ASSIGNMENT
Performance Analysis Of Different Digital Modulation Scheme
Digital modulation techniques
ASK (Amplitude Shift Keying)Baseband
Data
ASK modulated
signal
1 10 0
Acos(t) Acos(t)
0,0
1),2cos()(
binary
binarytfAts c
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
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)
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…
Constellation Diagram of ASK
0,0
1),2cos()(
binary
binarytfAts c
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.
Frequency Shift Keying (FSK)
Signal Space for FSK
• Unlike ASK, here two orthogonal basis functions are required to represent s1 (t) and s2 (t).
• Signal space representation,
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).
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
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
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.
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)
• 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
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.
Probability of Error and the Distance Between Signals
… Ref (1)
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.
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
QPSK Waveform and Transmitter design
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
00011011
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/comm_ch08_digmod_en.pdf
2) BehrouzA. Forouzan , “Data Communications and Networking”, 4rdEdition, Chapter4, 2007
Thanks…
A special thanks to sir for guiding us…..