{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Chapter No.3 : The cellular concept system design fundamentals"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 3.1 Page No.61"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
" The number of channels available per cell for 4-cell reuse system = 165 channels\n",
"\n",
" One control channel and 160 voice channels would be assigned to each cell.\n",
"\n",
" \n",
" The number of channels available per cell for 7-cell reuse system = 95 channels\n",
"\n",
" Each cell would have one control channel, four cells would have 90 voice channels and three cells would have 91 voice channels.\n",
"\n",
" \n",
" The number of channels available per cell for 12-cell reuse system = 55 channels\n",
"\n",
" Each cell would have one control channel, eight cells would have 53 voice channels and four cells would have 54 voice channels.\n"
]
}
],
"source": [
"from math import ceil\n",
"# To compute the number of channels available per cell for a)four-cell reuse system a)seven-cell reuse system a)12-cell reuse system\n",
"\n",
"# Given data\n",
"B=33*10**6# # Total bandwidth allocated to particular FDD system in Hz\n",
"Bc=25*10**3# # Bandwidth per channel in Hz\n",
"Nc=2# # Number of simplex channels\n",
"Bc=Bc*Nc# # Channel bandwidth in Hz\n",
"\n",
"Ntotal=B/Bc# # Total number of channels\n",
"\n",
"#a) To compute the number of channels available per cell for four-cell reuse system\n",
"N=4# # frequency reuse factor\n",
"chpercell=Ntotal/N# # number of channels available per cell for four-cell reuse system\n",
"\n",
"# Displaying the result in command window\n",
"print \"\\n The number of channels available per cell for 4-cell reuse system = %0.0f channels\"%(chpercell)\n",
"print \"\\n One control channel and 160 voice channels would be assigned to each cell.\"\n",
"\n",
"# b) To compute the number of channels available per cell for seven-cell reuse system\n",
"N=7# # frequency reuse factor\n",
"chpercell=ceil(Ntotal/N)# # number of channels available per cell for seven-cell reuse system\n",
"\n",
"# Answer is varrying due to round-off error\n",
"\n",
"# Displaying the result in command window\n",
"print \"\\n \\n The number of channels available per cell for 7-cell reuse system = %0.0f channels\"%(chpercell)\n",
"print \"\\n Each cell would have one control channel, four cells would have 90 voice channels and three cells would have 91 voice channels.\"\n",
"\n",
"# c) To compute the number of channels available per cell for 12-cell reuse system\n",
"N=12# # frequency reuse factor\n",
"chpercell=Ntotal/N# # number of channels available per cell for seven-cell reuse system\n",
"\n",
"# Displaying the result in command window\n",
"print \"\\n \\n The number of channels available per cell for 12-cell reuse system = %0.0f channels\"%(chpercell)\n",
"print \"\\n Each cell would have one control channel, eight cells would have 53 voice channels and four cells would have 54 voice channels.\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 3.2 Page No.72"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
" Signal to noise ratio for n=4 with frequency reuse factor N=7 = 18.66 dB\n",
"\n",
" Signal to noise ratio for n=3 with frequency reuse factor N=7 = 12.05 dB\n",
"\n",
" Signal to noise ratio for n=3 with frequency reuse factor N=12 = 15.56 dB\n",
"\n",
" Since SIR is for n=3 with frequency reuse factor N=7 greater than the minimum required, so N=12 is used.\n"
]
}
],
"source": [
"from math import sqrt, log10\n",
"from __future__ import division\n",
"# To find frequency reuse factor for path loss exponent (n) a)n=4 b)n=3\n",
"\n",
"# Given data\n",
"SIdB=15# # Signal to interference(dB)\n",
"io=6# # Number of cochannel cell\n",
"\n",
"# For n=4\n",
"n1=4# # Path loss exponent\n",
"N1=7# # First consideration: frequency reuse factor N=7\n",
"DR1=sqrt(3*N1)# # Co-channel reuse ratio\n",
"si1=(1/io)*(DR1)**n1# # Signal to interference\n",
"sidB1=10*log10(si1)# # Signal to interference(dB)\n",
"\n",
"# For n=3\n",
"n2=3# # Path loss exmponent\n",
"si=(1/io)*(DR1)**n2# # Signal to interference for first consideration: frequency reuse factor N=7\n",
"sidB=10*log10(si)# # Signal to interference(dB)\n",
"\n",
"N2=12# # second consideration : frequency reuse factor N=12 since sidB<SIdB \n",
"DR2=sqrt(3*N2)# # Co-channel reuse ratio\n",
"si2=(1/io)*(DR2)**n2# # Signal to interference\n",
"sidB2=10*log10(si2)# # Signal to interference(dB)\n",
"\n",
"# Displaying the result in command window\n",
"print \"\\n Signal to noise ratio for n=4 with frequency reuse factor N=7 = %0.2f dB\"%(sidB1)\n",
"print \"\\n Signal to noise ratio for n=3 with frequency reuse factor N=7 = %0.2f dB\"%(sidB)\n",
"print \"\\n Signal to noise ratio for n=3 with frequency reuse factor N=12 = %0.2f dB\"%(sidB2)\n",
"print \"\\n Since SIR is for n=3 with frequency reuse factor N=7 greater than the minimum required, so N=12 is used.\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 3.4 Page No.80"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
" Total number of users for 1 channel = 1\n",
"\n",
" Total number of users for 5 channel = 11\n",
"\n",
" Total number of users for 10 channel = 40\n",
"\n",
" Total number of users for 20 channel = 111\n",
"\n",
" Total number of users for 100 channel = 809\n"
]
}
],
"source": [
"# To find number of users for Number of channels (C) a)C=1 b)C=5 c)C=10 d)C=20 e)C=100\n",
"\n",
"# Given data\n",
"GOS=0.005# #G rade of Service\n",
"Au=0.1# # Traffic intensity per user\n",
"\n",
"# a)To find number of users for C=1\n",
"C1=1# # Number of channels\n",
"A1=0.005# # Total traffic intensity from Erlangs B chart\n",
"U1=(A1/Au)# # Number of users\n",
"U1=1# # Since one user could be supported on one channel\n",
"\n",
"# b)To find number of users for C=5\n",
"C2=5# # Number of channels\n",
"A2=1.13# # Total traffic intensity from Erlangs B chart\n",
"U2=round(A2/Au)# # Number of users\n",
"\n",
"# c)To find number of users for C=10\n",
"C3=10# # Number of channels\n",
"A3=3.96# # Total traffic intensity from Erlangs B chart\n",
"U3=round(A3/Au)# # Number of users\n",
"\n",
"# Answer is varrying due to round off error\n",
"\n",
"# d)To find number of users for C=20\n",
"C4=20# # Number of channels\n",
"A4=11.10# # Total traffic intensity from Erlangs B chart\n",
"U4=round(A4/Au)# # Number of users\n",
"\n",
"# Answer is varrying due to round off error\n",
"\n",
"# e)To find number of users for C=100\n",
"C5=100# # Number of channels\n",
"A5=80.9# # Total traffic intensity from Erlangs B chart\n",
"U5=round(A5/Au)# # Number of users\n",
"\n",
"# Displaying the result in command window\n",
"print \"\\n Total number of users for 1 channel = %0.0f\"%(U1)\n",
"print \"\\n Total number of users for 5 channel = %0.0f\"%(U2)\n",
"print \"\\n Total number of users for 10 channel = %0.0f\"%(U3)\n",
"print \"\\n Total number of users for 20 channel = %0.0f\"%(U4)\n",
"print \"\\n Total number of users for 100 channel = %0.0f\"%(U5)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 3.5 Page No.83"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
" Total number of users in system A = 47280\n",
"\n",
" The percentage market penetration of system A = 2.36\n",
"\n",
" \n",
" Total number of users in system B = 44100\n",
"\n",
" The percentage market penetration of system B = 2.205\n",
"\n",
" \n",
" Total number of users in system C = 43120\n",
"\n",
" The percentage market penetration of system C = 2.156\n",
"\n",
" \n",
" Total number of users in all 3 systems = 134500\n",
"\n",
" The combined Market penetration percentage of all systems = 6.725\n"
]
}
],
"source": [
"from __future__ import division\n",
"# To find number of users for a)system A b)system B c)system C\n",
"\n",
"# Given data\n",
"GOS=0.02# # Grade of Service (Probability of bloacking)\n",
"lamda=2# # Average calls per hour\n",
"H=(3/60)# # Call duration in seconds\n",
"\n",
"Au=lamda*H# # Traffic intensity per user\n",
"\n",
"# a)To find number of users for System A\n",
"C1=19# # Number of channels used\n",
"A1=12# # Traffic intensity from Erlang B chart\n",
"U1=round(A1/Au)# # Number of users per cell\n",
"cells1=394\n",
"TU1=U1*cells1# # Total number of users\n",
"MP1=TU1/(2*10**6)*100# # Market penetration percentage\n",
"\n",
"# b)To find number of users for System B\n",
"C2=57# # No. of channels used\n",
"A2=45# # Traffic intensity from Erlang B chart\n",
"U2=round(A2/Au)# # Number of users per cell\n",
"cells2=98\n",
"TU2=U2*cells2# # Total no. of users\n",
"MP2=TU2/(2*10**6)*100# # Market penetration percentage\n",
"\n",
"# c)To find number of users for System C\n",
"C3=100# # Number of channels used\n",
"A3=88# # traffic intensity from Erlang B chart\n",
"U3=round(A3/Au)# # Number of users per cell\n",
"cells3=49\n",
"TU3=U3*cells3# # Total no. of users\n",
"MP3=TU3/(2*10**6)*100# # Market penetration percentage\n",
"\n",
"TU=TU1+TU2+TU3# # Total number of users in all 3 systems\n",
"MP=TU/(2*10**6)*100# # Combined Market penetration percentage\n",
"\n",
"# Displaying the result in command window\n",
"print \"\\n Total number of users in system A = %0.0f\"%(TU1)\n",
"print \"\\n The percentage market penetration of system A = %0.2f\"%(MP1)\n",
"print \"\\n \\n Total number of users in system B = %0.0f\"%(TU2)\n",
"print \"\\n The percentage market penetration of system B = %0.3f\"%(MP2)\n",
"print \"\\n \\n Total number of users in system C = %0.0f\"%(TU3)\n",
"print \"\\n The percentage market penetration of system C = %0.3f\"%(MP3)\n",
"print \"\\n \\n Total number of users in all 3 systems = %0.0f\"%(TU)\n",
"print \"\\n The combined Market penetration percentage of all systems = %0.3f\"%(MP)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 3.6 Page No.84"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
" Number of cells in given system = 31 cells\n",
"\n",
" \n",
" Number of channels per cell in given system = 95 channels/cell\n",
"\n",
" \n",
" Traffic intensity in given system = 84 Erlangs/cell\n",
"\n",
" \n",
" Maximum carried traffic in given system = 2604 Erlangs\n",
"\n",
" \n",
" Total number of users = 86800 users\n",
"\n",
" \n",
" Number of mobiles per unique channel = 130 mobiles/channel\n",
"\n",
" \n",
" Theoretically maximum number of served mobiles is the number of available channels in the system.\n",
"\n",
" Theoretical Maximum number of users could be served at one time = 2945 users\n",
"It is 3.4% of customer base.\n"
]
}
],
"source": [
"# To find a)Number of cells in given area b)Number of channels/cell c)Traffic intensity per cell d)Maximum carried traffic e)Total number of users for 2% GOS f) Number of mobiles per unique channel g)Maximum number of users could be served at one time\n",
"\n",
"# Given data\n",
"Area=1300# # Total coverage area in m**2\n",
"R=4# # Radius of cell in m\n",
"N=7# # Frequecy reuse factor\n",
"S=40*10**6# # Allocated spectrum in Hz\n",
"Ch=60*10**3# # Channel width in Hz\n",
"\n",
"# a)Number of cells\n",
"CA=2.5981*R**2# # Area of hexagonal cell in m**2\n",
"Nc=round(Area/CA)# # Number of cells\n",
"\n",
"# Displaying the result in command window\n",
"print \"\\n Number of cells in given system = %0.0f cells\"%(Nc)\n",
"\n",
"# b)Number of channels/cell\n",
"C1=round(S/(Ch*N))# # Number of channels\n",
"\n",
"# Displaying the result in command window\n",
"print \"\\n \\n Number of channels per cell in given system = %0.0f channels/cell\"%(C1)\n",
"\n",
"# c) Traffic intensity per cell\n",
"C1=95# # Number of channels from b)\n",
"GOS=0.02# # Grade of service\n",
"A=84# # Traffic intensity from Erlang B chart\n",
"\n",
"# Displaying the result in command window\n",
"print \"\\n \\n Traffic intensity in given system = %0.0f Erlangs/cell\"%(A)\n",
"\n",
"# d)Maximum carried traffic\n",
"traffic=Nc*A# # Maximum carried traffic\n",
"\n",
"# Displaying the result in command window\n",
"print \"\\n \\n Maximum carried traffic in given system = %0.0f Erlangs\"%(traffic)\n",
"\n",
"# e)Total number of users for 2% GOS \n",
"trafficperuser=0.03# # Given traffic per user\n",
"U=traffic/trafficperuser# # Total number of users\n",
"\n",
"# Displaying the result in command window\n",
"print \"\\n \\n Total number of users = %0.0f users\"%(U)\n",
"\n",
"# f) Number of mobiles per unique channel\n",
"C=666# # Number of channels\n",
"mobilesperchannel=round(U/C)# # Number of mobiles per unique channel\n",
"\n",
"# Displaying the result in command window\n",
"print \"\\n \\n Number of mobiles per unique channel = %0.0f mobiles/channel\"%(mobilesperchannel)\n",
"\n",
"# g)Maximum number of users could be served at one time\n",
"print \"\\n \\n Theoretically maximum number of served mobiles is the number of available channels in the system.\"\n",
"C=C1*Nc# # Maximum number of users could be served at one time\n",
"\n",
"# Displaying the result in command window\n",
"print \"\\n Theoretical Maximum number of users could be served at one time = %0.0f users\"%(C)\n",
"print \"It is 3.4% of customer base.\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 3.7 Page 85"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
" Number of users per square km in given system = 62 users/sq km\n",
"\n",
" \n",
" Percentage of probability that delayed call have to wait longer than t=10 sec = 56.29 percent\n",
"\n",
" \n",
" Percentage of probability that call is delayed more than 10 sec = 2.81 percent\n"
]
}
],
"source": [
"from math import exp\n",
"# To find a)number of users per square km b)probability that delayed call have to wait longer than t=10sec c)probability that call is delayed more than 10 sec\n",
"\n",
"# Given data\n",
"R=1.387# # Radius of cell in m\n",
"Area=2.598*R**2# # Area of hexagonal cell in m**2\n",
"cellpercluster=4# # Number of cells/cluster\n",
"channels=60# # Number of channels\n",
"\n",
"channelspercell=channels/cellpercluster# # Number of channels per cell\n",
"\n",
"# a)To find number of users per square km\n",
"A=0.029# # Traffic intensity per user\n",
"delayprob=0.05# # Grade of service\n",
"traffic=9# # Traffic intensity from Erlang chart C\n",
"U1=traffic/A# # Total number of users in 5sq.km.\n",
"U=round(U1/Area)# # Number of users per square km\n",
"\n",
"# Displaying the result in command window\n",
"print \"\\n Number of users per square km in given system = %0.0f users/sq km\"%(U)\n",
"\n",
"# b)To find the probability that delayed call have to wait longer than t=10sec\n",
"lamda=1# # Holding time\n",
"H1=A/lamda# # Duration of call\n",
"H=H1*3600# # Duration of call in second\n",
"t=10\n",
"Pr=exp(-(channelspercell-traffic)*t/H)*100# # probability that delayed call have to wait longer than t=10sec.\n",
"\n",
"# Displaying the result in command window\n",
"print \"\\n \\n Percentage of probability that delayed call have to wait longer than t=10 sec = %0.2f percent\"%(Pr)\n",
"\n",
"# c)To find the probability that call is delayed more than 10 sec\n",
"Pr10=delayprob*Pr# # probability that call is delayed more than 10 sec\n",
"\n",
"# Displaying the result in command window\n",
"print \"\\n \\n Percentage of probability that call is delayed more than 10 sec = %0.2f percent\"%(Pr10)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 3.8 Page 89"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
" Number of channels without use of microcell = 300 channels\n",
"\n",
" \n",
" Number of channels with the use of lettered microcells = 660 channels\n",
"\n",
" \n",
" Number of channels if all base stations are replaced by microcells = 1020 channels\n"
]
}
],
"source": [
"# To find number of channels in 3 km by 3 km square centered around A in Figure 3.9 for a)without use of microcell b)with the use of lettered microcells c)all base stations are replaced by microcells\n",
"\n",
"# Given data\n",
"R=1# # Cell radius in km\n",
"r=0.5# # Micro-cell radius in km\n",
"Nc=60# # Number of channels in base station\n",
"\n",
"# a)To find number of channels without use of microcell\n",
"Nb1=5# # Number of base stations in given area\n",
"N1=Nb1*Nc# # Number of channels without use of microcell\n",
"\n",
"# b)To find number of channels with the use of lettered microcells\n",
"Nb2=6# # Number of lettered microcells\n",
"Nb2=Nb1+Nb2# # Total number of base stations in given area\n",
"N2=Nb2*Nc# # Number of channels with the use of lettered microcells\n",
"\n",
"# c)To find number of channels if all base stations are replaced by microcells\n",
"Nb3=12# # Number of all the microcells\n",
"Nb3=Nb1+Nb3# # Total number of base stations in given area\n",
"N3=Nb3*Nc# # Number of channels if all base stations are replaced by microcells\n",
"\n",
"# Displaying the result in command window\n",
"print \"\\n Number of channels without use of microcell = %0.0f channels\"%(N1)\n",
"print \"\\n \\n Number of channels with the use of lettered microcells = %0.0f channels\"%(N2)\n",
"print \"\\n \\n Number of channels if all base stations are replaced by microcells = %0.0f channels\"%(N3)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 3.9 Page 92"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
" Cell capacity of unsectored system = 1326 calls/hour\n",
"\n",
" \n",
" Cell capacity of 120 degree sectored system = 1008 calls/hour\n",
"\n",
" \n",
" Decrease in cell capacity in 120 degree sectored system = 0 percent\n"
]
}
],
"source": [
"# To analyze trunking efficiency capacity of sectoring and unsectoring\n",
"\n",
"# Given data\n",
"H=2/60# # Average call duration in hour\n",
"GOS=0.01# # Probability of blocking\n",
"\n",
"# Unsectored system\n",
"C1=57# # Number of traffic channels per cell in unsectored system\n",
"A=44.2# # Carried traffic in unsectored system\n",
"calls1=1326# # Number of calls per hour in unsectored system from Erlangs B table\n",
"\n",
"# 120 degree sectored system\n",
"C2=C1/3# # Number of traffic channels per antenna sector in 120 degree sectored system\n",
"calls2=336# # Number of calls per hour in 120 degree sectored system from Erlangs B table\n",
"Ns1=3# # Number of sectors\n",
"capacity=Ns1*calls2# # Cell capacity or number of calls handled by system per hour\n",
"\n",
"dif=calls1-capacity# # decrease in cell capacity in 120 degree sectored system\n",
"percentdif=(dif/calls1)*100# # decrease in cell capacity in 120 degree sectored system in percentage\n",
"\n",
"# Displaying the result in command window\n",
"print \"\\n Cell capacity of unsectored system = %0.0f calls/hour\"%(calls1)\n",
"print \"\\n \\n Cell capacity of 120 degree sectored system = %0.0f calls/hour\"%(capacity)\n",
"print \"\\n \\n Decrease in cell capacity in 120 degree sectored system = %0.0f percent\"%(percentdif)"
]
}
],
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