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Contribution of Multidimensional Trellis Coding in VDSL Systems

Contribution of Multidimensional Trellis Coding in VDSL Systems

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SETIT2005<br />

3.3 Simulation Results<br />

The <strong>VDSL</strong> system shall operate with a bit error<br />

ratio < 1 erroneous bit through 10 7 bits sent when<br />

operated over any loop with the noise models and<br />

simulation conditions specified <strong>in</strong> this section.<br />

Because <strong>of</strong> computer restrictions, we carried our<br />

simulations with a BER level equal to 10 -5 .<br />

Simulation defaults: We have simulated the 4D<br />

TCM method <strong>in</strong> the <strong>VDSL</strong> system described <strong>in</strong> Figure<br />

8 with three configurations <strong>of</strong> the truncation length K<br />

<strong>of</strong> the Viterbi decoder: K = 10, K = 125, and without<br />

truncation.<br />

The set <strong>of</strong> default parameters used <strong>in</strong> the<br />

simulations is listed below:<br />

• Number <strong>of</strong> Feed-Forward Equalizer (FFE)<br />

taps=32.<br />

• Roll-<strong>of</strong>f factor: α = 0. 2 .<br />

• Number <strong>of</strong> <strong>in</strong>formation bits per signal<strong>in</strong>g<br />

<strong>in</strong>terval=5.<br />

• Symbol rate: f baud = 2.16 MHz.<br />

• Carrier frequency: f c = 2.2275 MHz.<br />

• Sampl<strong>in</strong>g rate: f s = 4f baud = 8.64 MHz.<br />

• The sampl<strong>in</strong>g rate at the <strong>in</strong>put <strong>of</strong> the MMSE-FSE<br />

equalizer is L x f baud with L = 2.<br />

• Transmitted constellations = 32QAM for noncoded<br />

transmission, and 48QAM for trellis coded<br />

transmission.<br />

• The noise is additive, colored, and Gaussian<br />

ACGN. When whitened, its power spectral density<br />

(PSD) level is fixed to typically -140 dBm/Hz, which<br />

usually corresponds to the reference noise floor <strong>in</strong> the<br />

<strong>VDSL</strong> system.<br />

• As specified <strong>in</strong> the functional requirement<br />

documents (ETSI TS 101 270-1 v2.0.6 part1,<br />

2002)(ETSI TS 101 270-2 v2.0.3 part2, 2002), the<br />

PSD <strong>of</strong> the transmitted modulated signal is typically<br />

equal to -60 dBm/Hz.<br />

Simulation results: In tables 3 and 4, we show the<br />

cable range reaches and the channel capacity ga<strong>in</strong>s for<br />

the 4D TCM <strong>VDSL</strong> system.<br />

On one hand, Table 3 shows the difference <strong>in</strong> cable<br />

range reaches if we vary the truncation length K. For<br />

the values <strong>of</strong> K that exceed 125, the 4D TCM <strong>VDSL</strong><br />

cable range is typically constant. It is approximatively<br />

equal to 1270 m.<br />

On the other hand, the reach <strong>in</strong> the case <strong>of</strong> the<br />

32QAM non-coded <strong>VDSL</strong> system is typically equal to<br />

1180 m. In fact, the channel capacity associated for<br />

this value <strong>of</strong> the cable range is equal to 4.9823 bits.<br />

Beyond this value, the channel capacity becomes<br />

lower than the number <strong>of</strong> bits we want to send each<br />

signal<strong>in</strong>g <strong>in</strong>terval (b = 5). Thus, the 4D TCM <strong>VDSL</strong><br />

system gives a cable range ga<strong>in</strong> <strong>of</strong> 90m with the<br />

suitable value <strong>of</strong> K = 125.<br />

Table 4 shows the channel capacity ga<strong>in</strong> <strong>in</strong> terms<br />

<strong>of</strong> number <strong>of</strong> bits we can send through the channel for<br />

different values <strong>of</strong> cable ranges and K. We note that<br />

the use <strong>of</strong> the trellis Coded Modulation rather than the<br />

DQAM allows send<strong>in</strong>g 5 bits/signal<strong>in</strong>g <strong>in</strong>terval, even<br />

when the channel capacity (denoted bpsi <strong>in</strong> Table 4),<br />

calculated without tak<strong>in</strong>g <strong>in</strong>to account the ga<strong>in</strong><br />

<strong>in</strong>troduced by the TCM, is lower than 5. In our<br />

simulations, for K = 125 and BER = 10 -5 , the ga<strong>in</strong><br />

<strong>in</strong>troduced by the TCM <strong>in</strong>creases the channel capacity<br />

by 0.957 bits per signal<strong>in</strong>g <strong>in</strong>terval, which corresponds<br />

to 0.957 × 2.16 = 2.067 Mbps <strong>of</strong> rate ga<strong>in</strong>.<br />

Cable Length Erroneous Symbols BER<br />

K = 10<br />

1210 0 0<br />

1220 0 0<br />

1230 2 0.6e-5<br />

1240 6 e-5<br />

1250 6 1.2e-5<br />

1260 27 5.3e-5<br />

K = 125<br />

1260 0 0<br />

1270 0 0<br />

1280 5 1.2e-5<br />

1290 36 7e-5<br />

1300 39 9.7e-5<br />

Without Truncation<br />

1270 0 0<br />

1290 0 0<br />

1300 20 4.3e-5<br />

1400 247 5.22e-4<br />

Table 3. TCM SCM-<strong>VDSL</strong>: Cable range reaches for<br />

different values <strong>of</strong> the truncation length K<br />

K<br />

Cable<br />

Length<br />

Bpsi<br />

Ga<strong>in</strong><br />

10 1230 4.5822 0.4178<br />

125 1270 4.043 0.957<br />

No Trunc 1290 3.8172 1.1828<br />

Table 4. Channel capacity ga<strong>in</strong> for different values <strong>of</strong> K<br />

Conclusion<br />

The <strong>VDSL</strong> system is expected to be the solution to<br />

provide broadband services to residential and bus<strong>in</strong>ess<br />

on the exist<strong>in</strong>g copper plant.<br />

In this paper, we demonstrated that the <strong>Trellis</strong>-<br />

Coded Modulation with 4-dimensional rectangular<br />

constellations is superior to us<strong>in</strong>g 2D constellations.<br />

Us<strong>in</strong>g multi-dimensional rectangular constellations<br />

not only reduces the size <strong>of</strong> the constituent 2D<br />

constellations, but also improves the performance <strong>in</strong><br />

terms <strong>of</strong> both the cod<strong>in</strong>g ga<strong>in</strong> and cable range reaches.

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