The Limitations

The challenge for the modem designers is to exploit this configuration, to achieve the highest possible data rate. There is still a section of analogue line in the link, and this poses the greatest difficulty - the highest data rate is set by the slowest section. The digital line, from the ISP's modem to the user's local exchange, is almost error-free and can be considered as a perfect 64 kbit/s channel.

The restrictions imposed by the analogue telephone line are difficult to overcome. They relate mainly to the bandwidth of the channel, and the noise added to any signal passing through it.

The usable frequency range of the analogue line extends from approximately 200 Hz to 4 kHz. This is an artificial restriction, imposed to allow the network to carry many telephone calls at once. It is, however, universal, and limits the speed at which symbols can be transmitted.

As Figure 3 shows, frequencies above 4 kHz suffer severe loss. Unfortunately, this is not the only problem: associated with this signal loss characteristic is a varying time delay. All signals take a certain amount of time to travel the length of the cable; however, different frequencies are delayed by different amounts. A square pulse signal contains a wide range of frequencies, each of which will face a different delay, with the result that the received signal will look nothing like the original pulse! (Figure 4)

As long as the data rate is much lower than the channel bandwidth, there is no problem. As the data rate increases, however, the distortion becomes worse - eventually leading to Inter-Symbol Interference (ISI). This can cause severe data corruption, as the delayed echoes of one pulse merge with the next.

To these bandwidth problems is added noise. This term covers all forms of unwanted signal, received with the wanted data. Noise is always present, in every system, and sets the ultimate limit on performance. The critical measure in communications equipment is Signal to Noise Ratio: the wanted signal must be discernable from the noise if the data is to be recovered at the receiver. There are many different sources of electrical noise, but they can all be classified as either natural or man-made. One particularly important man-made form, for a modem, is quantisation noise.

Natural and man-made noise combines with the wanted signal as it travels through the analogue channel. Natural sources of noise are the result of the physical properties of materials. For example, any conductor at a temperature above absolute zero (-273 °C) will generate thermal noise. Man-made noise, or interference, is generated by other electrical equipment. Crosstalk between two cables is a common example.

Quantisation noise is not generated by an external source, but is a result of the analogue to digital conversion performed at the user's modem and at the exchange. The digital system can only represent a limited number of signal levels, so some information is always lost when converting from a continuously-varying analogue waveform. When analysing communication systems, it is convenient to represent the resulting error as a form of noise - it has a similar effect to natural noise. The telephone system uses 8 bits to sample the speech signal, resulting in 256 discrete signal levels and a fairly high level of quantisation noise.

To ensure that this quantisation noise is not distracting to the telephone user, a technique called companding is used. The human voice is predominantly quiet, so the companding system allocates more quantisation levels at the low end than at the high end of the signal range. The closely-spaced levels are able to represent the voice signal more accurately, reducing the noise. Unfortunately, modem signals tend to be more random, and use the whole range of signal levels. When companded, this has the detrimental effect of amplifying the natural noise, without improving the quantisation noise.

These are the problems facing all modem transmissions, and the reasons that speeds have so far been limited to 33.6 kbit/s.

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