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Hi This is a very good question:
Please see my comments below
QN:In the design of most OFDM systems before the zero padding there is an insertion of a 'zero' in the middle of the data carriers, why?
ANS: I am taking reference of 802.11a for your answer.
1. Typically OFDM bandwidth is 20MHz and (10MHz both side).
2. Say 64-carriers are used(1-DC,52-Carrier+Pilot,11-Zeros)
3. So Inter carrier spacing is 20MHz/64=312.5KHz
4. Typically we need Spectrum shaping filter to eliminate out of band signals beyond 20MHz.
5. We can't design a real time filter with rectangular shape like a gain of '1' until +/- 10MHz. zero after that.
6. We are using 52 carriers (11 zeros) means we are using only 16.25MHz out of 20MHz and rest can be used as filter roll off. (There is a spectrum loss here), even in this case the side band constellation will have attenuation.
7. It is just to make it possible in real time implementation with loosing a small % of spectrum. i.e. 11*312.5KHz.
QN: What and how do the pilot carriers work to make the OFDM system better?
ANS: Pilots are used to track the residual phase error if present after frequency correction. Without this correction the constellation points starts rotating either +ve/-ve angle. It is very much sensitive at higher constellation.
We estimates phase say Θ , from pilots, then we corrects by multiplying exp(-j*2*pi*Θ) before demapping.
Thanks "kpojha" for his very good answer on this thread as I quoted above. Can anyone please explain more in details on 4,5 for me. I don't really get it. Thank you.
4. Typically we need Spectrum shaping filter to eliminate out of band signals beyond 20MHz.
5. We can't design a real time filter with rectangular shape like a gain of '1' until +/- 10MHz. zero after that.
4. You must not be surprized that the RF signals are filtered. The channel bandwidth is 20 MHz, the rest of signals are not interested for the receiver, they are spurs and should be suppressed.
5. These perameters correspond to an ideal filter which cannot be implemented in real applications.
gain of 1 for in-band and infinite suppression for out-of-band assumes limited spectrum which corresponds to infinite in time domain signals. This is true also for filter characteristics - the limited frequency response means infinite impulse response (number of coefficients) and that is impossible.
So some trade-offs are made when the real systems are developed - and that i written in 6. - the desired signal occupies only 16.25 MHz, the smoothed transition from passband to stopband of a filter (roll-off) and finite out-of-band suppression - all that allows to implement such filter in practice
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