Question

(15 pts) Suppose two wireless devices A and B are perfectily sM0, The other devie available device can operate on ten channels from channel 1 to chayhop amongo operate o operate on 5 channels, 1. 3, 5, 7, and 9. Each device can r channels independently. In each time slot, each of them can c (say A 4. synchronized in time. One ly hop among the available choose a channel to operate on chooses a channel to transmit and B chooses a channel to receive following questions and justify your answers.hannel in one a) What is the probability A b) Can they achieve a higher probability if they knw c) If an attacker can operate on 10 channels from channe know the available channels of the other side? bility if they know the available channels of the other 1 to 10 and is trying to jam the ing t now which channel is chosen by the other side in prior)? the probability of successful communication between A and B, in one slot what is jamming for case a) and case b), respectively?

Answer 1

Part (a)

A and B would meet on the same channel if A chooses one of channels 1, 3, 5, 7 and 9 (the channels accessible to B) and then B also chooses the very same channel.

Now, A can choose any one of 10 channels and so

the probability A chooses one of channels 1, 3, 5, 7 and 9 = 5/10 = ½ ……………………………….. (1)

B has only 5 options for channels and so

the probability B chooses the very same channel (i.e., only one possibility) = 1/5………………….... (2)

Given A and B choose channels independently, the joint probability is the product of individual probabilities. Thus, the probability both will meet on the same channel

= (1/2) x (1/5) = 1/10 ANSWER

Part (b)

Here, A knows the 5 channel options B has and hence, for meeting on the same channel, A would pick one of these 5 channels only, for which the probability is: 1/5. As in the above case, the probability B chooses the very same channel (i.e., only one possibility) = 1/5. Going by the same theory as in (a),

the probability both will meet on the same channel = (1/5) x (1/5) = 1/25   ANSWER

Part (c)

In both scenarios, i.e., (a) and (b), the attacker must choose the very same channel as both A and B has chosen. Since the attacker has 10 channel options, the probability the attacker would get into the very same channel as both A and B = 1/10.

Thus, probability of successful jamming is:

(1/10) x (1/10) = 1/100 or 0.01 for (a) and

(1/25) x (1/10) = 1/250 or 0.004 for (b) ANSWER

DONE