Homework 3 (10 pts total)

Villanova University ECE 8708: Wireless Communications

Dr. David C. Burnett, Fall 2025

Recommended resources: Chapter 4, lecture notes

Problem 1 (5 pts)

In this problem we will generate our own received power estimates using different models.

Calculate received power after path loss using the two different methods below and plot all the results on the same graph. Plot on a log-log axis. Plot received power over a range of distances from 1 m to 1 km. (Assume 1 m is beyond the Fraunhofer distance.)

The link can be described with the following parameters:

• Transmitted power: +3 dBm
• Transmit antenna gain: 10 dBi
• Receive antenna gain: 0 dBi

Estimate path loss using two different methods:

• Path loss method (a): Use the typical free space path loss expression and plot a curve for each n value, n=2, 3, 4, 5.
• Path loss method (b): instead of changing the path loss exponent, generate a lognormal loss value between 0 and 40 dBm. We want 3 sigma on either side to capture the range, so this means the mean should be 20 dB and standard deviation should be 40/6 = 6.67 dB. Generate at least 10,000 points in total, with good logarithmic distribution over your plot's range of distances.

A good check to ensure your generated points are good is to visually ensure your points have a roughly d^2 trend, and the clustered points look to be mostly contained in a band 2-3 std dev wide.

Ensure your final plot is of good quality and includes a title, axis labels with units, a logspaced grid, a legend, and data that is plotted in a legible way that makes sense for the type of data. (For example, a line connecting each of your 10,000 points together would probably not result in a legible plot!)

In addition to creating the plot, answer the following questions:

1. What path loss exponent (n) value would you say best aligns with your lognormal error "data"?
2. What similar and dissimilar features do you observe between your plot and the measurements in Figure 4.17 in the book?

Problem 2 (5 pts)

(Based on a true story)

A team of field scientists are working at a site in the Dry Valleys, Antarctica and trying to contact McMurdo Station (80 km away) via radio to arrange a helicopter pickup. They are using commercial handheld GMRS radios with 2.5 W transmit power. The handheld transmitter and 30 m high receiver at McMurdo both use dipole antennas to receive in all azimuthal directions.

The signal gets from handheld transmitter to tower receiver via two paths: directly, and reflecting off the ice floating on McMurdo Sound. Using the two-ray loss assumptions for glancing angles:

1. What is the path loss between transmitter and receiver if the user is seated at a desk and holding the radio about 1 m off the ground?
2. Noticing the transmission is unreliable, a scientist stands on top of a 1 m barrel and uses a wired microphone so that the radio transmitter can be held high in the air: a total of 3 m off the ground. What is the path loss between transmitter and receiver now?
3. How many dB is the link improved by putting the handheld radio 2 m higher in the air?
4. How much power is received by the base station at the other end?
5. Comment on the base station received power: from your experience is that plenty of power to have a voice call? Not enough? Just right? Back up your claim with a signal to noise ratio based on the thermal noise expected over the typical bandwidth of a GMRS channel.