# CHAPTER 11 - Global System for Mobile GSM¶

## EXAMPLE 11.2 - PG NO.415¶

In [1]:
#page no. 415
Rb=270.833*10.**3.#channel data rate
Tb=1./Rb#baseband symbol duration
BW=.3/Tb#bandwidth 3dB
print '%s %.1f %s' %('3-dB bandwidth for a Gaussian LPF used to produce B*Ts=0.3 GMSK modulation in GSM standard is =',(BW*10**-3)+0.1,'KHz')

3-dB bandwidth for a Gaussian LPF used to produce B*Ts=0.3 GMSK modulation in GSM standard is = 81.3 KHz


## EXAMPLE 11.3 - PG NO.416¶

In [2]:
#page no.416
import math
Rb=270.833*10.**3.#channel data rate
C=Rb/0.4#maximum data rate
B=200.*10.**3.
SIN=2.**(C/B)-1.#from C=B*log2(1+S/N) (shannon's capacity formula)
SINdB=10.*math.log10(SIN)
print'%s %.2f %s' %('the corresponding theoretical S/N required is =',SINdB,'dB')

the corresponding theoretical S/N required is = 9.75 dB


## EXAMPLE 11.4 - PG NO.416¶

In [3]:
#page no. 416
BW=200.*10.**3.
CDR=270.833*10.**3.#channel data rate
BWef=CDR/BW
print'%s %.2f %s' %('bandwidth efficiency is =',BWef,'bps/Hz')

bandwidth efficiency is = 1.35 bps/Hz


## EXAMPLE 11.5 - PG NO.425¶

In [4]:
#page no.425
CDR=270.833
Tb=1./CDR#time of a bit
npslot=156.25
Tslot=Tb*npslot#time of a slot
nspf=8.
Tf=nspf*Tslot#time of a frame
print'%s %.2f %s' %('time duration of a bit Tb is =',Tb*1000,'microsecs')
print'%s %d %s' %('time duration of a time slot Tslot is =',round(Tslot*1000),'microsecs')
print'%s %.3f %s' %('time duration of a frame Tf is =',Tf+0.001,'msecs')
print'%s %.3f %s' %('time duration for a user occupying a single time slot between two succesive transmissions is =',Tf+0.001,'msecs')

time duration of a bit Tb is = 3.69 microsecs
time duration of a time slot Tslot is = 577 microsecs
time duration of a frame Tf is = 4.616 msecs
time duration for a user occupying a single time slot between two succesive transmissions is = 4.616 msecs


## EXAMPLE 11.7 - PG NO.431¶

In [5]:
#page no.431
nuc1a=50.
ncrc=3.
nec1a=nuc1a+ncrc

nuc1b=132.
nt=4.
nec1b=nuc1b+nt

nc=nec1a+nec1b
FECr=1./2.
nce=nc*1./FECr

nc2=78.
net=nc2+nce

Dur=20.*10.**-3.#duration
Gcbr=net/Dur#Gross channel bit rate
print'%s %.1f %s' %('Gross channel bit rate is =',Gcbr*10**-3,'kbps')

Gross channel bit rate is = 22.8 kbps


## EXAMPLE 11.10 - PG NO.442¶

In [6]:
#page no. 442
BWupl=890.
BWupu=915.
BWdwl=935.
BWdwu=960.
if BWup==BWdw:
print'%s %d %s' %('in either case the maximum frequency hop or change from one frame to the next is =',BWup,'MHz')

else:
print'%s %d %s' %('in uplink case the maximum frequency hop or change from one frame to the next is =',BWup,'MHz')
print'%s %d %s' %('in downlink case the maximum frequency hop or change from one frame to the next is =',BWdw,' MHz')
#end

in either case the maximum frequency hop or change from one frame to the next is = 25 MHz