# what is the frequency selective channel and doubly-selective channel

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.

thanks

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.

• @Eng.Badr why is that? – AlexTP May 21 '18 at 11:36
• the best channel is AWGN where it is easier to estimate channel. In general, selective characteristics makes channels unpredictable that in turn makes everything worse. Non time selective = no Doppler = no ICI (assuming frame/sample/frequency offsets are correctly estimated and compensated). Maybe I misunderstood what you mean. Again, why do you say that? – AlexTP May 21 '18 at 12:35
• It's ok Alex, .. do you have any contact, If I have a question I will chat with you directly. .. if possible. – New_student May 21 '18 at 12:56
• @Eng.Badr we don't do direct consultations here. If you want to ask something, please do it publicly, so that we can all help you, and everyone can profit from the exchange of knowledge (you're of course free to ask, it's just that asking for private consultation is simply not how this site works). – Marcus Müller May 28 '18 at 16:30