ece 4710: lecture #26 1 bpsk bpsk m(t) is binary baseband signal, e.g. m i = ±1 and i = 1, 2 ...

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 )(


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


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


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


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


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


/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


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


QPSK Generation

QPSK

)(ts

)2sin(sin)2cos(cos)( tfAtfAts ciccic

icAtx cos)( icAty sin)(


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


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


MPSK PSD

MPSK PSD for Rectangular Pulse Modulation

Spectral Sidelobes


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


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!!


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%


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


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

ece 4710: lecture #26 1 bpsk bpsk m(t) is binary baseband signal, e.g. m i = ±1 and i = 1, 2 ...

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