How does SC-FDE modifies $E_b$ (in AWGN function) In lot of matlab scripts of SC-FDE simulations I see $E_b = N$ (being $N$ the length of the block to be transmitted through the channel and Eb energy per bit) to generate the AWGN. I would like to understand why is that, and more specifically:
Assuming, instead of a block length $N$, I have 2 sequences length $N/2$. I FFT() each one, concatenate the frequency-domain sequences and send the result (of length $N$) through the channel. What would my $E_b$ in AWGN function be?
Here $E_b=N$ means $N$ pulses (i.e. PHY waveforms) of unit energy represent one information bit.
I suppose it is due to the S/P (serial to parallel) block that translates each bit of information to a vector of size $N$. So it is implicitly assumed that the energy of each component of the vector is one.

Regarding your second question, you should consider the number of information bits. If you have one bit of information to generate the two vectors of size $N/2$, then again $E_b=\frac{N/2+N/2}{1}=N$.