GATE EC 2014 Set 2 — Question 32
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Communications → Information Theory → AWGN Channel Capacity
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Question
The capacity of a band-limited additive white Gaussian noise (AWGN) channel is given by bits per second (bps), where is the channel bandwidth, is the average power received and is the one-sided power spectral density of the AWGN.For a fixed , the channel capacity (in kbps) with infinite bandwidth () is approximately
Correct answer
(A) 1.44
Solution
The channel capacity is given by the Shannon-Hartley theorem formula:We need to find the limit of as the bandwidth approaches infinity:Let . As , . Substituting :Using the identity :Since , we have:Given and :Converting to kbps:Therefore, the correct option is (A).
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