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I. Previously on IET. QPSK Modulation over AWGN Channels. E S  Energy per Symbol. Symbol Error given transmitted : Noise on Cosine axis < or Noise on Sine axis <. BER of QPSK over AWGN Channels. Notes: Define N 0 Total Noise Power

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Qpsk modulation over awgn channels
QPSK Modulation over AWGN Channels

ES  Energy per Symbol

Symbol Error given transmitted :

Noise on Cosine axis <

or Noise on Sine axis <


Ber of qpsk over awgn channels
BER of QPSK over AWGN Channels

Notes:

  • Define N0 Total Noise Power

    • N0/2  Noise Power over Cosine axis, i.e., σ2=N0/2

    • N0/2  Noise Power over Sine axis, i.e., σ2=N0/2

  • Each symbol MOST LIKELY corresponds to a single bit (Gray Coding)

    • Eb = ES/2

    • Pb ≈ Pe/2

01

11

10

00

Gray Coding: Neighbor constellations points vary in only one bit


Union bound for qpsk ber performance
Union Bound for QPSK BER Performance

Given transmitted :

ES  Energy per Symbol

2

1

4

3


Union bound for qpsk ber performance1
Union Bound for QPSK BER Performance

Given transmitted :

ES  Energy per Symbol

2

1

d12 : Euclidian distance between constellation points 1 & 2

P12 : Probability received signal closer to constellation point 2 than constellation point 1 given constellation point 1 transmitted


Union bound for qpsk ber performance2
Union Bound for QPSK BER Performance

Given transmitted :

ES  Energy per Symbol

1

3

d13 : Euclidian distance between constellation points 1 & 3

P13 : Probability received signal closer to constellation point 3 than constellation point 1 given constellation point 1 transmitted


Union bound for qpsk ber performance3
Union Bound for QPSK BER Performance

Given transmitted :

ES  Energy per Symbol

1

4

d14 : Euclidian distance between constellation points 1 & 4

P14 : Probability received signal closer to constellation point 4 than constellation point 1 given constellation point 1 transmitted


Union bound for qpsk ber performance4
Union Bound for QPSK BER Performance

Given transmitted :

ES  Energy per Symbol

2

1

4

3



Union bound for 8 psk modulation ber
Union Bound for 8 PSK Modulation BER

ES  Energy per Symbol

M=8

001

011

000

dmin

Θ

001

010

110

101

111


Union bound for 16 qam modulation ber
Union Bound for 16 QAM Modulation BER

ES  Energy per Symbol

M=16

0010

0011

0001

0000

dmin

0110

0111

0101

0100

1110

1111

1101

1100

1010

1011

1001

1000