low-complexity channel estimation for wireless ofdm systems eugene golovins neco ventura...

Low-Complexity Channel Low-Complexity Channel Estimation for Wireless OFDM Estimation for Wireless OFDM

SystemsSystems

Eugene Golovins Eugene Golovins Neco VenturaNeco [email protected] [email protected]

[email protected]@crg.ee.uct.ac.za

E. GolovinsE. Golovins- 2 -UCT-COE Seminar

26/07/200726/07/2007

OutlineOutline

-- Introduction-- Introduction

-- Radio channel model-- Radio channel model

-- Pilot-assisted OFDM system-- Pilot-assisted OFDM system

-- Blind OFDM system-- Blind OFDM system


26/07/200726/07/2007

IntroductionIntroduction OFDM has been found OFDM has been found efficient in reducing efficient in reducing

severe effects of the frequency-selective fading severe effects of the frequency-selective fading (inherent to the urban and indoor radio (inherent to the urban and indoor radio channels)channels)

High-capacity subcarrier modulation High-capacity subcarrier modulation techniques (e.g., QAM) require accurate techniques (e.g., QAM) require accurate estimation of the channel frequency response estimation of the channel frequency response (CFR) for coherent detection at the receiver(CFR) for coherent detection at the receiver

Channel estimator must satisfy 3 requirements:Channel estimator must satisfy 3 requirements: rely on the least possible training overheadrely on the least possible training overhead achieve performance close to optimalachieve performance close to optimal be of the least possible computational complexitybe of the least possible computational complexity


26/07/200726/07/2007

Baseband OFDM systemBaseband OFDM system


26/07/200726/07/2007

Channel modelChannel model Two kinds of impairments in the fading Two kinds of impairments in the fading channel:channel:

-- dispersion (frequency selectivity) – due to -- dispersion (frequency selectivity) – due to multipath propagationmultipath propagation

-- time variability (Doppler effect) – due to the -- time variability (Doppler effect) – due to the relative motion of TX and RX antennasrelative motion of TX and RX antennas

Adopted model – quasi-static approximation Adopted model – quasi-static approximation of the WSSUS process :of the WSSUS process :

-- channel response does not change on the -- channel response does not change on the interval of one OFDM symbolinterval of one OFDM symbol

-- multipath response is comprised of an arbitrary -- multipath response is comprised of an arbitrary number of the statistically independent path-number of the statistically independent path-gains, delayed at fixed time intervalsgains, delayed at fixed time intervals

-- inter-symbol variation of the path-gains is -- inter-symbol variation of the path-gains is governed by the Doppler random process with governed by the Doppler random process with Jakes’s spectrumJakes’s spectrum


26/07/200726/07/2007

Channel frequency Channel frequency response (CFR)response (CFR) Example of CFR of the considered fading channel Example of CFR of the considered fading channel

::

sT2RMS

ss TNT cpmax 7

Tf /01.0D (max. Doppler freq.)(max. Doppler freq.)

(max. delay spread)(max. delay spread)

(RMS delay spread)(RMS delay spread)


26/07/200726/07/2007

Frequency-domain block Frequency-domain block processing processing NNdd data subsymbols are transmitted in block of data subsymbols are transmitted in block of NNdd+P+N+P+Ncpcp

subsymbols, with subsymbols, with PP pilot subsymbols and a cyclic prefix of pilot subsymbols and a cyclic prefix of length length NNcpcp L L - 1 (- 1 (LL = expected CIR length) = expected CIR length)

Receiver processes blocks in frequency domain by taking Receiver processes blocks in frequency domain by taking FFT of each received blockFFT of each received block

Typically the size of the processing block Typically the size of the processing block N = NN = Ndd+P+P is 5 is 5 to 10 times to 10 times NNcpcp

Last NNcpcpsub-symbolsrepeated

NNccsub-symbols

Block of N subsymbolsCP

Fre

qu

en

cy

(su

bca

rrie

rs)

Time (OFDM symbols / blocks)

OFDM time-frequency grid

Temporal block structure

N


26/07/200726/07/2007

Pilot-assisted systemPilot-assisted system Channel estimator operates only in 1D (across freq. Channel estimator operates only in 1D (across freq.

domain) computing channel distortions for each domain) computing channel distortions for each OFDM symbol separatelyOFDM symbol separately

Known pilot sequence is transmitted on a small Known pilot sequence is transmitted on a small fraction of subcarriers (fraction of subcarriers (PP) to train the estimator) to train the estimator

Interpolation of pilots in frequency is performed to Interpolation of pilots in frequency is performed to get CFR estimate in the full bandget CFR estimate in the full band

Fre

qu

en

cy

(su

bca

rrie

rs)

Time (OFDM symbols)

NPilot subcarrier

Data subcarrier


26/07/200726/07/2007

Design definition of the Design definition of the constrained estimatorconstrained estimator

Anticipated CIR lengthAnticipated CIR length Number of pilot subcarriersNumber of pilot subcarriers

Received subsymbols at the pilot Received subsymbols at the pilot positions:positions:

LP

Tpp]D[ 10

PYY ppp WhBFCXY

contains reference values of contains reference values of PP pilot pilot subsymbolssubsymbols

is the selection matrix that is needed to is the selection matrix that is needed to extract pilot samples of the CFRextract pilot samples of the CFR

is the zero-padding matrixis the zero-padding matrix (from (from LL up to up to NN))

is the WGN vector at the pilot is the WGN vector at the pilot subcarrierssubcarriers

is the CIR vector (to be found)is the CIR vector (to be found)

T10 NHH hBFH

pp XX diag]D[ C

B

pW

NNL 1cp

h


26/07/200726/07/2007

Constrained Least Squares Constrained Least Squares (CLS) estimator(CLS) estimator Minimise the quadratic difference between the Minimise the quadratic difference between the

received pilot subsymbols and the reference pilot received pilot subsymbols and the reference pilot values being affected by the assumed CFR modelvalues being affected by the assumed CFR model

::

pY pX

hBFH

hBFCXYhBFCXYh pppp]D[

H

]D[)( J

ppCLSCLS YXCFBSBFH H]D[

HHHˆ

1

]D[H]D[

HHH BFCXXCFBS ppCLS

For the equipowered (For the equipowered ( ) ) and equispaced (and equispaced ( , , ) ) pilot subcarriers (optimal training structure) pilot subcarriers (optimal training structure) we have:we have:

ppp θXX pparg

integerPN IBFCCFB PHHH

ppCLSesep YθCFBBFH H

]D[HHH

p

1ˆP


26/07/200726/07/2007

Flow chart of the CLS schemeFlow chart of the CLS scheme


26/07/200726/07/2007

Constrained linear Minimum Constrained linear Minimum MSE (CMMSE) estimatorMSE (CMMSE) estimator

Minimise MSE between the CFR estimate Minimise MSE between the CFR estimate and the assumed CFR model and the assumed CFR model with respect to with respect to QQ ::

Computation of is of large Computation of is of large complexity if complexity if PP is big. Can we design the is big. Can we design the CMMSE estimator in the transform-domain CMMSE estimator in the transform-domain form ?form ?

pCMMSE YQH ˆ

hBFH

hBFYQhBFYQQ pp H

E1

)(N

M

ppppHHHH

CMMSE YXXXCRCCRH 1]D[

1

]D[H]D[

2wgn

HH1~~ˆ

HH~~FBRBFR hhHH is the design CFR is the design CFR

correlation matrixcorrelation matrix

is the design CIR is the design CIR correlation matrixcorrelation matrix

is the design setting for the WGN is the design setting for the WGN variancevariance

hhR~

CMMSEH

2wgn

~


26/07/200726/07/2007

Low-complexity CMMSE design-Low-complexity CMMSE design-formform Applying the matrix inversion identities, one can show thatApplying the matrix inversion identities, one can show that

For the equipowered and equispaced pilot For the equipowered and equispaced pilot subcarriers:subcarriers:

ppCMMSECMMSE YXCFBSBFH H]D[

HHHˆ

CLSCLShhhh

CMMSE SSRRS12

wgn~~~

pphhhh

CMMSEesep YθCFBIRRBFH H

]D[HHH

1

pp~1~~1ˆ

RNSPP2wgn

2pp

~~ RNS

p

~RNS hhhh RIR

~)

~(1

~p RNSP CLS

esepCMMSE

esep HH ˆˆ


26/07/200726/07/2007

What if the parameters are not What if the parameters are not known ?known ? Generally the true CIR correlation matrix and Generally the true CIR correlation matrix and

the true are not known, therefore the the true are not known, therefore the optimum CMMSE design ( optimum CMMSE design ( , , ) is ) is hardly achievablehardly achievable

2 practical approaches are possible:2 practical approaches are possible: robust mode, when (similar to the CLS robust mode, when (similar to the CLS

scheme)scheme) recursive mode (dynamic estimation of and )recursive mode (dynamic estimation of and )

hhR

pSNR

hhhh RR ~pp

~SNRRNS

IR hh1~ L

hhR pSNR


26/07/200726/07/2007

Recursive CMMSE estimatorRecursive CMMSE estimator

is the precision matrix of is the precision matrix of the CIR+noise mixture described asthe CIR+noise mixture described as

CLShh

CLSCMMSE STSIS ~~2wgn

ppCMMSECMMSE YXCFBSBFH H]D[

HHHˆ

1~~

12wgn~~

hhCLS

hhhhRSRT

whYXCFBSh ppCLS H]D[

HHH~

CLShh

CLSCMMSE STSIS )(ˆ)1(ˆ)(ˆ ~~2wgn iii

Substitute with Substitute with CMMSES

)(ˆ ~~ ihh

T is an estimate of obtained for the is an estimate of obtained for the iith th OFDM symbolOFDM symbol

is an estimate of for the (is an estimate of for the (ii-1)th OFDM -1)th OFDM symbolsymbol

hhT ~~

)1(ˆ 2wgn i 2

wgn


26/07/200726/07/2007

Recursive CMMSE estimator Recursive CMMSE estimator (cont.)(cont.) LetLet thenthenH

~~~~ )(~

)(~

)1(ˆ)1()(ˆ iiii hhRRhhhh

)1(ˆ)1(ˆ)1(~

)1(~

)2(ˆ)1()1(ˆ1H1H2

wgn2wgn

iiiiLii hShhSh CLSCLS

])1(ˆ)(~

)(~

trace[)1(

)1(ˆ)(~

)(~

)1(ˆ)1(

1)(ˆ)(ˆ

~~H

~~H

~~1

~~~~

iii

iiiiii

hh

hhhhhhhh Thh

ThhITRT

)1()1(~ H

]D[HHH ii ppCLS YXCFBSh

)1()1(ˆ)1(ˆ H]D[

HHH iii ppCMMSE YXCFBSh

For the equipowered and equispaced pilot For the equipowered and equispaced pilot subcarriers:subcarriers: )(ˆ)1(ˆ1

)(ˆ ~~1

p1

2p

iiRNSPP

ihh

CMMSEesep TIS

)]1(ˆ)1(ˆ)1(

~)1(

~[)2(ˆ)1()1(ˆ HH-1

p-1p iiiiLPiRNSiRNS hhhh


26/07/200726/07/2007

Initial settings:Initial settings: During the initialisation period, until the reliable During the initialisation period, until the reliable

estimate of is obtained, estimator operates in the estimate of is obtained, estimator operates in the robust mode (as CLS), i.e. robust mode (as CLS), i.e.

Flow chart of the recursive Flow chart of the recursive CMMSECMMSE

hhT ~~

CLSCMMSE SS

0)1(ˆ 2wgn IT

hhL )1(~~


26/07/200726/07/2007

Optimisation of pilotsOptimisation of pilots To achieve the best CFR estimation accuracy To achieve the best CFR estimation accuracy

under the total transmit power constraint:under the total transmit power constraint:-- pilot subcarriers must be equipowered and -- pilot subcarriers must be equipowered and

equispaced in the bandequispaced in the band

-- pilot-to-data (PDR) power ratio for the CLS and -- pilot-to-data (PDR) power ratio for the CLS and CMMSE (worst-case CIR correlation) estimators with CMMSE (worst-case CIR correlation) estimators with one-tap equalisation is determined asone-tap equalisation is determined as

SNRLN

SNRPN

N

P

PN

1

1)(2d

2p

opt

SNRPNP

NSNR

opt

optp

Pilot subcarrier

Data subcarrier


26/07/200726/07/2007

Theoretical/simulation resultsTheoretical/simulation results System configuration:System configuration:

(subcarriers), (pilots), (CP length), 16QAM (subcarriers), (pilots), (CP length), 16QAM Average PDR set to optimal calculated forAverage PDR set to optimal calculated for

Channel model:Channel model: (modelled CIR length), (modelled Doppler spread)(modelled CIR length), (modelled Doppler spread)

64N 16P 16cp N

16L Tf 01.0D

minSNR


26/07/200726/07/2007

MSE & BER performance (case MSE & BER performance (case 1)1)

)(cp

0

b

PNb

NNSNR

N

E

Channel – non-sample-spaced: Channel – non-sample-spaced:

2-path UPDP,2-path UPDP, NT2.3rms

)4( b


26/07/200726/07/2007

MSE performance (case 2)MSE performance (case 2)

Channel – sample-spaced: Channel – sample-spaced: Exponential PDP,Exponential PDP, NTrms


26/07/200726/07/2007

Impact of the number of pilot Impact of the number of pilot subcarriers on the system subcarriers on the system

performanceperformanceChannel – sample-spaced: Channel – sample-spaced: Exponential PDP,Exponential PDP, NTrms

)(

)(

cp0

b

NN

PNb

N

ESNR

)4( b


26/07/200726/07/2007

Dependence of SNR gain at Dependence of SNR gain at equaliser’s output on PDRequaliser’s output on PDR

CMMSE estimator used CMMSE estimator used Channel – non-sample-spaced: Channel – non-sample-spaced:

2-path UPDP,2-path UPDP, NT2.3rms


26/07/200726/07/2007

Blind systemBlind system Minimises training overhead to just one pilot Minimises training overhead to just one pilot

subcarrier (reference phase acquisition)subcarrier (reference phase acquisition) Detection is performed on a portion of Detection is performed on a portion of

subcarriers subcarriers ((DD L L + 1+ 1))

Detected subsymbols are fed forward to the Detected subsymbols are fed forward to the channel estimation and interpolation channel estimation and interpolation algorithm (e.g., CLS, CMMSE) to get CFRalgorithm (e.g., CLS, CMMSE) to get CFR

The optimal data detection involves an The optimal data detection involves an exhaustive search across the lattice of exhaustive search across the lattice of MMDD points (points (MM – modulation constellation size), – modulation constellation size), yielding a vector of yielding a vector of DD detected subsymbols detected subsymbols satisfyingsatisfying *

D][

12wgn

HHHH]D[

Tminargˆ DDhh

DD

X

D XYICFBRBFCYXX


26/07/200726/07/2007

Simulation resultsSimulation results System configuration:System configuration:

(total subcarriers), (detectable (total subcarriers), (detectable subcarriers), subcarriers),

(CP length), QPSK, equi-powered (CP length), QPSK, equi-powered subcarrierssubcarriers

CLS channel estimation based on detected CLS channel estimation based on detected subsymbolssubsymbols

Channel model:Channel model:2-path uniform PDP with2-path uniform PDP with

64N 8D

8cp N

8LNT2.2rms


26/07/200726/07/2007

MSE & BER performanceMSE & BER performance


26/07/200726/07/2007

Problems to investigateProblems to investigate Use a reduced-complexity suboptimal blind Use a reduced-complexity suboptimal blind

detection algorithm, e.g. V-BLAST, instead of detection algorithm, e.g. V-BLAST, instead of computationally prohibitive exhaustive search computationally prohibitive exhaustive search

Optimise Optimise DD value to allow for fast operation value to allow for fast operation and satisfactory performanceand satisfactory performance

Optimise transmit power distribution between Optimise transmit power distribution between the detectable subcarriers and othersthe detectable subcarriers and others

Combine blind algorithm with optional time-Combine blind algorithm with optional time-domain interpolation to improve performancedomain interpolation to improve performance

Determine whether the blind receiver is more Determine whether the blind receiver is more efficient than the pilot-assisted oneefficient than the pilot-assisted one


26/07/200726/07/2007

[1][1] E. Golovins, and N. Ventura. “Comparative analysis of low complexity channel estimation techniques for the pilot-assisted E. Golovins, and N. Ventura. “Comparative analysis of low complexity channel estimation techniques for the pilot-assisted wireless OFDM systems,” in wireless OFDM systems,” in Proc. Southern African Telecommun. Networks and Applications Conf. (SATNAC)Proc. Southern African Telecommun. Networks and Applications Conf. (SATNAC) , Sep. 2006., Sep. 2006.

[2][2] E. Golovins, and N. Ventura. “Optimisation of the pilot-to-data power ratio in the MQAM-modulated OFDM systems with E. Golovins, and N. Ventura. “Optimisation of the pilot-to-data power ratio in the MQAM-modulated OFDM systems with MMSE channel estimation,” to appear in MMSE channel estimation,” to appear in Proc. Southern African Telecommun. Networks and Applications Conf. (SATNAC)Proc. Southern African Telecommun. Networks and Applications Conf. (SATNAC) , , Sep. 2007.Sep. 2007.

[3][3] E. Golovins, and N. Ventura, “Design and performance analysis of low-complexity pilot-aided OFDM channel estimators,” in E. Golovins, and N. Ventura, “Design and performance analysis of low-complexity pilot-aided OFDM channel estimators,” in Proc. 6Proc. 6thth IEEE Intern. Workshop on Multi-Carrier and Spread Spectrum (MC-SS) IEEE Intern. Workshop on Multi-Carrier and Spread Spectrum (MC-SS) , May 2007., May 2007.

[4][4] E. Golovins, and N. Ventura, “Modified order-recursive least squares estimator for the noisy OFDM channels,” in E. Golovins, and N. Ventura, “Modified order-recursive least squares estimator for the noisy OFDM channels,” in Proc. 5Proc. 5thth IEEE IEEE Commun. and Netw. Services Research Conf. (CNSR)Commun. and Netw. Services Research Conf. (CNSR) , May 2007., May 2007.

[5][5] E. Golovins, and N. Ventura, “Low-complexity constrained LMMSE estimator for the sparse OFDM channels,” to appear in E. Golovins, and N. Ventura, “Low-complexity constrained LMMSE estimator for the sparse OFDM channels,” to appear in Proc. IEEE Africon 2007 Conf.Proc. IEEE Africon 2007 Conf., Sep. 2007., Sep. 2007.

Published workPublished work


26/07/200726/07/2007

Experimental OFDM model in Experimental OFDM model in SimulinkSimulink


26/07/200726/07/2007

…….….…

[email protected]@crg.ee.uct.ac.za

low-complexity channel estimation for wireless ofdm systems eugene golovins neco ventura...

Documents

received pilot subsymbols

pilot positions

pilot samples

channel response

pilot subcarriers optima

frequency domain

reference pilot values

radio channel model