ensc327 communication systems 27: digital bandpass ... · 7.2 binary amplitude-shift keying (bask)...
TRANSCRIPT
ENSC327
Communication Systems
27: Digital Bandpass Modulation
(Ch. 7)
1
Jie Liang
School of Engineering Science
Simon Fraser University
Outline
� 7.1 Preliminaries
� 7.2 Binary Amplitude-Shift Keying (BASK)
� 7.3 Phase-Shift Keying (PSK)
� 7.4 Frequency-shifting Keying (FSK)
2
� 7.4 Frequency-shifting Keying (FSK)
� 7.7 M-ary Digital Modulation
� 7.8 Mapping of digitally modulated waveforms onto
constellations of signal points
7.1 Preliminaries
� If the channel is low-pass (e.g., coaxial cable), we can transmit
the pulses corresponding to digital data directly.
� If the channel is band-pass (e.g. wireless, satellite), we need to
use the digital data to modulate a high-freq sinusoidal carrier:
)2cos()( tfAtc φπ +=
3
)2cos()(ccc
tfAtc φπ +=
1. and 0represent to and 0 use : πφc
� Amplitude-Shift Keying (ASK):
� Use two Ac’s to represent 0 and 1.
� Phase-Shift Keying (PSK):
� Frequency-Shift Keying (ASK):
� use two fc’s to represent 0 and 1.
7.1 Preliminaries
� The amplitude of the carrier is usually chosen as
such that the carrier has unit energy measured over
.2
b
c
TA =
4
such that the carrier has unit energy measured over
one bit duration.
7.2 Binary Amplitude-Shift Keying
(BASK)
� In BASK, the modulated wave is
==
0. symbolfor ,0
1, symbolfor ),2cos(2
)2cos(2
)()(tf
T
E
tfT
tbts c
b
b
c
b
ππ
5
� This is a special case of Amplitude Modulation (AM):
( ) ,)2cos()(1)( tftmkAtscacπ+=
� Therefore the BASK spectrum has a carrier component.
� Envelope detector can be used to demodulate the digital signal.
� b(t) is the on-off signalling coding of the input binary data.
7.2 Binary Amplitude-Shift Keying
(BASK)
� The average transmitted signal energy is
6
7.3 Phase-Shift Keying (PSK)
� We first consider binary PSK (BPSK):
−=+
=
0. symbolfor ),2cos(2
)2cos(2
1, symbolfor ),2cos(2
)(
tfT
Etf
T
E
tfT
E
ts
c
b
c
b
c
b
b
πππ
π
7
−=+ 0. symbolfor ),2cos()2cos( tfT
tfT
c
b
c
b
πππ
� The two possible values are called antipodal signals.
� A special case of DSB-SC:
� No carrier component in the freq domain.
� BPSK has constant envelope � constant transmitted power. Desired in
many systems.
� But cannot use envelope detector in the receiver, need coherent
detection.
7.3 Phase-Shift Keying (PSK)
� Detection of BPSK signals:
� Coherent DSB-SC receiver
� Sample & decision-making: new to digital communication
� Can reduce error rate. Advantage over analog comm.
8
Quadriphase-Shift Keying (QPSK)
� Recall Chap 3.5: Quadrature-amplitude modulation (QAM):
� Transmit two DSB-SC signals in the same spectrum region.
� Use two modulators with orthogonal carriers.
9
)2sin()()2cos()()( :signal dTransmitte21
tftmAtftmAtsccccππ +=
� The two signals do not affect each other.
Quadriphase-Shift Keying (QPSK)
� QAM can be generalized to digital modulation
� In QPSK, the transmitted signal has four possible phases:
π/4, 3π/4, 5π/4, 7π/4.
≤≤−+= ,0 ),
4)12(2cos(
2)(
TtitfT
Ets c
i
π
π
i=1i=2
10
=
elsewhere. ,04)( Tts
i
� Index i: 1, 2, 3, 4.
� Each signal can represent two bits of binary data, called dibits.
� Tb: bit duration.
� T: Symbol duration.
� It’s easy to see that the energy of si(t) is E. This is the Symbol Energy.
� Since each symbol represents 2 bits, the average transmitted energy per bit
is
i=3 i=4
Quadriphase-Shift Keying (QPSK)
�To see the link with QAM:
≤≤−+=
elsewhere. ,0
,0 ),4
)12(2cos(2
)(Ttitf
T
Ets c
i
π
π
22 EEπ
π
π
π
−−−=
11
)2sin(2
)()2cos(2
)(
)2sin()4
)12sin((2
)2cos()4
)12cos((2
)(
21tf
Ttatf
Tta
tfiT
Etfi
T
Ets
cc
cci
ππ
π
π
π
π
+=
−−−=
Quadriphase-Shift Keying (QPSK)
� Detection of QPSK:
� Similar to QAM
� Two coherent BPSK detectors.
)2sin(2
)()2cos(2
)()(21
tfT
tatfT
tatscciππ +=
12
� Two coherent BPSK detectors.
7.4 Frequency-Shift Keying (FSK)
=
=
=
2. i toscorrespond 0 symbolfor ),2cos(2
1, i toscorrespond 1 symbolfor ),2cos(2
)(
1
tfE
tfT
E
tsb
b
b
i
π
π
� Binary FSK (BFSK): symbol 0 and 1 are represented
by two sinusoidal waves with different frequencies
13
� f1 and f2 can be chosen such that neighboring signals
have continuous phases. This can reduce the bandwidth of
the transmitted waveforms.
� This is called the Sunde BFSK.
= 2. i toscorrespond 0 symbolfor ),2cos(
22tf
T
E
b
bπ
Frequency-Shift Keying (FSK)
� Example:
14
Continuous phase
can reduce bandwidth
7.7 M-ary Digital Modulation
� M-ary PSK
� M-ary QAM
� M-ary FSK
� Mapping waveforms to signal points
15
� Mapping waveforms to signal points
7.7 M-ary Digital Modulation
� During each symbol interval of duration T, the
transmitter sends one of M possible signal s1(t), …,
sM(t). M is usually a power of 2: M = 2^m.
� M-ary modulation is necessary if we want to conserve
16
M-ary modulation is necessary if we want to conserve
the bandwidth.
� But M-ary system needs more power and more
complicated implementation to achieve the same
error rate as binary system.
M-ary Phase-Shift Keying
� Generalization of the QPSK
.0 1,-M0,...,i ),2
2cos(2
)( TtiM
tfT
Ets
ci≤≤=+=
π
π
� This can be expressed as
17
Signal Space Diagram
� As the increase of M, the receiver of the M-ary
modulation can become more complicated, because
for each input symbol, a naive receiver needs to
compare with M references.
18
� It is thus necessary to simplify the signal
representation and therefore reduce the complexity of
the receiver.
� The concept of signal space is useful here.
Signal Space Diagram
� The signals si(t) can be written as
19
� We can visualize the transmitted signals as points in a
K-dimensional space, with axes { })(tjφ
M-ary Phase-Shift Keying
� In M-ary PSK: ( ) ( ).2sin22
sin2cos22
cos)( tfT
iM
EtfT
iM
Etscciπ
π
π
π
−
=
� We can define two orthonormal basis functions:
20
� {si(t)} can be represented by
points on a signal space diagram.
� The coordinate of each point:
8-PSK
� In MPSK, the distance from the origin to
each point is equal to the signal energy E.
M-ary QAM
� Recall Chap 3.5: QAM
)2sin()()2cos()()(21
tftmAtftmAtsccccππ +=
� If m1(t) and m2(t) are discrete, we get digital QAM:
22 EEππ −=
21
).2sin(2
)2cos(2
)( 00 tfbT
Etfa
T
Ets
ciciππ −=
� Example of signal space
diagram: 16-QAM
Possible values for ai, bi:
-3, -1, 1, 3.
Envelope is not constant.
Mapping of Modulated Waveforms
to Constellations of Signal Points
� The correlator method is used in receiver in many systems:
� Calculate the correlation of input with a pulse template,
� Sample the output of the correlator,
� Compare the sample with some thresholds to decode the bits.
� For example, in BPSK, the template is simply the basis function:
22
function:
).2cos(2
)(1
tfT
tc
b
πφ =
� If the transmitter sends s1(t):
its correlation with the basis function is:
Mapping of Modulated Waveforms
to Constellations of Signal Points
� If the transmitter sends s2(t):
its correlation with the basis function is:
� This can be represented by a one-dimensional diagram:
23
� This can be represented by a one-dimensional diagram:
Mapping of Modulated Waveforms
to Constellations of Signal Points
� This diagram is useful in studying the effect of the noise.
� When noise is considered, the received signal will be
noise. is )( ),()()( tntntstriiii
+=
� The output of the correlator will be
24
( ) .)()()()()('0
10
1 ii
T
ii
T
iiivsdtttnsdtttntss
bb
+=+=+= ∫∫ φφ
� The output of the correlator will be
The noise ni(t) introduces some disturbs to the position of the desired point on the signal space diagram.
Decoding could be wrong if the noise is too large.
BPSK:
Mapping of Modulated Waveforms
to Constellations of Signal Points
� BFSK:
).2cos(/2)(
),2cos(/2)(11
tfTEts
tfTEtsbb
π
π
=
=
� The transmitted signals can be written as:
25
).2cos(/2)(
),2cos(/2)(
22
11
tfTt
tfTt
b
b
πφ
πφ
=
=
).2cos(/2)(22tfTEts
bbπ=
� The receiver takes correlation of the received signal with two basis functions:
Mapping of Modulated Waveforms
to Constellations of Signal Points
� If s1(t) is sent, the outputs of the two correlators are:
26
� If s2(t) is sent, the outputs are:
Mapping of Modulated Waveforms
to Constellations of Signal Points
� So each signal can be represented by a point on a 2-D diagram:
φ
27
1φ
2φ
The noise introduces some disturbs to the position of the desired point on the signal space diagram.
Decoding could be wrong if the noise is too large.
Mapping of Modulated Waveforms
to Constellations of Signal Points
� Compare the diagrams of BPSK and BFSK, we can see that the distance of the two points are
� Since noise changes the position of the signal in the signal
28
� Since noise changes the position of the signal in the signal space diagram at the receiver, we can see from these figures that BPSK is more robust to noise than the BFSK.
� This will be studied in details in Chapter 10.
2bE
2bE
BPSK:BFSK: