# Chapter 6: Terrestrial Mobile Radio Propagation¶

## Example 6.1, page 186¶

In [11]:
import math

#Initialisation
c=3*10**8                                   #speed of light
f=400*10**6                                 #frequency in Hz
l1=15*10**3                                 #distance in m
l2=15*10**3                                #distance in m
l=30*10**3                                 #distance in m
k=1.33                                     #k factor
d1=15                                      #distance in Km
d2=15                                      #distance in Km
re=6370                                    #distance in Km

#Calculation
h=c*f**-1                                  #wavelength in m
ho=(500*d1*d2)/(k*re)                      #Earth bulge

#Results
print'(1) Fresnel radius, r1 = %d m'%r1
print'(2) h0 = %.2f m'%ho

(1) Fresnel radius, r1 = 75 m
(2) h0 = 13.28 m


## Example 6.2, page 223¶

In [103]:
import math

#Initialisation
f=400                                       #frequency in MHz
k=1.33                                       #k factor
er=3                                         #dielectric conductivity
sg=10**-4                                    #Earth effective conductivity
eo=8.85*10**-12                              #permittivity of free space
re1=8500                                     #Effective Earth radius in Km
c=3*10**8                                    #speed of light
B=1
d=50

#Calculation
kh=1.6*10**-3                               #horizontal polarization using Fig. 6.2
kv=5*10**-3                                 #vertical polarization using Fig. 6.2
X=2.2*B*f**(1*3**-1)*re1**(-2*3**-1)*d      #normalized length of the path
FX=11+10*math.log10(X)-17.6*X               #distance attenuation value

#Results
print'(1) Kh = %.1f x 10**-3'%(kh*10**3)
print'    Kv = %.1f x 10**-3'%(kv*10**3)
print'(2) F(X) = %.2f dB'%FX

(1) Kh = 1.6 x 10**-3
Kv = 5.0 x 10**-3
(2) F(X) = -20.36 dB


## Example 6.3, page 228¶

In [17]:
import math

#Initialisation
f=300*10**6                              #frequency in Hz
l1=4*10**3                               #distance in m
l2=6*10**3                               #distance in m
h1=20                                    #height in m
c=3*10**8                                #speed of light
d1=4                                     #distance in km
d2=6                                     #distance in km
m=0.13
n=1.99

#Calculation
h=c*f**-1                                 #wavelength
l=l1+l2
r1=math.sqrt(l1*l2*h/l)
rat=h1/r1                                 #ratio
a=math.sqrt((2*(d1+d2))/(h*d1*d2))
v=0.0316*h1*a
jv=6.9+20*math.log10(1.585)              #knife-edge obstacle loss
k=8.2+12*n
Tmn=k*m
A=jv+Tmn                                 #rounded obstacle loss

#Results
print'(1) Ratio = %f'%rat
print'(2) Loss J(v) = %.1f dB'%jv
print'(3) Loss A = %.2f dB'%A

(1) Ratio = 0.408248
(2) Loss J(v) = 10.9 dB
(3) Loss A = 15.07 dB


## Example 6.4, page 233¶

In [115]:
import math

#Initialisation
f=150*10**6                             #frequency in Hz
c1=3*10**8                              #speed of light
h11=60                                  #in metre
d11=2000                                  #in metre
d1=259.6                                  #in metre
b=2000                                  #in metre
a=250                                  #in metre
h21=80                                  #in metre
d21=7259                                  #in metre
c=7250                                  #in metre

#Calculation
h=c1*f**-1                                                #wavelength
v1=h11*math.sqrt((2*(h*d1)**-1)+(1*d11**-1))
L1=6.9+20*math.log10(math.sqrt((v1-0.1)**2+1)+v1-0.1)     #path diffraction loss
v2=h21*math.sqrt((2*(h*d11)**-1)+(1*d21**-1))
L2=6.9+20*math.log10(math.sqrt((v2-0.1)**2+1)+v2-0.1)     #path diffraction loss

#Results
print'Diffraction loss L1 = %.2f dB'%L1
print'                 L2 = %.2f dB'%L2

Diffraction loss L1 = 24.79 dB
L2 = 19.12 dB


## Example 6.5, page 239¶

In [19]:
import math

#Initialisation
f=450*10**6                                 #frequency in Hz
q1=1.282                                    #cumulative distribution value
q2=1.645                                    #cumulative distribution value

#Calculation
sg=3.8+1.6*math.log10(450)                  #standard deviation
fm=fm2-fm1                                 #gain
#Results
print'Antenna gain = %.2f dB'%fm

Antenna gain = 2.92 dB


## Example 6.6, page 240¶

In [24]:
import math

#Initialisation
q90=1.282                              #cumulative distribution value of 90%
sl=8                                   #standard deviation
q97=1.881                              #cumulative distribution value of 97%
pt=5                                   #transmitter power

#Calculation
p=fm1-fm                               #power in dB
p1=pt*10**(p/10)                       #power in watt

#Results
print'(2) New transmitter power = %d W'%p1

(1) Fade margin for received signal = 10.256 dB
(2) New transmitter power = 15 W


## Example 6.7, page 241¶

In [25]:
import math

#Initialisation
d= 50*10**3                                       #distance in m

#Calculation
sl1=5.3                                           #location standard deviation
st1=3                                             #time standard deviation
sl2=6.2                                           #location standard deviation
st2=2                                             #time standard deviation
sv=math.sqrt(sl1**2+st1**2)                      #total standard deviation of VHF
su=math.sqrt(sl2**2+st2**2)                      #total standard deviation of UHF

#Results
print'(1)for VHF, sigmaL = %.1f dB '%sl1
print'            sigmaT = %.1f dB '%st1
print'   for UHF, sigmaL = %.1f dB '%sl2
print'            sigmaT = %.1f dB '%st2
print'(3) Standard deviation values, sigmaVHF = %.1f dB'%sv
print'                               sigmaUHF = %.1f dB'%su

(1)for VHF, sigmaL = 5.3 dB
sigmaT = 3.0 dB
for UHF, sigmaL = 6.2 dB
sigmaT = 2.0 dB
(3) Standard deviation values, sigmaVHF = 6.1 dB
sigmaUHF = 6.5 dB


## Example 6.9, page 245¶

In [27]:
import math

#Initialisation
d=5                                       #in dB
h=20                                      #Transmitter initial height

#Calculation
ht=h*10**(0.25)                           #Transmitter ultimate antenna height

#Results
print'(1) Antenna Height = %.2f m'%round(ht)

(1) Antenna Height = 36.00 m


## Example 6.10, page 246¶

In [28]:
import math

#Initialisation
f=1800*10**6                                 #frequency in Hz
c=3*10**8                                    #speed of light

#Calculation
h=c*f**-1                                  #wavelength
hv=20*h                                    #in metre
dh=10*h                                    #in metre

#Results
print'hv = %.2f m '%hv
print'dh = %.2f m '%dh

hv = 3.33 m
dh = 1.67 m


## Example 6.11, page 262¶

In [44]:
import math

#Initialisation
p1=20                                    #transmitter power
g=6                                       #gain
h1=20                                    #height in metre

#Calculation
ct=p1/10                                  #Power gain
ch=(h1*30**-1)**2                         #height gain
cg=g*4**-1                                #antenna gain
co=10*math.log10(ct*ch*cg)                #Total effects

#Results
print'(1) Power gain, Ct = %.f'%ct
print'    Height gain = %.2f'%ch
print'    Antenna gain = %.1f'%cg
print'(2) Total effects = %.2f dB'%co

(1) Power gain, Ct = 2
Height gain = 0.44
Antenna gain = 1.5
(2) Total effects = 1.25 dB


## Example 6.12, page 262¶

In [52]:
import math

#Initialisation
g1=10                                    #transmitter gain
ct=15                                    #power in watt

#Calculation
g2=g1-2.2                                #gain in dBd
cg=g2-6                                  #Antenna gain
ct1=ct*10**-1
ct2=10*math.log10(ct1)                   #Power gain
ch=(ct*30**-1)**2
ch1=10*math.log10(ch)                     #Height gain
ct3=ct1*0.5
ct4=10*math.log10(ct3)
co=ct4+cg+ch1                              #Total effects

#Results
print'(1) Power gain, Ct = %.2f'%ct2
print'    Height gain = %.2f'%ch1
print'    Antenna gain = %.1f'%cg
print'(2) Total effects = %.2f dB'%co

(1) Power gain, Ct = 1.76
Height gain = -6.02
Antenna gain = 1.8
(2) Total effects = -5.47 dB


## Example 6.13, page 265¶

In [59]:
import math

#Initialisation
cl=6                                            #Coupler loss
dl=1                                            #Duplexer Loss
bf=6.5                                          #BTS feeder loss
ba=12                                           #BTS antenna gain
pl=138                                          #Path loss
pg=15                                          #Pathlength in km
ta=2                                           #Terminal antenna gain
tf=0.5                                          #Terminal feeder loss

#Calculation
ptb=prm+cl+dl+bf-ba+pl-ta+tf                    #BTS transmitter power in dbBm
pw=10**((ptb-30)/10)

#Results
print'BTS transmitter power = %.2f dBm'%ptb
print'                      = %d W'%pw

BTS transmitter power = 40.00 dBm
= 10 W


## Example 6.14, page 265¶

In [4]:
import math

#Initialisation
pm=2                                    #transmitter power
ld=1                                    #Duplexer losses
lp=138                                  #Path loss
lfm=0.5                                 #terminal feeder losses
lfb=6.5                                 #transmitter feeder losses
gt=12                                   #BTS transmitter antenna gain
i=3

#Calculation
ptm=10*math.log10(pm*10**3)
prb=ptm-ld-lp-lfm-lfb+gt+gr

#Results
print'BTS received power = %.1f dBm'%pr

BTS received power = -96.0 dBm


## Example 6.15, page 265¶

In [61]:
import math

#Initialisation
t1=25                                 #terminal transmitter power
t2=2                                  #terminal transmitter power
gd=3                                  #correction factor of receiver antennas
lc=5                                  #coupler loss

#Calculation
ptb=10*math.log10(t1*10**3)
ptm=10*math.log10(t2*10**3)
tg=gd+ga+lc                            #total gain on the uplink

#Results
print'Transmitting gain in downlink = %.1f dBm'%p
print'Receiving gain in uplink = %.1f dBm'%ga
print'total gain on the uplink = %.1f dBm'%tg

Transmitting gain in downlink = 11.0 dBm
Receiving gain in uplink = 5.0 dBm
total gain on the uplink = 13.0 dBm


## Example 6.16, page 269¶

In [62]:
import math

#Initialisation
f=450                                                     #frequency in MHz
d=25                                                      #distance in m
hb=30
hm=5

#Calculation
fsl=32.4+(20*math.log10(f))+(20*math.log10(d))           #free space loss
lp=120+(40*math.log10(d))-(20*math.log10(hb))-(20*math.log10(hm))    #path loss
lm=76.3-10*math.log10(hm)
l=(40*math.log10(25))+(20*math.log10(f))-(20*math.log10(hb))+lm   #path loss based on the clutter factor model

#Results
print'(1) Free space loss = %.1f dB'%fsl
print'(2) Loss = %.1f dB'%lp
print'(3) Loss based on clutter factor = %.1f dB'%l

(1) Free space loss = 113.4 dB
(2) Loss = 132.4 dB
(3) Loss based on clutter factor = 148.7 dB


## Example 6.17, page 271¶

In [63]:
import math

#Initialisation
pt=30                                      #transmitter power in watt
d=15                                      #distance in km
gt=3                                       #transmitter gain
ht=30                                       #transmitter height in m
no=3.77*10**14

#Calculation
gt1=10**(gt*10**-1)
pt1=gt1*pt
e=88*math.sqrt(pt1)*pt*hr/(2*d**2)           #Field strength
pr1=(e**2)/(2*no)                            #Recieved power

#Results
print'Field strength = %f V/m'%e
print'Recieved power = %.2f pW'%(pr1*10**12)

Field strength = 181.556596 V/m
Recieved power = 43.72 pW


## Example 6.18, page 274¶

In [76]:
import math

#Initialisation
f=420                                         #frequency in Hz
h1=40                                         #height in m
h2=5                                         #height in m
d=15                                         #distance in km

#Calculation
A=69.55+26.16*math.log10(f)-13.82*math.log10(h1)        #Hata parameters
B=44.9-6.55*math.log10(h1)
C=2*(math.log10(f*28**-1))**2+5.4
D=4.78*(math.log10(420))**2-18.33*math.log10(f)+40.94
E1=3.2*(math.log10(11.75*h2))**2-4.97
E2=(((1.1*math.log10(f))-0.7)*h2)-((1.56*math.log10(f))-0.8)
L3=A+B*math.log10(d)-D                                  #in open area;
L2=A+B*math.log10(d)-C                                 #in suburban area;
L1=A+B*math.log10(d)-E1                                 #in large cities;
L11=A+B*math.log10(d)-E2                                #in small cities;

#Results
print'In large cities L1 = %.2f dB'%L1
print'In small cities L1 = %.2f dB'%L11
print'In suburban area L2 = %.2f dB'%L2
print'In open area L2 = %.2f dB'%L3

In large cities L1 = 151.45 dB
In small cities L1 = 148.86 dB
In suburban area L2 = 148.33 dB
In open area L2 = 130.75 dB


## Example 6.19, page 275¶

In [79]:
import math

#Initialisation
f=1800                                                     #frequency in MHz
d=10                                                      #distance in m
hb=40
hm=3
A=132.57                                                 #Hata model data
B=34.4                                                  #Hata model data

#Calculation
E2=(((1.1*math.log10(f))-0.7)*hm)-((1.56*math.log10(f))-0.8)
lp=46.3+33.9*math.log10(f)-13.82*math.log10(hb)+(44.9-6.55*math.log10(hb)-E2+hm)
L=A+B+-E2

#Results
print'Path loss based on COSTâ€“Hata model,'
print'         Lp = %.2f dB'%lp
print'Path loss based on Hata model,'
print'         Lp = %.2f dB'%L

Path loss based on COSTâ€“Hata model,
Lp = 167.56 dB
Path loss based on Hata model,
Lp = 162.61 dB


## Example 6.20, page 277¶

In [93]:
import math

#Initialisation
pt=20                           #transmitter power in watt
Hb=30                           #in metre
Hm=3                           #in metre
gt=14.2                          #trasmitter gain in dB
f=450                             #frequency in MHz
gm=-2                            #in dBd
gr2=-2.2                         #in dBi
r1=10
n=20
hb=10
hm=10

#Calculation
gt1=gt+gr2
pr1=-62-38*math.log10(r1)-20*math.log10(f*900**-1)+7          #received signal level in suburban
pr2=-64-43*math.log10(r1)-20*math.log10(f*900**-1)+7          #received signal level in urban
ao=10*math.log10(2)+(gr2-6)                                   #in dB (wrong value calculated in textbook)
pr11=-62-38*math.log10(r1)-20*math.log10(f*900**-1)+ao        #received signal level in rural
pr22=-64-43*math.log10(r1)-20*math.log10(f*900**-1)+ao        #received signal level in cities
ptd=10*math.log10(pt*10**3)                                   #in dBm
lp1=ptd-pr11                                                  #Path loss in rural area
lp2=ptd-pr22                                                  #Path loss in cities area

#Results
print'(2) In the suburban area, Pr = %.1f dBm'%pr1
print'    In the urban area, Pr = %.1f dBm'%pr2
print'(3) Path loss in rural area Lp = %.1f dB'%lp1           #(wrong value calculated in textbook)
print'    Path loss in cities area Lp = %.1f dB'%lp2          #(wrong value calculated in textbook)

(2) In the suburban area, Pr = -87.0 dBm
In the urban area, Pr = -94.0 dBm
(3) Path loss in rural area Lp = 142.2 dB
Path loss in cities area Lp = 149.2 dB