This document discusses and compares different digital modulation schemes including ASK, FSK, BPSK, and QPSK. It provides details on how each scheme works including signal space representation, constellation diagrams, decision regions, and probability of error calculations. The key advantages of each scheme are highlighted, such as PSK being less susceptible to noise than ASK and QPSK providing twice the bandwidth efficiency of BPSK. References are also provided for additional information.

1. ASSIGNMENT
Performance Analysis Of Different
Digital Modulation Scheme

2. Digital modulation techniques

3. ASK (Amplitude Shift Keying)
Baseband
Data
ASK
modulated
signal
1 10 0
Acos( t) Acos( t)
0,0
1),2cos(
)(
binary
binarytfA
ts c

4. Signal Space Representation for ASK
• Clearly, there is one basis function of unit energy
• Then,
• Average energy per bit
• A binary ASK system is therefore characterized by having a
signal space that is one-dimensional

5. Probability of Error for ASK
• Dependence of the error probability on the distance between
two signal points. In general, is
• Thus, for ask Probability of Error is:
… Ref (1)

6. Concept of a constellation diagram
• A constellation diagram helps us to define the amplitude and
phase of a signal when we are using two carriers…

7. Constellation Diagram of ASK
0,0
1),2cos(
)(
binary
binarytfA
ts c

8. Use of ASK
• The simplest and most common form of ASK operates as a
switch. (OOK)
• Very high speeds over optical fiber.
• Frequency Spectrum of ASK,
• Here, we can choose our fc so that the modulated signal
occupies available bandwidth.

9. Frequency Shift Keying (FSK)

10. Signal Space for FSK
• Unlike ASK, here two orthogonal basis functions are
required to represent s1 (t) and s2 (t).
• Signal space representation,

11. Decision Regions of FSK
• Signal space diagram for binary FSK
• The receiver decides in favor of s1 (t) if the received signal point
represented by the observation vector r falls inside region R1. This
occurs when r1 > r2
• When r1 < r2 , r falls inside region R2 and the receiver decides in
favor of s2 (t).

12. Probability of Error for FSK
… Ref (1)Dependence of the error probability on the
distance between two signal points. In general, is
Thus,
Identical to that of ASK

13. Binary Phase-Shift Keying (BPSK)
• Modulation
0 ≤ t ≤ Tb , where Tb is bit duration
• Eb transmitted signal energy per bit, i.e.
• The pair of signals differ only in a relative phase shift of 180
degrees

14. Signal Space Representation for BPSK
• Clearly, there is one basis function of unit energy
• Then,
• A binary PSK system is therefore characterized by having
a signal space that is in one-dimension.

15. Decision Rule of BPSK
• Then the optimum decision boundary is the midpoint of the line
joining these two message points
 Decision rule:
• Guess signal s1 (t) (or binary 1) was transmitted if the received
signal point r falls in region R1 (r > 0)
• Guess signal s2 (t) (or binary 0) was transmitted otherwise (r ≤ 0)

16. • Since the signals s1(t) and s2(t) are equally likely to be
transmitted, the average probability of error is
• Dependence of the error probability on the distance
between two signal points. In general, is
Probability of Error for BPSK

17. Constellation Diagram and Advantages of PSK
• Noise can change the amplitude easier than it can change the
phase. In other words, PSK is less susceptible to noise than ASK.
• PSK is superior to FSK because we do not need two carrier
signals.

18. Probability of Error and the Distance
Between Signals
… Ref (1)

19. Quadrature Phase Shift Keying (QPSK)
• In QPSK, we parallelize the bit stream so that every
two incoming bits are split up and PSK a carrier
frequency.
• One carrier frequency is phase shifted 90 from the
other - in quadrature.
• The two PSK signals are then added to produce one
of 4 signal elements.

20. Quadrature Phase Shift Keying (QPSK):
• Also a type of linear modulation scheme
• The phase of the carrier takes on 1 of 4 equally spaced
values, such as 0, /2, , and 3 /2 where each value of phase
corresponds to a unique pair of message bits.
• The QPSK signal for this set of symbol states may be defined
as:
( ) cos(2 ( ))c cs t A f t t
Where, ϕ(t)= 0, 90, 180, 270
( ) cos ( ).cos(2 ) sin ( )sin(2 )c c c cS t A t f t A t f t
…(1)
Simplifying Equation 1
This Gives the Idea about Transmitter design

21. QPSK Waveform and Transmitter design

22. QPSK Constellation Diagram
• Quadrature Phase Shift Keying has twice the
bandwidth efficiency of BPSK since 2 bits are
transmitted in a single modulation symbol.
Carrier phases
{0, /2, , 3 /2}
Q
I
00
01
10
11

23. References:
1) Meixia Tao, “Principles of Communications”, Shanghai Jiao
Tong University, Chapter 8: Digital Modulation Techniques
, Textbook: Ch 8.4 – 8.5, Ch 10.1-10.5
http://iwct.sjtu.edu.cn/Personal/mxtao/course_comm/com
m_ch08_digmod_en.pdf
2) BehrouzA. Forouzan , “Data Communications and
Networking”, 4rdEdition, Chapter4, 2007

24. Thanks…
A special thanks to sir
for guiding us…..