College of Computer Science Northeastern University COM3525: Wireless Networks

Winter 2002 February 4^th, 2002

Assignment 2 (Due February 14^th, 2002)

Problem 1 (10 points):

Textbook problem 7.7, page 199.

Problem 2 (10 points):

Textbook problem 7.8, page 199.

Problem 3 (10 points):

Today’s wireless data systems design are mainly focusing on the physical layer and MAC layer. Some research work is being done at higher layers. List three issues that involve higher network layers and that require special attention because of the physical layer in of the wireless channel.

Problem 4 (10 points):

An Ad Hoc network using IEEE802.11 has 4 nodes: N1, N2, N3, N4. Assume that SIFS is 1 unit of time, PIFS 2 units of time, DIFS 3 units of time, and slot time is 2 (these value are not the real values but are taken to simplify the packets scheduling).

Assume that at the beginning the channel is idle (no transmission), and that at instant 1, N2 has a packet to be sent to N4. At instant 2, both N1 and N3 have a packet to be sent to N4. Assume that the random number generator (for backoff) will give the following values for N1: 2, 5, … and for N2: 4, 3, … and for N3: 1, 4, … Assume that we don’t use RTS/CTS or fragmentation, and that all data packets have the same length: 6 units of time and that the Ack packet has length 3 units of time. Furthermore the channel Bit Error Rate is assumed to be 0. Show the execution of the DCF mode of IEEE802.11.

Problem 5 (10 points):

The goal of this exercise is to compute the BER using some simple assumptions. Consider a binary digital communication at bitrate 50bps. The receiver is mobile and is moving toward the transmitter at speed 10m/s and the communication is over 1500MHZ frequency band.

What is the value of the frequency of Doppler shift?

Consider fadings (due to Doppler shift) of the received signal strength R below 0.1*R_RMS. What is the average fade duration?

Assume that a bit is lost whenever the received signal strength R of any portion of the bit is below 0.1*R_RMS. What would be the BER of this communication?

Problem 6 (10 points):

Assume that we are using a (7,4) Hamming code for communication over a channel subject to burst-errors. Propose a scheme that can be combined with the (7,4) Hamming code and that is capable of tolerating bursts of error of length 5.

Problem 7 (10 points):

Assume that we use a convolutional code with the following trellis representation:

Use the Viterbi algorithm to decode the following received sequence:

11 00 01 00 01 10 10 10 10 10 10 10

Problem 8 (10 points):

Build the trellis representation for the following convolutional code:

Problem 9 (10 points):

In the previous problem, what is the “minimum distance” of such a code?