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A communication channel with AWGN operating at a signal to noise ratio SNR >> 1 and bandwidth B has capacity C1. If the SNR is doubled keeping B constant, the resulting capacity C2 is given by

1. C2 = 2C1
2. C2 = C1 + B
3. C2 = C1 + 2B
4. C2 = C1 + 0.3B

Correct answer: C2 = C1 + B

Solution

By Shannon, C = B*log2(1+SNR). For SNR>>1 this is approximately B*log2(SNR). Doubling SNR raises capacity by B*log2(2) = B, so C2 = C1 + B.

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