# Why does SNR have an impact on the bit rate?

I have some confusion regarding the impact of SNR on the bit rate. For example, if I have a QPSK-OFDM system, then my bit rate will be 2bits mutiplied by the number of sub-carriers of the OFDM modulation over the symbol time. How can I account for the SNR in this case?

• This is the transmit bit rate. At receiver, the better SNR, the lower reception error probability, thus the expected correctly received bit rate does depend on SNR. – AlexTP Oct 18 '18 at 8:23

$$\textrm{BER} = \frac{1}{2} \left(1 - \sqrt{ \frac{L/N \times \textrm{SNR}}{2 + L/N \times \textrm{SNR}}} \right)$$
Where $$N$$ is the number of subcarrier and $$L$$ is the channel diversity. $$\textrm{SNR} = p/\sigma^2$$ .. where $$p$$ is the transmitted signal power, and $$\sigma$$ is the variance.