Demodulation & Bit Error Rate Testing ELEC 433 - Spring 2013 - - PowerPoint PPT Presentation

Demodulation & Bit Error Rate Testing

ELEC 433 - Spring 2013 Michael Wu & Evan Everett

Demodulation

• Assumes mapping & constellation known at

receiver

• Simply de-maps constellation points to bits
• Needs to know transmitter’s mapping
• I/Q can be de-mapped independently
• Thresholds define boundaries between

symbols

Demodulation - 16 QAM

• 1
• 1/3

1/3 1 I Q

Demodulation - 16 QAM

• 1
• 1/3

1/3 1 I Q

I Q

Demodulation - 16 QAM

• 1/2

1/2

• 1/2

1/2

Amplitude Offsets

I Q

Amplitude Offsets

I Q

Amplitude Offsets

I Q

I Q

Phase Offset

64 QAM

I Q

Phase Offset

64 QAM

Demodulation - QPSK

• QPSK is very easy to demodulate
• You’ve already built the slicer (in the Costas

loop)

• Amplitude offsets can’t cause errors
• Huge phase error tolerance

Demodulation - QPSK

I Q 00 11

Demodulation - QPSK

I Q 00 11

Demodulation - QPSK

I Q 00 11

Demodulation - QPSK

• Phase ambiguity is only problem
• QPSK and (QPSK ± Nπ/2) are identical
• Resolve with training or differential encoding

Differential Encoding

• Encode data in phase transition
• Performance hit due to memory
• One error screws up two symbol periods
• Required at both Tx and Rx

Normal Mapping

00 11 10 01 +0 00 +π/2 01

• π/2

10 +π 11

Differential Mapping

Differential Encoding Example

A D C B +0 00 +π/2 01

• π/2

10 +π 11

01 00 10 11 10 11 10

User Data: Phase Transition:

C

+π/2

• π/2

π

• π/2

Symbol to Send: A

C

• π/2

A

π

D C B D

Phase Difference: +π/2 0 -π/2 π

• π/2

π

• π/2

Received Data:

01 00 10 11 10 11 10

Differential Encoding Example

A D C B +0 00 +π/2 01

• π/2

10 +π 11

01 00 10 11 10 11 10 D

User Data: Phase Transition: +π/2 0 -π/2 π

• π/2

π

• π/2

Symbol to Send: C

D C B D A B

Phase Difference: +π/2 0 -π/2 π

• π/2

π

• π/2

Received Data:

01 00 10 11 10 11 10

Differential Encoding

Encoding Decoding

Concatenate LUT Slice Rx data z-1 data bits

Suggested Implementations

data bits Concatenate prev symbol LUT Tx Symbol Modulation

Bit Error Rate Testing

• Transmitter sends periodic frames
• Frame =
• ROM of bits indexed by counter works for this
• Receiver knows same bit sequence
• Correlator looks for header to find beginning
• f frame
• Counters track total bits and bits in error
• Don’t do division (error/total) in hardware

Pseudo-Random bits Header

Header Correlation

• Header needs good autocorrelation characteristic
• High autocorrelation when aligned, low when not
• Delta function would be ideal autocorrelation
• Barker codes and MLS well-suited

Received Signal

Random bits Header

Reference Frame

Correlator Threshold

Random bits Header

Header Correlation

• Header needs good autocorrelation characteristic
• High autocorrelation when aligned, low when not
• Delta function would be ideal autocorrelation
• Barker codes and MLS well-suited

Received Signal

Random bits Header

Reference Frame

Correlator Threshold

1

Random bits Header Random bits

Header Correlation

• Header needs good autocorrelation characteristic
• High autocorrelation when aligned, low when not
• Delta function would be ideal autocorrelation
• Barker codes and MLS well-suited

Received Signal

Random bits Header

Reference Frame

Correlator Threshold

Random bits Header Random bits Header

Autocorrelation Example

−40 −20 20 40 −0.2 0.2 0.4 0.6 0.8 1 1.2 Lag (samples) Sample Autocorrellation

20 40 60 80 −1 1 n x[n]

5 10 15 −1 1 x[n]

−20 −10 10 20 −0.2 0.2 0.4 0.6 0.8 1 1.2 Lag (samples) Sample Autocorrellation

Length-63 MLS Length-13 Barker Code

Lab 9 Summary

• Implement differential encoded QPSK modulator/

demodulator

• Implement BER testing subsystem
• Correllator to align transmitted and received frames

for bitwise comparison

• Simulink AWGN channel between Tx and RX to verify
• Characterize over-the-air BER performance of

your design