Question

A communication channel is having a bandwidth of 3000 Hz. The transmitted power is such that the received Signal-to-Noise ratio is 1023. The maximum data rate that can be transmitted error-free through the channel is:
1. 3 Kbps
2. 30 Kbps
3. 3 Mbps
4. 300 Kbps

Answer 1

Correct Answer - Option 2 : 30 Kbps

Concept:

Shannon’s channel capacity is the maximum bits that can be transferred error-free. Mathematically, this is defined as:

\( C = B~{\log _2}\left( {1 + \frac{{\rm{S}}}{{\rm{N}}}} \right){\rm{bits}}\)

B = Bandwidth of the channel

\(\frac{S}{N}=\) Signal to noise ratio

Note: In the expression of channel capacity, S/N is not in dB.

Calculation:

Given B = 3 kHz and SNR = 1023

Channel capacity will be:

\({\rm{C}} = 3~{\log _2}\left( {1 + 1023} \right){\rm{kbits}}/{\rm{sec}}\)

C = 30 kbps