The "textbook" OFDM block diagram is as the below figure. But I wonder if it satisfies the sampling theorem. Here, we have N points $X[k]$ before IFFT, and
$$x[n]=\frac{1}{\sqrt{N}}\sum_{k=0}^{N-1} X[k] \mathrm{e}^{\displaystyle -j\frac{2\pi k n}{N}}$$
This derives from the analog signal
$$x(t)=\sum_{k=0}^{N-1}\mathrm{e}^{\displaystyle -j 2\pi f_k t}=\sum_{k=0}^{N-1}\mathrm{e}^{\displaystyle -j 2\pi k\Delta f t} $$, where $\Delta f$ is the subcarrier space.
We then sample this signal with a sampling frequency $f_s>2f_{max}=2(N-1)\Delta f$, which can be taken as $f_s=2N\Delta f$. The time domain sample points are at
$$nt_s=n/f_s=\frac{n}{2N\Delta f}$$
Then we define
$$x(nt_s):=x[n]=\sum_{k=0}^{N-1}\mathrm{e}^{\displaystyle -j \frac{2\pi k n}{2N}} $$
and then we define a expanded
$$\tilde{x}[n]:=\begin{cases} x[n], 0\le n\le N-1\\ 0, 2N-1\ge n\ge N\\\end{cases}$$ $$
That means we should do a length $2N$ IFFT rather than a length $N$ IFFT
$$ \tilde{x}[n]=\sum_{k=0}^{2N-1}\mathrm{e}^{\displaystyle -j \frac{2\pi k n}{2N}}$$
Is the textbook wrong?