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As known, the pilot insertion in OFDM can be either bock type or comb type, I think comb type is appropriate for double-selective channel while block type is for frequency selective channel:

enter image description here

In the above figure, it means that we perform the iFFt in Vertical direction and then send the data horizontally. Suppose we have the size frame is $M$ x $N$ which means we perform $M-$point iFFT for each column before transmitting the whole frame through the channel.

At receiver side, we receive the frame as follows, in figure $(b)$ pilot location index is 1:4:end, and in figure $(a)$ pilot location index is $x$:4:end, and $x = 1 : N$. is that right?

The received frame is of length $MN$x$1$, how can we deal with it to estimate and equalize the channel? suppose we use the LS for estimation? ... I think in figure $(b)$ it's possible to reshape the received frame into $M$x$N$ after that perform $M$-point FFT and then get the estimated channel $h_{est}$ as $h_{est} = P_r./P_o$ such that $P_r$ and $P_o$ denote received and original pilot, respectively. finally we interpolate to get the estimated channel. Is that Right?

If so, What's about the channel estimation in figure $(a)$ ? how can we deal with it ?

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    $\begingroup$ Pilot location should be in $(b)$, $1:4:N$ and vice versa because after adding the guard interval the frame is reshaped vertically. $\endgroup$ – Zeyad_Zeyad Mar 29 '20 at 7:09
  • $\begingroup$ I modified it. thank you $\endgroup$ – Fatima_Ali Mar 29 '20 at 7:11
  • $\begingroup$ "Can be either block or comb type": Or something completely different; in fact, modern communication standards tend to have both, and a set of randomly or diagonally inserted carriers to track the channel. $\endgroup$ – Marcus Müller Mar 29 '20 at 10:42
  • $\begingroup$ OK .. Thank you. Could you please add more details about those new methods ? $\endgroup$ – Fatima_Ali Mar 29 '20 at 11:02
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In both cases, you need to interpolate the channel between the pilots you've got. Both cases are typically suboptimal, since they'd only work perfectly for (a) actual block-fading (which is a convenient model, but doesn't look like reality) or (b) for a channel that is perfectly interpolatable from just a few points of observation in frequency (but that would imply you have designed an OFDM system with too many subcarrier, and that has other downsides).

You'd usually need both, because over the course of a longer data transmission, the channel might change, so there's need for regularly estimating more than just a few subcarriers. And because you cannot just guess the subcarrier state from a pilot some (up to) $\frac Q2$ subcarriers away, in general.

Modern systems tend to solve this by having something like (a) at the beginning of a frame, and then distributing pilots in a pseudorandom, or in a diagonal way throughout the frame, so that you get updates on the channel behaviour over time. Due to having updated your channel state info underway, you can space your pilot blocks further apart (i.e. increase $Q$), thus not reducing your data symbol rate by a lot.

LTE does that. There's a lot of resources you can find when searching for "LTE pilots", but linking to any of these here is a bit futile, since I don't know which background you're coming from.

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  • $\begingroup$ Thank you for your response. "Modern systems tend to solve this by having something like (a) at the beginning of a frame, and then distributing pilots in a pseudorandom, or in a diagonal way throughout the frame" .. If you have any documents/reference explaining that part, that will be appreciated, and does that work well with double-selective channel ? $\endgroup$ – Fatima_Ali Mar 29 '20 at 13:27
  • $\begingroup$ yes, next paragraph in the answer describes a reference, namely LTE. Lots of documents out there. $\endgroup$ – Marcus Müller Mar 29 '20 at 13:31
  • $\begingroup$ @MarcusMüller I think in first case of block-type pilot insertion, no need to interpolate since you are going to estimate the channel based on whole symbol and equalize the data symbols by the estimated channel. Right ? Or you mean estimate the channel of whole frame ? $\endgroup$ – Zeyad_Zeyad Mar 30 '20 at 11:06
  • $\begingroup$ @Fatima_Ali if you can create the MATAB code of block-type estimation using both methods (with and without interpolation) and let us know the results, it will be really appreciated. $\endgroup$ – Zeyad_Zeyad Mar 30 '20 at 11:08
  • $\begingroup$ @Zeyad_Zeyad you typically start your frame by a pilots-only symbol – otherwise, you can't do anything useful with the symbols you receive, because you don't have any phase information, and would need to wait until you get enough phase information for every carrier to even decode such things as headers. Anything you do afterwards is always interpolation – even if it's just zero order hold. $\endgroup$ – Marcus Müller Mar 30 '20 at 11:31

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