what is the frequency selective channel and doubly-selective channel
Example. For a channel that can be modeled by LTI system, we send an impulse-like signal and receive channel impulse reponse $h(\tau)$ where $\tau$ is delay.

Frequency-flat channel means $h(\tau) \sim \delta(0)$ or for discrete-time version, $h[n] \sim \delta_0$.

Frequency-selective channel means $h(\tau) \neq \delta(0)$ or for $\tau &gt; 0,h(\tau) \neq 0$.

Now if we do the measure at time $t=t_1$ and $t=t_2$, $h(\tau,t_1) = h(\tau,t_2)$, the channel is called non time-selective (anyone remember the name?).

If we do the measure at time $t=t_1$ and $t=t_2$, $h(\tau,t_1) \neq h(\tau,t_2)$, the channel is time-selective.

Doubly selective is simply both time-selective and frequency-selective.