Question

5. Suppose that are to design a wireless network with the following constraints and properties: • Cells are arranged in a conventional hexagonal layout, with equal sized hexagons. • Each cell has an area of 1 km • The number of cells per frequency-reuse cluster may be N = 1,3, 4,7 or 12. • The path-loss exponent is a = 3.5. • The minimum acceptable SIR is 11 dB. • There are 144 available channels (i.e., 144 calls can be supported at any given time). • Each user offers traffic with an intensity of 0.1 Erlangs. • The call blocking probability must not exceed 0.01. Answer the following: (a) Suppose that the system does not use sectorization i.e., the base stations use omnidirectional antennas). What is the minimum value of N that satisfies the given SIR requirement? In computing the SIR, you only need to consider the first tier of interference and you may assume that all interferers are distance D = RV3N away (i.e., the "rough" approximation), where R is the radius of the cell. (b) Using the value of N found in part (a), determine the user density (ie., the number of users per square kilometer) that can be supported by your network at the specified call blocking probability. (c) Repeat parts (a) and (b), but this time assume that the system uses ideal 120-degree sectorized antennas (i.e., each cell is divided into three sectors). Again, only considering first-tier interferers, and assuming they are all at distance D = R 3N, determine the minimum value of N that satisfies the SIR requirement. Then determine the user density that can be supported by the network. Hint: The cluster size N is not given and must be determined using the required SIR, the given path loss exponent, and the cell-sectorization technique.

Answer 1

Dolls Given: Area = 1 km² 7 or 12 Area = 1 km? N = 1, 3, 4 , exponent = d = 3.5 SIR = 1 1 dB path loss Min Call traffic intensity = 0.1 Erlangs (Say Au) Blocking probability = Grade of Service (Cres) G.o.5 = 0.01 = 1% I a) Given that wouldirecti i = no. of U Omnidirectional antenna co channel interfering cells Now, SIRE 11 dB = ISIR = Now, Considering given asi 10%o.. . (SIR) dg 10 log(SIR) 12.88 1st layer of interfering SIR & SIR = SER - (). EN)

i) Lets take N = 1 - (SIR)= (√3x1) 3.5 - N= 1 - 1.139 - 1.139 < 12.88 ? N=1 will not work !") hats take N c 3 7.79 I (SIR) = (3x3) N: 3 7.79€ 12.88 i N= 3 will not work " Lets take (SIR) N = 4 (J3 x n ) - 12.899 N=h 12.894 > 12.88 the system satisfies :. for N=4 SIR the given

b) Gos = 0.01 Y. Now, as found from part (a) N 4 We know, Au= 0.1 Ex longs & hannels - 15h By using Erlang B-chart. . (can be found De getoo No. of channels per cell = Inh. in the Book = 144.36 10 = 36 : A = 18.47 .. I found from Erlong B chart be with the help at I C and G.o.s. - A = U. Au cell. U = Total U number of users in a À 18:42 1 - Au 0.1 LU= 184.7 ñ 185 users per cel

A Now, given are used. that 120° sectorized antennas Cie divided into 3 sectors) I io = 6 - 2 Now All in as the part process (a), remains same just to becomes 2 u SIP= Coleja (434) * lo 2 above Repeat part (a) & (6) using the formula. you will find Nghe And then find User density (u) by using new N.