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DQPSKDQPSKDQPSK

Session 2 RF Modulation and Demodulation

教材：以课堂讲义为主。

主要参考书：

[1]“Microwave and RF Design: A System Approach”, Michael Steer, SciTech Publishing, 2010

其它参考书：

[2] “射频电路设计-理论与应用”，Reinhold Ludwig等著，王子宇等译，电子工业出版社，2002

[3] “射频微电子学”，拉扎维著，余志平等译，清华大学出版社，2006

[4] RF and Microwave Circuit Design for Wireless Communications, Lawrence Larson, Artech House, 1997

[5]”无线网络RF工程：硬件、天线和传播“， Daniel M.Dobkin 著 ，科学出版社 ，2007

“Microwave and RF Design: A System Approach”,

Chapter 1

Modulation Techniques

Chapter 1, §1.1–§1.4

Modulation Schemes

- The process of converting baseband information to RF is called modulation
- There are two types of modulations
- Analog modulation
- Digital modulation

Modulation Schemes

Analog modulation

- AM Amplitude modulation
- FM Frequency modulation (used in 1G AMPS)
- PM Phase modulation

Modulation Schemes

Basic digital modulation

ASK Amplitude shift keying

FSK Frequency shift keying

PSK Phase shift keying

Modulation Schemes

Digital modulation

MSK Minimum shift keying (a form of FSK)

GMSK Minimum shift keying using Gaussian filtered data

BFSK Binary frequency shift keying

BPSK Binary phase shift keying

QPSK Quadrature PSK (QPSK is also referred to as quarternary PSK, quadraphase PSK, and quadra PSK)

π/4-DQPSK π/4 Differential encoded QPSK

OQPSK Offset QPSK

SOQPSK Shaped Offset QPSK

SBPSK Shaped BPSK

FOQPSK Feher Offset QPSK

8PSK 8-state phase shift keying

3π/8-8PSK 3 π/8, 8-state phase shift keying

16PSK 16-state phase shift keying

QAM Quadrature amplitude modulation

Analog modulation

FM*

AM

PM

AM Amplitude modulation

FM Frequency modulation (used in 1G AMPS)

PM Phase modulation

Analog Modulation

- Modulation is the process of varying some characteristic of a radio signal in order toconvey information

Voltage

Time

Note that frequency and phasemodulation look very similar with this kind of input.

- This analog waveform modulates a sine-wave.
- The basic, unchanging, steady radio signal without modulation is called a “carrier”.

Characteristics that can be modulated:

Amplitude

e.g. AM radio broadcasting

Frequency

e.g.FM broadcasting, Voice transmission in AMPS cellular

Phase

Amplitude Modulation (AM)

Analog Modulation

The First Radio System to Transmit Voice were based on amplitude modulation.

Amplitude Modulation (AM)

Analog Modulation

The First Radio System to Transmit Voice were based on amplitude modulation.

PAR Peak-to-Average Ratio of AM

Analog Modulation

PAR is an important metric for modulation formats

Determines how amplifier must be designed for specified distortion.

PAR Peak-to-Average Ratio of AM

Analog Modulation

PAR Peak-to-Average Ratio of AM

PAR Peak-to-Average Ratio of AM

PAR Peak-to-Average Ratio of AM

PAR Peak-to-Average Ratio

CW

Envelope

AM (100%)

vpeak

ENVELOPE

PAR = 4.26 dB

vaverage= ½ vpeak

RF Power

With FM amplitude distortion does not matter as there is no information in the amplitude of the signal.

FM

PAR = 0 dB

AMPLITUDE

FDMA

FREQUENCY

Bandwidth: Narrow Band CommunicationAnalog Modulation

AM

The majority of modulation formats result in narrow band communication systems

These were the easiest modulation schemes for most of the 20th century and dictated the assignment of radio into narrow band channels.

1912: Regulation began with the sinking of the Titanic.

Analog Modulation

Bandwidth

- The two other analog modulation schemes commonly used are Phase Modulation (PM) and Frequency Modulation (FM) . Both FM and PM are called angle modulation. FM is more used than PM in analog modulation.
- The signals produced by the two schemes are identical.
- The difference is how the signals are generated
- In PM, the phase of the carrier depends on the instantaneous level of the baseband signal.
- In FM, the amplitude of the baseband signal determines the frequency of the carrier.
- The result in both cases is that the bandwidth of the time-varying signal is spread.
- A receiver must compress the spread-out information to re-create the original narrowband signal, and this can be thought of as processing gain, as the compression of correlated signals significantly increases the tolerance to noise.

fc

Sideband

Lower

Sideband

Analog ModulationBandwidth

Time-Domain

(as viewed on an

Oscilloscope)

Frequency-Domain

(as viewed on a

Spectrum Analyzer)

Voltage

Voltage

0

Frequency

Time

fc

fc

fc

The bandwidth occupied by a signal depends on:

- input information bandwidth
- modulation method
- Information to be transmitted, called “input” or “baseband”
- bandwidth usually is small, much lower than frequency of carrier
- Unmodulated carrier
- the carrier itself has Zero bandwidth!!
- AM-modulated carrier
- Notice the upper & lower sidebands
- total bandwidth = 2 x baseband
- FM-modulated carrier
- Many sidebands! bandwidth is a complex mathematical function
- PM-modulated carrier
- Many sidebands! bandwidth is a complex mathematical function

fc

fc

Analog Modulation

Frequency Modulation & BandwidthTime-Domain

(as viewed on an

Oscilloscope)

Frequency-Domain

(as viewed on a

Spectrum Analyzer)

Voltage

Voltage

0

Frequency

Time

The bandwidth requirement for a frequency modulated signal is difficult to determine for arbitrary modulating signals as the frequency spectrum of this signal extends indefinitely but the amplitude of the spectrum falls off rapidly.

The bandwidth occupied by a signal depends on:

- input information bandwidth
- modulation method
- Information to be transmitted, called “input” or “baseband”
- bandwidth usually is small, much lower than frequency of carrier
- FM-modulated carrier
- Many sidebands! bandwidth is a complex mathematical function

Analog FM：How Much Bandwidth is Required?

Input Signal

Voltage

fi=

input signal frequency

Time

Voltage

frequency

deviation

Carrier

fc

Frequency

fc-fi

fc+fi

Sidebands

Voltage

fc+2fi

fc-2fi

fc+3fi

fc-3fi

Frequency

c

Carson’s Rule

Bandwidth Required = 2 x (highest input frequency + frequency deviation)=2(fi+∆f)

As time passes, the carrier moves back and forth in frequency in exact step with the input signal

- frequency deviation is proportional to the input signal voltage
- a group of many sidebands is created, spaced from carrier by amounts N xfi
- relative strength of each sidebandN depends on Bessel functionNof (input signal freq./freq. deviation)

Analog FM：How Much Bandwidth is Required?

Theoretical Analysis:

The βf is frequency modulation index

The ∆f is the peak frequency deviation

The fm is the modulating frequency

Analog FMHow Much Bandwidth is Required?

The βf is frequency modulation index

The ∆f is the peak frequency deviation

The fm is the modulating frequency

a group of many sidebands is created, spaced from carrier by amounts N xωm

relative strength of each side band N depends on Bessel function Nof (freq. deviation/ input signal freq.)

Analog FMHow Much Bandwidth is Required?

The βf is frequency modulation index

The ∆f is the peak frequency deviation

The fm is the modulating frequency

It is called Carson’s rule.

The bandwidth BT depends on βf and fm. 98% of total power is contained in the Bf given by:

Narrowband and Wideband FM

The difference between Narrowband FM and Wideband FM.

The best rule of thumb formula is Carson’s Rule:

Bandwidth Required = BT = 2 x (highest input frequency + frequency deviation)

Let\'s replace this by

BT = Bandwidth Required

f = frequency deviation

fm = highest input frequency (bandwidth of modulating signal)

So BT=2 * (f+ fm)

Narrowband FM is when f << fm and then it can be shown that the bandwidth required is 2 * fm but only for Frequency Shift Keying (FSK) which is a two state form of FM.

Wideband FM is when f>> fm and then it can be shown that the bandwidth required is 2 * f.

PAR Peak-to-Average Ratio

CW

Envelope

AM (100%)

PAR = 4.26 dB

FM

PAR = 0 dB

With FM amplitude distortion does not matter as there is no information in the amplitude of the signal.

AMPS (Advanced Mobile Phone System)

- AMPS (Advanced Mobile Phone System): 1G
- 800 MHz Cellular FM band
- Up-link(TX): 824–849 MHz, 25MHz range
- Downlink(RX): 869–894 MHz, 25MHz range
- 21 control channels and 395 voice channels (416 channels, FDMA).
- Control channels are dedicated to digital data transmissions, providing access and paging functions (FSK).
- Voice channels carry the analog voice (FM).
- Each AMPS channel has a one way bandwidth of 30 kHz, for a total of 60 kHz for each duplex channel.
- Supervisory audio tones (SATs)
- SAT is a high pitched, inaudible tone that helps the system distinguish between callers on the same channel but in different cells. One of three tones, at 5970 Hz, 6000 Hz, or 6030 Hz, is transmitted by the base station and repeated back by the mobile.
- Blank and Burst
- When a base station needs to communicate information to the mobile during a conversation, it will temporarily mute the audio path and send a burst of digital data. These periods, known as blank-and-burst, generally last less than half a second, and are rarely noticed by the user.

30 KHz. Channel

fc

Analog FM is used on : Analog Cellular (1G) Voice ChannelsAnalog Modulation

Time-Domain

(as viewed on an

Oscilloscope)

Frequency-Domain

(as viewed on a

Spectrum Analyzer)

Voltage

Voltage

Voice

0

Frequency

Time

Voltage

Voltage

SAT

0

6KHz

Frequency

Time

Voltage

Two signals simultaneously modulate the AMPS cellular voice channel:

- user’s voice waveform
- fm: complex, many frequencies approx. 300Hz (0.3KHz) to 3500 Hz (3.5KHz).
- ∆f: peak deviation limited to +/- 12 KHz
- BT:2(fm + ∆f)=2(3.5+12)KHz=31KHz
- Supervisory Audio Tone (“SAT”)
- fm: tone frequency 5970, 6000, or 6030 Hz (5.97kHz, 6KHz, or 6.03KHz).
- ∆f: peak deviation set as +/- 2.0 KHz.
- BT:2(fm + ∆f)=2(6.03+2)KHz=16.06KHz
- The resulting composite FM signal fits within the assigned 30 KHz.-wide channel
- Signaling Tone at 10 KHz with +/- 8 kHz. deviation is also transmitted in occasional bursts for call control. BT=36KHz

Analog FM is used on : Analog Cellular (1G) Voice Channels

Analog Modulation

-15

15

LOWER

UPPER

Adjacent Channels Overlap but through frequency planning a basestation does not transmit on adjacent channels. The adjacent channel is used in another cell in the cluster.

CHANNEL

ADJACENT

ADJACENT

OVERLAP

OVERLAP

CHANNEL

CHANNEL

AMPLITUDE

0

-30

30

-17.5

-12.5

17.5

12.5

Basic digital modulations

ASK Amplitude shift keying

FSK Frequency shift keying

PSK Phase shift keying

Digital modulation

MSK Minimum shift keying (a form of FSK)

GMSK Minimum shift keying using Gaussian filtered data(used in 2G: GSM, Bluetooth)

BFSK Binary frequency shift keying

BPSK Binary phase shift keying (Used in Wifi: 802.11b, Bluetooth)

QPSK Quadrature PSK (QPSK is also referred to as quarternary PSK, quadraphase PSK, and quadra PSK)(used in 2G: IS-95(CDMA),3G:UMTS,LTE and Wifi:802.11b)

π/4-DQPSK π/4 Differential encoded QPSK (Used in extended data rate of Bluetooth)

OQPSK Offset QPSK (Used in 2G: NADC(CDMA))

SOQPSK Shaped Offset QPSK

SBPSK Shaped BPSK

FOQPSK Feher Offset QPSK

8PSK 8-state phase shift keying (Used in 2.5G: EDGE)

3π/8-8PSK 3 π/8, 8-state phase shift keying（Used in EDGE）

16PSK 16-state phase shift keying

QAM Quadrature amplitude modulation (used in 3G:LTE, Wifi 802.11g)

- In analog modulation, frequency modulation is more used than phase modulation.
- In digital modulation , phase modulation is more used than frequency modulation.

ASK Amplitude shift keying

FSK Frequency shift keying

PSK Phase shift keying

Digital Modulation

Voltage

1 0 1 0

Time

- For example, let this digital waveform modulate a signal. No more continuous analog variations, now we’re “shifting” between discrete levels. We call this “shift keying”.
- The steady radio signal without modulation is called a “carrier”.

Amplitude Shift Keying

ASK example: digital microwave

Frequency Shift Keying

FSK example:control messages in AMPS cellular; TDMA cellular

Phase Shift Keying

PSK examples: TDMA cellular, GSM

Amplitude Shift Keying (ASK)

Digital Modulation

FSK (Frequency Shift Keying)

Input Signal

Voltage

1 0 0 1 0

Time

Output Signal

Time

Voltage

fc

Frequency

E.G. AMPS Analog Radio (signaling)

- Input signal is Manchester-encoded data (no DC component)
- 10 KB rate
- Output Signal is FSK-modulated
- +/- 8 KHz deviation
- Binary 0 = transition fc @ +8 to -8 KHz
- Binary 1 = transition fc @ -8 to +8 KHz.
- On voice channels, when system messages must be sent, the FM voice and SAT modulation is briefly muted and replaced by FSK (this is called “blank and burst” mode)
- On control channels, FSK data is transmitted exclusively (no voice)

FSK Modulation

Digital Modulation

0 T

0 T/2 T

1 0

X

Modified forms of FSK: MSK & GMSKDigital Modulation

MSK Minimum Shift Keying

NRZ Data

FILTER

FSK Modulated

Output

FSK Modulator

1 0 1

Carrier

GMSK

Gaussian Minimum Shift Keying

Input: Binary Data

Gaussian Filter

MSK Modulator

GMSK

Output

- MSK and GMSK are forms of FSK
- input signal is pre-filtered to eliminate abrupt shifts
- this reduces the spectrum occupied by the output signal
- MSK
- The frequency shift never produces a phase discontinuity; this reduces spectrum required
- the output spectrum still contains sidelobes
- GMSK: Used in GSM, Side lobes in output spectrum are prevented by the gaussian pre-filtering
- Generates narrow power spectrum
- Spectrally efficient modulation technique
- BER is slightly worse than MSK. This is a worthwhile tradeoff since error control coding is available

Digital Modulation

Constellation Diagram

(IQ Modulation)

In real world, a signal is represented as following:

It can be expended as:

If I(t) and Q(t) are defined:

I(t) or Q(t）is called the in-phase or quadrature component repectivelly.

I/Q representation for S(t) is :

Digital Modulation

Constellation Diagram

Q

I(t) and Q(t）can be expressed in IQ diagram or constellation diagram in real signal space. It is called signal space diagram.

(I,Q)

I

IQ Diagram

Digital Modulation

Constellation Diagram

S(t) can be represented in following way: .

If SC(t) is defined as:

So that

SC(t) is representation of S(t) in complex plane

Digital Modulation

Constellation Diagram

SC(t)

jQ

I+jQ

IQ diagram or constellation diagramcan be expressed in complex plane.

I

IQ or constellation diagram

in complex plane

Digital Modulation

Constellation Diagram

Serial bit stream

serial to parallel

b0b1b2b3b4b5b6b7b8b9…

bi is either binary 1 or binary 0

FSK Modulation

Constellation Diagram

Voltage

1 0 1 0

Time

Q

I

1

It is hard to represent FSK in I-Q diagram because frequency is changed

?

BPSK(Binary Phase Shift Keying) (1)

PSK(Phase Shift Keying)

- A theoretical definition of a symbol is a waveform, a state, an event or a significant condition of the communication channel that persists for a fixed period of time. Simply, a symbol is an electrical waveform that can present one or more bits.
- In IQ diagram a symbol is a point.
- In BPSK (Binary Phase Shift Keying) a symbol carries a binary bit. States: 21=2

Voltage

1 0 1 0

Time

b0b1b2b3b4b5b6b7b8 b9…→b0, b1, b2, b3, b4, b5, b6, b7, b8 , b9,…

BPSK(Binary Phase Shift Keying) (1)

Digital Modulation

PSK(Phase Shift Keying)

b0, b1, b2, b3, b4, b5, b6, b7, b8 , b9,…

serial to parallel

b0, b1, b2, b3, b4, b5, b6, b7, b8 , b9,…

0

BPSK(Binary Phase Shift Keying) (1)

Digital Modulation

PSK(Phase Shift Keying)

Q

jQ

IQ diagram or constellation diagram in real signal space

IQ diagram or constellation diagram in complex plane

Symbol bi

Symbol bi

(0,1)

j

binary 0

binary 0

bianry 1

binary 1

I

I

(-1,0)

-1

1

(1,0)

(0,-1)

-j

BPSK(Binary Phase Shift Keying) (1)

Digital Modulation

PSK(Phase Shift Keying)

b0, b1, b2, b3, b4, b5,…

BPSK(Binary Phase Shift Keying) (1)

PSK(Phase Shift Keying)

LPF

Digital Demodulation:BPSK-1

b0, b1, b2, b3,…

BPSK(Binary Phase Shift Keying) (3)

Digital Modulation

PSK(Phase Shift Keying)

Voltage

1 0 1 0

Time

b0b1b2b3b4b5b6b7b8 b9…→b0, b1, b2, b3, b4, b5, b6, b7, b8 , b9,…

PSK(Phase Shift Keying): BPSK-2

Digital Modulation

b0, b1, b2,…

serial to parallel

b0, b1, b2, b3, b4, b5, b6, b7, b8 , b9,…

b0, b1, b2,…

PSK(Phase Shift Keying): BPSK-2

Digital Modulation

IQ diagram or constellation diagram in real signal space

IQ diagram or constellation diagram in complex plane

Q

jQ

Symbol bi

Symbol bi

binary 1

binary 1

1+j

(1,1)

j

(0,1)

1

-1

(-1,0)

(1,0)

I

I

(0,-1)

-j

(-1,-1)

-1-j

binary 0

binary 0

QPSK (Quadrature Phase Shift Keying)

Voltage

- In QPSK (Quadrature Phase Shift Keying)
- a symbol carries to two binary bits.
- states: 22=4

1 0 1 0

Time

b0b1b2b3b4b5b6b7b8b9…→b0b1, b2b3, b4b5, b6b7, b8b9 ,…

I is for b0, b2, b4, b6, b8 ,…

Q is for b1, b3, b5, b7, b9 ,…

QPSK (Quadrature Phase Shift Keying)

I is for b0, b2, b4, b6, b8 ,…

serial to parallel

b0b1, b2b3, b4b5, b6b7, b8b9 ,…

Q is for b1, b3, b5, b7, b9 ,…

PSK: QPSK (Quadrature Phase Shift Keying)

IQ diagram or constellation diagram in real signal space

IQ diagram or constellation diagram in complex plane

Q

Symbol bibi+1

jQ

Symbol bibi+1

binary 01

binary 11

binary 01

binary 11

(-1,1)

(1,1)

-1+j

1+j

j

(0,1)

I

1

(-1,0)

(1,0)

-1

I

(0,-1)

-j

(-1,-1)

(1,-1)

-1-j

1-j

binary 00

binary 10

binary 00

binary 10

Digital demodulation: QPSK

LPF

I is for b0, b2, b4,…

b0b1, b2b3, b4b5,…

parallel

to serial

Q is for b1, b3, b5,…

LPF

Digital demodulation: QPSK

LPF

I is for b0, b2, b4,…

Carrier

recovery

Symbol timing

recovery

b0b1, b2b3, b4b5,…

parallel

to serial

900 phase shifter

Q is for b1, b3, b5,…

LPF

QPSK: More practical

Digital Modulation

Ik is for b0, b2, b4, b6,…

Waveform shaping

b0b1, b2b3, b4b5, b6b7,…

serial to parallel

Waveform shaping

- Without the waveform shaping the I(t) and Q(t) have very sharp transition. This leads to large spectral spreads in the modulated waveform.
- To limit the spectrum of RF signal s(t), the waveform of i(t) and Q(t) is shaped, usually by low pass filtering.

Qk is for b1, b3, b5, b7,…

p

3p/2

2p

0

Digital Modulation

PSK: QPSK (Quadrature Phase Shift Keying)Sc(t)

jQ

I+jQ

I

jQ

1+j

–1 +j

Constellation

Points

x

QPSK

I

+

Signal Constellation

p/2

x

I

–1 – j

1 – j

Q

PSK: QPSK (Quadrature Phase Shift Keying)

- Quadrature: four possible phase shift amounts; therefore, each symbol carries two bits (efficient!)
- phase ambiguity of ordinary QPSK
- Highly bandwidth-efficient
- Two bits per hertz
- Each constellation point represents two bits. A transition from one constellation point to the next only requires one hertz of bandwidth.
- RF Phasor has zero amplitude for part of the time and so the modulated RF has a high PAR.
- Carrier recovery!

Q

01

11

A

B

2

1

I

C

D

00

10

Digital Modulation

QPSK Modulation Problem- Two Big Problems:
- The trajectory goes through zero.
- (The phasor has very small amplitude for many cycles.)
- Carrier recovery will loose the carrier. There must be some signal for this to work.
- 2. The trajectory returns on itself.

DPSK(Differential Phase Shift Keying)

Digital Modulation

- Differential phase shift keying (DPSK) is a phase modulation that conveys data by changing the phase of the carrier wave.
- For BPSK and QPSK there is an ambiguity of phase if the constellation is rotated. This problem can be overcome by using the data to change rather than set the phase.
- In differentially BPSK (DPSK) a binary \'1\' may be transmitted by adding 180° to the current phase and a binary \'0\' by adding 0° to the current phase.
- In differentially QPSK (DQPSK), the phase-shifts are 0°, 90°, 180°, -90° corresponding to data \'00\', \'01\', \'11\', \'10\'.

e0, e1, e2, e3,…

DBPSK

b0, b1, b2, b3,…

e0, e1, e2, e3,…

Differential encoder

serial to parallel

0

- If input bk is a binary \'1‘,ek changes state (from binary \'0\' to binary \'1\' or from binary \'1\' to binary \'0\').
- If input bk is a binary ‘0‘, ek remains in its previous state.

DBPSK

IQ diagram or constellation diagram in real signal space

Q

(0,1)

- If input bk is a binary \'1‘,ek changes state (from binary \'0\' to binary \'1\' or from binary \'1\' to binary \'0\').
- If input bk is a binary ‘0‘, ek remains in its previous state.

bk 1

ek: 0

ek: 1

I

(-1,0)

bk 1

(1,0)

(0,-1)

Digital demodulation: DBPSK

LPF

e0, e1, e2, e3,…

parallel

to serial

Differential decoder

b0, b1, b2, b3,…

LPF

DQPSK

b0b1, b2b3, b4b5,…

I is for ek

ck: b0, b2, b4, …

Differential encoder

serial to parallel

dk:b1, b3, b5,…

Q is for fk

DQPSK

In differentially QPSK (DQPSK), the phase-shifts are 0°, 90°, 180°, -90° corresponding to data \'00\', \'01\', \'11\', \'10\'.

DQPSK

- In differentially QPSK (DQPSK), the phase-shifts are 0°, 90°, 180°, -90° corresponding to data \'00\', \'01\', \'11\', \'10\'.

Q

binary 01

binary 11

(-1,1)

(1,1)

I

(-1,-1)

(1,-1)

binary 00

binary 10

DQPSK

Q

binary 01

binary 11

(-1,1)

(1,1)

I

(-1,-1)

(1,-1)

binary 00

binary 10

DQPSK

Q

binary 01

binary 11

(-1,1)

(1,1)

I

(-1,-1)

(1,-1)

binary 00

binary 10

Q

binary 01

binary 11

(-1,1)

(1,1)

I

(-1,-1)

(1,-1)

binary 00

binary 10

Q

binary 01

binary 11

(-1,1)

(1,1)

I

(-1,-1)

(1,-1)

binary 00

binary 10

Q

binary 01

binary 11

(-1,1)

(1,1)

I

(-1,-1)

(1,-1)

binary 00

binary 10

p/4 QPSK

There are two kinds of mode for QPSK : Mode A and Mode B

Mode A

Q

Mode B

Q

Binary 11

Binary 11

Binary 01

p/2

3p/4

p/4

I

0

p

I

Binary 01

Binary 10

5p/4

7p/4

Binary 00

Binary 10

Binary 00

3p/2

p/4 QPSK

By combining these two modes we can get p/4 QPSK

(11)B

p/2

(11)A

(01)A

3p/4

p/4

p/4 QPSK Signal Constellation

p

0

(10)B

(01)B

5p/4

7p/4

(00)A

(10)A

3p/2

(00)B

QPSK Quadrature Phase Shift Keying

Quadrature: four possible phase shift amounts; therefore, each symbol carries two bits (efficient!)

p/4:The constellation at each symbol is rotated p/4 from the previous symbol.

highly bandwidth-efficient

p/4 QPSK

Constellation rotates from symbol to symbol to avoid going through the origin.

From n-1 to n

SYMBOL n

SYMBOL n-1

Q

Q

Binary 11

Binary 11

Binary 01

p/2

3p/4

p/4

I

0

p

I

Binary 01

Binary 10

5p/4

7p/4

From n to n+1

Binary 00

Binary 10

Binary 00

3p/2

Digital Modulation

p/4 QPSK

Theoretical analysis:

The transmitted signal :

The φ(t) is the phase term. It is constant over a symbol period TS , therefore

It can be expanded as:

where

Digital Modulation

The phase φk for the k-th symbol can be expressed as:

Where φk-1 is the phase for the (k-1)-th symbol and ∆φk is the phase change:

Digital Modulation

In π/4–QPSK modulation, a symbol carries 2 bits of information. There are 8 states for the symbol.

A symbol changes from one state to another state in the following way:

Digital Modulation

If initial point (symbol0) is (10)B , which is ( 1, 0) in constellation diagram, I0=1 and Q0=0 thus symbol1 is given by:

Q

(11)A

1

p/2

3p/4

p/4

(01)A

I

0

p

-1

1

(10)B

5p/4

7p/4

(00)A

(10)A

-1

3p/2

Digital Modulation

If initial point (symbol0) is , which is (11)A in constellation diagram,

I0= and Q0= , thus symbol1 is given by:

Q

(11)B

(11)A

1

p/2

3p/4

p/4

00

10

01

I

0

p

-1

1

(10)B

(01)B

11

5p/4

7p/4

-1

3p/2

(00)B

p/4 QPSK

Transition from one symbol to next symbol.

Q

(11)B

p/2

(11)A

(01)A

3p/4

p/4

I

0

p

(10)B

(01)B

5p/4

7p/4

(00)A

(10)A

3p/2

Constellation rotates from symbol to symbol to avoid going through the origin.

(00)B

Digital Modulation

p/4 DQPSK

- In π/4–DQPSK modulation
- information is transmitted as changes of phase.
- a symbol carries 2 bits of information. The 2 bits of information is related to the phase ∆ φk in following way.

Digital Modulation

p/4 DQPSK

If initial point (symbol0) is ( 1, 0) in constellation diagram, I0=1 and Q0=0 thus

If the input symbol is 00, ∆ φk = π/4

If the input symbol is 01, ∆ φk =3π/4

If the input symbol is 11, ∆ φk =-3π/4

If the input symbol is 10, ∆ φk =- π/4

Digital Modulation

p/4 DQPSK

If initial point (symbol0) is ( 1, 0) in constellation diagram, I0=1 and Q0=0 thus

Q

1

p/2

3p/4

p/4

00

I

01

0

p

-1

1

11

10

5p/4

7p/4

-1

3p/2

Digital Modulation

p/4 DQPSK

If initial point (symbol0) is in constellation diagram,

I0= and Q0= thus

If the input symbol is 00, ∆ φk = π/4

If the input symbol is 01, ∆ φk =3π/4

If the input symbol is 11, ∆ φk =-3π/4

If the input symbol is 10, ∆ φk =- π/4

Digital Modulation

p/4 DQPSK

If initial point (symbol0) is in constellation diagram,

I0= and Q0= thus

Q

1

p/2

3p/4

p/4

00

01

I

10

0

p

-1

1

11

5p/4

7p/4

-1

3p/2

p/4 DQPSK

Constellation rotates from symbol to symbol to avoid going through the origin.

SYMBOL 2

SYMBOL 1

SYMBOL 3

Q

Q

Q

p/2

3p/4

p/4

3p/4

p/4

I

I

I

0

p

5p/4

5p/4

7p/4

7p/4

3p/2

The information is in the transition.

Digital Modulation

Q

p/4 DQPSK

p/2

3p/4

p/4

I

Example

p

0

Input symbol: 00, 01, 10, 11, 01, 01

5p/4

7p/4

3p/2

Offset QPSK(OQPSK)

Digital Modulation

- Avoid IQ transitions passing through the origin on the constellation diagram.
- There are two bits per symbol.
- One bit is used to directly modulate the RF signal ,whereas the other bit is delayed by half a symbol period.

OQPSK

I is for b0, b2, b4, b6

serial to parallel

Data: b0b1, b2b3, b4b5, b6b7

half bit delay

Q is for b1, b3, b5, b7

OQPSK

b0b1b2b3b4b5b6b7b8b9…→b0b1, b2b3, b4b5, b6b7, b8b9 ,…

bi: 1 1 0 0 1 0 0 1 → 1 1, 0 0, 1 0, 0 1

Q

binary 01

binary 11

QPSK

(-1,1)

(1,1)

Ts=2Tb

I

b7

d(t)

b0

b1

b4

b6

b5

b2

b3

1

1

0

0

0

1

1

0

(-1,-1)

(1,-1)

dI(t)

b4

b0

binary 00

binary 10

b2

b6

1

1

1

1

0

0

0

0

dQ(t)

b7

b1

b3

b5

1

1

1

1

0

0

0

0

OQPSK

b0b1b2b3b4b5b6b7b8b9…→b0b1, b2b3, b4b5, b6b7, b8b9 ,…

bi: 1 1 0 0 1 0 0 1 → 1 1, 0 0, 1 0, 0 1

Q

binary 01

binary 11

OQPSK

(-1,1)

(1,1)

Ts=2Tb

I

d(t)

b7

b0

b1

b4

b6

b5

b2

b3

1

1

0

0

0

1

1

0

(-1,-1)

(1,-1)

dI(t)

b4

b0

binary 00

binary 10

b2

b6

In OQPSK the maximum phase change for a bit transition is 90o. A total phase change could be 180o during one symbol. Avoid 180o phase jump in bit transition in QPSK.

1

1

1

1

0

0

0

0

dQ(t)

b7

b1

b3

b5

Ts/2=Tb

1

1

1

1

0

0

0

0

Minimum Shift Keying (MSK)

Digital Modulation

- Similar to OQPSK, MSK is encoded with the Q component delayed by half the symbol period.
- Instead of square pulses used in OQPSK, MSK encoded each bit as a half sinusoid.
- MSK can also be viewed as a continuous phase frequency shift keyed signal with a frequency separation of half the bit rate.

MSK

DI is for b0, b2, b4, b6

Sinusoidal shaping filter

serial to parallel

b0b1, b2b3, b4b5, b6b7

Sinusoidal shaping filter

half bit delay

DQ is for b1, b3, b5, b7

MSK

b4

b0b1b2b3b4b5b6b7b8b9…→b0b1, b2b3, b4b5, b6b7, b8b9 ,…

bi: 1 1 0 0 1 0 0 1 → 1 1, 0 0, 1 0, 0 1

Q

MSK

binary 11

binary 01

Ts=2Tb

(1,1)

(-1,1)

I

d(t)

b7

b0

b1

b4

b6

b5

b2

b3

1

1

0

0

0

1

1

0

(-1,-1)

(1,-1)

Tm=4Tb

binary 00

binary 10

I(t)

b4

b0

b6

b2

A sinusoidal filter is used to shape the waveform.

1

1

0

1

1

0

0

0

Q(t)

b7

b1

b3

b5

Ts/2=Tb

1

1

1

1

0

0

0

0

MSK

DI is for b0, b2, b4, b6

Sinusoidal shaping filter

serial to parallel

b0b1, b2b3, b4b5, b6b7

Sinusoidal shaping filter

half bit delay

DQ is for b1, b3, b5, b7

BPSK

FSK

Gaussian Minimum Shift Keying (GMSK)

Digital Modulation

- GMSK is a variant of MSK with waveform shaping coming from Gaussian low pass filter instead sinusoidal filter.
- GMSK is used in GSM cellular wireless system
- GMSK has the advantage of reducing sideband power, which recduce the out-band interference in adjacent frequency channels.
- Gaussian filter has a frequency response F(w) and impulse time response h(t) as following

GMSK

Gaussian low pass filter

DI is for b0, b2, b4, b6

serial to parallel

b0b1, b2b3, b4b5, b6b7

Gaussian low pass filter

half bit delay

DQ is for b1, b3, b5, b7

GMSK

b4

b0b1b2b3b4b5b6b7b8b9…→b0b1, b2b3, b4b5, b6b7, b8b9 ,…

bi: 1 1 0 0 1 0 0 1 → 1 1, 0 0, 1 0, 0 1

Q

MSK

binary 11

binary 01

Ts=2Tb

(1,1)

(-1,1)

I

d(t)

b7

b0

b1

b4

b6

b5

b2

b3

1

1

0

0

0

1

1

0

(-1,-1)

(1,-1)

Tm=4Tb

binary 00

binary 10

I(t)

b4

b0

b6

b2

Gaussian low pass filter is used to shape the waveform.

1

1

1

0

0

0

0

1

Q(t)

b7

b1

b3

b5

Ts/2=Tb

1

1

1

1

0

0

0

0

0 T

0 T/2 T

1 0

X

Modified forms of FSK: MSK & GMSKDigital Modulation

MSK Minimum Shift Keying

NRZ Data

FILTER

FSK Modulated

Output

FSK Modulator

1 0 1

Carrier

GMSK

Gaussian Minimum Shift Keying

Input: Binary Data

Gaussian Filter

MSK Modulator

GMSK

Output

- MSK and GMSK are forms of FSK
- input signal is pre-filtered to eliminate abrupt shifts
- this reduces the spectrum occupied by the output signal
- MSK
- The frequency shift never produces a phase discontinuity; this reduces spectrum required
- the output spectrum still contains sidelobes
- GMSK: Used in GSM, Side lobes in output spectrum are prevented by the gaussian pre-filtering
- Generates narrow power spectrum
- Spectrally efficient modulation technique
- BER is slightly worse than MSK. This is a worthwhile tradeoff since error control coding is available

QAM Modulation

- The digital modulation schemes described so far modulate the phase or frequency of a carrier to convey binary data and the constellation points lie on a circle of constant amplitude. The effect of this is to provide some immunity to amplitude changes to the signal.
- However, much more information can be transmitted if the amplitude is varied as well as the phase. With sophisticated signal processing it is possible to reliably use Quadrature Amplitude Modulation (QAM).
- The most common form of QAM is square QAM, or rectangular QAM with an equal number of I and Q states.
- The most common forms are 16-QAM, 64-QAM, 128-QAM, and 256-QAM.
- The constellation points are closer together with high-order QAM and so are more susceptible to noise and other interference. Thus high-order QAM can deliver more data, but less reliably, than can lower-order QAM.

16-QAM

- In 16QAM (Quadrature Amplitude Modulation)
- a symbol carries to 4 binary bits.
- states: 24=16
- Level conversion is used in QAM

bkbk+1

2 to 4 level conversion

16-QAM

b0b1b2b3b4b5b6b7…→ b0b1b2b3 , b4b5b6b7, …

b0b1, b4b5,…

2 to L(22=4) level conversion

Low pass filter

serial to parallel

b0b1b2b3, b4b5b6b7,…

2 to L(22=4) level conversion

Low pass filter

b2b3, b6b7,…

bkbk+1

2 to 4 level conversion

16-QAM

Q

b2b3

16-QAM

b0b1b2b3

10 10

11 10

01 10

00 10

3

10 11

11 11

01 11

00 11

1

b0b1

-3

-1

1

3

I

-1

10 01

11 01

01 01

00 01

-3

10 00

11 00

01 00

00 00

64-QAM

- In 64QAM
- a symbol carries to 6 binary bits.
- states: 26=64
- Level conversion is used in QAM

bk-1bkbk+1

2 to 8 level conversion

64-QAM

b0b1b2b3b4b5b6b7…→ b0b1b2b3 b4b5，b6b7 b8b9b10b11 b12, …

b0b1b2, b6b7b8,…

2 to L(23=8) level conversion

Low pass filter

serial to parallel

b0b1b2b3b4b5, b6b7b8b9b10b11,…

2 to L(23=8) level conversion

Low pass filter

b3b4 b5, b9b10b11,…

bk-1bkbk+1

2 to 8 level conversion

001

000

8PSK

Modulation

010

111

011

nnn

100

110

101

16PSK

Modulation

16QAM

Modulation

QPSK

Modulation

nnnn

nnnn

11

01

10

00

ComparisonDigital Modulation

Review: Major Modulation Formats

Analog modulation

AM Amplitude modulation

FM Frequency modulation

PM Phase modulation

Digital modulation

FSK Frequency shift keying

PSK Phase shift keying

MSK Minimum shift keying (a form of FSK)

GMSK Minimum shift keying using Gaussian filtered data

BFSK Binary frequency shift keying

BPSK Binary phase shift keying

QPSK Quadrature PSK (QPSK is also referred to as

quarternary PSK, quadraphase PSK, and quadra PSK)

π/4-DQPSK π/4 Differential encoded QPSK

OQPSK Offset QPSK

SOQPSK Shaped Offset QPSK

SBPSK Shaped BPSK

FOQPSK Feher Offset QPSK

8PSK 8-state phase shift keying

3π/8-8PSK 3 π/8, 8-state phase shift keying

16PSK 16-state phase shift keying

QAM Quadrature amplitude modulation

Summary

- Analog Modulation
- PM and FM look the same

Digital Modulation

Techniques that yield almost square spectra and hence high spectral efficiency.

Exercises

1. Consider two uncorrelated analog signals combined together. One signal is denoted x(t) and the other y(t), where x(t) = 0.1 sin (109t) and y(t) = 0.05 sin (1.01 · 109t). What is the PAR of this combined signal? Express PAR in decibels.

2. An FM signal has a maximum frequency deviation of 20 kHz and a modulating signal between 300 Hz and 5 kHz. What is the bandwidth required to transmit the modulated RF signal when the carrier is 200 MHz? Is this considered to be narrowband FM or wideband FM?

3. The sequence of bits 0100110111 is to be transmitted. Take these data in pairs, that is, as 01 00 11 01 11. These pairs, one bit at a time, drive the I and Q channels. Show the transitions on constellation diagrams for following modulations:

(1) QPSK modulation.

(2) OQPSK

(3) π/4-DQPSK

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