Essentially, phase modulation is just like frequency modulation, except that the amplitude of
the modulating signal causes a shift in the reference (or center) carrier phase. The difference
between FM and phase modulation (PM) is this: for a given modulation signal amplitude,
phase varies only with the modulating signal's amplitude and not the modulating signal's
frequency. FM, on the other hand, varies directly with the modulating signal's amplitude but
inversely with the modulating signal's frequency. In other words, using FM, the lower the
frequency is, the greater will be the deviation for a given amplitude. That is all (from a practical
aspect) there is in the way of theoretical difference. It is possible to obtain FM from a
PM generation or PM from an FM generation; it is all in how the modulating signal is presented.
Please note that a continuing change in phase is a change in frequency.

Encoding Data

To increase the data rate for a particular modulation scheme without increasing the line's
baud rate requirements (baud is the line modulation rate), the digital data may be encoded.
One of the earliest examples of encoding is the process called di-bit encoding. In it, a buffer
holds the input data to be transmitted, and decisions are made on every two bits. As an
example, use 2,400 bps. Logic is constructed so a decision is made every 1/1,200th of a
second rather than at the bit rate of 1/2,400th a second. Examining the bits in pairs is the
reason for this decrease in decision-making frequency. Four possible combinations will be
possible from the two binary digits, but a decision about which one of the four combinations
is needed only has to be made 1,200 times a second rather than 2,400 times a
second. This is now a four-state signal. Figure 7-5 illustrates the phase modulation technique
that is used to transmit the four states.

This is type of phase modulation is called continuous phase modulation or continuous
phase shift keying (PSK). The last transmitted phase becomes the reference for the next
transmitted phase. Obviously, a long string of 1s or zeros could cause a continuous change
in phase, and the transmit frequency would change. If the change is significant enough the
receiver will lose synchronization. This can be remedied by inserting circuitry and logic that
causes predictable state changes at the modulator and removing the changes upon demodulation;
this circuitry is known as a scrambler.

The resulting four state modulation is referred to as "quaternary phase shift keying"
(QPSK). It reduces the line bandwidth required for a given data rate signal. Of course, the
laws of physics won't give something for nothing, and in this case the something is signalto-
noise ratio. The QPSK method requires a signal-to-noise ratio that is higher than that of
the uncoded signal. At the demodulator, the last received phase becomes the new zero reference
phase. This phenomenon is called "differentially coherent detection." Multiple-bit
systems form the basis for modern data transmission technology.

Tri-bit systems have been used that have eight different phase positions. Newer techniques
allow five or six bits to be encoded. A selection is then made from thirty-two (five-bit) or
sixty-four (six-bit) data states and choosing the phase change that makes the largest change
of phase for the bit combination being encoded. This technique is called "trellis-coded"
modulation; so called because when the possible states are graphically located the resulting
image is that of a trellis. Trellis-coded modulation requires the use of a selection algorithm,
which is usually executed by a microprocessor. In most "standard" modems, not only are
phase shifts selected; the amplitude modulation of the particular phase is also selected (typically
one half or full power). This results in a particularly large trellis. Trellis-coded
modulation is how 33.6 Kbps duplex (a total of 67.2 Kbps for both directions) makes it
down a 1,200-baud wireline. The number of bits encoded fools the line into thinking only
six hundred decisions a second were made in each direction. Figure 7-6 is a representation
of trellis coding, showing the first 90° of phase difference. Twelve decisions are possible: six
for each 15° change in phase shifts and another six regarding whether they are at half or
full power. For four quadrants this means forty-eight possible states. Typically, five bits are
used; this would give thirty-two actual states required, and thirty-two times six hundred (the
allowable decisions made in one direction) would give a data rate of 19,200 bps. There are
more combinations than decisions because the algorithm always chooses the maximum
deviation for that combination. The receive demodulator must have the same algorithm.

The point of this discussion should be to emphasize the importance of having identical
selection algorithms at each end; without them, detection will be impossible.

Demodulation is the reverse of modulation. Once the phase combination is recovered then
that particular combination of bits is placed in the output register and transmitted at the bit
rate. Note that you may modulate information as fast as you want. If it cannot be demodulated
then you cannot use it; it is just that simple.