I asked the question about to recover signal from the real part of IFFT OFDM system before,

Recover signal from the real part of IFFT.

thanks for the responses from the DSP experts in this forum.  I am working on the frequency offset estimation for this type signal. Since the received signal is a real value, the frequency offset estimation algorithm like correlation between the signal and its cyclic prefix for the complex OFDM system could not be applied. Google search didn't generate any meaningful results. Any advice to solve this problem is welcome.

Give the real part to a Hilbert Transformer.Hilbert Transformer will shift phase of all +ve frequencies by -Pi/2.All Negative frequencies will be shifted in phase by +pi/2.

Add the original real signal with Hilbert Transformer output multiplied by +j (Sqrt of -1).You will get a complex signal.Now you can do frequency offset estimation and correction.

@ Frank_os

what do you mean by frequency offset? is it frequency residue left over from oscillators between Tx & Rx ? 

@ Mannai_Murali,

Your reply is too involved to understand. 

Frankly I don't know what the problem is in the first place so I can't understand your answer. Can you explain those Hilbert steps and what do you eventually do with it.

I have the view that "to begin with" there must be "something" in the real signal itself to work out if it is off centre but just having a real signal off centre and putting it back sounds unrealistic.

Kaz

  You are right,  the frequency offset means the frequency difference between the TX and RX due to the oscillators.