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 --&gt; ifft --&gt; adding CP --&gt; upsampling --&gt; conv channel --&gt; adding noise


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

delay --&gt; downsampling --&gt; CP removal --&gt; fft --&gt; MMSE equalizer --&gt; 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.
In simulation, we do upsample to simulate the &quot;analog&quot; signal which is a continuous signal in reality but we represent it as a high-time-resolution in our digital/discrete simulation. When we upsample our data before going through the channel, we should also upsample the &quot;impulse response&quot; (IR) of the channel. It means that the timing-base of both signal and IR of channel must be same. For example, without upsampling, take for example of a channel with an IR of {4,0,0,3,0,1.5,0,0,0}. First, We may apply our signal (without upsampling) to this channel. Then, we upsample our signal with a factor of 2 and want to apply that to this channel again. this time we have to upsample our channel's IR with a factor of 2 just like the signal. So, the upsampled channel'IR would be: {4,0,0,0,0,3,0,0,1.5,0,0 ....}. So, the time-base or time-resolution of both signal and channel should be equal.