# OFDM channel estimation

As we know, if we want to get the time domain response of the channel $h[n]$, we can first get the frequency domain response of the channel $H[k]=Y[k]/X[k]$. And then we do IFFT.

But now one OFDM symbol includes some null subcarriers. So we don't need to get the $H[K]$ on these null subcarriers. But under this circumstance, how do we get the time response of the channel $h[n]$?

• Thanks. Sorry I don't have enough reputation. It doesn't allow me to "add a comment". Maybe it's the only way I can chat with you. You said "You should take all 64 values, not just the non-zero values.", but because some null sub-carriers exist, I can't calculate the $H[k]$ when the $k$ responded to the null sub-carriers. Because $H[K]=\frac{Y[K]}{X[K]}$, and $X[k]=0$. Thanks.
– w xd
Dec 7, 2015 at 6:17
• Set those values to zero before doing IFFT. This corresponds to an oversampling of the resulting impulse response.
– Deve
Dec 7, 2015 at 13:08

If some values in $X[k]$ are zero, you cannot determine the impulse response of the complete channel bandwidth ($-f_\mathrm s / 2 \ldots f_\mathrm s / 2$, with sampling frequency $f_\mathrm s$). The IFFT of the estimated $\hat H[k]$ is rather a low pass filtered version of the channel. This might or might not be what you want.

In reality, you can never measure the complete bandwidth of a channel, as it is virtually infinitely large. For a communication system it is usually sufficient to know the channel transfer function of the band in which you intend to transmit a signal. If you transmit only on a fraction of subcarriers of an OFDM system you're effectively narrowing the transmission band and you might be satisfied with knowing the impulse response of this narrower band.

• thank you so much. But now,for example,we have 64 subcarriers in one ofdm symbol.And it include 12 null subcarriers.Now we can calculate the H[k] in other 52 subcarriers.How can I get the time domain response of the channel? Just IFFT{H[K](1-52)}? Thank you.
– w xd
Dec 5, 2015 at 12:07
• @wxd The IFFT of $\hat H[k]$ can be interpreted as an estimation of the channel impulse response, yes. Make sure there is no inter-symbol interference. You should take all 64 values, not just the non-zero values. And if you intend to use this impulse response in convolutions, use the circular convolution ((I)DFT is repeated periodically)
– Deve
Dec 6, 2015 at 12:53
• @wxd: Please STOP making answer posts. Please just comment. Please REMEMBER your login here. Otherwise, please stay away. We (the moderators) do not need the extra overhead of dealing with people who are not interested in following the pretty mild rules here on DSP.SE.
– Peter K.
Dec 7, 2015 at 12:43