What's the computational complexity of MMSE equalizer in OFDM system
For a SISO channel, assuming you have estimated channel coefficients for each sub-carrier $k$, the MMSE equalizer is 
$$
\hat{h}_k=\frac{h_k^*}{|h_k|^2 + \frac{\sigma_x^2}{N_0}}
$$
So you can see already there is a multiplication in the numerator ($h_k^*$), and then there is a division by a term in the denominator. So for all $N$ subcarrier, this itself will be $2O(N) \rightarrow O(N)$ for large $N$. There is additional $|h_k|^2$ computation which is basically multiplication with conjugate. So if you have precomputed SNR ($\frac{\sigma_x^2}{N_0}$) and $h_k$ for all sub-carriers, complexity should still be linear on $N$. But this is a very simplified assumption because in most practical OFDM packets, there a pilot sequence periodically present so you may need to update $h_k$ using available pilot sequence.