Consider a PCM communication system with the following specifications: • Data bandwidth: 4 kHz. Sampling rate: 20% over the Nyquist rate. Quantization levels: 8. • Line code: Polar nonreturn-to-zero (NRZ). • Transmission nower: 12 mW

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Consider a PCM communication system
with the following specifications:
• Data bandwidth: 4 kHz.
• Sampling rate: 20% over the
Nyquist rate.
• Quantization levels: 8.
• Line code: Polar nonreturn-to-zero
(NRZ).
• Transmission power: 12 mW.
• Bit transmission probability:
Po = 20%.
• Channel noise PSD: 5 µW.
If a matched filter (MF) is used at the
receiver with a normalising factor of
c = 1/AT,, find the following:
Transcribed Image Text:Consider a PCM communication system with the following specifications: • Data bandwidth: 4 kHz. • Sampling rate: 20% over the Nyquist rate. • Quantization levels: 8. • Line code: Polar nonreturn-to-zero (NRZ). • Transmission power: 12 mW. • Bit transmission probability: Po = 20%. • Channel noise PSD: 5 µW. If a matched filter (MF) is used at the receiver with a normalising factor of c = 1/AT,, find the following:
1.
Find the bit rate Rp
kbps.
Find the transmission
bandwidth BT
kHz.
3.
BFind the bit period 76
msec.
Find the bit period A
%3D
V.
5.
Find the noise variance after
MF, o2
W.
6.
The optimal detection
threshold, Yopt
V.
7.
The BER =
Hint: Use the approximation
„2
2
Q(x) =
e
Transcribed Image Text:1. Find the bit rate Rp kbps. Find the transmission bandwidth BT kHz. 3. BFind the bit period 76 msec. Find the bit period A %3D V. 5. Find the noise variance after MF, o2 W. 6. The optimal detection threshold, Yopt V. 7. The BER = Hint: Use the approximation „2 2 Q(x) = e
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