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射频工程基础 Fundamentals of RF Engineering. 学时 :60/20 学分 : 3.5. 孙利国 中国科技大学信息学院电子工程与信息科学系. 第二讲 射频调制与解调 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:

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Fundamentals of rf engineering

射频工程基础Fundamentals of RF Engineering

学时:60/20

学分: 3.5

孙利国

中国科技大学信息学院电子工程与信息科学系


第二讲 射频调制与解调

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

Reference

“Microwave and RF Design: A System Approach”,

Chapter 1

Modulation Techniques

Chapter 1, §1.1–§1.4


Modulation schemes
Modulation Schemes

  • The process of converting baseband information to RF is called modulation

  • There are two types of modulations

    • Analog modulation

    • Digital modulation


Modulation schemes1
Modulation Schemes

Analog modulation

  • AM Amplitude modulation

  • FM Frequency modulation (used in 1G AMPS)

  • PM Phase modulation


Modulation schemes2
Modulation Schemes

Basic digital modulation

ASK Amplitude shift keying

FSK Frequency shift keying

PSK Phase shift keying


Modulation schemes3
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
Analog modulation

FM*

AM

PM

AM Amplitude modulation

FM Frequency modulation (used in 1G AMPS)

PM Phase modulation


Analog modulation1
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
Amplitude Modulation (AM)

Analog Modulation

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


Amplitude modulation am1
Amplitude Modulation (AM)

Analog Modulation

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


Par peak to average ratio of am
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.



Analog Modulation

PAR Peak-to-Average Ratio of AM


Analog Modulation

PAR Peak-to-Average Ratio of AM


Analog Modulation

PAR Peak-to-Average Ratio of AM


Analog Modulation

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


Bandwidth narrow band communication

TIME

AMPLITUDE

FDMA

FREQUENCY

Bandwidth: Narrow Band Communication

Analog 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 modulation2
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


Analog modulation3

Upper

Sideband

Lower

Sideband

Analog Modulation

Bandwidth

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


    Frequency modulation bandwidth

    fc

    fc

    Analog Modulation

    Frequency Modulation & Bandwidth

    Time-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

    Analog Modulation

    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 required1

    Analog Modulation

    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 fm how much bandwidth is required2

    Analog Modulation

    Analog FM:How Much Bandwidth is Required?

    Theoretical Analysis:

    The βf is frequency modulation index


    Analog fm how much bandwidth is required3
    Analog FMHow Much Bandwidth is Required?


    Analog fm how much bandwidth is required4
    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 fm how much bandwidth is required5
    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
    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.


    Analog Modulation

    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.


    Analog Modulation

    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.


    Analog fm is used on analog cellular 1g voice channels

    Voltage

    30 KHz. Channel

    fc

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

    Analog 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 channels1
    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


    Digital Modulation

    Basic digital modulations

    ASK Amplitude shift keying

    FSK Frequency shift keying

    PSK Phase shift keying


    Digital Modulation

    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)


    Digital Modulation

    • 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
    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
    Amplitude Shift Keying (ASK)

    Digital Modulation


    Fsk frequency shift keying

    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
    FSK Modulation

    Digital Modulation


    Modified forms of fsk msk gmsk

    1 0

    0 T

    0 T/2 T

    1 0

    X

    Modified forms of FSK: MSK & GMSK

    Digital 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 modulation1
    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 modulation2
    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 modulation3
    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 modulation4
    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 modulation5
    Digital Modulation

    Constellation Diagram

    Serial bit stream

    serial to parallel

    b0b1b2b3b4b5b6b7b8b9…

    bi is either binary 1 or binary 0


    Ask modulation

    Q

    I

    ASK Modulation

    Digital Modulation

    Constellation Diagram

    Voltage

    1 0 1 0

    Time

    0

    1


    Fsk modulation1

    Digital Modulation

    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

    ?


    Psk modulation

    Q

    I

    Digital Modulation

    PSK Modulation

    Constellation Diagram

    Voltage

    1 0 1 0

    Time

    1

    -1


    Bpsk binary phase shift keying 1

    Digital Modulation

    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 11
    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 12
    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 13
    BPSK(Binary Phase Shift Keying) (1)

    Digital Modulation

    PSK(Phase Shift Keying)

    b0, b1, b2, b3, b4, b5,…


    Bpsk binary phase shift keying 14

    Digital Modulation

    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
    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
    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 21
    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

    Digital Modulation

    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 keying1

    Digital Modulation

    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 ,…


    Digital Modulation

    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

    Digital Modulation

    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 qpsk1

    Digital Modulation

    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
    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,…


    Psk qpsk quadrature phase shift keying

    p/2

    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 keying1

    Digital Modulation

    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!


    Qpsk trajectory

    Q

    I

    I

    I

    I

    Q

    Q

    Q

    Q

    01

    11

    A

    B

    I

    C

    D

    00

    10

    Digital Modulation

    QPSK Trajectory

    B

    B

    D

    A

    symbols

    0

    1

    1

    0

    1

    1

    0

    1

    bits

    Complex Phasor Plane:


    Qpsk modulation problem

    3

    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
    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'.


    Digital Modulation

    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.


    Digital Modulation

    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

    Digital Modulation

    Digital demodulation: DBPSK

    LPF

    e0, e1, e2, e3,…

    parallel

    to serial

    Differential decoder

    b0, b1, b2, b3,…

    LPF


    Dqpsk

    Digital Modulation

    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


    Dqpsk1

    Digital Modulation

    DQPSK

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


    Dqpsk2

    Digital Modulation

    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


    Dqpsk3

    Digital Modulation

    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


    Dqpsk4

    Digital Modulation

    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


    Dqpsk5

    Digital Modulation

    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


    Dqpsk6

    Digital Modulation

    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


    Dqpsk7

    Digital Modulation

    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


    P 4 qpsk

    Digital Modulation

    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 qpsk1

    Digital Modulation

    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 qpsk2

    Digital Modulation

    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 modulation6
    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 modulation7
    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 modulation8
    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 modulation9
    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 modulation10
    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 qpsk3

    Digital Modulation

    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 modulation11
    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 modulation12
    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 modulation13
    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 modulation14
    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 modulation15
    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

    Digital Modulation

    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 modulation16
    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


    4 dqpsk

    M

    frequency

    π/4-DQPSK

    Digital Modulation

    Time-domain representation of a π/4-DQPSK modulated

    signal using an NRZ data sequence.

    FLAT SPECTRUM IN-BAND SPECTRALLY EFFICIENT

    SPECTRUM:

    frequency

    M = main channel


    Offset qpsk oqpsk
    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

    Digital Modulation

    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


    Oqpsk1

    Digital Modulation

    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


    Oqpsk2

    Digital Modulation

    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
    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.


    Digital Modulation

    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


    Digital Modulation

    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


    Digital Modulation

    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
    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


    Digital Modulation

    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


    Digital Modulation

    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


    Modified forms of fsk msk gmsk1

    1 0

    0 T

    0 T/2 T

    1 0

    X

    Modified forms of FSK: MSK & GMSK

    Digital 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

    Digital Modulation

    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

    Digital Modulation

    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 qam1

    Digital Modulation

    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 qam2

    Digital Modulation

    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


    16 qam3

    Digital Modulation

    16-QAM

    Q

    b2b3

    16-QAM

    b0b1b2b3

    b0b1

    I

    QAMis combination of amplitude modulation and phase modulation.


    64 qam

    Digital Modulation

    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 qam1

    Digital Modulation

    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



    Comparison

    nn

    001

    000

    8PSK

    Modulation

    010

    111

    011

    nnn

    100

    110

    101

    16PSK

    Modulation

    16QAM

    Modulation

    QPSK

    Modulation

    nnnn

    nnnn

    11

    01

    10

    00

    Comparison

    Digital Modulation


    Review major modulation formats
    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
    Summary

    • Analog Modulation

      • PM and FM look the same

    Digital Modulation

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


    Exercises
    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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