# Examination of a satellite QPSK link

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

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#### Solution Preview

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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

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 ...

#### 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