Determine the channel made by a radio link with carrier

Question

Assignment:

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

PTx(ƒ)= 10^-2/2B rect (ƒ/2B) [W/Hz], B= 1 MHz

The channel is characterized by the frequency response

G_Ch(ƒ) = G₀ rect (ƒ/2B_Ch)

With G₀ = 0.1, B_Ch= 1 GHz and has output impedance 100Ω and noise temperature T_S = T₀. At the channel output we have an amplifier with input impedance 100Ω, 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.