What is the capacity of an additive white Gaussian noise channel with bandwidth of 1 MHz, power of 10W and noise power spectral density of No/2 = 10(−9)W/Hz?a)17.4 Mbit/sb)12.28 Mbit/sc)26.56 Mbit/sd)6.64 Mbit/sCorrect answer is option 'B'. Can you explain this answer?

Question

What is the capacity of an additive white Gaussian noise channel with bandwidth of 1 MHz, power of 10W and noise power spectral density of No/2 = 10(&minus;9)W/Hz?a)17.4 Mbit/sb)12.28 Mbit/sc)26.56 Mbit/sd)6.64 Mbit/sCorrect answer is option 'B'. Can you explain this answer?

Answer

Additive white Gaussian noise (AWGN) is a basic noise model used in information theory to mimic the effect of many random processes that occur in nature.
The modifiers denote specific characteristics: Additive because it is added to any noise that might be intrinsic to the information system.
The capacity of an additive white Gaussian noise channel by Shanon's formula:

Where B refers to the bandwidth of the channel
SNR means Signal to Noise Ratio : can be defined as the ratio of relevant to irrelevant information in an interface or communication channel.
SNR now can be calculated as,

In the above problem, S is the signal power which is equivalent to 10 W.
Bandwidth = 1 MHz
Noise power spectral density of No/2 = 10⁽⁻⁹⁾ W/Hz

Answer

The capacity of an additive white Gaussian noise (AWGN) channel can be calculated using the formula:

C = B * log2(1 + SNR)

where C is the capacity in bits per second, B is the bandwidth in Hz, and SNR is the signal-to-noise ratio.

In this case, the bandwidth is given as 1 MHz, which is equal to 1,000,000 Hz. The power is given as 10W, and the noise power spectral density is given as No/2 = 10(-10).

The signal-to-noise ratio (SNR) can be calculated as:

SNR = (signal power) / (noise power)

The signal power can be calculated using the formula:

signal power = power * bandwidth

In this case, the signal power is:

signal power = 10W * 1,000,000 Hz = 10^7 W*Hz

The noise power can be calculated as:

noise power = noise power spectral density * bandwidth

In this case, the noise power is:

noise power = 10(-10) * 1,000,000 Hz = 10^(-3) W*Hz

Now, we can calculate the SNR:

SNR = (signal power) / (noise power)
= (10^7) / (10^(-3))
= 10^10

Finally, we can calculate the capacity:

C = B * log2(1 + SNR)
= 1,000,000 Hz * log2(1 + 10^10)
≈ 23.25 Mbps

Therefore, the capacity of the AWGN channel is approximately 23.25 Mbps.

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