Chapter 7: Line of Sight Propagation

Example 7.1, page 293

In [10]:
import math

#Initialisation
h=200                                #height in m
d=30*10**3                           #distance in km
R=40*10**-6                           #height in km


#Calculation
phi=math.atan(h*d**-1)               # in radian
phi1=phi*180/math.pi                 # in degree
n=math.cos(phi1)
r=round(n)/R                         #radius

#Results

print'Radius = %.1f km'%r

Radius = 25000.0 km

Example 7.2, page 294

In [8]:
import math

#Initialisation
h=500                                #height in m
a=0.000315
b=0.0001361
Re=6370000                           #radius of earth in m


#Calculation
n=1+(a*math.exp(-b*h))                
n1=(n-1)*10**6                         #Refraction index
c=(a*b*math.exp(-b*h))
R=1/c                                  #Radius of path curvature in km
d=1-(Re/R)
K=1/d                                  #K-factor

#Results
print'(1) Refraction index = %d '%n1
print'(2) Radius of path curvature = %d kM'%(R/10**3)
print'(3) K-factor = %.3f'%K 

(1) Refraction index = 294 
(2) Radius of path curvature = 24968 kM
(3) K-factor = 1.343

Example 7.3, page 299

In [50]:
import math

#Initialisation
k1=1.3                                 #K-factor
k2=0.7                                 #K-factor
H1=1200                                #sea level in m
H2=1400                                #sea level in m
re=6370*10**3                          #radius of earth in m
f=15*10**9                             #frequency in Hz
a1=0.6
d1=15*10**3                            #distance in m
d2=20*10**3                            #distance in m
c=3*10**8                              #speed of light
d=30*10**3                             #distance in m
h2=25.24       
r2=11.55
a2=0.3


#Calculation
h1=500*d1*d2/(k1*re)
h=c*f**-1
r1=math.sqrt((d1*d2*h)/d)
H11=H1+h1+a1*r1                      #in meter
H22=H2+h2+a2*r2                      #in meter

#Results
print'(1) H1 = %d m'%H11              #wrong calculation in textbook
print'(2) H2 = %d m'%H22

(1) H1 = 19322 m
(2) H2 = 1428 m

Example 7.4, page 302

In [3]:
import math

#Initialisation
hr=-1                       #obstacle height and fresnel radius ratio

#Calculation
Ad=-20*hr+10                 #Diffraction loss in dB
Ad2=16                       #from fig 7.8
Ad3=43

#Results
print'(1) Obstacle loss = %.1f dB'%Ad
print'(2) Knife edge obstacle = %.1f dB'%Ad2
print'(3) Rounded obstacle = %.1f dB'%Ad3

(1) Obstacle loss = 30.0 dB
(2) Knife edge obstacle = 16.0 dB
(3) Rounded obstacle = 43.0 dB

Example 7.5, page 306

In [55]:
import math

#Initialisation
d1=10                                               #distance in km
d2=25                                               #distance in km
re=6370                                            #earth radius in km               
k=0.5                                               #climatic factor
f=4*10**9                                           #frequency in Hz
c=3*10**8                                          #speed of light
d=35                                               #distance in km
h3=400                                             #height in m

#Calculation
ho=(500*d1*d2)/(k*re)                                #Earth buldge in m
h=c*f**-1                                             #wavelength in m
r1=math.sqrt(d1*10**3*d2*10**3*h*(d*10**3)**-1)       #fresnel radius
amsl=h3+ho+13.9                                       #AMSL

#Results
print'(1) Earth buldge = %.2f m'%ho
print'(2) Fresnel radius = %.1f m'%r1
print'(3) AMSL = %.1f m '%amsl

(1) Earth buldge = 39.25 m
(2) Fresnel radius = 23.1 m
(3) AMSL = 453.1 m

Example 7.6, page 309

In [6]:
import math

#Initialisation
pt=500                                        #Transmitter power in mW
gt=42                                         #transmitter antenna gain in dB
gr=44                                         #receiver antenna gain in dB
lbt=2.6                                       #transmitter branching loss in dB
lbr=3                                         #receiver branching loss in dB
flt=45                                        #transmitter feeder length
flr=35                                        #receiver feeder length
fls=6.5                                       #feeder loss
prx=-72                                       #Receiver sensitivity
d=30                                          #path distance in km
f=8.4                                         #frequency in ghz

#Calculation
ptx=10*math.log10(pt)                         #transmitter threshold level
lft=flt*fls/100
lfr=flr*fls/100
eirp=ptx+gt-lbt-lft                            #Transmitter effective power
sg=ptx-prx
fsl=92.4+20*math.log10(f)+20*math.log10(d)
rsl=ptx+gt+gr-fsl-lft-lfr-lbt-lbr
fm=rsl-prx

#Results
print'EIRP = %.2f dBm'%eirp
print'SG = %.2f dBm'%sg
print'FSL = %.2f dB'%fsl
print'RSL = %.2f dBm'%rsl
print'FM = %.2f dB'%fm

EIRP = 63.46 dBm
SG = 98.99 dBm
FSL = 140.43 dB
RSL = -38.24 dBm
FM = 33.76 dB

Example 7.7, page 315

In [24]:
import math

#Initialisation
f=15                                          #frequency in GHz
f1=18                                         #frequency in GHz
R=50                                          #rain intensity
ah=1.154
kh=0.0367
d=20                                          #distance in kM

#Calculation
yr=kh*R**ah
do=35*math.exp(-0.015*R)                       #distance in kM
de=d/(1+(d/do))                                #distance in kM
Ao=yr*de                                       #Rain Loss in dB
phi=(f**2)/(1+10**-4*f**2)
phi1=(f1**2)/(1+10**-4*f1**2)
H=1.12*10**-3*((phi1/phi)**0.5)*(phi*Ao)**0.55
Ah=Ao*(phi1/phi)**(1-H)
Av=(300*Ah)/(335+Ah)                           #Rain Loss in dB


#Results
print'(1) Rain Loss, A = %.2f dB'%Ao
print'(2) rain loss for vertical polarization, Av = %.2f dB'%Av

(1) Rain Loss, A = 30.34 dB
(2) rain loss for vertical polarization, Av = 32.53 dB

Example 7.8, page 322

In [26]:
import math

#Initialisation
A=99.8                                      #in percent
l=1250                                      #radio link in km
C=155*10**6                                 #in bps
T=24*60*60                                  #Total measurement time

#Calculation
U=100-A
u=U/100
ue=u*l/2500
uep=ue*0.3                              #propagation unavailability value
M=C*uep*T*10**-3                        #number of errored bits due to propagation

#Results
print'Maximum delay bit error per day = %d bits per day'%M

Maximum delay bit error per day = 4017600 bits per day

Example 7.9, page 324

In [39]:
import math

#Initialisation
h=24                                #hours
m=60                                #minutes
s=60                                #seconds


#Calculation
dm=0.004*h*m*(1250*2500**-1)          #Maximum degraded minutes
ses=0.00054*h*m*s*(1250*2500**-1)     #Severely errored seconds

#Results
print'(1) Maximum degraded minutes per day = %.2f min'%dm
print'(2) Severely errored seconds per day = %.2f s'%ses

(1) Maximum degraded minutes per day = 2.88 min
(2) Severely errored seconds per day = 23.33 s

Example 7.10, page 331

In [36]:
import math

#Initialisation
Aa=15                                    #Transmitter antenna discrimination
Ab=25                                    #Receiver antenna discrimination
AD=110                                  #path in km                     
s=35                                    #fading in dB

#Calculation
Ad=20*math.log10(AD*CD**-1)               #Distance discrimination
CD=30                                       #path in km 
si=Aa+Ab+Ad                                 #in dB
si2=si-s                                    #in dB

#Results
print'(1) S/I = %.1f dB'%si
print'(2) S/I = %.1f dB'%si2

(1) S/I = 51.3 dB
(2) S/I = 16.3 dB

Example 7.11, page 333

In [32]:
import math

#Initialisation
kq=2.6*10**-6                                 #geoclimatic coefficient
f=6                                           #frequency in GHz
d=45                                          #distance in Km
gc=0.098                                      #GC factor
ab=0.25                                       #geoclimatic factor

#Calculation
po=kq*f*gc*d**3                              #In country
po1=0.3*ab*(f*4**-1)*(d*50**-1)**3           #In mountainous area



#Results
print'Fading occurrence probability'
print'(1) In country = %.2f'%po
print'(2) In mountainous area = %.3f'%po1

Fading occurrence probability
(1) In country = 0.14
(2) In mountainous area = 0.082

Example 7.12, page 340

In [23]:
import math

#Initialisation
dn=70                                       #dN = 70
d1=1000                                     #height from sea level in m
d2=1400                                      #height from sea level in m
d=45                                         #radio link distance in km

#Calculation
K=10**(-4.2-0.0029*-dn)                      #Climate factor
ep=(d2-d1)/d                                 #magnitude of the path inclination
po=K*d**3*(1+ep)**(-1.2)*10**(0.033*6-1)      #Fading occurrence probability


#Results
print'(1) Climate factor K = %.4f = 10^-4'%K
print'(2) Fading occurrence probability Po = %.2f percent'%po

(1) Climate factor K = 0.0001 = 10^-4
(2) Fading occurrence probability Po = 0.10 percent

Example 7.13, page 342

In [13]:
import math

#Initialisation
fm=35                               #fade margin
po=0.092                            #fading occurrence probability

#Calculation
pw=po*10**(-fm*10**-1)               #deep fading occurrence 


#Results
print'Deep fading occurrence probability, Pw = %.1f x 10^-5'%(pw*10**5)

Deep fading occurrence probability, Pw = 2.9 x 10^-5

Example 7.14, page 343

In [51]:
import math

#Initialisation
d=20                                      #distance in kM
po=0.02                                   #fading occurrence probability at 20 Km
d1=25                                     #distance in kM
d2=40                                     #distance in kM
fm1=30                                    #link in kM
fm2=35                                   #link in kM
fm3=40                                    #link in kM
tr=30*24*60           


#Calculation
po1=po*(d1*d**-1)**3                   #fading occurrence probability at 25 Km
po2=po*(d2/d)**3                       #fading occurrence probability at 40 Km
pw=po*10**(-fm1*10**-1)                #fade margin at 30
pw1=po1*10**(-fm2*10**-1)             #fade margin at 35
pw2=po2*10**(-fm3/10)                  #fade margin at 40
u=pw+pw1+pw2                           #total fade margin
to=u*tr                                #network outage time

#Results
print'(1) Fading occurrence probability at 20 = %.2f'%po
print'    Fading occurrence probability at 25 = %.3f'%po1
print'    Fading occurrence probability at 40 = %.2f'%po2
print'(2) Fade margin at 30 = %.1f x 10^-5'%(pw*10**5)
print'    Fade margin at 35 = %.2f x 10^-5'%(pw1*10**5)
print'    Fade margin at 40 = %.2f x 10^-5'%(pw2*10**5)
print'    Total fade margin = %.2f x 10**-5'%(u*10**5)
print'(3) Network outage time , To = %.3f min per month'%(to)

(1) Fading occurrence probability at 20 = 0.02
    Fading occurrence probability at 25 = 0.039
    Fading occurrence probability at 40 = 0.16
(2) Fade margin at 30 = 2.0 x 10^-5
    Fade margin at 35 = 1.24 x 10^-5
    Fade margin at 40 = 1.60 x 10^-5
    Total fade margin = 4.84 x 10**-5
(3) Network outage time , To = 2.089 min per month

Example 7.15, page 344

In [10]:
import math

#Initialisation
ur=0.001                  #unavailability budget for hypothetical circuit
d=50                      #path-length in km
A=0.25                    #area conditions
B=1                       #area conditions
f=8                       #frequency in GHz


#Calculation
pw=ur*(d*(d*d)**-1)             #deep fading occurrence probability
po=6*10**-7*A*B*f*(d**3)        #fading occurrence probability of desirable link
FM=-math.log10(pw/po)*10        #fade margin

#Results
print'Fade margin = %.1f dB'%FM

Fade margin = 38.8 dB
In [ ]: