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Lecture14 DSL Technology Digital Subscriber Line Ref: Vaidy-paper.pdf

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Data Communication, lecture142 Different ways to connect Modem (POTS - Plain Old Telephone System) ISDN Wireless Cable Modem (North America) xDSL

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Data Communication, lecture143 POTS Modem V.34+ Maximum Speed: 33.6 Kbps Expected Speed: 28.8 – 33.6 K Availability: Everywhere Symmetric

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Data Communication, lecture144 POTS Modem V.90 (x2; K56Flex; V.92) Maximum Speed: 56 Kbps Expected Speed: 40 - 50 Kbps Availability: Almost everywhere Asymmetric Relative to distance

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Data Communication, lecture145 ISDN BRI (Basic Rate Interface) 2B + C Two 64 Kbps B Channels One 16 Kbps C Channel Typically 128 - 144 Kbps Availability: Limited, Outdated Symmetric

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Data Communication, lecture146 ISDN North America: 23B + D (1536 Kbps) Europe: 30B + D (1984 Kbps) 64 Kbps B Channels One 64 Kbps D Channel Availability: Not for the general public Symmetric

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Data Communication, lecture147 Wireless Different wireless schemes proposed, planned and implemented throughout the world. Via satellite or ground antennas Bandwidth: A few Kbps to many Mbps Symmetrical or Asymmetrical Deployment issues: Spectrum licensing, interference, line of sight requirements, noise problems, bandwidth limitations…

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Data Communication, lecture148 Cable Modem Competes with DSL Cable TV is widespread in North America Satellite TV the norm for the rest of the world Based on NAs Cable TV infrastructure (Coaxial) Bandwidth is shared among all users (like Ethernet) Maximum Speed: 30 - 50 Mbps Expected Speed: depends on number of users Asymmetric, uplink limited to 128Kbps by modem Everybody's download speed is greatly impacted if upload link is saturated

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Data Communication, lecture149 xDSL Advantages Speed (several Mbps) Always connected Uses and can even share POTS wiring Disadvantages Speed dependant on distance to center Availability

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Data Communication, lecture1410 xDSL Varieties ADSL: Asymmetric DSL SDSL: Symmetric DSL VDSL: Very high speed DSL

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Data Communication, lecture1411 ADSL Maximum speed depends on distance and contract –8 Mbps for 2.7 Km –6 Mbps for 3.7 Km –2 Mbps for 4.9 Km –1.5 Mbps for 5.7 Km Such is the case for the uplink (up to 800 Kbps) Can share the regular phone line May or may not require a splitter Different Standards

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Data Communication, lecture1412 SDSL Maximum speed –2 Mbps for Europe –1.5 Mbps for NA Up to 6.7 Km Range Can not share the regular phone line Different Standards

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Data Communication, lecture1413 VDSL Only for short distances –55 Mbps for 300 m –27 Mbps for 500 m –13 Mbps for 1500 m Such is the case for the uplink (up to 19 Mbps) Can share the regular phone line Different Standards Fiber To The Neighborhood (FTTN) / Fiber To The Curb (FTTC)

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Data Communication, lecture1414 How it works It all comes down to bandwidth! For POTS it is 4 KHz The installed wires can handle a lot more depending on length and wire gauge DSL isnt the first to utilize the extra bandwidth, ISDN used some of it too (generally < 0.1 MHz) ADSL can use up to 1.5 MHz Normal POTS voice uses the bottom 4 KHz, so a single line can be shared

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Data Communication, lecture1415 How it works Carrierless Amplitude / Phase (CAP) 0 – 4 Khz: POTS 25 – 160 Khz: Upstream 0.24 – up to 1.5 Ghz: Downstream d d d d d d

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Data Communication, lecture1416 How it works Discrete MultiTone (DMT) Divides the 1.5 Mhz available bandwidth to 250 x 6 KHz regions The lower 3 regions are reserved for POTS Each channel is 4 KHz wide (2 KHz space between them) One way to think about it is that each channel is assigned a virtual modem Some of the lower channels are bidirectional

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Data Communication, lecture1417 How it works Discreet MultiTone (DMT) The official ANSI standard More complex to implement More flexibility on lines of differing quality

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Data Communication, lecture1418 How it works Line Sharing May or may mot require a splitter / low pass filter One of the key benefits of DSL Only on some types of DSL

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Data Communication, lecture1419 How it works VDSL Different standards (again!) VDSL Alliance (Alcatel, Texas Instruments) supports Discrete MultiTone (DMT) VDSL Coalition (Lucent, Broadcom) supports Carrierless Amplitude Phase (CAP) Normal POTS voice uses the bottom 4 KHz, so a single line can be shared

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Data Communication, lecture1420 DSL Equipment DSL Transceiver (Modem) At the customer side Generaly have USB or Ethernet connections Some combine routers, switches, etc.

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Data Communication, lecture1421 The Future… In NA the competition is between Cable and DSL Higher upstream speeds / symmetric configurations for VDSL VDSL Already requires at least Fiber To The Neighborhood (FTTN) because of its bandwidth requirements Many phone companies are planning Fiber To The Curb (FTTC) The next leap could be Fiber To The Home (FTTH) Not in the near future though!

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Data Communication, lecture1422 telephone lines (twisted-pair channels) which were originally intended to carry speech signals (about 4 kHz bandwidth) are today used to carry several megabits of data per second. This has been possible because of efficient use of high frequency regions which suffer from a great deal of line attenuation and noise.

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Data Communication, lecture1423 Communication channels can be wireless or wire-line channels, or a combination of both. In any case they introduce linear and nonlinear distortions, random noise, and deterministic interference. The transmission of information with high rate and reliability under such unfavorable conditions has been possible because of fundamental contributions from many disciplines such as information theory, signal processing, linear system theory, and mathematics.

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Data Communication, lecture1424 The Noisy Channel

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Data Communication, lecture1425 The transmitted signal power P is proportional to the mean square value of x(n). Assume that x(n) is a wide sense stationary random process. Then the power is the integral of the power spectrum. Assumptions

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Data Communication, lecture1426 That is: P = We can decrease the error probability by transmitting more power. For fixed power, the error probability increases with bit rate. Note that the power spectrum of x(n) tells us how its power is distributed in frequency.

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Data Communication, lecture1427 we can increase the achievable rate (for fixed error probability and transmitted power). The idea is to pour more power in the regions where the channel gain is large and noise spectrum is small.

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Data Communication, lecture1428 Ideal equalizer (zero-forcing equalizer).

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Data Communication, lecture1429 The effective power spectrum of noise at receiver is equal to:

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Data Communication, lecture1430 If C(z) has zeros close to the unit circle, then 1/C(z) has poles near the unit circle and the noise gain can be large. In frequency regions where S qq (j ω) is small, we should allocate more power.

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Data Communication, lecture1431 Power Allocation and Water-Filling Strategy

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Data Communication, lecture1432 If we imagine a bowl with its bottom shaped like S qq (j ω), then S xx (j ω) is the height of water filling the bowl, with λ denoting the uniform water level everywhere. The choice of λ depends on the total available power P and P e.

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Data Communication, lecture1433 How do we shape the power spectrum S xx (j ω) to satisfy the water-filling type of power allocation? This is tricky because we do not have a great deal of freedom to shape things, especially that x(n) is user generated data! the different subband channels carry different parts of a single input stream (DMT).

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Data Communication, lecture1434 Expander

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Data Communication, lecture1435 Decimator

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Data Communication, lecture1436 Interleaving

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Data Communication, lecture1437 Example: M=3

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Data Communication, lecture1438 It is clear that we can regard v(n) as a time-domain multiplexed or TDM version of the individual signals v k (n). The components v k (n) are also called the polyphase components of v(n) with respect to M.

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Data Communication, lecture1439 Deinterleaving

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Data Communication, lecture1440 The Digital Transmultiplexer (a Filter bank)

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Data Communication, lecture1441 It was originally intended to convert data between time division multiplexed (TDM) format and frequency division multiplexed (FDM) format. F k (z) are called transmitting filters or interpolation filters.

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Data Communication, lecture1442 The k th transmitting filter has output:

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Data Communication, lecture1443 Discrete Multi-Tone Modulation (DMT) Parsing Stage

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Data Communication, lecture1444 Parsing Stage Here s(n) represents binary data to be transmitted over a channel. This data is divided into nonoverlapping b-bit blocks. The b bits in each block are partitioned into M groups

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Data Communication, lecture1445 The collection of symbols: {x 0 (n), x 1 (n), …, x M–1 (n)} referred to as the DMT symbol. The sample x k (n) is typically a PAM or a QAM symbol Notice that for a given constellation, the power can be increased or decreased by scaling the distance between the code-words.

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Data Communication, lecture1446 We therefore have the freedom to allocate different powers for different sub-band channels. In this way the classical water-filling rule can be approximated.

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Data Communication, lecture1447 The transmitting filters f k (n) create the M-fold higher rate signals u k (n) as before, which are then added to produce the composite signal x(n). In principle, the DMT idea is similar to sub-band coding, where a signal x(n) to be quantized is first decomposed into sub-ands.

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Data Communication, lecture1448 A simple fact:

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Data Communication, lecture1449 Thus the transfer function D km (z) from x m (.) to y k (.) is the decimated version of the product-filter H k (z)C(z)F m (z). If m k then the symbol y k (n) is affected by x m (i) resulting in interband interference. Similarly if D kk (z) is not a constant then y k (n) is affected by x k (i), i n. (Intraband interference).

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Data Communication, lecture1450 Perfect Recovery (PR) DMT Systems If interband and intraband interferences are eliminated, the DMT system is said to be free from intersymbol interference (ISI). In this case, we have the perfect symbol recovery or PR property.

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Data Communication, lecture1451 Biorthogonal DMT we have perfect symbol recovery if and only if the transmitting and receiving filters satisfy the biorthogonality property defined as:

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Data Communication, lecture1452

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Data Communication, lecture1453 This means that the impulse response g km (n) of the product filter G km (z)= H k (z)F m (z) has the Nyquist(M) or zero-crossing property: g km (Mn) = 0 for k m and g kk (Mn) = δ(n)

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Data Communication, lecture1454 Example: M=3

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Data Communication, lecture1455 Channel Noise The only remaining distortion is due to the channel noise. The received symbol can be written as: y k (n) = x k (n) + q k (n) where q k (n) is the channel noise filtered through H k (z)/C(z) and decimated.

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Data Communication, lecture1456

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Data Communication, lecture1457 Optimization of DMT Note that: The variance of the symbol x k (n) represents its average power P k. x k (n) comes from a b k -bit constellation with equal probability for all codewords. We assume that the noise q k (n) is Gaussian with variance square-root of σ qk.

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Data Communication, lecture1458 The most important point to note is that the power P can be minimized by carefully controlling the variances of the noise components q k (n) at the detector inputs. The only freedom we have in order to control the power of noise is the choice of the filters H k (z). But we have to control these filters under the constraint that {H k, F m } is biorthogonal.

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Data Communication, lecture1459 Since the scaled system { α k H k, F m /α m } is also biorthogonal it appears that the noise variances can be made arbitrarily small by making α k small. The problem is that the transmitting filters F m (z)/α m will have correspondingly larger energy which means an increase in the power actually fed into the channel.

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Data Communication, lecture1460 Orthonormal DMT systems We can regard the subchannel signal u k (n) as belonging to a subspace spanned by the basis functions: Note that:

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Data Communication, lecture1461 The composite signal x(n) which enters the channel is therefore a linear combination of the basis functions from all the channels. We say that a set of M filters {F k (z)} is orthonormal if these basis functions are orthogonal to each other, and each of them is normalized to have unit energy.

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Data Communication, lecture1462 For perfect symbol recovery the transmiting and receiving filters in any orthonormal filter bank are related by: which is called time reversed-conjugation.

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Data Communication, lecture1463 Example:

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Data Communication, lecture1464 Here f 0 (n) is chosen as a rectangular pulse of length M and: This is called the DFT filter bank because it can be implemented with a DFT matrix and an inverse DFT (IDFT) matrix

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Data Communication, lecture1465 Optimal Orthonormal DMT Systems

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Data Communication, lecture1466 ADSL services Is used for data transmission on twisted pair channels ( Telephone Lines)

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Data Communication, lecture1467

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Data Communication, lecture1468

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Data Communication, lecture1469 Nominally 1.5 Mbps (range is 500 kbps to 12 Mbps) downstream. Roughly about 1/3 to 1/10 of this rate as upstream ADSL is world-wide standardized in ITU Standard G.992.1 and uses DMT.

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Data Communication, lecture1470 The symbol rate is T s = 250µs. The downstream modulation uses 256 subchannels. Each subchannel is 4.3125 kHz wide. In each subchannel the sampling rate is 1/T =2.208 MHz. The cyclic prefix is 40 samples. So, each time-domain symbol contains then 512+40 or 552 samples. Hermetian symmetry is used to create a real signal for transmission over the band from 0 to 1.104 MHz. Typically, the first 2-3 tones near DC and DC are not used to prevent interference into voiceband telephony (POTS= plain old telephone service),

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Data Communication, lecture1471 Upstream transmission uses 32 tones to frequency 138 kHz. Tone 256 is also not used. Tone 64 (276 kHz) is reserved for pilot signal (known point in 4 QAM sent continuously) that is used to recover the symbol and sampling rates. The sampling rate upstream is 276 kHz and the cyclic prefix is 5 samples for a block size of 69 samples. Upstream is then exactly 1/8 downstream. Downstream tones may or may not share the upstream band.

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Data Communication, lecture1472

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Data Communication, lecture1473

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Data Communication, lecture1474 A maximum power of 20.5 dB is permitted in downstream, and 14.5 dB upstream. The maximum number of bits permitted to be loaded on to any single tone is b n =15.

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