Consider s Tx (t) the signal at the input of the channel. s Tx (t) has a Gaussian amplitude…

Consider sTx(t) the signal at the input of the channel. sTx(t) has a Gaussian amplitude probability density function with zero mean and power density given by

The channel is characterized by the frequency response

With  GHz and has output impedance  and noise temperature TS = T0. At the channel output we have an amplifier with input impedance  gain 50 dB and noise figure 6 dB.

a) What is the probability that the signal at the amplifier input port takes values in the interval [−0.5, 0.5] V?

b) What is the SNR (in dB) at the receiver output?

c) Consider now the channel made by a radio link with carrier 1 GHz, length 50 km, transmit and receive antennas with gains 12 dB e 15 dB, respectively, and noise temperature of the receive antenna of 250 K. Determine the output SNR (in dB) for this system.


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