Digital Subscriber Line (DSL) deployment is evolving to ever higher bit rates resulting in the use of broader spectra. The DSL flavor using the broadest spectrum today is known as VDSL. The reach performance of VDSL is upstream limited as the upstream bands use the highest frequencies. These high frequencies experience more channel attenuation, resulting in smaller SNR values. In this contribution, a way of increasing the upstream reach performance is described. After investigating the VDSL transceiver, the reach performance of a VDSL modem is identified to be dominated by the echo power. Therefore, limiting the downstream echo yields a better upstream receive signal. This results in trading off downstream bit rate for more upstream bit rate. The way to optimally limit the echo isderived and high performance gains can be achieved. Finally, the optimal solution is approximated with a near optimal solution with considerably less complexity. The near-optimal solution performs very well compared to the optimal solution

Cendrillon, Raphael

Moonen, Marc

Van Acker, Katleen

Van den Bogaert, Etienne

Verlinden, Jan

University of Queensland eSpace

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E. Van den Bogaert, K. Van Acker and J. Verlinden are with the Research & Innovation Department 
of Alcatel, Francis Wellesplein 1, B-2018 Antwerpen, Belgium 
phone: +32 3 2407689. Fax: +32 3 2404886,  
{etienne.van_den_bogaert, katleen.van_acker, jan.vj.verlinden}@alcatel.be 
R. Cendrillon and M. Moonen are with the ESAT/SCD Department of the Katholieke Universiteit 
Leuven, Kasteelpark Arenberg 10, B-3001 Heverlee (Leuven), Belgium 
{raphael.cendrillon, marc.moonen}@esat.kuleuven.ac.be 
 
 
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Digital Subscriber Line (DSL) deployment is evolving to 
ever higher bit rates resulting in the use of broader spectra. 
The DSL flavor using the broadest spectrum today is 
known as VDSL.  
The reach performance of VDSL is upstream limited as 
the upstream bands use the highest frequencies. These 
high frequencies experience more channel attenuation, 
resulting in smaller SNR values. In this contribution, a 
way of increasing the upstream reach performance is 
described. 
After investigating the VDSL transceiver, the reach 
performance of a VDSL modem is identified to be 
dominated by the echo power. Therefore, limiting the 
downstream echo yields a better upstream receive signal. 
This results in trading off downstream bit rate for more 
upstream bit rate. The way to optimally limit the echo is 
derived and high performance gains can be achieved. 
Finally, the optimal solution is approximated with a near-
optimal solution with considerably less complexity. The 
near-optimal solution performs very well compared to the 
optimal solution. 
 
. 


Digital Subscriber Line (DSL), VDSL, waterfilling, 
echo limitation, spectrum management. 
 
 
 ,1752'8&7,21
 
The new xDSL flavors are the answer to an increasing 
demand for higher bit rates. Such high bit rates can be 
achieved by, on the one hand, increasing the quality of the 
signal at the receiver and, on the other hand, by using 
broadband spectra. This resulted in the use of frequencies 
as high as 12 MHz as defined in the VDSL standards [1], 
[2]. With VDSL, data rates as high as 52 Mbps can be 
achieved enabling a broad range of applications such as 
video-conferencing, on line education and video on 
demand. 
VDSL systems are designed as Frequency Division 
Duplex (FDD) systems. Downstream and upstream have 
separated frequency bands. The standards have adopted 4 
different frequency bands with the higher bands allocated 
for upstream. This means that for relatively long loops, the 
upstream will suffer more from the loop attenuation. The 
VDSL reach performance is thus upstream limited. 
Looking to VDSL transceivers, the design is focused 
on flexibility for the frequency band allocation. The VDSL 
transceivers are desired to support various band plans 
within one system. The result is that no analog filtering 
occurs in the frequency range starting from 138 kHz up to 
12 MHz, which means that no analog filters separate 
upstream from downstream. The drawback of this flexible 
implementation is the echo sensitive behavior of VDSL. 
Indeed, the echo PSD is attenuated by the hybrid only, 
resulting in an attenuation of the echo with only 12 to 20 
dB. The incoming echo power is therefore the dominant 
input power at the receiver. 
The sensitive behavior towards echo can be explained 
by the fact that VDSL signals have a large Peak-to-
Average Ratio (PAR). The Analog-to-Digital Converter 
(ADC) has a limited voltage range and a limited bit 
precision, which results in a Crest factor, the ratio between
max9  of the ADC and   9  of the incoming signal. 
Therefore, an LNA is implemented to amplify the 
incoming signal to match the desired input power at the 
ADC. As a result, the higher the echo power, the lower the 
gain of the LNA which results in a low far-end signal 
amplification.  
In this document, the behavior of the SNR is studied in 
function of the echo power and a simple equation is 
derived to optimize the overall downstream and upstream 
bit rate. The aim is to increase the reach of VDSL 
deployment by increasing the upstream bit rate. 
The optimal transmit PSD allocation is derived for 
increasing reach performance. When applying this scheme 
for long loops, it results in an optimal power back-off 
equation for downstream transmit PSD. Simulations show 
a high increase in bit rates for the upstream direction, 
resulting in a much better reach performance. 
Finally, the optimal power back-off scheme is 
approximated with a near-optimal solution. The near-
optimal solution has the advantage to be less complex and 
furthermore, simulations show a small performance loss 
compared to the optimal scheme. 
 
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A simplified architecture of the analog front end is 
depicted in Fig. 1. In the transmitter, the digital signal 
coming from the FFT is converted in the Digital-to-Analog 
Converter (DAC). Once converted, the signal is amplified 
by the Programmable Gain Amplifier (PGA) to match the 
wanted PSD on the line. The hybrid is designed to 
separate the transmit signal going to the line from the 
receive signal coming from the line. Unfortunately, the 
hybrid has no perfect echo rejection such that a certain 
amount of echo mixes with the far-end signal. This signal 
is mixed in time domain, but frequency multiplexed. The 
far-end signal together with the echo is amplified by the 
Low Noise Amplifier (LNA) to match the  9  the ADC is 
designed for. The output of the ADC is feeding the FFT of 
the receiver. 
 
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The  9  of the signal at the ADC has to be as close as 
possible to the design input voltage of the ADC. The value 
of  9  can be calculated in the frequency domain and is 
given by (1). 
 
 ( )∑−
=
⋅=
12
0
2


	 
 N36'=9  (1) 
with Z being the real part of the input impedance of the 
ADC and k, the tone index. The Nyquist frequency is 
given by tone index K. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Fig. 1   Simplified VDSL analog front-end 
 
 
As Z is fixed with the design, 29  is proportional to 
the sum over the frequencies of the input PSD at the ADC. 
The input PSD is made out of signal, noise and echo. 
From (1) one knows that the larger the echo, the lower the 
LNA may boost the incoming signal. The Analog Front- 
End (AFE) is designed to introduce low noise compared to 
the quantisation noise of the ADC, increasing the gain of 
the LNA increases thus the Signal-to-Noise Ratio (SNR). 
This results in a higher bit rate. The solution is then to 
apply power back-off at the near-end to lower the echo 
enabling an LNA boost. 
 
& 9'6/EDQGSODQ
 
The standard VDSL band plans [1] are designed with the 
first band corresponding to a downstream band. From Fig. 2 
one can see that VDSL is upstream limited as the line 
attenuation increases with frequency. A solution for 
increasing the reach is to boost the upstream PSD and to 
apply downstream power back-off. This study only focuses 
on downstream power back-off. 
 
 
 
 
 
 
 
 
Fig. 2   ANSI VDSL band plan 998 
DAC 
PGA  
 Hybrid    
LNA  
ADC 
From FFT  Towards FFT 
Towards line          
Dn     Up   Dn           Up             
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Consider one line and call the CO as modem 1 and the 
CPE as modem 2, define the downstream rate as R1, with 
transmit PSD S1 at the CO, and the upstream rate as R2, 
with transmit PSD S2 at the CPE. The purpose is to 
maximize the upstream rate while keeping the downstream 
rate above a particular target rate. This resumes to 
optimizing a weighted rate sum as shown in [5]. The sum 
of the weighted rates, using the Shannon formula, is given 
by (2). 
 
 
( )
( ) ( )
( )( )
( ) ( ) ( )( )( )∑
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 
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α
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(2) 
 
with ( )N6   the transmit PSD on tone k of modem L, 
( )N1 	  the noise PSD on tone k at modem L and ( )NK 
   the 
channel transfer function from the DAC of modem M to the 
input of the LNA of modem L. The PGA is included in the 
channel transfer function as shown in Fig. 3. The gain of the 
LNA of modem L is represented by K and 4  
represents the quantisation noise introduced by the ADC 
of modem L. 
 
 
 
 
 
 
 
 
Fig. 3   Transfer functions and additive noises 
 
Equation (2) shows that as long as ( ) 2  KN1 ⋅  is 
smaller than 4 , the gain of the LNA can be increased to 
increase the SNR. The AWGN on the line is much lower 
than the quantisation noise as, for ambient temperature, 
AWGN is theoretically equal to –173 dBm/Hz compared 
to the typical ADC noise floor of –140 dBm/Hz. In 
practice, the measured level of AWGN varies between  
–160 and –155 dBm/Hz [4]. In case FEXT has to be taken 
into account, FEXT is in general at least 20 dB lower than 
the far-end signal. This means that for the tones with the 
received signal PSD more or less 12 dB higher than the 
quantisation noise, resulting in a 1 bit loading, the FEXT 
noise is at least 8 dB below the quantisation noise. This 
means the LNA can boost the signal without increasing the 
noise substantially, which results in a better SNR. 
The gain of the LNA can be found by applying the 
power restrictions at the input of the ADC given by (3) 
 
 
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222
=
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(3) 
 
with ( )NK & &  corresponding to the echo transfer function at 
modem L, from the DAC up to the input of the LNA, on 
tone k. '(*),+3  represents the maximum input power of the 
ADC of modem L. Looking at (3), the LNA gain is closely 
related to the transmit power of both modems. For long 
lines the echo mostly dominates the input power at the CO. 
If the echo power changes, the LNA gain will have to 
scale to achieve the optimal input power at the ADC. 
 
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Equation (3) can be approximated by (4) as for long lines, 
the attenuation of the far-end signal is much higher than 
the attenuation of the echo. The echo power is thus much 
larger than the far-end power and the noise on the line.  
 
 ( ) ( )[ ] -- ./!0
1
2 22
34
. 3NKN6K ≈⋅ ∑ 22  (4) 
 
Using the Lagrange multipliers to take the ADC power 
restriction into account gives us the cost function (5). 
 
 
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2
222
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111
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22
11
λ
λ
(5) 
 
The goal is to maximize this cost function. The derivative 
of this cost function should then be equal to zero. The 
derivative to ( )N61  equals 
 
 ( ) ( ) ( ) 0
2
11
2
1
11
1
=−
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∂
=
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N6
5
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with  
 
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signal 
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( ) ( ) ( ) ( )2ln12212 22
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K
4
N1
NK
N6
5
 
(7) 
 
which finally yields 
 
 
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( )
( )
( )
( )
( )NK
K
4
N1
N
NK
K
4
N1
NKK
N6
	
	
	
2
21
2
2
2
2
21
2
2
2
2
11
2
1
1
2
2
1
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1




+
Γ−=




+
Γ−



=
β
α
λ (8) 
 
The optimal downstream power back-off resumes to a 
ZHLJKWHGZDWHUILOOLQJ solution as can be seen from (8). A 
similar formula can be found for ( )N6 2 . 
As for VDSL the reach performance is upstream 
limited, our goal is to transmit at maximum PSD for the 
upstream and to shape the downstream PSD in order to 
achieve better reach performance. The shape of the 
downstream transmit PSD is given by (8). 
 
% 6LPXODWLRQUHVXOWV
 
Fig. 4 shows the simulation results for the rate-reach 
performance when the downstream transmit PSD is 
reduced by applying weighted waterfilling. The two upper 
curves represent the downstream rate-reach performances. 
The most upper curve shows the downstream rate when no 
power back-off is applied and the second most upper 
curve shows the downstream bit rate when power back-off 
is applied. The latter results in an upstream rate increase as 
shown by the two lowest curves. As can be seen from the 
figure, even for relatively short loops a large increase in 
bit rate can be achieved for upstream, as long as the target 
bit rate for downstream is achieved. This scheme offers the 
possibility to increase the reach for particular services. 
The simulation results show that for very short loops the 
approximation of (4) does not hold. Indeed, for very short 
loops, the echo power is not the dominant power at the 
input of the ADC. Reducing the echo will therefore not 
induce any significant performance gain. 
 
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%$&.2))
 
Equation (8) shows the frequency dependency of β(k), the 
weighted waterfilling level. This weighted waterfilling 
level is inversely proportional to the squared echo transfer 
function as given in (9). 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Fig. 4   Reach performance increase with the optimal DS transmit PSD 
reduction 
 
 ( ) ( )NKN 211
1
~β
 (9) 
 
Downstream power back-off depends therefore on the 
frequency behavior of the echo transfer function. On 
frequencies with larger echo attenuation, less power back-
off has to be applied. This frequency dependency 
increases the complexity, as for each frequency a different 
power back-off value has to be computed. A simplified 
solution is introduced here and the reach performance is 
compared with the optimal solution for downstream power 
back-off. 
The frequency dependency of β(k) is only due to the 
frequency dependency of the echo transfer function. As the 
echo transfer function varies only between more or less 12 
and 20 dB, a good approximation is to take only into 
account the average of the echo transfer function. It gives 
a constant waterfilling level βc over the entire bandwidth 
equal to  
 
 ( )2ln
1
2
_11
2
1 1
α
λ
β






KK
=  (10) 
 
where K
_11  represents the average echo transfer 
function 
 
Applying downstream power back-off by implementing 
waterfilling is nearly optimal in DSL channels. This 
solution makes it possible to implement downstream 
power back-off with a simple transceiver algorithm. 
Simulation results are shown in Fig. 5. The figure 
shows also the performance of the optimal scheme. From 
0 200 400 600 800 1000 1200 1400 1600 1800
0
10
20
30
40
50
60
70
80
Reach [m]
Bi
t r
at
e 
[M
bp
s]
DS Power Back−Off with AWGN
DS without DS PBO
US without DS PBO
DS with weighted DS PBO
US with weighted DS PBO
the figure one can see that the difference in reach 
performance is negligible.  
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Fig. 5   Comparison between the optimal and the near optimal power 
back-off 
 
 &21&/86,21
 
This study focuses on the optimal power allocation for 
improved rate-reach VDSL performance. Upstream and 
downstream channels are impacting each other due to the 
echo leakage at both CO and CPE. The study starts from a 
simplified analog front-end and a general bit rate 
optimization is derived. As the VDSL reach performance 
is upstream limited, the results of optimal power allocation 
can be used to improve reach performance by improving 
the upstream bit rate. This is achieved by trading some 
downstream bit rate for upstream bit rate. Looking at the 
optimal power allocation for downstream, it turns out to be 
a weighted waterfilling with frequency dependency. 
Furthermore, a simplified, near-optimal solution is 
presented with much less complexity. The frequency 
dependency of the weighted waterfilling is averaged out 
over the frequencies such that the near-optimal solution 
becomes traditional waterfilling. The reach performance of 
the near-optimal solution is comparable to the optimal 
solution. 
 
5
   
	 

 
[1] “Very-high bit-rate Digital Subscriber Lines (VDSL) Metallic 
Interface, Part 3: Technical Specification of a Multi-Carrier 
Modulation Transceiver,” ANSI Std. T1E1.4/2002-099, 2002. 
[2] “Very high speed Digital Subscriber Line (VDSL); Part 1: 
Functional requirements,” ETSI TS 101 270-1 v1.2.1 (1999-10). 
[3] Leon W. Couch II, “Digital and Analog Communication Systems,” 
Prentice Hall . 
[4] T. Starr, M. Sorbara, J. M. Cioffi and Peter J. Silverman, “DSL 
advances,”. Prentice Hall Communications Engineering and 
Emerging Technologies Series. 
[5] R. Cendrillon, M. Moonen, J. Verlinden, T. Bostoen and W. Yu, 
“Optimal Multi-user Spectrum Management for Digital Subscriber 
Lines,” accepted to ICC 2004. 
0 200 400 600 800 1000 1200 1400 1600 1800
0
10
20
30
40
50
60
70
80
DS Power Back−Off with AWGN
Reach [m]
Bi
t r
at
e 
[M
bp
s]
DS with weighted DS PBO
US with weighted DS PBO
DS with waterfilled DS PBO
US with waterfilled DS PBO
 


Waterfilled VDSL Echo Limitation for Rate-Reach Performance Improvement

https://espace.library.uq.edu.au/view/UQ:9940/alcatel_echo.pdf

Waterfilled VDSL Echo Limitation for Rate-Reach Performance Improvement

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