1. Fundamentals of Cellular and Wireless Networks
Lecture ID: ET-IDA-xxx
, v08
Prof. W. Adi
Tutorial-7
Common Mobile Modulation Techniques

2. } Carson´s rule Problem 1:
In US AMPS cellular system FM modulator the maximum deviation frequency fd=12 kHz and the
modulated signal bandwidth is fm=4kHz
Determine the modulation index
Determine the upper bound of the frequency bandwidth
For AMPS FM transmission, If SNRin= 10 dB, determine the SNRout of the FM detector.
Determine the possible number of duplex channels for a total of 20 MHz available RF bandwidth (Assume channel bandwidth from 2)
Compute the number of possible channels and SNRout if the modulation index is doubled.
Solution 1:
For FM Modulation: f =  f / fm
BT  2 (f + 1) fm = 2( f + fm) (upper bound)
BT  2  f (lower bound)
SNR factor = [SNR]out / [SNR]in  3 (f2 + f3)
f =  f / fm = 12 kHz/4 kHz = 3
2. BT  2 (f + 1) fm = 2 (3 + 1) 4 kHz = 32 kHz
[SNR]out  [SNR]in x 3 (f2 + f3) = 10 x 3 ( )= 1080 = dB
Number of channels / 2 x 32 kHz = 625 channels
BT  2 (f + 1) fm = 2 (2x3 + 1) 4 kHz = 56 kHz
frequency deviation is also doubled  f = f fm = (2x3) 4 = 24 kHz
Number of channels / 2 x 56 kHz = 178 channels
[SNR]out  [SNR]in x 3 (f2 + f3) = 10 x 3 ( )= 7560 = dB
} Carson´s rule

3. „Mobility“ and Doppler Shift
BST
Vr = v cos  vr 
 =90º ‘
fc-fd fc
fc+fd A v B ‘ v
Clasical Doppler Spectrum C
V‘r
Cos  =0 => vr=0
v . cos 
fd = f = 
Fading effects due to Doppler shift
If the modulated symbol time is Ts = 1/R
Where R is the symbol rate then:
Fast fading Ts > Tc
Channel changs during one symbole time
Slow fading Ts < Tc
Channel stable during one symbole time
Coherence time Tc due to Doppler shift is the time duration over which the channel response is essentially invariant
Tc  0.423/fd

4. Solution 2:  Problem 2: v . cos  f =
A Mobile station moving with a speed of 200 Km/h and transmitting a carrier signal of 990 MHz
Determine the maximum Doppler frequency shift fd
Determine the coherence time Tc
What is the minimum symbol rate at which the digital modulated signal needs no equalization (slow fading consideration).
At which speed would a symbole be seriously distorted if the modulator is working with a symbol rate of fs =500 symbols/sec
Solution 2:
1. Carrier wavelength  = c/f = m/s / 990 x 106 Hz = 0.3 m
maximum for cos =1 => fd = v /  = [ /3600] /0.3 = 185 Hz
Tc  / fd= 0.423/185 = 2.28 ms
If Ts < Tc then the channel is considerd flat within the symbole time
=> fs > 1/Tc = 1/ 2.28 x 10-3 = 437 symbole/Second
Distortion starts if fs = 1/Tc = 1/ (0.423/ fd) => fd = fs
substituting in maximum Doppler shift formula v = fd 
=> v = fs  = x 500 x 0.3 = m/sec = km / (1/3600) = km/hour
fc-fd fc
fc+fd
Clasical Doppler Spectrum
f =
v . cos  
Fading effects due to Doppler shift
Fast fading Ts > Tc
Channel changs during one symbole time
Slow fading Ts < Tc
Channel stable during one symbole time

5. Problem 3:
Using a digital PSK modulation technique with the following constellation diagram
1. Determine the voltage amplitude for the cosine wave modulation signal
2. Draw the following modulated bit stream
1 volt/division

6. Solution 3: -45o t wave form of cos t +2 A -45o - 2 A 2 45o 2 t
-45o
+45o
135o
225o
+45o
2.8 v +2
135o
+45o A
-45o
- 2
225o
1 volt/division
Voltage amplitude = A
A2=
=> A = 2.8 volt A 2
45o 2
0o o  o o -45o