](n,m)

refers to the (n, m)-th element of matrix A Similarly, [A](n,)

refers to the vector whose elements are given by then-th row

of matrixA A†refers to the conjugate transpose of matrixA.

diag(A) refers to the matrix of all-zeros except with diagonal

elements identical toA.

II VECTOREDDSLAND THE XDSL ENVIRONMENT

xDSL is a family of technologies which make use of

twisted-pair copper telephone wires to transmit digital data

[6] [7] xDSL operates on the same physical twisted-pair

copper wiring as Plain Old Telephone Service (POTS) by using the higher frequency bands, while POTS is restricted

to the lower frequency band (less than 4 kHz) Different frequency bands are used for different DSL technologies For example, in Asymmetric Digital Subscriber Line (ADSL) the maximum frequency used is 1.1 MHz, in ADSL2plus the maximum frequency used is 12 MHz, and in Very high bit-rate DSL (VDSL) the maximum frequency used is 30 MHz There are dedicated frequency bands for upstream and downstream transmission For most DSL technologies, the frequency bandwidth is allocated asymmetrically where a larger portion is allocated for downstream transmission than for upstream transmission

xDSL technology uses Discrete Multi-Tone (DMT) trans-mission, a scheme which is similar to Orthogonal Frequency-Division Multiplexing (OFDM) DMT is a transmission tech-nique which divides the available frequency spectrum into many sub-channels or frequency tones The main difference between DMT and OFDM transmission is that DMT is also capable of optimizing the bit and energy distribution over the sub-channels (e.g., channel partitioning or bit-loading) [6] The basic idea is to transmit the data in parallel over each frequency tone (note that some frequency tones might transmit no data, while others can transmit a lot of data) More information on DMT transmission and the xDSL environment can be found in [3]

A System Model

Consider a DSL network with a set of users (modems)

N = {1, , N} and frequency tones (sub-carriers) K = {1, , K} Using synchronous DMT modulation, there is

no Inter-Carrier Interference (ICI) and transmissions can be modeled independently on each tone k as follows:

The vector xk  [x1

k , , x n

k]T contains the transmitted signals for all users on frequency tone k, where x n

k is the transmitted signal by user n on frequency tone k Similarly,

yk  [y1

k , , y N

k ]T andzk  [z1

k , , z N

k ]T wherey n

k is the received signal for usern on frequency tone k Likewise, z n

k

is the additive noise for user n on frequency tone k which

contains thermal noise, alien crosstalk and radio frequency interference.Hk is anN × N matrix such that [H k](n,m) is the channel gain from transmitterm to receiver n on frequency

tone k, and is defined as h n,m k The transmit PSD of user n

on frequency tonek is defined as s n

k  E{|x n

k |2}/Δ f, where

E{·} denotes expected value, and Δ f denotes the frequency tone spacing

When the number of users is large enough, the interference

is well approximated by a Gaussian distributed random vari-able, and hence the achievable bit-rate of usern on frequency

tonek is defined as:

b n

k  log2



1 + 1 Γ

|h n,n k |2s n k



m=n |h n,m k |2s m

k +σ n k



,

where Γ is the Signal to Noise Ratio (SNR) gap which is a function of the desired Bit Error Rate (BER), coding gain, and noise margin [7], and σ n

k  E{|z n

k |2}/Δ f is the noise

power density of usern on frequency tone k The achievable

data-rate for user n is therefore R n =f s

k b n

k, wheref sis the DMT symbol rate

There are two types of physical power constraints imposed

on the transmitted signals for each user The first constraint is

a total power constraint (over all frequency tones for a single

user), denoted by P n for user n The second constraint is a

per-frequency tone maximum power constraint, referred to as

a spectral mask The spectral mask constraint for user n on

frequency tonek is denoted by s n,mask k The power constraints

can be summarized as follows:

k

s n

k ≤ P n for alln,

0≤ s n

k ≤ s n,mask k for alln, k.

(2)

B xDSL Network Configurations

Fig 1 shows a typical xDSL network As shown in Fig 1,

the twisted-pair copper wire is run through binders There

are sections of the network where all the lines belong to

a particular CO or DSLAM There are also sections where

the binder is shared between the CO and a DSLAM Optical

fiber wire is run to a CO and/or to DSLAMs Twisted-pair

copper wire is run from the CO and/or the DSLAMs to various

Junction Wire Interfaces (JWIs) Twisted-pair copper wire is

then run from the JWIs to the CPs and/or office buildings

For this particular network (e.g., binder type B), due to the

long length of the CO relative to the DSLAM, the DSLAM

lines can cause severe crosstalk to the CO users (this is known

as the near-far problem) Note that type B binders can also

correspond to binders shared by lines from two DSLAMs It is

worthwhile to note that loops where the CO directly connects

to a JWI and/or CPs (i.e., binder type A) are becoming less and

less common This is due to the fact that channel attenuation

increases with line length, especially at higher frequencies

As such, it is far more difficult to achieve higher data-rates

for longer lines Lines corresponding to binder type A are

often very long in length (e.g., on the order of kilometers) As

such, network topologies similar to binder type C (i.e., FTTx)

are becoming increasingly popular since they are capable of

achieving higher data-rates

The two types of network configurations corresponding to

binders B and C, as shown in Fig 1, will be discussed in more

details in Sections II-B1 and II-B2, respectively

1) Binders With Multiple Disturbing Loops: The first

binder configuration type is where there are multiple loops

sharing a binder Binder B in Fig 1 is an example of this

type of binder configuration Binder B is shared between the

loop from the CO to the JWI and CPs at the top right of the

diagram and the loop between a DSLAM and the JWI and

CPs in the middle of the diagram

One of the challenges of managing networks involving

binders with multiple disturbing loops is known as the

near-far problem The near-near-far problem is caused by the fact that

for twisted-copper pair wires, the attenuation increases with

length Hence, when the receivers from one bundle of lines

is in close proximity to the transmitters of another bundle,

they receive large amounts of crosstalk More specifically, for

binder B in Fig 1, for downstream transmission, the DSLAM lines will cause strong crosstalk to the CO lines

Another challenge of binders with multiple disturbing loops

is that from a network operator point-of-view, it is far more challenging to apply coordinated vectored spectrum man-agement since the lines are not all co-located For such scenarios, vectored spectrum management can be applied to each disturbing loop separately treating the crosstalk from other loops as background noise

While such binder configurations are still quite common

in practice, in recent years, the focus has been on binders with co-located lines Co-located binder configurations will

be discussed in Section II-B2

2) Binders With Co-located Lines: The second binder

con-figuration type is where all the lines are co-located at either the transmitter or the receiver This corresponds to binder C

in Fig 1 For this network binder configuration, optical fiber wire is run to a node (e.g., DSLAM) and then twisted-pair copper wire is run to a JWI and the CPs Note that while Fig 1 shows binder C servicing a building, this binder type can also service various CPs within a neighborhood

There are several benefits of binders with co-located lines from a network operator point-of-view One of the main advantages is that such networks do not suffer as drastically from the near-far problem described in Section II-B1; however,

it can still cause significant performance degradation if the crosstalk is not properly managed Another benefit of binders with co-located lines is that such networks are well-suited for vectored spectrum management since all lines are co-located at either the transmitter or receiver, making joint signal processing simpler

The emergence of FTTx networks has molded the binder topologies of DSL systems In particular, as optical fiber runs closer to each CP, there is less of a requirement for DSLAMs located at geographically separate locations to share a binder Moreover, for FTTN, FTTC and FTTB networks, it is far more common to deploy a single DSLAM (the size of which may vary) to service the customers in its distribution area rather than to have multiple DSLAMs sharing a binder Hence, in recent years, much interest in binders corresponding to binder

C has developed, since they are becoming increasingly more popular from a practical perspective

C Channel Knowledge Availability

DSL systems consist of twisted-pair copper wires in static cable binders and typically, do not move; hence, the DSL chan-nel is considered very slow time-varying As such, the DSL channel is assumed to be time-invariant if new measurements are taken often enough Hence, Vectored DSL assumes full channel knowledge Full channel knowledge can be gained through the use of loop testing There are two types of DSL loop tests: Single Ended Loop Test (SELT) and Double Ended Loop Test (DELT)

SELT measurements are initiated by the DSLAM without using the CP Equipment (CPE) More specifically, SELT mea-surements provide loop qualifications, such as the wire gauge and the length of the loop Since SELT measurements do not require a CPE, they are often used to preemptively measure

B

DSLAM:

Digital Subscriber Line Access Multiplexer

JWI:

Junction Wire Interface DSLAM

DSLAM Fiber Links

Fiber Links

Central Office

C

Fig 1 Example of a typical xDSL Network.

the loop characteristics prior to installing the CPE SELT

measurements can also provide the direct channel attenuation

and the background noise present on the line

DELT measurements are initiated by the DSLAM but

require coordination with the CPE As such, DELT

mea-surements can provide more detailed on-the-fly meamea-surements

of the loop characteristics; however, they require compatible

CPEs DELT measurements can provide full channel

knowl-edge, as well as the background noise for all lines in both the

upstream and downstream directions

SELT and DELT measurements can be combined to provide

the best results for service providers [8] SELT is more useful

than DELT during the pre-installation phase, while DELT is

more useful once the CPE is connected [8] Once the CPE

is connected, SELT measurements can still be useful when

locating line faults in situations where the line conditions are

too poor for DELT

D MIMO Transmission: Downstream vs Upstream

Vectored DSL transmission makes use of concepts

origi-nally developed for Multiple Input Multiple Output (MIMO)

systems [9] A wireless MIMO system consists ofN T transmit

antennas and N R receive antennas, where N T and N R are

not necessarily equal As well, for a wireless MIMO system,

all the N T transmit antenna are co-located and all the N R

received antennas are co-located Hence, for a wireless MIMO

system, pre-coding and/or interference cancellation (using

MUD) can be performed MIMO DSL transmission differs

from wireless MIMO systems in the following ways First,

N T = N R since each “antenna” corresponds to the end of

a twisted-pair copper wire Second, MIMO DSL systems are

typically not co-located at both ends Typically, MIMO DSL

systems are co-located at one end or can be grouped into

clusters of lines which are each co-located at one end (e.g.,

corresponding to a multi-user MIMO wireless system)

ADSL and VDSL transmission makes use of FDD, where

there are separate bandwidths for upstream and downstream

transmission and, hence, the two transmission cases can be

dealt with independently Fig 2(a) shows how upstream

vectored transmission applies to DSL networks Since all the receivers are co-located and full channel knowledge is assumed, the crosstalk can be mitigated by MUD interfer-ence cancelling Similarly, Fig 2(b) shows how downstream vectored transmission applies to DSL networks Since all the transmitters are co-located and full channel knowledge is assumed, the signals can be pre-distorted using pre-coding so that they arrive at each CP crosstalk-free

E Multi-Segment Problems

There are several multi-segment issues with regards to Vectored DSL, including vector clusters, the differences be-tween inter-crosstalk and intra-crosstalk, and alien-crosstalk generated from mixed xDSL networks (e.g., some ADSL lines and some VDSL2 lines) The multi-segment issues listed above will be discussed in what follows

Vector clusters refers to implementing vectoring over a subset of the lines (or several subsets of lines) For example,

if a DSLAM is servicing 192 customers, rather than applying vectoring across all 192 lines, it might be more computa-tionally efficient to cluster the customers into four groups of

48 lines and apply vectoring to each cluster separately As such, the intra-crosstalk refers to crosstalk within the particular cluster and inter-crosstalk refers to the crosstalk from one cluster to another

Inter-crosstalk and intra-crosstalk also arise whenever binders have multiple disturbing loops as discussed in Section II-B1 and shown in binder B of Fig 1 In particular, the CO and DSLAM represent two vector clusters Also note that it is possible that both the CO and DSLAM could apply vector clustering on their respective lines resulting in additional vector clusters

The effects of intra-crosstalk can be removed using vector-ing; however, the effects of inter-crosstalk cannot be removed

by vectoring, instead, the inter-crosstalk must be mitigated using spectrum management techniques (i.e., DSM levels 1 and 2) A survey of spectrum management techniques is given in [3] Note that inter-crosstalk refers to crosstalk from

(a) Upstream

(b) Downstream Fig 2 Vectored DSL transmission.

lines that the network operator has control of and can apply

spectrum management to

Similar to inter-crosstalk, is crosstalk generated from

sce-narios where there are mixed xDSL networks (e.g., some

ADSL and some VDSL2 lines) Such scenarios typically arise

when different service providers are sharing a binder and

as such neither one has control over the other’s lines For

such scenarios, the crosstalk generated is referred to as

alien-crosstalk and it is treated as background noise

III VECTOREDTRANSMISSION Vectored transmission for DSL can be grouped into three

main methods: downstream transmission, upstream

transmis-sion, and joint transmitter-receiver transmission In the joint

transmitter-receiver transmission, pre-coding and cancellation

can be performed at the transmitter and receiver sides This

transmission style is only practical in cases where both the

transmitter and receiver are co-located On the other hand,

as discussed in Section II-D, customers are not usually

co-located In this case, pre-coding at the transmitter is

appro-priate for downstream transmission and cancellation at the

receiver is appropriate for upstream transmission

A Downstream Transmission

The network configuration in downstream DSL transmission

makes it often impossible for interference cancellation to

occur at the receiver side However, since the signals are

transmitted from the same location, pre-coding can still be

applied to pre-distort so that the signals arriving at the CPEs

are crosstalk-free This section presents the two main methods

for applying vectoring in downstream transmission: the

Zero-Forcing (ZF) pre-coder [10], and the Tomlinson-Harashima

Pre-coder (THP) [11]

1) Zero-Forcing: Unlike the THP, the ZF method is a rather

simplistic linear pre-coder that uses the channel inverse for

pre-coding Under this method, the resulting received signal

is given by

yk =Hk(H−1

k ˜xk) +zk (3)

It is evident that the ZF method has the potential to pre-distort the signal such that the signal is interference free when

it arrives at the receiver end However, there is the possibility that applying the inverse as the pre-coder can lead to large transmit power increases and can violate the transmit power

or spectral mask constraints, especially if the channel matrix

is ill-conditioned Yet, [12] showed that in cases where the transmitters are co-located, the channel matrix is row-wise diagonal dominant which leads to a near-optimal ZF method This Row-Wise Diagonal Dominance (RWDD) stems from the fact that the crosstalk signal transmitted from one line to an-other to propagate through the full length of the disturber’s line just like the direct signal Thus, both the direct and crosstalk signals travel the same distance but the crosstalk signals are being additionally attenuated by the insulation between cables Hence, the diagonal element, [Hk](n,n), dominates the other elements on the same row, [Hk](n,m)

We established previously that the ZF method can increase the total transmit power In a similar manner, the ZF method can also increase the PSD However, there exists an upper bound on the allowable PSD known as the PSD mask In order

to guarantee that the PSD mask remains intact, [12] proposed

to use a scaling factor on the pre-coding matrix The scaling factor,β k, ensures that any PSD-mask-compliant input to the pre-coder will remain compliant once pre-coded The scaling factor for each user is obtained by satisfying the following constraint:

s n,mask

k > E|x n k |2

=E 1

β n k

[H−1

k ](n,) x˜n

k2

β n k



m∈N

[H−1

k ](n,m)2

E|˜x n

k |2

β n k



m∈N

[H−1

k ](n,m)2

˜

s n,mask k

Therefore, β n

k = 

m∈N |[H −1

k ](n,m) |2 However, since the scaling factor must be identical for each user, the final scaling

factor is selected as the largest among all users:

β k max

n β n

k

The resulting pre-coder isH−1

k β −1

k and the effective received signal vector is:

yk = 1

The effective channel gain in (4) is the same for all users and

depends on the worse β n

k Hence, [12] further proposed the Diagonalizing Pre-coder (DP)

The DP has the form:

yk =Hk

 1

β kH−1

k diag(Hk)˜xk

 +zk

The corresponding scaling factor for the DP is given by:

βdiag

n



m∈N

|[H −1 k ](n,m) h m,m k |2.

The effective received signal vector is therefore given by:

yk = 1

βdiag

k

diag(Hk)˜xk+zk

The effective bit-rate using the DP is given by:

b n

k = log2



Γ(βdiag

k )2

|h n,n k |2s˜n k

σ n k



2) Tomlinson-Harashima pre-coder: The THP method for

vectoring is based on its original application for channel

equalization developed independently by Tomlinson [13] and

Harashima [14] At the transmitter, it is a two-step non-linear

pre-coder The input of the THP, ˜xk, is converted into an

intermediate variable defined as (xk)int, which is used to

generate the true transmitted signal, xk The first step begins

by taking the QR decomposing of the complex channel such

that:

H† k =QkRk ,

where Qk is a unitary matrix andRk is an upper triangular

matrix By setting the pre-coder matrix to Qk, the received

signal can be modeled as

yk=Hk(Qk(xk)int) +zk

= (QkRk)†Qk(xk)int+zk

The first step of the THP method effectively transforms the

transmission channel into the lower triangular matrix R† in

(7) It can be easily seen thaty n

k =n m=1[R† k](n,m)(x m

k)int+

z n

k Hence, usern = 1 transmits crosstalk-free and every other

usern = 2, , N experiences crosstalk from users 1, , n−

1, respectively The second step of the THP takes advantage

of the fact that with the transmitted signal of user n = 1

known, the crosstalk induced from that user to other users

is also known and the transmitted signals of users 2, , N

can be recursively pre-distorted Once the recursive process is

completed, each user experiences crosstalk-free transmission

R† k=

⎡

⎢

⎢

⎣

r 1,1

r 1,2

k r 2,2

. .

r 1,N

k r 2,N

k · · · r k N,N

⎤

⎥

⎥

The second step of the THP is to find the values of

˜

x n

k corresponding to crosstalk-free transmission for all users Hence, it is required that the following equality be satisfied:

⎡

⎢r

1,1

0 r k N,N

⎤

⎥

⎡

⎢x˜

1

k

˜

x N k

⎤

⎥

⎦=

⎡

⎢

⎢

r 1,1

r 1,2

k r 2,2

k · · · 0

.

r 1,N

k r 2,N

k · · · r N,N k

⎤

⎥

⎥

⎡

⎢(x

1

k)int

(x N

k)int

⎤

⎥

⎦

In order to ensure the spectral mask constraint is satisfied after pre-coding, (xn

k)int should be set as [11] when using real-valued constellations:

(x n

k)int=mods n,mask

k



˜

x n

k − n−1 m=1

r m,n k

r k n,n(x m k )int



,

where modM[a]  a − √ Ma+ √ √ M M /2

The process can be easily transformed for the complex constellation case

Similarly, at the receiver, a second modulo operation is applied to estimate the transmitted symbol as follows:

ˆ

x n

k =mods n,mask

k

 y n k

r k n,n



= ˜x n

k + z n

k

r n,n k

Based on the RWDD discussed in Section III-A1,|h n,n k | 

|h n,m k | for m = n which implies that H k is almost diagonal and hence in the QR decomposition, Qk is almost equal to the identity matrix Thus,|r k n,n | ≈ |h n,n k | due to RWDD.

The bit-rate of user n on frequency tone k can be written

as:

b n

k = log2



1 +|r n,n

k |2s n k

Γσ n k



≈ log2



1 +|h n,n

k |2s n k

Γσ n k



.

It is apparent that the ordering in the THP method will affect the performance This is studied in [15] where it is shown that there are O(N!) K possible combinations of ordering to determine the optimal ordering However, in a similar manner

to the zero-forcing method, the RWDD characteristic of the downstream DSL channel implies that the channel is almost diagonal and hence, in the QR decomposition,Qk is almost equal to identity Thus the diagonal elements ofRkare similar

to those ofHkand the benefits of finding the optimal ordering are far outweighed by its complexity

B Upstream Transmission

The network configuration in upstream DSL transmission makes it often impossible for pre-coding to occur at the trans-mitter side; however, since the signals are all received at the same location at the CO or DSLAM, interference cancellation can be used to remove the crosstalk from each user’s signal This section discusses two methods for vectored upstream transmission: the Decision-Feedback Canceller (DFC) and the

ZF canceller The former is a non-linear canceller that decodes one user at a time and uses the estimate to decode the next user The latter is similar to the downstream ZF method discussed in Section III-A1, where the channel inverse is used

1) Decision-Feedback Canceller: The optimal solution in

upstream vectoring in the Minimum Mean-Squared Error

(MMSE)-sense lies in the use of Integer Least Square (ILS)

programming The least square arises from using MMSE

estimation of the transmitted signal while the integer stems

from the transmitted symbols being selected from a discrete set

as in the following optimization problem for each frequency

tonek:

min

{ˆx n

k ∈A n

k } n∈N



n∈N

|ˆx n

k − x n

k |2,

where A n

k is the constellation of the n-th user on the k-th

frequency tone However, the ILS problem is NP-hard and

relies on searching for the optimal solution Based on the

VDSL2 standard, this would require decoding 1000 symbols

per second per sub-carrier per user Hence, an ILS-based

solution is not feasible Instead, the DFC provides a

suit-able approximation to the optimal solution Mathematically,

upstream transmission on frequency tonek can be written as:

˜

yk=Qkyk =Qk

Hkxk+zk

whereQk is the interference cancellation matrix

The DFC makes use of QR decomposition of a matrix,

similarly to the THP in Section III-A2 The DFC selects Qk

from the QR decomposition of Hk =QR as Qk =Q† As

such, DFC transmission can be expressed as [11]:

˜

yk =Q† kQkRkxk+zk

=Rkxk+Q† kzk , (9) where (9) follows from the fact that Qk is a unitary matrix

Moreover, since Qk is a unitary, the noise, Q† kzk, remains

Gaussian

The DFC essentially transforms the transmission channel

into an upper-triangular matrix,Rk, shown in (9) Since the

components of Q† kzk are uncorrelated, the input,xk, can be

recovered using the decoding procedure that follows First,

note that ˜y n

k =N

m=n r k n,m x m

k + [Q† k](n,)zk Hence, ˜y N

k is received crosstalk-free (with some additive noise) and thus

x N

k can be decoded Next, ˜y N−1

k contains only crosstalk information from x N

k , which is now known and therefore it can be decoded By recursively decoding the received signal

(ordered from user N to user one), the full transmitted signal

can be recovered

Mathematically, the estimate for then-th transmitted signal,

ˆ

x n

k, can be expressed as:

ˆ

x n

k =Decode



˜

y n k

r k n,n −

N



m=n+1

r k n,m

r n,n k

ˆ

x m k



, n = N, N−1, , 1.

The crosstalk will be completely cancelled if each transmitted

signal is correctly decoded

Since the receivers are co-located, the crosstalk signal

trans-mitted from one line (disturber) to another line (victim) must

propagate through the full length of the disturber’s line [10]

As well, since the insulation between linesn (disturber) and m

(victim) increases the attenuation,|h n,n k |  |h m,n k | for n = m.

This can be described as Column-Wise Diagonal Dominance

(CWDD) [10] in Hk Due to CWDD, |h n,n k |  |h m,n k | for

n = m which implies that H k is almost diagonal and hence

in the QR decomposition,Qk is almost equal to the identity

matrix Thus,|r n,n k | ≈ |h n,n k |.

The bit-rate of user n on frequency tone k can be written

as:

b n

k = log2



1 +|r k n,n |2s n

k

Γσ n k



≈ log2



1 +|h n,n k |2s n

k

Γσ n k



.

Like with the THP covered in Section III-A2, the DFC also depends on the decoding order However, unlike the THP, the benefits of ordering can be substantial [15]

Another similar DFC method can be derived based on the MMSE criteria with a similar decoding procedure [16] How-ever, the MMSE-based DFC does not preserve the Gaussian properties of the noise and the difference in performance with the ZF-based method (Section III-B2) becomes minimal at large SNR

2) Zero-Forcing Canceller: The ZF canceller sets Qk =

H−1

k Hence, the ZF transmission can be expressed as follows:

˜

yk =H−1

k yk

=xk+H−1

Therefore, ideally the crosstalk is removed entirely Note that (10) can be re-written as:

˜

y n

k =x n

k+ [H−1 k ](n,)zk

Based on CWDD, |h n,n k |  |h m,n k | for n = m, H k is approximately diagonal and hence,||[H −1

k ](n,) ||2≈ |h n,n k | −2

As such, the modified noise PSD for usern on frequency tone

k, ˜σ n

k, can be written as [10]:

˜

σ n

k  E

[H−1

k ](n,)zk2

Δf ,

=||[H −1

k ](n,) ||2σ n

k ,

≈ σ k n

|h n,n k |2.

Since |h n,n k |2 < 1, the modified noise PSD is larger than

the original noise PSD Hence, ZF can entirely remove the crosstalk at the expense of increasing the noise and the bit-loading of usern on frequency tone k can be written as:

b n

k = log2



1 + 1 Γ

s n k

||[H −1

k ](n,) ||2σ n

k



≈ log2



1 + 1 Γ

|h n,n k |2s n k

σ n k



C Joint Transmitter-Receiver Processing

In scenarios where both the transmitter and receiver are co-located, Vectored DSL can apply both pre-coding at the trans-mitter and interference cancellation at the receiver Singular Value Decomposition (SVD) can be used to obtain the pre-coding and the interference cancellation matrices [17] Under this scheme, Vectored DSL does not increase the total transmit power and each channel has a gain equal to the corresponding eigenvalue of the channel matrix However, this scheme can only be applied when all transmitters and receivers are co-located, in order for joint signal processing to take place Although such scenarios are rare, using SVD can be practical

in scenarios where data is transmitted over a bundle of twisted copper pair linking the source and the destination and hence, allows for processing to be performed at both the transmitter and receiver

The SVD method decomposes the channel matrix as

fol-lows:

Hk =UkΛkV† k ,

whereUk andVk are unitary matrices, and Λk is a diagonal

matrix with non-negative real numbers The goal is to have Λk

be the effective channel Hence,Vkis used for pre-coding and

Uk for cancellation

The pre-coding matrix pre-multiplies the data vector ˜xk

with Vk Similarly, the cancellation matrix post-multiplies

the received signal vector yk with U† k This results in the

following received signal vector after cancellation:

˜

yk =U† kyk

=U†

k(Hkxk+zk)

=U† kHkxk+U† kzk

=U† kHkVkx˜k+U† kzk

= Λkx˜k+U†

kzk

The effective channel through the SVD decomposition method

is Λkand hence, is crosstalk free SinceU† kis unitary, the new

noise vectorU† kzk remains white The resulting bit-rate under

the SVD decomposition method is given by:

b n

k = log2



1 + 1 Γ

|[Λ k](n,n) |2s n

k

σ n k



.

D Downstream and Upstream Zero-Forcing

The row-wise and colomn-wise diagonal dominance of the

DSL channel in downstream and upstream transmission results

in ZF being optimal [10], [12] The bounds on the

near-optimality were further investigated in [18] and a tight rate

approximation was produced in [19] In cases where the noise

at each user is correlated (e.g., the non-cancelled crosstalk

from ADSL users), the upstream ZF will amplify the noise

at the receiver In these cases, the use of the non-linear DFC

may be more appropriate Yet, the linear and the near-optimal

properties make zero-forcing a good and simple algorithm

for many vectoring cases Moreover, it lends itself to partial

crosstalk cancellation (covered in Section VI)

IV VECTOREDDSL DATA-RATE The data-rate increase of Vectored DSL is apparent using

either measured channel data and channel models On one

hand, measured channel data confirms the ability for Vectored

DSL to meet higher data-rate demands and shows how well

the channel model can predict true data-rates On the other

hand, the use of channel models allow for simple evaluation

of the potential throughput gains of Vectored DSL in various

scenarios

The channel model used is the American National Standards

Institute (ANSI) model which is an empirical model for

generating the direct and crosstalk channel gains based on

the 99% worst-case That is, 99% of the time, the direct and

crosstalk gains will be better than the ones generated using the

model Although this model remains pessimistic, it is suitable

for generating custom test cases Unless mentioned otherwise,

a 26-AWG gauge wire is assumed when using this model

−140

−120

−100

−80

−60

−40

−20 0

Frequency (MHz)

ANSI direct gain ANSI crosstalk gain

Fig 3 Channel gains from the ANSI model and from measured data for 25 500-m users sampled at every 100 frequency tone.

Three types of illustrative examples are provided in this section The first involves measured data and focuses on the case where all lines are 500 m and all use the ZF diagonalizing precoder bit-rate (5) to calculate the downstream performance and the ZF precoder bit-rate (11) for upstream performance While the lengths of lines within a DSL network can vary, FTTN networks typically consist of lines up to 500

m Hence, the 500-m measured data case provides a realistic assessment of a typical FTTN network The second illustrative example makes use of channel models in order to evaluate the performance of scenarios involving equal length users,

at varied line lengths Finally, the third illustrative example focuses on the most common case of unequal line lengths, using channel models

The measured data was taken by Morawski, Ho-Van, and Zhao, in the Broadband Communications Research Laboratory

at McGill University The setup consisted of 25 500-m long 26-AWG twisted copper pairs bundled together The channel gains (i.e., direct and crosstalk) and the background noise were measured for each line

The comparison between the ANSI model and the measured data can be observed in Fig 3 for the direct and crosstalk channel gains Fig 4 shows the measured background noise for both upstream and downstream transmission directions

A 500-m Performance Using Measured Data

For the 25-user 500-m measured data, the achievable rate

is calculated using a flat transmit PSD scheme for both non-vectored and non-vectored transmission A total transmit power

of 11.5 dBm per user is used for upstream and downstream transmission For vectored transmission, the ZF method is used with an effective flat PSD Fig 5 shows the achievable rate in the upstream direction for each of the 25 users Similarly, Fig 6 shows the achievable rate for each user in the downstream direction In both transmission directions, the Vectored DSL gain is clear and shows that vectoring increases the data-rate for each user by around 50%

0 2 4 6 8 10 12 14 16 18

−150

−145

−140

−135

−130

−125

−120

Frequency (MHz)

−140 dBm background noise Noise profile upstream Noise profile downstream

Fig 4 Background noise PSD of -140 dBm/Hz compared to the measured

background noise PSD in the 25 500-m users setup sampled at every 100

frequency tone.

0

5

10

15

20

25

30

35

User #

Flat PSD Non−Vectored

Fig 5 Achievable upstream rate for each user using the 25 500-m user

measured data.

B Performance Using Channel Model

While using measured data provides realistic assessments

of the performance, it is far more difficult to obtain measured

data for generalized scenarios (i.e., varied line lengths) As

such, in order to investigate the performance of scenarios for

various line lengths, ANSI channel models are used

When using the ANSI channel models, the channels become

symmetrical and identical for all users with identical line

lengths Thus, the resulting data-rates will be identical for

each user if the same parameters are used Hence, instead

of showing the data-rate for each user at a given distance, we

show the achievable data-rate per user at various line lengths

Fig 7 shows the achievable rate in the upstream direction

for various lengths of a bundle of 25-users Similarly, Fig 8

shows the achievable rate in the downstream direction The

vectored gain is quite remarkable when the length is within

500 m This coincides with the measured data performance

gains discovered in Section IV-A At long distances, the direct

0 20 40 60 80 100 120

User #

Flat PSD Vectored Flat PSD Non−Vectored

Fig 6 Achievable downstream rate for each user using the 25 500-m user measured data.

0 10 20 30 40 50 60 70 80 90 100

Distance (m)

Flat PSD Vectored Flat PSD Non−Vectored

Fig 7 Achievable upstream rate per user in a 25-user setup over different lengths.

and crosstalk channel gains are so low that removing crosstalk does not have any substantial benefit This can be particularly observed in the upstream transmission at lengths above 1000

m This further reinforces the benefits of DSL with respect

to length and further justifies the adoption of the FTTx type network topologies

Comparing the results from the measured case to the channel model, we see that the measured non-vectored rates are slightly better than predicted by the rate-reach results This

is due to the rate-reach results using the more pessimistic 99% worst-case model On the other hand, the vectored rates are slightly worse than predicted by the rate-reach model This is because as crosstalk is cancelled, the background noise becomes main interferer, and because the measured background noise is greater than that used by the empirical model in the better low-frequency downstream and much greater in the upstream bands, as shown in Fig 4

0 500 1000 1500

0

50

100

150

200

250

Distance (m)

Flat PSD Vectored Flat PSD Non−Vectored

Fig 8 Achievable downstream rate per user in a 25-user setup over different

lengths.

C Near-Far Case

The previous two Vectored DSL performance assessments

only give an insight on its gains when every user has the

same line lengths However, scenarios like binder C in Fig 1

are very common, where a near-far effect can be observed

Fig 9 and Fig 10 show the gain of vectoring over one

implementation of binder C for upstream and downstream

transmissions, respectively In this implementation, there are

25 users with uniformly distributed lengths between 500 and

1000 m One can observe that the most important gain is on the

far users (with longer line lengths) in the upstream direction

This is because the far users no longer receive large crosstalk

from the near users; without vectoring, the far users would

receive large amount of crosstalk from the near users

It is interesting to note that the performance gain increase

per-line is dependent on each user’s own line length, regardless

of whether or not all lines are of equal length This is due to the

fact that once the crosstalk has been removed, it is as though

each line is operating independently Hence, a performance

increase of at least 50% should be expected for non-equal

line lengths as well, depending on the amount of crosstalk

present in the system prior to vectoring

V VECTOREDDSL IMPLEMENTATION

This section discusses practical implementation issues

re-garding Vectored DSL and discusses some potential solutions

A Vectoring Types

A DSLAM services up to 192 or 384 or more customers

depending on the size of the shelf [1] Within each DSLAM

are line-cards, each consisting of 24, 48 or more lines (or

pairs) [1] Vectored DSL can be performed in one of two

vectoring modes: DSLAM level or line-card level vectoring

[1] (also referred to as NodeScale or LineCard vectoring by

[20]) DSLAM level vectoring performs joint vectoring across

all line-cards in a particular DSLAM, while line-card vectoring

applies vectoring separately for each line-card and treats the

crosstalk generated by other line-cards as noise Intra-line-card

0 10 20 30 40 50 60

User #

Flat PSD Vectored Flat PSD Non−Vectored

Fig 9 Achievable upstream rate for each user in the 25-user near-far scenario The line length for each user increases from user #1 towards user

#25.

0 20 40 60 80 100 120

User #

Flat PSD Vectored Flat PSD Non−Vectored

Fig 10 Achievable downstream rate for each user in the 25-user near-far scenario The line length for each user increases from user #1 towards user

#25.

crosstalk (i.e., within the same line-card) is typically 8-10 dB larger than the line-cards crosstalk; however, the inter-line-card crosstalk still provides significant coupling

DSLAM level vectoring mode has the potential to partially

or fully cancel the crosstalk in the entire DSLAM, leading

to significant rate improvements at a high computational cost Line-card level vectoring provides a small rate increase; however, its computational complexity is significantly reduced

as compared to that of DSLAM level vectoring

An alternative to full DSLAM level vectoring or line-card level vectoring is to applying vectoring across the dominant sources of crosstalk Typically, there are only a handful of dominant crosstalk sources limiting the system performance

If the dominant crosstalk signals are suppressed using vec-toring, then the only weaker crosstalk signals would remain Clearly, optimal performance is achieved by cancelling all the crosstalk signals [21]; however, often simply suppressing the the strongest crosstalk signals is sufficient to achieve close

to optimal performance for both DSLAM level vectoring