different types of digital modulation schemes.docx
TRANSCRIPT
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Different Types of Digital Modulation Schemes
Digital modulation techniques
Amplitude Shift Keying (ASK):
Change amplitude with each symbol
Frequency constant
Low bandwidth requirements
Very susceptible to interference
Frequency Shift Keying (FSK):
Change frequency with each symbol
Needs larger bandwidth
Phase Shift Keying (PSK):
Change phase with each symbol
More complex
Robust against interference
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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:
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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
s( t )={A cos(2 πf c t ) , binary 10 , binary 0
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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.
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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).
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Probability of Error for FSK
Dependence of the error probability on the distance between two signal points. In
general, is
Thus,
Identical to that of ASK
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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)
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Probability of Error for BPSK
• Dependence of the error probability on the distance between two signal points. In
general, is
• Since the signals s1(t) and s2(t) are equally likely to be transmitted, the average
probability of error is
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.
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Probability of Error and the Distance Between Signals
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, p/2, p, and
3p/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:
s(t) = Ac cos( 2π fct + Φ (t)) Where, ϕ(t)= 0, 90, 180, 270
Simplifying Equation 1
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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.
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