You can think of it as follows: a signal with bandwidth B_c is described by B_c complex-valued samples per second (according to the sampling theorem). The signal that fits into a coherence interval with coherence time T_c is determined by B_c T_c samples.

When using OFDM, the cyclic prefix is removing a fraction of the coherence time (i.e., you are not allowed to create just any signal because it needs to repeat itself in a particular way), which is taken into consideration in (2.18) where the number of useful samples (tau_c) is specified.

]]>1) In formula (2.17), Ts/Tu*N_smooth*N_slot is the length of a coherence interval measured in samples, I am not sure what is the “sample” here? I think it should be “OFDM symbol”.

2) In my opinion, Bc*Tc = tau_c = (Ns*Ts/Tu)*N_smooth*N_slot (data samples) is the length of coherence interval measured in data samples and if we want to measure in OFDM symbol unit, I think it should be: Bc*Tc/ (Ns*Ts/Tu) = N_smooth*N_slot (OFDM symbols).

[with Ns is the number of data symbol in useful part of 1 OFDM symbol]. ]]>