# Should we upsample the channel when upsample the signal

I have an OFDM system with Number of sub-carriers $$N= 1024$$, modulated data using $$QAM$$ modulation is transmitted via those subcarriers as follows:

modulation --> ifft --> adding CP --> upsampling --> conv channel --> adding noise


Then at the receiving side, the received signal is processed as follows, discarding the channel

delay --> downsampling --> CP removal --> fft --> MMSE equalizer --> demodulation


The issue which I am facing in that system is in the equzlizer step, When using the original channel, I can not get the performance back. Howenver, when I estimate that channel after the step of fft and then use the estimated channel, The performance is OK !!

Why does that issue happens? I think because of the upsampling step, because when I don't upsample the signal, that becomes fine but when I use the upsampline and use then equalize using the original channel, I can't get the performance back.

• Can you clarify what exactly you are doing when you use the original channel? What do you do with the channel to correct for that channel distortion? Jun 16 '20 at 13:03
• with the original channel $h$, I just use $H = fft(h,N)$; and then use MMSE equalizer using the frequency-domain channel $H$. where in the second case where I can get the performance well, I replace $h$ by the estimate channel gotten from LS estimation. Jun 16 '20 at 13:12
• But your correcting for the channel, not applying it again. If the channel was minimum phase you would use the inverse of the channel and not the channel itself (for example)--but given most channels are NOT minimum phase we can't simply invert it. So I am trying to see how you are using the channel directly but still don't quite follow. Jun 16 '20 at 13:16
• @DanBoschen After obtaining $H$ I calculate the equalizer coefficients $Gz = conj(H)/(H.*conj(H) + 1./Beta)$ where * means multiplication. Then I multipy the received signal after the fft by the equalizer coefficient $Gz$, is that right? When I calculate $H$ based on the estimated channel, It's ok, but when I calculate it using the original channel $h$, I can't get the performance back. Jun 17 '20 at 0:44
• I am sorry I am not completely following, I think I would need to see the actual data/processing in detail. Hopefully someone else recognizes this more immediately to help you! Jun 17 '20 at 2:45