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First of all, I would say you need more simulation points to make the curve smoother. You can't make a definite judgment based on these curves. Can you increase the number of simulation points, and report back? Of course with Doppler effect, BER should be worse if not handled at the receiver, but if you have a common Doppler scaling factor for all paths, ...

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The SNR is the ratio of $S$, the power in the signal $s(t)$, and $N$, the power in the noise $n(t)$. So, $$\text{SNR}_\text{dB} = 10\log_{10}\frac{S}{N}.$$ When using RMS values, we have $S = s_\text{RMS}^2/R$ and $N = n_\text{RMS}^2/R$. The resistances cancel out and then $$\text{SNR}_\text{dB} = 20\log_{10}\frac{s_\text{RMS}}{n_\text{RMS}}.$$

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Look at one OFDM symbol at the point where it is transmitted, i.e. right before it enters the channel. Figure out its average power, $P$, or its average energy, $E = PT$, where $T$ is the symbol's duration. Also, figure out how many information bits, $I$, are carried by the symbol. In your simulation, $E_b = E/I$. To get a desired $E_b/N_0$, calculate \$\...

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