Topic: Communication Systems
An Ideal power limited communication channel with additive white Gaussian noise with 1 MHz band width and Signal to Noise ratio of 15 is transmitting the information at theoretical maximum rate. If the Signal to Noise ratio is reduced to 7, how much bandwidth is required to maintain same rate
- A. $15/7$ MHz
- B. $4/3$ MHz
- C. 2 MHz
- D. None of these
Answer: B. $4/3$ MHz
Explanation: $C_{1}=B_{1}log_{2}(1+\frac{S}{N}) = 10^{6}log_{2}(1+15) = 4\times10^{6}~bits/sec$. $C_{2}=B_{2}log_{2}(1+\frac{S}{N}) = B_{2}log_{2}(1+7) = 3B_{2}~bits/sec$. To maintain the same capacity $C_{1}=C_{2} \Rightarrow 4\times10^{6}=3B_{2} \Rightarrow B_{2}=\frac{4}{3}~MHz$.