Skipper this is from the Jan. 97 issue of BoardWatch magazine........
LET'S GET TECHNICAL
The following shouldn't be published in a magazine -ever. J-School Graduates - DON'T TRY THIS AT HOME. But we're going to attempt a simplified explanation of how modern modems work, why an increase to 56 kbps connections over regular analog lines is feasible, and why it will only work at that speed in one direction.
Modems are designed to pass digital data over analog telephone lines designed to pass audio in the frequency range of near zero Hz to just above 4000 Hz. There's actually about 3500 Hz of this that is usable by a modulated audio carrier.
The classic explanation of modems is that they convert digital bits and bytes to a series of audio tones by MODULATING a carrier. And at the receiving end, they DEMODULATE this carrier by detecting the tones and converting them back into digital bits.
Actually, this has been only conceptually true for over a decade. At about the point of movement from 300 bps to 1200 bps modems, the entire concept of TONES went out the window. You simply can't pass tonal changes over analog lines much faster than 600 times per second. Recall that we used to refer to the speed of modems as BAUD. Baud refers to the state change transmitted which in the frequency modulation days was equivalent to the number of bits per second transmitted.
Today's modems encode data to allow each change in state in the audio waveform to represent a variable number of data bits. So the entire concept of BAUD becomes somewhat irrelevant. We want to know how fast data can transit the connection in bits per second (bps) or characters per second (cps). What you have to do to the waveform to get them there is not terribly interesting.
This was done by varying two waveform variables that can be controlled and using them to symbolically represent data. One thing you can do over analog lines is make a sound wave or carrier LOUDER or softer with regards to varying its AMPLITUDE. The other thing you can alter is the frequency or pitch of the carrier. But with regards to frequency, you can actually detect more minute changes in PHASE of an audio carrier wave by comparing it to a reference carrier. The audio carrier is essentially a sinusoidal oscillation that goes through a 360 degree cycle with each oscillation. We can detect fairly small phase differences between sinusoidal waveforms. And so phase-shift keying or PSK became a preferred modulation technique. Since this requires a stable frequency, frequency modulation has largely been abandoned.
Using these two variables, phase and amplitude, we can use the various state combinations as SYMBOLS to represent binary data. In this way, we can transmit a number of binary bits via a single symbol. Let's look at a simple example:
<Picture>Figure 3
First, audio or sound is a simple oscillation or vibration. The nature of such vibrations is that they are regular, and they are repetitive. The rate of repetition is of course the frequency. The higher the speed of the oscillation - the higher the heard "pitch" of the tone. But the oscillation itself appears as a sine wave as shown in Figure 3. One complete cycle of the wave can be marked off much as you would a circle, in degrees. By comparing an audio sine wave with a reference, you can detect the "difference" in the two waves as a function of "phase angle."
Two modems, in the process of the initial handshake, can synchronize internal reference generators to establish a reference waveform. They can then transmit phase modulated waveforms between them. By comparing the received modulated waveform to the reference waveform, they can detect phase angle differences. We can use these phase angle differences to represent data.
<Picture>Figure 4
Figure 4 shows phase angles of 0 degrees, 90 degrees, 180 degrees, and 270 degrees. We can arbitrarily use these phase states to represent binary data as follows:
0 degrees0090 degrees01180 degrees10270 degrees11
Note that by transmitting a SINGLE symbol in one of FOUR states, we can actually pass TWO bits of binary data. This is rather magnified by using finer divisions of phase-state:
0 degrees00045 degrees00190 degrees010135 degrees011180 degrees100225 degrees101270 degrees110315 degrees111
We now have 8 phase states, but we also now represent THREE binary bits via the transmission of a SINGLE phase-state symbol. A single change in phase of the sinusoidal waveform allows us to transmit three bits of data.
The other variable we can easily manipulate is the SIZE or AMPLITUDE of the waveform. Since this is attenuated in various ways by the telephone lines along the way, again during the initial training sequence between modems the two modems have to agree that a signal THIS loud is a significant amplitude level, while a signal THAT loud would be recognized as a DIFFERENT amplitude level.
The addition of amplitude allows us to increase the amount of data transmitted.
Amplitude
Phase
Binary Data
Level 10 degrees0000Level 145 degrees0001Level 1 90 degrees0010Level 1135 degrees0011Level 1 180 degrees0100Level 1 225 degrees0101Level 1270 degrees0110Level 1 315 degrees0111Level 20 degrees1000Level 245 degrees1001Level 2 90 degrees1010Level 2135 degrees1011Level 2 180 degrees1100Level 2 225 degrees1101Level 2270 degrees1110Level 2 315 degrees1111
In this example, using two amplitude variations, and our 8 phase states, we can transmit 4 bits of data for each unique combination - let's call these quantization levels. For each single and instantaneous change in amplitude and phase, we can transmit FOUR bits of data. Better than the old compound interest trick, eh? Figure 5 shows a very basic CONSTELLATION using two levels of amplitude and eight phase angle states to represent four data bits with a single symbol transmission.
<Picture>Figure 5
If we add another amplitude level, we get five bits per symbol. And if we continue to add finer phase angles, and finer amplitude levels, we can further this into ever finer quantization levels or points. And these points represent ever larger strings of binary data.
The array of symbols using various combinations of amplitude and phase, diagrammed as in figure 5, is referred to as a CONSTELLATION - it rather looks a bit like a star chart. The mission in developing higher data rates is to define ever more populated constellations. In this way, ever longer strings of binary data can be conveyed with a single instantaneous transmission of a waveform state change.
So why not just have a thousand amplitude levels and use phase states every 1/100th of a degree to get some REALLY fast data rates?
As we increase the number of symbols in the constellation, the symbols are of course closer together - in either amplitude or phase or both. They therefore become increasingly difficult to differentiate from each other on the receiving end - particularly toward the center of the constellation (low amplitudes). They also are jittered about by the vagaries of the analog line environment which has its own inductance, capacitance, noise, etc. Various ingenious means have been developed to run some test data back and forth between two modems to "train" or test the line to factor out some of these factors in the line itself - usually referred to as EQUALIZATION.
But the important part to note is that the problem of data transmission is almost entirely one of DETECTION at the receiving end. It is actually pretty easy to MODULATE a waveform that you are transmitting with a very high degree of precision. But to receive a waveform and detect whether or not it is actually at 90 degrees phase shift or an 85 degrees phase shift is much more difficult. It is similarly more difficult to detect differences in closely spaced amplitude levels from more coarsely differentiated levels.
The reason I wanted to go through all of this explanation is that the real reason that 56 kbps speeds are possible is not so much that the data is being transmitted in digital form between the ISP and the telco central office. It is that in doing so we have ELIMINATED SEVERAL DIGITAL/ANALOG and ANALOG/DIGITAL conversions. These conversions tend to warp the constellation - and they are much more difficult to equalize or counter than the relatively simple problems posed by analog line characteristics.
Again note that it is much easier to convert a digital signal to a fairly precise analog waveform for transmission, than it is to analyze a received analog waveform, detect small variations in phase and amplitude, and create a digital signal from that information.
As it so happens, the telephone system has already been converted to digital technology. Almost all connections between central offices are done digitally and increasingly over fiber. Really, the only analog portion of the system in most areas is the last link from central office switch to the customer's home - as little as a few hundred feet to as high as 18,000 feet and more of 24 or 26 gauge copper. The rest of the system is a maze of 64 kbps digital channels and the telco system itself uses what could be thought of a kind of modem, a MU LAW CODEC, to do the conversions between the digital internal network and the analog local loop.
<Picture>Figure 6
Figure 6 shows the problem. With a typical analog ISP connection, the signal from the ISP going downstream must be converted from digital to analog with a digital to analog converter in the modem. This is transmitted to the telco central office switch over an analog local loop line. So the analog transmission is actually converted there to digital using this MU CODEC at the switch.
At the customer's local loop from the CO switch, the data is again converted from digital within the switch to analog for transmission to the end user, again using the mu codec.
The back channel works pretty much the same. Analog signals from the customers modem and local loop are received at the switch and converted to digital via a mu codec coming into the switch, then again through a mu codec back to analog for transmission via the local loop to the ISP.
The important element here is actually the mu codecs at the telco switch. These codecs use 256 non-uniformly spaced quantization levels largely unrelated to the digital to analog conversion in the data modems we know and love. They use 8 data bits to represent each of the 256 quantization points, and transmit this 8-bit data at an 8000 Hz rate for a total bandwidth of 64 kbps - note the similarity to the data rate for each channel of the T-Carrier and as it so happens, very similar to the 64 kbps data rate of each channel of ISDN.
If the modem at the ISP simply took digital data, and converted it to digital data compatible with the central office switch, and if we connect the ISP directly to the telco switch with a trunkside digital link like a 24 X56 kbps T-Carrier, or a 23B+D PRI ISDN line, we have eliminated the conversion in the ISP modem, and HALF of the codecs at the CO switch. We've essentially moved that conversion right into the ISP equipment room where we have to do one anyway. We've also eliminated the attendant loss inherent in conversion and more pointedly, in the Analog to Digital part (the hard part) of this conversion.
Now, examine the customer side of the telco switch. In going from the switch to the local loop, DOWN to the customer, we are still performing a MU CODEC Digital to Analog conversion. Recall that we said we can convert digital signals to an analog waveform with great precision. But on the UPSTREAM side, at the telco switch we are converting an incoming analog waveform to digital data - much more difficult to do accurately.
This is why with the new 56 kbps technology, we can achieve data rates of 56 kbps, and in some cases marginally higher, DOWNSTREAM to the customer. This is really limited by the speed of the digital connection between the ISP and the CO. But we are still limited to 33.6 kbps in the back channel UPSTREAM from the customer to the ISP. And the center of all of this is NOT so much the pure clean digital signal from the ISP location to the telco switch (oh, it doesn't hurt), but rather the elimination of half of the mu codecs at the telco switch itself. And again, the digital to analog portion of the codec, downstream to the customer, is much more accurate than the analog to digital portion of the codec, coming back up. |
