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# Examination of a satellite QPSK link

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A satellite communication link transmits a QPSK signal at a rate of 64 ksps. The transmitter and receiver have ideal RRC filters with alpha = 0.2. At the input to the QPSK demodulator in the receiver, the CNR is 19.0 dB under normal conditions (no rain in the link, known as clear air conditions). Assume an implementation margin of 0 dB.

a. What is the bandwidth occupied by the QPSK signal?
b. What is the BER at the output of the receiver in clear air conditions, and the average time between errors? Give your answer in years, days, or hours as appropriate.
c. Rain in the satellite to earth path causes the CNR to fall to 13.6 dB. What, approximately, is the BER at the output of the receiver, and the average time between errors? Give your answer in hours, minutes, or seconds, as appropriate.
[Use the Q (z) table below to estimate BER]

z Q(z) z Q(z)
0 0.5
2.0 2.280 E-2 5.1 1.701 E-7
2.1 1.791 E-2 5.2 9.981 E-8
2.2 1.394 E-2 5.3 5.799 E-8
2.3 1.075 E-2 5.4 3.372 E-8
2.4 8.220 E-3 5.5 1.902 E-8
2.5 6.227 E-3 5.6 1.073 E-8
2.6 4.674 E-3 5.7 6.000 E-9
2.7 3.476 E-3 5.8 3.320 E-9
2.8 2.562 E-3 5.9 1.820 E-9
2.9 1.871 E-3 6.0 9.979 E-10
3.0 1.354 E-3 6.1 5.310 E-10
3.1 9.702 E-4 6.2 2.827 E-10
3.2 6.889 E-4 6.3 1.490 E-10
3.3 4.847 E-4 6.4 7.778 E-11
3.4 3.378 E-4 6.5 4.021 E-11
3.5 2.332 E-4 6.6 2.058 E-11
3.6 1.595 E-4 6.7 1.043 E-11
3.7 1.081 E-4 6.8 5.236 E-12
3.8 7.252 E-5 6.9 2.603 E-12
3.9 4.821 E-5 7.0 1.281 E-12
4.0 3.174 E-5 7.1 6.244 E-13
4.1 2.070 E-5 7.2 3.014 E-13
4.2 1.337 E-5 7.3 1.440 E-13
4.3 8.558 E-6 7.4 6.816 E-14
4.4 5.423 E-6 7.5 3.194 E-14
4.5 3.404 E-6 7.6 1.482 E-14
4.6 2.117 E-6 7.7 6.810 E-15
4.7 1.303 E-6 7.8 3.098 E-15
4.8 7.948 E-7 7.9 2.396 E-15
4.9 4.800 E-7 8.0 6.226 E-16
5.0 2.872 E-7

#### Solution Preview

Question
A satellite communication link transmits a QPSK signal at a rate of 64 KSymbols/s. The transmitter and receiver have ideal RRC filters with  = 0.2. At the input to the QPSK demodulator in the receiver, the CNR is 19.0 dB under normal conditions (no rain in the link, known as clear air conditions). Assume an implementation margin of 0 dB.
a. What is the bandwidth occupied by the QPSK signal?
b. What is the BER at the output of the receiver in clear air conditions, and the average time
between errors (give your answer in years, days, or hours as appropriate).
c. Rain in the satellite to earth path causes the CNR to fall to 13.6 dB.
What, approximately, is the BER at the output of the receiver, and the average time between
[Use the Q (z) table below to estimate BER]

z Q(z) z Q(z)
0 0.5
2.0 2.280 E-2 5.1 1.701 E-7
2.1 1.791 E-2 5.2 9.981 E-8
2.2 1.394 E-2 5.3 5.799 E-8
2.3 1.075 E -2 5.4 3.372 E-8
2.4 8.220 E-3 5.5 1.902 E-8
2.5 6.227 E-3 5.6 1.073 E-8
2.6 4.674 E-3 5.7 6.000 E-9
2.7 3.476 E-3 5.8 3.320 E-9
2.8 2.562 E-3 5.9 1.820 E-9
2.9 1.871 E-3 6.0 9.979 E-10
3.0 1.354 E-3 6.1 5.310 E-10
3.1 9.702 E-4 6.2 2.827 E-10
3.2 6.889 E-4 6.3 1.490 E-10
3.3 4.847 E-4 6.4 7.778 E-11
3.4 3.378 ...

#### Solution Summary

A satellite QPSK link is examined and certain parameters including occupied bandwidth, BER in clear sky conditions, rain fade conditions and average time between errors determined

\$2.19

## Examination of a Terrestrial Communications Link

See the attached file.

A terrestrial radio link is used to send digital data over a long distance. The RF channel has a bandwidth of 250 kHz. The transmitter and receiver have ideal RRC filters with Rolloff = 0.25.

a. What is:
i. The maximum symbol rate that can transmitted over this link without ISI?
ii. The bit rate with QPSK modulation?
iii. The noise bandwidth of the receiver?

b. The receiving system has a noise temperature of 1000 K and the received signal at the input to the receiver has a power level of 121.5 dBW. The receiver has an implementation margin of 0.5 dB. What is the CNR at the receiver output?

c. What is the bit error rate of the received signal and the time between errors?

d. Rain occasionally affects the link and the received carrier falls to -132.0 dBW. The noise power in the receiver remains unchanged. What is the bit error rate of the received signal and the time between errors when these conditions apply?

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