Simulink Tutorial on Digital Modulation Methods - Cengage Learning

13.9. 16-ARY QUADRATURE AMPLITUDE-SHIFT KEYING (16-QAM) 631
2. Why do we observe nodes at t = 0.5T and t = 1.5T in the eye patterns at the
transmitter for α = 1? To solve this problem you can go back to Pulse Shape in
the main menu.
SOLUTION
1. For α = 0, raised-cosine and square-root raised-cosine pulses are identical and
there is zero ISI at the receiver. Therefore, for small rolloff factors α → 0, the
BER due to ISI decreases compared to α = 0.5. For large rolloff factors, the
impulse response decreases quite fast. However, the ISI to the next neighbor is
relatively strong. This can be observed from the convolution of two raised-cosine
pulses as displayed from the menu Pulse Shape > Convolution and depicted in
Figure 13.22. Therefore, for large rolloff factors α → 1, the BER is higher than
for α = 0.5.
2. For raised-cosine-pulses with α = 1, we have:
gT
⎧
� � ⎪⎨
kT
=
2 ⎪⎩
1, k = 0
1
2 , k =±1
0, otherwise
Therefore, we observe nodes in the eye pattern at 2k+1
2 T.
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