Drawbacks of OFDM Systemswebmail.aast.edu/~khedr/Courses/VT/OFDM/lecture_thrtn_frtn_sync.pdf ·...

58
Drawbacks of OFDM Systems High sensitivity to carrier frequency offsets (CFO) High peak-to-average power ratios (PAPR) problem Limited Frequency Diversity MC 2007 c Jian (Andrew) Zhang 31

Transcript of Drawbacks of OFDM Systemswebmail.aast.edu/~khedr/Courses/VT/OFDM/lecture_thrtn_frtn_sync.pdf ·...

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Drawbacks of OFDM Systems

High sensitivity to carrier frequency offsets (CFO)

High peak-to-average power ratios (PAPR) problem

Limited Frequency Diversity

MC 2007 c©Jian (Andrew) Zhang 31

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PAPR Problem

OFDM suffers from high PAPR defined as,

ξ =maxt∈[0,T ] |x(t)|2

Pav=

maxt∈[0,T ] |x(t)|2E{|x(t)|2} (7)

Large PAPR implies larger dynamic range of signals and causesproblems in power amplifier, ADC and so on.

PAPR can be characterized by CCDF.

MC 2007 c©Jian (Andrew) Zhang 35

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CCDF of PAPRComplementary cumulative distribution function (CCDF): Probabilitythat the PAPR of an OFDM symbol exceeds a given threshold

MC 2007 c©Jian (Andrew) Zhang 36

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Aalborg University

Troels B. Sørensen {[email protected]}; Department of Electronics Systems, Aalborg University

Time synchronizationsPacket detection

Frame synchronization

Frequency synchronizationsCarrier frequency synchronizationSampling frequency synchronization

Cause of synchronization error:Asynchronous transmission => unknown transmit times Circuit elements are never ideal

Local oscillators are never idealFrequency offset Phase noise

Clocks are never idealFrequency offsetjitter

Synchronization Issues in OFDM SystemsSynchronization Issues in OFDM Systems

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Aalborg University

Troels B. Sørensen {[email protected]}; Department of Electronics Systems, Aalborg University

• What are their impacts of synchronization error?

• Time domain effect

• Incorrect packet start => packet detection error, packet loss

• Incorrect symbol window => Inter-symbol Interference.

• Carrier freq. offset => phase rotation on symbol

• Sampling freq. offset => incorrect sampling instant.

•Frequency domain effect

•Incorrect packet start => rotation of constellation

•Incorrect symbol window => rotation of constellation

•Carrier freq. offset => Inter-Carrier-Interference

•Sampling freq. offset => Inter-Carrier-Interference

Synchronization Issues in OFDM SystemsSynchronization Issues in OFDM Systems

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Aalborg University

Troels B. Sørensen {[email protected]}; Department of Electronics Systems, Aalborg University

Frequency Synchronization Frequency Synchronization 1. Carrier Frequency synchronization2. Sampling frequency synchronization

What is the cause for Carrier Frequency Offset Error ?Mismatch in local oscillator frequency between transmitter and ReceiverPhase noise of the local oscillator at Transmitter and receiver

How does it effect the system ?Loss in orthogonally between sub-carriers Inter carrier interferenceCan be partly compensated; Partly irreducible noise floor

What are the mitigation strategies ?Using Training sequenceUsing Pilots

Page 7: Drawbacks of OFDM Systemswebmail.aast.edu/~khedr/Courses/VT/OFDM/lecture_thrtn_frtn_sync.pdf · Drawbacks of OFDM Systems High sensitivity to carrier frequency offsets (CFO) ... Timing

Aalborg University

Troels B. Sørensen {[email protected]}; Department of Electronics Systems, Aalborg University

Carrier Frequency offsetCarrier Frequency offset

0 1 2 3 4 5 6 7

Frequency

Am

plit

ud

e

Carrier Frequency offset

sub-carriers

Peak

Nulls

Peaks at other’s null

Attenuation

ICI

Page 8: Drawbacks of OFDM Systemswebmail.aast.edu/~khedr/Courses/VT/OFDM/lecture_thrtn_frtn_sync.pdf · Drawbacks of OFDM Systems High sensitivity to carrier frequency offsets (CFO) ... Timing

CFO Sensitivity

Received signal with a frequency offset fo

rk =

N−1∑

m=0

HmXmej2πk(m+ǫ)/N + nk , k ∈ [0, N − 1] (5)

where ǫ = fo/∆f is the normalized CFO.After transferring to frequency domain

Rℓ =N−1∑

k=0

rke−j2πℓk/N = XℓHℓsin(πǫ)

N sin(πǫ/N)ejπǫ(N−1)/N + Iℓ + Zℓ

where Iℓ =∑N−1

l=0,l 6=ℓ XlHlsin(πǫ)

N sin(π(l−ℓ+ǫ/N))ejπǫ(N−1)/Nejπ(l−ℓ)/N is

the ICI term.Different to single carrier systems, CFO causes ICI in OFDMsystems.

MC 2007 c©Jian (Andrew) Zhang 32

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Page 14Wireless Networking Design Seminar DesignGuideNovember, 2001

Page 14Agilent Technologies

Inter-Carrier Interference(ICI) Due to Frequency Offset

1/T

FFT

T

T

FFT

No frequency offset

With frequency offset

FFT window

Integer number of cycles of the sub-carrier ensures that the nulls of the spectrum lands on the FFT bin, condition to avoid inter-carrier interference (ICI)

Page 10: Drawbacks of OFDM Systemswebmail.aast.edu/~khedr/Courses/VT/OFDM/lecture_thrtn_frtn_sync.pdf · Drawbacks of OFDM Systems High sensitivity to carrier frequency offsets (CFO) ... Timing

Page 15Wireless Networking Design Seminar DesignGuideNovember, 2001

Page 15Agilent Technologies

OFDM Operation (ICI problem)

10 20 30 40 50 600 70

0.5

1.0

0.0

1.5

Index

ma

g(F

1)

10 20 30 40 50 600 70

-0.02

-0.01

0.00

0.01

0.02

-0.03

0.03

Index

rea

l(T

1)

Symbol to be transmitted(Magnitude spectrum)

I-channel signal(after IFFT)

Recovered symbolcontains ICI

DemodulatedI-channel signal

10 20 30 40 50 600 70

-0.02

-0.01

0.00

0.01

0.02

-0.03

0.03

Index

rea

l(R

T1

)

10 20 30 40 50 600 70

0.5

1.0

0.0

1.5

Index

ma

g(R

F1

)

Frequency offset = 60 kHz

FFT

I-Q Demodulator

IFFT

I-Q Modulator

N_Tones

N2

RandomPhase=NoPhase1=0.0

Power1=.010 WFrequency1=(FCarrier-0.06) MHz

TStep=tstep sec

N_Tones

N1

Phase1=0.0

Power1=.010 WFrequency1=FCarrier MHz

TStep=tstep sec

RectToCx

R1

NumericSink

RF1

FFT_Cx

F17

Direction=ForwardSize=64

Order=6

TimedToFloatT5

TimedToFloatT4

QAM_DemodExtOsc

Q2

PhaseImbalance=0GainImbalance=0

Sensitivity=0.5

FloatToTimedF16

TStep=0.0 sec

FloatToTimedF15

TStep=0.0 sec

FFT_CxF11

Direction=Inverse

Size=64Order=6

WaveFormCxW1

Period=64Periodic=YES

ControlSimulation=NOValue="(0) (0) (0) (1+j) "

CxToRectC1

QAM_ModExtOscQ1

PhaseImbalance=0GainImbalance=0

VRef=1 VPower=0.01 W

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Page 16Wireless Networking Design Seminar DesignGuideNovember, 2001

Page 16Agilent Technologies

Effects of Frequency Offset – Without Frequency Correction

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

real(iq[1,::])

ima

g(i

q[1

,::])

-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0

-2

-1

0

1

2

real(iq[2,::])

ima

g(i

q[2

,::])

-15 -10 -5 0 5 10 15

-10

-5

0

5

10

15

real(iq[3,::])

ima

g(i

q[3

,::])

AA=0Freq. Offset = 0 HzFreq. Offset / Freq. Spacing = 0%

AA=1Freq. Offset = 3.125 kHzFreq. Offset / Freq. Spacing = 1%

AA=2Freq. Offset = 31.25 kHzFreq. Offset / Freq. Spacing = 10%

AA=3Freq. Offset = 156.25 kHzFreq. Offset / Freq. Spacing = 50%

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

-1.0

-0.5

0.0

0.5

1.0

real(iq[0,::])

ima

g(i

q[0

,::])

Freq. Offset / Freq. Spacing

0%

1%

10%

50%

IndexAA=0.000

40

AA=1.00040

AA=2.00040

AA=3.00040

ReceiverEVM

1.198E-5

0.025

0.268

2.840

Frequency offset expressed as a percentage of sub-carriers frequency spacing (∆f=312.5kHz):

0% 1% 10% 50%

Why you needfrequency offset correction:

assume freq. offset=3kHz (1%),requires:oscillator stability: 3k/5.8G=0.5ppm!

Dr. M. Khedr
Stamp
Dr. M. Khedr
Rectangle
Page 12: Drawbacks of OFDM Systemswebmail.aast.edu/~khedr/Courses/VT/OFDM/lecture_thrtn_frtn_sync.pdf · Drawbacks of OFDM Systems High sensitivity to carrier frequency offsets (CFO) ... Timing

CFO Sensitivity (cont.)

MC 2007 c©Jian (Andrew) Zhang 33

Dr. M. Khedr
Rectangle
Page 13: Drawbacks of OFDM Systemswebmail.aast.edu/~khedr/Courses/VT/OFDM/lecture_thrtn_frtn_sync.pdf · Drawbacks of OFDM Systems High sensitivity to carrier frequency offsets (CFO) ... Timing

CFO Sensitivity - SNR Degradation

For relatively small frequency errors, the degradation in dB can beapproximated by

SNRloss =10

3 ln 10(πTsǫ)

2Es/N0dB (6)

MC 2007 c©Jian (Andrew) Zhang 34

Page 14: Drawbacks of OFDM Systemswebmail.aast.edu/~khedr/Courses/VT/OFDM/lecture_thrtn_frtn_sync.pdf · Drawbacks of OFDM Systems High sensitivity to carrier frequency offsets (CFO) ... Timing

Loss of orthogonality (by frequency offset)

ψ k (t) = exp( jk2πt / T ) y ψ k +m ( t) = exp j2π (k + m)t / T( )

ψ k +mδ (t) = exp j2π (k + m + δ ) / T( ) con δ ≤ 1 / 2

Transmission pulses

Reception pulse with offset δ δ δ δ

2 4 6 8 10 12 14 16-60-55-50-45-40-35-30-25-20-15-10

Total ICI due to loss of orthogonality

Carrier position within the band (N=16)

ICI i

ndB

δ =0.05

δ =0.02

δ =0.01

δ =0.005

δ =0.002

δ =0.001

Practical limitδδδδ assumed r.v.Gaussian σ=δ

0-0.4 -0.3 -0.2 -0.1 0.1 0.2 0.3 0.4

Frequency offset: ∂

Inte

rfere

nce:

Im(�)

/T e

ndB

Loss for 8 carriers

m=1

m=3m=5m=7

-70

-60

-50

-40

-30

-20

-10

0

Im(δ ) = exp jk 2πt / T( )exp − j(k + m + δ )2πt / T( )dt0

T

� =T 1 − exp(− j2πδ )( )

j2π(m + δ )

Im (δ) =T sin πδπ m + δ

Im2 (δ)

m� ≈ Tδ( )2 1

m 2m =1

N −1

� ≈ Tδ( )2 2314

for N >> 1 (N > 5 Is enough)

Interference betweenchannels k and k+m

Summing up ∀ m

Asymetric

Page 15: Drawbacks of OFDM Systemswebmail.aast.edu/~khedr/Courses/VT/OFDM/lecture_thrtn_frtn_sync.pdf · Drawbacks of OFDM Systems High sensitivity to carrier frequency offsets (CFO) ... Timing

Loss of orthogonality (time)

Xi = c0 ψ k (t)ψ l* ( t − τ )dt

−T / 2

− T / 2+τ

� + c1 ψ k (t)ψ l* (t − τ )dt

−T / 2+τ

T / 2

�Let us assumea misadjustment ττττ

2 consecutivesymbols

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.0810

15

20

25

30

35

40

45

Typical deviation for the relative misadjustment

ICI i

ndB

N=8

N=64

ICI due to loss of orthogonaliy

τ assumed an Uniform r.v.

Max. practical limit

Doubling N means 3 dB more ICI

EXi

2

T 2

� �

� � = 4

τT

� �

2 12

+ 012

= 2τT

� �

2 ICI ≈ 20log 2τT

� � , τ << T

Per carrier

In average, the interferingpower in any carrier is

Xi

T≈

2mπ τT

mπ= 2

τT

Or approximately,when τ<<T

independenton m

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-50

-45

-40-35

-30

-25

-20

-15-10

-5

0

Relative misadjustment τ

Inte

rfer

ence

endB

Loss for 16 carriers

m=1

m=5

m=10

Then Xi = 2Tsenmπ

τT

mπ, c0 ≠ c1

0, c0 = c1

� �

� �

Zone of interest

if m=k-l

Page 16: Drawbacks of OFDM Systemswebmail.aast.edu/~khedr/Courses/VT/OFDM/lecture_thrtn_frtn_sync.pdf · Drawbacks of OFDM Systems High sensitivity to carrier frequency offsets (CFO) ... Timing

Aalborg University

Troels B. Sørensen {[email protected]}; Department of Electronics Systems, Aalborg University

Example transmission formatExample transmission formatTiming Synchronization

IEEE 802.11a Frame format

Page 17: Drawbacks of OFDM Systemswebmail.aast.edu/~khedr/Courses/VT/OFDM/lecture_thrtn_frtn_sync.pdf · Drawbacks of OFDM Systems High sensitivity to carrier frequency offsets (CFO) ... Timing

Aalborg University

Troels B. Sørensen {[email protected]}; Department of Electronics Systems, Aalborg University

Example transmission formatExample transmission formatTiming Synchronization

IEEE 802.11a Preamble (source IEEE 802.11a standard)

•t1,t2….t10 are identical

• t1,t2,…..t10 are of duration ¼ times the FFT duration • => the sub—carrier spacing is 4 times more than in the Data part

•T1 and T2 are also identical

•They are of same duration as the normal OFDM symbol

Page 18: Drawbacks of OFDM Systemswebmail.aast.edu/~khedr/Courses/VT/OFDM/lecture_thrtn_frtn_sync.pdf · Drawbacks of OFDM Systems High sensitivity to carrier frequency offsets (CFO) ... Timing

Aalborg University

Troels B. Sørensen {[email protected]}; Department of Electronics Systems, Aalborg University

Packet Detection and AGCPacket Detection and AGC

First training tasks of a digital receiver:

Packet detectionDetect start of a signal, based on detecting energy jump or by acorrelator exceeding some threshold

Automatic Gain ControlAdjust RF gain such that A/D converter gets appropriate signal input level with best possible Signal-to-Quantization+ClippingNoise Ratio

Key Performance parameters:1) 1) Probability of missed detect = missing a valid packet2) Probability of false alarm = detecting a non-valid packet

1) gives packet errors, 2) gives higher power consumption by spending processing power on non-valid packets, and it can also lead to missed detects as a valid packet comes in while the receiver thinks it is already decoding a packet.

Page 19: Drawbacks of OFDM Systemswebmail.aast.edu/~khedr/Courses/VT/OFDM/lecture_thrtn_frtn_sync.pdf · Drawbacks of OFDM Systems High sensitivity to carrier frequency offsets (CFO) ... Timing

Packet Detection - Signal Energy Detection

Received Signal Energy Detection: Compare the decisionvariable mn with a predefined threshold where mn is the receivedsignal energy accumulated over some window of length M

mn =M−1∑

k=0

|rn−k |2 (1)

Calculation of mn can be simplified by noting that it is a movingsum of the received signal energy (Sliding window);Sometimes implemented in analog domain to mitigate the impactof RF circuit including AGC;A fixed threshold does not work well.

MC 2007 c©Jian (Andrew) Zhang 7

Page 20: Drawbacks of OFDM Systemswebmail.aast.edu/~khedr/Courses/VT/OFDM/lecture_thrtn_frtn_sync.pdf · Drawbacks of OFDM Systems High sensitivity to carrier frequency offsets (CFO) ... Timing

Double Sliding Window Packet Detection

Double Sliding Window Packet Detection: Let mn be the ratio ofthe received energy within two consecutive sliding windows.

mn =

∑M1−1k=0 |rn+k |2

∑M2−1ℓ=0 |rn−ℓ|2

(2)

The value of mn is more stable;The peak point of mn is approximately equal to the received SNR(SNR+1).

MC 2007 c©Jian (Andrew) Zhang 8

Page 21: Drawbacks of OFDM Systemswebmail.aast.edu/~khedr/Courses/VT/OFDM/lecture_thrtn_frtn_sync.pdf · Drawbacks of OFDM Systems High sensitivity to carrier frequency offsets (CFO) ... Timing

Packet Detection - Delay and Correlate Algorithm

Exploiting the periodicity of the short training symbols in thepreamble

Algorithm similar to the approach presented in Schmidl and Cox[1]

mn =

∑M−1k=0 rn+k r∗n+k+D

2

(∑M−1

k=0 |rn+k+D|2)2 (3)

where D is the period of the short training symbols, andgenerally M ≥ D.

MC 2007 c©Jian (Andrew) Zhang 9

Page 22: Drawbacks of OFDM Systemswebmail.aast.edu/~khedr/Courses/VT/OFDM/lecture_thrtn_frtn_sync.pdf · Drawbacks of OFDM Systems High sensitivity to carrier frequency offsets (CFO) ... Timing

Aalborg University

{petarp,imr}@kom.aau.dk ; Department of Electronics Systems, Aalborg University

Packet Detection contPacket Detection cont……Timing Synchronization

Page 23: Drawbacks of OFDM Systemswebmail.aast.edu/~khedr/Courses/VT/OFDM/lecture_thrtn_frtn_sync.pdf · Drawbacks of OFDM Systems High sensitivity to carrier frequency offsets (CFO) ... Timing

Packet Detection - Performance Comparison

The decision statistic mn for IEEE802.11a preamble in 10dB SNR

MC 2007 c©Jian (Andrew) Zhang 10

Page 24: Drawbacks of OFDM Systemswebmail.aast.edu/~khedr/Courses/VT/OFDM/lecture_thrtn_frtn_sync.pdf · Drawbacks of OFDM Systems High sensitivity to carrier frequency offsets (CFO) ... Timing

Aalborg University

Troels B. Sørensen {[email protected]}; Department of Electronics Systems, Aalborg University

Implementing a simple packet detection algorithmImplementing a simple packet detection algorithmTiming synchronization

Packet Detect

saturation

ADC range

Noise region Packet region

Time axis

AGC Gain

AGC Control during packet detection

+vmax

-vmax

+vmax

+vmax

Page 25: Drawbacks of OFDM Systemswebmail.aast.edu/~khedr/Courses/VT/OFDM/lecture_thrtn_frtn_sync.pdf · Drawbacks of OFDM Systems High sensitivity to carrier frequency offsets (CFO) ... Timing

2004/4/29 WLAN group5

timing synchronization (I)Using correlator:

From the delay correlate structure, the decision is calculate as

1*

0

L

n n k n k Dk

c r r−

+ + +=

=∑1 1

2*

0 0

L L

n n k D n k D n k Dk k

p r r r− −

+ + + + + += =

= =∑ ∑

( )

2

2n

nn

cm

p= 16L 16,D where ==

Z-D

( )*

C

P

| |2

( )2

mnCn

Pn

rn

Page 26: Drawbacks of OFDM Systemswebmail.aast.edu/~khedr/Courses/VT/OFDM/lecture_thrtn_frtn_sync.pdf · Drawbacks of OFDM Systems High sensitivity to carrier frequency offsets (CFO) ... Timing

2004/4/29 WLAN group6

timing synchronization (II): Double sliding window

The double sliding window packet detection algorithm calculates two consecutive sliding windows of the received energy The basic principle is to form the decision variable as a ratio of total energy contained inside the two windows as follows

nm

Page 27: Drawbacks of OFDM Systemswebmail.aast.edu/~khedr/Courses/VT/OFDM/lecture_thrtn_frtn_sync.pdf · Drawbacks of OFDM Systems High sensitivity to carrier frequency offsets (CFO) ... Timing

2004/4/29 WLAN group9

The effect of CFOIn OFDM system, if there is any mismatch between the frequency and phase of Tx and Rx, it will result CFOThere are two destructive effects caused by CFO

One is the reduction of signal amplitude It will result in ICI which is caused by the loss of the subcarriers orthogonality

The FFT output for each subcarrier will contain interference term from other subcarrier

Page 28: Drawbacks of OFDM Systemswebmail.aast.edu/~khedr/Courses/VT/OFDM/lecture_thrtn_frtn_sync.pdf · Drawbacks of OFDM Systems High sensitivity to carrier frequency offsets (CFO) ... Timing

2004/4/29 WLAN group10

Math analysis of ICI An OFDM transmission symbol is given by the N point complex modulation sequence

After passing through channel, the received sequence can be expressed as

The output of the FFT for k th subcarrier consisting of three components

21 j nkkN

n kk k

x X eN

π

=−

= ∑

( )21 j n kkN

n k k nk k

y X H e wN

π ε+

=−

⎡ ⎤= +⎢ ⎥

⎢ ⎥⎣ ⎦∑

21

0

j knNN

k n k k kn

Y y e S I Wπ−−

=

= = + +∑

Page 29: Drawbacks of OFDM Systemswebmail.aast.edu/~khedr/Courses/VT/OFDM/lecture_thrtn_frtn_sync.pdf · Drawbacks of OFDM Systems High sensitivity to carrier frequency offsets (CFO) ... Timing

2004/4/29 WLAN group11

Cont’d

Then ,the variance of interference signal

Generally, the interference power is proportional to the frequency offset

( ) ( )( ) ( )

Nklj

NNjk

klkl

llk ee

NklN

HXI−−−

≠−=

⎪⎪⎭

⎪⎪⎬

⎪⎪⎩

⎪⎪⎨

⎟⎠⎞

⎜⎝⎛ +−

= ∑ππε

εππε 1

sin

sin

( ) ( )2222 sin5947.0 πεHXIE k ≤

Page 30: Drawbacks of OFDM Systemswebmail.aast.edu/~khedr/Courses/VT/OFDM/lecture_thrtn_frtn_sync.pdf · Drawbacks of OFDM Systems High sensitivity to carrier frequency offsets (CFO) ... Timing

2004/4/29 WLAN group12

SNR degradation

The degradation D is given by

where

OFDM 31

10ln10

0

2

NE

RfND s⎟⎠⎞

⎜⎝⎛ ∆

≈ π

carrier Single 31

10ln10 2

⎟⎠⎞

⎜⎝⎛ ∆

≈RfD π

carrier singelfor /1 , OFDMfor / TRTNR ==

Page 31: Drawbacks of OFDM Systemswebmail.aast.edu/~khedr/Courses/VT/OFDM/lecture_thrtn_frtn_sync.pdf · Drawbacks of OFDM Systems High sensitivity to carrier frequency offsets (CFO) ... Timing

2004/4/29 WLAN group13

CFO estimation Using the correlator that takes maximum likelihood estimation (MLE) to estimate the CFO The received signal is

The correlator output is

( )

2 2

2

2

tx s rx s

tx rx s

s

j f nT j f nTn n

j f f nTn

j f nTn

r s e e

s e

s e

π π

π

π ∆

=

=

=

*

0

22

0

s

L

k k Dk

Lj f DT

nk

z r r

e sπ ∆

+=

=

=

=

Page 32: Drawbacks of OFDM Systemswebmail.aast.edu/~khedr/Courses/VT/OFDM/lecture_thrtn_frtn_sync.pdf · Drawbacks of OFDM Systems High sensitivity to carrier frequency offsets (CFO) ... Timing

2004/4/29 WLAN group14

Cont’dFinally, the frequency error estimator is formed as

The algorithm is simple and can use the same hardware of the delay and correlate algorithm

( )1 arg2 s

f zDTπ

∆ = −

Page 33: Drawbacks of OFDM Systemswebmail.aast.edu/~khedr/Courses/VT/OFDM/lecture_thrtn_frtn_sync.pdf · Drawbacks of OFDM Systems High sensitivity to carrier frequency offsets (CFO) ... Timing

2004/4/29 WLAN group15

Algorithm of CFOThe CFO algorithm is based on packet detection algorithm when packet is detected over the thresholdThe algorithm is described as

Then, the coarse CFO is

( ) ( )( )

1*

01

2

0

L

n k n k Dk

L

n k Dk

r rC nM n

P n r

+ + +=−

+ +=

= =∑

( )( ) ( )1 arg |

2coarse M n THs

f C nDTπ

>∆ =

Page 34: Drawbacks of OFDM Systemswebmail.aast.edu/~khedr/Courses/VT/OFDM/lecture_thrtn_frtn_sync.pdf · Drawbacks of OFDM Systems High sensitivity to carrier frequency offsets (CFO) ... Timing

2004/4/29 WLAN group16

Algorithm of the fine CFODuring short preamble, we get the coarse CFO , in this algorithm the correlator can be used again The algorithm is described as

The fine estimation of CFO is

( ) ( )

( ) ( )( )( )

' exp 2

exp arg /

long long coarse

long s

r k r k j k f

r k jk C m DT

π∧⎛ ⎞= − ∆⎜ ⎟

⎝ ⎠

= − ⋅

( )2 1 *' '1 arg 64

2

L

L

L

N

l l N Lfinel NL s

f r r NN Tπ

−∧

−=

⎛ ⎞∆ = =⎜ ⎟

⎝ ⎠∑

Page 35: Drawbacks of OFDM Systemswebmail.aast.edu/~khedr/Courses/VT/OFDM/lecture_thrtn_frtn_sync.pdf · Drawbacks of OFDM Systems High sensitivity to carrier frequency offsets (CFO) ... Timing

2004/4/29 WLAN group17

Cont’d After finishing the acquisition of CFO, both coarse and fine estimation is available

Therefore, the received signal is described as

exp 2 k k coarse finer r j f f kπ∧ ∧ ∧⎛ ⎞⎛ ⎞= − ∆ + ∆⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠

Page 36: Drawbacks of OFDM Systemswebmail.aast.edu/~khedr/Courses/VT/OFDM/lecture_thrtn_frtn_sync.pdf · Drawbacks of OFDM Systems High sensitivity to carrier frequency offsets (CFO) ... Timing

Aalborg University

Troels B. Sørensen {[email protected]}; Department of Electronics Systems, Aalborg University

Frame or Symbol Synchronization Frame or Symbol Synchronization

Goal:To align the symbol window to reduce Inter symbol interference. i.e. To identify and locate the FFT window.

Why do we need itPacket detection gives the approximate start of the frame, we need to find the exact start of the FFT window Otherwise, there will be ISI and irreducible error floor.

General method is using cross correlation in time domain; Can bedone based on

Training sequenceCyclic prefix

Page 37: Drawbacks of OFDM Systemswebmail.aast.edu/~khedr/Courses/VT/OFDM/lecture_thrtn_frtn_sync.pdf · Drawbacks of OFDM Systems High sensitivity to carrier frequency offsets (CFO) ... Timing

Aalborg University

Troels B. Sørensen {[email protected]}; Department of Electronics Systems, Aalborg University

Cyclic Prefix based Frame Synchronization Cyclic Prefix based Frame Synchronization

Cross Correlate two portions of the received signal with a separation of “N” samples, where “N” is the number of samples in a FFT.Find the peaks of the correlation coefficientsThe location of the peaks gives the starting point of the frame or the FFT window

Frames in OFDM transmission systems

GI symbol GI symbol GI symbol

Co

rre

latio

nc

oe

ffic

ien

t

Time axis

Page 38: Drawbacks of OFDM Systemswebmail.aast.edu/~khedr/Courses/VT/OFDM/lecture_thrtn_frtn_sync.pdf · Drawbacks of OFDM Systems High sensitivity to carrier frequency offsets (CFO) ... Timing

Aalborg University

{petarp,imr}@kom.aau.dk ; Department of Electronics Systems, Aalborg University

Frame or symbol timing Frame or symbol timing Timing synchronization

Frames in OFDM transmission systems

GI symbol GI symbol GI symbol

Time axis

Effect of channel convolution

Ideal FFT window

True FFT window

due to channel

Need for Frame synchronization

Page 39: Drawbacks of OFDM Systemswebmail.aast.edu/~khedr/Courses/VT/OFDM/lecture_thrtn_frtn_sync.pdf · Drawbacks of OFDM Systems High sensitivity to carrier frequency offsets (CFO) ... Timing

Aalborg University

{petarp,imr}@kom.aau.dk ; Department of Electronics Systems, Aalborg University

Synchronization Using Cyclic PrefixSynchronization Using Cyclic Prefix

Perform autocorrelation over guard interval to find both timing and frequency offset

Average over several OFDM symbols to reduce undesired correlation sidelobes of random data

Tdelay

dtTG

∫OFDMsignal Timing

Findmaximumcorrelation

ConjugationEstimatephase of

maximumFrequencyoffset

Page 40: Drawbacks of OFDM Systemswebmail.aast.edu/~khedr/Courses/VT/OFDM/lecture_thrtn_frtn_sync.pdf · Drawbacks of OFDM Systems High sensitivity to carrier frequency offsets (CFO) ... Timing

Aalborg University

Troels B. Sørensen {[email protected]}; Department of Electronics Systems, Aalborg University

Cyclic Prefix based Frame Synchronization Cyclic Prefix based Frame Synchronization

• Cyclic prefix based synchronization is prone to errors because of channel convolution in the Guard Interval (Cyclic prefix region)• Algorithm can be improved following similar steps as frame synchronization using training sequence• Implementation can be optimized ………..needs detailed analysis of the system and the algorithm

• We generally use a two stage algorithm• Acquisition using Training sequence• Tracking using cyclic prefix

Page 41: Drawbacks of OFDM Systemswebmail.aast.edu/~khedr/Courses/VT/OFDM/lecture_thrtn_frtn_sync.pdf · Drawbacks of OFDM Systems High sensitivity to carrier frequency offsets (CFO) ... Timing

Aalborg University

Troels B. Sørensen {[email protected]}; Department of Electronics Systems, Aalborg University

Synchronization with Special Training SymbolsSynchronization with Special Training Symbols

Use matched filter matched to special training symbol

Choose training symbol such that

Peak-to-average power ratio is minimal

Multipliers can be as simple as possible

Input

Σ

xc0

T T T

c1 x xcN-1

Findmaximum

Symboltiming

Page 42: Drawbacks of OFDM Systemswebmail.aast.edu/~khedr/Courses/VT/OFDM/lecture_thrtn_frtn_sync.pdf · Drawbacks of OFDM Systems High sensitivity to carrier frequency offsets (CFO) ... Timing

Aalborg University

Troels B. Sørensen {[email protected]}; Department of Electronics Systems, Aalborg University

Effects of Frame Synchronization Errors Effects of Frame Synchronization Errors

• Constellation rotation

• Correctable by channel equalization

• ISI error floor• Performance measure of algorithm in terms of SNR loss

−1.5 −1 −0.5 0 0.5 1 1.5−1.5

−1

−0.5

0

0.5

1

channel Compensation

rxConstellationChCompPhUnrxConstellationChUnComptxConstellation

constellation rotation due to frame synch error

Page 43: Drawbacks of OFDM Systemswebmail.aast.edu/~khedr/Courses/VT/OFDM/lecture_thrtn_frtn_sync.pdf · Drawbacks of OFDM Systems High sensitivity to carrier frequency offsets (CFO) ... Timing

Aalborg University

Troels B. Sørensen {[email protected]}; Department of Electronics Systems, Aalborg University

Carrier Frequency Synchronization (1)Carrier Frequency Synchronization (1)

Carrier Frequency offset estimation using training sequence;

Two step procedure

EstimationCompensation

Two stage Estimation in time domain Coarse frequency acquisition using short training sequence

Short Training sequences are obtained by using only ¼ th of the number of FFT sub-carriers

In case of IEEE 802.11a it is 16 and hence sub-carrier spacing of 4 times that of the normal OFDM symbol

Fine frequency synchronization using long Training SequenceLong Training sequence has as many sub-carriers as the normal

OFDM symbolIn case of IEEE 802.11a the spacing is 312.5 kHz

Page 44: Drawbacks of OFDM Systemswebmail.aast.edu/~khedr/Courses/VT/OFDM/lecture_thrtn_frtn_sync.pdf · Drawbacks of OFDM Systems High sensitivity to carrier frequency offsets (CFO) ... Timing

Aalborg University

Troels B. Sørensen {[email protected]}; Department of Electronics Systems, Aalborg University

Carrier Frequency Synchronization (2)Carrier Frequency Synchronization (2)

CompensationTime domain de-rotation of the phase of the incoming samples

First coarse correction is done,

Coarse offset corrected signal are used for fine frequency correction

Combined Coarse + Fine frequency estimate is compensated together

Page 45: Drawbacks of OFDM Systemswebmail.aast.edu/~khedr/Courses/VT/OFDM/lecture_thrtn_frtn_sync.pdf · Drawbacks of OFDM Systems High sensitivity to carrier frequency offsets (CFO) ... Timing

Symbol Timing

Refers to the task of finding the precise moment of when individualOFDM symbols start and end.

OFDM is relatively robust to timing errors thanks to the guardinginterval

As long as the timing error is smaller than the guarding intervaland does not cause multipath signals spread out of the guardinginterval, timing error only causes a phase shift which can beabsorbed by the channel coefficients in the stage of channelestimation.

MC 2007 c©Jian (Andrew) Zhang 11

Page 46: Drawbacks of OFDM Systemswebmail.aast.edu/~khedr/Courses/VT/OFDM/lecture_thrtn_frtn_sync.pdf · Drawbacks of OFDM Systems High sensitivity to carrier frequency offsets (CFO) ... Timing

Symbol Timing - Timing Shift

In practical systems using the correlator timing algorithm, the syncpoint is usually obtained by left shifting the estimated timing point byseveral samples.

Question: What about zero-padding?MC 2007 c©Jian (Andrew) Zhang 13

Page 47: Drawbacks of OFDM Systemswebmail.aast.edu/~khedr/Courses/VT/OFDM/lecture_thrtn_frtn_sync.pdf · Drawbacks of OFDM Systems High sensitivity to carrier frequency offsets (CFO) ... Timing

Symbol Timing - Auto-correlation based algorithm

When two consecutive identical training symbols are available, thedelay and correlator method proposed by Schmidl and Cox can beapplied.

mn =|P(n)|2(R(n))2 (5)

where P(n) =∑M−1

k=0 r∗n+k rn+k+M and R(n) =∑M−1

k=0 |rn+k+M |2.

This algorithm can efficiently collect all the multipath energywhen a training sequence with constant modulas in frequencydomain is chosen.(Proof)

The output of P(n) can also be used to calculate fractional CFO.

Increased noise due to autocorrelation

MC 2007 c©Jian (Andrew) Zhang 15

Page 48: Drawbacks of OFDM Systemswebmail.aast.edu/~khedr/Courses/VT/OFDM/lecture_thrtn_frtn_sync.pdf · Drawbacks of OFDM Systems High sensitivity to carrier frequency offsets (CFO) ... Timing

Carrier Frequency Offset (CFO) Estimation

Two types of CFO can be estimated separately

Fractional CFO estimation

Integral CFO estimation

Channel effects on the estimation

General autocorrelation estimator

Joint MLE estimator

MC 2007 c©Jian (Andrew) Zhang 17

Page 49: Drawbacks of OFDM Systemswebmail.aast.edu/~khedr/Courses/VT/OFDM/lecture_thrtn_frtn_sync.pdf · Drawbacks of OFDM Systems High sensitivity to carrier frequency offsets (CFO) ... Timing

General Fractional CFO Estimator[2, 1]

Time domain data-aided estimator: operating over received timedomain training signal consisted of at least two repeated symbols.Down-sampled signal with CFO fo in the receiver:

r(t) = y(t)ej2πfo t ,

rk = r(t)t=kTs = ykej2πǫk/N , (6)

where y(t) = x(t) ∗ h(t). If we let

z =M−1∑

k=0

rk r∗k+D =M−1∑

k=0

yky∗k+De−j2πǫD/N (7)

It is easy to arrange training symbols to yield yk = yk+D, and we get

ǫ =−N2πD

∠z. (8)

The idea is also applicable in frequency domain.MC 2007 c©Jian (Andrew) Zhang 18

Page 50: Drawbacks of OFDM Systemswebmail.aast.edu/~khedr/Courses/VT/OFDM/lecture_thrtn_frtn_sync.pdf · Drawbacks of OFDM Systems High sensitivity to carrier frequency offsets (CFO) ... Timing

General Fractional CFO Estimator (con.)

Estimation range: ǫ < N/(D) - Inversely proportional to D

Question: What’s the relationship between the accuracy ofestimates and D?

Consider the SINR of the following signal

z =M−1∑

k=0

rk r∗k+D = e−j2πǫD/NM−1∑

k=0

|yk |2

+M−1∑

k=0

ykej2πǫk/Nn∗k+D +

M−1∑

k=0

y∗k e−j2πǫ(k+D)/Nnk +

M−1∑

k=0

nkn∗k+D

SINR = γz =PM−1

k=0 |yk |2

σ2n(2+

Mσ2n

PM−1k=0 |yk |

2)

MC 2007 c©Jian (Andrew) Zhang 19

Page 51: Drawbacks of OFDM Systemswebmail.aast.edu/~khedr/Courses/VT/OFDM/lecture_thrtn_frtn_sync.pdf · Drawbacks of OFDM Systems High sensitivity to carrier frequency offsets (CFO) ... Timing

Integer CFO Estimation

Integer CFO causes symbol shifting at subcarriers.

This property can be exploited to estimate the integer CFOaccording to the autocorrelation of symbols.

[1] provides such an algorithm by requiring training sequenceswith good autocorrelation properties.

MC 2007 c©Jian (Andrew) Zhang 27

Page 52: Drawbacks of OFDM Systemswebmail.aast.edu/~khedr/Courses/VT/OFDM/lecture_thrtn_frtn_sync.pdf · Drawbacks of OFDM Systems High sensitivity to carrier frequency offsets (CFO) ... Timing

Page 20Wireless Networking Design Seminar DesignGuideNovember, 2001

Page 20Agilent Technologies

Effects of Oscillator Phase Noise

IQModulator

IQModulator

QAMMappingQAM

MappingPilot

InsertionPilot

Insertion

IFFT(TX)

FFT(RX)

IFFT(TX)

FFT(RX)

G.I.Addition

& Windowing

G.I.Addition

& Windowing

DACDAC

HPA

RemoveG.I.

RemoveG.I.

ChannelCorrectionChannel

Correction

LNA

AGC Amp

Rx Lev. Det.

DataIn

ADCADC

Timing & Frequency

Synchronization

Timing & Frequency

Synchronization

QAMDemapping

QAMDemapping

DataOut

Frequencycorrectedsignal

Symbol Timing

Oscillator Phase Noise

De-interleaving/FEC Decoding/De-Scrambling

De-interleaving/FEC Decoding/De-Scrambling

Scrambling/FEC Coding/Interleaving

Scrambling/FEC Coding/Interleaving

Note: A practical oscillator does not produce a carrier at exactly one frequency, but rather a carrier that is phase modulated by random phase jitter, As a result, the frequency is never perfectly constant, thereby causing ICI.

Page 53: Drawbacks of OFDM Systemswebmail.aast.edu/~khedr/Courses/VT/OFDM/lecture_thrtn_frtn_sync.pdf · Drawbacks of OFDM Systems High sensitivity to carrier frequency offsets (CFO) ... Timing

Page 21Wireless Networking Design Seminar DesignGuideNovember, 2001

Page 21Agilent Technologies

Effects of Oscillator Phase Noise

1/T

FFT Bin Spacing is 1/T

Page 54: Drawbacks of OFDM Systemswebmail.aast.edu/~khedr/Courses/VT/OFDM/lecture_thrtn_frtn_sync.pdf · Drawbacks of OFDM Systems High sensitivity to carrier frequency offsets (CFO) ... Timing

Page 24Wireless Networking Design Seminar DesignGuideNovember, 2001

Page 24Agilent Technologies

Effects of Oscillator Phase Noise (continued)

-1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

-1.0

-0.5

0.0

0.5

1.0

real(iq[0,::])

ima

g(i

q[0

,::]

)

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

real(iq[1,::])

ima

g(i

q[1

,::]

)

-1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

-1.0

-0.5

0.0

0.5

1.0

real(iq[2,::])

ima

g(i

q[2

,::]

)

Index

40

ReceiverEVM_pnAA=0.000 AA=1.000 AA=2.000

1.199E-5 0.143 0.014

8 10 12 14 16 18 20

1E-5

1E-4

1E-3

1E-2

1E-1

5E-1

BER_pn.DF.CN

BE

R_

pn -3dB linewidth=30Hz

-3dB linewidth=3HzIdeal

-3dB linewidth=30Hz -3dB linewidth=3HzIdeal

Dr. M. Khedr
Rectangle
Page 55: Drawbacks of OFDM Systemswebmail.aast.edu/~khedr/Courses/VT/OFDM/lecture_thrtn_frtn_sync.pdf · Drawbacks of OFDM Systems High sensitivity to carrier frequency offsets (CFO) ... Timing

Aalborg University

{petarp,imr}@kom.aau.dk ; Department of Electronics Systems, Aalborg University

Sampling Frequency SynchronizationSampling Frequency SynchronizationFrequency Synchronization

Time Domain view of sampling frequency error

Ideal Sampling locations

Sampling with T’>T

Sampling with T’<T

Over Sample

Missed sample

Page 56: Drawbacks of OFDM Systemswebmail.aast.edu/~khedr/Courses/VT/OFDM/lecture_thrtn_frtn_sync.pdf · Drawbacks of OFDM Systems High sensitivity to carrier frequency offsets (CFO) ... Timing

Basic Symbol Timing Algorithm - cross-correlationbased

Basic timing algorithms are similar to single carrier systems, e.g.,a correlator can be applied with local input identical to thetransmitted signal, the output of the correlator is then used as areference to determine the sync point.

yn = arg maxn

M−1∑

k=0

rn+ksk∣

∣ (4)

where M is the length of the correlating window.The correlator-based timing algorithm will pick up the strongestmultipath, which is not necessary the first multipath. ISI may becaused in this case.The ideal sync point should correspond to the first multipathchannel when Tg ≥ Td .

MC 2007 c©Jian (Andrew) Zhang 12

Page 57: Drawbacks of OFDM Systemswebmail.aast.edu/~khedr/Courses/VT/OFDM/lecture_thrtn_frtn_sync.pdf · Drawbacks of OFDM Systems High sensitivity to carrier frequency offsets (CFO) ... Timing

Aalborg University

Troels B. Sørensen {[email protected]}; Department of Electronics Systems, Aalborg University

Sampling Frequency Offset CompensationSampling Frequency Offset CompensationFrequency Synchronization

Constellation rotation due to sampling frequency offset

Page 58: Drawbacks of OFDM Systemswebmail.aast.edu/~khedr/Courses/VT/OFDM/lecture_thrtn_frtn_sync.pdf · Drawbacks of OFDM Systems High sensitivity to carrier frequency offsets (CFO) ... Timing

Aalborg University

{petarp,imr}@kom.aau.dk ; Department of Electronics Systems, Aalborg University

Conclusion of Synchronization Issues Conclusion of Synchronization Issues OFDM Synchronization

•We have discussed• Synchronization error source• Types of synchronization

• Time• Packet detection• Frame synchronization

• Frequency• Carrier Frequency synchronization• Sampling Frequency synchronization

• Examined how they effect the system• Seen as example some of estimation and compensation Algorithms