Digital Modulation 02 1s

8/3/2019 Digital Modulation 02 1s

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Digital Modulation Lecture 02

Digital Modulation Techniques

Richard Harris


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Communication Systems 143.332 - Digital Modulation Slide 2

Objectives

To be able to compute the bit rate and symbol rate fora given system.

To be able to determine the bandwidth requirements

To be able to describe the various popular forms ofdigital modulation and implement them on simple datainputs


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References

Digital and Analog Communication Systems 6

th

Edition, Leon W. Couch II (Prentice Hall)

Digital Modulation in Communication Systems AnIntroduction (Hewlett Packard Application Note 1298)

Principles of Digital Modulation, by Dr Mike Fitton,[email protected] TelecommunicationsResearch Lab Toshiba Research Europe Limited


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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


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Bit Rate and Symbol Rate - 1

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

per second to create a basebandsignal with a bandwidth of W Hz, thenNyquist has shown that r2W.

For a double-sideband modulatedwave whose transmission bandwidthis BT Hz, BT= 2Wso that rBT.

Bit Rate

Bit rate is the frequency of a systembit stream.

Take, for example, a radio with an 8

bit sampler, sampling at 10 kHz forvoice.

The bit rate, the basic bit streamrate in the radio, would be eight bitsmultiplied by 10K samples persecond, or 80 Kbits per second.

To understand and compare different modulation format efficiencies, it is

important to first understand the difference between bit rate and symbolrate. The signal bandwidth for the communications channel neededdepends on the symbol rate, not on the bit rate. (Ignore sync and error)

Bit RateSymbol rate =

Number of bits transmitted per symbol


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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 wouldbe identical at 80Kbits per second.

For the QPSK example, the symbol rate will be 40Kbitsper second.

Symbol rate is sometimes called the baud rate. Notethat the baud rate is not the same as bit rate. (Theseterms are often confused.)

If more bits can be sent with each symbol, then thesame amount of data can be sent in a narrowerspectrum.

This is why modulation formats that are more complexand use a higher number of states can send the sameinformation over a narrower piece of the RF spectrum.

01 00

1011

QPSK State Diagram


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Bandwidth Requirements

Consider the two modulation schemes depicted in thefigures 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 ineight-state Phase Shift Keying (8PSK) as shown on the right. It is a variation ofPSK. 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.


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Digital Modulation Basics

The bit rate defines the rate at which information ispassed.

The baud(or signalling) rate defines the number ofsymbols per second.

Each symbol represents n bits, and has Msignalstates, where M = 2n.

This is called M-ary signalling.

The maximum rate of information transfer through abaseband channel is given by:

Capacity fb = 2 W log2M bits per second

where W = bandwidth of modulating baseband signal


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The Symbol Clock

The symbol clock represents the frequency and exacttiming of the transmission of the individual symbols.

At the symbol clock transitions, the transmitted carrieris at the correct I/Q (or magnitude/phase) value to

represent a specific symbol (a specific point in theconstellation).


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Additional Binary BandpassSignalling Examples

The diagram to the right shows a

number of additional BinaryBandpass signalling examples thatwill be considered further in thecoming lectures.

Unipolar and bipolar modulation areshown for reference.

OOK

On-off keying or Amplitude ShiftKeying (ASK)

PSK and BPSK Binary Phase Shift Keying

DSB-SC Double Side Band Suppressed

carrier


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Binary Keying

Binary Keying definition:

The bits in a message stream switch the modulationparameters (amplitude, frequency and phase) from one stateto another. This process is called binary keying.

Binary keying is a process that makes the values of amplitude,phase or frequencyof the carrier signal change in sympathywith 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


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Binary Amplitude Shift Keying

As shown in the diagram in the following slides, the transmitted

signal for BASK is a sinusoid whose amplitude is changed by on-off keying (OOK) so that a 1 is represented by the presence of asignal 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 wehave

1

cos 2 , when 0( )

0 otherwise

c b f t t T p t

< =

0)(0 =tp


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Double Side Band - SuppressedCarrier

The Double Side Band - Suppressed Carrier (DSB-SC)signal is essentially an AM signal that has asuppressed 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:

( ) ( )c

g t A m t =

( ) ( )cosc cs t A m t t =


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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 BinaryAmplitude Shift Keying

p1(t)

-2.5

-2

-1.5

-1-0.5

0

0.5

1

1.5

2

2.5


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Binary or Bi-Phase Shift Keying

One of the simplest forms of digital

modulation is Binary or Bi-Phase ShiftKeying (BPSK).

One application where this is used is fordeep space telemetry.

The phase of a constant amplitude carriersignal moves between zero and 180degrees.

On an Iand Qdiagram, the Istate has two

different values.

There are two possible locations in the statediagram, so a binary one or zero can besent.

BPSKOne bit per symbol

Bit rate = Symbol rate


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Binary Phase-Shift Keying 2

This is illustrated in the chart above. Notice the 180o phase shiftsindicated by the arrow.

p1(t)

-1

-0.5

0

0.5

1

p1(t)

1 10


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Binary Phase-Shift Keying 3

The above equations describe the waveforms forBPSK. 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 +=


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Binary Phase-Shift Keying - 4

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

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

The complex envelope is given by

ttmAts cc sin)()( =

)()( tmjAtg c=


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Quadrature Phase Shift Keying QPSK - 1

A more common type of phase modulation is

Quadrature Phase Shift Keying (QPSK).

QPSK is used extensively in applicationsincluding:

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 BPSKsystems (I and Q), and therefore exhibits thesame performance but twice the bandwidthefficiency.

01 00

1011

QPSK State Diagram


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Quadrature Phase Shift Keying QPSK - 2

Quadrature Phase Shift Keying can be filtered usingraised cosine filters (see later for details) to achieveexcellent out of band suppression.

Large envelope variations occur during phase

transitions, thus requiring linear amplification.


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Nyquist & Root-Raised CosineFilters

The Nyquist bandwidth is the

minimum bandwidth that can beused to represent a signal.

It is important to limit the spectraloccupancy of a signal, to improvebandwidth efficiency and removeadjacent channel interference.

Root raised cosine filters allow an

approximation to this minimumbandwidth. More discussion on the details of

these filters later.


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Types of Quadrature Phase ShiftKeying

Conventional QPSK has transitions through zero (ie. 180o phasetransitions). 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 /4-QPSK the set of constellation points are toggled for each

symbol, so transitions through zero cannot occur. This schemeproduces 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

/4 QPSK

I

(-1,1) (1,1)

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


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QPSK Summary comments

Quadrature means that the signal shifts between

phase states that are separated by 90 degrees (/2radians). The signal shifts in increments of 90 degreesfrom 45 to 135, 45, or 135 degrees.

These points are chosen as they can be easilyimplemented using an I/Q modulator.

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

There are four states because 22 = 4. It is therefore amore bandwidth-efficient type of modulation thanBPSK - potentially twice as efficient.


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Frequency Shift Keying

Frequency Modulation and Phase Modulation areclosely related.

A static frequency shift of +1 Hz means that the phaseis constantly advancing at the rate of 360 degrees per

second (2 rad/sec), relative to the phase of theunshifted signal.


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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 0

c

c

A t

s t A t

+

= +


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OscillatorFreq = f

1

OscillatorFreq = f2

ElectronicSwitch

Binary data inputm(t)

Controlline


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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

= +

=

( )( )

( ) ( )

j t

c

t

f

g t A e

t D m d

=

=


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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 typicallyused.

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


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Applications for FSK

FSK (Frequency Shift Keying) is used

in many applications includingcordless and paging systems.

Some of the cordless systems include

DECT (Digital Enhanced CordlessTelephone)

and CT-2: Cordless Telephone 2

CT-2 is a second generation cordlesstelephone system that allows users toroam away from their home basestations and receive service in publicplaces. Away from the home basestation, the service is one way outboundfrom the phone to a telepoint that iswithin range.

DECT Phone


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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 ifanother 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:

1cos 2 , when 0( )

0, otherwisem b A f t t T p t

< =

0cos 2 , when 0( )

0, otherwise

n b f t t T p t < =


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Binary Frequency-Shift Keying - 2

p1(t)

-1

-0.5

0

0.5

1

p1(t)


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Minimum Shift Keying - 2

The minimum frequency shift which yields

orthogonality of Iand Qis that which results in aphase shift of /2 radians per symbol (90 degreesper symbol).

FSK with this deviation is called MSK (MinimumShift Keying). The deviation must be accurate in

order to generate repeatable 90 degree phaseshifts.

MSK is used in the GSM (Global System for MobileCommunications) cellular standard.

A phase shift of +90 degrees represents a data bitequal to 1, while 90 degrees represents a 0.

The peak-to-peak frequency shift of an MSK signalis equal to half of the bit rate.


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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 amplifiersamplitude-transfer function, generating spectral re-growth, a

component of adjacent channel power.

Therefore, more efficient amplifiers (which tend to be lesslinear) can be used with constant-envelope signals, reducing

power consumption.


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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 waveformscausing the frequency shift.

If those waveforms have fast transitions or a high slew rate, then thespectrum 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).


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DPSK 1

Recovery of the data stream from a PSK modulated

wave requires synchronous demodulation The receiver must reconstruct the carrier exactlyso 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 andthis has the effect of simplifying the receiver.

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

It remains constant whenever a 0 appears in thestream.


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DPSK - 3

Thus we see that the receiver only needs to detect

phase changes. It does not need to search for specificphase values.

p1(t)

-1

-0.5

0

0.5

1

p1(t)

1 0 1

180phase shifts


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DPSK - 4

A further example showing how the phase changes

and is processed and finally demodulated.

Original datastream

0 1 0 0 1 1 0 0 0 1 1 1 0 0 0

Relative Phase Angle

0 + + + +2 +3 +3 +3 +3 +4 +5 +6 +6 +6 +6Processed datastream

0 1 1 1 0 1 1 1 1 0 1 0 0 0 0Demodulated Datastream

0 1 0 0 1 1 0 0 0 1 1 1 0 0 0

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Digital Modulation 02 1s