Int. J. Communications, Network and System Sciences, 2010, 3, 477-482
doi:10.4236/ijcns.2010.35064 Published Online May 2010 (http://www.SciRP.org/journal/ijcns/)
Research on Access Network Intrusion Detection System
Based on DMT Technology
Lingxi Wu, Jie Zhan, Qiange He, Shuiyan He
Hunan University of Science and Technology, Xiangtan, China
Received January 19, 2010; revised March 1, 2010; accepted April 7, 2010
Abstract
Analysis is done on the inter-carrier interference (ICI) that caused by multi-carrier communication system
frequency offset. The application model of DFT/IDFT in ADSL access network is analyzed further; the
hardware detection and software analysis scheme of the system are proposed for the accessing network. Ex-
periments have proved that monitoring system can filter the network data flow and carry on statistical and
analysis, achieving real-time monitoring.
Keywords: DMT, ICI, Intrusion Detection, DFT/IDFT
1. Introduction
The Discrete Multi-Tone DMT () technology has been
applied successfully on the ADSL (Asymmetric Digital
Subscriber Line) transmission system, and has developed
the broadband transmission system that based on Twist-
Pair. The problems of network detection and monitoring
will be inherent in the development of network, yet the
rapid development of the network has been ahead of the
real-time monitoring. To solve it, data detection system
based on DMT technology has been studied systemati-
cally, and data acquisition equipment has been devised,
which can achieve filtering analysis and statistics of the
network data stream with no influence on the user and
the phone company end of the line.
2. Multi-carrier Communication System
Modeling
QAM (Quadrature Amplitude Modulation) is the basis of
DMT, Model use multiple QAM constellation diagram
encoders, and each constellation diagram encoder use a
different carrier frequency, The DMT code element that
were formed by summing all the carries transmitted
through the channel. If the receiver can separate sine
waves from cosine waves on different frequencies, each
wave can be decoded independently, the method of en-
coded and decoded are consist with the QAM signals; to
ensure no interference from f1 to fn sub-channel, we must
make sure that a sine and cosine wave in one sub-chan-
nel are orthogonality with any other sub-channels, and its
formula is as follow [1,2]:
0cos() cos()0
Tnt mtdt
 

0cos( )sin()0
Tnt mtdt
 

0sin( )sin()0
Tnt mtdt
 

n and m are unequal integers, and ω is the base rate.
By the expression of orthogonality, we concluded the
each sub-channel frequency must be an integral multiple
of base frequency, and the code element period T is re-
ciprocal of the base frequency or an integral multiple of
the reciprocal of the base frequency. Two situations wo-
uld appear: First, the frequency offset is an integral mul-
tiple of sub-carrier; second, the frequency offset is not an
integral multiple of sub-carriers; both of two situations
will make system characteristics deteriorate. Assuming
the number of carrier is limited, Figure 1 is a block diagram
of a DMT communication system model [3], and ac-
cording to the system, we make the following discussion:
During the ‘i’ symbol cycle, Assuming the original
data symbol is｛a0,i, a1,i ,…, an-1,i｝, after IDFT calculate, we
can get:
1
,,
0
12
exp
N
ki li
l
jlk
ba
NN






 (1)
Therefore, we can get the output signal x(t) as follow:
1
,
0
x( )exp(2)
N
cki
k
kT
tjftbpt
N







 (2)

L. X. WU ET AL. 478
x
(
t
)
h(t)
exp(-j2π( f
c
+ Δf ) t )
ADC
and
BPF
z
N-1，i
z
0，i
b
0，i
a
0，i
b
N-1，i
a
N-1，i
y
N
1
i
y
0，i
y(t)
n-point
DFT
high-speed
Data stream split into
low speed
Data stream
N-point
IDFT
parallel/serial
conversion
DAC
and
LP F
Serial/parallel
Conversion
n( t )
0,i
a
0,i
b
1,
N
i
a
1,
N
i
b

exp( j2)
c
f
t

exp(j2() )
c
f
ft



0,i
Z
0,i
y
1,
N
i
Z

1,
N
i
y
()nt
Figure 1. Multi-carrier communication system modeling.
fc represent the carrier frequency, p(t) represent the im-
pulse response of low-pass filter used in the transmitter
system, but there is the frequency deviation Δf at the re-
ceiving end, after down-conversion and low-pass filter
the y(t) signal is :
1
0,
0
()exp( 2)
N
cki
k
kT
ytjftbq tN




 


 (3)
q(t) represent the combination impulse response get by
multiplying low-pass filter of the transmitter and band-
pass filter of the receiver, θ0 is the phase difference be-
tween receiver local oscillator and RF carrier. If q(t) can
meet the Nyquist criterion at the moment kT/N, then we
sample y(t) at the same time.
We can get:
0
,,
2
exp( )exp
ki ki
jfkT
yjb N






(4)
According to the DFT formula,
1
,,
0
2
exp, (0,1,,1)
N
mi ki
k
jkm
Zym N
N




 


 (5)
Substituting (1) and (4) into (5), we can get:
11
,0,
00
12()
exp( )exp
NN
mi li
lk
jklm fT
Zja
NN








 (6)
According to the sum formula
1
0
Nk
k
u


=1
1
N
u
u

, (1-6)
can be simplified:
 

1
,0,
0
1exp 2
1exp( )2
1exp
N
mi li
l
jlmfT
Zja
NjlmfT
N















(7)
From:
1exp( 2)[exp()exp()]exp()
2sin exp()
jjjj
jj





 (8)
Make:


1lm fT
 


2
lm fT
N



,
(8) can be express as follow：
1
11
,0,
022
1
1
0,12
02
2sin exp() 1exp( )()
2sin exp()
sin 1exp()exp( ())
sin
N
mi li
l
N
li
l
jj
Zja
Njj
ja j
N














1
,0,
0
exp( )
N
mililm
l
Z
jac 



 (9)
Among of them,
1sin(())(1)( )
exp
()
sin( )
lm
lm fTNlm fT
cj
lm fT
NN
N



 




 

(10)
0
1 sin()1
=exp
sin( )
f
TN
cjfT
fT
NN
N









(11)
c0, c1, …, cn-1 are complex weighting coefficients, corre-
sponding to input data symbols 0. 1,1, ,,,
ii ni
aa a

 , then
we can get the symbols transmitted in mth sub-channel as
follow (N is the number of coefficients):
1
0
,,
0
exp( )
N
milmli
l
Z
jca 




1
00
0, ,
0
exp( )exp( )
N
mil mli
l
lm
jcaj ca 





 (12)

L. X. WU ET AL. 479
The first item of the formula is data symbol of weig-
hted mathematical expectation, the second item is the ICI
caused by Δf. If Δf = 0, then Zm,i = exp(jθ0) am,i, (m = 0,
1,…,N – 1). Note: Each complex symbol will be influ-
enced by the phase deviation factor θ0. If Δf ≠ 0, the in-
ter-channel interference (ICI) will occur. Figure 2 shows
the relationship between the real part, imaginary part,
modulus of the complex weighting coefficient and the
sub-carrier number N in case of the two kinds of Δf T.
When the frequency deviation increases, the stable zone
quickly narrows, the modulus value rapidly increases,
indicating ICI increases significantly
3. ADSL System Based on Multi-carrier
Technology
According to the model [3,4], assume T is the cycle, we
derive the waveform expression that added up sine and
cosine waves :
Xcos()Ysin()0
() 0
nn
ntntt T
St else
  

 (13)
The waveform shows the influence that a single sub-
channel n operate on DMT code element, according to
Nyquist theorem, sampling the signal, sampling frequ-
ency is 2Nf, sampling value is:
Xcos()Ysin()
22
Xcos()Ysin()021
Kn n
nn
kk
Sn n
Nf Nf
nknk kN
NN



 
(14)
Make the Discrete Fourier Transform (DFT) to these
2N points as follow:
21 2/2
0
// //
21
0
/
Xcos()Ysin()
XY
22
(XY)
(XY)2-
0
NjmkN
mn n
k
jnk Njnk Njn k Njn k N
N
nn
k
jmkN
nn
nn
nk nk
Se
NN
ee ee
j
e
Nj mn
Nj mNn
else

 























 





(15)
From (14) and (15), we conclude that the output can
be mapped to a complex number by making DFT to the
signal, the value of encoder X-axis (cosine amplitude)
represents the real part of the complex number, the value
of Y-axis (sine amplitude) represents the imaginary part
of the complex number, then it is a way to generate DMT
code element. If make Inverse Fourier transform to Sm,
we can deduce Sk:
21 2/2
0
/(2)/
1
2
1(XY )(XY )
2
1(XY)(cos()sin ())
2
(XY)(cos()sin())
Xcos() Ysin()021
NjmkN
Km
m
jmkNjN nkN
nn nn
nn
nn
nn
SSe
N
je je
nk nk
jj
NN
nk nk
jj
NN
nknk kN
NN











 



 



 




(16)
real
lmag
abs
real
lmag
abs
0.8
0.6
0.4
0.2
0
-0.2
0.8
0.6
0.4
0.2
0
-0.2
-15 -10 -5 0 5 10 15
deltaf T = 0.1 deltaf T = 0.3
Weighted coefficient Weighted coefficient
-15 -10 -5 0 5 10 1
5
Figure 2. Carrier frequency deviation and synchronization features.

L. X. WU ET AL. 480
The DMT modem can be achieved with DFT and
IDFT. From (13) it can be derived the complex number
N(Xn - jYn) to the n th sub-channel, express that a com-
plex number can represents a sub-channel of DMT, N
sub-channels have N complex numbers, plus N conjugate
complex numbers (Xn + jYn), we can get 2N complex
numbers, from (14) ,we can get Sk through making IDFT
to 2N complex numbers. So we can get DMT modulation,
demodulation program, this program has been applied to
ADSL modem. In the ADSL, ATU-C downstream
modulator uses 256 windows, which is 256 complex
numbers, the interval of windows is 4.1325 kHz. Fre-
quency range is from 4.3125 kHz to 1.104 MHz, accord-
ing to code analysis, the IDFT of downstream DMT can
be expressed as:
511 /256
0
,0, ,511
jmk
Km
m
SSe k



 (17)
Sm is the complex number value or expanded conjugate
complex number made by QAM constellation encoding
for each sub-carrier, Sk is the time-domain sample sequ-
ence after DMT modulation, and the time-domain wave-
form can be generated after parallel-serial conversion
and DAC.
The upstream DMT modulation of ATU-R uses 32
windows, 32 complex numbers represent the coding re-
sults of each sub-channel constellation, the audio interval
is 4.3125 kHz, frequency range from 4.3125 kHz to 138
kHz. According to the code analysis that the DMT of
IDFT in the upstream can be expressed as:
63 /64
0
,0,,63
jmk
Km
m
SSe k



 (18)
4. Research on Intrusion Detection System
The principle is shown in Figure 3. The structure of col-
lector mainly consists of the DSLAM Simulation Module
[5-7], Modem Simulation Module and Data Interface
Module and so on. The end of ADSL Modem accesses to
the DSLAM simulation module of data acquisition
equipment, the end of Telecommunications Bureau ac-
cesses to the ADSL Modem Simulation Module of data
acquisition. After the upstream signals input DSLAM
USB
CY7C68001 Data Interface
Module
FPGA
MTC MTC
Driver Driver
POTS
splitter
POTS
splitt er
XTAL XTAL
Memor
y
Memor
y
Modem
Simulation
Module
DSLAM
Simulation
Module
the Central office
end-user
UTOPIA CTRL_E UTOPIA CTRL_E
Figure 3. Hardware block diagram of data acquisition system.

L. X. WU ET AL. 481
database
file 、data、packet processing
and data output
data analysis layer
Protocol Analysis
datagram
IP data segment
（Telnet、FTP、HTTP、SMTP、POP、IP Phone etc.）
application protocol analyzer layer
（TCP，UDP）
Transmission protocol analyzer layer
（IP、ICMP、ARP etc.）
Internet protocol analyzer layer
SIGNAL ACQUIRING DEVICE
IP datagram
file data、audio data、
Web data、mail data
user data
data segment
UDP datagram
A
pplication data
Data Processing data acquisition
database
data analysis layer
file、data、packet processing
and data output
file data、audio data、
Web data、mail data
user data
(Telnet、FTP、HTTP、SMTP、POP、IP Phone etc.)
application protocol analyzer layer
Application data
(TCP、UDP)
Transmission protocol analyzer layer
UDP datagram
IP data segment
(IP、ICM P 、ARP etc.)
Internet protocol analyzer layer
IP datagram
SIGNAL ACQUIRING DEVICE
IP data segment
Data Processing
UDP datagram
Protocol Analysis Data acquisition
Figure 4. System software descriptions.
simulation module, we complete DMT demodulation and
send the demodulated signal to the interface module,
then send to the computer by USB interface. Meanwhile,
the upstream signal is also sent to the ADSL Modem
Simulation Module, complete the transmission of up-
stream data to Telecommunications Bureau. After down-
stream signals input the ADSL Modem Simulation Mod-
ule, we complete DMT demodulation and send the de-
modulated signal to the interface module, and then send
to the computer through USB interface. Downstream sig-
nal is also sent to DSLAM Simulation Module, and
complete the transmission of downstream signal to the
user. The normal signals of consumer are connected di-
rectly with the dedicated POTS access between the two
simulation modules. So, the device joined Telecommu-
nications Bureau and user ADSL Modem, it will not af-
fect the user’s normal voice and data communications,
both of them are not aware of the existence of the device.
Through the UTOPIA interface [8,9], we extract the cell,
and encapsulate the cell to get USB packets, and transmit
to the computer through the USB interface to analyses
the data, the process includes two parts (data processing
and protocol analyzer), in order to restore the data effec-
tively and accurately from the obtained data, we must
make out the software , according to the system request
the software hierarchy is shown in Figure 4.
5. Conclusions
The distance of data transmission on the Twist-Pair is
limited, and the variety of circuit characteristics will af-
fect the status of circuit connection which may cause
normal users can’t explore the Internet, Meanwhile net-
work data transferring is bidirectional and the upstream
and downstream data transferring are asymmetry that
makes a great deal of difference from other wired or
wireless audio and video signal transmission. In this pa-
per, the data acquisition system is a data receiving sys-
tem. In process of the upstream and downstream data
processing, there are several technical difficulties in data
extraction, separation, storage, etc, and our program can
solve these problems well. It brings new solutions to the
data acquisition system for detecting network data tra-
nsmission and eliminating network failure, particularly it
can solve the problems of monitoring the real-time.
6. Acknowledgements
This paper is supported by Natural Science Foundation

L. X. WU ET AL. 482
of Hunan Provincial, China (Grant No. 07JJ6128).
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[4] “ITU-T Recommendation G.992.3, Asymmetric digital
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[5] J. Heinanen, “RFC1483: Multi-protocol Encapsulation
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