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.