Determine the power density of the noise

Question

Assignment:

A narrowband radio transmission system has a transmit antenna with constant gain (g_Ant,Tx) _dB= 10dB and a receive antenna with constant gain (g_Ant,Rc)_dB. The receive antenna is modeled as a noisy resistor with noise temperature TS = 120 K, and is followed by a preamplifier with gain n (gA)dB = 20 dB and noise figure (FA)dB = 7 dB. Let the receiver be matched, and let the input signal have bandwidth B = 5 MHz and center frequency f₀ = 500 MHz. Determine:

a) The power density of the noise, in dBm/Hz, at the preamplifier output.

b) The required transmitted power for guaranteeing an output SNR of 20 dB at a distance of L = 300 m.

c) The maximum distance that guarantees an output SNR of 20 dB with a transmitted power of (P_Tx)dBm = 10 dBm.