Also by exploiting the memory inserted
into the transmit signal when applying the cross-correlator, the optimum demodulator now becomes
a trellis decoder (Viterbi sequence estimator). In continuing with the original FQPSK modulation
scheme, the number of states to be used in the trellis decoder is 16 [68??“71].
2.2.9 M-ary Frequency Shift Keying (FSK)
Earlier we have presented binary FSK and discussed the optimal choices of the modulation index and
where the orthogonality principle plays a role. In this subsection, we will discuss increasing the number
of modulation levels in FSK to M, which is commonly called M-ary FSK or M-level FSK [72, 73].
First, let us consider the following simple example for illustrative purposes. If a sinusoid is represented
as a vector, then the orthogonal binary and ternary FSK modulation schemes can be viewed as
in Fig. 2.87, using the Cartesian coordinate system. It is easy to convey this point in two and three
dimensions; higher dimensions have decision regions that are more difficult to draw.
102 CHAPTER TWO
FIGURE 2.87 Comparison of binary and ternary FSK signal constellation diagrams.
n
S1
S2
Decision Line
BFSK (M = 2)
S1
S2
Decision Line
S3
MFSK (M = 3)
n
Above we see that the distance between any two signal vectors is constant.
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