# 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 '15 at 6:17
• Set those values to zero before doing IFFT. This corresponds to an oversampling of the resulting impulse response. – Deve Dec 7 '15 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.
• @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 '15 at 12:53