Can the DFT can be performed without normalization? If we have OFDM system with $N$ sub-carriers, the DFT matrix can be expressed as follows:
$F = dfmtx(N)/sqrt(N)$
My question, is it possible and practical to use the matrix without Normalization, it means use the iDFT as $F = (dfmtx(N))'$, and then at the receiver end, I will multiply with  that matrix and divided by $N$  (like this $dfmtx(N)/N)$ to get scalar diagonal matrix whose diagonal elements are 1?
thank you
Yes.  In fact, depending on your receiver architecture, you may not need the divide by $N$ in the receiver.
Generally, in a receiver you care about the relative phases of the bins (or possibly their strengths with respect to some other part of the same signal).  So there's no reason to do that multiply if you don't want to.
If you're working with fixed-point math, just make sure that you don't experience over- or under-flow.