GATE EC 2026 Set 1 — Question 55
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Communications → Information Theory → AWGN Channel Capacity
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Question
Let the relevant bandwidth () of a digital communication system be and , where is Boltzmann’s constant and ‘’ is equivalent noise temperature of the receiver. The power () of signal received through an additive Gaussian channel is .Which of the following options is/are TRUE about Shannon capacity () of the channel?
Correct answer
(C) C 3B
Solution
Given:
Bandwidth
Noise power spectral density
Signal power Step 1: Calculate the total noise power () in dBm.
Step 2: Calculate the Signal-to-Noise Ratio () in dB.
Step 3: Convert to linear scale.
Step 4: Calculate the Shannon Capacity ().
Using the change of base formula:
Step 5: Evaluate the options.
(A) (False)
(B) (False)
(C) (True)
(D) (False)Thus, only option (C) is correct.
Bandwidth
Noise power spectral density
Signal power Step 1: Calculate the total noise power () in dBm.
Step 2: Calculate the Signal-to-Noise Ratio () in dB.
Step 3: Convert to linear scale.
Step 4: Calculate the Shannon Capacity ().
Using the change of base formula:
Step 5: Evaluate the options.
(A) (False)
(B) (False)
(C) (True)
(D) (False)Thus, only option (C) is correct.
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