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A communication channel with AWGN operating at a signal to noise ratio $S N R \gg 1$ and bandwidth $B$ has capacity $C_{1}$. If the $S N R$ is doubled keeping $B$ constant, the resulting capacity $C_{2}$ is given by

1. $C_{2} \approx 2 C_{1}$
2. $C_{2} \approx C_{1}+B$
3. $C_{2} \approx C_{1}+2 B$
4. $C_{2} \approx C_{1}+0.3 B$