56Kbps Modem

On September 10, 1996, Rockwell Semiconductor Systems shocked the communications industry with its announcement of a revolutionary new dial up modem technology for communicating across the Public Switched Telephone Network (PSTN) at rates up to 56 Kbps*. Since that time, Rockwell’s 56Kbps technology has been supported and adopted by most of the communications related companies in the world as the way to communicate at rates up to 56Kbps.

Prior to this announcement, the modem communications industry had convinced itself that communications across the PSTN were limited by Shannon’s Theorem to rates below 35Kbps. Although Rockwell published a white paper describing its 56Kbps technology shortly after the public announcement, and submitted its technology for standardization to both the ITU and the ANSI TR30 committees, there have been continual requests for an in-depth discussion of how
the technology works, with particular emphasis on how this technology gets around the so-called Shannon Limit. This paper
attempts to address these issues.

Modem Fundamentals

Before describing how Rockwell’s 56Kbps technology works, let me first discuss how a traditional analog voice band modem works.

The voice band telephone channel is a bandpass channel, traditionally thought of as operating from about 300 Hz to 3,000 Hz.
Modem modulations, therefore, had to operate within this band. Early modems used tones (e.g., FSK) which fell within this frequency band for communicating data but the information density was not very high (the number of bits per hertz was significantly less than one).
Quadrature amplitude modulation (QAM) was a significant improvement, offering information densities of multiple bits per hertz.

Figure 1: Approximate frequency response of the filters associated with the codec in the line card.

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An ordinary telephone call will go through at least two of these filters, causing significant high frequency rolloff, usually 35 dB or more at 4Khz.

QAM operates by modulating a carrier sine wave signal in both amplitude and phase. Each unique combination of amplitude and phase is known as a "symbol". In the general case, a symbol is defined as an information carrying token which is sent from the transmitter to the receiver.

In the early days of modems, these tokens were called "baud" in honor of the French inventor Emile Baudot who, in 1875, invented a 5 bit code for representing the alphabet. Each 5 bits were a token communicating a letter of the alphabet or a control code. Recently, however, the term baud has become corrupted in common usage, with people using baud to mean bits per second. This is a throwback to the early days of modems when a baud carried only one bit (so the baud rate and the bit rate were the same). Thus, 300 bit per second modems became 300 baud modems in techie-talk. The problem is
that after a baud started carrying multiple bits, people were still using baud to mean bits per second. For modem designers, hearing someone describe a modem as a "9600 baud" or a "28.8 baud" modem is like fingernails on a blackboard. To avoid this, the modem cognoscenti began using the term "symbol".

Now, when you modulate a sine wave, the resulting signal is no longer a single frequency sine wave. The resulting signal will be a range of frequencies, related to the signal which is modulated onto the carrier. Assuming random bits, the bandwidth of a modulated QAM signal is equal to the symbol rate. That is, if you send 2400 symbols per second, the bandwidth of the modem signal will be 2400 hz. The V.32 modulation, for example, uses a carrier of 1800 hz and a symbol rate of 2400 symbols per second. The bandwidth of the signal, therefore, is from 600 hz to 3000 hz.

Over time, modem designers began to realize that the telephone network was getting better and that more bandwidth was available. Newer modem modulations began to take advantage of these higher bandwidth channels. The highest V.34 rate, for example, uses a carrier of 1959 hz, and a symbol rate of 3429 symbols per second, giving a bandwidth from about 244 hz to 3674 hz.

QAM, you’ll recall, is a modulation of a signal in both amplitude and phase. And when you talk of amplitude and phase, you immediately think of vectors. It turns out that modem designers use the concept of vectors to visualize the