Chapter 14: Satellite Access

Example 14.1, Page 381

In [1]:
import math
#Variable Declaration

Btr=36  #Transponder Bandwidth(MHz)
B=3    #Carrier Bandwidth(MHz)
EIRP=27  #saturated EIRP(dBW)
BO=6   #Back off loss(dB)
LOSSES=196  #Combined losses(dB)
GTR=30   #Earth station G/T ratio(dB)
k=228.6  #Value of k(dB)
#Calculation

Btr1=10*math.log10(Btr*10**6)  #Converting transponder Bandwidth into decibels
B1=10*math.log10(B*10**6)  #Converting carrier Bandwidth into decibels

CNR=EIRP+GTR-LOSSES+k-Btr1 #Carrier to noise ratio for single carrier operation(dB)
CNR=round(CNR)
alpha=-BO
K=alpha+Btr1-B1  #Fraction of Bandwidth actually occupied(dB)
K=10**(K/10)  #Converting decibels to ratio
K=round(K)

#Results

print "The downlink carrier to noise ratio is",CNR,"dB"
print "Fraction of Bandwidth actually occupied is",K
print "No. of carriers that would be accommodated without backoff is",Btr/B

The downlink carrier to noise ratio is 14.0 dB
Fraction of Bandwidth actually occupied is 3.0
No. of carriers that would be accommodated without backoff is 12

Example 14.2, Page 396

In [2]:
import math

#Variable decalration

N=40     #No.of bits
E=5      #Maximum number of errors allowed
p=10**-3 #Average probability of error in transmission

#Calculation

Pmiss=0
for i in range(E+1,N):
  Pmiss=Pmiss+(math.factorial(N)/float((math.factorial(i)*math.factorial(N-i))))*(p**i)*((1-p)**(N-i))

Pmiss=Pmiss*10**12
Pmiss=round(Pmiss,1)

#Result

print "The probability of miss is",Pmiss,"*10^-12"

The probability of miss is 3.7 *10^-12

Example 14.3, Page 397

In [3]:
import math

#Variable decalration

N=40     #No.of bits
E=5      #Maximum number of errors allowed

#Calculation

Pfalse=0
for i in range(0,E+1):
  Pfalse=Pfalse+(math.factorial(N)*2**-N)/float((math.factorial(i)*math.factorial(N-i)))



Pfalse=Pfalse*10**7
Pfalse=round(Pfalse,1)

#Result

print "The probability of miss is",Pfalse,"*10^-7"

The probability of miss is 6.9 *10^-7

Example 14.4, Page 399

In [4]:
#Variable ecalration
Lf=120832     #Total frame length
Tb=14         #Traffic burts per frame
Rb=2          #Reference bursts per frame
T=103         #Guard interval(symbols)
P=280         #Preamble Symbols
R=P+8         #Reference channel symbols with addition of CDC
#Calculation

OH=2*(T+R)+Tb*(T+P)   #Overhead Symbols

nF=1-(OH/float(Lf))   #Frame Efficiency
nF=round(nF,3)

#Result

print "Hence the frame efficiency of INTELSAT frame is",nF

Hence the frame efficiency of INTELSAT frame is 0.949

Example 14.5, Page 400

In [5]:
#Variable Declaration

Lf=120832   #Number of symbols per frame
Tf=2        #Frame period(ms)
nF=0.949    #INTELSAT fram efficiency from Example 14.4
#Calculation

Rs=(Lf/float(Tf))*10**-3  #Symbol rate(megasymbol/s)
Rt=Rs*2     #Transmission Rate
n=nF*Rt*10**3/64   #Voice channel capacity
n=round(n)
#Result

print " The voice channel capacity for the INTELSAT frame is",n,"Channels"

 The voice channel capacity for the INTELSAT frame is 1792.0 Channels

Example 14.6, Page 408

In [6]:
#Variable Declaration

CNR=87.3   #Downlink Carrier to noise ratio(dBHz)
BER=10**-5  #Bit Error Rate Required
R=0.2   #Roll off factor
EbN0R=9.5   #Eb/N0 ratio(dB)

#Calculation
Rb=CNR-EbN0R  #Maximum Transmission Rate(dBb/s)
Rb1=10**(Rb/10) #Maximum Transmission Rate(b/s)
BIF=Rb1*1.2*10**-6/2  #IF Bandwith required
BIF=round(BIF,2)
#Result

print "The Maximum Transmission rate is",Rb,"dBb/s"
print "The IF bandwidth required is",BIF,"MHz"

The Maximum Transmission rate is 77.8 dBb/s
The IF bandwidth required is 36.15 MHz

Example 14.7, Page 410

In [7]:
#Variable Declaration

T1=1.544  #Bit rate from sec.10.4(Mb/s)
R=62     #Bit rate from sec.10.4(dBMb/s)
EbN0R=12 #Required Eb/N0 ratio for uplink(dB)
LOSSES=212 #Transmission losses of uplink(dB)
GTR=10   #G/T ratio for earth station(dB/K)
G1=46   #Uplink antenna gain(dB)
Rd=74   #Downlink Transmission Rate(dBb/s)
#Calculation
CNR=EbN0R+R  #Carrier to noise ratio for uplink(dB)
EIRP=CNR-GTR+LOSSES-228.6 #EIRP of earth station antenna
P=EIRP-G1   #Transmitted Power Required(dBW)
P=10**(P/float(10))   #Transmitted Power Required(Watts)
P=round(P,2)

Ri=Rd-R   #Rate increase with TDMA operation(dB)
P1=1.4+Ri  #Uplink power increase required for TDMA operation(Watts)
P2=10**(P1/float(10))
P2=round(P2,1)
#Results

print "Earth station transmission power required for transmission of T1 baseband signal is",P,"Watts"

print "Uplink power increase required for TDMA operation is",P1,"dBWatts or",P2,"Watts"

Earth station transmission power required for transmission of T1 baseband signal is 1.38 Watts
Uplink power increase required for TDMA operation is 13.4 dBWatts or 21.9 Watts

Example 14.8, Page 429

In [8]:
import math
#Variable Declaration

BIF=36   #Bandwidth of channel over which carriers are spread(MHz)
R=0.4  #Rolloff factor for filtering
Rb=64   #Information bit rate(kb/s)
BER=10**-5  #Bit error rate required
EbN0R=9.6 #Eb/N0 ratio for BER given from Fig.10.18

#Calculation

Rch=BIF*10**6/(1+R) #Rate of unspreaded signal(chips/s)
Gp=Rch/(Rb*10**3)     #Processing gain
Gp1=round(10*math.log10(Gp))  #Processing gain(dB)
EbN0R1=10**(EbN0R/float(10))  #Converting Eb/N0 into ratio
K=1+(1.4*Gp/EbN0R1)  #Number of channels
K=math.floor(K)

#Result
print "The Processing Gain is",Gp1,"dB"
print "An estimate of maximum number of channels that can access the system is",K

The Processing Gain is 26.0 dB
An estimate of maximum number of channels that can access the system is 62.0