Constant Envelope Modulation Schemes

Constant Envelope Modulation• Amplitude of the carrier is constant,

regardless of the variation in the modulating signal– Better immunity to fluctuations due to fading. – Better random noise immunity– Power efficient

• They occupy larger bandwidth

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Frequency Shift Keying (FSK)

• The frequency of the carrier is changed according to the message state (high (1) or low (0)).

Continues FSK

Integral of m(x) is continues.

))(22cos()(

))(2cos()(

t

fc

c

dxxmktfAts

tfAts

0)(bit Tt0 )22cos()(

1)(bit Tt0 )22cos()(

b2

b1

tffAts

tffAts

c

c

One frequency encodes a 0 while another frequency encodes a 1 (a form of frequency modulation).

FSK Bandwidth• Limiting factor: Physical capabilities of the

carrier• Not susceptible to noise as much as ASK

• Applications– On voice-grade lines, used up to 1200bps– Used for high-frequency (3 to 30 MHz) radio transmission– used at higher frequencies on LANs that use coaxial cable

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Binary Frequency Shift Keying (BFSK)

• The most common form of FSK is Binary FSK (BFSK)• Two binary values represented by two different frequencies

( f1 and f2 )

• less susceptible to noise than ASK• used for

1. up to 1200bps on voice grade lines2. high frequency radio (3 to 30MHz)3. even higher frequency on LANs using coaxial cable

0),2cos(

1),2cos()(

2

1

binarytfA

binarytfAts

0 0 1 1 0 1 0 0 0 1 0

f2 f2 f1 f1 f2 f1 f2 f2 f2 f1 f2

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Multiple FSK (MFSK)

• More than two frequencies (M frequencies) are used• More bandwidth efficient compared to BFSK• More susceptible to noise compared to BFSK• MFSK signal:

elementsignalperbitsofnumberL

elementssignaldifferentofnumberM

frequencydifferencethef

frequencycarrierthef

fMiff

where

MitfAts

L

d

c

dci

ii

2

)12(

1),2cos()(

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Multiple FSK (MFSK)

• MFSK signal:

• Period of signal element

• Minimum frequency separation

• MFSK signal bandwidth:

elementsignalperbitsofnumberL

elementssignaldifferentofnumberM

fMiff

where

MitfAts

L

dci

ii

2

)12(

1),2cos()(

ddd MffMW 2)2(

periodbitTperiodelementsignalTLTT bsbs ::,

)(2/12)/(12/1 ratebitLfTfLTfT dbdbds

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Example

• With fc=250KHz, fd=25KHz, and M=8 (L=3 bits), we have the following frequency assignment for each of the 8 possible 3-bit data combinations:

• This scheme can support a data rate of:

KHzMfWbandwidth

KHzf

KHzf

KHzf

KHzf

KHzf

KHzf

KHzf

KHzf

ds 4002

425111

375110

325101

275100

225011

175010

125001

75000

8

7

6

5

4

3

2

1

KbpsHzbitsLfT db 150)25)(3(22/1

dci fMiff )12(

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Example

• The following figure shows an example of MFSK with M=4. An input bit stream of 20 bits is encoded 2bits at a time, with each of the possible 2-bit combinations transmitted as a different frequency.

dc

dc

dc

dc

dci

fffi

fffi

fffi

fffi

fMiff

3411

310

201

3100

)12(

4

3

2

1

FSK Coherent Detection

Noncoherent FSK

Relationship between baud rate and bandwidth in FSK

Minimum frequency-shift keying

Minimum frequency-shift keying or minimum-shift keying (MSK) is a particularly spectrally efficient form of coherent FSK. In MSK the difference between the higher and lower frequency is identical to half the bit rate.

As a result, the waveforms used to represent a 0 and a 1 bit differ by exactly half a carrier period. This is the smallest FSK modulation index that can be chosen such that the waveforms for 0 and 1 are orthogonal.

A variant of MSK called GMSK is used in the GSM mobile phone standard.

MSK modulation

MSK reception

Minimum Shift Keying spectra

Relationship between baud rate and bandwidth in FSK

Gaussian Minimum frequency-shift keying

•Gaussian minimum shift keying or GMSK is a continuous-phase frequency-shift keying modulation scheme.

•It is similar to standard minimum-shift keying (MSK); however the digital data stream is first shaped with a Gaussian filter before being applied to a frequency modulator.

•This has the advantage of reducing sideband power, which in turn reduces out-of-band interference between signal carriers in adjacent frequency channels.

GMSK spectral shaping

GMSK spectra shaping

EE 552/452 Spring 2007

Simple GMSK modulation and demodulation

Digital GMSK demodulator