5. Bandpass Digital Modulation
11/3/20
Digital Communications
Prof. Hesham Tolba
Alexandria University
Faculty of Engineering
Electrical Engineering Department
Alexandria
2020
Prof. Hesham Tolba
Digital Communications
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
1
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Passband Data Transmission
11/3/20
Digital Communications
Prof. Hesham Tolba
Prof. Hesham Tolba
Digital Communica/ons
2
1
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Objectives …
q We learn from this chapter the following:
q Each digital band-pass modulation scheme is defined by a
transmitted signal with a unique phasor representation.
q At the receiving end, digital demodulation techniques
encompass different forms, depending on whether the receiver
is coherent or noncoherent.
q Two ways of classifying digital modulation schemes are
(a) by the type of modulation used,
(b) whether the transmitted data stream is in binary or
!-ary form.
11/3/20
Prof. Hesham Tolba
Digital Communica=ons
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
3
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Topics
q Different methods of digital modulation, namely, phase-shift
keying, quadrature-amplitude modulation, and frequency-shift
keying, and their individual variants.
q Coherent detection of modulated signals in additive white
Gaussian noise, which requires the receiver to be synchronized
to the transmitter with respect to both carrier phase and bit
timing.
q Noncoherent detection of modulated signals in additive white
Gaussian noise, disregarding phase information in the received
signal
11/3/20
Digital Communications
Prof. Hesham Tolba
Prof. Hesham Tolba
Digital Communica=ons
4
2
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Introduction
11/3/20
Prof. Hesham Tolba
Digital Communications
Introduction
Some Preliminaries
Binary ASK [BASK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
5
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
-ary
Digital
Modulation Schemes
!
Introduction
q In baseband data transmission, an incoming serial data stream
is represented in the form of a discrete pulse-amplitude
modulated wave that can be transmitted over a low-pass channel
(e.g., a coaxial cable).
q Transmission of data stream over a band-pass channel, (e.g.,
wireless and satellite channels), requires a modulation
strategy configured around a sinusoidal carrier whose
amplitude, phase, or frequency is varied in accordance with the
information-bearing data stream, is used.
q Digital modulation techniques dealing with band-pass data
transmission are studied in this chapter.
11/3/20
Digital Communications
Prof. Hesham Tolba
Prof. Hesham Tolba
Digital Communications
6
3
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Introduction …
q The primary aim of the chapter is to describe some important
digital band-pass modulation techniques used in practice.
q We describe three basic modulation schemes: amplitude-shift
keying, phase-shift keying, and frequency-shift keying,
followed by some of their variants.
q This is followed by describing coherent & noncoherent
detection.
q Coherent system, in which, the receiver is synchronized to the
transmitter with respect to carrier phase; otherwise, the
system is said to be noncoherent.
q A noncoherent system offers the practical advantage of reduced
complexity but at the cost of degraded performance.
11/3/20
Prof. Hesham Tolba
Digital Communications
Introduction
Some Preliminaries
Binary ASK [BASK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
7
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Some Preliminaries
11/3/20
Digital CommunicaBons
Prof. Hesham Tolba
Prof. Hesham Tolba
Digital Communications
8
4
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Some Preliminaries
q Given a binary source, the modulation process involves
switching or keying the amplitude, phase, or frequency of a
sinusoidal carrier between a pair of possible values in
accordance with symbols 0 & 1.
q Consider the sinusoidal carrier
& ' = #! cos ,-$! ' + %!
where #! is the carrier amplitude, $! is the carrier frequency
& %! is the carrier phase.
11/3/20
Prof. Hesham Tolba
Digital Communications
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
9
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Some Preliminaries …
q Given these parameters, we identify three forms of binary
modulation:
1. Binary amplitude shift-keying (BASK), in which the carrier
amplitude is keyed between the two possible values used to
represent 0 & 1.
2.
Binary phase-shift keying (BPSK), in which the carrier phase
is keyed between the two possible values (e.g., 0° & 180°)
used to represent 0 & 1.
3.
Binary frequency-shift keying (BFSK), in which the carrier
frequency is keyed between the two possible values used to
represent 0 & 1.
11/3/20
Digital Communications
Prof. Hesham Tolba
Prof. Hesham Tolba
Digital Communications
10
5
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Some Preliminaries …
Illustrative waveforms for
the three basic forms of
signaling binary information.
(a)Amplitude-shift keying.
(b)Phase-shift keying.
(c)Frequency-shift keying
with continuous phase.
11/3/20
Prof. Hesham Tolba
Digital Communications
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
11
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Some Preliminaries …
q In the digital communications literature, the usual practice is
to assume that the carrier has unit energy measured over one
symbol (bit) duration.
q Thus, the carrier amplitude is
#! =
"
/#! where 0$ is the bit
duration.
q We may thus express the carrier in the equivalent form
!" =
,/ cos '()!" + +!
0$
q It should be noted that decreasing the bit duration has the
effect of increasing the transmission bandwidth requirement of
a binary modulated wave.
11/3/20
Digital CommunicaBons
Prof. Hesham Tolba
Prof. Hesham Tolba
Digital Communica=ons
12
6
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Some Preliminaries …
q The spectrum of a digitally modulated wave (e.g., BASK, BPSK &
BFSK), is centered on the carrier frequency.
q It is normal practice to assume that the carrier frequency is
large compared with the “bandwidth” of the incoming binary data
stream that acts as the modulating signal ($! ≫ 2; 2 is the BW
of the binary wave).
q The modulated wave is defined by
3 ' = 4 ' &(') where 4 ' denotes
an incoming binary wave.
q Assuming
%! = 7, the modulated wave can be expressed as
9 ' =
11/3/20
,/ 4(') cos ,-$! '
0$
Prof. Hesham Tolba
Digital Communications
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
13
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Some Preliminaries …
q We may express the transmitted signal energy per bit,
:$, as
#!
:$ = ; 9(') " <'
%
#
"
= /#! ∫% ! 4(') " &>9 ,-$! ' " <'
#
#
= &/#! ∫% ! 4(') " <' + &/#! ∫% ! 4(') " &>9
#
≈ &/#! ∫% ! 4(') " <'
?-$! ' <'
q In words, for linear digital modulation schemes, the
transmitted signal energy (on a per bit basis) is a scaled
version of the energy in the incoming binary wave responsible
for modulating the sinusoidal carrier.
11/3/20
Digital Communications
Prof. Hesham Tolba
Prof. Hesham Tolba
Digital Communications
14
7
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Performance Metrics
q
Probability of Error
q
Power Spectra
q Baseband power spectral density
q
Bandwidth Efficiency
q The ratio of the data rate in bits/sec to the effectively
utilized channel bandwidth
A=
11/3/20
B$
C
Prof. Hesham Tolba
DE3/GH
Digital Communications
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
15
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Probability of Error
q A major goal of passband data transmission systems is the
optimum design of the receiver so as to minimize the average
probability of symbol error I' in the presence of AWGN.
q Depending on the method of digital modulation under study, the
evaluation of proceeds in one of two ways:
q In case of certain simple methods such as coherent BPSK and
coherent BFSK, exact formulas are derived for I' .
!-ary PSK
and coherent !-ary FSK, we resort the use of the union bound
for deriving an approximate formula for I' .
q In case of more elaborate methods such as coherent
11/3/20
Digital Communications
Prof. Hesham Tolba
Prof. Hesham Tolba
Digital Communications
16
8
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Power Spectra
q Studying the power spectra of the modulated signals is
important in two contexts: occupancy of the channel BW and cochannel interference in multiplexed systems.
q Given a modulated signal, we may describe it in terms of its
in-phase and quadrature-phase components as
9 ' = 9( ' JK3 ,-$! ' − 9) ' 3MN ,-$! '
= BO 9P (') QRE ,-$! '
q We also have
9P ' = 9( ' + S 9) ' ,
QRE ,-$! ' = JK3 ,-$! ' + S 3MN ,-$! '
Where 9P ' is the complex envelope of the modulated signal 9 ' ;
9( ' and 9) ' and therefore 9P ' are all lowpass signals.
11/3/20
Prof. Hesham Tolba
Digital Communications
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
17
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Power Spectra …
T* $ denote the power spectral density of the complex
envelope 9P ' (aka baseband power spectral density).
q The power spectral density, T+ $ of the bandpass signal 9 '
a frequency-shifted version of T* $ , except for a scaling
factor, as
q Let
is
U
T $ − $! + T* $ + $!
? *
q It is therefore sufficient to evaluate T* $ .
T+ $ =
9P ' is a lowpass signal, the calculation of T* $ should
be simpler than the calculation of T+ $ .
q Since
11/3/20
Digital CommunicaBons
Prof. Hesham Tolba
Prof. Hesham Tolba
Digital Communications
18
9
5. Bandpass Digital ModulaBon
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Bandwidth Efficiency
q Recalling that the channel BW and transmitted power constitute
the two primary communication resources.
q The efficient utilization of these resources provides the
motivation to search for spectrally efficient schemes.
q The primary objective of spectrally efficient modulation is to
maximize the BW efficiency defined as the ratio of the data
rate in bits/sec to the effectively utilized channel BW.
q A secondary objective is to achieve this BW efficiency at a
minimum practical expenditure of average power (or minimum
average SNR).
11/3/20
Prof. Hesham Tolba
Digital Communications
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
19
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Bandwidth Efficiency …
q The BW efficiency may be expressed as
A=
B*
C
DMW3/3/GH
with the data rate denoted by B* and the BW by C.
q The BW efficiency is the product of two independent factors:
q Possible use of multilevel encoding
qIn multilevel encoding, transmission is carried out on the
basis of blocks of bits rather than single bits.
Spectral
shaping
q
qChannel BW is reduced by the use of pulse shaping filters
that smooth out the sharp transitions in the transmitted
waveform.
11/3/20
Digital Communications
Prof. Hesham Tolba
Prof. Hesham Tolba
Digital Communications
20
10
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Passband Transmission Model
q We may model a passband data transmission system as shown.
Functional model of passband data transmission system.
q There is assumed to exist a message source that emits one
symbol every 0 sec, with the symbols belonging to an alphabet
of ! symbols: X& , X" , …, X,.
11/3/20
Prof. Hesham Tolba
Digital Communications
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
21
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Passband Transmission Model …
Y-priori probabilities I X& , I X" , …, I X,
message source output.
q The
q When the
specifies the
! symbols of the alphabet are equally likely, we have
&
I- = I X- = , for all a
!-ary output of the message source is presented to an
encoder producing a corresponding vector 9- made up of Z real
elements, Z ≤ !.
q The
9- as input, the modulator then constructs a
distinct signal 9- (') of duration 0$ sec as the representation of
the symbol X- .
q With the vector
11/3/20
Digital Communications
Prof. Hesham Tolba
Prof. Hesham Tolba
Digital Communica=ons
22
11
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Passband Transmission Model …
q The signal
9- (') is an energy signal, as shown by
#
:- = ∫% ! 9"- (')<',
q
a=1, 2, …, M
9- (') is transmitted every 0$ sec.
q The particular signal chosen for transmission depends on the
incoming message and possibly on the signals transmitted in
preceding time slots.
q With a sinusoidal carrier, the feature that is used by the
modulator to distinguish one signal from another is a step
change in the amplitude, frequency, or phase of the carrier.
q Sometimes, a hybrid form of modulation that combines changes in
both amplitude and phase or amplitude and frequency is used.
11/3/20
Prof. Hesham Tolba
Digital Communications
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
23
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Passband Transmission Model …
q The bandpass communication channel is assumed to have two
characteristics:
1. The channel is linear, with a BW that is wide enough to
accommodate the transmission of the modulated signal 9- (')
with negligible or no distortion.
2. The channel noise is the sample function of a WGN process of
zero mean and PSD Z. /,.
q The receiver consists of a detector followed by a signal
transmission decoder, performs two functions:
1. It reverses the operations performed in the transmitter.
2. It minimizes the effect of channel noise on the estimate X
f
computed for the transmitted symbol X- .
11/3/20
Digital Communications
Prof. Hesham Tolba
Prof. Hesham Tolba
Digital Communications
24
12
5. Bandpass Digital ModulaBon
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Binary ASK [ASK]
11/3/20
Prof. Hesham Tolba
Digital Communications
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
25
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Binary ASK [BASK]
q BASK is one of the earliest forms of digital modulation used in
radio telegraphy at the beginning of the twentieth century.
q To formally describe BASK, consider a binary data stream which
is of the ON–OFF signaling variety 4 ' , defined by
4 ' =g
:$ ,
7,
hKi DMNjik 3klDKm U
hKi DMNjik 3klDKm 7
q Then, multiplying by the sinusoidal carrier wave, we get the
BASK wave
9 ' =n
11/3/20
Digital Communications
Prof. Hesham Tolba
,:$/ JK3 ,-$ ' ,
!
0$
7,
Prof. Hesham Tolba
hKi 3klDKm U
hKi 3klDKm 7
Digital Communications
26
13
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Binary ASK [BASK] …
$! may have an arbitrary value,
consistent with transmitting the modulated signal anywhere in
the electromagnetic radio spectrum.
q The carrier frequency
q When a bit duration is occupied by symbol 1, the transmitted
signal energy is o/ ; When the bit duration is occupied by
symbol 0, the transmitted signal energy is zero.
q On this basis, we may express the average transmitted signal
energy as :012 = :$/,.
q For this formula to hold, the two binary symbols must be
equiprobable.
11/3/20
Prof. Hesham Tolba
Digital Communications
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
27
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Generation/Detection of ASK Signals
q A BASK signal is readily generated by using a product modulator
with two inputs.
q One input is the modulating signal (the ON–OFF signal
! " = $ %! ,
3,
q The sinusoidal carrier wave
4 ' ):
'() *+,-). /.0*(1 2
'() *+,-). /.0*(1 3
& ' =
"
/#! cos ,-$! '
supplies the
other input.
q A property of BASK, is the nonconstancy of the envelope of the
modulated wave.
q Accordingly, the simplest way for BASK detection is to use an
envelope detector.
11/3/20
Digital Communications
Prof. Hesham Tolba
Prof. Hesham Tolba
Digital Communications
28
14
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Binary PSK [PSK]
11/3/20
Prof. Hesham Tolba
Digital Communications
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
29
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Binary PSK [BPSK]
q In the simplest form of PSK known as BPSK, the pair of signals
and used to represent symbols 1 and 0, respectively, are
defined by
9- ' =
,:$/ JK3 ,-$ ' ,
!
0$
hKi 3klDKm U JKiiQ3EKNqMNr WK a = U
− ,:$/0 JK3 ,-$! ' ,
$
hKi 3klDKm 7 JKiiQ3EKNqMNr WK a = ,
where , ≤ " ≤ ." , with ." denoting the bit duration and /" denoting the
transmitted signal energy per bit;
q To ensure that each transmitted bit contains an integral number of
cycles of carrier wave, )! is chosen to be 0! /." .
11/3/20
Digital Communications
Prof. Hesham Tolba
Prof. Hesham Tolba
Digital Communications
30
15
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Binary PSK [BPSK] …
q A pair of sinusoidal waves, and which differ only in a relative
phase-shift of radians as defined above, are referred to as
antipodal signals.
q BPSK differs from BASK in an important respect: the envelope of
the modulated signal is maintained constant at the value for
all time '.
q This property has two important consequences:
1. The transmitted energy per bit, is constant; equivalently,
the average transmitted power is constant.
2.
Demodulation of BPSK cannot be performed using envelope
detection; rather, we have to look to coherent detection.
11/3/20
Prof. Hesham Tolba
Digital Communica=ons
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
31
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Binary PSK [BPSK] …
q In case of BPSK, there is only one basis function of unit
energy, namely,
%& ' =
q Thus, we may
,:$/ JK3 ,-$ '
!
0$
express the transmitted signals in terms of +# "
as
9& ' = :$%& ' , 7 ≤ ' ≤ 0$ ,
9" ' = − :$%& ' , 7 ≤ ' ≤ 0$
11/3/20
Digital Communications
Prof. Hesham Tolba
Prof. Hesham Tolba
Digital Communications
32
16
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Binary PSK [BPSK] …
q BPSK is therefore characterized by having a signal space that
is one-dimensional (Z = U), with a signal constellation
consisting of two message points (! = ,).
q The coordinates of the message points are
#!
9&& = ; 9& ' %& ' <' = + :$
%
#!
9"& = ; 9" ' %& ' <' = − :$
%
11/3/20
Prof. Hesham Tolba
Digital Communica=ons
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
33
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Binary PSK [BPSK] …
q The signal-space diagram for BPSK
is as shown.
q The message point corresponding
to 1# " is located at 1## = + /"
and the message point
corresponding to 1$ " is located
at 1$# = − /" .
q The figure shows also example
waveforms of antipodal signals
representing 1# " and 1$ " .
q Note that the shown constellation
has minimum average energy.
11/3/20
Digital CommunicaBons
Prof. Hesham Tolba
Prof. Hesham Tolba
Signal-space diagram for coherent BPSK
system. The waveforms depicting the
transmitted signals +" 3 & +# 3 ,
displayed in the inserts, assume 4$ = ".
Digital Communications
34
17
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Error Probability of BPSK
q To realize a rule for making a decision in favor of symbol 1 or
symbol 0, we apply the following rule:
Observation vector 3 lies in the region 4% if the
Euclidean Distance 3 − 1& is minimum for 5 = 6.
q We partition the shown signal space into
two regions:
q The set of points closest to message
point 1 at / " .
q The set of points closest to message
point 2 at − / " .
4# and 4$ , according to the
message point around which they are constructed.
q The decisions regions are marked as
11/3/20
Prof. Hesham Tolba
Digital Communications
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
35
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Error Probability of BPSK …
q The decision rule
9& (') was transmitted if the received signal point
falls in s& ,
q Decide 9" (') was transmitted if the received signal point
falls in s" .
q Decide
q Two kind of erroneous decisions may be made
q 9" (') is transmitted, but the received signal falls inside
s& ,
and so the receiver decides in favor of 9& ' ;
q 9& (') is transmitted, but the received signal falls inside s" ,
and so the receiver decides in favor of 9" ' .
11/3/20
Digital Communications
Prof. Hesham Tolba
Prof. Hesham Tolba
Digital Communications
36
18
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Error Probability of BPSK …
q Considering the 1st kind of error
q We note from the shown figure
that the decision region
associated to 9& (') is described
by
4#: , < 3# < ∞
where the observable element t&
is related to the received
signal t(') by
(!
3# = < 3(")+# " ?"
'
11/3/20
Prof. Hesham Tolba
Digital Communications
37
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Error Probability of BPSK …
q The conditional probability density function of random, variable
@# , given that symbol 0 was transmitted, is defined by
B
B
))" 3# |, =
DEF −
3 − 1$# $
C* #
(C*
B
B
$
=
DEF −
3# + /"
C
(C*
*
q The conditional probability of the receiver deciding in favor of
symbol 1, given that symbol 0 was transmitted, is therefore
+
G#' = < ))" 3# |, ?3#
'
=
11/3/20
Digital Communications
Prof. Hesham Tolba
+
B
(C*
< DEF −
'
Prof. Hesham Tolba
B
3 + /"
C* #
Digital Communications
$
?3#
38
19
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Error Probability of BPSK …
q Putting
from t&
&
u = 6 t& + :$ and changing the variable integration
%
to u, we may rewrite
G#' =
=
U 9
;
456 −8# <u
- 7! /6%
2
erfc
9
%!
>%
v%& the conditional
probability of the receiver deciding in favor of symbol 0,
given that symbol 1 was transmitted, also has the same value as
v&% (symmetric signal space).
q Considering the 2nd kind of error,
11/3/20
Prof. Hesham Tolba
Digital Communica=ons
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
39
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Error Probability of BPSK …
v%& & v&% (assuming equiprobable symbols), we
find that the average probability of symbol error (the bit
error rate for coherent BPSK) is
q Thus, averaging
I' =
11/3/20
Digital Communications
Prof. Hesham Tolba
U
erfc
,
Prof. Hesham Tolba
:$
Z.
Digital Communications
40
20
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Generation/Detection of BPSK Signals
q To generate the BPSK signal, we use a product modulator
consisting of two components:
i. Non-return-to-zero level encoder – the input binary data
sequence is encoded in polar form with symbols 1 & 0
represented by the constant-amplitude levels: :$ and − :$,
respectively.
ii.Product modulator multiplies the levelencoded binary wave by the
sinusoidal carrier &(') of
amplitude ,/0$ to produce
the BPSK signal.
11/3/20
Prof. Hesham Tolba
(a) BPSK modulator.
Digital Communications
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
41
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Generation/Detection of BPSK Signals …
q The BPSK receiver consists of four sections:
i.
Product modulator - supplied with a locally generated
reference signal that is a replica of the carrier wave
ii. Low-pass
filter - removes the double-frequency components of
the product modulator output and pass the zero-frequency
components.
iii.Sampler
- uniformly samples the output of the low-pass
filter at ' = a0$ xyQiQ a = 7, ±U, ±,, …; the local clock governing
the operation of the sampler is synchronized with the clock
in the transmitter.
11/3/20
Digital Communications
Prof. Hesham Tolba
Prof. Hesham Tolba
Digital Communications
42
21
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Generation/Detection of BPSK Signals …
iv. Decision-making
device - compares the output sampled value
to an externally supplied threshold, every seconds. If the
threshold is exceeded, the device decides in favor of symbol
1; otherwise, it decides in favor of symbol 0.
(b) BPSK Coherent Detector
11/3/20
Prof. Hesham Tolba
Digital Communications
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
43
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Generation/Detection of BPSK Signals …
q The described BPSK receiver is said to be coherent, i.e., the
sinusoidal reference in the receiver is synchronous in phase &
frequency, with the carrier wave used in the modulator.
q This requirement can be achieved by using a phase-locked loop.
q In addition to synchrony with respect to carrier phase, the
receiver also has an accurate knowledge of the interval
occupied by each binary symbol.
q The coherent BPSK detection follows a procedure similar to that
described for the demodulation of a DSB-SC modulated wave with
the additions of the sampler and the decision-making device.
q The rationale for this similarity builds on: BPSK is simply
another form of DSB-SC modulation.
11/3/20
Digital Communications
Prof. Hesham Tolba
Prof. Hesham Tolba
Digital Communications
44
22
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
BPSK Transmitter & Receiver
Block diagrams for (a) binary PSK transmitter and (b) coherent binary PSK receiver.
11/3/20
Prof. Hesham Tolba
Digital Communica=ons
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
45
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Power Spectra of BPSK
q The complex envelope of a binary PSK wave consists of an in-
phase component only.
q The in-phase component equals
7 ≤ ' ≤ 0$, where
? " =
+{ '
9%!
,
@!
3,
or −{ '
during the interval
3 ≤ " ≤ @!
41/4BC4)4
q Assume that the binary wave is random, with symbols 1 & 0
equally likely and the symbols transmitted during the different
time slots are statistically independent,
q The PSD of such a wave is equal to the energy spectral density
of the symbol shaping function
11/3/20
Digital Communications
Prof. Hesham Tolba
Prof. Hesham Tolba
divided by the symbol duration.
Digital Communications
46
23
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Power Spectra of BPSK …
q Hence, the baseband power spectral density of a binary PSK
signal equals
,:$3MN" -0$$
T* $ =
-0$$ "
= ,:$3MNJ " -0$$
q This power spectrum falls off
as the inverse square of
frequency, as shown.
Power spectra of binary PSK and FSK signals.
11/3/20
Prof. Hesham Tolba
Digital Communications
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
47
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Quadriphase Shift Keying
[QPSK]
11/3/20
Digital Communications
Prof. Hesham Tolba
Prof. Hesham Tolba
Digital Communications
48
24
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Quadriphase Shift Keying
q An important goal of digital communication is the efficient
utilization of channel BW.
q This goal is attained by a bandwidth-conserving modulation
scheme: quadriphase-shift keying (QPSK).
q In QPSK, information carried by the transmitted signal is
contained in the phase of a sinusoidal carrier.
q The phase of the sinusoidal carrier takes on one of four
equally spaced values, such as
11/3/20
Prof. Hesham Tolba
:⁄ , <:⁄ , =:⁄ , >:⁄ .
;
;
;
;
Digital Communications
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
49
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Quadriphase Shift Keying …
q For this set of values, the transmitted signal is defined as
9- ' = n
7,
,:/ &>9 ,-$! ' + (,a − U) -/ ,
0
?
7≤'≤0
Qm3QxyQiQ
where a = U, ,, } & ?; E is the transmitted signal energy/symbol
and T is the symbol duration.
q Each one of the four equally spaced phase values corresponds to
a unique pair of bits called a dibit.
11/3/20
Digital Communications
Prof. Hesham Tolba
Prof. Hesham Tolba
Digital Communications
50
25
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Quadriphase Shift Keying …
q We may choose the foregoing set of phase values to represent
the Gray encoded set of dibits: 10, 00, 01, and 11.
q In this form of encoding, we see that only a single bit is
changed from one dibit to the next.
q The symbol duration (i.e., the duration of each dibit) is twice
the bit duration, as shown by 0 = ,0$.
q The transmitted signal can be rewritten as
9- ' =
,:/ JK3 (,a − U) -/ &>9 ,-$! ' − ,:/ 3MN (,a − U) -/ 3MN ,-$! '
0
?
0
?
where a = U, ,, } & ?.
11/3/20
Prof. Hesham Tolba
Digital Communications
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
51
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Signal-Space Diagram of QPSK
q Based on the previous representation:
q There are two orthonormal basis functions,
%& ' and %" ' ,
contained in the expansion of 9- ' .
q%& ' and %" ' are defined by a pair of quadrature
carriers:
%& ' = ,/0 JK3 ,-$! ' ,
7≤'≤0
%? ' =
,/ 3MN ,-$ ' ,
!
0
7≤'≤0
q There are four message points, and the associated signal
vectors are defined by
: &>9 (,a − U) :⁄;
9- =
, a = U, ,, }, ?
− : &>9 (,a − U) :⁄;
11/3/20
Digital Communications
Prof. Hesham Tolba
Prof. Hesham Tolba
Digital Communications
52
26
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Signal-Space Diagram of QPSK …
q The values of the elements of the signal vectors, namely,
9-& and 9-" are as shown.
11/3/20
Prof. Hesham Tolba
Digital Communications
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
53
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Signal-Space Diagram of QPSK …
q A QPSK signal has a two-
dimensional signal constellation
(Z = ,) and four message points
(! = ?) whose phase angles
increase in counterclockwise
direction, as shown.
q As with BPSK, the QPSK signal
has a minimum average energy.
Signal-space diagram of QPSK
system
11/3/20
Digital Communications
Prof. Hesham Tolba
Prof. Hesham Tolba
Digital Communications
54
27
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Example
q The sequences and waveforms involved in the generation of a
QPSK signal are as shown.
a) Input binary sequence.
b) Odd-numbered bits of input
sequence and associated
binary PSK wave.
c) Even-numbered bits of input
sequence and associated
binary PSK wave.
d) QPSK waveform defined as
9 ' = 9-& %& ' + 9-" %? ' .
11/3/20
Prof. Hesham Tolba
Digital Communications
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
55
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Example …
q To define the decision rule for the detection of the transmitted
data sequence, we partition the signal space into four regions, in
accordance with the following equation:
Observation vector t lies in the region s- if the
Euclidean Distance t − 9@ is minimum for Å = a.
q The individual regions are defined by the set of
points closest to the message point represented
by signal vectors 1# , 1$ , 1, & 1- .
q This is accomplished by constructing the
perpendicular bisectors of the square formed by
joining the four message points and then marking
off the appropriate regions 4# , 4$ , 4, & 4- , as shown.
11/3/20
Digital Communications
Prof. Hesham Tolba
Prof. Hesham Tolba
Digital Communications
56
28
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Error Probability of QPSK
q In a coherent QPSK system, the received signal
by
t '
is defined
7≤'≤0
a = U, ,, }, ?
Where Ç ' is the sample function of a WGN process of zero mean
and PSD Z. /,.
t ' = 9- ' + Ç ' ,
q The observation vector
t has two elements, t& and t" defined by
'!
'!
D" = E D(")H" " I"
&
= % J(/ (9K − 2)
=±
11/3/20
É
D# = E D(")H# " I"
L
+ O"
M
%
+ O"
9
&
= − % J(/ (9K − 2)
=∓
Prof. Hesham Tolba
L
+ O#
M
%
+ O#
9
Digital Communications
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
57
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Error Probability of QPSK …
q The observable elements are sample values of independent
Gaussian RVs with mean values ± :/, and ∓ :/, with a common
variance Z. /,.
q The decision rule is to decide that 9& ' was transmitted if the
received signal point associated with the observation vector t
falls inside s& , 9" ' was transmitted if t falls inside s" , and
so on.
t (i.e., the in-phase
channel output t& & the quadrature channel output t" ) may be
characterized by:
q The signal energy/bit is :/,.
q The noise spectral density is Z. /,.
q The two element of the observation vector
11/3/20
Digital CommunicaBons
Prof. Hesham Tolba
Prof. Hesham Tolba
Digital Communications
58
29
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Error Probability of QPSK …
I' obtained for a coherent BPSK system, we may now
state that the average probability of bit error in each channel
of the QPSK system is
q Hence, using
H. =
B
DIJK
'
//'
B
= DIJK
C*
'
/
'C*
q The bit errors in the in-phase & quadrature-phase channels of
coherent QPSK system are statistically independent.
11/3/20
Prof. Hesham Tolba
Digital Communications
59
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Error Probability of QPSK …
q Accordingly, the average probability of a correct decision is
"
I! = U − IA
"
U
= U − QihJ
,
= U − QihJ
7
"6%
:
,Z.
&
+ ; QihJ "
7
"6%
q The average probability of symbol error for coherent QPSK is
therefore
I' = U − I!
= QihJ
11/3/20
Digital CommunicaBons
Prof. Hesham Tolba
7
"6%
Prof. Hesham Tolba
&
− ; QihJ "
Digital Communications
7
"6%
60
30
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Error Probability of QPSK …
q In the region
:/,Z. ≫ U, we may approximate I' for QPSK as
:
,Z.
I' ≈ QihJ
q The previous formula may also be derived using the signal space
diagram.
q Since the four message points of this diagram are circularly
with respect to the origin, we may apply
-
2
I,)
R( ≤ S 4)'J
,
9
9 >%
)*"
'() -11 K
)+,
11/3/20
Prof. Hesham Tolba
Digital Communications
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
61
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Error Probability of QPSK …
q In a QPSK system, since there are two bits/symbol, the transmitted
signal energy/symbol is twice the signal energy/bit, as
: = ,:$
q Thus expressing the average probability of symbol error in terms of
the ratio /" /C* , we may write
I' ≈ QihJ
11/3/20
Digital CommunicaBons
Prof. Hesham Tolba
Prof. Hesham Tolba
:$
Z.
Digital Communications
62
31
5. Bandpass Digital ModulaBon
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Error Probability of QPSK …
q With Gray coding used for the incoming symbols, the Bit Error Rate of
QPSK is exactly
MNO =
B
DIJK
'
/"
C*
q Thus, a coherent QPSK system achieves the same BER as a
coherent BPSK system for the same bit rate and same :$/Z. but
uses ONLY half the channel BW.
11/3/20
Prof. Hesham Tolba
Digital Communications
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
63
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Generation of QPSK Signals
q To generate the QPSK signal, the incoming binary data stream is
first converted into polar form by a non-return-to-zero level
encoder.
o/ /, & − o/ /,
where the resulting binary wave is next divided by means of a
demultiplexer into two separate binary waves.
q Symbols 1 and 0 are thereby represented by
q These two binary waves (demultiplexed waves) are used to
modulate the pair of quadrature carriers.
q Finally, the two BPSK signals are subtracted to produce the
desired QPSK signals, as shown in the next slide.
11/3/20
Digital Communications
Prof. Hesham Tolba
Prof. Hesham Tolba
Digital Communications
64
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5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Generation of QPSK Signals …
Block diagram of a QPSK transmitter.
11/3/20
Prof. Hesham Tolba
Digital Communications
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
65
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Detection of QPSK Signals
Ö-channel and
quadrature Ü-channel with a common input, as shown.
q Each channel is itself made up of a product modulator, LPF,
sampler, and decision-making device.
q The QPSK receiver consists of an in-phase
Block diagram of a coherent QPSK receiver.
11/3/20
Digital CommunicaBons
Prof. Hesham Tolba
Prof. Hesham Tolba
Digital Communica=ons
66
33
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
QPSK Transmitter & Receiver
Block diagrams of (a) QPSK transmitter and (b) coherent QPSK
receiver.
11/3/20
Prof. Hesham Tolba
Digital Communications
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
67
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Power Spectra of QPSK
q Assume that the binary wave at the modulator input is random, with
symbols 1 & 0 equally likely and the symbols transmitted during the
different time slots are statistically independent, we note:
−." ≤ " ≤
or −P " , and similarly for
q Depending on the dibit sent during the signaling interval
." , the in-phase component equals +P "
the quadrature component.
q The
P " denotes the symbol shaping function, defined by
P" =
/
,
.
,≤"≤.
,,
DQRDSTDID
q Hence, the in-phase and quadrature components have a common PSD,
namely /RUVK $ ). .
11/3/20
Digital Communications
Prof. Hesham Tolba
Prof. Hesham Tolba
Digital Communications
68
34
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Power Spectra of QPSK …
q The in-phase & quadrature
components are statistically
independent.
q Accordingly, the baseband PSD of
the QPK signal equals the sum of
the individual PSDs of the inphase and quadrature component,
so we may write
T* $ = ,:3MNJ " 0$
= ?:$3MNJ " ,0$$
T* $ ,
normalized with respect to ?:$,
versus the normalized frequency $0$.
q The shown figure plots
11/3/20
Prof. Hesham Tolba
Power spectra of QPSK and
MSK signals.
Digital Communications
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
69
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Offset QPSK [OQPSK]
q The signal space diagram, which embodies all the possible phase
transitions of a QPSK signal, shows that:
q The carrier phase change by ±180∘ whenever both the in-phase
and quadrature components of the QPSK signal change sign
(e.g., dibit 01 ➞ dibit 10).
q The carrier phase change by ±90∘ whenever
the in-phase or quadrature component
changes sign (e.g., dibit 10 ➞ dibit
00).
q The carrier phase is unchanged when
neither in-phase or quadrature component
changes sign (e.g., dibit 10 is
transmitted in 2 successive symbol
intervals).
11/3/20
Digital Communications
Prof. Hesham Tolba
Prof. Hesham Tolba
Digital Communications
70
35
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Offset QPSK [OQPSK] …
q The carrier phase may jump by ±90∘ or ±180∘ every two-bit
(dibit) duration.
q This property can be of particular concern when the QPSK signal
is filtered during the course of transmission over a channel.
q Such a filtering action can cause the carrier amplitude, and
therefore the envelope of the QPSK signal, to fluctuate.
q Fluctuations of this kind are undesirable as they tend to
distort the received signal;
q The net result is a reduced opening of the eye diagram.
q These fluctuations may be reduced by using a variant of QPSK
known as the OQPSK.
11/3/20
Prof. Hesham Tolba
Digital Communications
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
71
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Offset QPSK [OQPSK] …
q OQPSK is also referred to as staggered QPSK (SQPSK).
q In OQPSK, the demultiplexed binary wave is delayed by one bit
duration with respect to the other demultiplexed binary wave.
q The two basis functions of OQPSK are
%& ' =
,/ JK3 ,-$! ' ,
0
%? ' =
,/ 3MN ,-$! ' ,
0
7≤'≤0
0
}0
≤'≤
,
,
H. " is exactly the same as that for QPSK,
but H/ " is different from that for QPSK.
q This modification has the effect of confining the likely
occurrence of phase transitions to 0° and ±90∘, as shown in the
next slide.
11/3/20
Digital Communications
Prof. Hesham Tolba
Prof. Hesham Tolba
Digital Communications
72
36
5. Bandpass Digital ModulaBon
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Offset QPSK [OQPSK] …
q The shown figure shows possible paths for switching between the
message points in (a) QPSK and (b) offset QPSK.
Possible paths for switching between the message points in (a) QPSK & (b) offset QPSK.
11/3/20
Prof. Hesham Tolba
Digital Communications
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
73
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Offset QPSK [OQPSK] …
q However, the ±90∘ phase transitions in OQPSK occur twice as
frequently but with a reduced range of amplitude fluctuations,
compared with QPSK.
q Since there are ±180∘ phase transitions in QPSK in addition to
the ±90∘ phase transitions ➞ the amplitude fluctuations in
OQPSK have a smaller amplitude than in QPSK.
q OQPSK has exactly the same probability of symbol error in an
AWGN as QPSK.
q Hence, the probability of symbol error for OQPSK is
I' ≈ QihJ
11/3/20
Digital Communications
Prof. Hesham Tolba
Prof. Hesham Tolba
:
,Z.
Digital Communications
74
37
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Example
q Parts (a) and (b) of the shown figure depict the waveforms of
QPSK and OQPSK, both of which are produced by the binary data
stream 0011011001 with the following composition over the
interval 7 ≤ ' ≤ U70$.
q Examining the two waveforms,
we find the following:
i. In QPSK: the carrier phase
undergoes jumps of 0°, ±90∘,
or ±180∘ every ,0$ seconds.
ii.In OQPSK: the carrier phase
experiences only jumps of
0° or ±90∘ every 0$ seconds.
11/3/20
Prof. Hesham Tolba
Graphical comparison of phase
transitions in QPSK and OQPSK.
Digital Communications
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
!/4-Shifted QPSK
75
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
q An ordinary QPSK signal may reside in either one of the two
commonly used constellations shown below.
q These constellations are shifted by à/4 radians with respect to
each other.
q In this à/4-Shifted QPSK,
the carrier phase used for
the transmission of
successive symbols is
alternately picked from one
of the two QPSK shown
constellations and then the
other.
Two commonly used signal constellations of QPSK
11/3/20
Digital CommunicaBons
Prof. Hesham Tolba
Prof. Hesham Tolba
Digital Communications
76
38
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
!/4-Shifted QPSK …
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
q Therefore, a à/4-Shifted QPSK signal may reside in any one of
EIGHT possible phase states.
q
q
q
q
8 possible phase states for
the p/4-shifted QPSK modulator.
11/3/20
q
The 4 dashed lines emanating from each possible
message point defines the phase transitions
that are feasible in W/4-Shifted QPSK.
Phase transitions from one symbol to another
are restricted to ±W/4, ±3W/4 radians.
Hence, envelope variations due to filtering are
significantly reduced.
W/4-Shifted QPSK signals can be noncoherently
detected thereby considerably simplifying the
receiver design.
W/4-Shifted QPSK signals can be differently
encoded.
Prof. Hesham Tolba
Digital Communications
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
!/4-Shifted DQPSK
77
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
q à/4-Shifted QPSK signals can be differently encoded, leading to
DQPSK.
q The generation of à/4-Shifted DQPSK symbols, represented by the
symbol pair (I, Q ), is described by the following relationships:
Ö@ = JK3 ã@B& + åã@
Ü@ = 3MN ã@B& + åã@
= JK3 ã@
= 3MN ã@
where ã@B& is the absolute phase
angle of symbol Å − U, and åã@ is
the differentially encoded phase
change defined in accordance
with the shown table.
11/3/20
Digital CommunicaBons
Prof. Hesham Tolba
Prof. Hesham Tolba
Correspondence between input dibit and
phase change for C/4-Shifted DQPSK.
Digital Communications
78
39
5. Bandpass Digital ModulaBon
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Example
q Consider the input binary sequence 00101001,
suppose that the phase angle ã. = à/4 in the
shown constellation is assigned as the initial
phase state of the à/4-Shifted DQPSK modulator.
q Then, arranging the input binary sequence as a
sequence of dibits and following the convention
of the previous table, we get the results shown
in the table.
C/4-Shifted DQPSK results.
11/3/20
Prof. Hesham Tolba
Digital Communications
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
79
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Detection of !/4-Shifted DQPSK
t ' , the receiver first computes
the projections of t ' onto the basis functions %& ' and %" ' .
q The resulting outputs (I & Q ) are applied to the shown
differential detector.
q Given the noisy channel output
Block diagram of the p/4-shifted DQPSK detector.
11/3/20
Digital Communications
Prof. Hesham Tolba
Prof. Hesham Tolba
Digital Communications
80
40
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Detection of !/4-Shifted DQPSK …
q The differential detector consists of the following components:
q Arctangent computer extracting the phase angle ã of the
channel output.
q Phase-difference computer to determine the change in the
phase ã over one symbol interval.
q Modulo-2à correction logic for correcting errors due to the
possibility of phase angles wrapping around the real axis.
q It operates as follows:
If åã@ < −Ué7°
If åã@ > Ué7°
êGëí
êGëí
åã@ = åã@ + }ì7°
åã@ = åã@ − }ì7°
where åã@ denotes the computed phase difference between ã@ and
ã@B& representing the phase angles of the channel output for
symbols U and U − 2, respectively.
11/3/20
Prof. Hesham Tolba
Digital Communica=ons
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
81
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Binary FSK [BFSK]
11/3/20
Digital CommunicaBons
Prof. Hesham Tolba
Prof. Hesham Tolba
Digital Communications
82
41
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Binary FSK [BFSK]
q In the simplest form of FSK known as BFSK, symbols 0 and 1 are
distinguished from each other by transmitting one of two
sinusoidal waves that differ in frequency by a fixed amount.
q A typical pair of sinusoidal waves is described by
9- ' =
,:$/ &>9 ,-$ ' ,
&
0$
hKi 3klDKm U JKiiQ3EKNqMNr WK a = U
,:$/ &>9 ,-$ ' ,
"
0$
hKi 3klDKm 7 JKiiQ3EKNqMNr WK a = ,
where :$ is the transmitted signal energy/bit.
11/3/20
Prof. Hesham Tolba
Digital Communications
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
83
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Binary FSK [BFSK] …
$& & $" are chosen in such a way that they
differ from each other by an amount equal to the reciprocal of
the bit duration 0$, the BFSK signal is referred to as Sunde’s
BFSK after its originator.
q When the frequencies
q This modulated signal is a continuous-phase signal in the sense
that phase continuity is always maintained, including the
inter-bit switching times.
q An example of Sunde’s BFSK is shown in the next slide.
11/3/20
Digital Communications
Prof. Hesham Tolba
Prof. Hesham Tolba
Digital Communications
84
42
5. Bandpass Digital ModulaBon
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Binary FSK [BFSK] …
q An example of Sunde’s BFSK produced by the input binary
sequence 0011011001 for a bit duration 0$ = U sec.
q Part (a) of the figure
displays the waveform of the
input sequence, and part (b)
displays the corresponding
waveform of the BFSK signal.
q The latter part of the figure
clearly displays the phasecontinuous property of Sunde’s
BFSK.
11/3/20
Prof. Hesham Tolba
(a) Binary sequence and its non-return-to-zero
level-encoded waveform. (b) Sunde’s BFSK signal.
Digital Communications
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
85
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Continuous-Phase FSK [CPFSK]
q Sunde’s BFSK is the simplest form of a family of digitally
modulated signals known collectively as continuous-phase FSK
(CPFSK) signals, which exhibit the following distinctive
property:
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
between symbols 0 and 1
q The CPFSK signal is a continuous-wave modulated wave like any
other angle-modulated wave experienced in the analog world,
despite the fact that the modulating wave is itself
discontinuous.
11/3/20
Digital Communications
Prof. Hesham Tolba
Prof. Hesham Tolba
Digital Communications
86
43
5. Bandpass Digital ModulaBon
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Continuous-Phase FSK [CPFSK] …
ï$ in the transmitted
frequency from symbol 0 to symbol 1, or vice versa, is equal to
the bit rate of the incoming data stream.
q In Sunde’s BFSK, the overall excursion
q Another special form of CPFSK is known as minimum shift keying
(MSK).
q In MSK, the binary modulation process uses a different value
for the frequency excursion .
q This new modulated wave offers superior spectral properties
to Sunde’s BFSK.
11/3/20
Prof. Hesham Tolba
Digital Communications
87
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Binary FSK [BFSK] …
q A BFSK signal is described by
9- ' = n
7,
,:$
/0 &>9 ,-$- ' ,
$
7 ≤ ' ≤ 0$
Qm3QxyQiQ
where a = U, ,; :$ is the transmitted signal energy/bit; the
transmitted frequencies $- = (4$ E&)/#! for a fixed integer ñ! & a =
U, ,.
9& ' and 9" ' are orthogonal, but not normalized to
have unit energy.
q The signals
11/3/20
Digital Communications
Prof. Hesham Tolba
Prof. Hesham Tolba
Digital Communications
88
44
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Binary FSK [BFSK] …
q The most useful form for the set of orthonormal basis functions is
described by
'Z ![1 '() " ,
%
."
+3 " = Y
, ≤ " ≤ ."
,,
DQRDSTDID
where 6 = B, '
1%2 for where 6 = B, ' & X = B, ' is
q Correspondingly, the coefficient
(!
1%2 = < 1% " + 4 " ?"
=
11/3/20
'
(!
∫'
$5 !
Z(! K]R '()% "
Prof. Hesham Tolba
$Z K]R
(!
'()2 " ?"
Digital Communica=ons
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
89
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Binary FSK [BFSK] …
q Carrying out the integration, the
formula for 1%2 simplifies to
9-G = g
:$ ,
7,
a=S
a≠S
q Unlike BPSK, BFSK is characterized
by having a signal-space diagram
that is two-dimensional (C = ')
with two message points (^ = '),
as shown.
Signal-space diagram for binary
FSK system.
11/3/20
Digital CommunicaBons
Prof. Hesham Tolba
Prof. Hesham Tolba
Digital Communications
90
45
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Binary FSK [BFSK] …
q The two message points are defined by the vectors
9& =
%!
3
and
9" =
q The Euclidean distance
equal to
3
%!
9& − 9"
is
,:$.
q The shown figure also includes a
couple of waveforms representative
of signals 9& ' and 9" ' .
11/3/20
Prof. Hesham Tolba
Signal-space diagram for binary
FSK system.
Digital Communications
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
91
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Generation of BFSK Signals
q The shown block diagram that
describes a scheme for
generating the BFSK signal,
consists of:
q On–off level encoder, the
output of which is a
constant amplitude of in
response to input symbol 1
and zero in response to
input symbol 0.
11/3/20
Digital Communications
Prof. Hesham Tolba
Prof. Hesham Tolba
Block diagram for binary FSK
transmitter
Digital Communications
92
46
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Generation of BFSK Signals …
q Pair of oscillators,
q
$& and $" differ by an integer multiple of the bit rate
U/0$ in accordance with $- = (4$ E&)/#! , for a fixed integer ñ!
& a = U, ,.
q When the input symbol is 1, the upper oscillator is
switched on and signal 9& (') is transmitted, while the
lower oscillator is switched off, and vice-versa.
11/3/20
Prof. Hesham Tolba
Digital Communications
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
93
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Coherent Detection of BFSK Signals
q To coherently detect the original binary sequence given the
noisy received signal t('), we may use the shown receiver.
Block diagram for coherent BFSK receiver.
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Digital Communications
Prof. Hesham Tolba
Prof. Hesham Tolba
Digital Communications
94
47
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Coherent Detection of BFSK Signals
q It consists of two correlators with a common input, supplied
with locally generated coherent reference signals %& (') & %" (').
q The correlator outputs are then subtracted, one from the other;
the resulting difference ò is then compared with a threshold of
zero.
q If ò > 7, the receiver decides
in favor of 1.
ò < 7, it decides in favor
of 0.
q If
ò = 7, the receiver makes a
random guess in favor of 1 or
0.
q If
11/3/20
Block diagram for coherent BFSK
receiver.
Prof. Hesham Tolba
Digital Communications
95
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Error Probability of BFSK
t has two elements t& and t" that are
defined by, respectively
q The observation vector
#!
#!
t& ' = ; t ' %H ' <'
and
t" (') = ; t ' %? ' <'
%
%
where t ' is the received signal, whose form depends on which
symbol was transmitted.
t ' equals 9& ' + Ç('),
where Ç(') is the sample function of a white Gaussian noise
process of zero mean and power spectral density Z. /,.
q Given that symbol 1 was transmitted,
q If symbol 0 was transmitted,
11/3/20
Digital CommunicaBons
Prof. Hesham Tolba
t '
Prof. Hesham Tolba
equals 9& ' + Ç(').
Digital Communications
96
48
5. Bandpass Digital ModulaBon
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Error Probability of BFSK …
q Applying the decision rule of
&
Observation vector t lies in the region s- if ∑6
GI& tG 9@G − " :@
maximum for Å = a, where :@ is the transmitted energy
is
assuming the use of coherent detection
at the receiver, we find that the
observation space is partitioned into
two decision regions, labeled s& & s"
as shown.
q The receiver decides in favor of symbol
1 if the received signal point t falls
inside region s& , i.e., when t& > t" .
11/3/20
Prof. Hesham Tolba
Digital Communications
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
97
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Error Probability of BFSK …
t& < t" , the received signal point falls inside
and the receiver decides in favor of symbol 0.
q If we have
region s"
q To proceed further, we define a new Gaussian random variable
ö
whose sample value ò is
ò = t& − t"
q The mean value of the random variable
ö depends on which binary
symbol was transmitted.
õ&
and t" , have mean
q Given that symbol 1 was sent, the Gaussian random variables
and õ" , whose sample values are denoted by t&
values equal to :$ and zero, respectively.
11/3/20
Digital Communications
Prof. Hesham Tolba
Prof. Hesham Tolba
Digital Communications
98
49
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Error Probability of BFSK …
q Correspondingly, the conditional mean of the random variable
ö
given that symbol 1 was sent is
: ö|U = : t& |U − : t" |U
= + :$
t& and t"
have mean values equal to zero and − :$, respectively.
q Given that symbol 0 was sent, the random variables
q Correspondingly, the conditional mean of the random variable
ö
given that symbol 0 was sent is
: ö|7 = : t& |7 − : t" |7
= − :$
11/3/20
Prof. Hesham Tolba
Digital Communications
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
99
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Error Probability of BFSK …
q The variance of the random variable
ö is independent of which
binary symbol was sent.
õ& and õ" are statistically
independent, each with a variance equal to Z. /,, it follows
that
ùji ö = ùji õ& + ùji õ"
= Z.
q Suppose we know that symbol 0 was sent, the conditional
probability density function of the random variable ö is then
given by
"
U
ò + :$
$J ò|7 =
QRE −
,-Z.
,Z.
q Since the random variables
11/3/20
Digital Communications
Prof. Hesham Tolba
Prof. Hesham Tolba
Digital Communications
100
50
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Error Probability of BFSK …
t& > t" or, equivalently, ò > 7 corresponds
to the receiver making a decision in favor of symbol 1, we
deduce that the conditional probability of error given that
symbol 0 was sent is
q Since the condition
I&% = û ò > 7|3klDKm 7 xj3 3QNW
9
= ∫% $J ò|7 <ò
=
11/3/20
&
9
QRE
∫
%
":6%
Prof. Hesham Tolba
−
KE 7!
"6%
#
<ò
Digital Communications
101
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Error Probability of BFSK …
ò + :$ / Z. = u and changing the variable of
integration from ò to u, we may rewrite the previous equation
as
&
9
L#
7!
I&% =
∫ 7 /6 QRE − <u = Ü
q By setting
":
!
%
"
6%
I%& , the conditional probability of
error given that symbol 1 was sent, has the same value as in
the previous equation.
q Similarly, we may show the
I&% and I%& and assuming equiprobable symbols, we
find that the average probability of bit error (BER) for BFSK
using coherent detection is
q Averaging
I' = Ü
11/3/20
Digital Communications
Prof. Hesham Tolba
Prof. Hesham Tolba
7!
6%
Digital Communications
102
51
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Observations
q For a BFSK receiver to maintain the same BER as in a BPSK
receiver, the bit energy-to-noise density ratio, :$/Z. , has to
be doubled.
q This result is in perfect accord with their signal-space
diagrams, where we see that
q in a BPSK system the Euclidean distance between the two
message points is equal to , :$,
q in a BFSK system the corresponding distance is
,:$.
:$, the minimum distance <MNO in BPSK is,
times
that in BFSK.
,
q Recall that the probability of error decreases exponentially as
<"MNO ; hence the difference between the two BERs.
q For a prescribed
therefore,
11/3/20
Prof. Hesham Tolba
Digital Communica=ons
103
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Power Spectra of BFSK Signals
$& and $" differ by
an amount equal to the bit rate U/0$, and their arithmetic mean
equals the nominal carrier frequency $! ;
q Consider the case of Sunde’s FSK, for which
q As mentioned previously, phase continuity is always maintained,
including inter-bit switching times.
q We may express this special BFSK signal as a frequency-
modulated signal, defined by
9 ' =
11/3/20
Digital Communications
Prof. Hesham Tolba
-'
,:$
/0 JK3 ,-$! ' ±
,
$
0$
Prof. Hesham Tolba
Digital Communications
7 ≤ ' ≤ 0$
104
52
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Power Spectra of BFSK Signals
q We may reformulate
9 ' =
=
9 '
in the expanded form
,:$/ JK3 ± -' JK3 ,-$ ' − ,:$/ 3MN ± -' 3MN ,-$ '
!
!
0$
0$
0$
0$
,:$/ JK3 -' JK3 ,-$ ' ∓ ,:$/ 3MN -' 3MN ,-$ '
!
!
0$
0$
0$
0$
+ sign: transmitting symbol 0; - sign: transmitting symbol 1.
q Assuming that symbols 1 & 0 are equally likely and the symbols
transmitted in adjacent time slots are statistically
independent, we may make two observations on the in-phase and
quadrature components of a CP-BFSK signal.
11/3/20
Prof. Hesham Tolba
Digital Communications
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
105
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Power Spectra of BFSK Signals …
1.
The in-phase component
It is completely independent of the input binary wave.
2. It equals
,:$⁄0$ JK3 -'⁄0$ for all time '.
3. The PSD of this component consists of two delta functions
weighted by the factor :$⁄,0$ and occurring at $ = ± U⁄,0$.
1.
2.
The quadrature component
1. It is directly related to the input binary sequence.
2. During the signaling interval 7 ≤ ' ≤ 0$ , it equals −r(')
when we have symbol 1 and +r(') when we have symbol 0, with
r(') denoting a symbol-shaping function defined by
P " =Y
,,
11/3/20
Digital Communications
Prof. Hesham Tolba
("
'/"
Z. RUV
,
"
."
Prof. Hesham Tolba
, ≤ " ≤ ."
DQRDSTDID
Digital Communica=ons
106
53
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Power Spectra of BFSK Signals …
q The energy spectral density of
_6 ) =
{ '
is defined by
`/" ." K]R$ (." )
($ a.$" )$ − B
$
q The PSD of the quadrature component equals
üP $ /0$.
q The in-phase and quadrature components of the binary FSK signal
are independent of each other.
q Accordingly, the baseband PSD of Sunde’s FSK signal equals the
sum of the power spectral densities of these two components, as
shown by
/"
B
B
`/" ." K]R$ (." )
b7 ) =
'."
c )−
11/3/20
'."
+c )+
Prof. Hesham Tolba
'."
+
($ a.$" )$ − B
$
Digital Communications
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
107
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Power Spectra of BFSK Signals …
q Recalling that the following relationship between baseband
modulated power spectra is
TQ $ =
U
T $ − $! + T* $ + $!
? *
where $! is the carrier frequency.
q From the previous equations, we find that the power spectrum of
the BFSK signal contains two discrete frequency components, one
&
&
located at $! +
= $& and the other located at $! −
= $" ,
"#!
"#!
with their average powers adding up to U/, the total power of
the BFSK signal.
11/3/20
Prof. Hesham Tolba
Digital Communications
q The presence of these two discrete frequency components
108
provides a practical basis for synchronizing the receiver with
the transmitter.
Digital Communications
Prof. Hesham Tolba
54
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Power Spectra of BFSK Signals …
q The presence of these two discrete frequency components
provides a practical basis for synchronizing the receiver with
the transmitter.
q From the previous analysis, we may make the following
statement:
The baseband power spectral density of a binary FSK
signal with continuous phase ultimately falls off
as the inverse fourth power of frequency.
11/3/20
Prof. Hesham Tolba
Digital Communications
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
109
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Power Spectra of BFSK Signals …
q Plots of the baseband power spectra of
both BFSK & BPSK are as shown.
q The difference in the falloff rates of
these spectra can be explained on the
basis of the pulse shape { ' .
q The smoother the pulse, the faster the
drop of spectral tails to zero.
q Thus, since BFSK with continuous phase
has a smoother pulse shape, it has lower
sidelobes than BPSK does.
11/3/20
Digital Communications
Prof. Hesham Tolba
Prof. Hesham Tolba
Digital Communications
Power spectra of BPSK &
BFSK signals.
110
55
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Power Spectra of BFSK Signals …
q Suppose the FSK signal exhibits phase discontinuity at the
inter-bit switching instants, which arises when the two
oscillators supplying the basis functions with frequencies $&
and $" operate independently of each other.
q In this discontinuous scenario, we find that power spectral
density ultimately falls off as the inverse square of
frequency.
q Accordingly, we may state:
A binary FSK signal with continuous phase does not
produce as much interference outside the signal band
of interest as a corresponding FSK signal with
discontinuous phase does.
11/3/20
Prof. Hesham Tolba
Digital Communications
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
111
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Summary of BASK, BPSK & BFSK
q BASK, BPSK, and BFSK are the digital counterparts of AM, PM &
FM, respectively.
q Both BASK & BPSK exhibit discontinuity.
q It is possible to configure BFSK
in such a way that phase
continuity is maintained across
the entire input binary data
stream.
q The BFSK waveform plotted in part
(d) of the figure is an example
of minimum-shift keying, which
exhibits this property.
11/3/20
Digital Communications
Prof. Hesham Tolba
Prof. Hesham Tolba
The three basic forms of signaling
binary information. (a) Binary data
stream. (b) ASK. (c) PSK. (d) CPFSK
Digital Communications
112
56
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Summary of BASK, BPSK & BFSK …
q The shown table presents a summary of the three binary
modulation schemes: BASK, BPSK, and BFSK
11/3/20
Prof. Hesham Tolba
Digital Communications
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
113
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Minimum Shift Keying [MSK]
11/3/20
Digital Communications
Prof. Hesham Tolba
Prof. Hesham Tolba
Digital Communications
114
57
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Minimum-Shift Keying [MSK]
q In the coherent detection of BFSK signal, the phase information
contained in the received signal is not fully exploited, other
than to provide for synchronization of the receiver to the
transmitter.
q By proper use of the continuous-phase property when performing
detection it is possible to improve the noise performance of
the receiver significantly.
q This improvement is achieved at expense of increased system
complexity.
11/3/20
Prof. Hesham Tolba
Digital Communications
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
115
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Minimum-Shift Keying [MSK]
q Consider a CPFSK signal, defined for the signaling interval
' ≤ 0$ as:
9 ' =
,:$/ JK3 ,-$ ' + ã(7) ,
&
0$
hKi 3klDKm 7
,:$/ JK3 ,-$ ' + ã(7) ,
"
0$
hKi 3klDKm U
7≤
where :$ is the transmitted signal energy/bit, 0$ is the bit
duration, $& and $" represent binary symbols 1 and 0,
respectively.
ã(7), denoting the value of the phase at time ' =
,
sums
up
the
past history of the FM process up to time ' = 7.
7
q The new term
11/3/20
Digital Communications
Prof. Hesham Tolba
Prof. Hesham Tolba
Digital Communications
116
58
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Minimum-Shift Keying [MSK] …
q Using the phase of the previous bit, guarantee phase continuity
➞ MSK is called Modulation with memory.
q Another useful way of representing the CPFSK signal
9(') is to
express it as a conventional angle-modulated signal:
9 ' =
,:$/ JK3 ,-$ ' + ã(')
!
0$
where ã(') is the phase of 9(') at time '.
ã(') is a continuous function of time, we find
that the modulated signal 9(') is itself also continuous at all
times, including the inter-bit switching times.
q When the phase
11/3/20
Prof. Hesham Tolba
Digital Communications
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
117
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Minimum-Shift Keying [MSK] …
q The phase
!(#) of a CPFSK signal increases or decreases
linearly with time during each bit duration of 0$ seconds, as
shown by
-†
ã ' =ã 7 ±
',
7 ≤ ' ≤ 0$
0$
where the “+” corresponds to sending symbol 1 and the “-”
corresponds to sending symbol 0; the dimensionless parameter †
is to be defined.
ã ' into 9 ' , and then comparing the previous two
equations representing 9 ' , we deduce the following pair of
relations:
†
†
$! +
= $& &
$! −
= $"
,0$
,0$
q Substituting
11/3/20
Digital Communications
Prof. Hesham Tolba
Prof. Hesham Tolba
Digital Communica=ons
118
59
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Minimum-Shift Keying [MSK] …
q Solving this pair of equations for
$! =
and
$! and †, we get
U
$ + $"
, &
† = 0$ $& − $"
$! is, therefore, the arithmetic
mean of the transmitted frequencies $& and $" .
q The nominal carrier frequency
$& and $" , normalized
with respect to the bit rate U/0$, defines the dimensionless
parameter †, which is referred to as the deviation ratio.
q The difference between the frequencies
11/3/20
Prof. Hesham Tolba
Digital Communica=ons
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
119
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Minimum-Shift Keying [MSK] …
q From
ã ' =ã 7 ±
:R
#!
', 7 ≤ ' ≤ 0$
⟹
ã 0$ − ã 7 = É
-†, hKi 3klDKm U
−-†, hKi 3klDKm 7
q That is, sending “1” increases the phase of a CPFSK signal
by -† radians, sending “0”
9 '
reduces it by an equal amount.
ã ' with time ' follows a path
consisting of a sequence of straight lines, the slopes of which
represent frequency changes.
q The variation of phase
11/3/20
Digital Communications
Prof. Hesham Tolba
Prof. Hesham Tolba
Digital Communications
120
60
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Minimum-Shift Keying [MSK] …
q Possible paths starting from
' = 7, are as shown.
q This plot is called a phase tree.
q The tree makes clear the transitions
of phase across successive signaling
intervals.
q The phase of a CPFSK signal is an
odd or even multiple of -† radians
at odd or even multiples of the bit
duration 0$, respectively.
11/3/20
Prof. Hesham Tolba
phase tree
Digital Communications
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
121
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Minimum-Shift Keying [MSK] …
q Sunde’s FSK case:
q In this case, the deviation ratio
† is exactly unity.
q The phase change over one bit interval is
±- radians.
+- radians is exactly the same as a change
of −- radians, modulo ,-.
q But, a change of
q It follows, therefore, that in the case of Sunde’s FSK there
is no memory.
q That is, knowing which particular change occurred in the
previous signaling interval provides no help in the current
signaling interval.
11/3/20
Digital Communications
Prof. Hesham Tolba
Prof. Hesham Tolba
Digital Communica=ons
122
61
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Minimum-Shift Keying [MSK] …
† = U/,, the phase can take on only the
two values ±-/, at odd multiples of 0$, and only the two values
0 and - at even multiples of 0$, as shown.
q When the deviation ratio
q This second graph is called a phase trellis, since a “trellis”
is a treelike structure with re-emerging branches.
q Each path from left to right through the
trellis corresponds to a specific binary
sequence at the transmitter input.
q For example, the path shown in boldface
corresponds to the binary sequence
1101000 with ã 7 = 7.
11/3/20
Prof. Hesham Tolba
Phase trellis; boldfaced path
represents the sequence 1101000
Digital Communications
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
123
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Minimum-Shift Keying [MSK] …
† = U/, because the phase can take on only the two
values ±-/, and the two values 0 & -, at odd multiples of 0$
and even multiples of 0$, respectively.
q We focus on
† = U/,, the frequency deviation (i.e., the difference
between the $& and $" ) equals ½ the bit rate.
q With
q Hence,
The frequency deviation % = '/) is the
minimum frequency spacing that allows the
two FSK signals representing symbols 1 and
0 to be coherently orthogonal.
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Prof. Hesham Tolba
Digital Communications
124
62
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Minimum-Shift Keying [MSK] …
q In other words, symbols 1 and 0 do not interfere with one
another in the process of detection.
q It is for this reason that a CPFSK signal with a deviation
ratio of one-half is commonly referred to as minimum shiftkeying (MSK).
ï$ from binary symbol 1
to symbol 0, or vice versa, is ½ the bit rate, as shown by
q In MSK, the overall frequency excursion
&
ï$ = $& − $" = "#
!
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Prof. Hesham Tolba
Digital Communications
125
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Minimum-Shift Keying [MSK]
q The unmodulated carrier frequency is the arithmetic mean of the
two transmitted frequencies $& and $" ; that is
$! =
U
$ + $"
, &
$& and $" in terms of the carrier frequency $! and
overall frequency excursion ï$, we have
q Expressing
$& = $! +
11/3/20
Digital Communications
Prof. Hesham Tolba
ï$
, for symbol 1.
,
Prof. Hesham Tolba
&
$" = $! −
Digital Communications
ï$
, for symbol 0
,
126
63
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Minimum-Shift Keying [MSK] …
q Accordingly, we formally define the MSK signal as the angle-
modulated wave
,:$/
0$ &>9 ,-$! ' + ã(')
9 ' =
where ã(') is the phase of the MSK signal.
q When
$& is transmitted (symbol 1), ã(') assumes the value
ST
:3
for symbol 1
ã ' = ,- " ' = "# ,
!
q When $" is transmitted (symbol 0), ã(') assumes the value
ã ' = ,- −
ST
"
:3
' = − "# ,
!
for symbol 0
' = 0$, the transmission of symbol 0
decreases the phase of 9 ' by :⁄" radians.
q This means that at time
11/3/20
Prof. Hesham Tolba
Digital Communica=ons
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
127
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Example – OQPSK vs. MSK
OQPSK signal components
(a) Modulating signal for in-phase
component.
(b) Modulated waveform of in-phase
component.
(c) Modulating signal for quadrature
component.
(d) Modulated waveform of quadrature
component.
(e) Waveform of OQPSK signal obtained
by subtracting (d) from (b).
11/3/20
Digital Communications
Prof. Hesham Tolba
Prof. Hesham Tolba
Digital Communica=ons
128
64
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Example – OQPSK vs. MSK
…
MSK signal components
(a) Modulating signal for in-phase
component.
(b) Modulated waveform of in-phase
(c) Modulating signal for
quadrature component
(d) Modulated quadrature component.
(e) Waveform of MSK signal obtained
by subtracting (d) from (b).
11/3/20
Prof. Hesham Tolba
Digital Communications
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
129
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Observations
q Comparing the results plotted in the previous two figures, we
may make the following observation.
q Although the OQPSK and MSK are derived from different
modulation principles, the MSK from FSK and the OQPSK from PSK,
these two digitally modulated waves are indeed closely related.
q The basic difference between them lies merely in the way in
which the binary symbols in their in-phase and quadrature
components are level-encoded.
q In OQPSK, the level-encoding is based on rectangular pulses,
with one binary wave shifted from the other binary wave by one
bit duration.
q In MSK, the level-encoding is based on the half cycle of a
cosinusoid.
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Digital Communications
Prof. Hesham Tolba
Prof. Hesham Tolba
Digital Communications
130
65
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Observations …
q Similar to OQPSK, MSK is encoded with bits alternating
between quadrature components, with the Q component delayed by
half the symbol period.
q However, instead of square pulses as OQPSK uses, MSK encodes
each bit as a half sinusoid.
q This results in a constant-modulus signal (constant envelope
signal), which reduces problems caused by non-linear
distortion.
11/3/20
Prof. Hesham Tolba
Digital Communica=ons
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
131
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Formulation of MSK
q Comparing the results plotted in the previous two figures, we
may make the following observation.
9 ' =
,:$/ JK3 ã(') JK3 ,-$ ' − ,:$/ 3MN ã(') 3MN ,-$ '
!
!
0$
0$
q In light of this equation, we make two identifications:
q
9( ' =
:$ JK3 ã(')
with the carrier
q
is the in-phase (I ) component associated
"
/#! JK3 ,-$! ' .
9) ' = :$ 3MN ã(') is the quadrature-phase (Q ) component
associated with the the the 90∘-phase shifted-carrier.
11/3/20
Digital Communications
Prof. Hesham Tolba
Prof. Hesham Tolba
Digital Communications
132
66
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Formulation of MSK …
q Reformulating the previous equation, we can write
9( ' = Y& ' JK3 ,-$. ' ,
9) ' = Y" (') 3MN ,-$. ' .
Y& ' & Y" (') are two binary waves that are extracted from
the incoming binary data stream through demultiplexing and
offsetting, in a manner similar to OQPSK.
q The
q As such, they take on the value +1 or -1 in symbol intervals of
duration 0 = ,0$ where 0$ is the bit duration of the incoming
binary data stream.
q
Y& ' & Y" (') are respectively weighted by the sinusoidal
functions JK3 ,-$. ' & 3MN ,-$. ' , where $. is to be determined.
11/3/20
Prof. Hesham Tolba
Digital Communica=ons
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
133
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Formulation of MSK …
$. , we use the previous equations to reconstruct the
original angle-modulated wave 9(') in terms of the data signals
Y& ' & Y" (').
q To define
q In so doing, we obtain
ã ' = − tanB&
= − tanB&
11/3/20
Digital Communications
Prof. Hesham Tolba
9) '
9( '
Y" '
tan ,-$. '
Y& '
Prof. Hesham Tolba
Digital Communications
134
67
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Formulation of MSK …
q on the basis of which we recognize two possible scenarios that
can arise:
1.
The Y? ' = YH(') scenario arises when two successive binary
symbols (constituting a dibit) in the incoming data stream
are the same (i.e., both are 0s or 1s); hence,
ã ' = − tanB& tan ,-$. '
2.
= − ,-$. '
The Y? ' = −YH(') scenario arises when two successive binary
symbols (constituting a dibit) in the incoming data stream
are different; hence,
ã ' = tanB& tan ,-$. '
11/3/20
Prof. Hesham Tolba
= ,-$. '
Digital Communications
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
135
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Formulation of MSK …
q The two previous equations are respectively of similar
mathematical forms as
ã ' = ,-
ST
"
ã ' = ,- −
:3
' = "# ,
ST
"
!
for symbol 1
:3
' = − "# ,
!
for symbol 0
q Accordingly, we may now formally define
&
$. = ;#
!
11/3/20
Digital Communications
Prof. Hesham Tolba
Prof. Hesham Tolba
Digital Communications
136
68
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Formulation of MSK …
q To sum up, given a non-return-to-zero level encoded binary wave
of prescribed bit duration 0$ and a sinusoidal carrier wave of
frequency $! we may formulate the MSK signal by proceeding as
follows:
1.
Use the given binary wave 4 ' to construct the binary
demultiplexed-offset waves Y& ' & Y" (').
2.
Use $. =
3.
Use 9( ' = Y& ' JK3 ,-$. ' & 9) ' = Y" (') 3MN ,-$. ' to determine the
in-phase component and quadrature component respectively
from which the MSK signal 9 ' follows.
&
;#!
to determine the frequency $. .
11/3/20
Prof. Hesham Tolba
Digital Communications
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
137
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Formulation of MSK …
d , is , or ( depending on the past history of the
modulation process, we find that in the interval −." ≤ " ≤ ." , the
polarity of cos d " depends only on d(,), regardless of the sequence
of 1s and 0s transmitted before or after " = ,.
q Since the phase
q Thus, for this time interval, the in-phase component consists of the
half-cycle cosine pulse:
'/"
Z. K]R d "
"
= e# " K]R '()* "
18 " =
=
=±
11/3/20
Digital Communications
Prof. Hesham Tolba
$5!
Z(! K]R d ,
$5!
Z(! K]R
K]R
9
"
$(!
9
"
$(!
, −." ≤ " ≤ ."
Prof. Hesham Tolba
Digital Communica=ons
“+” for ã 7 = 7
“-” for ã 7 = -.
138
69
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Formulation of MSK …
7 ≤ ' ≤ ,0$,
consists of the half-cycle sine
q In a similar way, we may show that, in the interval
the quadrature component of 9 '
pulse:
,:$/ 3MN ã '
0$
= Y" ' 3MN ,-$. '
9) ' =
=
"7!
=±
11/3/20
/#! 3MN ã 0$
"7!
/#! 3MN
:
"#!
3MN
' ,
:
"#!
'
0 ≤ ' ≤ 20$
Prof. Hesham Tolba
“+” for ã 0$ = -/,
“-” for ã 0$ = −-/,.
Digital Communications
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
139
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Formulation of MSK …
q
The in-phase and quadrature components of the MSK signal differ from each
other in:
q they are in phase quadrature with respect to each other and
q the polarity of the in-phase component V0 " depends on W 3 , whereas the
polarity of the quadrature component V1 " depends on W @! .
q
Since the phase states W 3 & W @! can each assume only one of two possible
values, any one of the following four possibilities can arise:
1. W 3 = 3 and W @! = L/9, which occur when sending symbol 1.
2. W 3 = L and W @! = L/9, which occur when sending symbol 0.
3. W 3 = L and W @! = −L/9 (or, equivalently, YL/9 modulo 9L), which occur
when sending symbol 1.
4. W 3 = 3 and W @! = −L/9, which occur when sending symbol 0.
q
This fourfold scenario means that the MSK signal itself can assume one of
four possible forms, depending on the values of the phase-state pair: W 3
and W @! .
11/3/20
Digital Communications
Prof. Hesham Tolba
Prof. Hesham Tolba
Digital Communications
140
70
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Signal Space Diagram
%H ' and %? '
characterizing the generation of MSK are defined by the
following pair of sinusoidally modulated quadrature carriers:
q The two orthonormal basis functions
'Z K]R ( K]R '() " ,
!
."
'."
(
+? " = 'Z. RUV
RUV '()! " ,
"
'."
+> " =
, ≤ " ≤ ."
, ≤ " ≤ ."
q With the formulation of a signal-space diagram, we may rewrite
9 '
in a compact form as
9 ' = 9& %& ' + 9" %" ' ,
7 ≤ ' ≤ 0$
where the coefficients 9& and 9" are related to the phase
states ã 7 & ã 0$ , respectively.
11/3/20
Prof. Hesham Tolba
Digital Communications
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
141
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Signal Space Diagram …
q To evaluate
1# & 1$ :
(!
$(!
1# = < 1 " +# " ?"
@(!
= /" K]R d(,) ,
1$ = < 1 " +$ " ?"
'
−." ≤ " ≤ ."
= /" RUV d(." ) ,
, ≤ " ≤ ."
q Examining the previous equations leads to three observations:
Both integrals are evaluated for a time interval equal to twice
the bit duration.
2. The lower and upper limits of the integral in (7.190) used to
evaluate s1 are shifted by the bit duration Tb with respect to
those used to evaluate s2.
3. The time interval , ≤ " ≤ ." , for which the phase states d , &
d ." are defined, is common to both integrals.
1.
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Digital Communications
Prof. Hesham Tolba
Prof. Hesham Tolba
Digital Communications
142
71
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Signal Space Diagram …
q It follows, therefore, that the signal
constellation for an MSK signal is
two-dimensional (Z = ,), with four
possible message points (! = ?), as
shown.
q In a counterclockwise direction, the
coordinates of the message points
are:(+ :$, + :$), (− :$, + :$),
(− :$, − :$), (+ :$, − :$).
q The signal-space diagram of MSK is
similar to that of QPSK:both of them
have four message points in a twodimensional space.
11/3/20
Prof. Hesham Tolba
Signal-space diagram for
MSK system.
Digital Communications
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
143
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Signal Space Diagram …
q In QPSK: moving from one message
point to an adjacent one, is
produced by sending a two-bit symbol
(i.e., dibit).
q In MSK: moving from one message
point to an adjacent one, is
produced by sending a binary symbol,
0 or 1.
q Each symbol shows up in two
opposite quadrants, depending on
the value of the phase-pair: ã(7)
& ã(0$).
11/3/20
Digital Communications
Prof. Hesham Tolba
Prof. Hesham Tolba
Digital Communications
Signal-space diagram for
MSK system.
144
72
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Signal Space Diagram …
ã(7) &
ã(0$), as well as the corresponding values of 9& & 9" that are
calculated for the time intervals −0$≤ ' ≤ 0$ & 7 ≤ ' ≤ ,0$,
respectively.
q The shown table presents a summary of the values of
11/3/20
Prof. Hesham Tolba
Digital Communications
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
145
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Signal Space Diagram …
q The 1st column of this table indicates whether symbol 1 or
symbol 0 was sent in the interval 7 ≤ ' ≤ 0$.
9& & 9" , have opposite
signs when symbol 1 is sent in this interval, but the same sign
when symbol 0 is sent.
q The coordinates of the message points,
q Accordingly, for a given input data sequence, we may use the
entries of the table to derive on a bit-by-bit basis the two
sequences of coefficients required to scale %& ' & %" ' , and
thereby determine the MSK signal 9(').
11/3/20
Digital Communications
Prof. Hesham Tolba
Prof. Hesham Tolba
Digital Communications
146
73
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Example …
q The sequences and waveforms
involved in the generation of an
MSK signal for the binary
sequence 1101000 are as shown.
q
$& = ®/?0$ & $" = }/?0$.
' = 7, ã 7 = 7; the sequence of
phase states is as shown, modulo
,-.
q At
11/3/20
Prof. Hesham Tolba
Digital Communica=ons
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
147
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Example …
q The polarities of the two sequences of factors used to scale
the time functions %H '
11/3/20
Digital Communications
Prof. Hesham Tolba
and %? '
Prof. Hesham Tolba
are as shown.
Digital Communications
148
74
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Example …
q These two sequences are offset
relative to each other by an
interval equal to the bit duration
0$ .
q The waveforms of the resulting two
components of 9('), namely,9H%H '
9?%? ' , are shown.
and
q Adding these two modulated
waveforms, we get the desired MSK
signal 9(') shown.
11/3/20
Prof. Hesham Tolba
Digital Communications
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
149
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Generation of MSK Signals
† = U/,, the shown block diagram may be used to generate
the MSK signal.
q With
Block diagram for MSK transmitter.
11/3/20
Digital Communications
Prof. Hesham Tolba
Prof. Hesham Tolba
Digital Communications
150
75
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Generation of MSK Signals
q The advantage of this method is that the signal coherence and
deviation ratio are largely unaffected by variations in the
input data rate.
$! = ñ! /?0$ & the
other of frequency U/?0$) are applied to a product modulator to
produce two phase-coherent sinusoidal waves at frequencies $& &
$" .
q Two input sinusoidal waves (one of frequency
%H ' &
,
which
are
multiplied
with
two
binary
waves
%? '
jH ' & Y? ' ,
both of which have a bit rate equal to U/,0$.
q The filter outputs are linearly combined to produce
11/3/20
Prof. Hesham Tolba
Digital Communications
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
151
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Coherent Detection of MSK Signals
q The block diagram of the coherent MSK receiver is as shown.
Block diagram coherent MSK receiver.
11/3/20
Digital Communications
Prof. Hesham Tolba
Prof. Hesham Tolba
Digital Communications
152
76
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Coherent Detection of MSK Signals …
q In both cases, the integration interval is 20$ seconds, and the
integration in the quadrature channel is delayed by 0$ seconds
with respect to that in the in-phase channel.
q The resulting in-phase and quadrature channel correlator
outputs, t& & t" , are each compared with a threshold of zero;
estimates of the phase ã(7) & ã(0$) are then derived in the
manner described previously.
q These phase decisions are interleaved so as to estimate the
original binary sequence at the transmitter input with the
minimum average probability of symbol error in an AWGN channel.
11/3/20
Prof. Hesham Tolba
Digital Communications
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
153
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Error Probability of MSK …
q In the case of an AWGN channel, the received signal is given by
t ' =9 ' +Ç '
where 9 ' is the transmitted MSK signal and Ç ' is the sample
function of a WGN process of zero mean and PSD Z. /,.
q To decide whether symbol 1 or symbol 0 was sent in the interval
7 ≤ ' ≤ 0$, say, a procedure for the use of t ' to detect the
phase states ã(7) & ã 0$ has to be stablished.
11/3/20
Digital CommunicaBons
Prof. Hesham Tolba
Prof. Hesham Tolba
Digital Communica=ons
154
77
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Error Probability of MSK
ã(7), the received signal t ' is
projected onto the reference signal %& ' over the interval −0$≤
' ≤ 0$, obtaining
q For the optimum detection of
@"
*2 = +
=
Z@"
*(#),2 # -# = .2 + 02
1! 234 !(5) + 02 ,
−7! ≤ # ≤ 7!
the sample value of a
Gaussian RV of zero
mean and variance >% /9.
11/3/20
Prof. Hesham Tolba
Digital Communications
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
155
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Error Probability of MSK …
t& > 7, the receiver chooses
© 7 = 7; if t& < 7, it chooses the estimate ã
© 7 = -.
the estimate ã
q From the signal-space diagram: if
ã 0$ , the received
signal t ' is projected onto the reference signal %" ' over the
interval 7 ≤ ' ≤ ,0$, obtaining,
q Similarly, for the optimum detection of
"#!
t" = ;
%
=
t(')%" ' <' = 9" + Ç"
:$ 3MN ã(7) + Ç" ,
7 ≤ ' ≤ 0$
the sample value of
another Gaussian RV of
zero mean and variance
6%/".
t" > 7, the receiver chooses
©
the estimate ã 0$ = −-/,; if t" < 7, it chooses the estimate
© 0$ = -/,.
ã
q From the signal-space diagram: if
11/3/20
Digital Communications
Prof. Hesham Tolba
Prof. Hesham Tolba
Digital Communications
156
78
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Error Probability of MSK …
q To reconstruct the original binary sequence, we interleave the
above two sets of phase estimates in accordance with the
previous table, by proceeding as follows:
© 7 =7 & ã
© 0$ = −-/,, or alternatively if ã
© 7 =
q If estimates ã
©
- & ã 0$ = −-/, , then the receiver decides in favor of
symbol 0.
© 7 =- & ã
© 0$ = −-/,, or alternatively if ã
© 7 =
q If estimates ã
© 0$ = -/,, then the receiver decides in favor of symbol
7 & ã
1.
q From the signal-space diagram, the coordinates of the four
message points characterizing the MSK signal are identical to
those of the QPSK signal.
11/3/20
Prof. Hesham Tolba
Digital Communications
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
157
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Error Probability of MSK …
q The zero-mean noise variables in the previous equations have
exactly the same variance as those for the QPSK signal
mentioned previously.
q It follows, therefore, that the BER for the coherent detection
of MSK signals is given by
I' = Ü
"7!
6%
which is the same as that of QPSK.
q In both MSK and QPSK, this good performance is the result of
coherent detection being performed in the receiver on the basis
of observations over ,0$ seconds.
11/3/20
Digital Communications
Prof. Hesham Tolba
Prof. Hesham Tolba
Digital Communications
158
79
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Power Spectra of MSK Signals
q Assume that the input binary wave is random, with symbols 1 and 0
being equally likely and the symbols sent during adjacent time slots
being statistically independent.
q Under these assumptions, three observations were made:
1.
Depending on the value of phase state d(,), the in-phase component
equals +g(") or −g("), where the pulse-shaping function
("
'/"
Z. K]R
,
P " =Y
"
'."
,,
q The energy spectral density of
−." ≤ " ≤ ."
DQRDSTDID
g(") is
h'/" ." K]R '(." )
_6 ) =
($
Bi.$" )$ − B
11/3/20
Prof. Hesham Tolba
$
Digital Communications
159
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Power Spectra of MSK Signals …
q The PSD of the in-phase component equals
üP $ /,0$.
2. Depending on the value of phase state ã(0$), the in-phase
component equals +r(') or −r('), where the pulse-shaping
function
P " =Y
("
'/"
Z. RUV
,
"
'."
,,
, ≤ " ≤ '."
DQRDSTDID
q Despite the difference in which the time interval over two
adjacent time slots is defined, we get the same energy
spectral density as in
h'/" ." K]R '(." )
_6 ) =
($
Bi.$" )$ − B
11/3/20
Digital Communications
Prof. Hesham Tolba
Prof. Hesham Tolba
Digital Communica=ons
$
160
80
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Power Spectra of MSK Signals …
q Hence, the in-phase and quadrature components have the
same PSD.
3.
The in-phase and quadrature components of the MSK signal
are statistically independent;
q It follows that the baseband power spectral density of 9(')
is given by
üP $
T* $ = ,
,0$
=
<"7! #! UVW ":#! T
:#
&X##! T# B&
"
q A plot of the baseband power spectrum is shown in the next
slide.
11/3/20
Prof. Hesham Tolba
Digital Communications
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
161
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Power Spectra of MSK Signals …
) ≫ B/." the baseband power spectral density of the MSK signal
falls off as the inverse fourth power of frequency,
q For
q In the case of the QPSK signal it falls
off as the inverse square of frequency.
q Accordingly, MSK does not produce as
much interference outside the signal
band of interest as QPSK does.
q This is a desirable characteristic of
MSK, especially when the digital
communication system operates with a
bandwidth limitation in an interfering
environment.
11/3/20
Digital Communications
Prof. Hesham Tolba
Prof. Hesham Tolba
Digital Communications
Power spectra of QPSK and MSK
signals.
162
81
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Summary
† = 7. ®.
† = 7. ® corresponds to the minimum frequency spacing that allows
two FSK signals to be coherently orthogonal,
The name MSK implies the minimum frequency separation that
allows orthogonal detection.
MSK is attractive because the phase continuity yields high
spectral efficiency, and the constant-envelope yields excellent
power efficiency.
q Phase discontinuity (for example QPSK) ➞ a relatively large
percentage of the power to occur outside of the intended band
(e.g., high fractional out-of-band power), leading to poor
spectral efficiency.
The primary drawback is the high implementation complexity
required for an optimal receiver.
q MSK is a special type of CPFSK with a deviation ratio
q
q
q
q
11/3/20
Prof. Hesham Tolba
Digital Communications
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
163
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Observations
q The desirable properties of MSK are as follows
q modulated signal with constant envelope;
q relatively narrow-bandwidth occupancy;
q coherent detection performance equivalent to that of QPSK.
q The out-of-band spectral characteristics of MSK signals do not
satisfy the stringent requirements of certain applications such
as wireless communications.
q This practical limitation of MSK can be overcome by modifying
its power spectrum into a more compact form while maintaining
the constant-envelope property of the MSK signal.
q This modification can be achieved through the use of a
premodulation LPF (a baseband pulse-shaping-filter).
11/3/20
Digital Communications
Prof. Hesham Tolba
Prof. Hesham Tolba
Digital Communications
164
82
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Observations …
q The pulse-shaping filter should satisfy the following
conditions:
q Frequency response with narrow BW and sharp cutoff
characteristics
qto suppress the high-frequency components of the modified
frequency-modulated signal.
q Impulse response with relatively low overshoot;
qto avoid excessive deviations in the instantaneous
frequency of the modified frequency-modulated signal.
11/3/20
Prof. Hesham Tolba
Digital Communica=ons
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
165
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Observations …
q Evolution of a phase trellis with the carrier phase of the
modulated signal assuming the two values ±-/, at odd
multiples of the bit duration 0$ and the two values 0 and at even multiples of 0$ as in MSK.
qTo ensure that the modified frequency-modulated signal can
be coherently detected in the same way as the MSK signal,
or it can be noncoherently detected as a simple binary FSK
signal if so desired.
q These conditions can be satisfied by passing an NRZ-level-
encoded binary data through a baseband pulse-shaping filter
whose impulse response is defined by a Gaussian function.
q The resulting method of binary FM is referred to as Gaussian-
filtered minimum-shift keying (GMSK).
11/3/20
Digital Communications
Prof. Hesham Tolba
Prof. Hesham Tolba
Digital Communica=ons
166
83
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Gaussian Minimum Shift
Keying [MSK]
11/3/20
Prof. Hesham Tolba
Digital Communications
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
167
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Gaussian MSK [GMSK]
q GMSK is similar to standard minimum-shift keying (MSK);
however, the digital data stream is first shaped with
a Gaussian filter before being applied to a frequency modulator
q GMSK typically has much narrower phase shift angles than most
MSK modulation systems.
q This has the advantage of reducing sideband power, which in
turn reduces out-of-band interference between signal carriers
in adjacent frequency channels.
11/3/20
Digital Communications
Prof. Hesham Tolba
Prof. Hesham Tolba
Digital Communications
168
84
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Gaussian MSK [GMSK] …
q Let
k denote the 3-dB baseband BW of the pulse-shaping filter.
q We may then define the transfer function
m "
l )
and impulse response
of the pulse-shaping filter as:
$
'(
'($ $ $
ln ' )
and
m
"
=
kDEF
−
k "
l ) = DEF −
p
ln '
ln '
'
k
q The response of this Gaussian filter to a rectangular pulse of unit
amplitude and duration ." , centered on the origin, is given by
(!/$
P " =<
m " − q ?q
@(!/$
=
(!/$
'(
'($ $
k<
DEF −
k "−q
ln '
ln '
@(!/$
11/3/20
Prof. Hesham Tolba
$
?q
Digital Communications
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
169
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Gaussian MSK [GMSK] …
{ ' provides the basis for building the GMSK
modulator, with the dimensionless time–bandwidth product 20$
playing the role of a design parameter.
q The pulse response
{ ' is noncausal and,
therefore, not physically realizable for real-time operation.
q Unfortunately, the pulse response
{ ' is nonzero for ' < −0$/,, where ' = −0$/, is
the time at which the input rectangular pulse (symmetrically
positioned around the origin) is applied to the Gaussian
filter.
q Specifically,
q For a causal response,
{ '
must be truncated and shifted in
time.
11/3/20
Digital CommunicaBons
Prof. Hesham Tolba
Prof. Hesham Tolba
Digital Communications
170
85
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Gaussian MSK [GMSK] …
q The shown Figure presents plots of
{ ' , which has been truncated at ' =
± ,. ®0$ and then shifted in time by
' = ,. ®0$.
q The plots shown here are for three
different settings: 20$ = 7. ,, 7. ,®
and 7. }.
20$ is reduced, the time spread
of the frequency-shaping pulse is
correspondingly increased.
q As
Frequency-shaping pulse 6 B shifted in
time by $. C(! and truncated at = ±$. C(!
for varying time–BW product F(! .
11/3/20
Prof. Hesham Tolba
Digital Communications
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
171
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Gaussian MSK [GMSK] …
q Power spectra of MSK and GMSK for
varying time-BW product are as
shown.
q The curve for the limiting condition
20$ = ∞ corresponds to the case of
ordinary MSK.
20$ < U, increasingly more of
the transmit power is concentrated
inside the passband of the GMSK
signal.
q When
11/3/20
Digital Communications
Prof. Hesham Tolba
Prof. Hesham Tolba
Power spectra of MSK and GMSK signals
for varying time–bandwidth product.
Digital Communications
172
86
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Gaussian MSK [GMSK] …
q The processing of NRZ binary data by a Gaussian filter
generates a modulating signal that is no longer confined to a
single bit interval as in ordinary MSK, as shown.
q That is, the tails of the Gaussian impulse response of the
pulse-shaping filter cause the modulating signal to spread out
to adjust symbol intervals.
q The net result is the generation of ISI, the extent of which
increases with decreasing 20$.
20$ offers a tradeoff between spectral compactness and system performance loss.
q The value assigned to the time–BW product
11/3/20
Prof. Hesham Tolba
Digital Communications
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
173
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Gaussian MSK [GMSK] …
q Recognizing that GMSK is a special kind of binary FM, we may
express its average probability of symbol error I' in the
presence of AWGN by the empirical formula
I' = Ü
Y7!
6%
where, :$ is the signal energy per bit and Z. /, is the noise
spectral density, ´ is a constant whose value depends on the
time–bandwidth product 20$.
11/3/20
Digital Communications
Prof. Hesham Tolba
Prof. Hesham Tolba
Digital Communica=ons
174
87
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Gaussian MSK [GMSK] …
q The Gaussian filter increases the modulation memory in the
system and causes intersymbol interference.
q This leads to more difficult differentiation between different
transmitted data values ➞ more complex channel equalization
algorithms such as an adaptive equalizer at the receiver.
q GMSK has high spectral efficiency, but it needs a higher power
level than QPSK, for instance, in order to reliably transmit
the same amount of data.
q GMSK is most notably used in the Global System for mobile
communications (GSM) and the satellite communications, e.g. in
the Automatic Identification System (AIS) for maritime
navigation.
11/3/20
Example
Prof. Hesham Tolba
Digital Communications
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
175
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
q An important application of GMSK is in a standardized wireless
communication system known as GSM.
20$ of GSMK is standardized at 0.3, which
provides the best compromise between increased BW occupancy and
resistance to co-channel interference.
q For this application
q 99% of the RF power of GMSK signals is confined to a BW of 250
kHz (i.e., the sidelobes are virtually zero outside this
frequency band).
q The available spectrum is divided into 200 kHz-wide
subchannels.
q Each subchannel is assigned to as GSM system transmitting data
at 271 kb/s.
11/3/20
Digital Communications
Prof. Hesham Tolba
Prof. Hesham Tolba
Digital Communications
176
88
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Example …
q The power spectrum of a subchannel
in relation to its two adjacent
subchannels is as shown.
q The RF power spectrum of the
subchannel shown shaded is down by
an amount larger than 40 dB at the
carrier frequencies of both adjacent
subchannels.
q This means that the effect of co-
channel interference is practically
negligible.
11/3/20
Prof. Hesham Tolba
Power spectrum of GMSK signal
for GSM wireless communications.
Digital Communications
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
177
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Noncoherent Digital
Modulation Schemes
11/3/20
Digital Communications
Prof. Hesham Tolba
Prof. Hesham Tolba
Digital Communications
178
89
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Noncoherent Digital Modulation Schemes
q Coherent receivers require knowledge of the carrier wave’s
phase reference to establish synchronism with their respective
transmitters.
q In some communication environments, it is either impractical or
too expensive to phase-synchronize a receiver to its
transmitter.
q In situations of this kind, we resort to the use of noncoherent
detection by abandoning the use of phase synchronization
between the receiver and its transmitter.
q Doing so, the receiver performance is degraded in the presence
of channel noise.
11/3/20
Prof. Hesham Tolba
Digital Communications
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
179
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Noncoherent Detection of BASK Signals
q The generation of BASK signals involves the use of a single
sinusoidal carrier of frequency $! for symbol 1 and switching
off the transmission for symbol 0.
q The system designer would have knowledge of two system
parameters: $! & transmission BW, which is determined by the
bit duration 0$.
q It is therefore natural to make use of these known parameters
in designing the noncoherent receiver for BASK.
q The receiver consists of a BPF, followed by an envelope
detector, then a sampler, and finally a decision-making device,
as shown in the next slide.
11/3/20
Digital Communications
Prof. Hesham Tolba
Prof. Hesham Tolba
Digital Communications
180
90
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Noncoherent Detection of BASK Signals …
Noncoherent BASK receiver; the integer for the sampler equals %, ±&, ±", …
$! and a BW
equal to the transmission bandwidth of the BASK signal.
q The BPF is designed to have a mid-band frequency
q It is assumed that the ISI produced by the filter is
negligible, which, in turn, requires that the rise time and
decay time of the response of the filter to a rectangular pulse
be short compared to the bit duration 0$.
11/3/20
Prof. Hesham Tolba
Digital Communications
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
181
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Noncoherent Detection of BASK Signals …
q The BPF produces a pulsed sinusoid for symbol 1 & ideally, no
output for symbol 0.
q The envelope detector traces the envelope of the filtered
version of the BASK signal.
q The decision-making device working in conjunction with the
sampler, regenerates the original binary data stream by
comparing the sampled envelope-detector output against a preset
threshold every seconds; this operation assumes the
availability of bit-timing in the receiver.
q In the absence of channel noise and channel distortion, the
output (on a bit-by-bit basis) would be an exact replica of the
original binary data stream applied to the transmitter.
11/3/20
Digital Communications
Prof. Hesham Tolba
Prof. Hesham Tolba
Digital Communications
182
91
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Noncoherent Detection of BFSK Signals
q
In the case of BFSK, the transmissions of symbols 1 and 0 are represented by
two carrier waves of frequencies [" & [# respectively, with adequate spacing
between them.
q
In light of this characterization, we may build on the noncoherent detection
of BASK by formulating the shown noncoherent BFSK receiver.
Noncoherent BFSK receiver; the two samplers operate synchronously, with - = %, ±&, ±", …
11/3/20
Prof. Hesham Tolba
Digital Communications
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
183
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Noncoherent Detection of BFSK Signals …
q The receiver consists of two paths, one dealing with frequency
$& & the other dealing with frequency $" :
q Path 1 uses a BPF of mid-band frequency $& .
qThe filtered version of the incoming BFSK signal is
envelope-detected and then sampled at time ' = a0$, a =
7, ±U, ±,, … to produce the output ¨& .
q Path 2 uses a BPF of mid-band frequency $" .
qThe filtered version of the BFSK signal is envelopedetected and then sampled at time ' = a0$, a = 7, ±U, ±,, to
produce a different output ¨" .
q The two BPFs have the same BW, equal to the transmission BW of
the BFSK signal.
11/3/20
Digital Communications
Prof. Hesham Tolba
Prof. Hesham Tolba
Digital Communications
184
92
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Noncoherent Detection of BFSK Signals …
q The ISI produced by the filters is assumed to be negligible.
¨& & ¨" are applied to a
comparator, where decisions on the composition of the BFSK
signal are repeated every seconds.
q The outputs of the two paths,
q The availability of bit timing is assumed in the receiver.
q Recognizing that the upper path corresponds to symbol 1 and the
lower path corresponds to symbol 0, the comparator decides in
favor of “1” if is greater than at the specified bit-timing
instant; otherwise, the decision is made in favor of “0”.
q In noise-free environment & no channel distortion, the receiver
output (on a bit-by-bit basis) would be a replica of the
original binary data stream applied to the transmitter input.
11/3/20
Prof. Hesham Tolba
Digital Communications
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
185
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Differential PSK [DPSK]
q Both ASK & FSK lend themselves naturally to noncoherent detection
whenever it is impractical to maintain carrier-phase
synchronization.
q In case of PSK, we cannot have noncoherent detection because the
term “noncoherent” means having to do without carrier-phase
information.
q To get around this difficulty, we employ a “pseudo PSK” technique
known as differential PSK (DPSK), which permits the use of
noncoherent detection.
q DPSK eliminates the need for a coherent reference signal at the
receiver by combining two basic operations at the transmitter:
q Differential encoding of the input binary wave.
q PSK.
11/3/20
Digital Communications
Prof. Hesham Tolba
Prof. Hesham Tolba
Digital Communications
186
93
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Differential PSK [DPSK] …
q In DPSK,
q To send symbol 0, we phase advance the current signal waveform by
180∘, and
q To send symbol 1 we leave the phase of the current signal waveform
unchanged.
q Correspondingly, the receiver is equipped with a storage capability
(i.e., memory) designed to measure the relative phase difference
between the waveforms received during two successive bit intervals.
q Provided the unknown phase r varies slowly (i.e., slow enough for it
to be considered essentially constant over two bit intervals), the
phase difference between waveforms received in two successive bit
intervals will be essentially independent of r.
11/3/20
Prof. Hesham Tolba
Digital Communications
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Generation of
187
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
DPSK Signals
q The differential encoding process at the transmitter input starts
with an arbitrary 1st bit, serving merely as reference.
?& denote the differentially encoded sequence with this
added reference bit.
q Let
?& , the transmitter performs the following two
operations:
q If the incoming binary symbol s & is 1, then the symbol ? & is
unchanged with respect to the previous symbol ?&@# .
q If the incoming binary symbol s & is 0, then the symbol ? & is
changed with respect to the previous symbol ?&@# .
q To generate
?& is used to phase-shift a sinusoidal carrier
wave with phase angles 0 and W radians, representing symbols 1 and
0, respectively.
q The generated
11/3/20
Digital Communications
Prof. Hesham Tolba
Prof. Hesham Tolba
Digital Communications
188
94
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Generation of DPSK Signals …
q The DPSK transmitter consists, as shown, of a logic network and a
one-bit delay element (acting as the memory unit) interconnected so
as to convert the raw binary sequence s& into a differentially
encoded sequence ?& .
q This sequence is amplitude-level encoded and then used to modulate a
carrier wave of frequency )! thereby producing the desired DPSK
signal.
Block diagram for DPSK transmitter
11/3/20
Prof. Hesham Tolba
Digital Communications
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
189
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Detection of DPSK Signals
q In DPSK, the phase-modulated pulses pertaining to two
successive bits are identical except for a possible sign
reversal.
q Hence, the preceding pulse serves the purpose of a locally
generated reference signal.
q On this basis, we may formulate the shown receiver for the
detection of DPSK signals.
Block diagram for DPSK receiver; for the sampler, integer - = %, ±&, ±", …
11/3/20
Digital Communications
Prof. Hesham Tolba
Prof. Hesham Tolba
Digital Communications
190
95
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Detection of DPSK Signals …
q Comparing the DPSK detector and the coherent BPSK detector, we
see that the two receiver structures are similar except for the
source of the locally generated reference signal.
q Given knowledge of the reference bit inserted at the very
beginning of the incoming binary data stream, the DPSK signal
is detectable.
q In particular, applying the sampled output of the LPF to a
decision-making device supplied with a prescribed threshold,
detection of the DPSK signal is accomplished.
q If the threshold is exceeded, the receiver decides in favor of
symbol 1; otherwise, the decision is made in favor of symbol 0.
q It is assumed that the receiver is supplied with bit-timing
information for the sampler to work properly.
11/3/20
Prof. Hesham Tolba
Digital Communica=ons
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
191
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Generation/Detection of DPSK Signals …
Block diagrams of (a) DPSK transmitter and
(b) DPSK receiver.
11/3/20
Digital Communications
Prof. Hesham Tolba
Prof. Hesham Tolba
Digital Communica=ons
192
96
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Example
4@ given in the 1st row
of the shown table and using symbol 1 as the 1st reference bit,
we may construct the differentially encoded stream <@ in row
3 of the table.
q Starting with the binary data stream
Illustration of the Generation and Detection of DPSK Signal
11/3/20
Prof. Hesham Tolba
Digital Communications
193
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Example …
q The 2nd row is the delayed version of
<@
by one bit.
k, the symbol <@ is the complement of the modulo2 sum of 4@ and <@B& .
q For each index
q The 4th row defines the phase of the transmitted DPSK signal.
q The last two rows pertain to the DPSK receiver.
q Row 5 of the table defines the polarity (positive or
negative) of the LPF output in the receiver.
q The final row of the table defines the binary data stream
produced at the receiver output, which is identical to the
input binary data stream at the top of the table, as it should
be in a noise-free environment.
11/3/20
Digital Communications
Prof. Hesham Tolba
Prof. Hesham Tolba
Digital Communications
194
97
5. Bandpass Digital ModulaBon
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
"-ary Digital Modulation
Schemes
11/3/20
Prof. Hesham Tolba
Digital Communications
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
195
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
!-ary Digital Modulation Schemes
!-ary digital modulation scheme, we send
any one of ! possible signals 9& ' , 9" ' , …, 9, ' , during each
signaling (symbol) interval of duration 0.
q By definition, in an
! = ,] where X is an integer.
q Under this condition, the symbol duration 0 = X0$ , where 0$ is
the bit duration.
q In almost all applications,
!-ary modulation schemes are preferred over binary
modulation schemes for transmitting digital data
over bandpass channels when the requirement is to
conserve bandwidth at the expense of both increased
power and increased system complexity.
11/3/20
Digital Communications
Prof. Hesham Tolba
Prof. Hesham Tolba
Digital Communications
196
98
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
"-ary Digital Modulation Schemes …
q In practice, we rarely find a communication channel that has
the exact bandwidth required for transmitting the output of an
information-bearing source by means of binary modulation
schemes.
Thus, when the BW of the channel is less than
the required value, we resort to an 9-ary
modulation scheme for maximum BW conservation.
11/3/20
Prof. Hesham Tolba
Digital Communications
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
197
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
"-ary PSK
!-ary modulation schemes for BW conservation
can be illustrated by considering first the transmission of
information consisting of a binary sequence with bit duration
0$ .
q The capability of
q Using binary PSK, for example, we would require a channel BW
that is inversely proportional to the bit duration 0$.
X bits to produce a symbol and
use an !-ary PSK scheme with ! = ,] and symbol duration 0 =
X0$, then the BW required is proportional to U/(X0$).
q However, if we take blocks of
!-ary PSK provides
a reduction in transmission bandwidth by a factor X = log " !
over binary PSK.
q This simple argument shows that the use of
11/3/20
Digital Communications
Prof. Hesham Tolba
Prof. Hesham Tolba
Digital Communications
198
99
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
"-ary PSK …
!-ary PSK, where the phase of the
carrier takes one of ! possible values, namely ã- = (,a − U) :⁄,,
where a = U, ,, … , !.
q QPSK is a special case of
q During each interval of duration
0, one of the ! possible
signals
9- ' =
,:/ &>9 ,-$! ' + ,- (a − U) ,
0
!
a = U, ,, … , !
is sent, where : is the signal energy/symbol, $! = ñ! /0 for some
fixed integer ñ! .
11/3/20
Prof. Hesham Tolba
Digital Communications
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
199
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
"-ary PSK …
q Using a well-known trigonometric identity, we may expand the
previous equation as
9- ' =
−
,(a − U)
!
,: 3MN
a−U
!
: JK3
q The discrete coefficients
,/ JK3 ,-$! '
0
,/ 3MN ,-$! ' ,
0
: JK3
":
(a − U)
,
a = U, ,, … , !
and − : 3MN
":
,
a−U
are respectively referred to as the in-phase and quadrature
components of the !-ary PSK signal 9- ' .
11/3/20
Digital Communications
Prof. Hesham Tolba
Prof. Hesham Tolba
Digital Communications
200
100
5. Bandpass Digital ModulaBon
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
"-ary PSK …
q That is,
: JK3
":
(a − U)
,
"
+
: 3MN
":
,
a−U
"
= :
for all a
!-ary PSK modulation has the unique property that
the in-phase and quadrature components of the modulated signal
9- ' are interrelated in such a way that the discrete envelope
of the signal is constrained to remain constant at the value :
for all !.
q Accordingly,
11/3/20
Prof. Hesham Tolba
Digital Communications
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
201
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
"-ary PSK …
q The modulation strategy of QPSK is an example of
M-ary PSK with
the number of phase levels ! = ?.
9- ' may be expanded in terms of the two orthonormal basis
functions %& ' & %" ' :
q Each
%& ' =
%? ' =
11/3/20
Digital Communications
Prof. Hesham Tolba
,/ JK3 ,-$! ' ,
0
7≤'≤0
,/ 3MN ,-$! ' ,
0
7≤'≤0
Prof. Hesham Tolba
Digital Communications
202
101
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
"-ary PSK …
q The scaling factor
"⁄
#
assures unit
energy over the interval 0 for both
%& ' & %" ' .
q On this basis, we may represent the
in-phase and quadrature component for
a = U, ,, … , ! as a set of points in this
two dimensional diagram, as shown for
! = é.
q The signal constellation of
M-ary PSK
is two-dimensional.
11/3/20
Prof. Hesham Tolba
Digital Communications
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
203
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
!-ary PSK …
! message points are
equally spaced on a circle of
radius : and center at the
origin, as illustrated, for
the case of octaphase shiftkeying.
q The
q As shown, the signal-space
diagram is circularly
symmetric.
q The squared length from the
origin to each signal point is
equal to the signal energy :.
11/3/20
Digital CommunicaBons
Prof. Hesham Tolba
Prof. Hesham Tolba
(a) Signal-space diagram for octaphaseshift keying (i.e., , = ^). The
decision boundaries are shown as dashed
lines. (b) Signal-space diagram
illustrating the application of the
union bound for octaphase-shift keying.
Digital Communica=ons
204
102
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
"-ary PSK …
q Suppose that the transmitted signal corresponds to the message
point X- , whose coordinates along the %& - and %" -axes are + :
& 0, respectively.
:/Z. is large
enough to consider the nearest two message
points, on either side of X& , as optional
candidates for being mistaken for X& due to
channel noise, as shown for the case ! = é.
q Suppose that the ratio
q The Euclidean distance of each of these
two points from XH is
<&" = <&^ = , : 3MN
11/3/20
Prof. Hesham Tolba
!
Digital Communications
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
"-ary PSK …
q Hence, using
205
;
U
<-@
I' ≤ ∞ QihJ
,
,
,
Z
.
@I&
hKi jmm a
@_-
yields the average probability of symbol error for coherent !ary PSK as
:
I' ≈ QihJ
3MN
Z.
!
where it is assumed that ! ≥ ?.
! = ?, the previous equation reduces to the same form given
for QPSK.
q For
11/3/20
Digital Communications
Prof. Hesham Tolba
Prof. Hesham Tolba
Digital Communications
206
103
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Power Spectra of !-ary PSK
!-ary PSK is defined by 0 = 0$ log " ! ,
where 0$ is the bit duration.
q The symbol duration of
q Proceeding in a manner similar to
that described for a QPSK signal,
we may show that baseband PSD of
an !-ary PSK signal is given by
T* $ = ,:3MNJ " 0$
= ,:$ log " ! 3MNJ " 0$$ log " !
T* $ /2:$ versus the
normalized frequency $0$ for
! = 2, 4, 8 are shown.
q Plots of
11/3/20
Power spectra of ,-ary PSK signals
for , = 2, 4, 8.
Prof. Hesham Tolba
Digital Communications
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
207
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
BW Efficiency of !-ary PSK
!-ary PSK signals possess a main lobe
bounded by well-defined spectral nulls.
q The power spectra of
q The spectral width of the main lobe provides a simple and
popular measure for the BW of !-ary PSK.
!-ary PSK signals (the main
"
spectral lobe of !-ary signals) is given by C = Where 0 is
#
the symbol duration (recall that 0 = 0$ log " ! ).
q The channel BW required to pass
q Hence, we may redefine the BW in terms of the bit rate
C=
11/3/20
Digital Communications
Prof. Hesham Tolba
B$ as
,B$
log " !
Prof. Hesham Tolba
Digital Communications
208
104
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
BW Efficiency of !-ary PSK …
q Based on this formula, the BW efficiency of
!-ary signals is
given by
B$ log " !
=
C
,
q The shown table gives the values
of calculated from the previous
equation for varying !.
±=
BW efficiency of ,-ary PSK signals.
As the number of states, !, is increased, the BW efficiency
is improved at the expense of error performance.
q To ensure that there is no degradation in error performance, we
have to increase :$/Z. to compensate for the increase in !.
11/3/20
Prof. Hesham Tolba
Digital Communications
209
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
"-ary QAM
q Suppose next that the constraint of
/ K]R
$9
(6
G
− B)
$
+
/ RUV
$9
G
6−B
$
= /
for all 6
that characterizes !-ary PSK modulation is removed.
q Then, the in-phase & quadrature components of the resulting !ary modulated signal are permitted to be independent of each
other.
q The mathematical description of the new modulated signal has
the form
1% " =
11/3/20
Digital Communications
Prof. Hesham Tolba
'/*Z
'/*Z
. e% K]R '()! " −
. s% RUV '()! " ,
Prof. Hesham Tolba
Digital Communications
6 = B, ', … , ^
210
105
5. Bandpass Digital ModulaBon
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
!-ary QAM …
Y- in the in-phase component and
the level parameter 4- in the quadrature component are
independent of each other for all a.
q Note that he level parameter
q This new modulation scheme is called
≤-ary quadrature
amplitude modulation (QAM).
:. is the energy of the signal
pertaining to a particular value of the index a for which the
amplitude of the modulated signal is the lowest.
q Note also that the constant
q
!-ary QAM is a hybrid form of !-ary modulation, in the sense
that it combines amplitude-shift keying & phase-shift keying.
11/3/20
Prof. Hesham Tolba
Digital Communications
211
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
!-ary QAM …
q It includes two special cases:
i.
If 4- = 7 for all a, the modulated signal 9- '
equation reduces to
9- ' =
,:./ Y JK3 ,-$ ' ,
!
0 -
of the previous
a = U, ,, … , !
which defines !-ary amplitude-shift keying (!-ary ASK).
&/"
:. = : and the constraint :Y"- + :4"= :, for all a is
satisfied, then the modulated signal 9- ' reduces to !-ary
PSK as in
,9- ' = ,:/0 &>9 ,-$! ' +
(a − U) ,
a = U, ,, … , !
!
ii. If
11/3/20
Digital Communications
Prof. Hesham Tolba
Prof. Hesham Tolba
Digital Communications
212
106
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
"-ary QAM …
q The shown figure portrays the signal-space representation of
!-ary QAM for ! = Uì, with each signal point being defined by a
pair of level parameters Y- and 4- , where a = U, ,, }, ?.
(a) Signal-space diagram of G-ary QAM for G = #H; the message points in each quadrant are
identified with Gray-encoded quadbits. (b) Signal-space diagram of the corresponding 4-PAM signal.
11/3/20
Prof. Hesham Tolba
Digital Communica=ons
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
213
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
"-ary QAM …
q The signal points are distributed uniformly on a rectangular grid.
q The rectangular property of the signal-space diagram is testimony to
the fact that the in-phase and quadrature components of ^-ary QAM
are independent of each other.
^-ary PSK, the different signal points of ^-ary QAM are
characterized by different energy levels, and so they should be.
q Unlike
q Each signal point in the constellation corresponds to a specific
quadbit, which is made up of 4 bits.
q Assuming the use of Gray encoding, only one bit is changed as we go
from each signal point in the constellation horizontally or
vertically to an adjacent point, as illustrated.
11/3/20
Digital CommunicaBons
Prof. Hesham Tolba
Prof. Hesham Tolba
Digital Communica=ons
214
107
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
"-ary FSK
!-ary FSK, the transmitted signals are defined
for some fixed integer ñ as follows:
9- ' = ,:/0 &>9
(ñ + a) ,
7 ≤ ' ≤ 0,
a = U, ,, … , !
0 !
q In one form of
where $! = ñ! ⁄,0 for some integer value ñ! .
q The ! transmitted signals are all of equal duration 0 and
equal energy :.
q With the individual signal frequencies separated from each
other by U/[,0] Hz, the signals in the previous equation are
orthogonal; i.e., they satisfy the condition
:, hKi a = S
#
∫% 9- ' 9G ' <' = É7, hKi a ≠ S
11/3/20
Prof. Hesham Tolba
Digital Communications
215
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
"-ary FSK …
9- ' themselves,
except for energy normalization, as a complete orthonormal set
of basis functions, as shown by
q Hence, we may use the transmitted signals
%d ' =
U
:
9- ' ,
hKi 7 ≤ ' ≤ 0,
a = U, ,, … , !
!-ary FSK is described by an !-dimensional
signal-space diagram.
q Accordingly, the
!-ary FSK signals, the optimum
receiver consists of a bank of ! correlators or matched
filters, with %d ' providing the basis functions.
q For the coherent detection of
11/3/20
Digital Communications
Prof. Hesham Tolba
Prof. Hesham Tolba
Digital Communica=ons
216
108
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
"-ary FSK …
' = Å0, the receiver makes decisions based
on the largest matched filter output in accordance with the ML
decoding rule.
q At the sampling times
q An exact formula for the probability of symbol error is,
however, difficult to derive for a coherent !-ary FSK system.
q We may use the union bound to place an upper bound on the
average probability of symbol error for !-ary FSK.
11/3/20
Prof. Hesham Tolba
Digital Communications
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
217
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
"-ary FSK …
<MNO in !-ary FSK is
equiprobable symbols, we get
q Since the minimum distance
I' ≤ (! − U)Ü
,:, assuming
:
Z.
!, this bound becomes increasingly tight as the
ratio :⁄Z. is increased.
q For fixed
q It is a good approximation to
q For
I' for values of I' ≤ U7B< .
! = , (i.e., BFSK), the above-bound of becomes an equality.
11/3/20
Digital Communications
Prof. Hesham Tolba
Prof. Hesham Tolba
Digital Communications
218
109
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Power Spectra of !-ary FSK Signals
!-ary FSK signals is much more
complicated than that of !-ary PSK signals.
q The spectral analysis of
q A case of particular interest occurs
when the frequencies assigned to the
multilevels make the frequency
spacing uniform and the frequency
deviation † = U/,.
! signal frequencies
are separated by U/,0, where 0 is the
symbol duration.
q That is, the
† = U/,, the baseband power
spectral density of !-ary FSK
signals is as shown for ! = ,, ?, é.
q For
11/3/20
Prof. Hesham Tolba
Power spectra of G-ary PSK signals
for G = $, -, J.
Digital Communications
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
219
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Bandwidth Efficiency of !-ary FSK Signals
!-ary FSK signal are
detected coherently, the adjacent signals need only be
separated from each other by a frequency difference U/,0 so as
to maintain orthogonality.
q When the orthogonal signals of an
q Hence, we may define the channel bandwidth required to transmit
!-ary FSK signals as
C=
!
,0
q For multilevels with frequency assignments that make the
frequency spacing uniform and equal to U/,0, the bandwidth C
contains a large fraction of the signal power.
11/3/20
Digital Communications
Prof. Hesham Tolba
Prof. Hesham Tolba
Digital Communications
220
110
5. Bandpass Digital Modulation
11/3/20
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Bandwidth Efficiency of !-ary FSK Signals …
0 = 0$ log " !, using B$ = U/0$, we
may redefine the channel bandwidth C for !-ary FSK signals as
q Recalling that the symbol period
C=
q The bandwidth efficiency of
±=
11/3/20
B$ !
, log " !
!-ary signals is therefore
B$ , log " !
=
C
!
Prof. Hesham Tolba
Digital Communications
Introduction
Some Preliminaries
Binary ASK [BASK]
Binary PSK [BPSK]
Quadriphase Shift Keying [QPSK]
221
Binary FSK [BFSK]
Minimum Shift Keying [MSK]
Gaussian MSK [GMSK]
Noncoherent Digital Modulation Schemes
! -ary Digital Modulation Schemes
Bandwidth Efficiency of !-ary FSK Signals …
q The shown table gives the values of
± for varying !.
! tends to increase the
bandwidth efficiency of !-ary PSK signals, but it also tends
to decrease the bandwidth efficiency of !-ary FSK signals.
q Increasing the number of levels
!-ary PSK signals are spectrally efficient,
whereas !-ary FSK signals are spectrally inefficient.
q In other words,
11/3/20
Digital Communications
Prof. Hesham Tolba
Prof. Hesham Tolba
Digital Communications
222
111