TR-30.3/00-12-885B
F.1
Crosstalk
This section presents the rationale that corresponds to the determination of crosstalk signals
for evaluating xDSL communications systems.
F.1.1 Cable crosstalk models
F.1.1.1
Near end crosstalk, NEXT
Crosstalk noise that occurs when a receiver on a disturbed pair is located at the same end of the cable as
the transmitter of a disturbing pair is called Near-End-Crosstalk (NEXT).
F.1.1.1.1
Simplified NEXT model
The simplified NEXT model has loss values of 57 dB, 61.1 dB, and 67.1 dB for 49 disturbers, 10
disturbers, and 1 disturber, respectively, at a frequency of 80 kHz and a linear (log-log) slope of –15 dB
per decade. The simplified NEXT model is expressed by
NEXT f , n  S ( f )  X N  n 0.6  f 3 / 2
15
where X N  8.536  10 , n  number of disturbers, f  frequency in Hz, and S ( f ) is the power
spectrum of the interfering system.
F.1.1.2
Far end crosstalk, FEXT
Crosstalk noise that occurs when a receiver on a disturbed pair is located at the other end of the cable as
the transmitter of the disturbing pair is called Far-End-Crosstalk (FEXT). The FEXT model is expressed
by
2
FEXT[f , n, l ]  S(f )  H(f )  X F  n 0.6  l  f 2
where H (f ) is the magnitude of the insertion gain transfer function affecting the disturber signal,
X F  7.74  1021 , n  number of disturbers, l  the coupling path length in feet, f  frequency in Hz,
and S(f ) is the power spectrum of the interfering system.
The FEXT model assumes the insertion gain transfer function is computed for the total cable path
located between the interfering transmitter and the victim receiver. On the other hand, the coupling loss
is computed only over the coupling path length l . The coupling path length is the length of cable over
which the victim receiver and far-end disturbing transmitter have a common cable path.
F.1.1.3
FSAN method for combining crosstalk contributions from unlike types of disturbers
Instead of directly adding the crosstalk power terms, each term is first arbitrarily raised to the power
1/0.6 before carrying out the summation. Then, after the summation, the resultant expression is raised to
the power 0.6. This can be expressed as:
N

Xtalk  f , n   n i

i 1





N

  Xtalk f , n i 1/ 0.6 


 i 1

0.6
,
where Xtalk is either NEXT or FEXT, n is the total number of crosstalk disturbers, N is the number of
n
types of unlike disturbers and j is the number of each type of disturber. Example uses of this equation
are given in the following subsections.
F.1.1.3.1
Example application of two NEXT terms
Take the case of two sources of NEXT at a given receiver. In this case there are n1 disturber systems of
spectrum S1 (f ) and n2 disturber systems of spectrum S 2 (f ) .
The combined NEXT is expressed as:


3
0.6
NEXT f , n    S1 (f ) X N f 2 n1

F.1.1.3.2

1
0.6

 S (f ) X
2
N
f
3
2
n2
0.6

1
0.6



0.6
Example application of three FEXT terms
Take the case of three sources of FEXT at a given receiver. In this case there are n1 disturber systems of
spectrum S1 (f ) at range l 1 , a further n 2 disturber systems of spectrum S 2 (f ) at range l 2 and yet another
n 3 disturber systems of spectrum S 3 (f ) at range l 3 .
The expected crosstalk is built in exactly the same way as before, taking the base model for each source,
raising it to power 1/0.6, adding these expressions, and raising the sum to power 0.6:
1
1


  S1 (f )] H 1 (f ) 2 X F f 2 l 1 n10.6  0.6   S 2 (f ) H 2 (f ) 2 X F f 2 l 2 n 2 0.6  0.6






FEXT [f , n, l ]  

1
2
0 .6 
0.6

  S 3 (f ) H 3 (f ) X F f 2 l 3 n 3 





0 .6
F.1.2 Evaluating Crosstalk at the DUT’s in Connection Type 2
F.1.2.1 Definitions
Loop L: Loop under test connecting the two DUT’s and consisting of Loop L1 + Loop L2 as defined
below.
Loop L1: The part of Loop L before the intermediate crosstalk injection point.
Loop L2: The part of Loop L after the intermediate crosstalk injection point.
HNXLn(f): Near-end crosstalk transfer function of Loop Ln.
HFXLn(f): Far-end crosstalk transfer function of Loop Ln.
SCO(f): Single interfering signal at the CO injection point
SINT(f): Single interfering signal at the intermediate injection point
SCPE(f): Single interfering signal at the CPE injection point
SXCo(f): Total crosstalk seen by the CO DUT from single disturbers at the injection points
SXCPE(f): Total crosstalk seen by the CPE DUT from single disturbers at the injection points
HLn(f): transfer function of Loop Ln
ln: length of Loop Ln
n CO,K : number of crosstalk disturbers of type K at the CO injection point (from tables 1-26)
n CPE,K : number of crosstalk disturbers of type K at the CPE injection point (from tables 1-26)
n IN,K : number of crosstalk disturbers of type K at the INT injection point (from tables 1-26)
PSDCO,K: PSD mask of crosstalk disturber type K at the CO injection point
PSDCPE,K: PSD mask of crosstalk disturber type K at the CPE injection point
PSDINT,K: PSD mask of crosstalk disturber type K at the INT injection point
PSDX CO(f): Power Spectral Density (PSD) of the total crosstalk seen by the CO DUT
PSDX CPE(f): Power Spectral Density (PSD) of the total crosstalk seen by the CPE DUT
Nco: number of unlike disturbers at the CO injection point
Ncpe: number of unlike disturbers at the CPE injection point
Nint: number of unlike disturbers at the INT injection point
F.1.2.2 Simplified Connection Type 2 Diagram
The block diagram describing the basic configuration of a “Connection Type 2” loop is copied below:
Figure C5—Connection Type 2 – Remote Terminal
The above diagrams can be simplified to show the essential physical relationships between the devices
under test and single disturber sources at each of the injection points. Using the symbols defined earlier,
the simplified diagram is shown below:
Loop L
Loop L1
Loop L2
S INT(f)
S CPE(f)
S CO(f)
CPE DUT
DSLAM
DUT
Figure F1
F.1.2.3 Crosstalk Model for Simplified Connection Type 2 Diagram
The simplified diagram in Figure 1 allows us to model the crosstalk effects of single disturber sources on
the DUT’s in a type 2 connection as shown in the diagram below:
Interfering Intermediate
DSLAM Downstream
Signal (SINT)
HFXL2(f)
DUT CO
DSLAM


HL(f)
HNXL (f)
HNXL (f)
Interfering CO
DSLAM Downstream
DUT CPE
HFXL (f)
HFXL (f)
Signal (SCO)
Interfering CPE
Upstream Signal
(SCPE)
Figure F2
From this diagram, we can derive expressions for the crosstalk seen at the DUT’s from single disturber
sources as shown below*:
SXCo(f) = Sco(f)*HNXL(f)+ SCPE (f)*HFXL (f)
SXCPE(f) = SCPE (f)*HNXL(f)+ SCO (f)*HFXL (f) + SINT(f)* HFXL2 (f)
F.1.2.4 Extending the Model to Multiple Disturbers and Loop Segments
The expressions in section F.1.1 can be used to model the crosstalk transfer functions (using the loop
transmission transfer functions) and to extend the above model to accommodate multiple disturbers of
unlike types. Using the symbols defined earlier and applying the F.1.1 equations to the F.1.2.3
equations, the resulting expressions for the total crosstalk seen at each DUT are given below:
Expressions for Total Crosstalk at the CO: (note 1)
PSDXCO(f) = [ (K=1-Nco) (PSDCO,K(f)*XN *nCO,K 0.6 *f 3/2 ) 1/0.6 ] 0.6 +
[ (K=1-Ncpe) (PSDCPE,K(f)*HL(f)2*XF*nCPE,K0.6 *lL*f 2) 1/0.6 ]0.6
Expressions for Total Crosstalk at the CPE: (note 1)
PSDXCPE(f) = [(K=1-Ncpe) (PSDCPE,K(f)*XN *nCPE,K 0.6 *f 3/2 ) 1/0.6 ] 0.6 +
[(K=1-Nco) (PSDCO,K(f)*HL(f)2*XF*nCO,K0.6 *lL*f 2) 1/0.6 ]0.6 +
[(K=1-Nint) (PSDINT,K(f)*HL2(f)2*XF*nINT,K0.6 *lL2*f 2) 1/0.6 ]0.6
Expressions for the transmission loop transfer functions can be derived from expressions in section
A.2.1.2 of T1.417 Spectrum Management for Loop Transmission Systems.
Figure F3 below shows where the calculated values of PSDXCO and PSDXCPE are injected in the test
setup diagram.
Note 1: The actual crosstalk values specified in the Impairment Combination tables do not include the FEXT
component in these equations because it has been assumed that the NEXT component that traverses the loop to the
other end will result in a crosstalk component that is a sufficient approximation of FEXT.
PSDXCO(f)
(CO Composite
Interferer*)
UUT
PSDXCPE(f)
(CPE Composite
Interferer*)
Loop Simulator
* Simulation composite of different interferers from different injection points. Transfer
function needs to include the effects of loops and bridged taps.
Figure F3
Home Wiring
+
Drop
UUT