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Digital Modulation – Lecture 02

Digital Modulation Techniques

© Richard Harris

Communication Systems 143.332 - Digital Modulation Slide 2

Objectives

• To be able to compute the bit rate and symbol rate for a given system.

• To be able to determine the bandwidth requirements• To be able to describe the various popular forms of

digital modulation and implement them on simple data inputs


References

• Digital and Analog Communication Systems – 6th

Edition, Leon W. Couch II (Prentice Hall)• Digital Modulation in Communication Systems – An

Introduction (Hewlett Packard Application Note 1298)• Principles of Digital Modulation, by Dr Mike Fitton,

[email protected] Telecommunications Research Lab Toshiba Research Europe Limited


Presentation Outline

• Bit and Symbol Rates• Bandwidth requirements• Symbol clock• Overview of Binary Keying• Description of the popular forms of digital modulation

– BASK (OOK)– BPSK, QPSK– FSK, MSK– DPSK


Bit Rate and Symbol Rate - 1

• Symbol Rate:– If symbols are generated at a rate of r

per second to create a baseband signal with a bandwidth of W Hz, then Nyquist has shown that r ≤ 2W.

– For a double-sideband modulated wave whose transmission bandwidth is BT Hz, BT = 2W so that r ≤ BT.

• Bit Rate– Bit rate is the frequency of a system

bit stream. – Take, for example, a radio with an 8

bit sampler, sampling at 10 kHz for voice.

– The bit rate, the basic bit stream rate in the radio, would be eight bits multiplied by 10K samples per second, or 80 Kbits per second.

To understand and compare different modulation format efficiencies, it isimportant to first understand the difference between bit rate and symbolrate. The signal bandwidth for the communications channel needed depends on the symbol rate, not on the bit rate. (Ignore sync and error…)

Bit RateSymbol rate = Number of bits transmitted per symbol


Bit Rate and Symbol Rate - 2

• The state diagram opposite represents QPSK (more details later).

• Notice that for each constellation point two bits are transmitted.

• If only one bit was being transmitted per symbol, then in the previous example the symbol and bit rates would be identical at 80Kbits per second.

• For the QPSK example, the symbol rate will be 40Kbits per second.

• Symbol rate is sometimes called the baud rate. Note that the baud rate is not the same as bit rate. (These terms are often confused.)

• If more bits can be sent with each symbol, then the same amount of data can be sent in a narrower spectrum.

• This is why modulation formats that are more complex and use a higher number of states can send the same information over a narrower piece of the RF spectrum.

01 00

1011

QPSK State Diagram


Bandwidth Requirements

• Consider the two modulation schemes depicted in the figures below:

BPSKOne bit per symbol

Bit rate = Symbol rate

8PSK3 bits per symbol

Symbol rate = 1/3 Bit rate

• An example of how symbol rate influences spectrum requirements can be seen in eight-state Phase Shift Keying (8PSK) as shown on the right. It is a variation of PSK. There are eight possible states that the signal can transition to at any time.

• The phase of the signal can take any of eight values at any symbol time. Since 23 = 8, there are three bits per symbol. This means the symbol rate is one third of the bit rate.


Digital Modulation Basics

• The bit rate defines the rate at which information is passed.

• The baud (or signalling) rate defines the number of symbols per second.

• Each symbol represents n bits, and has M signal states, where M = 2n.– This is called M-ary signalling.

• The maximum rate of information transfer through a baseband channel is given by:– Capacity fb = 2 W log2M bits per second

• where W = bandwidth of modulating baseband signal


The Symbol Clock

• The symbol clock represents the frequency and exact timing of the transmission of the individual symbols.

• At the symbol clock transitions, the transmitted carrier is at the correct I/Q (or magnitude/phase) value to represent a specific symbol (a specific point in the constellation).


Additional Binary BandpassSignalling Examples

• The diagram to the right shows a number of additional Binary Bandpass signalling examples that will be considered further in the coming lectures.

• Unipolar and bipolar modulation are shown for reference.

• OOK– On-off keying or Amplitude Shift

Keying (ASK)• PSK and BPSK

– Binary Phase Shift Keying• DSB-SC

– Double Side Band – Suppressed carrier


Binary Keying

• Binary Keying definition:– The bits in a message stream switch the modulation

parameters (amplitude, frequency and phase) from one state to another. This process is called binary keying.

– Binary keying is a process that makes the values of amplitude, phase or frequency of the carrier signal change in sympathy with the values of the bits in the binary signal stream.

• Basic actions can be classified as:– ASK – Amplitude Shift Keying– PSK – Phase Shift Keying– FSK – Frequency Shift Keying


Binary Amplitude Shift Keying

• As shown in the diagram in the following slides, the transmittedsignal for BASK is a sinusoid whose amplitude is changed by on-off keying (OOK) so that a 1 is represented by the presence of a signal and a 0 is represented by the absence of a signal.

• The modulated pulse can be described mathematically when signal ‘1’ is present as:

• where Tb is the bit duration (in sec). When signal ‘0’ is present we have

1

cos 2 , when 0( )

0 otherwisec bA f t t T

p tπ < ≤⎧

= ⎨⎩

0)(0 =tp


Double Side Band - Suppressed Carrier

• The Double Side Band - Suppressed Carrier (DSB-SC) signal is essentially an AM signal that has a suppressed discrete carrier.

• This signal is given by the following equation:

• where m(t) is assumed to have a zero dc level for the suppressed carrier case.

• The complex envelope for this is given by:

( ) ( )cg t A m t=

( ) ( )cosc cs t A m t tω=


On-off Keying - OOK

• OOK– On-off keying is also known as Amplitude Shift Keying (ASK)– The above graph shows a time domain representation of Binary

Amplitude Shift Keying

p1(t)

-2.5-2

-1.5-1

-0.50

0.51

1.52

2.5


Binary or Bi-Phase Shift Keying

• One of the simplest forms of digital modulation is Binary or Bi-Phase Shift Keying (BPSK).

• One application where this is used is for deep space telemetry.

• The phase of a constant amplitude carrier signal moves between zero and 180 degrees.

• On an I and Q diagram, the I state has two different values.

• There are two possible locations in the state diagram, so a binary one or zero can be sent.

BPSKOne bit per symbol

Bit rate = Symbol rate


Binary Phase-Shift Keying – 2

• This is illustrated in the chart above. Notice the 180o phase shifts indicated by the arrow.

p1(t)

-1

-0.5

0

0.5

1

p1(t)

1 10

⎩⎨⎧ ≤<−

=

⎩⎨⎧ ≤<

=

otherwise 00 when 2cos

)(

otherwise 00 when 2cos

)(

0

1

bc

bc

TttfAtp

TttfAtp

π

π


Binary Phase-Shift Keying – 3

• The above equations describe the waveforms for BPSK. Note that it can also be referred to as phase-reversal keying or PRK.

• Let

• Where m(t) is given in the figure below:

)](cos[)( tmDtAts pcc += ω


Binary Phase-Shift Keying - 4

• Typically, m(t) has peak values of ±1 and Dp = π/2 radians, thus

• BPSK is equivalent to DSB-SC with polar data waveform.

• The complex envelope is given by

ttmAts cc ωsin)()( −=

)()( tmjAtg c=


Quadrature Phase Shift Keying –QPSK - 1

• A more common type of phase modulation is Quadrature Phase Shift Keying (QPSK).

• QPSK is used extensively in applications including: – CDMA (Code Division Multiple Access) cellular

service, – Wireless local loop, – Iridium (a voice/data satellite system) and – DVB-S (Digital Video Broadcasting - Satellite).

• QPSK is effectively two independent BPSK systems (I and Q), and therefore exhibits the same performance but twice the bandwidth efficiency.

01 00

1011

QPSK State Diagram


Quadrature Phase Shift Keying –QPSK - 2

• Quadrature Phase Shift Keying can be filtered using raised cosine filters (see later for details) to achieve excellent out of band suppression.

• Large envelope variations occur during phase transitions, thus requiring linear amplification.


Nyquist & Root-Raised Cosine Filters

• The Nyquist bandwidth is the minimum bandwidth that can be used to represent a signal.

• It is important to limit the spectral occupancy of a signal, to improve bandwidth efficiency and remove adjacent channel interference.

• Root raised cosine filters allow an approximation to this minimum bandwidth.– More discussion on the details of

these filters later.


Types of Quadrature Phase Shift Keying

• Conventional QPSK has transitions through zero (ie. 180o phase transitions). A highly linear amplifier is required.

• In Offset QPSK, the transitions on the I and Q channels are staggered. Phase transitions are therefore limited to 90o.

• In π/4-QPSK the set of constellation points are toggled for each symbol, so transitions through zero cannot occur. This scheme produces the lowest envelope variations.

• All QPSK schemes require linear power amplifiers.

(-1,1) (1,1)

(1,-1)(-1,-1)

Conventional QPSK

Q

I

Offset QPSK

Q

I

(-1,1) (1,1)

(1,-1)(-1,-1)

Q

π/4 QPSK

I

(-1,1) (1,1)

(1,-1)(-1,-1)


QPSK – Summary comments

• Quadrature means that the signal shifts between phase states that are separated by 90 degrees (π/2 radians). The signal shifts in increments of 90 degrees from 45 to 135, –45, or –135 degrees.

• These points are chosen as they can be easily implemented using an I/Q modulator.

• Only two I values and two Q values are needed and this gives two bits per symbol.

• There are four states because 22 = 4. It is therefore a more bandwidth-efficient type of modulation than BPSK - potentially twice as efficient.


Frequency Shift Keying

• Frequency Modulation and Phase Modulation are closely related.

• A static frequency shift of +1 Hz means that the phase is constantly advancing at the rate of 360 degrees per second (2π rad/sec), relative to the phase of the unshifted signal.


Frequency Shift Keying – 1

• Frequency Shift Keying– Discontinuous phase FSK– Where f1 = mark frequency; f2 = space frequency

1 1

2 2

cos( ) for sending a 1( )

cos( ) for sending a 0c

c

A ts t

A tω θω θ

+⎧= ⎨ +⎩



OscillatorFreq = f1

OscillatorFreq = f2

Electronic Switch

Binary data inputm(t)

Control line



• Continuous phase FSK

FrequencyModulator

(Carrier freq = fc)

Binary data inputm(t) FSK Output

Where

( ) cos ( )

Re{ ( ) }c

t

c c f

j t

s t A t D m d

g t e ω

ω λ λ−∞

⎡ ⎤= +⎢ ⎥⎣ ⎦=

∫

( )( )

( ) ( )

j tc

t

f

g t A e

t D m d

θ

θ λ λ−∞

=

= ∫


Frequency Shift Keying - 4

• In FSK, the frequency of the carrier is changed as a function of the modulating signal (data) being transmitted. The amplitude is unchanged.

• In Binary FSK (BFSK or 2FSK), a “1” is represented by one frequency and a “0” is represented by another frequency.

• The bandwidth occupancy of FSK depends on the spacing of the twosymbols. A frequency spacing of 0.5 times the symbol period is typically used.

• FSK can be expanded to a M-ary scheme, employing multiple frequencies as different states.


Applications for FSK

• FSK (Frequency Shift Keying) is used in many applications including cordless and paging systems.

• Some of the cordless systems include – DECT (Digital Enhanced Cordless

Telephone) and

– CT-2: Cordless Telephone 2• CT-2 is a second generation cordless

telephone system that allows users to roam away from their home base stations and receive service in public places. Away from the home base station, the service is one way outbound from the phone to a telepoint that is within range.

DECT Phone


Binary Frequency-Shift Keying - 1

• Here the modulated wave is a sinusoid of constant amplitude whose presence at one frequency means a 1 is present and if another frequency is present then this means a 0 is present.

• When signal 1 is present, the pulse can be described as:

• When signal 0 is present, the pulse can be described as:

1

cos 2 , when 0( )

0, otherwisem bA f t t T

p tπ < ≤⎧

= ⎨⎩

0

cos 2 , when 0( )

0, otherwisen bA f t t T

p tπ < ≤⎧

= ⎨⎩


Binary Frequency-Shift Keying - 2

p1(t)

-1

-0.5

0

0.5

1

p1(t)


Minimum Shift Keying - 1

• Since a frequency shift produces an advancing or retarding phase, frequency shifts can be detected by sampling the phase at each symbol period.

• Phase shifts of (2N + 1) π/2 radians are easily detected with an I/Q demodulator.– At even numbered symbols, the polarity of the I channel

conveys the transmitted data, – At odd numbered symbols the polarity of the Q channel

conveys the data. • This orthogonality between I and Q simplifies

detection algorithms and hence reduces power consumption in a mobile receiver.


Minimum Shift Keying - 2

• The minimum frequency shift which yields orthogonality of I and Q is that which results in a phase shift of ± π/2 radians per symbol (90 degrees per symbol).

• FSK with this deviation is called MSK (Minimum Shift Keying). The deviation must be accurate in order to generate repeatable 90 degree phase shifts.

• MSK is used in the GSM (Global System for Mobile Communications) cellular standard.

• A phase shift of +90 degrees represents a data bit equal to “1”, while –90 degrees represents a “0”.

• The peak-to-peak frequency shift of an MSK signal is equal to half of the bit rate.


Comments on FSK and MSK - 1

• FSK and MSK produce constant envelope carrier signals, which have no amplitude variations. – This is a desirable characteristic for improving the power

efficiency of transmitters.• Amplitude variations can exercise nonlinearities in an amplifier’s

amplitude-transfer function, generating spectral re-growth, a component of adjacent channel power.

– Therefore, more efficient amplifiers (which tend to be less linear) can be used with constant-envelope signals, reducing power consumption.


Comments on FSK and MSK - 2

• MSK has a narrower spectrum than wider deviation forms of FSK. • The width of the spectrum is also influenced by the waveforms

causing the frequency shift. – If those waveforms have fast transitions or a high slew rate, then the

spectrum of the transmitter will be broad. • In practice, the waveforms are filtered with a Gaussian filter,

resulting in a narrow spectrum. – In addition, the Gaussian filter has no time-domain overshoot, which

would broaden the spectrum by increasing the peak deviation.• MSK with a Gaussian filter is termed GMSK (Gaussian MSK).


DPSK – 1

• Recovery of the data stream from a PSK modulated wave requires synchronous demodulation– The receiver must reconstruct the carrier exactly so that it

can detect changes in the phase of the received signal.• Differential PSK eliminates the need for the

synchronous carrier in the demodulation process and this has the effect of simplifying the receiver.

• At the transmitter, we process the data stream to give a modulated wave where the phase changes by πradians whenever a 1 appears in the stream.

• It remains constant whenever a 0 appears in the stream.


DPSK - 2

• Differential Phase-Shift Keying– Binary data are first differentially encoded and then passed to

the BPSK modulator.• Example 1:

1

1

Note: if 1,if 0,

n n n

n n n

d e ed e e

−

−

= ≠

= =


DPSK - 3

• Thus we see that the receiver only needs to detect phase changes. It does not need to search for specific phase values.

p1(t)

-1

-0.5

0

0.5

1

p1(t)

1 0 1

180° phase shifts


DPSK - 4

• A further example showing how the phase changes and is processed and finally demodulated.

Original datastream0 1 0 0 1 1 0 0 0 1 1 1 0 0 0Relative Phase Angle0 +π +π +π +2π +3π +3π +3π +3π +4π +5π +6π +6π +6π +6πProcessed datastream0 1 1 1 0 1 1 1 1 0 1 0 0 0 0Demodulated Datastream0 1 0 0 1 1 0 0 0 1 1 1 0 0 0

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