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ECE 4710: Lecture #26 1
BPSK
BPSK m(t) is binary baseband signal, e.g. mi = ±1 and i = 1, 2
Two possible phase states for carrier » i = 0°, 180° for mi = ±1
Polar form of complex envelope
Signal Constellation Diagrams Plot g(t) in polar coordinate system Visual representation of modulation format
)](2cos[)](2cos[)( ttfAtmDtfAts ccpcc
ijceAtg )(
ECE 4710: Lecture #26 2
BPSK Signal Constellation
iip jc
mDjc eAeAtg )(
cj
c AeAtg 0)(
BPSK2,11 imi
"1"11 m
cj
c AeAtg 180)(
"0"12 m
“1”“0”Real
(In-Phase)
Imaginary
(Quadrature)
0jceA
)(tg
180jceA
cAcA
signal digital level- 2 DACbit M
ECE 4710: Lecture #26 3
Digital input information signal, m(t), with more than two levels used as input to Tx modulator Generate multi-level bandpass signal “Level” is misleading
» Implies signal amplitude» Could be multi-frequency or multi-phase signal
Serial binary input converted to multi-level signal by DAC
Multi-Level Signaling
(sps) (bps) 1 R
DT
Rb
ECE 4710: Lecture #26 4
Multi-Level Signaling
t
T1 0 0 1 0 0 1 1
T1 0
0 10 0 1 1 t
Binary Input
M = 4-Level DAC Output
ECE 4710: Lecture #26 5
QPSK & MPSK
Multi-level digital input to Phase Modulator (PM) M-ary Phase Shift Keying MPSK
For M = 4 Quadrature Phase Shift Keying QPSK
QPSK m(t) is multi-level baseband signal, e.g. mi = -3,-1,+1,+3
Four possible phase states for carrier Quadrature phase states 90° difference
» i = 0°, 90°, 180°, and 270° for mi = -3,-1,+1,+3
/4 QPSK Quadrature phase states
» i = 45°, 135°, 225°, and 315°
» Carrier phase shifted by 45° wrt QPSK 45° = /4
ECE 4710: Lecture #26 6
QPSK Constellation
iip jc
mDjc eAeAtg )(
"00"0 c
jc AeA
QPSK4..13,1,1,3 imi
“00”“11”I
Q)(tg
cAcA 270,180,90,0i
"01"90 c
jc jAeA
"11"180 c
jc AeA
"10"270 c
jc jAeA
“01”
“10”
cjA
cjASignal points
located on circle
of radius Ac
ECE 4710: Lecture #26 7
/4 QPSK Constellation
iip jc
mDjc eAeAtg )(
"00"45 jceA
/4 QPSK4..13,1,1,3 imi
“00”
“11”
I
Q)(tg
315,225,135,45i
"01"135 jceA
"11"225 jceA
"10"315 jceA
“01”
“10”
45° = /4
ix
iy
Signal points located on circle
of radius Ac
ECE 4710: Lecture #26 8
QPSK Generation
Use m(t) to drive phase modulator (PM) Not normally done in high performance systems
Quadrature Tx Cartesian form of PSK complex envelope
Use two quadrature carriers modulated by x and y components of complex envelope
» Quadrature carriers 90° phase difference sin(2fc t) & cos(2fc t)
)()()( )( tyjtxeAtg tjc
iciici AyAx sin&cos QPSKfor 4and..2,1 MMi
ECE 4710: Lecture #26 9
QPSK Generation
QPSK
)(ts
)2sin(sin)2cos(cos)( tfAtfAts ciccic
icAtx cos)( icAty sin)(
ECE 4710: Lecture #26 10
MPSK Envelope
For rectangular baseband pulse shapes the envelope of BPSK, QPSK, MPSK signals is approximately constant Ac ( not Ac(t) )
Polar Baseband Modulation
BPSK Bandpass
Signal
0 1 0 1 0 1
180° Phase Change Between 1/0 Bits
Constant
Envelope
ECE 4710: Lecture #26 11
MPSK Envelope
Constant envelope no amplitude modulation (AM) During data transitions the envelope is constant
because of nearly instantaneous phase transitions but this requires very large BW signal!
Rectangular pulse shape produces (sin x / x)2 PSD Large undesirable spectral sidelobes for f > 1 / Ts
» Spectrally inefficient» Signal interference between adjacent frequency users
Adjacent Channel Interference (ACI) in cellular radio
Spectral sidelobes eliminated with RC filter» MPSK signal will have time-varying amplitude because of pulse
shaping to minimize signal BW no longer constant envelope
ECE 4710: Lecture #26 12
MPSK PSD
MPSK PSD for Rectangular Pulse Modulation
Spectral Sidelobes
ECE 4710: Lecture #26 13
BPSK with Pulse Shaping
Polar Baseband Modulation
1 0 1 0 1 0 BPSK
Bandpass Signal
Raised Cosine Filter Minimize Signal BW
Time-varying amplitude creates AM modulation for PSK signals
Note that signal amplitude gradually goes to ~zero at transition period between bits
ECE 4710: Lecture #26 14
AM QPSK
Pulse shaping creates time-varying QPSK amplitude Amplitude goes to zero for 180° bit transitions
causing signal to pass thru origin of
constellation diagram
90° transitions cause amplitude
to stay constant
Necessary to minimize
signal BW“00”“11”
I
Q)(tg
“01”
“10”
AM!!
ECE 4710: Lecture #26 15
AM QPSK
RC filtering minimizes QPSK signal BW Primary Advantage
AM modulation of QPSK has one major disadvantage Class A or B linear amplifiers required to preserve AM on
QPSK and therefore preserve spectral efficiency» Poor DC to RF efficiencies typically 40-65%» Serious problem for mobile communication applications
Increase battery capacity requirements by 40-50%
High efficiency non-linear Class C amplifiers have DC to RF efficiencies of 80-90%
ECE 4710: Lecture #26 16
AM QPSK
What happens if non-linear Class C amplifiers are used on pulse-shaped QPSK anyway? Non-linear amplification significantly distorts AM pulse
shaping Spectral sidelobes regenerated by non-linear
amplification Advantage of pulse-shaped signal BW is lost
f
PSD
1 / Ts = FNBW
RC Pulse Shaped
RC Pulse Shaped after Class C RF Amplifier
Spectral Regeneration
ECE 4710: Lecture #26 17
AM QPSK
How can we keep minimal signal BW and still use efficient non-linear Class C amplifiers for mobile applications that want to use PSK signals? Offset Quadrature Phase Shift Keying OQPSK /4 Differential QPSK
Both techniques seek to minimize transitions thru origin of constellation diagram Limit amplitude modulation Allow for efficient Class C amplifiers with pulse-shaped
PSK signals