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Channel Estimation and Interference Nulling inBlock-Hopping OFDMA
Sameer Vermani Hari Palaiyanur
Wireless Foundations
Department of Electrical Engineering and Computer Science
University of California, Berkeley
EE224B Project
() Simple OFDMA Channel Estimation EE224B 1 / 23
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Outline
1 Introduction to OFDMA
2 Channel Estimation
3 A Simple, Robust Estimate
4 Interference Nulling
5 Conclusion
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OFDM - Introduction
Being considered as a modulation and multiple access method for 4th
generation networks
IEEE 802.11a/g wireless LAN (WiFi) IEEE 802.16a/d/e wireless broadband access system (WiMax)
In ODFM, data transmitted on set of parallel low-bandwidth carriers
Results in robustness to multipath Little or no equalization for ISI required
In conventional OFDM, single user transmits on all subcarriers
TDMA used to support multiple users Static allocation fails to utilize multiuser diversity
() Simple OFDMA Channel Estimation EE224B 3 / 23
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OFDM - Introduction
Being considered as a modulation and multiple access method for 4thgeneration networks
IEEE 802.11a/g wireless LAN (WiFi) IEEE 802.16a/d/e wireless broadband access system (WiMax)
In ODFM, data transmitted on set of parallel low-bandwidth carriers
Results in robustness to multipath Little or no equalization for ISI required
In conventional OFDM, single user transmits on all subcarriers
TDMA used to support multiple users Static allocation fails to utilize multiuser diversity
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OFDM - Introduction
Being considered as a modulation and multiple access method for 4thgeneration networks
IEEE 802.11a/g wireless LAN (WiFi) IEEE 802.16a/d/e wireless broadband access system (WiMax)
In ODFM, data transmitted on set of parallel low-bandwidth carriers
Results in robustness to multipath Little or no equalization for ISI required
In conventional OFDM, single user transmits on all subcarriers
TDMA used to support multiple users Static allocation fails to utilize multiuser diversity
() Simple OFDMA Channel Estimation EE224B 3 / 23
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OFDMA - Introduction (contd)
OFDMA allows different users to transmit in the same symbol duration
Multiuser diversity ensures at least some carriers are assigned to good user Hopping sequence ensures frequency and interference diversity Can allot multiple frequencies to each user
Block-Hopping OFDMA
Commonly used for uplink in OFDMA systems Allocate contiguous set of tones to every user over adjacent OFDM
symbols
Make users hop randomly across bandwidth
() Simple OFDMA Channel Estimation EE224B 4 / 23
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OFDMA - Introduction (contd)
OFDMA allows different users to transmit in the same symbol duration
Multiuser diversity ensures at least some carriers are assigned to good user Hopping sequence ensures frequency and interference diversity Can allot multiple frequencies to each user
Block-Hopping OFDMA
Commonly used for uplink in OFDMA systems Allocate contiguous set of tones to every user over adjacent OFDM
symbols
Make users hop randomly across bandwidth
() Simple OFDMA Channel Estimation EE224B 4 / 23
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Block-Hopping OFDMA
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Advantages of block-hopping
Able to capture frequency and interference diversity by allocating
multiple time-frequency grids
Users in Hold state synchronized at block level granularity
Due to contiguous allocation of tones and symbols
channel is highly correlated within a time-frequency block reduction in resources needed for channel estimation at receiver easier to estimate spatial covariance matrix of out-of-cell interference
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Advantages of block-hopping
Able to capture frequency and interference diversity by allocating
multiple time-frequency grids
Users in Hold state synchronized at block level granularity
Due to contiguous allocation of tones and symbols
channel is highly correlated within a time-frequency block reduction in resources needed for channel estimation at receiver easier to estimate spatial covariance matrix of out-of-cell interference
() Simple OFDMA Channel Estimation EE224B 6 / 23
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Advantages of block-hopping
Able to capture frequency and interference diversity by allocating
multiple time-frequency grids
Users in Hold state synchronized at block level granularity
Due to contiguous allocation of tones and symbols
channel is highly correlated within a time-frequency block reduction in resources needed for channel estimation at receiver easier to estimate spatial covariance matrix of out-of-cell interference
() Simple OFDMA Channel Estimation EE224B 6 / 23
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Problem Motivation
Typically, channel estimation makes use of
Pilot tones inserted in the block Channel statistics over block
Knowledge of channel statistics difficult to obtain Need to devise techniques that do not require explicit knowledge of
channel statistics Technique needs to be invariant to power delay profile and doppler
spectrum shapes
() Simple OFDMA Channel Estimation EE224B 7 / 23
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Problem Motivation
Typically, channel estimation makes use of
Pilot tones inserted in the block Channel statistics over block
Knowledge of channel statistics difficult to obtain Need to devise techniques that do not require explicit knowledge of
channel statistics Technique needs to be invariant to power delay profile and doppler
spectrum shapes
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System Model
Users allotted blocks consisting of Ntcontiguous tones
Ns contiguous OFDM symbols Nppilots Nd=NtNs Np data symbols
h = [h1, h2, . . . , hN]
t, vector ofN=NtNschannel gains Columns of block channel gains are stacked to get
h
- Pilot Location
- Data Location
Time
Frequency
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S M d l ( d)
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System Model (contd)
Vector of received signal at pilot locations can be written as
y p=
Eph p+
I0n
where
h p is vector of channel gains at pilot locations Ep is energy of pilot symbol I0 is Thermal noise plus interference energy at pilots
We assume noise plus interference to be independent across the block
n is complex Gaussian with iid circularly symmetric CN(0, 1)entries
() Simple OFDMA Channel Estimation EE224B 9 / 23
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Ch l C l ti
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Channel Correlation
Given limited pilot resources, want to utilize correlation in channel toestimate
Decorrelation in time depends on user velocity and power angular
spectrum Decorrelation in frequency depends on delay spread and shape of power
delay profile Typical scenario: time and frequency correlation decoupled
LetCbeNNcovariance matrix ofh, i.e. C= E[h h ]
C=Ct Cfwhere CtisNs Ns time covariance matrix, same for all tones Cf isNtNtfrequency covariance matrix, same for all symbols denotes Kronecker product of matrices
() Simple OFDMA Channel Estimation EE224B 10 / 23
MMSE Ch l E ti t
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MMSE Channel Estimate
y p
received signal at the pilots
h p
channel at pilot locations
h
channel over entire block
MMSE estimate ofh is
h = E[
h y p]E[y py p]1y p
LetCp,p=E
[h ph
p]and C:
,p=E
[h h
p]MMSE estimate simplifies to
h =E
1/2p C:,p(Cp,p+ I0INp )
1y pwhereINp is identity matrix of sizeNp.
This expression requires knowledge of correlation matrixC.
() Simple OFDMA Channel Estimation EE224B 11 / 23
MMSE Channel Estimate
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MMSE Channel Estimate
y p
received signal at the pilots
h p
channel at pilot locations
h
channel over entire block
MMSE estimate ofh is
h = E[
h y p]E[y py p]1y p
LetC
p,p=E
[h
ph
p]andC:
,p=E
[hh
p]MMSE estimate simplifies to
h =E
1/2p C:,p(Cp,p+ I0INp )
1y pwhereINp is identity matrix of sizeNp.
This expression requires knowledge of correlation matrixC.
() Simple OFDMA Channel Estimation EE224B 11 / 23
MMSE Channel Estimate
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MMSE Channel Estimate
y p
received signal at the pilots
h p
channel at pilot locations
h
channel over entire block
MMSE estimate ofh is
h = E[
h y p]E[y py p]1y p
LetCp,p=
E
[h
ph
p]and C:
,p=E
[hh
p]MMSE estimate simplifies to
h =E
1/2p C:,p(Cp,p+ I0INp )
1y pwhereINp is identity matrix of sizeNp.
This expression requires knowledge of correlation matrixC.
() Simple OFDMA Channel Estimation EE224B 11 / 23
MMSE Channel Estimate
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MMSE Channel Estimate
y p
received signal at the pilots
h p
channel at pilot locations
h
channel over entire block
MMSE estimate ofh is
h = E[
h y p]E[y py p]1y p
LetCp,p=
E
[h
ph
p]and C:
,p=E
[hh
p]MMSE estimate simplifies to
h =E
1/2p C:,p(Cp,p+ I0INp )
1y pwhereINp is identity matrix of sizeNp.
This expression requires knowledge of correlation matrixC.
() Simple OFDMA Channel Estimation EE224B 11 / 23
Low Rank Correlation Matrix
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Low Rank Correlation Matrix
Knowledge of channel statistics difficult to obtain; can still assume upper
bounds on delay spread and doppler spread.
Want to utilize the fact: In a typical block-hopping setup,Chas low
numerical rank. Ct=UttU
t , Cf =UffU
f
SinceC=Ct Cf, it turns out that
C= UU, U=Ut
Uf, = t
f
() Simple OFDMA Channel Estimation EE224B 12 / 23
Low Rank Correlation Matrix
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Low Rank Correlation Matrix
Knowledge of channel statistics difficult to obtain; can still assume upper
bounds on delay spread and doppler spread.
Want to utilize the fact: In a typical block-hopping setup,Chas low
numerical rank. Ct=UttU
t , Cf =UffU
f
SinceC=Ct Cf, it turns out that
C= UU, U=Ut
Uf, = t
f
() Simple OFDMA Channel Estimation EE224B 12 / 23
Low Rank Correlation Matrix (contd)
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Low Rank Correlation Matrix (cont d)
0 1 2 3 4 5 6 7 8 9160
140
120
100
80
60
40
20
0
20
eigenvalues index
10log10
(
i)
Ordered eigenvalues of Ct
Doppler Spread = 200HzJakes Spectrum
1 2 3 4 5 6 7 890
80
70
60
50
40
30
20
10
0
10
eigenvalue index
10log10
(
i)
Ordered eigenvalues of Cf
Delay Spread 5 s
Uniform Power Delay Profile
Figure:Time and frequency correlation matrix eigenvalues, for a block with 8 tonesand 8 symbols. Tone spacing is 10kHz, OFDM symbol duration is 100s. We haveassumed Jakes Doppler Spectrum and Uniform Power Delay Profile
() Simple OFDMA Channel Estimation EE224B 13 / 23
Low Rank Correlation Matrix (contd)
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Low Rank Correlation Matrix (cont d)
0 2 4 6 8 10 1260
50
40
30
20
10
0
10
20
eigenvalues index
10log10
(
i)
Largest 12 eigenvalues of C
Doppler Spread = 200HzJakes Doppler Spectrum
Delay Spread = 5 sUniform Power Delay Profile
Low rank structure is invariant to shapes of delay profile and doppler
spectrum. Verified for exponential PDP and uniform doppler spectrum
Numerical rank ofCis at most 3. Rank reduced to 2 for doppler spreads
typically observed for pedestrian users
Underlying assumption: can ignore components with relative magnitude
less than 30 dB
() Simple OFDMA Channel Estimation EE224B 14 / 23
Low Rank Correlation Matrix (contd)
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Low Rank Correlation Matrix (cont d)
0 2 4 6 8 10 1260
50
40
30
20
10
0
10
20
eigenvalues index
10log10
(
i)
Largest 12 eigenvalues of C
Doppler Spread = 200HzJakes Doppler Spectrum
Delay Spread = 5 sUniform Power Delay Profile
Low rank structure is invariant to shapes of delay profile and doppler
spectrum. Verified for exponential PDP and uniform doppler spectrum
Numerical rank ofCis at most 3. Rank reduced to 2 for doppler spreads
typically observed for pedestrian users
Underlying assumption: can ignore components with relative magnitude
less than 30 dB
() Simple OFDMA Channel Estimation EE224B 14 / 23
Low Rank Correlation Matrix (contd)
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Low Rank Correlation Matrix (cont d)
0 2 4 6 8 10 1260
50
40
30
20
10
0
10
20
eigenvalues index
10log10
(
i)
Largest 12 eigenvalues of C
Doppler Spread = 200HzJakes Doppler Spectrum
Delay Spread = 5 sUniform Power Delay Profile
Low rank structure is invariant to shapes of delay profile and doppler
spectrum. Verified for exponential PDP and uniform doppler spectrum
Numerical rank ofCis at most 3. Rank reduced to 2 for doppler spreads
typically observed for pedestrian users
Underlying assumption: can ignore components with relative magnitude
less than 30 dB
() Simple OFDMA Channel Estimation EE224B 14 / 23
Taylor meets Karhunen and Loeve
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Taylor meets Karhunen and Loeve
1 2 3 4 5 6 7 80.8
0.6
0.4
0.2
0
0.2
0.4
0.6
Component Index
Value
ofComponentofEigenvector
Three dominant eigenvectors of Ct
First eigenvectorSecond eigenvectorThird eigenvector
Doppler Spread = 200HzJakes Spectrum
1 2 3 4 5 6 7 80.8
0.6
0.4
0.2
0
0.2
0.4
0.6
Component Index
Value
ofComponentofEigenvector
Three dominant eigenvectors of Cf
First eigenvectorSecond eigenvectorThird eigenvector
Delay Spread 5 s
Uniform Power Delay Profile
Figure:Realization of three dominant eigenvectors ofCtandCf, for a block with 8
tones and 8 symbols. Tone spacing is 10kHz, OFDM symbol duration is 100s.
KL decomposition coincides with Taylor series expansion of channel!
() Simple OFDMA Channel Estimation EE224B 15 / 23
Eigenvector Interpretation
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Eigenvector Interpretation
0
5
10
0
5
100.2
0
0.2
Time
Second Eigenvector
Frequency
Value
ofeige
nvector
0
5
10
0
5
100.2
0
0.2
Time
Third Eigenvector
Frequency
Value
ofeigenve
ctor
0
5
10
0
5
10
0.3
0.2
0.1
0
Time
First Eigenvector
Frequency
Value
ofeige
nvector
Figure:Realization of three dominant eigenvectors ofC, for a block with 8 tones and8 symbols. Tone spacing is 10kHz, OFDM symbol duration is 100s. Dominant
eigenvectors are constant in time and frequency, constant in time, linear in
frequency, and linear in time, constant in frequency.
() Simple OFDMA Channel Estimation EE224B 16 / 23
Simplified Channel Estimate
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S p ed C a e st ate
Simplified estimate done by finding components of channel along three
dominant eigenmodes shown previously
Essentially a projection onto the three canonical eigenvectors Does not require explicit knowledge of channel statistics Require just bounds on delay spread and doppler spread Works for most delay profile and doppler spectrum shapes
() Simple OFDMA Channel Estimation EE224B 17 / 23
Simplified Channel Estimate
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p
Simplified estimate done by finding components of channel along three
dominant eigenmodes shown previously
Essentially a projection onto the three canonical eigenvectors Does not require explicit knowledge of channel statistics Require just bounds on delay spread and doppler spread Works for most delay profile and doppler spectrum shapes
() Simple OFDMA Channel Estimation EE224B 17 / 23
Comparison of channel estimates
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p
0
2
4
6
8
0
2
4
6
80
0.5
1
1.5
Symbols
Channel Magnitude over the block
Tones 0
2
4
6
8
0
2
4
6
80
0.5
1
1.5
Symbols
Channel Magnitude over the block for MMSE estimate
Tones 0
2
4
6
8
0
2
4
6
80
0.5
1
1.5
Symbols
Channel Magnitude over the block for simple model estimate
Tones
Figure:Comparison of performance of simplifed channel estimation to MMSE.Jakes Doppler Spectrum with 200Hz Doppler Spread. Uniform Power Delay Profile
with delay spread 5s.
() Simple OFDMA Channel Estimation EE224B 18 / 23
Interference Nulling
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g
Now, consider uplink of an OFDMA system where users have single
antennas and base station has multiple (Nr) receive antennas
TheNrdimensional received signal vector y in one symbol-tone slot isy = h s+
NIk=1
g ksk+w
where h CNr is the vector of channel gains from the user to the BS,g k CNr is the vector of channel gains from out-of-cell interfererktothe BS, w CN(0,N0INr)is thermal noise, andNIis the number ofinterferers
The effective noise is
n =NI
k=1
g ksk+w
andRnn= E[n n ] =NIk=1 E[g kg k] +N0INr
() Simple OFDMA Channel Estimation EE224B 19 / 23
Interference Nulling
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g
Now, consider uplink of an OFDMA system where users have single
antennas and base station has multiple (Nr) receive antennas
TheNrdimensional received signal vector y in one symbol-tone slot isy = h s+
NIk=1
g ksk+w
where h CNr is the vector of channel gains from the user to the BS,g k CNr is the vector of channel gains from out-of-cell interfererktothe BS, w CN(0,N0INr)is thermal noise, andNIis the number ofinterferers
The effective noise is
n =NI
k=1
g ksk+w
andRnn= E[n n ] =NIk=1 E[g kg k] +N0INr
() Simple OFDMA Channel Estimation EE224B 19 / 23
Interference Nulling
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Now, consider uplink of an OFDMA system where users have single
antennas and base station has multiple (Nr) receive antennas
TheNrdimensional received signal vector y in one symbol-tone slot isy = h s+
NIk=1
g ksk+w
where h CN
r is the vector of channel gains from the user to the BS,g k CNr is the vector of channel gains from out-of-cell interfererktothe BS, w CN(0,N0INr)is thermal noise, andNIis the number ofinterferers
The effective noise isn =
NIk=1
g ksk+w
andRnn= E[n n ] =NIk=1 E[g kg k] +N0INr
() Simple OFDMA Channel Estimation EE224B 19 / 23
Interference Nulling (contd)
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In interference dominated regime, n is far from being white andmatched filtering is no longer the optimal strategy for estimating
transmitted symbols.Optimal strategy is to whiten noise before projecting,
R1/2nn
y = R1/2nn h s+ n
Hence, the unbiased LLSE estimate ofs can be written as
s=
hR1nn
yhR1nn
h
Can be viewed as finding correct filter weightsd so that s=
d
y
If we normalizeE[|s|2] =1, then the perceived post-processing SNR,SNRpostis defined as
SNRpost= |d h |2d Rnn
d
() Simple OFDMA Channel Estimation EE224B 20 / 23
Interference Nulling (contd)
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In interference dominated regime, n is far from being white andmatched filtering is no longer the optimal strategy for estimating
transmitted symbols.Optimal strategy is to whiten noise before projecting,
R1/2nn
y = R1/2nn h s+ n
Hence, the unbiased LLSE estimate ofs can be written as
s=
hR1nn
yhR1nn
h
Can be viewed as finding correct filter weightsd so that s=
d
y
If we normalizeE[|s|2] =1, then the perceived post-processing SNR,SNRpostis defined as
SNRpost= |d h |2d Rnn
d
() Simple OFDMA Channel Estimation EE224B 20 / 23
Interference Nulling (contd)
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In interference dominated regime, n is far from being white andmatched filtering is no longer the optimal strategy for estimating
transmitted symbols.Optimal strategy is to whiten noise before projecting,
R1/2nn
y = R1/2nn h s+ n
Hence, the unbiased LLSE estimate ofs can be written as
s=
hR1nn
yhR1nn
h
Can be viewed as finding correct filter weightsd so that s=
d
y
If we normalizeE[|s|2] =1, then the perceived post-processing SNR,SNRpostis defined as
SNRpost= |d h |2d Rnn
d
() Simple OFDMA Channel Estimation EE224B 20 / 23
Interference Nulling (contd)
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In interference dominated regime, n is far from being white andmatched filtering is no longer the optimal strategy for estimating
transmitted symbols.Optimal strategy is to whiten noise before projecting,
R1/2nn
y = R1/2nn h s+ n
Hence, the unbiased LLSE estimate ofs can be written as
s=
hR1nn
yhR1nn
h
Can be viewed as finding correct filter weightsd so that s=
d
y
If we normalizeE[|s|2] =1, then the perceived post-processing SNR,SNRpostis defined as
SNRpost= |d h |2d Rnn
d
() Simple OFDMA Channel Estimation EE224B 20 / 23
Interference Nulling (contd)
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In interference dominated regime, n is far from being white andmatched filtering is no longer the optimal strategy for estimating
transmitted symbols.Optimal strategy is to whiten noise before projecting,
R1/2nn
y = R1/2nn h s+ n
Hence, the unbiased LLSE estimate ofs can be written as
s=
hR1nn
yhR1nn
h
Can be viewed as finding correct filter weightsd so that s=
d
y
If we normalizeE[|s|2] =1, then the perceived post-processing SNR,SNRpostis defined as
SNRpost= |d h |2d Rnn
d
() Simple OFDMA Channel Estimation EE224B 20 / 23
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Interference Covariance Estimation
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As seen previously, LLSE estimate requires knowledge ofRnn, so we
need to estimate it.
At pilot locations, can estimate noise using our channel estimate and
knowledge of transmitted symbol
n k= y k h kskwherekrefers to thekth pilot location, y kis the received signal vector,and
h kis the estimated channel vector
Form an estimate ofRnnby usingn k,
Rnn= 1
Np
Npk=1
n kn
k
() Simple OFDMA Channel Estimation EE224B 21 / 23
Interference Covariance Estimation
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As seen previously, LLSE estimate requires knowledge ofRnn, so we
need to estimate it.
At pilot locations, can estimate noise using our channel estimate and
knowledge of transmitted symbol
n k= y k h kskwherekrefers to thekth pilot location, y kis the received signal vector,and
h kis the estimated channel vector
Form an estimate ofRnnby usingn k,
Rnn= 1
Np
Npk=1
n kn
k
() Simple OFDMA Channel Estimation EE224B 21 / 23
Performance of interference nulling
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0 5 10 15 20 255
10
15
20
25
30
35
40
Simplified Channel Estimation
Preprocessing SNR in dB
Postproc
essingSNRi
ndB
Postprocessing SNR for pilot aided channel and interference estimation
Full MMSE ChannelEstimation
True Rnn
and channel knowledge
Matched filter usingthe true channel
Rank 2 Interference, 4 antennas
Iot
=10
Figure:Post processing SNR achieved through pilot aided interference and channelestimation.
() Simple OFDMA Channel Estimation EE224B 22 / 23
Summary
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Devised techniques for channel estimation in block-hopping OFDMA
that do not require explicit knowledge of channel statistics
The techniques are invariant to shapes of power delay profile and doppler
spectrum
With multiple receive antennas, used channel estimation to get to an
estimate of spatial interference covariance matrix
Nulling of out-of-cell interference with simplified channel and
interference covariance estimate gives close to MMSE performance till
high SNR
Small loss at high SNR is a price to pay for not having to obtain channel
statistics over block
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Summary
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Devised techniques for channel estimation in block-hopping OFDMA
that do not require explicit knowledge of channel statistics
The techniques are invariant to shapes of power delay profile and doppler
spectrum
With multiple receive antennas, used channel estimation to get to an
estimate of spatial interference covariance matrix
Nulling of out-of-cell interference with simplified channel and
interference covariance estimate gives close to MMSE performance till
high SNR
Small loss at high SNR is a price to pay for not having to obtain channel
statistics over block
() Simple OFDMA Channel Estimation EE224B 23 / 23
Summary
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Devised techniques for channel estimation in block-hopping OFDMA
that do not require explicit knowledge of channel statistics
The techniques are invariant to shapes of power delay profile and doppler
spectrum
With multiple receive antennas, used channel estimation to get to an
estimate of spatial interference covariance matrix
Nulling of out-of-cell interference with simplified channel and
interference covariance estimate gives close to MMSE performance till
high SNR
Small loss at high SNR is a price to pay for not having to obtain channel
statistics over block
() Simple OFDMA Channel Estimation EE224B 23 / 23
Summary
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Devised techniques for channel estimation in block-hopping OFDMA
that do not require explicit knowledge of channel statistics
The techniques are invariant to shapes of power delay profile and doppler
spectrum
With multiple receive antennas, used channel estimation to get to an
estimate of spatial interference covariance matrix
Nulling of out-of-cell interference with simplified channel and
interference covariance estimate gives close to MMSE performance till
high SNR
Small loss at high SNR is a price to pay for not having to obtain channel
statistics over block
() Simple OFDMA Channel Estimation EE224B 23 / 23
Questions?
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() Simple OFDMA Channel Estimation EE224B 24 / 23