# The channel capacity under the Gaussian noise environment for a discrete memoryless channel with a bandwidth of 4 MHz and SNR of 31 is.

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

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Correct Answer - Option 1 : 20 Mbps

Concept

The capacity of a band-limited AWGN channel is given by the formula:

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

C = Maximum achievable data rate (in bits/sec)

B = channel bandwidth

$\frac{S}{N}$ = Signal to Noise power

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

Calculation:

Given B.W. = 4 MHz, S/N = 31

The channel capacity will be:

$C = (4\times 10^6)~{\log _2}\left( {1 + 31} \right)$

C = 20 Mbps