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QPSK Receiver

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QPSK Receiver

Integrate&DumpMF

2 stufiger Prozess

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Phasor diagram

• We can represent the BPSK signal using a phasor diagram which shows the two possible BPSK states.

• This is referred to as a signal constellation.

0˚180˚

90˚

270˚

0˚ = binary 1180˚ = binary 0

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Noise effects - BPSK

0˚180˚

90˚

270˚

10 dB SNR

0˚180˚

90˚

270˚

0˚180˚

90˚

270˚

20 dB SNR

2 dB SNR

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QPSK Receiver

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• In order to increase the data rate without increasing bandwidth, we can further increase the number of bits per symbol.

• In the 8-PSK constellation below, 8 possible phase shifts allow 3 bits to be transmitted by each symbol.

M-ary PSK

0˚180˚

90˚

270˚

0˚ = binary 000

45˚ = binary 001

90˚ = binary 011

315˚ = binary 100

270˚ = binary 101

135˚ = binary 010

180˚ = binary 110

225˚ = binary 111

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Noise effects (8-PSK)

• What is the relative likelihood of an error?

0˚180˚

90˚

270˚

10 dB SNR

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Squaring loop

• Recover frequency using squaring

0 cos(2 )cA f t

( ) ( ) cos(2 )c cu t A m t f t LowpassFilter

0 ( )2cA A m t

SquaringDevice

BandpassFilter

2 21( )[1 cos(4 )]

2 c cA m t f t

Limiter(or PLL)

FrequencyDivider

2 21( )cos(4 )

2 c cA m t f t

0 cos(4 )cA f t

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Costas Loop

180 Grad Unsicherheitengl. „Phase Ambiguity“

Bekannte Präambel notwendig

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Costas loop

• Goal of Costas loop: e0

0 cos(2 )c eA f t ( )

( ) cos(2 )c c

u t

A m t f t

BasebandLPF

0 ( ) cos( )2c

e

A Am t

BasebandLPF 0 ( )sin( )

2c

e

A Am t

LPFVCO

-90Phase shift

0 sin(2 )c eA f t

201[ ( )] sin(2 )2 2,

ce

e

A Am t

for small

sin(2 )eK