Tutorial 3 Cellular design and Traffic Engineering 1. (a) Prove that ...

EE5401 CELLULAR MOBILE COMMUNICATIONS 

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Tutorial 3 

Cellular design and Traffic Engineering 

1. (a) Prove that for a hexagonal geometry, the co-channel reuse ratio is 

2 2 

given by Q = 3N 

, where N = i + ij + j 

(b) Show that the frequency reuse factor for a cellular system is given by 

k S , where k is the average number of channels per cell and S is the 

total number of channels available to the cellular service provider. 

(c) For i=3, j=2, draw the layout of the cellular structure. 

2. [Textbook] (a) A cellular service provider decides to use a digital TDMA 

scheme which can tolerate a signal-to-interference ratio of 15dB in the 

worst case. Find the optimal value of N for (i) omni-directional antennas, 

(ii) 120° sectoring, and (iii) 60° sectoring. Should sectoring be used? If 

so, which case should be used? Assume a path loss exponent of n=4. 

(Please thought over the significant of the results) 

(b) If n=3, is there any change in your design decision? 

[Ans: (a)(i) N=7 (ii) N=3 (iii) N=3, 120° sectoring should be used. (b)(i) N=12 (ii) N=7 (iii) 

N=4, 60° sectoring should be used] 

3. [Textbook] For a N=7 system with a P(block)=1% and average call length 

of 2 minutes, find the traffic capacity loss due to trunking for 57 channels 

when going from omni-directional antennas to 60° sectored antennas. 

Assume that blocked calls are cleared and the average per user call rate 

is λ = 1 per hour. [Ans : from 1326 users to 738 users, a drop of 44%] 

4. [Textbook] Assume that a cell named “Radio Knob” has 57 channels, each 

with an effective radiated power of 32W and a cell radius of 10 km. The 

GOS is established to be a probability of blocking of 5% (assuming 

blocked calls are cleared). Assume the average call holding time is 2 

minutes, and each user averages 2 calls per hour. Further, assume the 

cell has just reached its maximum capacity and must be split into 4 new 

microcells to provide 4 times the capacity in the same area. 

(a) What is the current capacity of the “Radio Knob” cell? 

(b) What is the radius and transmit power of the new cells? 

(c) If traffic is uniformly distributed, what is the new traffic carried by 

each cell? Will the probability of blocking in these new cells be 

below 0.1% after the split? 

[Ans : (a) 772 users (b) 2 W (c) 12.75 Erlangs, so blocking probability below 0.1%] 

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5. [Textbook] A receiver in an urban cellular radio system detects a 1 mW 

signal at d = d 0 = 1m from the transmitter. In order to mitigate cochannel 

interference effects, it is required that the signal received at any 

base station receiver from another base station transmitter which 

operates with the same channel must be below –100dBm. A 

measurement team has determined that the average path loss exponent 

in the system is n = 3. (a) Determine the major radius of each cell if a 7- 

cell reuse pattern is used. (b) What is the major radius if a 4-cell reuse 

pattern is used? [Ans: (a) >470.1 m (b) >621.9 m] 

6. [96/97 Exam] Assume a 4-cell reuse pattern. A total of 96 channels are 

available for each cluster. In a specific cluster the traffic load is not 

uniformly distributed over the cells. To cater for the different 

requirements, the available channels are allocated as follows: {42, 30, 18, 

6} for the cells in the cluster. 

(a) Given a blocking probability of 2%, what traffic loads can each cell 

accommodate? 

(b) Due to interference problems, 120 degrees sectorisation is 

introduced into the system. What traffic loads can each cell now 

accommodate? Explain possible differences. 

(c) Assume that we can categorize the traffic patterns into 3 classes. 

Short message of duration 20sec/call, normal calls of duration 4 

min/call and teenage gossiping of duration 1.5 hours/call. Let 

there be 5 normal calls and 10 short message for each teenager 

calling. How many calls per hour can be accommodated on 

average in the cluster when sectorisation is not used? 

[Ans: (a) 32.8, 21.9, 11.5, 2.28 Erlang (b) 24.6, 15.24, 6.84, 0.67 Erlang (c) 580 calls/hr] 

7. [96/97 Exam] Shadowing is experienced in each cell. The shadowing 

follows a log-normal distribution with a shadowing spread of 5 dB. The 

transmitted power is P t =10W, the cell radius of R=3km, the reference 

distance is d 0 =1km, and the carrier frequency is 900MHz. The 

environment is described by a path loss exponent of α = 3. 5 . 

(a) Assuming shadowing losses only, what is the probability that the 

received signal level is 3 times smaller than the average level? 

(b) Assuming that satisfactory performance is possible for a signal 

level above the threshold level γ = −63. 46 dBm, what is the 

coverage percentage at the boundary of the cell given shadowing? 

(c) If the transmit power is increased by a factor of 3, what cell size 

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should be used to maintain the same coverage at the boundary? 

[Hint : If no knowledge is given for d6.34 km] 

9. [Textbook] A PCS licenssee plans to build out a 30 MHz license in the 

new US PCS band of 1850MHz to 1880MHz (reverse line) and 1930MHz 

to 1960 MHz (forward lind). They intend to use DCS1900 radio 

equipment. DCS1900 provides a GSM-like service and supports 8 users 

per 200kHz radio channel using TDMA. Because of GSM’s digital 

techniques, GSM vendors have convinced the licensee that when the path 

loss exponent is equal to 4, GSM can be deployed using 4-cell reuse. 

(a) How many GSM radio channels can be used by the licensee? 

(b) If each DCS1900 base station can support a maximum of 64 radio 

channels. How many users can be supported by the base station 

during fully loaded operation? 

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(c) 

(d) 

(e) 

(f) 

(g) 

(h) 

If the licensee wishes to cover a city having a circular shaped area 

of 2500 sq km, and the base stations use 20W transmitter powers 

and 10dB gain omni-directional antennas, determine the number 

of cells required to provide forward link coverage to all parts of the 

city. Assume 4-cell reuse, and let n=4 and the standard deviation 

of 8dB hold as the path loss model for each cell in the city. Also 

assume that a required signal level of –90dBm must be provided 

for 93% of the coverage area in each cell, and that each mobile uses 

a 0dB gain antenna. Assume d 0 =1km. 

For your answer in (c), define in exact detail a suitable channel 

reuse scheme for each cell in the city, and define the channels used 

by each cell. Your scheme should include details such as how 

many channels each base station should use, what the nearest 

reuse distance should be, and other issues which clearly define 

how to assign channels geographically throughout the city? You 

may assume that users are distributed uniformly throughout the 

city, that each cell is equal distance from its neighbors, and you 

may ignore the effect of control channels (that is, assume all radio 

channels carry only voice users). 

How many (I) cells (base stations) (ii) total radio channels (iii) 

total user channels (there are 8 user channels per radio channel) 

are available throughout the entire city, based on your answer in 

(d)? The total number of user channels is equal to the maximum 

capacity of the system and is a hard limit on the number of users 

that can be simultaneously served at full capacity. 

If each base station costs $500,000, and each radio channel within 

the base station costs $50,000, what is the cost of the system in (e)? 

This is the initial cost of the system. 

If the system in (d) is designed for 5% blocking probability at startup, 

what is the maximum number of subscribers that can be 

supported at start-up? This is the number of phones that may be 

initially subscribed at start-up. Assume that each user channel is 

trunked along with the other user channels on other radio 

channels within the base station. 

Using your answer in (g), what is the average cost per user needed 

to recoup 10% of the initial system buildout cost after one year if 

the number of subscribers is static during year 1? 

[Ans : (a) 150 (b) 512 (c) 10 (d) Cluster size = 4, 38, 38, 37, 37 (e) 10, 375, 3000 (f) 

$23.75x10**6 (g) 3x10**4 (h) $79.17] 

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10. [Textbook, Jon Mark] .Consider a cellular system in which there are a 

total of 1001 radio channels available for handling traffic. Suppose the 

area of a cell is 6 km 2 and the area of the entire system is 2100 km 2 . 

(a) Calculate the system capacity if the cluster size is 7 

(b) How many times would the cluster of size 4 have to be replicated in 

order to approximately cover the entire cellular area? 

(c) Calculate the system capacity if the cluster size is 4. 

(d) Does decreasing the cluster size increase the system capacity? 

Explain. 

Consider the case when cell cluster of size 7. Given that the traffic load 

per user is 0.03 Erlangs and the average number of calls per hour per 

user is 1.5, for an Erlang-C system with a probability of delaying a call 

being 5%, determine 

(e) The traffic load per cell 

(f) The number of users per km 2 that can be supported by this system 

(g) The mean duration of a call 

(h) The probability that a delayed call will have to wait for more than 

10s, and 

(i) The probability that a call will be delayed for more than 10s. 

[Ans : (a) 50,050 (b) ≈ 87 (c) 87,000 (d) yes (e) 122.98 Erlangs (f) 683 (g) 72s (h) 0.062 

(i) 0.0031] 

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Tutorial 3 Cellular design and Traffic Engineering 1. (a) Prove that ...

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