B. P. Lathi, Zhi Ding - Modern Digital and Analog Communication Systems-Oxford University Press (2009)

382 PRINCIPLES OF DIGITAL DATA TRANSMISSION
This choice of minimum frequency separation is known as the minimum shift FSK. Since it
forms an orthogonal set of symbols, it is often known as orthogonal signaling.
We can in fact describe the minimum shift FSK geometrically by applying the concept of
orthonormal basis functions in Sec. 2.6. Let
1/J;(t) =
#. ( i-1 )
cos 2rr Ji + -- t
2T b
i = 1, 2, ... , M
It can be simply verified that
Thus, each of the FSK symbol can be written as
(f;
A cos 2nfm t = Ay 2
1/Jm (t)
m = I, 2, . .. , M
The geometrical relationship of the two FSK symbols for M = 2 is easily captured by Fig. 7 .36.
The demodulation of M-ary FSK signals follows the same approach as the binary FSK
demodulation. Generalizing the binary FSK demodulators of Fig. 7 .33 we can apply a bank of
M coherent or noncoherent detectors to the M-ary FSK signal before making a decision based
on the strongest detector branch.
Earlier in the PSD analysis of baseband modulations, we showed that the baseband digital
signal bandwidth at the symbol interval of T b can be approximated by 1 /T b . Therefore, for the
minimum shift FSK, ti./ = (M - l)/(4T b ), and its bandwidth according to Carson's rule is
approximately
M-3
2(1:i.f + B) = --
2Tb
In fact, it can be in general shown that the bandwidth of an orthogonal M -ary scheme
is M times that of the binary scheme [see Sec. 10.7, Eq. (10.123)]. Therefore, in an M-ary
orthogonal scheme, the rate of communication increases by a factor of log 2 M at the cost of
M-fold transmission bandwidth increase. For a comparable noise immunity, the transmitted
power is practically independent of M in the orthogonal scheme. Therefore, unlike M-ary ASK,
M-ary FSK does not require more transmission power. However, its bandwidth requirement
increases almost linearly with M (compared with binary FSK or M-ary ASK).
Fi g
ure 7.36
Binary FSK
symbols in the
two-dimensional
orthogonal
signal space.
'Pl (t)
0 '-------------•