Illustrative Scenarios of Wireless Channels

To analyze the impact of mobility and multipath propagation on wireless communication by computing Doppler spread, coherence time, delay spread, and coherence bandwidth under different scenarios, please follow the following steps:

Case 01

1. Input the distance between the transmitter and the receiver ($r$), velocity of the receiver ($v$) (can be negative if moving away), and the carrier frequency ($f_c$).
2. Observe the changes in Doppler shift and coherence time with change in the input parameters.
   • Increasing receiver velocity increases Doppler shift and reduces coherence time, indicating faster channel variation and the need for more frequent channel estimation.
   • Higher carrier frequency also increases the Doppler shift, further reducing channel stability.

Case 02

1. Input the Distance between transmitter and receiver ($r$), distance between the transmitter and the obstacle ($d$), and the carrier frequency ($f_c$).
2. Observe the changes in delay spread and coherence bandwidth with a change in the input parameters.
   • Larger separation between direct and reflected paths increases delay spread, reducing coherence bandwidth and introducing frequency-selective fading.
   • Smaller delay spread leads to a wider coherence bandwidth, indicating a flatter channel that is easier to equalize.

Case 03

1. Repeat the above steps for a different set of inputs for both Doppler shift and delay spread.
2. Compare and analyze the results by observing how mobility and multipath affect wireless performance.
   • High mobility primarily impacts time variation (Doppler shift and coherence time), while strong multipath primarily impacts frequency selectivity (delay spread and coherence bandwidth).
   • Interpreting these trends helps relate simulation outcomes to practical system design choices such as pilot spacing, modulation scheme selection, and equalization requirements.