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
- $C_{2} \approx 2 C_{1}$
- $C_{2} \approx C_{1}+B$
- $C_{2} \approx C_{1}+2 B$
- $C_{2} \approx C_{1}+0.3 B$