How is the rate improved if we double the SNR?

Doubling the Signal-to-Noise Ratio (SNR) generally leads to an improvement in the rate of communication systems, as it allows for clearer signal transmission with less interference from noise. According to Shannon's capacity theorem, the maximum achievable data rate increases logarithmically with SNR, meaning that doubling the SNR can lead to an increase in capacity and thus higher data rates. Specifically, this can translate to nearly a 1.5-fold increase in the channel capacity in ideal conditions. Overall, improved SNR contributes to enhanced performance and efficiency in data transmission.