1. Modulation Techniques
Dr. J. Martin Leo Manickam
Professor

2. Challenges in Mobile Communication
Channel
fading
Energy
Bandwidth

3. Digital Modulation Digital signal is converted into analog bit stream
Type
Constant
variable
ASK
a(t)
FSK
PSK
QAM

4. Classification Linear modulation
Non linear (constant envelope) modulation
Amplitude of the transmitted signal varies linearly with message signal
Bandwidth efficient
QPSK, OQPSK
Amplitude of the transmitted signal does not vary with the amplitude of the message signal
Power efficient class C amplifiers can be used
Low out of band radiation
Limiter-discriminator can be used for demodulation
FSK,MSK, GMSK

5. BPSK
BPSK is equivalent to a DSB/SC

6. Binary PSK

7. PSD of a BPSK signal

8. Null-to-null bandwidth
Observation
Pulse shape
Null-to-null bandwidth
90 percent
energy
Rectangular
2Rb
1.6Rb
Raised cosine pulse (0.5)
< 2Rb
1.5Rb

9. QPSK

10. PSD of QPSK signal

11. Constant Envelope modulation

12. Binary FSK

13. Minimum Shift Keying (MSK)
Phase information is used to improve the noise performance of the receiver
CPFSK signal (0≤t ≤Tb)
Eb – transmitted signal energy
Tb – Bit duration
Θ(0) – value of the phase at t=0, sums up the past history of the modulation process upto t=0.

14. DPSK signal can also be represented as

15. Phase tree
At time t =Tb,

16. Phase trellis (h=1/2)

17. Signal space diagram Quadrature component will be half cycle sine wave
In-phase component will be half cycle cosine wave
+ sign corresponds to
- sign corresponds to
+ sign corresponds to
- sign corresponds to

18. As and can each assume two possible values, any one of four possible values can arise
Orthonormal basis functions
symbol 1

19. The MSK signal can represented by
Where s1 and s2 are related to the phase states
and , respectively.
Evaluating s1 and s2:

20. Signal space of MSK is two dimensional with four message points
Observation
Both integrals are evaluated for a time interval equal to twice the bit duration
Both lower and upper limits of the product integration used to evaluate s1 are shifted by Tb w.r.t those used to evaluate the s2.
The time interval , for which the phase states and are defined are common to both intervals
Signal space of MSK is two dimensional with four message points

21. Signal space characterization of MSK
Transmitted binary symbol
Phase states
(radians)
Coordinates of message points s1 s2 1

23. Optimum detection of
If x1 > 0, receiver choose the estimate
If x1 < 0, receiver choose the estimate
if x2 > 0, receiver choose the estimate
If x2 < 0, receiver choose the estimate

24. Estimates Symbol – 0 Symbol – 1 Probability of error
Same as that of the BPSK and QPSK

26. PSD of MSK MSK has lower sidelobes than QPSK and OQPSK Faster roll off
Less spectrally efficient
Main lobe of MSK is wider
Bandlimiting is easier
Continuous phase
Amplified using non linear amplifiers
Constant phase
Simple modulation and demodulation

27. GMSK modulation Sidelobe levels of the spectrum are further reduced
Pulse shaping filter requirements
Narrow bandwidth
Sharp cutoff frequencies
Low overshoot
Carrier phase must be ±π/2 at odd multiples and two values 0 and π at even multiples
Gaussian LPF
FM Transmitter
NRZ data
GMSK output

28. Impulse response
Transfer function
parameter related to B, the 3dB baseband bandwidth by
GMSK filter may be completely specified by B and the basedand symbol duration T

29. PSD of a GMSK signal When BT = ∞, GMSK is equivalent to MSK
When BT decreases, sidelobe levels falls off rapidly
At BT = 0.5, peak of the sidelobe level is 30 db and 20 db below the main lobe for GMSK and MSK
Reducing BT increases the error rate produced by the LPF due to ISI

31. Table 6.3 Occupied RF bandwidth (for GMSK and MSK as a fraction of Rb). Containing the given percentage of power BT
90%
99%
99.9%
99.99%
0.2 GMSK
0.52
0.79
0.99
1.22
0.25GMSK
0.57
0.86
1.09
1.37
0.5 GMSK
0.69
1.04
1.33
2.08
MSK
0.78
1.20
2.76
6.00
GMSK is spectrally tighter than MSK
GMSK spectrum is compact at smaller values of BT but degradation due to ISI increases.

32. GMSK Bit error rate
is a constant related to BT by

33. GMSK Receiver (Fig. 6.43)

34. Combined Linear and Constant Envelope Modulation Techniques
Varying envelope and phase (or frequency) of an RF carrier (M-ary modulation)
Two or more bits are grouped together to form symbols and one of M possible symbols are is transmitted during each symbol period
Bandwidth efficient
Power inefficient
Poor error performance (closely located message points

35. M - ary Phase Shift Keying (MPSK)
Carrier phase takes on one of M possible values
Where Es is the energy per symbol = (log2M)Eb
Ts is the symbol period = (log2M)Tb
In quadrature form
Orthonormal basis function:

36. M – ary PSK can be expressed as
Signal space is 2D and the M-ary message points are equally spaced on a circle of radius at the origin
Distance between the adjacent
symbols is equal to
Average symbol error prob.
Q function defined as
8 - PSK

37. Bandwidth and power efficiency of M-ary PSK signals2 4 8 16 32 64
0.5 1
1.5
2.5 3
Eb / No for
BER = 10-6
10.5 14
18.5
23.4
28.5
B: First null bandwidth of M-ary PSK signals

38. M-ary PSK PSD, for M = 8,16 (PSD for both rectangular and RCF pulses for fixed Rb
When M increases (fixed Rb)
First null bandwidth decreases
Bandwidth efficiency increases
Constellation is densely packed
Power efficiency decreases
More sensitive to the timing jitter

39. M-ary Quadrature amplitude modulation (QAM)
Amplitude and phase of the transmitted signal are varied
Where Emin - energy of the signal with the lowest amplitude and ai and bi are a pair of independent integers chosen according to the location of the particular point
No constant energy per symbol
No constant distance between possible symbol states
Si(t) is detected with higher probability than others

40. Ortho normal basis functions
Coordinates of ith message point:
Where is an element of L by L matrix given by
Where

41. Constellation Diagram for 16-QAM:
LXL matrix is given by
Probability of Error:

42. Bandwidth and Power efficiency of QAM4 16 64
256
1024
4096 1 2 3 5 6
Eb / No for
BER = 10-6
10.5 15
18.5 24 28
33.5
Power spectrum and bandwidth efficiency of QAM is identical to M-ary PSK
Power efficiency is superior than M-ary PSK

43. M-ary Frequency Shift Keying (MFSK)
Transmitted signal
Where for some fixed integer nc
Transmitted signals Si(t) themselves can be used as a complete ortho normal basis functions
M-dimensional signal space, minimum distance is

44. Average probability of symbol error:
Coherent detection:
Non coherent detection:
Channel Bandwidth:
Coherent MFSK:
Non Coherent MFSK:

45. Bandwidth and Power Efficiency of Coherent MFSK2 4 8 16 32 64
0.4
0.57
0.55
0.42
0.29
0.18
Eb / No for
BER = 10-6
13.5
10.8
9.3
8.2
7.5
6.9
Can be amplified by using non-linear amplifiers with no performance degradation
When M increases,
bandwidth efficiency decreases
Power efficiency increases

46. Performance of Digital modulation in Slow Flat-fading channels
Multiplicative gain variation
Received signal can be expressed as
- channel gain
- phase shift of the channel
n(t) - is the additive gaussian noise
Assumptions
Attenuation and phase shift remains constant

47. Probability of Error in slow flat-fading channel
Choose the possible range for signal strength due to fading
Average the probability of error of the particular modulation in AWGN channel over possible range of signal strength
- Probability of error for an arbitrary modulation at a specific value of SNR X,
- pdf of X due to the fading channel
Eb and No are the average energy per bit and noise PSD in a non-fading AWGN channel
- instantaneous power values of the fading channel, w.r.t the non fading

48. For rayleigh fading channels ,fading amplitude has rayleigh distribution
is the average value of the signal to noise ratio

49. For large values of Eb/N0:
For GMSK

51. Observations Flat-fading channel AWGN channel
Error rate is inversely proportional to SNR
Higher power required
BER of 10-3 to 10-6, dB SNR
AWGN channel
Exponential relationship between error rate and SNR
Lower power required
BER of 10-3 to 10-6, dB SNR

52. Digital Modulation in frequency selective channels
Caused by multipath time delay spread or time varying Doppler spread
Produces ISI
Impose bounds on data rate and BER
Errors occurs due to ISI when
Main (undelayed) signal component is removed through multipath cancellation
Non-zero value of delayed spread (d)
Sampling time shifted as a result of delay spread
Small delay spread results flat fading
Large delay spread results timing errors and ISI

53. MSK
OQPSK
QPSK
BPSK

54. MSK
OQPSK
QPSK
BPSK