NWA-PCUG Newsletter Article
How Analog Modems Function & DSL
by John Hunt, October 2000
(click to email author)

For many years the switched telephone system (the so-called Dialup Network) has limited the bandwidth of transmission to a range of approximately 300 to 3300 cycles per second. This bandwidth is more than adequate for really excellent transmission of voice; there is currently no worldwide interest in changing these limitations. The limitation applies to the entire telephone network, including long distance and trunks between central offices in large cities, the only exception being the purely copper wire path from the telco central office to the subscribers premises, called the "Last Mile" in telco jargon.

When interest in telephonic transmission of digital data first emerged (about 1964) it was immediately recognized that it would be necessary to convert the digital data stream to audio signals compatible with the frequency response limitations of the network.

The earliest modems, which were limited to 300 bits per second, employed a simple frequency shift scheme. Binary ones were represented by one frequency and zeroes by a second. The appropriate sine wave was transmitted for the duration of the entire bit period, in this case 1/300 of a second, or several complete cycles of the waveform. This simple signaling scheme permitted easy recognition of the data bits at the receiving end, even in the presence of modest electrical line noise. Each sine wave string was called a symbol in modem jargon.

In the next thirty years a continuing effort was expended in a very successful campaign to increase the transmission bit rate while maintaining affordability of the technology. The ultimate triumph of this effort was the attainment of speeds of 33 kilobits on really high quality lines, with automated drop back to the vicinity of 28 kilobits per second for normal telephone lines. (It should be remembered that the telephone line in this connotation is the Last Mile; the purely digital transmission of the signals over the main body of the telephone network merely served to provide a highly faithful digital representation of the analog pseudo-voice signals on the Last Mile). The latest and best of these successive steps toward faster data rates was codified in a standard called v34, issued by the International Telecommunications Union. The modern analog modems are commonly called v34 modems.

The simple frequency shift procedure for the 300 bit per second modems transmitted only a single binary bit per transmission symbol. It was soon recognized that improvements in speed could be achieved by using more complex symbols, each conveying more than one bit. From this point on all the transmissions used a single fixed frequency, with the symbols manipulating the phase angle and magnitude of the symbol. The first success in this long string of successive improvements over three decades used four different phase angles for the symbol, thereby encoding two binary bits in each symbol.

By the time of the v34 modems, the galaxy of symbols had been increased to 16 different phase angles evenly distributed over the available 360 degrees of phase, and 16 different symbol voltage magnitudes. This combination of 256 different symbols encoded eight bits per symbol, but at the cost of a major increase in the complexity of symbol generation and recognition, especially in the presence of noise or imperfect transmission line characteristics. The choice of eight bits per symbol was dictated entirely by a compromise between generation/recognition complexity and resultant speed, and was only related to our old friend the 8-bit byte by coincidence. To transmit as many symbols in a given time as possible the duration time for each symbol was shortened, finally reaching a sine wave burst of only about 200 degrees of a single cycle! These short symbols are now called wavelets.

At least three problems had to be addressed before an economically viable v34 modem could be offered:

1) The imperfect transmission line characteristics of the Last Mile for
typical line lengths distort both the phase angle and magnitude of the
received wavelet.
2) The proposed wavelets have low frequency and dc components in their
spectrum which fall outside the telco passband.
3) How can we affordably generate and recognize these complex

The first problem was solved by transmitting test wavelets of specified magnitude and phase angle during the handshake period at the start of a modem communication session.

Fortunately the line characteristics change only over a period of hours or even days, but of course the compensation for the observed attenuation and phase shift was necessarily adjusted for the line currently in use, as observed by measuring the test pattern. The required compensation varied immensely for all of the possible line conditions encountered.

The second problem was solved by modulating the analog stream of successive wavelets on a fixed frequency audio carrier, the latter located in the middle of the 300 to 3300 cycle passband. This process, which for the simple amplitude modulation employed has been well understood for eighty years, is analogous to the modulation of entertainment audio on the carrier of AM radio stations.

The third problem would have been virtually insurmountable fifteen years ago, at least at a decent level of reliability, cost, and complexity. As in almost everything else in the computer world, the solution lay in a marriage of exotic mathematics and the implementation of the resultant computations in very powerful stored program computers. The importance of this technique has resulted in the development of special processor chips which are uncommonly gifted at very high speed arithmetic at very low cost. The chips are called "Signal Processors"; almost every year sees the introduction of incredible improvements in these devices, which are very widely employed for many purposes unrelated to communications. The processor simply computes what the desired analog waveform voltage will be at very frequent time intervals across the width of the wavelets, then sends this value to a digital to analog converter to generate the actual pseudo voice audio which is transmitted over the phone lines (including those portions which use digital transmission). At the receiving end the process is conceptually reversed, with the incoming analog signal being sampled and converted to digital at frequent intervals, then analyzed by a signal processor.

All modern analog modems accordingly have a/d and d/a converters along with signal processors and their attendant rom program memory. A few years ago (and totally unrelated to DSL) modem designers recognized that a new method of speeding up analog modems might be possible; this became the so-called 56k family of modems so widely used today, and called v90 by the International Telecommunications Union. The 56k modems simply reverse the procedure for digital voice transmission to carry data signals over the Last Mile, using the existing digital channel of the telephone system for everything short of the Last Mile. Just as a very faithful duplication of voice audio can be achieved by a digital representation of the audio, an audio channel (the Last Mile) can equally provide a very faithful reproduction of a digital data stream. This process requires no change in telco hardware. Because of the existence of a/d and d/a converters as well as signal processors in the v34 modem designs, it was possible to completely redirect the efforts of the processor in the modem by simply altering the program (stored in rewriteable rom in the better modems).

At last, DSL

DSL is made possible by the characteristics of the copper twisted pair which make up the Last Mile. If the copper wires are disconnected at both end from existing hardware, and if the frequency response of the copper pair is then measured, it will be seen that the line transmits useful signals far beyond the bandwidth limitations of normal voice (called POTS, for Plain Old Telephone Service). For example a three mile length of copper pair might exhibit an attenuation at one megahertz of about 40 decibels compared to low voice frequencies. Forty decibels is a 100-fold reduction in voltage level at 1 Mhz. While this sounds discouraging, it still can provide useful communications, even in the presence of electrical noise on the average installation.

In recognition of this fact about the copper pairs (knowledge which dates back at least a century) an effort began a few years ago to permit transmission of entertainment video over the phone lines. With the enormous growth in popularity of the internet this early goal was soon abandoned in favor of providing fast internet service at modest cost. This was a much easier target, as an electrifying improvement in internet service can be provided with bit rates of the order of 600 kilobits per second, about one fifth of that required for mediocre television. Additionally, the maximum rate for internet can be adjusted expediently to accommodate current line conditions, while the rate for television must be maintained at the already high value to avoid intolerable picture quality.

The proposed internet service presumed the existence of new electronics and both ends of the Last Mile, as well as high speed internet digital data coming into the telco central office to which the subscriber's copper line is connected. Since all central offices have an immense digital traffic already, the provision of additional digital capacity was not a problem.

The earliest effort that found its way into customer use employed a transmission scheme which was called CAP (for Carrierless Amplitude and Phase). CAP was a literal extension of the technology used in the v34 modems, modified to take into account the fact that the 1 Mhz bandwidth of the raw copper pair is about three hundred times that available for dialup modems. From pure bandwidth considerations this would imply digital transmission at speeds as high as 10 megabits per second. By reducing this goal by a factor of ten, simplifications in design were made possible to increase the economic attractiveness of the proposed new scheme. DSL service using CAP modems began in quantity about two years ago.

An alternative transmission method very different from CAP was proposed about a year later. This technology was called DMT (for Discrete Multi-Tone, a somewhat misleading name). It was almost universally recognized to be materially superior to CAP, and received widespread support from industry giants like Intel, MicroSoft, IBM, Apple, etc.

DMT now is the basis for the current rapid growth in DSL availability. The existing CAP installations, mainly in Verizon country in New York and New England, are scheduled for hardware replacement at both ends of the Last Mile in the near future.

DMT employs a concept which sounds like it was conceived by a madman. The reasoning of the DMT creators was as follows:

Years ago (as far back as the 1920s) long distance voice was carried by a technology called Frequency Division Multiplexing, which placed a large number of voice channels side by side, each with its own frequency band, on a wide bandwidth single copper line.

This procedure is exactly analogous to the method by which multiple channels of entertainment television are delivered over coaxial cable to most homes today. Why not simply duplicate this procedure to carry many voice bandwidth channels over the Last Mile, using an individual v34 technology modem on each of these hundreds of channels to transmit a portion of the digital traffic?

Cost, physical size, power consumption, heat dissipation, and reliability aside, it is an idea that certainly has appeal, and in fact could have been implemented (if one could fine a sufficiently romantic financial backer) years ago. Before abandoning this fanciful suggestion, pause a moment to consider how the v34 modems mathematically modeled the 256-symbol galaxy of phase/amplitude wavelets, then calculated the effect of modulating the symbol stream onto an analog path in the center of the 300-3300 hertz available spectrum for dialup transmission. Clearly a second path could be added by doubling the number of numerical calculations, using a new numerical criteria for a carrier in the middle of say, the range 4300 to 7300 hertz, exactly 4khz above the original scheme (but of course requiring more bandwidth).

Because of the incredible speed of modern signal processor chips, with fairly sophisticated calculations being performed more than a billion time a second, it is possible to simply increase calculation speed by a factor of 256, distributing the resulting individual v34-like channels over 256 adjacent 4khz bands from 25khz to about 1.1mhz. Furthermore, the unused bandwidth below 25 khz can now be use for POTS over the very same metallic pair that carry the exotic DSL signals! The lower limit of the DSL bands was deliberately raised to 25 khz to permit the use of extremely inexpensive inductor/capacitor filters to separate the DSL and POTS ranges.

It should be recognized that 256 simultaneous v34-like channels are actually physically present in the composite analog signal presented to the copper pair, even if the method of creating these channels somewhat boggles the imagination.

At the receiving end the signals are digitized, then mathematically analyzed to reverse the signal process described above. The modems at the two ends of the line are virtually identical, although those at the telco central office, called DSLAMs, are packaged entirely differently to provide most economical provisioning of multiple channels for the various subscribers.

An interesting aspect of the DMT encoding method in comparison to the earlier CAP method (and one which probably was a major factor in the selection of DMT) is the effect of impulse noise on the two techniques. Much of the worst noise on telephone lines is in the form of infrequent narrow impulses perhaps one microsecond in width. CAP transmits a series of very short duration wavelets; these very short wavelets are very vulnerable to the noise impulses which blanket a substantial portion of the wavelet. DMT transmits 256 long time durations wavelets simultaneously, the long duration wavelets are relatively unbothered by the very short noise impulses. Thus CAP has infrequent noise victims, but the infrequent requests for retransmission (each of which requires the time of a round trip on the internet backbone) is very disruptive. In contrast, DMT will either survive the noise pulses on all channels or disastrously fail all channels. An occasional total disaster is much less objectionable from a retransmission standpoint than minor but frequent retransmission requests.

There is a bit of oversimplification in the above discussion, all of it directed at avoiding discussion of some incredibly arcane mathematics which the author does not pretend to understand. It is impossible to overstate the immense debt that modern electronics owes to mathematicians, none of whose names we could possible recite.

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