Assignment 2.Sol (2)

THE UNIVERSITY OF WESTERN ONTARIO FACULTY OF ENGINEERING DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING SE 410a – WIRELESS LANs AND WANs Assignment # 2 (Solutions) [Release Date: November 3, 2006; Submission Date: November 20, 2006]

1. If a provider has 20 cells to cover the whole service area, with each cell having 40 channels, how many users can the provider support if a blocking probability of 2% is required? Assume that each user makes an average of three calls per hour and each call duration is an average of three minutes. Number of channels/cell = 40 Offered traffic at GOS of 2% = 30.997 Erlangs/cell Carried traffic = 0.98 x 30.997=30.377 Erlangs/cell Total traffic carried = 30.377 x 20 = 607.54 Erlangs Traffic Intensity per user = 3x (3/60) =0.15 Erlang Total Number of users that can be supported is = 607.54/.15=4050 2. Two service providers, I and II, are planning to provide cellular service to an urban area. Provider I has 20 cells to cover the whole area, with each cell having 40 channels, and provider II has 30 cells, each with 30 channels. How many users can be supported by the two providers if a GOS of 2% is required? Assume that each user makes an average of three calls per hour and each call lasting an average of 3 minutes. PROVIDER I Number of channels/cell = 40 Offered traffic at GOS of 2% = 30.997 Erlangs/cell Carried traffic = 0.98 x 30.997=30.377 Erlangs/cell Total traffic carried = 30.377 x 20 = 607.54 Erlangs Traffic Intensity per user = 3x (3/60) =0.15 Erlang Total Number of users that can be supported is = 607.54/.15=4050 PROVIDER II Number of channels/cell = 30 Offered traffic at GOS of 2% = 21.932 Erlangs/cell Carried traffic = 0.98 x21.932=21.493 Erlangs/cell Total traffic carried = 21.493 x 30 = 644.80 Erlangs Traffic Intensity per user = 3x (3/60) =0.15 Erlang Total Number of users that can be supported is = 644.80/.15=4298 Totally 8,348 users can be accommodated

3. In a cellular system, the received power at the mobile unit is -98 dBm. The cell structure is a seven-cell reuse pattern. If the thermal noise power is -120 dBm and Co-Channel Interference (CCI) from each interfering station is -121 dBm, calculate the Signal-to-CCI Ratio and the overall Signal-to-Noise Ratio (Ratio of received signal power divided by sum of thermal noise and CCI). Converting dBm to mW, we obtain signal power Ps  10 9.8 mW. The thermal noise power = Pthermal = 10 12 mW, CCI Power is PCCI =10 12.1 mW (a) Overall Signal-to-Noise Ratio =



Power ( signal ) Power (thermal )  TotalCCIPo wer

10 9.8 =27.48=14.39dB 1012  6  10 12.1

10 9.8 (b) Signal-to-CCI Ratio  =33.254=15.22 dB 6  10 12.1 4. An analog cellular system has a total of 33 MHz of bandwidth and uses two 25 kHz simplex channels to provide full duplex voice and control channels. (a) What is the number of channels available per cell for a frequency reuse factor of (i) 4 cells; (ii) 7 cells; and (iii) 12 cells? (b) Assume that 1 MHz is dedicated to control channels but that only one control channel is needed per cell. Determine a reasonable distribution of control channels and voice channels in each cell for the three frequency reuse factors of part (a). a. The total number of available channels is K= 33000/50 = 660. For a frequency reuse factor N, each cell can use K/N channels. For N = 4, K/N = 165 channels For N = 7, K/N = 94 channels For N = 12, K/N = 55 channels b. 32 MHz is available for voice channels for a total of 640 channels. For N = 4, we can have 160 voice channels and one control channel per cell For N = 7, we can have 4 cells with 91 voice channels and 3 cells with 92 voice channels, and one control channel per cell. For N = 12, we can have 8 cells with 53 voice channels and 4 cells with 54 voice channels, and one control channel per cell. 5. A telephony connection has duration of 23 minutes. This is the only connection made by this caller during the course of an hour. How much is the amount of traffic in Erlangs, of this connection? (23/60) = 0.383 Erlangs

6. A cellular system uses FDMA with a spectrum allocation of 12.5 MHz in each direction, a guard band at the edge of the allocated spectrum of 10 kHz, and a channel bandwidth of 30 kHz. What is the number of available channels? Total bandwidth = 12.5 x 2 M Hz Guard band = 10 x 2 k Hz Therefore, Number of Duplex Channels= (12.5x2 M Hz-10x2 kHz)/60 kHz = 208 Or, 416 simplex channels 7. Consider a 7-cell system covering an area of 3100 km 2 . The traffic in the seven cells is as follows: Cell 1 2 3 4 5 6 7 number Traffic 30.8 66.7 48.6 33.2 38.2 37.8 32.6 (Erlangs ) Each user generates an average of 0.03 Erlangs of traffic per hour, with a mean holding time of 120s. The system consists of a total of 395 channels and is designated for a GOS of 0.02. (i) Determine the number of subscribers in each cell (ii) Determine the number of calls per hour per subscriber (iii) Determine the number of calls per hour in each cell (iv) Determine the number of channels required in each cell (v) Determine the total number of subscribers (vi) Determine the average number of subscribers per channel (vii) Determine the subscriber density in per km 2 (viii) What is the radius of each cell? (i) Number of subscribers = Traffic/0.03 Cell number Subscribers

1 1026.7

2 2223.3

3 1620.0

4 1106.7

5 1273.3

6 1260.0

7 1086.7

(ii) Number of calls per hour per subscriber = 0.03/(120/3600) = 0.9 (iii) Multiply results of part (i) by 0.9 Cell number Calls per hour

1 924

2 2001

3 1458

4 996

5 1146

6 1134

7 978

(iv) The table in the problem statement gives the value of A. Use P = 0.02. Find N. Cell number Channels

1 40

2 78

3 59

4 43

5 48

6 48

7 42

(v) Total number of subscribers = the sum of the values from part (a) = 9597 (vi)From (d), the total number of channels required = 358 Average number of subscribers per channel = 9597/358 = 26.8 (vii) Subscriber density = 9597/3100 = 3.1 subscribers per km2 (viii)Total traffic = the sum of the values from table in the problem statement = 287.9 (ix)Erlangs per km2 = 287.9/3100 = 0.09 (x) The area of a hexagon of radius R is A = 1.5R 2 3 . For A = 3100/7 = 442.86 km2 we have R = 13 km

8. A cellular system with 7-cell clusters has the following average number of calls at a given time: Cell number, i Average number of calls per unit time ( i ) 1 900 2 2000 3 2500 4 1100 5 1200 6 1800 7 1000 If the system is assigned 49 traffic channels, how would you distribute the channel if (a) Static allocation is used (b) A simple borrowing scheme is used (c) A dynamic channel allocation scheme is used (a) Distribute the channels according to the traffic load of each cell 7

Let

   i . Then, the number of channels allocated to cell i is equal to

Ci 

i 1

i  49 . The channel allocation is shown below: 

Cell number, i 1 2 3 4 5

Average number of calls per unit time ( i ) 900 2000 2500 1100 1200

Number of Channels, Ci 4 9 12 5 6

6 7

1800 1000

8 5

(b) Allocate seven channels to each cell and borrow channels from adjacent cells with low traffic (c) Channels are allocated dynamically as new call arrival in the system and is achieved by keep all free channels in a central pool