Homework 2 (10 pts total)

Villanova University ECE 8708: Wireless Communications

Dr. David C. Burnett, Fall 2025

Recommended resources: Chapter 3, lecture notes

Problem 1 (3 pts)

Revision from in-class numerical example. Assume a change in receiver architecture has resulted in the required signal to interference ratio to drop from 15 dB to only 7 dB. What is the smallest valid cluster size that should be used for maximum capacity if the path loss exponent is (a) n = 4, (b) n = 3, or (c) n = 2 ?

Again, assume that there are 6 cells contributing co-channel interference all of them are at the same distance from the mobile.

Problem 2 (2 pts)

Revision from in-class numerical example. How many users can be supported with 2% blocking probability for the following number of trunked channels?

(a) 1 (do your best to extrapolate based on the figure) (b) 5 (c) 10 (d) 20 (e) 100.

Assume each user almost always texts instead of calls, so they only generate 0.001 erlangs and the system is "blocked calls cleared" type.

Problem 3 (3 pts)

Villanova's student population is about 10,000 undergrad and grad students. Minus absences and commuters who only come to campus part time, and adding staff, let's assume that campus has about 10,000 people on any given day. Assume each person makes one call per day on average. Our design goal is a blocking rate of 0.2% or less.

(a) Say we have 90 channels allocated across campus. How long should each person's call last at most, on average, to ensure we reach our intended blocking rate?

(b) Repeat (a) but assume we only have 1/3 of the channels: 30 channels are available across campus. How long should each person's call last now? Why doesn't the call duration scale by 1/3 too?

(c) Repeat (a) but assume we only have 1/9 of the channels: 10 channels are available across campus. How long should each person's call last now? Why doesn't the call duration scale by 1/9 too?

Problem 4 (2 pts)

Open-ended problem

Anecdotally, Dr. Burnett observes about 2 in every 300 people actively talking on their phone in a 10 minute period walking across campus. Just like in Problem 3, assume campus has about 10,000 people on any given day.

(a) Use this information to estimate the number of erlangs this observation represents. There are several correct answers, so explain your reasoning for how you interpreted the data.

(b) Given your answer in (a), determine how many channels we need across campus to ensure a blocking probability of 1% or less.