Suppose we have an OFDM system with N=1024 subcarriers, and we use Np pilot subcarriers from the index set Ip for channel estimation. Suppose the channel under consideration is a fast fading Rayleigh Channel, and assume the channel tap locations are static and the tap magnitudes vary in a correlated fashion, say as per a Bessel function as given in Ch. 3 of Andrea Goldsmith's : "Wireless Communications".

As per this model, the channel taps (channel impulse response coefficients) are generated by Wide Sense Stationary Uncorrelated Scattering and each tap varies independently of the other. Further, in time, each tap value changes in a correlated manner depending on the past tap value. For example, the first tap of the impulse response may decrease (0.998,0.996..0.885) over the OFDM symbol duration.

This gives the following problem. In an OFDM symbol, we have N time samples (ignoring cyclic prefix). For each time sample, we have an impulse response vector that varies slowly from one sample to the next, in a correlated fashion. This means, for each time sample, we will have a corresponding Channel Frequency Response (CFR).

This time varying CFR is the main problem here. We are trying to estimate the channel. This can be done by taking the difference between the true value at that subcarrier and the estimated value at that subcarrier. The problem is, both true value and estimated value at a subcarrier seems to be ill defined. Since a subcarrier will be distributed over all samples thanks to the OFDM transformation, it seems there is no way to know what the true value of CFR will be at that instant if a simulation is done by generating channel impulse responses. Similarly, we do not know the position in time corresponding to the channel estimate.

Can we instead take a "median CFR" by finding the channel impulse response at the N/2th sample and taking the CFR of that impulse response? Is comparing the estimate with this median CFR the best way to go? Any advice or references to this topic is appreciated.