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 • 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.
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. • All three of them are examples of a band-pass process • Binary amplitude shift-keying (BASK) • The carrier amplitude is keyed between the two possible values used to represent symbols 0 and 1 • Binary phase-shift keying (BPSK) • The carrier phase is keyed between the two possible values used to represent symbols 0 and 1. • Binary frequency-shift keying (BFSK) • The carrier frequency is keyed between the two possible values used to represent symbols 0 and 1.
Decreasing the bit duration Tb has the effect of increasing the transmission bandwidth requirement of a binary modulated wave. • 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.
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. • The transmitted signal energy per bit
The band-pass assumption implies that |b(t)|2 isessentially constant over one complete cycle of the sinusoidal wave cos(4πfct) • 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.
7.2 Binary Amplitude-Shift Keying • The ON-OFF signaling variety • The average transmitted signal energy is ( the two binary symbols must by equiprobable)
Generation and Detection of ASK Signals • Generation of ASK signal : by using a produce modulator with two inputs • The ON-OFF signal of Eq. (7.9) • The sinusoidal carrier wave • Detection of ASK signal • The simplest way is to use an envelope detector, exploiting the nonconstant-envelope property of the BASK signal Fig. 7.1
Back Next Fig.7.1
Computation Experiment I: Spectral Analysis of BASK • The objective • To investigate the effect of varying the carrier frequency fc on the power spectrum of the BASK signal s(t), assuming that the wave is fixed. • Recall that the power spectrum of a signal is defined as 10 times the logarithm of the squared magnitude spectrum of the signal • To investigate the effect of varying the frequency of the square wave on the spectrum of the BASK signal, assuming that the sinusoidal carrier wave is fixed. • The two parts of Fig. 7.2 correspond to objective 1) • The two parts of Fig. 7.3 correspond to objective 2) Fig. 7.2(a) Fig. 7.2(b) Fig. 7.3(a) Fig. 7.3(b)
Back Next Fig.7.2(a)
Back Next Fig.7.2(b)
Back Next Fig.7.3(a)
Back Next Fig.7.3(b)
The spectrum of the BASK signal contains a line component at f=fc • When the square wave is fixed and the carrier frequency is doubled, the mid-band frequency of the BASK signal is likewise doubled. • When the carrier is fixed and the bit duration is halved, the width of the main lobe of the sinc function defining the envelope of the BASK spectrum is doubled, which, in turn, means that the transmission bandwidth of the BASK signal is doubled. • The transmission bandwidth of BASK, measured in terms of the width of the main lobe of its spectrum, is equal to 2/Tb, where Tb is the bit duration.
7.3 Phase-Shift Keying • Binary Phase-Shift Keying (BPSK) • The special case of double-sideband suppressed-carried (DSB-SC) modulation • The pair of signals used to represent symbols 1 and 0, • An antipodal signals • A pair of sinusoidal wave, which differ only in a relative phase-shift of π radians. • The transmitted energy per bit, Eb is constant, equivalently, the average transmitted power is constant. • Demodulation of BPSK cannot be performed using envelope detection, rather, we have to look to coherent detection as described next.
Generation and Coherent Detection of BPSK Signals • Generation • A product modulator consisting of two component • Non-return-to-zero level encoder • The input binary data sequence is encoded in polar form with symbols 1 and 0 represented by the constant-amplitude levels ; √Eb and - √Eb, • Product modulator • Multiplies the level-encoded binary wave by the sinusoidal carrier c(t) of amplitude √2/Tb to produce the BPSK signal Fig. 7.4
Detection • A receiver that consists of four sections • Product modulator; supplied with a locally generated reference signal that is a replica of the carrier wave c(t) • Low-pass filter; designed to remove the double-frequency components of the product modulator output • Sampler ; uniformly samples the output of the low-pass filter, the local clock governing the operation of the sampler is synchronized with the clock responsible for bit-timing in the transmitter. • Decision-making device ; compares the sampled value of the low-pass filter’s output to an externally supplied threshold. If the threshold is exceed, the device decides in favor of symbol 1, otherwise, it decides in favor of symbol 0. • What should the bandwidth of the filter be ? • The bandwidth of the low-pass filter in the coherent BPSK receiver has to be equal to or greater than the reciprocal of the bit duration Tb for satisfactory operation of the receiver. Fig. 7.4
Back Next Fig.7.4
Computer Experiment II: Spectral Analysis of BPSK • The objectives • To evaluate the effect of varying the carrier frequency fc on the power spectrum of the BPSK signal, for a fixed square modulating wave. • To evaluate the effect of varying modulation frequency on the power spectrum of the BPSK signal, for a fixed carrier frequency. Fig. 7.5(a) Fig. 7.5(b) Fig. 7.6(a) Fig. 7.6(b)
Back Next Fig.7.5(a)
Back Next Fig.7.5(b)
Back Next Fig.7.6(a)
Back Next Fig.7.6(b)
Comparing these two figures, we can make two important observations • BASK and BPSK signals occupy the same transmission bandwidth, which defines the width of the main lobe of the sinc-shaped power spectra. • The BASK spectrum includes a carrier component, whereas this component is absent from the BPSK spectrum. With this observation we are merely restating the fact that BASK is an example of amplitude modulation, whereas BPSK is an example of double sideband-suppressed carrier modulation • The present of carrier in the BASK spectrum means that the binary data stream can be recovered by envelope detection of the BASK signal. • On the other hand, suppression of the carrier in the BPSK spectrum mandates the use of coherent detection for recovery of the binary data stream form the BASK signal
Quadriphase-Shift Keying • An important goal of digital communication is the efficient utilization of channel bandwidth • In QPSK (Quadriphase-shift keying) • The phase of the sinusoidal carrier takes on one of the four equally spaced values, such as π/4, 3π/4, 5π/4, and 7π/4 • Each one of the four equally spaced phase values corresponds to a unique pair of bits called dibit
In reality, the QPSK signal consists of the sum of two BPSK signals • One BPSK signal, represented by the first term defined the product of modulating a binary wave by the sinusoidal carrier this binary wave has an amplitude equal to ±√E/2 • The second binary wave also has an amplitude equal to ±√E/2
The two binary waves defined in Eqs (7.16) and (7.17) share a common value for the symbol duration • The two sinusoidal carrier waves identified under points 2 and 3 are in phase quadrature with respect to each other. They both have unit energy per symbol duration. These two carrier waves constitute an ortho-normal pair of basis functions • Eqs. (7.16) and (7.17) identity the corresponding dibit, as outlined in Table 7.1 Table.7.1
Back Next Table 7.1
Generation and Coherent Detection of QPSK Signals • Generation • The incoming binary data stream is first converted into polar form by a non-return-to-zero level encoder • The resulting binary wave is next divided by means of a demultiplexer into two separate binary waves consisting of the odd- and even- mumbered input bits of b(t) – these are referred to as the demultiplexed components of the input binary wave. • The two BPSK signals are subtracted to produce the desired QPSK signals Fig. 7.7(a)
Back Next Fig.7.7(a)
Detection • The QPSK receiver consists of an In-phase and quadrature with a common input. • Each channel is made up of a product modulator, low-pass filter, sampler, and decision-making device. • The I- and Q-channles of the receiver, recover the demultiplexed components a1(t) and a2(t) • By applying the outputs of these two channels to a multiplexer, the receiver recovers the original binary sequence • Each of the two low-pass filters must be assigned a bandwidth equal to or greater than the reciprocal of the symbol duration T Fig. 7.7(b)
Back Next Fig.7.7(b)
Offset Quadriphase-Shift Keying (OQPSK) • The extent of amplitude fluctuations exhibited by QPSK signals may be reduced by using a variant of quadriphase-shift keying • The demultiplexed binary wave labeled a2(t) is delayed by one bit duration with respect to the other demultiplexed binary wave labled a1(t) • ±90◦ phase transitions occur twice as frequency but with a reduced range of amplitude fluctuations. • Amplitude fluctuations in OQPSK due to filtering have a smaller amplitude than in QPSK.
Back Next Fig.7.8
Computer Experiment III : QPSK and OPQSK Spectra • QPSK Spectra • OQPSK Spectra • For the same parameters used for QPSK • QPSK occupies a bandwidth equal to one half that of BPSK Fig. 7.9(a) Fig. 7.9(b) Fig. 7.10(a) Fig. 7.10(b)
Back Next Fig.7.9(a)
Back Next Fig.7.9(b)
Back Next Fig.7.10(a)
Back Next Fig.7.10(b)
7.4 Frequency-Shift Keying • Binary Frequency-Shift Keying (BFSK) • Each symbols are distinguished from each other by transmitting one of two sinusoidal waves that differ in frequency by a fixed amount • Sunde’s BFSK • When the frequencies f1 and f2 are chosen in such a way that they differ from each other by an amount equal to the reciprocal of the bit duration Tb
Computer Experiment IV : Sunde’s BFSK • Waveform • Input binary sequence 0011011001 for a bit duration Tb=1s • The latter part of the figure clearly displays the phase-continuous property of Sunde’s BFSK • Spectrum • The spectrum contains two line components at the frequency f=fc±1(2Tb); which equal 7.5Hz and 8.5Hz for fc=8 Hz and Tb=1s • The main lobe occupies a band of width equal to (3/Tb)=3Hz, centered on the carrier frequency fc=8 Hz • The largest sidelobe is about 21 dB below the main lobe. Fig. 7.11 Fig. 7.12
Back Next Fig.7.11
Back Next Fig.7.12
Continuous-phase Frequency-Shift Keying • The modulated wave maintains phase continuity at all transition points, even though at those points in time the incoming binary data stream switches back and forth • Sunde’s BFSK, the overall excursion δf in the transmitted frequency from symbol 0 to symbol 1, is equal to the bit rate of the incoming data stream. • MSK (Minimum Shift Keying) • The special form of CPFSK • Uses a different value for the frequency excursion δf , with the result that this new modulated wave offers superior spectral properties to Sunde’s BFSK.
Minimum-Shift Keying • Overall frequency excursion δf from binary symbol 1 to symbol 0, is one half the bit rate • Define the MSK signal as the angle-modulated wave
Sunde’s BFSK has no memory; in other words, knowing which particular change occurred in the previous bit interval provides no help in the current bit interval.
Fig. 7.13 Fig. 7.14