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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



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OFDM - Introduction

Being considered as a modulation and multiple access method for 4thgeneration networks








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OFDM - Introduction

Being considered as a modulation and multiple access method for 4thgeneration networks








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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



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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



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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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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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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



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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


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.




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y p


h p


h



h = E[

h y p]E[y py p]1y p

LetC

p,p=E

[h

ph

p]andC:

,p=E

[hh


h =E







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y p


h p


h



h = E[

h y p]E[y py p]1y p

LetCp,p=

E

[h

ph

p]and C:

,p=E

[hh


h =E







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y p


h p


h



h = E[

h y p]E[y py p]1y p

LetCp,p=

E

[h

ph

p]and C:

,p=E

[hh


h =E





Low Rank Correlation Matrix


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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




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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


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




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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




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0 2 4 6 8 10 1260

50

40

30

20

10

0

10

20

eigenvalues index

10log10

(

i)









less than 30 dB




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0 2 4 6 8 10 1260

50

40

30

20

10

0

10

20

eigenvalues index

10log10

(

i)









less than 30 dB


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!


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.


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


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


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.


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




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g




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





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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



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




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R1/2nn

y = R1/2nn h s+ n


s=

hR1nn

yhR1nn

h


d

y



d




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R1/2nn

y = R1/2nn h s+ n


s=

hR1nn

yhR1nn

h


d

y



d




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R1/2nn

y = R1/2nn h s+ n


s=

hR1nn

yhR1nn

h


d

y



d




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R1/2nn

y = R1/2nn h s+ n


s=

hR1nn

yhR1nn

h


d

y



d



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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


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


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.


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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spectrum





high SNR




Summary


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spectrum





high SNR




Summary


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spectrum





high SNR




Questions?


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06hari sameer

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