Question

The channel capacity under the Gaussian noise environment for a discrete memory-less channel with a bandwidth of 4 MHz and SNR of 31 is
1. 20 Mbps
2. 4 Mbps
3. 8 kbps
4. 4 kbps

Answer 1

Correct Answer - Option 1 : 20 Mbps

Concept:

Channel capacity:

• Channel capacity is the maximum rate at which the data can be transmitted through a channel without errors.
• The capacity of a channel can be increased by increasing channel bandwidth as well as by increasing signal to noise ratio.
• Channel capacity (C) is given as,

          \(C=B \log_2(1+\frac{S}{N})\) 

Where,

B: Bandwidth

S/N: Signal to noise ratio

Analysis:

Channel capacity (C) is given as,

\(C=B \log_2(1+\frac{S}{N})\)

S/N = 31

C = B log₂31 = 4 × 5 Mbps = 20 Mbps

Hence, Option 1 is correct.