Question

3) A wireless receiver needs to meet the sensitivity requirement of -90 dBm. The channel bandwidth is 1 MHz. The data rate is 0.5 Mbps. The antenna temperature is 290 K. (Please show all steps to receive full credits) a) If Eb/No requirement is 10 dB. What is the SNR requirement in dB? (10 pts) b) [independent of (a)] If SNR requirement is 10 dB, what is the NF requirement in dB? (15 pts)

Answer 1

  
We have S_min = (S/N)_min kT_0B(NF) and we have SNR = E_b/N_0 middot f_b/B where S_min = Receiver sensitivity (S/N)_min = Minimum Signal to Noise ratio(SNR) k = Boltzmann�s constant = 1.38 times 10^-23 Joule/degree K T_0 = Absolute temperature in degree K B = Bandwidth NF = Noise figure f_b = Data rate Here given S_min = -90 dBm B = 1 MHz T_0 = 290 K Date rate = 0.5 Mbps We have SNR = E_b/N_0 middot f_b/B Where f_b is data rate and it was given as f_b = 0.5 Mbps Given E_b/N_0 = 10 dB = 10 Therefore SNR = (10)(0.5/1) = 5 = 10 log(5) SNR = 6.989 dB Given SNR = (S/N)_min = 10 dB Therefore NF = S_min/(SNR)kT_0B S_min = -90 dBm = 10^-12 Watt SNR = 10 dB = 10 NF = 10^_12/(10)(1.38 times 10^-23)(290)(1 times 10^6) = 24.9875 = 10 log(24.9875) = 13.977 dB Therefore NF = 13.977 dB

$\mathrm{where\;\;\;S_{min}=Receiver\;sensitivity}$

   $\mathrm{\left ( \frac{S}{N} \right )_{min}=Minimum\;Signal\;to\;Noise\;ratio(SNR)}$

$\mathrm{k=Boltzmann's\;constant=1.38\times10^{-23}Joule/^{0}K}$

$\mathrm{T_0=Absolute\; temperature\;in\;^{0}K }$

   $\mathrm{B=Bandwidth}$

$\mathrm{NF=Noise\;figure}$

$\mathrm{Here\;given\;\;S_{min}=-90\;dBm}\\$

   $\mathrm{B=1\;MHz}$

   $\mathrm{T_0=290\;K}$

   $\mathrm{Data\;rate=0.5\;Mbps}$

$\mathrm{\mathbf{(a)}}$

Where f_b  is data rate and it was given as  f_b = 0.5 Mbps

$\mathrm{Given\;\;\frac{E_b}{N_0}=10\; dB=10}$

   $\therefore \mathrm{SNR=(10)\left (\frac{0.5}{1} \right )}$

= 5

= 10 log(5)

SNR = 6.989 dB

$\mathrm{\mathbf{(b)}}$

  

   $\therefore \mathrm{NF=\frac{S_{min}}{(SNR)kT_0B}}$

S_min = -90 dBm = 10^-12 Watt

SNR = 10 dB = 10

$\mathrm{=24.9875}$

$\therefore \mathrm{NF=13.977\;dB}$