The following slide shows the impulse and frequency response of the channel. To categorize the channel behavior it is useful to consider how the channel varies. Observe the different notches in both time and frequency domain and how they change as the speed $v$ or the delay spread $\tau_\mathrm{rms}$ are modified. Increasing the $K\text{-Factor}$ will also impact the channel behavior. Both the impulse and frequency response are normalized in such a way that $\mathrm{E}\left[|h(t,\tau)|^2\right] = \mathrm{E}\left[|H(t,f)|^2\right] = 1$. In order to better characterize the channel the coherence time $T_\mathrm{C}$ and coherence bandwidth $B_\mathrm{C}$ can be defined. They are a measure for what time frame and what range of frequencies the channel can be considered constant. Coherence time and bandwidth are inversely proportionla to the Doppler frequency and delay spread [1][2]. $$ T_\mathrm{C} \sim \dfrac{1}{f_\mathrm{D}} \qquad B_\mathrm{C} \sim \dfrac{1}{\tau_\mathrm{rms}} $$ The user can modify coherence time and bandwidth indirectly by adjusting the speed $v$ and the delay spread $\tau_\mathrm{rms}$. In order to properly see the effects you might need to adjust the amount of symbols $N_\mathrm{Symbol}$.

There are two different types of fading in the time domain: slow and fast fading. And two different types of fading in the frequency domain: flat and frequency selective fading [2].

Slow and Fast Fading

Slow Fading:

• Definition: Slow fading occurs when the signal amplitude and phase change slowly over time, relative to the signal's transmission duration.
• Causes: It is typically caused by large, slow-moving obstacles or the movement of the receiver or transmitter over long distances, leading to gradual changes in the signal's multipath components.
• Characteristics: The signal variations are slow compared to the channel's coherence time, resulting in relatively stable channel conditions over short periods.

Fast Fading:

• Definition: Fast fading occurs when the signal amplitude and phase change rapidly over a short period of time or distance, relative to the signal's transmission duration.
• Causes: It is caused by the rapid movement of the receiver, transmitter or surrounding objects, leading to fast variations in the multipath components due to constructive and destructive interference.
• Characteristics: The signal variations are fast compared to the channel's coherence time, resulting in rapidly varyubg channel conditions.

Flat and Frequency Selective Fading

Flat Fading:

• Definition: Flat fading occurs when the bandwidth of the signal is much smaller than the coherence bandwidth of the channel.
• Characteristics: There is no frequency distortion within the signal bandwidth. The entire signal undergoes the same attenuation and phase shift.

Frequency Selective Fading:

• Definition: Frequency selective fading occurs when the signal bandwidth is larger than the coherence bandwidth of the channel.
• Characteristics: This results in frequency distortion because different parts of the signal spectrum are attenuated differently. It can cause ISI in digital communications.

[1] D. Tse and P. Viswanath, Fundamentals of Wireless Communication. Cambridge: Cambridge University Press, 2005.
[2] T. S. Rappaport, Wireless Communications: Principles and Practice. Prentice Hall PTR, 2002.