Pilot Symbol Based Detection andSynchronization for OFDM WLANs

Alan CoulsonCommunications TeamIndustrial Research Ltd

New Zealand

Introduction

� Detection and synchronization: problemdefinitions

� Pilot symbol assisted reception� Correlation-based algorithms: descriptions� Detection and synchronization: performance

results� Bit error rate performance: comparison of ideal,

analytical and simulation results

The Detection Problem

0 200 400 600 800 1000-3

-2

-1

0

1

2

3(a) Received Packet: Real Part (20dB SNR)

Am

plitu

de

Sample Number

0 200 400 600 800 1000-3

-2

-1

0

1

2

3(b) Received Packet: Imaginary Part (20dB SNR)

Am

plitu

de

Sample Number

The Synchronization Problem

The Tools

PRBS OFDM_1 OFDM_2 OFDM_N Trailer

(a) Basic OFDM Packet for Frequency Flat Fading Channel

(b) OFDM Packet for Time-Dispersive (Frequency-Selective) Channel

Guard interval / cyclic prefix

Pilot Symbol

Pilot Symbol

OFDM Block

OFDM_1 OFDM_2 OFDM_N Trailer

OFDM Block

PRBS

PRBS PRBS

1. Pilot Symbol

The Tools

R-SDecode

2 DataSink

DATA CLKDATA TRIG

FIRA/D PacketDetect

Parallel-to-Serial

FFTPLL SymbolTiming

DataDecision

MMSEUpdate

PacketTiming

Advance/Retard

Received Signal: � � � ���exp(j[2 t+ ]) (t- )r (t)=d

n nT-

� �� �u q,

u

t

n nu

SHARC 2 SHARC 3 SHARC 6 SHARC 1

2. OFDM Receiver Architecture

The Algorithms (1)

( ) 2 2 2

Hl l l L

j LT

P

L l a S e πν η+

−

=

≈ − +

r r

( ) { }22 2 2 Re

Hl l l

w

R

L a S σ η

=

≈ + +

r r

( ) ( ) ( )2 Sj nT

n Sr as nT e nTπν τ θτ η− − + = − +

Received sampled signal (flat fading), nth sample

L length, L lag sliding window correlation product

L length, 0 lag sliding window correlation product

The Algorithms (2)Detection variable 1 (positive means detection)

Frequency offset estimate

L length matched filter correlation product

( ) 12

2 2sincS

Hl l

Lj lT

LS

Q

LaS l e LST

πν τ θ φτ η− − − + +

=

≈ − +

n r

{ }{ }

Im1ˆ atan

2 Rel

l

P

LT Pν

π

=

1l l C l l LX P T R R += −

The Algorithms (3)Detection variable 2 (positive means detection)

Phase offset estimate

Timing offset estimate:

MMSE fit to phase of frequency domain data

{ }{ }

Imˆ atanRe

l

l

Q

Qθ

=

1 2l l l C lY Q Q T LS R+= + −

Results: Detection 1

-60 -40 -20 0 20 40 600

0.5

1

(a) Packet Detection Probability pX(|rl|2>TC

2), SNR/bit=20dB

p(P

acke

t D

etec

t)

Offset from Correlation Peak, l

TC2=0.5 0.5

0.6 0.60.7 0.7

0.8 0.80.90.9

1

-60 -40 -20 0 20 40 600

0.5

1

(b) Packet Detection Probability pX(|rl|2>TC

2), SNR/bit=40dB

p(P

acke

t D

etec

t)

Offset from Correlation Peak, l

TC2=0.5 0.5

0.6 0.60.7 0.7

0.8 0.80.9 0.9

1

-60 -40 -20 0 20 40 600

0.5

1

(c) Expected Value of Packet Detection Metric |rl|2

E{|r

l|2 }

Offset from Correlation Peak, l

SNR=20dBSNR=40dB

-120 -100 -80 -60 -40 -20 0 20 40 600

1

2

3

4

5x 10

7 (a) Correlation |Pl|2 and RSSI Rl

2 Outputs, SNR/bit=20dB

Exp

ecte

d V

alue

Offset from Correlation Peak, l

|Pl|2

Rl2

-60 -40 -20 0 20 40 600

0.2

0.4

0.6

0.8

1

(b) Packet Detection Metric |rl|2, SNR/bit=20dB

Exp

ecte

d V

alue

Offset from Correlation Peak, l

1. Detection statistics 2. Experimental comparison

Results: Frequency Offset Estimation

-10 -5 0 5 10 15 20 25 3010

-5

100

(a) Frequency Offset Estimation Error Variance

Var

ianc

e

SNR per Bit (dB), 20log10(aS/s w )

True Variance Gaussian ApproximationLinear Approximation

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8

10-2

100

102

(b) Frequency Offset Estimation Error Density

Pro

babi

lity

Estimation Error (radians), f

SNR=0:5:30dB

Results: Detection 2

-5 0 5 10 15 20 25 30 350

0.2

0.4

0.6

0.8

1

(a) Start of Packet Detection Probability pY(|r0"|2>TC2), TC

2=0.8

p(M

LS D

etec

t)

SNR per Bit (dB), 20log10(aS/s w )

tS=0:0.1:0.5

Ensemble

-5 0 5 10 15 20 25 30 350

0.5

1

1.5

(b) Expected Value of Start of Packet Detection Metric |r"|2

E{|r

0"|2 }

SNR per Bit (dB), 20log10(aS/s w )

tS=0:0.1:0.5

Ensemble

Results: Composite Detection

0 2 4 6 8 10 12 14 16 18 200

0.5

1

(a) Probability of Correct Packet Detection, TC22=0.8

p(de

tect

)

SNR per Bit (dB), 20log10(aS/s w )

TC12=0.6 TC1

2=0.8

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

10-20

100

(b) Probability of Noise-Only False Detection

Pro

babi

lity

Threshold of Correlation TC12=TC2

2

Sliding WindowMatched Filter

Composite

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

100

(c) Mean Time Between False Detections at 1 MHz Sample Rate

Tim

e (s

)

Threshold of Correlation TC12=TC2

2

Sliding WindowMatched Filter

Composite

Results: Phase Offset Estimation

-0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.20

5

10

15

20

25

30

35Phase Offset Estimation Error Density, SNR=20dB

Pro

babi

lity

Estimation Error (radians), a

Noise Onlypa(a|tS=0,f=0,n=0)

Timing Onlypa(a|tS=T/2)

Residual Frequency Onlypa(a|f=3s )

Composite Errorspa(a|tS=T/2,f=3s ,n=9kHz)

Ensemblepa(a)

Demonstration System

OFDM Tx spectrum

Prototype set-up

Results: Experimental Data 1

0 200 400 600-2500

-2000

-1500(a) Frequency Offset Estimate

Fre

quen

cy O

ffse

t (H

z)

OFDM Block Number

0 200 400 600-0.5

0

0.5(b) Timing Offset Estimate

Tim

ing

Off

set t

S/T

OFDM Block Number

-1 -0.5 0 0.5 1-1

-0.5

0

0.5

1(c) Received Data Constellation

Imag

inar

y P

art

Real Part

Decision Threshold

10 dB Estimated Receiver SNR

Results: Experimental Data 2

-0.5 0 0.5

-0.4

-0.2

0

0.2

0.4

0.6(a) Received Data Constellation

Imag

inar

y P

art

Real Part

Decision Threshold

0 100 200 300 400 500 600-4

-2

0

2

4(b) Received Data Phase

Pha

se (

radi

ans)

Bit Number

20 dB EstimatedReceiver SNR

Bit Error Rate Performance: Analytical

( )( )

( ) ( ) ( )

/ 20

/ 2 22

1erfc

2 2

.

TP T

e b T

ISI

w w wp

p p p d d d

π π

π π

τ α φ

µγσ σ

τ α φ τ α φ

− − −

= +

×

∫ ∫ ∫

BER for BPSK OFDM with frequency-, phase- and timing-offset estimation errors in an AWGN channel is

where second line functions are densities of parameterestimation errors

Bit Error Rate Performance: Results

-10 -5 0 5 10 1510

-6

10-5

10-4

10-3

10-2

10-1

100

BER for BPSK-Modulated OFDM in AWGN

BE

R

SNR per Bit (dB)

Ideal BPSK Analytical Pilot Symbol Based WLANSimulation Pilot Symbol Based WLAN

Summary

� Detection and synchronization: fundamental toWLAN operation

� Pilot symbol assisted reception using correlation-based algorithms: analysis facilitates setting ofkey threshold parameters

� Bit error rate performance: analytical andsimulation results closely approach ideal BPSK inan AWGN channel.