Simulink Tutorial on Digital Modulation Methods - Cengage Learning

13.9. 16-ARY QUADRATURE AMPLITUDE-SHIFT KEYING (16-QAM) 625
2. The trajectory is sampled at rate 1/T. From Figures 13.105 and 13.106 it can
be seen that s_c(2kT ) =±1 and s_s(2kT ) = 0, whereas s_c((2k + 1)T ) = 0
and s_s((2k + 1)T ) =±1. Therefore, sampling the trajectory at 2kT yields
an in-phase point in the scatter plot, whereas sampling at (2k + 1)T yields a
quadrature point.
MSK can be coherently demodulated in the same way as Offset-QPSK followed by
a differential decoder. Therefore, we do not have to deal with demodulation explicitly
here.
13.9 16-ary Quadrature Amplitude-Shift Keying
(16-QAM)
13.9.1 16-QAM with Square-Root Raised-Cosine Pulses
Examine 16-QAM with square-root raised-cosine pulses:
16-QAM > Root-RC
The <strong>Simulink</strong> model and the transmitter model are depicted in Figures 13.113 and
13.114. In 16-QAM, b = 4 bits are mapped on a signal-space constellation point.
Figure 13.113: <strong>Simulink</strong> model for 16-QAM with square-root RC pulses
You can view the signal-space constellation in Figure 13.115 by double-clicking on the
blue box signal-space Constellation.
TUTORIAL PROBLEM
Problem 13.22 [Gray Mapping] Check if the labeling is done according to a Gray
mapping, i.e., constellation points with minimum Euclidean distance differ in only one
bit. What is the purpose of using Gray mapping instead of an arbitrary mapping of bits
to constellation points? Is Gray mapping possible for higher-order QAM modulation?
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