# Modulation Techniques

**Topics:**Modulation, Phase-shift keying, Quadrature amplitude modulation

**Pages:**38 (5335 words)

**Published:**January 17, 2013

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

Receivers

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.

5

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.

7

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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