GATE EC 2025 Set 1 — Question 15
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Communications → Information Theory → AWGN Channel Capacity
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Question
Consider an additive white Gaussian noise (AWGN) channel with bandwidth and noise power spectral density . Let denote the average transmit power constraint. Which one of the following plots illustrates the dependence of the channel capacity on the bandwidth (keeping and fixed)?
Correct answer
(A) [figure]
Solution
Shannon capacity of the AWGN channel:
- As : .
- is strictly increasing and concave in (more bandwidth always helps, but with diminishing returns since the SNR falls).
- As : using for small ,
- (A) rises and flattens to an asymptote — correct.
- (B) grows linearly without bound — wrong (no saturation).
- (C) grows ever faster (convex) — wrong.
- (D) rises to a peak then falls — wrong; never decreases with .
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