Homework 6 (10 pts total)

Villanova University ECE 8708: Wireless Communications

Dr. David C. Burnett, Fall 2025

Recommended resources: Chapter 9, Chapter 6, lecture notes

Problem 1 (3 pts)

Based on Problem 9.7 and 9.8 in our textbook.

An unslotted ALOHA system has packet arrival times conforming to a Poisson process with arrival rate 10 packets per hour. If the bit rate is the same as in the IEEE 802.15.4 standard -- 250 kbps (remember: bits not Bytes) -- and each packet has length of 127 Bytes, find (a) the normalized throughput of the system as-is and (b) the packet arrival time that will result in throughput of the maximum reasonable throughput, about 5%.

Problem 2 (2 pts)

Repeat Problem 1 but using a wireless network that is more like Bluetooth LE: 1 Mbps data rate and packets 376 bits long. Assume the packet arrival rate is 10 per second; despite the specification technically allowing packets as slow as one every 30 seconds, my experience with BLE systems has shown that such systems crash if you set the packet repeat rate to be slower than once every 2 seconds, and they work erratically unless you set the packet repeat rate to once every 1 second or faster. Hence, we choose 10 packets per second to model a room with many independent Bluetooth LE systems running (earbuds, phones, laptops, smart watches, smart TVs, dishwashers...): at any particular time there is only one packet you care about and nine devices generating interference.

Bluetooth LE has time slots so slotted ALOHA would be more appropriate, but here we are attempting to model uncorrelated BLE transmissions in a room. Those transmissions will not conform to any particular time slot alignment.

Problem 3 (5 pts + 1 Extra Credit possible)

Use circuit simulation software of your choice (LTspice, Cadence Virtuoso, Xschem, etc.) to demodulate an FM waveform using an integrator and an envelope detector. In other words, implement the block diagram of Figure 6.8 in our book without the limiter. The limiter block only deals with amplitude which we can ignore in this simulation-only exercise. Please use an ideal opamp model and any diode model you wish. You will need to do the following:

  1. Create a frequency modulated waveform. There are lots of ways to do this in Python or Matlab. For example, you could choose a time duration and a timestep then make a frequency modulated message signal, make a carrier waveform, then mix them together by simply multiplying them.
  2. Import that waveform into a circuit simulator so that a voltage source "plays back" your generated waveform
  3. Set up an integrator circuit and an envelope detector circuit. Play around with R and C values of both circuits to try to get a good output that matches your original message.

To receive full credit for this problem, be sure to include the following.

Extra Credit challenge: use an audio signal as your message and find a way to convert your recovered signal, after the envelope detector, into an audio file. Listen to the output and compare with the original signal.

It's a good idea to plot waveforms often to ensure you are generating what you think you are generating!