Say we want to design an OFDM system and we have some parameters given to us, i.e. the coherence time $T_c$ and the max delay spread $T_m$.
It's clear to me why we need to ensure $T_s(N+N_{cp}) \ll T_c$ where $N_{cp}$ is the cyclic prefix in samples - we want the channel to stay coherent during the entire symbol. What is not clear is what happens to the constraint $T_s(N+N_{cp}) \gg T_m \Leftrightarrow B_N \ll B_c$. Apparently, in OFDM it suffices with $T_s N_{cp} \geq T_m$.
It makes intuitive sense in a way, but I'm still not sure exactly how the coherence bandwidth interacts with the subchannel bandwidths. Why don't we need to ensure $B_N \ll B_c$?