Topic: Communication Systems
A satellite communication link has both uplink and downlink $C/N_{0}$ of 50 dB-Hz. What would be overall link $C/N_{0}$?
- A. 25 dB-Hz
- B. 47 dB-Hz
- C. 53 dB-Hz
- D. 100 dB-Hz
Answer: B. 47 dB-Hz
Explanation: $CNR_{uplink} = 50~\text{dB-Hz} = 10^5$
$CNR_{downlink} = 50~\text{dB-Hz} = 10^5$
$\frac{1}{CNR_{overall}} = \frac{1}{CNR_{uplink}} + \frac{1}{CNR_{downlink}}$
$CNR_{overall} = \frac{10^5}{2} = 5 \times 10^4$
$CNR_{overall}(\text{in dB}) = 10\log_{10}(5 \times 10^4) \approx 47~\text{dB-Hz}$.
Note: If the uplink and downlink CNR are same, the overall CNR decreases by a factor of 2, i.e., 3 dB.