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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

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

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 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 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 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

ES Energy per Symbol

M=16

0010

0011

0001

0000

dmin

0110

0111

0101

0100

1110

1111

1101

1100

1010

1011

1001

1000

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