# CHAPTER 10-Wireless Communication Systems¶

## EXAMPLE 10.1- PG NO.351¶

In :
#page 351
BW=12.5*10.**3.
TDR1=512.#transmission data rate
SPef1=TDR1/BW#spectral efficiency

TDR2=1200.
SPef2=TDR2/BW

TDR3=2400.
SPef3=TDR3/BW
print'%s %.2f %s' %('the spectral efficiency at 512 bps transmission data rate =',SPef1,'bps/Hz')
print'%s %.3f %s' %('the spectral efficiency at 1200 bps transmission data rate =',SPef2,'bps/Hz')
print'%s %.3f %s' %('the spectral efficiency at 2400 bps transmission data rate =',SPef3,'bps/Hz')

the spectral efficiency at 512 bps transmission data rate = 0.04 bps/Hz
the spectral efficiency at 1200 bps transmission data rate = 0.096 bps/Hz
the spectral efficiency at 2400 bps transmission data rate = 0.192 bps/Hz


## EXAMPLE 10.2- PG NO.352¶

In :
#page no.352
TDR=1200.
T=60.
TN=TDR*T#total no. of bits in 60 sec
NP=576.#no. of bits in the preamble
NU=TN-NP#no. of usable bits

NS=32.
NA=32.
N16=16.*NA
N1B=NS+N16

NBPM=NU/N1B#no. of batches/min.
NPAPB=16.
NTPM=NBPM*NPAPB#no. of pages transmitted/min.
print'%s %d %s' %('no. of pages transmitted/min =',NTPM,'pages')

no. of pages transmitted/min = 2100 pages


## EXAMPLE 10.3- PG NO.353¶

In :
#page no.353
BW=25.*10.**3.#bandwidth of POCSAG=bandwidth of FLEX system

TDR1=1200.# transmission data rate
SPef1=TDR1/BW#spectral efficiency

TDR2=6400.
SPef2=TDR2/BW
print '%s %.3f %s' %('the spectral efficiency at 1200 bps transmission data rate in POCSAG paging system is =',SPef1,'bps/Hz')
print '%s %.3f %s' %('the spectral efficiency at 6400 bps transmission data rate in FLEX paging system is =',SPef2,'bps/Hz')

Cinc=TDR2/TDR1
print '%s %.1f %s' %('estimating increase in capacity is =',Cinc,'times')

the spectral efficiency at 1200 bps transmission data rate in POCSAG paging system is = 0.048 bps/Hz
the spectral efficiency at 6400 bps transmission data rate in FLEX paging system is = 0.256 bps/Hz
estimating increase in capacity is = 5.3 times


## EXAMPLE 10.6- PG NO.368¶

In :
#page no.368
Bt=12.5*10.**6.
Bg=10.*10.**3.
B2g=2.*Bg#Guard band on both the ends
ABW=Bt-B2g
Bc=30000.#channel bandwidth
N=ABW/Bc
print '%s %d %s' %('total no. of channels available in the system is =',N,'channels')

total no. of channels available in the system is = 416 channels


## EXAMPLE 10.8- PG NO.374¶

In :
#page no.374
ERPmax1dB=6.
ERPmax2dB=-2.
DiffdB=ERPmax1dB-ERPmax2dB
Diff=10.**(DiffdB/10.)
Rfree=5.*(Diff)**(1./2.)#free space-case(a)
Rtypc=5.*(Diff)**(1./4.)#signal attenuation is proportional to 4th power-case(b)
print '%s %.1f %s' %('maximum communication range in a free space propogation condition-case(a) is =',Rfree,'km')
print '%s %.1f %s' %('maximum communication range when signal attenuation is proportional to 4th power-case(b) is =',Rtypc,'km')

maximum communication range in a free space propogation condition-case(a) is = 12.6 km
maximum communication range when signal attenuation is proportional to 4th power-case(b) is = 7.9 km


## EXAMPLE 10.11- PG NO.381¶

In :
#page no. 381
import math
P4dBW=-34.
PdBm4=P4dBW-30.
PW4=10.**((PdBm4/10.))
print '%s %d %s %s' %('minimum power level of class IV phone is =',round(PW4*10**7),'*10**(-7)','mW')

ERP1dBW=6.
PdBm1=ERP1dBW-30.
PW1=10.**((PdBm1/10.))

print '%s %d %s %s' %('ERP of class I phone is =',round(PW1*10**3),'*10**(-3)','mW')
R=PW1/PW4
RdB=10.*math.log10(R)

print '%s %d %s %d' %('minimum power level for a Class I phone is greater than\nminimum power level of Class IV mobile phone by a factor of',RdB,'dB or',R)

minimum power level of class IV phone is = 4 *10**(-7) mW
ERP of class I phone is = 4 *10**(-3) mW
minimum power level for a Class I phone is greater than
minimum power level of Class IV mobile phone by a factor of 40 dB or 10000


## EXAMPLE 10.12- PG NO.384¶

In :
#page no.384
spfl=810*10**6
spfu=826*10**6
sprl=940*10**6
spru=956*10**6
BWf=spfu-spfl
BWr=spru-sprl

BWc=10./100.*BWf#BWf=BWr(universal standard)
BWv=BWf-BWc
nsc=1150.
BWmax=BWv/nsc
SPef=1.68
CDRmax=BWmax*SPef
FECcr=0.5
DRnmax=FECcr*CDRmax
print '%s %.1f %s' %('there is a speech coder with a max. data rate of is =',DRnmax*10**(-3),'Kbps')

there is a speech coder with a max. data rate of is = 10.5 Kbps


## EXAMPLE 10.13- PG NO.388¶

In :
#page no.388
d=40.*10.**0.
npf=6.
dts=d/npf#duration of a time slot of a voice frame
nbv=1944.
nbpts=nbv/npf#no. of bits per time slot
db=d/nbv#duration of a bit in secs
npg=6.
tg=db*npg#guard time in secs
c=3.*10.**8.
Disrt=c*tg
Dismx=Disrt/2.#max. distance
print '%s %.3f %s' %('duration of a time slot of a voice frame is =',dts,'msecs')
print '%s %d %s' %('no. of bits per time slot is =',nbpts,'bits')
print '%s %.2f %s' %('duration of a bit is',db*1000,'microsecs')
print '%s %d %s' %('guard time is =',tg*1000,'microsecs')
print '%s %.2f %s' %('maximum distance between a cell site and a mobile is =',Dismx/1000000.,'kilometres')

duration of a time slot of a voice frame is = 6.667 msecs
no. of bits per time slot is = 324 bits
duration of a bit is 20.58 microsecs
guard time is = 123 microsecs
maximum distance between a cell site and a mobile is = 18.52 kilometres


## EXAMPLE 10.14- PG NO.389¶

In :
#page no.389
dv=40.*10.**-3.
nps=1./dv
nbpv=1944.
TGrbr=nbpv*25.
TGrbaur=TGrbr/2.#2 bits/symbol for pi/4 qpsk mod
CBW=30.*10.**3.
BWef=TGrbr/CBW
print '%s %.1f %s' %('total gross bit rate for the RF signal is=',TGrbr/1000,'Kbps')
print '%s %.1f %s' %('total gross baud rate for the RF signal is =',TGrbaur/1000,'Kbps')
print '%s %.1f %s' %('bandwidth efficiency is =',BWef,'bps/Hz')

total gross bit rate for the RF signal is= 48.6 Kbps
total gross baud rate for the RF signal is = 24.3 Kbps
bandwidth efficiency is = 1.6 bps/Hz


## EXAMPLE 10.15- PG NO.391¶

In :
#PAGE NO. 391
Bt=12.5*10**6
Bc=30.*10.**3.
K=7#frequency reuse factor
N=Bt/Bc#total no. of available channels
M=N*(1./K)#user capacity per cell

Nu=3#no. of users/channel
NU=N*Nu
K1=4
M1=NU*(1./K1)

print '%s %d %s' %('capacity of 1G AMPS FDMA analog cellular system is =',round(M),'users per cell')
print '%s %d %s' %('capacity of 2G IS-136 TDMA digital cellular system is =',M1,'users per cell')

capacity of 1G AMPS FDMA analog cellular system is = 60 users per cell
capacity of 2G IS-136 TDMA digital cellular system is = 312 users per cell