Could anyone please help me to explain the frequency-selective channel and doubly-selective channel and the difference between them in brief and easy way. I have tried to check on internet, I couldn't get a clear explanation about them.
For more explanation, you can check this link https://www.cs.tut.fi/kurssit/TLT-5806/Invocom/p3-7/fading_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 $\tau > 0,h(\tau) \neq 0$.
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.