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234 CHAPTER NINE
Frequency Shift Keying (FSK) sets
M1n2 A sin 1vn t u2
where A is the fixed amplitude, vn is one of n different frequencies, and u is the
fixed phase. In the simplest form, n 2, and the waveform M looks like a sine
wave that slows down in frequency whenever the data is zero (v freq0 or freq1).
Phase Shift Keying (PSK) sets

M1n2 A sin 1v t un2

where A is the fixed amplitude, v is the fixed frequency, and un is one of n dif-
ferent phases. In the simplest form, n equals 2, and the waveform M looks like a
sine wave that inverts vertically whenever the data is zero (u 0 or 180 degrees).

Each modulation method has a corresponding demodulation method. Each modula-
tion method also has a mathematical structure that shows the probability of making
errors given a specific S/N ratio. We won’t go into the math here since it involves both
calculus and probability functions with Gaussian distributions. For further reading on
this, please see the following web site and PDF file:
www.sss-mag.com/ebn0.html
www.elec.mq.edu.au/ cl/files_pdf/elec321/lect_ber.pdf
What comes out of the calculations are called Eb/No curves (pronounced “ebb no”).
They look like the following figure, which shows a bit error rate (BER) versus an
Eb/No curve for a specific modulation scheme (see Figure 9-5).
Remember, Eb/No is the ratio of the energy in a single bit to the energy density of
the noise. A few observations about this graph:
The better the S/N ratio (the higher the Eb/No), the lower the error rate (BER). It
stands to reason that a better signal will work more effectively in the channel.
The Shannon limit is shown as a box. The top of the box is formed at a BER of
0.50. Even a monkey can get a data bit right half the time! The vertical edge of the
box is at an Eb/No of 0.69, the lower limit of the digital transmission we derived
earlier. No meaningful transmission can take place with an Eb/No that low; the
channel capacity falls to zero.
This graph shows the BER we can expect in the face of various Eb/No values in
the channel. Adjustments can be made. If the channel has a fixed No value that
cannot be altered, an engineer can only try to increase Eb, perhaps by increasing
the signal power pumped into the channel.