# Modulation Techniques

Topics: Modulation, Phase-shift keying, Quadrature amplitude modulation Pages: 38 (5335 words) Published: January 17, 2013
Introduction to Analog And Digital Communications

Second Edition

Simon Haykin, Michael Moher

Chapter 7 Digital Band-Pass Modulation Techniques
7.1 Some Preliminaries 7.2 Binary Amplitude-Shift Keying 7.3 Phase-Shift Keying 7.4 Frequency-Shift Keying 7.5 Summary of Three Binary Signaling Schemes 7.6 Noncoherent Digital Modulation Schemes 7.7 M-ary Digital Modulation Schemes 7.8 Mapping of Digital Modulation Waveforms onto Constellations of Signal Points 7.9 Theme Examples 7.10 Summary and Discussion

Digital band-pass modulation techniques
 Amplitude-shift keying  Phase-shift keying  Frequency-shift keying

 Coherent detection  The receiver is synchronized to the transmitter with respect to carrier phases  Noncoherent detection  The practical advantage of reduced complexity but at the cost of degraded performance

Lesson 1: Each digital band-pass modulation scheme is defined by a transmitted signal with a unique phasor representation. Lesson 2 : At the receiving end, digital demodulation techniques encompass different forms, depending on whether the receiver is coherent or noncoherent Lesson 3 : Two ways of classifying digital modulation schemes are (a) by the type of modulation used, and (b) whether the transmitted data stream is in binary or M-ary form. 3

7.1 Some Preliminaries

Given a binary source
 The modulation process involves switching ore keying the amplitude,

phase, or frequency of a sinusoidal carrier wave between a pair of possible values in accordance with symbols 0 and 1. c(t ) = Ac cos(2πf c t + φc ) (7.1)
 All three of them are examples of a band-pass process 1. Binary amplitude shift-keying (BASK)  The carrier amplitude is keyed between the two possible values used to represent symbols 0 and 1 2. Binary phase-shift keying (BPSK)  The carrier phase is keyed between the two possible values used to represent symbols 0 and 1. 3. Binary frequency-shift keying (BFSK)  The carrier frequency is keyed between the two possible values used to represent symbols 0 and 1. 4

 Decreasing the bit duration Tb has the effect of increasing the transmission

bandwidth requirement of a binary modulated wave.

Ac = c(t ) =

2 Tb

(7.2)

2 cos(2πf c t + φc ) (7.3) Tb

 Differences that distinguish digital modulation from analog modulation.  The transmission bandwidth requirement of BFSK is greater than that of BASK for a given binary source.  However, the same does not hold for BPSK.

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Band-Pass Assumption
 The spectrum of a digital modulated wave is centered on the carrier frequency

fc
 Under the assumption fc>>W,  There will be no spectral overlap in the generation of s(t)  The spectral content of the modulated wave for positive frequency is essentially separated from its spectral content for negative frequencies.

s (t ) = b(t )c(t ) (7.4) s (t ) = 2 b(t ) cos(2πf c t ) (7.5) Tb

 The transmitted signal energy per bit

Eb =

Tb

s (t ) dt

2

0

2 = Tb

Tb

0

b(t ) cos 2 (2πf c t )dt (7.6)
2

6

1 cos 2 (2πf c t ) = [1 + cos(4πf c t )] 2 1 T 1 T 2 2 b(t ) cos 2 (4πf c t )dt (7.7) Eb = b(t ) dt + Tb 0 Tb 0

b

b

 The band-pass assumption implies that |b(t)|2 is essentially constant

over one complete cycle of the sinusoidal wave cos(4πfct)

Tb

0

b(t ) cos 2 (4πf c t )dt ≈ 0
2

1 Eb ≈ Tb

Tb

b(t ) dt (7.8)

2

0

 For linear digital modulation schemes governed by Eq.(7.5), the

transmitted signal energy is a scaled version of the energy in the incoming binary wave responsible for modulating the sinusoidal carrier.

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7.2 Binary Amplitude-Shift Keying
 The ON-OFF signaling variety

 E , for binary symbol 1 (7.9) b(t ) =  b for binary symbol 0 0,  2 Eb cos(2πf c t ), for symbol 1  (7.10) s (t ) =  Tb  for symbol 0 0,  The average transmitted signal energy is ( the two binary symbols must by...

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