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# Examination of a terrestrial communications link

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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?

#### Solution Preview

Find solution as attached.

We have bandwidth

RRC filter roll-off

a.

(i) Symbol rate is determined from

(or )

(ii) For QPSK we have

Bit rate determined by

(iii) Noise bandwidth of the receiver is same as symbol rate (for RRC filter) thus noise bandwidth is

b. Noise temperature is , Input to receiver has power , receiver implementation margin is

The output carrier power is the input carrier power less the so we get

Noise power is

Where is Boltzmann's constant

Noise power is ...

#### Solution Summary

The solution discusses what is the maximum symbol rate that can transmit over the link without ISI, the bit rate with QPSK modulation, the noise bandwith of the receiver.

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