Contribution of Multidimensional Trellis Coding in VDSL Systems

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SETIT2005 SNR = 20 K 10 20 40 125 BER 0.0013 3.3e-4 1.5e-4 0 K 500 5000 No Trunc BER 0 0 0 Table 2. Effect of truncation length on the performance of the 4D TCM Code 3 Trellis Coding in Twisted Copper-Pair Passband Channels As specified in ANSI and ETSI (ETSI TS 101 270-1 v2.0.6 part1, 2002)(ETSI TS 101 270-2 v2.0.3 part2, 2002) functional documents, SCM-VDSL systems don’t use convolutional coding. In what follows, we will study the contribution of the TCM in the SCM-VDSL systems. The achievable gains for systems using the scheme consisting of 4D Trellis Coded Modulation have been analyzed in the previous section, and are typically equal to 4 dB for an AWGN channel. 3.1 SCM-VDSL system Figure 8 presents the SCM-VDSL system (T. Starr & M. Sorbara & J.M. Cioffi & P.J. Silverman, 2003) we used in our simulations. For the sake of simplification, the Reed-Solomon coding and interleaving functions, whose main purpose is to protect the data from Impulse Noise, have not been introduced in that system because the purpose of our study is not to investigate the impact of Impulse Noise on VDSL transmission, but to demonstrate the advantage of using the TCM rather than the DQAM modulation. fractionally spaced equalizer (MMSE) at a new sampling rate equal to 2×symbolrate because the input is now a baseband signal. The received symbols are decoded and compared to the originally transmitted data in order to compute the errors caused by the noise burst, and consequently, to compare the DQAM and TCM modulations. 3.2 Impairment Generator The impairment generator produces the noise that is injected into the simulation set. It includes both crosstalk noise and background noise. The crosstalk noise power level varies with the frequency, the length of the cable loop, and the transmit direction (Upstream or Downstream). The crosstalk model (ETSI TS 101 270-2 v2.0.3 part2, 2002) applied according to the test scenarios we choose is described below. Figure 9 defines a functional diagram of the composite impairment noise. This diagram has the following elements: 1. The three impairment "generators" G1, G2, and G3 generate noise as defined in (T. Starr & M. Sorbara & J.M. Cioffi & P.J. Silverman, 2003). 2. The transfer function H 1 (f, d) models the length and frequency dependency of the NEXT impairment as specified in (T. Starr & M. Sorbara & J.M. Cioffi & P.J. Silverman, 2003). 3. The transfer function H 2 (f, d) models the length and frequency dependency of the FEXT impairment as specified in (T. Starr & M. Sorbara & J.M. Cioffi & P.J. Silverman, 2003). NEXT noise Independent noise Generators G1 Crosstalk transfer functions H1(f,d) S1 FEXT noise G2 H2(f,d) S2 FSAN SUM Background noise Cable independent G3 S3 Figure 9. Functional diagram of the impairment noise composition Figure 8. VDSL Transmission Chain To satisfy the sampling theorem, the QAM symbols x k are over-sampled at the sampling rate 4×symbolrate, and are shaped using a raised cosine filter ϕ p (t) before being sent through the channel. Inter-Symbol Interference (ISI), Additive White Gaussian Noise (AWGN), and crosstalk impair singlecarrier transmission over the copper pairs. After being modulated and sent through the channel, an Additive White Gaussian and crosstalk Noises are superimposed to the channel output in the time domain. After crossing the whitening filter g(t), the data, brought back to the baseband, are sent through a low-pass filter in order to eliminate the whitened noise situated out of the frequency band. After that, they are sent through a finite minimum-mean-square-error Several deployment scenarios have been identified to achieve VDSL simulations. Each scenario (noise model) results in a length dependant PSD description of noise. Some of the three individual impairment generators G1, G2, and G3, are used more once in the same noise model. We denote six models, Type "A", Type "B", and Type "C" for cabinet modeling and Type "D", Type "E", and Type "F" for exchange modeling (ETSI TS 101 270-2 v2.0.3 part2, 2002). In our simulations, we chose Type "A" as the impairment modeling. Type "A" models (Cabinet) are intended to represent a mixed scenario including full ADSL where the VDSL system is placed in a distribution cable (up to ten of wire pairs) that is filled with many other transmission systems: 10 ADSL, 4 HDSL, and 20 ISDN interferers.
SETIT2005 3.3 Simulation Results The VDSL system shall operate with a bit error ratio < 1 erroneous bit through 10 7 bits sent when operated over any loop with the noise models and simulation conditions specified in this section. Because of computer restrictions, we carried our simulations with a BER level equal to 10 -5 . Simulation defaults: We have simulated the 4D TCM method in the VDSL system described in Figure 8 with three configurations of the truncation length K of the Viterbi decoder: K = 10, K = 125, and without truncation. The set of default parameters used in the simulations is listed below: • Number of Feed-Forward Equalizer (FFE) taps=32. • Roll-off factor: α = 0. 2 . • Number of information bits per signaling interval=5. • Symbol rate: f baud = 2.16 MHz. • Carrier frequency: f c = 2.2275 MHz. • Sampling rate: f s = 4f baud = 8.64 MHz. • The sampling rate at the input of the MMSE-FSE equalizer is L x f baud with L = 2. • Transmitted constellations = 32QAM for noncoded transmission, and 48QAM for trellis coded transmission. • The noise is additive, colored, and Gaussian ACGN. When whitened, its power spectral density (PSD) level is fixed to typically -140 dBm/Hz, which usually corresponds to the reference noise floor in the VDSL system. • As specified in the functional requirement documents (ETSI TS 101 270-1 v2.0.6 part1, 2002)(ETSI TS 101 270-2 v2.0.3 part2, 2002), the PSD of the transmitted modulated signal is typically equal to -60 dBm/Hz. Simulation results: In tables 3 and 4, we show the cable range reaches and the channel capacity gains for the 4D TCM VDSL system. On one hand, Table 3 shows the difference in cable range reaches if we vary the truncation length K. For the values of K that exceed 125, the 4D TCM VDSL cable range is typically constant. It is approximatively equal to 1270 m. On the other hand, the reach in the case of the 32QAM non-coded VDSL system is typically equal to 1180 m. In fact, the channel capacity associated for this value of the cable range is equal to 4.9823 bits. Beyond this value, the channel capacity becomes lower than the number of bits we want to send each signaling interval (b = 5). Thus, the 4D TCM VDSL system gives a cable range gain of 90m with the suitable value of K = 125. Table 4 shows the channel capacity gain in terms of number of bits we can send through the channel for different values of cable ranges and K. We note that the use of the trellis Coded Modulation rather than the DQAM allows sending 5 bits/signaling interval, even when the channel capacity (denoted bpsi in Table 4), calculated without taking into account the gain introduced by the TCM, is lower than 5. In our simulations, for K = 125 and BER = 10 -5 , the gain introduced by the TCM increases the channel capacity by 0.957 bits per signaling interval, which corresponds to 0.957 × 2.16 = 2.067 Mbps of rate gain. Cable Length Erroneous Symbols BER K = 10 1210 0 0 1220 0 0 1230 2 0.6e-5 1240 6 e-5 1250 6 1.2e-5 1260 27 5.3e-5 K = 125 1260 0 0 1270 0 0 1280 5 1.2e-5 1290 36 7e-5 1300 39 9.7e-5 Without Truncation 1270 0 0 1290 0 0 1300 20 4.3e-5 1400 247 5.22e-4 Table 3. TCM SCM-VDSL: Cable range reaches for different values of the truncation length K K Cable Length Bpsi Gain 10 1230 4.5822 0.4178 125 1270 4.043 0.957 No Trunc 1290 3.8172 1.1828 Table 4. Channel capacity gain for different values of K Conclusion The VDSL system is expected to be the solution to provide broadband services to residential and business on the existing copper plant. In this paper, we demonstrated that the Trellis- Coded Modulation with 4-dimensional rectangular constellations is superior to using 2D constellations. Using multi-dimensional rectangular constellations not only reduces the size of the constituent 2D constellations, but also improves the performance in terms of both the coding gain and cable range reaches.
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Contribution of Multidimensional Trellis Coding in VDSL Systems

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