# Chapter 5: Fundamentals of Cellular Communications¶

## Example 5.1, Page 130¶

In [2]:
#Variable declaration
ToCH=960.;# Total available channels
Cellarea=6.; #in km^2
Covarea=2000.;#in km^2
N1=4.;  # Cluster Size
N2=7.;  #Cluster Size

#Calculations
Area1=N1*Cellarea;#for N=4
Area2=N2*Cellarea;#For N=7
No_of_clusters1=round(Covarea/Area1);
No_of_clusters2=round(Covarea/Area2);
No_of_CH1=ToCH/N1;    # No of channels with cluster size 4
No_of_CH2=ToCH/N2;    # No of channels with cluster size 7
SysCap1=No_of_clusters1*ToCH;
SysCap2=No_of_clusters2*ToCH;

#Results
print 'System Capacity with cluster size 4 is %d channels'%SysCap1
print 'Number of clusters for covering total area with N equals 4 are %d'%No_of_clusters1
print 'System Capacity with cluster size 7 is %d channels'%SysCap2

System Capacity with cluster size 4 is 79680 channels
Number of clusters for covering total area with N equals 4 are 83
System Capacity with cluster size 7 is 46080 channels


## Example 5.2, Page 132¶

In [6]:
#Variable declaration
S_IAMP=18.;# S/I ratio in dB
S_IGSM=12.;# S/I ratio in dB
PPL=4.; # propogation path loss coefficient

#Calculations
# Using Equation 5.16 on page no 132, we get
N_AMP=(1./3)*((6*10**(0.1*S_IAMP))**(2/PPL));#reuse factor for AMPS

N_GSM=(1./3)*((6*10**(0.1*S_IGSM))**(2/PPL));#reuse factor for GSM

#Result
print 'Reuse Factor for AMP system is N = %.3f = approx %d \n'%(N_AMP,N_AMP+1);
print 'Reuse Factor for GSM system is N = %.3f = approx %d \n'%(N_GSM,N_GSM+1);

Reuse Factor for AMP system is N = 6.486 = approx 7

Reuse Factor for GSM system is N = 3.251 = approx 4



## Example 5.3, Page 132¶

In [12]:
import math

#Variable declaration
VCH=395.;#Total voice channels
CallHT=120.;#average call holding time in sec
Blocking=0.02;# 2%
PPL=4.;  #propogation path loss coefficient
N1=4.      #reuse factor
N2=7.;     #reuse factor
N3=12.;    #reuse factor

#Calculations&Results
No_of_VCH1=VCH/N1;  #for reuse factor N1
No_of_VCH2=VCH/N2;  #for reuse factor N2
No_of_VCH3=VCH/N3;  #for reuse factor N3
print 'NO of voice channels for N=4 are %d'%(round(No_of_VCH1));
print 'NO of voice channels for N=7 are %d'%(round(No_of_VCH2));
print 'NO of voice channels for N=12 are %d\n'%(round(No_of_VCH3));
# To find cell capacity
print 'calls per hour per cell for N=4 are %d'%(round(Ncall1));
print 'calls per hour per cell for N=7 are %d'%(round(Ncall2));
print 'calls per hour per cell for N=12 are %d  \n'%(Ncall3);
# To find S BY I
# N=(1/3)[6*(S/I)]**(2/PPL)
S_I1=10*(PPL/2)*(math.log10(N1)-math.log10(1./3)-(2./PPL)*math.log10(6));#Mean S/I (dB)

S_I2=10*(PPL/2)*(math.log10(N2)-math.log10(1./3)-(2./PPL)*math.log10(6));
S_I3=10*(PPL/2)*(math.log10(N3)-math.log10(1./3)-(2./PPL)*math.log10(6));

print 'Mean S/I(dB) for N=4 is %.1f'%S_I1
print 'Mean S/I(dB) for N=7 is %.1f'%S_I2
print 'Mean S/I(dB) for N=12 is %.1f'%S_I3

NO of voice channels for N=4 are 99
NO of voice channels for N=7 are 56
NO of voice channels for N=12 are 33

calls per hour per cell for N=4 are 2558
calls per hour per cell for N=7 are 1349
calls per hour per cell for N=12 are 724

Mean S/I(dB) for N=4 is 13.8
Mean S/I(dB) for N=7 is 18.7
Mean S/I(dB) for N=12 is 23.3


## Example 5.4, Page 154¶

In [18]:
import math

#Variable declaration
spectrum=12.5*10**6; #in Hz
CHBW=200*10**3;#in Hz
N=4.;#reuse factor
Blocking=0.02; # 2%
callHT=120.;#average call holding time in sec
PPL=4.;#propogation path loss coefficient
CntrlCH=3.; #No of control channels
Ts=8.; # No of voice channels per RF channel

#Calculations&Results
No_ofVCH=((spectrum*Ts)/(CHBW*N))-CntrlCH;
print 'No of voice channels for N=4 are %d'%(No_ofVCH)
print 'Calls per hour per cell for N=4 are %d calls/hour/cell \n '%(round(Ncall));
S_I=10*(PPL/2)*(math.log10(N)-math.log10(1./3)-(2./PPL)*math.log10(6));
print 'Mean S/I(dB) for N=4 is %.1f dB \n '%(S_I)

No of voice channels for N=4 are 122
Calls per hour per cell for N=4 are 3234 calls/hour/cell

Mean S/I(dB) for N=4 is 13.8 dB



## Example 5.5, Page 139¶

In [22]:
import math

#Variable declaration
VCH=395.;#Total allocated voice channels
CHBW=30.; # in kHz
Spectrum=12.5;  # in MHz
CallHT=120.; #Average call holding time in sec
Blocking=0.02; # 2%
PL=40.;  #slope of path loss in dBperdecade

#Calculations&Results
print "We consider only the ﬁrst tier interferers and neglect the effects of cochannel interference from the second and other higher tiers."
#FOR 120degree sectorization
#N=4
VCH11=(VCH/(4*3));
S_I11=PL*math.log10(math.sqrt(3*4))-10*math.log10(2);
#N=7
VCH12=(VCH/(3*7));
S_I12=PL*math.log10(math.sqrt(3*7))-10*math.log10(2);
#N=12
VCH13=VCH/(3*12);
S_I13=PL*math.log10(math.sqrt(3*12))-10*math.log10(2);
#For omnidirectional
#N=4
VCH21=VCH/(4);
S_I21=PL*math.log10(math.sqrt(3*4))-10*math.log10(6);
#N=7
VCH22=VCH/(7);
S_I22=PL*math.log10(math.sqrt(3*7))-10*math.log10(6);
#N=12
VCH23=VCH/(12);
S_I23=PL*math.log10(math.sqrt(3*12))-10*math.log10(6);
# For 60degree Sectorization
#N=3
VCH31=VCH/(6*3);
S_I31=PL*math.log10(math.sqrt(3*3))-10*math.log10(1);
#N=4
VCH32=VCH/(6*4);
S_I32=PL*math.log10(math.sqrt(3*4))-10*math.log10(1);
#N=7
VCH33=VCH/(6*7);
S_I33=PL*math.log10(math.sqrt(3*7))-10*math.log10(1);
#N=12
VCH34=VCH/(6*12);
S_I34=PL*math.log10(math.sqrt(3.*12))-10*math.log10(1);

print 'For Omnidirectional    Calls_per_hour_per_cellsite      Mean S_I ratio      SpecrtalEfficiency'
print 'For N=4                         %d                           %.1f          %.3f\n'%(Calls_hr_site21,S_I21,Seff21);
print 'For N=7                         %d                           %.1f          %.3f\n'%(Calls_hr_site22,S_I22,Seff22);
print 'For N=12                        %d                            %.1f          %.3f\n'%(Calls_hr_site23,S_I23,Seff23);

print 'For 120deg sector    Calls_per_hour_per_cellsite      Mean S_I ratio      SpecrtalEfficiency\n'
print 'For N=4                         %d                           %.1f          %.3f\n'%(Calls_hr_site11,S_I11,Seff11);
print 'For N=7                         %d                           %.1f          %.3f\n'%(Calls_hr_site12,S_I12,Seff12);
print 'For N=12                        %d                            %.1f          %.3f\n'%(Calls_hr_site13,S_I13,Seff13);

print 'For 60 deg Sector    Calls_per_hour_per_cellsite        Mean S_I ratio      SpecrtalEfficiency\n'
print 'For N=3                         %d                           %.1f          %.3f\n'%(Calls_hr_site31,S_I31,Seff31);
print 'For N=4                         %d                           %.1f          %.3f\n'%(Calls_hr_site32,S_I32,Seff32);
print 'For N=7                          %d                           %.1f          %.3f\n'%(Calls_hr_site33,S_I33,Seff33);
print 'For N=12                         %d                           %.1f          %.3f\n'%(Calls_hr_site34,S_I34,Seff34);

We consider only the ﬁrst tier interferers and neglect the effects of cochannel interference from the second and other higher tiers.
For Omnidirectional    Calls_per_hour_per_cellsite      Mean S_I ratio      SpecrtalEfficiency
For N=4                         2557                           13.8          0.016

For N=7                         1376                           18.7          0.016

For N=12                        724                            23.3          0.016

For 120deg sector    Calls_per_hour_per_cellsite      Mean S_I ratio      SpecrtalEfficiency

For N=4                         2172                           18.6          0.016

For N=7                         1088                           23.4          0.016

For N=12                        515                            28.1          0.016

For 60 deg Sector    Calls_per_hour_per_cellsite        Mean S_I ratio      SpecrtalEfficiency

For N=3                         2628                           19.1          0.016

For N=4                         1879                           21.6          0.016

For N=7                          896                           26.4          0.016

For N=12                         392                           31.1          0.016