Post on 06-Feb-2018
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
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
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
Aalborg University
Troels B. Sørensen {tbs@es.aau.dk}; 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
Aalborg University
Troels B. Sørensen {tbs@es.aau.dk}; 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
Aalborg University
Troels B. Sørensen {tbs@es.aau.dk}; 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
Aalborg University
Troels B. Sørensen {tbs@es.aau.dk}; 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
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
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 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
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!
CFO Sensitivity (cont.)
MC 2007 c©Jian (Andrew) Zhang 33
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
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
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
Aalborg University
Troels B. Sørensen {tbs@es.aau.dk}; Department of Electronics Systems, Aalborg University
Example transmission formatExample transmission formatTiming Synchronization
IEEE 802.11a Frame format
Aalborg University
Troels B. Sørensen {tbs@es.aau.dk}; 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
Aalborg University
Troels B. Sørensen {tbs@es.aau.dk}; 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.
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
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
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
Aalborg University
{petarp,imr}@kom.aau.dk ; Department of Electronics Systems, Aalborg University
Packet Detection contPacket Detection cont……Timing Synchronization
Packet Detection - Performance Comparison
The decision statistic mn for IEEE802.11a preamble in 10dB SNR
MC 2007 c©Jian (Andrew) Zhang 10
Aalborg University
Troels B. Sørensen {tbs@es.aau.dk}; 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
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
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
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
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−−
=
= = + +∑
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 ≤
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 ==
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 ∆
+=
−
=
=
=
∑
∑
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
∧
∆ = −
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
∧
>∆ =
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
−∧
−=
⎛ ⎞∆ = =⎜ ⎟
⎝ ⎠∑
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∧ ∧ ∧⎛ ⎞⎛ ⎞= − ∆ + ∆⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠
Aalborg University
Troels B. Sørensen {tbs@es.aau.dk}; 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
Aalborg University
Troels B. Sørensen {tbs@es.aau.dk}; 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
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
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
Aalborg University
Troels B. Sørensen {tbs@es.aau.dk}; 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
Aalborg University
Troels B. Sørensen {tbs@es.aau.dk}; 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
Aalborg University
Troels B. Sørensen {tbs@es.aau.dk}; 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
Aalborg University
Troels B. Sørensen {tbs@es.aau.dk}; 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
Aalborg University
Troels B. Sørensen {tbs@es.aau.dk}; 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
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
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
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
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
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
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
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 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 21Wireless Networking Design Seminar DesignGuideNovember, 2001
Page 21Agilent Technologies
Effects of Oscillator Phase Noise
1/T
FFT Bin Spacing is 1/T
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
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
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
Aalborg University
Troels B. Sørensen {tbs@es.aau.dk}; Department of Electronics Systems, Aalborg University
Sampling Frequency Offset CompensationSampling Frequency Offset CompensationFrequency Synchronization
Constellation rotation due to sampling frequency offset
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