# I. Previously on IET - PowerPoint PPT Presentation

1 / 12

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

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

I. Previously on IET

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

## I. Previously on IET

### 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

4

3

### 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 QPSK BER Performance

Given transmitted :

ES  Energy per Symbol

2

1

4

3

### 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

12