Homework 5 (10 pts total)

Villanova University ECE 8708: Wireless Communications

Dr. David C. Burnett, Fall 2025

Recommended resources: Chapter 5, lecture notes

Scenario for all problems

You are riding in a car being driven directly away from a multi-radio base station at 70 mph. You attempt to communicate with the base station using four different radios, each using one of the following carrier frequencies:

• 150 MHz ("2 meters" in ham radio world)
• 1900 MHz (classic mobile phone)
• 2.4 GHz (ISM band wifi, BLE, etc.)
• 60 GHz (5G, 6G, etc. high bandwidth bands)

Problem 1 (5 pts)

For each carrier frequency, calculate:

1. The Doppler shift of the signal
2. The percentage of a 2 MHz Bluetooth LE channel that shift represents
3. Coherent time (using 0.5 correlation function)

For each carrier frequency, also answer the following question: is Doppler shift something you need to worry about? Consider the Doppler shift in the context of a wireless channel. Also consider the calculated coherent time with respect to symbol times for wireless standards you are familiar with and/or discussed in class.

Problem 2 (1 pt)

When communicating at 60 GHz, how fast do you need to be traveling directly toward or away from the base station for coherence time to shrink to 1 us? To aid in inutitive interpretation, express your answer in miles per hour.

Problem 3 (4 pts)

For each of the four frequencies, calculate the limit of the environment's rms delay spread assuming we use symbol time 1/10th of the coherence time calculated in Problem 1 and using 0.5 correlation function.

Which of these frequencies are acceptable for communication while traveling at 70 mph and why? Consider the rms delay spreads you calculate with the rms delay spreads in Table 5.1 in the book. Remember that the inequalities to satisfy the requirements of any "good case" situations are "much greater than" and "much less than" rather than simply "greater than" or "less than."