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New HOWTO: Modem-HOWTO - page 20

Table of Contents

  • April 12, 2001
  19.  Appendix A:  How Analog Modems Work (technical) (unfinished)

  19.1.  Modulation Details

  19.1.1.  Intro to Modulation

  This part describes the modulation methods used for conventional
  modems.  It doesn't cover the high speed methods (modulus conversion)
  sometimes used by ``56k Modems (v.90)''.  But 56k modems also use the
  modulation methods described here.

  Modulation is the conversion of a digital signal represented by binary
  binary (0 or 1) into an analog signal something like a sine wave.  The
  modulated signal consists pure sine wave "carrier" signal which is
  modified to convey information.  A pure carrier sine wave, unchanging
  in frequency and voltage, provides no flow of information at all
  (except that a carrier is present).  To make it convey information we
  modify (or modulate) this carrier.  There are 3 basic types of
  modulation: frequency, amplitude, and phase.  They will be explained
  next.
  19.1.2.  Frequency Modulation

  The simplest modulation method is frequency modulation.  Frequency is
  measured in cycles per second (of a sine wave).  It's the count of the
  number of times the sine wave shape repeats itself in a second.  This
  is the same as the number of times it reaches it peak value during a
  second.  The word "Hertz" (abbreviated Hz) is used to mean "cycles per
  second".

  A simple example of frequency modulation is where one frequency means
  a binary 0 and another means a 1.  For example, for some obsolete 300
  baud modems 1070 Hz meant a binary 0 while 1270 Hz meant a binary 1.
  This was called "frequency shift keying".  Instead of just two
  possible frequencies, more could be used to allow more information to
  be transmitted.  If we had 4 different frequencies (call them A, B, C,
  and D) then each frequency could stand for a pair of bits.  For
  example, to send 00 one would use frequency A.  To send 01, use
  frequency B; for 10 use C; for 11 use D.  In like manner, by using 8
  different frequencies we could send 3 bits with each shift in
  frequency.  Each time we double the number of possible frequencies we
  increase the number of bits it can represent by 1.


  19.1.3.  Amplitude Modulation

  Once one understands frequency modulation example above including the
  possibilities of representing a few bits by a single shift in
  frequency, it's easier to understand both amplitude modulation and
  phase modulation.  For amplitude modulation, one just changes the
  height (voltage) of the sine wave analogous to changing the frequency
  of the sine wave.  For a simple case there could only be 2 allowed
  amplitude levels, one representing a 0-bit and another representing a
  1-bit.  As explained for the case of frequency modulation, having more
  possible amplitudes will result in more information being transmitted
  per change in amplitude.


  19.1.4.  Phase Modulation

  To change the phase of a sine wave at a certain instant of time, we
  stop sending this old sine wave and immediately begin sending a new
  sine wave of the same frequency and amplitude.  If we started sending
  the new sine wave at the same voltage level (and slope) as existed
  when we stopped sending the old sine wave, there would be no change in
  phase (and no detectable change at all).  But suppose that we started
  up the new sine wave at a different point on the sine wave curve.
  Then there would likely be a sudden voltage jump at the point in time
  where the old sine wave stopped and the new sine wave began.  This is
  a phase shift and it's measured in degrees (deg.)  A 0 deg. (or a 360
  deg.) phase shift means no change at all while a 180 deg. phase shift
  just reverses the voltage (and slope) of the sine wave.  Put another
  way, a 180 deg. phase shift just skips over a half-period (180 deg.)
  at the point of transition.  Of course we could just skip over say 90
  deg. or 135 deg. etc.  As in the example for frequency modulation, the
  more possible phase shifts, the more bits a single shift in phase can
  represent.


  19.1.5.  Combination Modulation

  Instead of just selecting either frequency, amplitude, or phase
  modulation, we may chose to combine modulation methods.  Suppose that
  we have 256 possible frequencies and thus can send a byte (8 bits) for
  each shift in frequency (since 2 to the 8 power is 256).  Suppose also
  that we have another 256 different amplitudes so that each shift in
  amplitude represents a byte.  Also suppose there are 256 possible
  phase shifts.  Then a certain points in time we may make a shift in
  all 3 things: frequency, amplitude and phase.  This would send out 3
  bytes for each such transition.

  No modulation method in use today actually does this.  It's not
  practical due to the relatively long time it would take to detect all
  3 types of changes.  The main problem is that frequent shifts in phase
  can make it appear that a shift in frequency has happened when it
  actually didn't.

  To avoid this difficulty one may simultaneous change only the phase
  and amplitude (with no change in frequency).  This is called phase-
  amplitude modulation.   It is also called quadrature amplitude
  modulation (= QAM) since there were only 4 possible phases
  (quadrature) in early versions of it.  This method is used today for
  the common modem speeds of 14.4k, 28.8k, and 33.6k.  The only
  significant case where this modulation method is not used today is for
  56k modems.  But even 56k modems exclusively use QAM (phase-amplitude
  modulation) in the direction from your PC out the telephone line.
  Sometimes even the other direction will also fall back to QAM when
  line conditions are not good enough.  Thus QAM (phase-amplitude
  modulation) still remains the most widely used method on ordinary
  telephone lines.


  19.2.  56k Modems (v.90)

  The "modulation" method used above 33.6k is entirely different than
  the common phase-amplitude modulation.  Since ordinary telephone calls
  are converted to digital signals at the local offices of the telephone
  company, the fastest speed that you can send digital data by an
  ordinary telephone call is the same speed that the telephone company
  uses over its digital portion of the phone call transmission.  What is
  this speed?  Well, it's close to 64kbps.  It would be 64k but
  sometimes bits are "stolen" for signalling purposes.  But if the phone
  Co. knows that the link is not for voice, bits may not get stolen.
  The case of 64k will be presented and then it will be explained why
  the actual speed is lower (56k or less --usually significantly less).

  Thus 64k is the absolute top speed possible for an ordinary telephone
  call using the digital portion of the circuit that was designed to
  send digital encodings of the human voice.  In order to use 64k, the
  modem must know exactly how the telephone company is doing its digital
  encoding of the analog signals.  This task is far too complicated if
  both sides of a telephone call have only an analog interface to the
  telephone company.  But if one side has a digital interface, then it's
  possible (at least in one direction).  Thus if your ISP has a digital
  interface to the phone company, the ISP may send out a certain digital
  signal over the phone lines toward your PC.  The digital signal from
  the ISP gets converted to analog at the local telephone office near
  your PC's location (perhaps near your home).  Then it's your modem's
  task to try to figure out exactly what that digital signal was.  If it
  could do this then transmission at 64k (the speed of the telephone
  company's digital signal) is possible in this direction.

  What method does the telephone company use to digitally encode analog
  signals?  It uses a method of sampling the amplitude of the analog
  signal at a rate of 8000 samples per second.  Each sample amplitude is
  encoded as a 8-bit (ASCII-like) byte.  (Note: 8 x 8000 = 64k)  This is
  called "Pulse Code Modulation" = PCM.  These bytes are then sent
  digitally on the telephone company's digital circuits where many calls
  share a single circuit using a time-sharing scheme known as "time
  division multiplexing".  Then finally at a local telephone office near
  your home, the digital signal is de-multiplexed resulting in the same
  digital signal as was originally created by PCM.  Then this signal is
  converted back to analog and sent to your home.  Each 8-bit byte
  creates a certain amplitude of the analog signal.  Your modem's task
  is to determine just what that PCM 8-bit byte was based on the analog
  amplitude it detects.

  This is (sort of) "amplitude demodulation" but not really.  It's not
  amplitude demodulation because there is no carrier.  Actually, it's
  called "modulus conversion" which is the inverse of PCM.  In order to
  determine the digital codes the telephone Co. used to create the
  analog signal, the modem must sample this analog signal amplitude at
  exactly the same points in time the phone Co. used when it created the
  analog signal.  To do this a timing signal is generated from a
  residual 4kHz signal on the analog phone line.  The creation of
  amplitudes to go out to your home/office at 8k amplitudes/sec sort of
  creates a 4kHz signal.  Suppose every other amplitude was of opposite
  polarity.  Then there would be a 4kHz sine-like wave created.  Each
  amplitude is in a sense a 8-bit symbol and when to sample amplitudes
  is known as "symbol timing".

  Now the encoding of amplitudes in PCM is not linear.  At low
  amplitudes an increment of 1 in the PCM byte represents a much smaller
  increment (delta) in analog signal amplitude than would be the case if
  the amplitude being sampled were much higher.  Thus for low amplitudes
  it's difficult to distinguish between adjacent byte values.  To make
  it easier to do this (for 56k modems) certain PCM codes representing
  very low amplitudes are not used.  This gives a larger delta between
  possible amplitudes and makes correct detection of them by your modem
  easier.  Thus half the amplitude levels are not used by v.90.  This is
  tantamount to each symbol (allowed amplitude level) representing 7
  bits instead of 8.  This is where 56k comes from: 7 bits/symbol x 8k
  symbols/sec = 56k bps.  Of course each symbol is actually generated by
  8-bits but only 128 bytes of the possible 256 bytes are actually used.
  There is a code table mapping these 128 8-bit bytes to 128 7-bit
  bytes.

  But it's a little more complicated that this.  If the line conditions
  are not nearly perfect, then even fewer possible levels (symbols) are
  used resulting in speeds under 56k.  Also due to US government rules
  prohibiting high power levels on phone lines, certain high amplitudes
  levels can't be used resulting in only about 53.3k at best for "56k"
  modems.

  Note that the digital part of the telephone network is bi-directional.
  Two such circuits are used for a phone call, one in each direction.
  The 56k signal is only used in one of these directions: from your ISP
  to your PC.  The other direction, from your home/office to the ISP,
  uses the conventional phase-amplitude modulation scheme with a maximum
  of 36.6kbps (and not 53.3kbps).  The analog portion of the circuit
  from your home/office to the nearest telephone Co. office was never
  intended to be bi-directional since it's only a single twisted pair.
  But due to sophisticated cancellation methods it's able to convey data
  simultaneously in both directions as explained in the next subsection.


  19.3.  Full Duplex on One Circuit

  Modern modems are able to both send and receive signals
  simultaneously.  One could call this "bidirectional" or "full duplex".
  This was once done by using one frequency for sending and another for
  receiving.  Today, the same frequency is used for both sending and
  receiving.  How this works is not easy to comprehend.

  Most of the telephone system "main lines" are digital with two
  channels in use when you make a telephone call.  What you say goes
  over one digital channel and what the other person says goes over the
  other (reverse) digital channel.  Unfortunately, the part of the
  telephone system which goes to homes (and many offices) is not digital
  but only a single analog channel.  If both modems were directly
  connected to the digital part of the phone system then bidirectional
  communication (sending and receiving at the same time) would be no
  problem because two channels would be available.

  But the end portion of the signal path goes over just one circuit.
  How can there be two-way communication on it simultaneously?  It works
  something like this.  Suppose your modem is receiving a signal from
  the other modem and is not transmitting.  Then there's no problem.
  But if your modem were to start transmitting (with the other received
  signal still flowing into your modem) it would drown out the received
  signal.  If the transmitted signal was a "solid" voltage wave applied
  to the end of the line then there is no way any received signal could
  be present at that point.

  But the transmitter has "internal impedance" and the transmitted
  signal applied to the end of the line is not solid (or strong enough)
  to completely eliminate the received signal coming from the other end.
  Thus while the voltage at the end of the line is mostly the stronger
  transmitted signal a small part of it is the desired received signal.
  All that is needed is to filter out this stronger transmitted signal
  and then what remains will be the signal from the other end which we
  want.  To do this, one only needs to get the pure transmitted signal
  directly from the transmitter (before it's applied to the line)
  amplify it a determined amount, and then subtract it from the total
  signal present at the end of the line.  Doing this in the receiver
  circuits leaves a signal which mostly came from the other end of the
  line.


  19.4.  Echo Cancellation

  A signal traveling down a line in one direction may encounter changes
  in the line that will cause part of the signal to echo back in the
  opposite direction.  Since the same circuit is used for bi-directional
  flow of data such echos will result in garbled reception.  One way to
  ameliorate this problem is to send training signals once in a while to
  determine the echo characteristic of the line.  This will enable one
  to predict the echos that will be generated by any given signal.  Then
  this prediction method is used to predict what echos the transmitted
  signal will cause.   Then this predicted echo signal is subtracted
  from the received signal.  This cancels out the echoes.
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