CHAPTER 1 INTRODUCTION
1.2 T OPOLOGY OF VDSL T EST L OOP
There are 8 test loop topologies listed in the VDSL draft standard, namely, from VDSL0 to VDSL7, and their purposes of test are summarized in Table 1.1 while their topologies are shown in Fig. 1.2. Table 1.2 enumerates short, medium, and long-range values for a nominal length variable in VDSL1 through VDSL4 [4]. In order to study the effect of loop length to the whole system, anther set of loops with length from 100 m to 1500 m is the second test set.
In this section, the DMT-based DSL system description and topology of VDSL test loops are introduced. The characteristics of these twisted-pair lines can be modeled by a mathematical method described in the next section.
Table 1.1 VDSL test loops
No. Rationale
VDSL0 Null loop
VDSL1 Range stress limit, underground cable
VDSL2 Flat-wire vertical drop, horizontal aerial cable on other section VDSL3 Reinforced-wire vertical drop, horizontal aerial cable on other section VDSL4 Bridged tap, horizontal aerial cable
VDSL5 Short loop test with bridged taps and various crosstalk VDSL6 Medium loop test with bridged taps and various crosstalk VDSL7 Long loop test with bridged taps and various crosstalk
Table 1.2 Nominal length for asymmetric VDSL loops
Variable Name Short Reach Medium Reach Long Reach x(VDSL1) 1000 ft. (304.8 m) 3000 ft. (914.4 m) 4500 ft.(1.3716 km) y(VDSL1) 1500 ft. (457.2 m) 3000 ft. (914.4 m) 4500 ft.(1.3716 km) z(VDSL2) 1500 ft. (457.2 m) 3000 ft. (914.4 m) 4500 ft.(1.3716 km) u(VDSL3) 1500 ft. (457.2 m) 3000 ft. (914.4 m) 4500 ft.(1.3716 km) v(VDSL4) 1000 ft. (304.8 m) 3000 ft. (914.4 m) 4500 ft.(1.3716 km)
FP flat untwisted pair TP1 0.4mm or 26-gauge TP2 0.5mm or 24-gauge TP3 DW10
2m TP2
VDSL0
x(=305/913/1372m) TP1
VDSL1
76.2m FP z-76.2 m TP2
VDSL2
76.2m TP3 u-76.2m TP2
VDSL3
VDSL4 v-91.4m TP1 S4_2 S4_3
VDSL5
S5_2 167 m 30.4m 76.2m
TP2 TP2 TP2
VDSL5
VDSL6
503m 198m TP1 TP2
VDSL5
VDSL7
503m 701m TP1 TP2 S4_2 = 91.4m, S4_3 = 45.7m, S5_2 = 15.2m TP2
Figure 1.4 Topologies of VDSL test loops.
Chapter 2
Channel Modeling
Most twisted-pair phone lines can be well-modeled for transmission at frequencies up to at least 30 MHz by using what is known as two-port modeling or “ABCD” theory [1][13][14][15][16]. The procedure for generating the channel modeling includes transmission-line RLCG characterization, RLGC to ABCD parameters conversion, multiple ABCD section integration, and transfer characteristics of a subscriber loop calculations, etc.
In this chapter, the basic theory of the channel modeling and their computer simulation results are included as well as the relative noise models such as crosstalk and background noises are introduced in this chapter.
2.1 Transmission-line RLCG Characterization
The R, L, C, and G parameters represent resistance, inductance, capacitance, and conductance per unit length of the transmission line, respectively. The two-port characterization of a transmission line can be derived from the per-unit length two-port model in Fig. 2.1.
I(x)
Figure 2.1 Incremental section of twisted-pair transmission line.
The RLCG can be fitted to the measured values which are frequency dependent. The other coefficients in the models are related to the types of twisted-pair lines and can be looked up in reference [1][14]. The curve-fitting RLCG values are listed as
4 4 2
where r0c (kΩ/kft) is the copper-line DC resistance; ac is characterizing the rise of resistance with frequency in the “skin” effect; (mH/kft) and ll0 ∞ (mH/kft) are the low- and high- frequency inductance, respectively; f (MHz) is the frequency at which R and L are calculated; fm (MHz) and b are characterizing the transition between low and high frequencies in the measured inductance values.
In this section, the transmission-line RLCG characterization is defined and the curve-fitting formulae of the RLCG parameters for twisted-pair line are also introduced.
These parameters can be converted to ABCD matrix parameters.
2.2 Conversion of RLGC to ABCD Parameters
In this section, we introduce how to convert the RLGC to ABCD parameters and the multiple ABCD section integration.
2.2.1 Two-Port Network and ABCD Parameters
I1 I2
A B
C D V2
V1
Figure 2.2 Two-port network model.
Fig. 2.2 shows a transmission model of two-port linear circuit. The terminal voltages and currents will be defined by the matrix relationship given by
⎥⎦
Where is a 2x2 matrix of 4 possibly frequency-dependent parameters, A, B, C, and D. All these parameters depend only on the network and not on external connections.
For example, ABCD parameters for a simple two-port network consisting of a series impedance, as shown in Fig. 2.3, can be derived as follows
Φ
Z
I1 I2
V1 V2
Figure 2.3 A series impedance as a two-port network.
N1 N2
I1 I2 I3
V1
I2
V2 V2 V3
Figure 2.4 Two two-port networks in series.
The ABCD parameters of two two-port networks in series can be obtained by equating the voltage and current of the first two-port network to that of the following network, as shown in Fig. 2.4. For two two-port networks in series, the input and output voltage and current relationship is represented as follows
⎥⎦
To derive the relationship between “RLCG” and “ABCD” parameters, some new variables have to be introduced. First, the impedance per unit length, Z, is defined as R+jwL and the admittance per unit length, Y, is G+jwC. By taking equations (2.6) and (2.7) into Fig. 2.1, the ABCD parameters of a unit-length twisted-pair line are expressed by
( ) ( ) ( )
The incremental section of twisted-pair transmission line is calculated by evaluating the voltage and currents at x=0 in terms of those at x=d. The following two-port representation is then obtained [4].
⎥⎦
where the propagation constant γ and characteristic impedance Z0 of the transmission line are defined, respectively, by
(
R+ jwL) (
⋅ G+ jwC)
= Z⋅YThe “ABCD” parameters are related to the propagation constant γ, characteristic impedance Z0, and length of a transmission line d. However, a subscriber loop is usually constructed by combining several different lines. In the next section, multiple ABCD section integration and the characteristics of bridged-tap are introduced.
2.2.2 ABCD Parameters of Multiple Sections and Bridged-taps
Since the ABCD matrix of a composite network consisting of two-port networks in series is obtained by the product of these two ABCD parameters matrices as shown in equation (2.7). A cascade of two-port networks has an equivalent two-port matrix that is the product of the component ABCD matrices, in order, as shown by
⎥⎦
Figure 2.5 Example of two-port cascades for twisted-pair line configurations.
Another more general configuration of loops with bridged-taps and various types of twisted-pair lines is shown in Fig. 2.5. The transmission matrix can be expressed as
0 1 2 3
⎥⎦
where Zs is the source impedance and Zt is the characteristic impedance of the bridged-tap section.
The impedance of the bridged-tap section Zt is computed according to the above formula, as a parallel (shunt) impedance, for the input impedance of a section of transmission line terminated with an open circuit (ZL=∞ ). The overall two-port matrix is simply the product of the 4 two-port matrices shown in Fig. 2.5 and equations (2.13) to (2.17). Circuits with multiple bridge-taps can be calculated by similar procedures as multiplying multi-section of two-port networks. The impedance of previous section then becomes a termination impedance for the next section working backwards towards the main transmission pair of interest. The calculation process is straightforward and recursive to build the whole loop models.
2.3 Transfer Characteristics of a Subscriber Loop
The computation of the transfer functions for twisted-pair transmission lines with multiple sections then simply becomes a process of multiplying the corresponding ABCD matrices of the cascaded two-port sections. The source voltage divider is modeled by equation (2.18) and the final output voltage, current and load are VL, IL, and ZL, respectively. The transfer function, H, is computed from the ratio of VL and Vs, as shown in equation (2.19).
In DSL case, the source impedance is matched to the characteristic impedance (which equals the input impedance of the line when the line is long) and all impedances are real over the higher frequency range for DSL transmission. In this case, the transfer function is simply 6 dB lower than the insertion loss. The transfer function, H, is called the channel modeling of a twisted-pair line. Usually, its form can be represented both in frequency-domain and time-domain by applying proper sampling time. A program to
generate the time- domain transfer function of xDSL implemented according to the theory mentioned above is developed, and some of the results used in VDSL are shown in the next section.
2.4 Simulation Results of the Channel Characteristics
In this section, some simulation results of the DSL channel characteristics will be illustrated. In the first test set, the VDSL test loops, VDSL0 to VDSL7 in Table 1.1, Table 1.2, and Fig. 1.4 in Chapter 1 are studied. The other test set is the TP1 (gauge #26) line with length from 100 m to 1500 m since the VDSL system limits its twisted-pair loop length up to 1500 m. This set of test loops is simulated to observe the relationship between channel characteristics and its length. In Fig. 2.6 and 2.7, the channel responses of VDSL0 to VDSL7 of short reach in Table 1.2 (about 300 to 450 m) are illustrated in both time-domain and frequency-domain. While the channel responses of the second test set are shown in Fig.
2.8 and Fig. 2.9.
From the simulation results, it can be seen that the time-domain channel response of VDSL4, which has two bridged-taps, contains several peaks, with a broader main peak. In addition, its frequency-domain channel response contains some notches. The SNR values at those notches are reduced and the number of bits carried are also decreased.
In general, the longer the loop, the broader the response will be. In addition, the delay becomes greater while the loop length gets longer.
0 20 40 60 80 100 120 140 160 180 200 Channel responses of VDSL test loops in time domain--medium
Mag. h [no ]
sample (T/4)
Figure 2.6 Time domain channel responses of VDSL0 to VDSL7.
0 50 100 150 200 250 300
Channel responses of VDSL--Frequency Domain
Mag. of H B(d)
Nth tone (N x 8625Hz)
Figure 2.7 Frequency domain channel responses of VDSL0 to VDSL7.
0 100 200 300 400 500 600 700
Channel responses of VDSL with various lengths
Mag. h [no ]
sample (T/4)
Figure 2.8 Time domain channel responses of TP1 lines of various lengths.
0 50 100 150 200 250 300 Channel responses of VDSL -Frequemcy Domain
Mag.
H B(d)
Nth tone (N*8625Hz)
Figure 2.9 Frequency domain channel responses of TP1 lines of various lengths.
2.5 Interference and Noise Models
In the above sections, the channel responses of the twisted-pair lines are derived.
However, in the real DSL operating environment, there are other effects, such as crosstalks, noises, etc. that will lower the performance of the DSL system. Besides the natural limitation of thermal noise, there are three other types of interference or noise that affect the performance of DSL system, i.e., crosstalk [17][18][19][20][21][22][23], impulse noise [17][24][25][26], and background noise [1].
2.5.1 Crosstalk
Telephone subscriber loops are organized in bundle groups of 10, 25, or 50 pairs, and several binder groups share a common physical shield in a cable. Due to capacitive and inductive coupling, there is crosstalk between the twisted-pair lines even though pairs are well insulated at DC. For DSL system, in which the signal bandwidth is much broader than that of voice frequency, the crosstalk becomes a dominant limitation to the whole transmission throughput.
Crosstalk coupling loss models have been developed for far end crosstalk (FEXT) [19]
and near end crosstalk (NEXT) [18][20][21] with the consideration of different number of disturbers. These crosstalk coupling loss models are based on twisted-pair lines within the same cable of significant length, usually longer than 300 m. The effect of crosstalk could be different if only a portion of twisted-pair lines are within the same cable. In this subsection, the formula of power spectrum density (PSD) of ADSL downstream are introduced and their induced FEXT and NEXT to the system are also discussed and simulated.
2
This equation gives the single sided PSD, where KADSL is the total transmitted power in Watts for the downstream ADSL transmitter before shaping filters, and is set such that the ADSL PSD will not exceed the maximum allowed PSD. f0 is the sampling frequency in Hz.
LPF is a low pass filter with a 3 dB point at 1104 kHz and 36 dB/octave rolloff.
09
HPF is a high pass filter with 3 dB points at 4 kHz and 25.875 kHz and 57.5-dB attenuation in the voice band, separating ADSL from POTS. With this set of parameters the PSDADSL-Disturber is the PSD of a downstream transmitter that uses all the sub-carriers.
A. FEXT Coupling Configurations
FEXT [1][2][19] is defined as the crosstalk effect between a receiving path and a transmitting path of DSL transceiver at opposite ends of two different subscriber loops within the same twisted-pair cable, as shown in Fig. 2.10.
Pair i Disturbed, far end Signal
source FEXT
Disturbing, far end Pair j
Figure 2.10 Illustration of FEXT.
The FEXT loss model is given by [2]
2 2
2
( )
)
( f H f k l f
H
FEXT=
channel× × ×
……….(2.25)where Hchannel (f) is the channel transfer function, k is the coupling constants, l is the coupling path length and f is the frequency. k is for n<50, 1%
worst-case disturbers with the coupling path length l in feet. If the meter of length is used, then the coupling constant k is changed to for n<50.
20 0.6
8.0 10× − ×( / 49)n
20 0.6
2.44 10× − ×( / 49)n The FEXT noise PSD is therefore given by
)
2( f H
PSD
PSD
ADSL−FEXT=
ADSL−Disturber×
FEXT ………...………..(2.26) In Fig. 2.12, the magnitude of these FEXT noises are shown in frequency domain.B. NEXT Coupling Configurations
NEXT [1][2][18][19] is defined as the crosstalk effect between a receiving path and a transmitting path of DSL transceivers at the same end of two different subscriber loops with in the same twisted-pair cable, as shown in Fig. 2.11.
NEXT
Pair i Pair j
Disturbed, near end Disturbing, near end Signal
source
Figure 2.11 Illustration of NEXT.
The PSD of the ADSL NEXT coupling into the upstream is defined as [2]
(
× 3/2)
0≤ <∞, <50×
= −
− PSD x f for f n
PSDADSL NEXT ADSL Disturber n ………..(2.27)
where xn =8.818 10× −14× n( / 49)0.6 or equivalently, xn =0.8536 10× −14×n0.6 . The integration of the induced NEXT over the band from 0 to 1.104 MHz for n=49 is –25.4 dBm.
Fig. 2.12 shows the simulation results of the PSD of 10-disturber downstream ADSL NEXT into the upstream as well as ADSL and VDSL FEXT with 300 m loop length.
0 0.5 1 1.5 2 2.5 x 106 -240
-220 -200 -180 -160 -140 -120 -100
frequency (Hz) PS
D B(d m/ HZ)
ADSL-DS-NEXT ADSL-DS-FEXT VDSL-FEXT AWGN
Figure 2.12 Simulation results of the PSD of 10-disturber downstream ADSL NEXT coupling into the upstream as well as ADSL and VDSL FEXT.
2.5.2 Impulse Noise
The origin of impulse noise is usually difficult to locate. It could come directly through some connections to the telephone subscriber loop or come from the influence of an electromagnetic field. Impulse noise is characterized as a random pulse waveform whose amplitude is much higher compared with the Gaussian-like background noise. Impulse noise is a major impairment for DSL system, especially due to the heavy DSL subscriber loop loss. While crosstalk and background noises impose a limit on transmission throughput over the twisted-pair telephone subscriber loop, the error caused by impulse
noise can be corrected with forward error correction codes. The required error correction coding overhead could reduce a small portion of the transmission throughput.
2.5.3 Background Noise
The loop plant noise level or the receiver front-end noise level becomes a limiting factor for the performance of a DSL system. The analysis of transmission performance over the twisted-pair subscriber loop has been based on the assumption of a received signal over an AWGN channel. The probability density of the background noise is very close to a Gaussian distribution. The histograms of the background noise are very similar to Gaussian density, except that they have short tails. Therefore, the Gaussian noise assumption is still valid.
Based on the results of noise survey, the background noise level for the twisted-pair telephone loop plant has been assumed to be -140 dBm/Hz. It is assumed that the loop plant background noise level is higher than the thermal noise of a receiver front-end electronic circuit whose noise power density is around -174 dBm/Hz.
In this chapter, the characteristics of twisted-pair line and some related interfaces and noises are studied to model their responses in both time-domain and frequency-domain, these responses are used thereafter to calculate the system performance.
Chapter 3 Bit Loading and Optimal Throughput of
DMT-based VDSL System
In this chapter1, the bit-loading [1][27] and throughput of a DMT-based VDSL system is studied to investigate its system performance. In the first section, the formulae of bit-loading calculations at each tone are given. In those formulae, the factors that affect the bit-loading of each tone can be well defined. Finally, the throughput of this system is computed. In the second section, two methods to increase the throughput of DMT-based VDSL systems, extending the FFT size or increasing the symbol rate, are discussed. The computer simulation results of optimal throughput vs. various sampling rate under different types of noise environments, such as AWGN noises, crosstalk, bridged-taps[28][29], etc., are then discussed.
1 Part of the content in this chapter has been published in:
S. T. Lin and C. H. Wei, “Optimal Channel Capacity Analysis for DMT VDSL System of Various Symbol Rates,” Proc. IEEE Globecom’01, San Antonio, U.S.A., pp.389-393, Nov. 2001
3.1 Bit Loading Calculations
The procedures of calculating the system bit-loading and its throughput are to compute the sub-channel SNRs first, then the number of bits per sub-channel, and the total system throughput.
The DMT-based system includes a set of independent sub-channels. And the overall capacity is the summation of each sub-channel. A subscript index, ‘i’, is used for recognizing the quantities of the ith sub-channel, such as Ci, SNRi, etc. The number of bits per symbol carried by the ith tone (sub-channel) can be calculated by [1][27]
2
2 2 2
log 1 i log 1 ( , )
i
SNR P
b σ
⎛ ⎞ ⎛ ⎞
= ⎜⎝ + Γ ⎟⎠= ⎜⎝ +Γ H d f ⎠⎟……….…(3.1)
The variables P and σ2 represent the transmission and noise power, respectively.
H(d,f) is the channel transfer function, which was calculated in Chapter 2. The variable, Γ, is called SNR gap, which is dependent on the error rate, system margin γm (6 dB), and coding gain γc (3 dB), as defined in (3.2) with error rate of 10-7[1][27].
9.8 γc γm
Γ = − + dB…...……….…………..(3.2)
The channel capacity of a loop can be calculated by applying its channel modeling into the above equations and obtained by summarizing the bits carried by each tone, as shown below.
)
From the previous derivation, the throughput of the DMT-based DSL system depends on the length of loop and the bandwidth used, as shown in the above equations. If the same FFT size (N=512) of the DMT system is maintained, the bandwidth of each sub-channel is proportional to its symbol rate. However, it becomes saturated after the symbol rate being increased to a certain value, as shown in reference [10]. It can also be observed from Fig.
2.7 and Fig. 2.9 that the magnitude of the channel response H(f) decreases in high frequency range especially for long loop.
To observe the relationship between the channel response and its capacity, the scaled channel response magnitude in frequency domain vs. the corresponding bit-loading is shown in Fig. 3.1. We use gauge #26 twisted-pair line with 1200 m as an example, the dotted line is the magnitude of the channel response “H(f)”. The solid line as a down-stair curve represents the bit-loading of each tone, its value depends on the signal-to-noise ratio (SNR), which is the corresponding magnitude of channel response represented as the dotted line. The channel capacity can be calculated by multiplying the total bit-loading of each tone with the symbol rate. All the test loops introduced in the first chapter are simulated. In Fig. 3.1, the result of 1200 m TP1 loop is illustrated as an example. As shown in Fig. 3.1, the SNR curve cause the numbers of bits loaded in each sub-channels decrease in decent order.
0 50 100 150 200 250 300 0
2 4 6 8 10 12 14 16 18
Bsit
Nth tone
Total: 18.30 Mbps SNR curve
Figure 3.1 Channel capacity of gauge #26 twisted-pair line with 8 kHz symbol rate.
Since the magnitude of the channel response decreases at high frequency, the bits carried are lowered in those corresponding sub-cannels. Those tones with bit-loading smaller than 2 are not activated; therefore, the channel capacity has its limitation even though the symbol rate can be increased much higher.
Currently, due to the increased population of fiber on the telecommunication network,
Currently, due to the increased population of fiber on the telecommunication network,