how cross-correlation divided by auto-correlation is implemented ?or should I do it?

I'm trying to detect the start of each OFDM symbol in a continuous OFDM data flow. Each OFDM is composed of a cyclic prefix part and the data part.
One OFDM example: 6 7 8 1 2 3 4 5 6 7 8.
The data part is [1 2 3 4 5 6 7 8], the cyclic prefix is [6 7 8]. As you can see, the first 3 samples are exactly the same as the last 3 samples.

Because of the similarities between prefix and the tail of OFDM symbol, we could do the following operations, and there're periodic peaks which indicate the start of an OFDM.


My question is,
1. ALmost every paper I read mentions this method, but there's division involved. Is it common to do this cross-correlation / auto-correlation in FPGA?(NOT IN MATLAB).
2. Any suggestions to how to implement this method? Or other algorithms that could help detection.

Thanks.

Use

A/b < c/d
A d < c d

For a b c d nonnegitive.

You are comparing ratios.

Edit:

A*d < c*b

thanks for ur suggestion.

I've decided to use the sign bit of the input signals to do the correlation. By doing this tons of hardware resources could be saved. The downside is that the angle might not be so accurate.