TELE 9753 Advanced Wireless Communications

Tutorial 1 – Introduction

Question 1

Cellular networks are migrating from micro cells that cover a few kilometers to small cells that cover only a few hundreds of meters to increase the network capacity. Name at least three design issues which are complicated by this trend.

Question 2

A. Fiber optic cable typically exhibits a bit error probability of Pb = 10−12. A form. of wireless modulation, DPSK, has Pb = 2γ/1 in some wireless channels, where γ is the average SNR. Find the average SNR required to achieve the same Pb in the wireless channel as in the fiber optic cable.

B. Assume a received power of −113 dBm at a user equipment (e.g., cell phone) at the cell edge. Also, assume the noise temperature and the receiving bandwidth of the user equipment are T = 300K (Kelvin) and B = 1 MHz, respectively. Calculate the received SNR of the user equipment. Note that the Boltzmann constant K = 1.38064852 × 10−23 Joule/Kelvin.

Question 3

Find the round-trip delay of data sent between a satellite and the earth. We consider geostationary earth orbit (GEO), medium earth orbit (MEO), and low earth orbit (LEO) satellites and assume the speed of light is 3×108 m/s. The distances from the GEO satellite, the MEO satellite, and the LEO satellite to the earth are 35,786 kms, 8,000 – 20,000 kms, and 500 – 2,000 kms, respectively. If the maximum acceptable delay for a voice system is 30 milliseconds, which of these satellite systems would be acceptable for two-way voice communication?

Home Work

Requirements

1. Write down your full name, student number, and signature.

2. Detail the steps of your analysis/calculations/solutions. A single answer without derivations or expla nations is not acceptable.

3. Hand in a hard copy in the following class.

Question 1

The current and future cellular networks are migrating to smaller cells and incorporating an increasing number of antennas at the transceivers to improve the quality of wireless transmission. Please name at least three benefits and three challenges brought by these two trends.

Question 2 (A modified version of Question 1.6 in Goldsmith’s book)

Suppose you are a service provider with 180KHz of bandwidth which you must allocate between voice and data users. The voice users require 20Khz of bandwidth, and the data users require 60KHz of bandwidth. So, for example, you could allocate all of your bandwidth to voice users, resulting in 9 voice channels, or you could divide the bandwidth to have 1 data channel and 6 voice channels, etc. Suppose further that this is a time-division system, with timeslots of duration T. All voice and data call requests come in at the beginning of a timeslot and both types of calls last T seconds. There are 9 independent voice users in the system: each of these users requests a voice channel with probability 0.7 and pays $0.50 if his call is processed. There are 3 independent data users in the system: each of these users requests a data channel with probability 0.6 and pays $1.20 if his call is processed. How should you allocate your bandwidth to maximize your expected revenue?

Question 3 (Question 1.10 in Goldsmith’s book)

Consider a square city that is 100 km2 . Suppose you design a cellular system for this city with square cells, where every cell (regardless of cell size) has 100 channels so can support 100 active users (in practice the number of users that can be supported per cell is mostly independent of cell size as long as the propagation model and power scale appropriately).

(a) What is the total number of active users that your system can support for a cell size of 1 km2?

(b) What cell size would you use if you require that your system support 250,000 active users?

Now we consider some financial implications based on the fact that users do not talk continuously. Assume that Friday from 5-6 pm is the busiest hour for cell phone users. During this time, the average user places a single call, and this call lasts 2 minutes. Your system should be designed such that the subscribers will tolerate no greater than a 2% blocking probability during this peak hour. Note that the blocking probability is computed using the Erlang B model: where C is the number of channels and A = UµH for U the number of users, µ the average number of call requests per unit time, and H the average duration of a call. (See any basic networking book or search this definition via Google for more details).

(c) How many total subscribers can be supported in the macrocell system (1 km2 cells) and in the microcell system (with cell size from part (b))?

(d) If a base station costs $500,000, what are the base station costs for each system?

(e) If users pay $50 a month in both systems, what will be the monthly revenue in each case. How long will it take to recoup the infrastructure (base station) cost for each system?