Section 6.8. Exercises

6.8. Exercises

1.	Consider a commercial wireless mobile telephone system whose transmitter and receiver are located 9.2 km apart. Both use isotropic antennas. The medium through which the communication occurs is not a free space, and it creates conditions such that the path loss is a function of d 3 and not d 2 . Assume that the transmitter operating at the frequency of 800 MHz communicates with a mobile receiver with the received power of 10 -6 microwatts. Find the effective area of the receiving antenna. Find the required transmission power.
2.	Assume that cellular networks were modeled by square cells Find the cell coverage area, and compare it to the one using hexagonal cells. Assume that the distance between the cell centers are identical in these two models. What are the disadvantages of this model compared to the one with hexagonal cells?
3.	A cellular network over 1,800 km 2 supports a total of 800 radio channels. Each cell has an area of 8 km 2 . If the cluster size is 7, find the system capacity. Find the number of times a cluster of size 7 must be replicated to approximately cover the entire area. What is the impact of the cluster size on system capacity?
4.	Consider a cellular network with 128 cells and a cell radius r =3 km. Let g be 420 traffic channels for a N = 7-channel cluster system. Find the area of each hexagonal cell. Find the total channel capacity. Find the distance between the centers of nearest neighboring cochannel cells.
5.	If cells split to smaller cells in high-traffic areas, the capacity of the cellular networks for that region increases . What would be the trade-off when the capacity of the system in a region increases as a result of cell splitting? Consider a network with 7-cell frequency reuse clustering. Each cell must preserve its base station in its center. Construct the cell-splitting pattern in a cluster performed from the center of the cluster.
6.	We would like to simulate the mobility and handoff in cellular networks for case 4 described in this chapter. Assume 25 mph k 45 mph within city and 45 mph k 75 mph for highway . Let d b be the distance a vehicle takes to reach a cell boundary, ranging from -10 miles to 10 miles. Plot the probability of reaching a cell boundary for which a handoff is required. Discuss why the probability of reaching a boundary decreases in an exponential manner. Show that the probability of reaching a cell boundary for a vehicle that has a call in progress is dependent on d b . Show the probabilities of reaching a cell boundary as a function of a vehicle's speed. Discuss why the probability of reaching a cell boundary is proportional to the vehicle's speed.
7.	Computer simulation project . Consider again the mobility in cellular networks for case 4 described in this chapter, but this time, we want to simulate the handoff for three states: stop, variable speed, and constant speed. For the variable-speed case, assume that the mobile user moves with a constant acceleration of K 1 m/h. Assume 25 m / h k 45 m / h within city and 45 m / h k 75 m / h for highway. Let d b be the distance a vehicle takes to reach a cell boundary, ranging from -10 miles to 10 miles. Plot the probability of reaching a cell boundary for which a handoff is required. Discuss why the probability of reaching a boundary decreases in an exponential manner. Show that the probability of reaching a cell boundary for a vehicle that has a call in progress is dependent on d b . Show the probabilities of reaching a cell boundary as a function of a vehicle's speed. Discuss why the probability of reaching a cell boundary is proportional to the vehicle's speed and that the probability of requiring a handoff decreases.