# minimum Signal to noise ratio (in dB) at the reciever

#### Mark?

Joined Jul 14, 2022
3
Hello Everybody,

im struggling with a task from an old exam.

Actual Task: What is the minimum signal to noise ratio in dB at the receiver?
First the data:
frequency band: 200-500kHz
transmitting power
: 30dBm-constant spectral power density over the frequency band
spectral power density of the noise at the receiver: N(f) = N0*(1-k*f/1MHz) with N0=-25dBm/Hz, k=3
attenuation between transmitter and receiver: D(f)= D0*(1+m*f/1MHz) with D0=3 dB, m=10
i have the 3 anwsers to choose: 16dB, 9,7db, 14dB and the fourth is again not on the picture.

The first task was to determine the spectral power density (in dBm/Hz) at the transmitter:
So i calculated : 30dBm - 10log(300kHz) = -24,77dBm/Hz
I assume that this is right, cause we have a few Answers to choose and it was : -24,8 dBm/Hz, -18 dBm/Hz, -16,8 dBm/Hz. The fourth one wasnt on the picture.

So i tried it with the transformed 30dBm in to the -24,77dBm/Hz but then i actually dont know how to go with the Noise and the Attenuation.
For the Noise i calculated: N=-25dBm/Hz*(1-3*f/1MHz) with f= 300kHz Bandwith and then comes -2,5dBm/Hz. SO this value hasnt to transform because it is in dBm/Hz.
So now i have: SNR=10^((-24,77 - 3dB - 30dB*f/1MHz + 2,5)/10) but this value is way to small because i have a negative number.
My problem is i dont know to handle the both formulas for the Noise and the Attenuation right.

Old Task: An old task as an example how we calcualted it before:
For such tasks before we calculated the SNR like:
SNR = 10^((Se(f)-N)/10)
Se(f)=S-D(f)

But in this case we had values given like:
transmission power: -60dbm/Hz
D(f)= (10 dB*f/16MHz) + 15dB
Noise at the receiver measured as -60dBm with 9kHz bandwidth-.
So we turn the -60dBm Noise in dBm/Hz : -60-10log(9000)= -99,54dBm/Hz and then
SNR=10^((-60dbm/Hz) - 10dB*f / 16MHz - 15dB + 99,54dBm/Hz)/10)
SNR=10^(2,45dBm/Hz-1dB*f/16MHz)
So in this case we never had to determine a minimum SNR, just the SNR at the receiver.

Maybe u guys can help me to get on the right way.
I hope the text is not to big and complicated, english is not my mother language.

Have a nice day.