LowComplexity Channel Estimation for Wireless OFDM Systems

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Low-Complexity Channel Estimation for Wireless
OFDM Systems

• Eugene Golovins Neco Ventura
• egolovins_at_crg.ee.uct.ac.za neco_at_crg.ee.uct.ac.z
  a

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Outline

• -- Introduction
• -- Radio channel model
• -- Pilot-assisted OFDM system
• -- Blind OFDM system

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Introduction

• OFDM has been found efficient in reducing severe
  effects of the frequency-selective fading
  (inherent to the urban and indoor radio channels)
  
• High-capacity subcarrier modulation techniques
  (e.g., QAM) require accurate estimation of the
  channel frequency response (CFR) for coherent
  detection at the receiver
• Channel estimator must satisfy 3 requirements
• rely on the least possible training overhead
• achieve performance close to optimal
• be of the least possible computational complexity

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Baseband OFDM system
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Channel model

• Two kinds of impairments in the fading channel
• -- dispersion (frequency selectivity) due to
  multipath propagation
• -- time variability (Doppler effect) due to the
  relative motion of TX and RX antennas
• Adopted model quasi-static approximation of
  the WSSUS process
• -- channel response does not change on the
  interval of one OFDM symbol
• -- multipath response is comprised of an
  arbitrary number of the statistically independent
  path-gains, delayed at fixed time intervals
• -- inter-symbol variation of the path-gains is
  governed by the Doppler random process with
  Jakess spectrum

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Channel frequency response (CFR)

• Example of CFR of the considered fading channel

(max. delay spread)
(RMS delay spread)
(max. Doppler freq.)
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Frequency-domain block processing

• Nd data subsymbols are transmitted in block of
  NdPNcp subsymbols, with P pilot subsymbols and
  a cyclic prefix of length Ncp ? L - 1 (L
  expected CIR length)
• Receiver processes blocks in frequency domain by
  taking FFT of each received block
• Typically the size of the processing block N
  NdP is 5 to 10 times Ncp

OFDM time-frequency grid
Temporal block structure
Frequency (subcarriers)
N
Time (OFDM symbols / blocks)
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Pilot-assisted system

• Channel estimator operates only in 1D (across
  freq. domain) computing channel distortions for
  each OFDM symbol separately
• Known pilot sequence is transmitted on a small
  fraction of subcarriers (P) to train the
  estimator
• Interpolation of pilots in frequency is performed
  to get CFR estimate in the full band

Pilot subcarrier Data subcarrier
Frequency (subcarriers)
N
Time (OFDM symbols)
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Design definition of the constrained estimator

• Anticipated CIR length
• Number of pilot subcarriers
• Received subsymbols at the pilot positions

contains reference values of P pilot
subsymbols is the selection matrix that is needed
to extract pilot samples of the CFR is the
zero-padding matrix (from L up to N) is the WGN
vector at the pilot subcarriers is the CIR
vector (to be found)
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Constrained Least Squares (CLS) estimator

• Minimise the quadratic difference between the
  received pilot subsymbols and the reference
  pilot values being affected by the assumed
  CFR model

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

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Flow chart of the CLS scheme
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Constrained linear Minimum MSE (CMMSE) estimator

• Minimise MSE between the CFR estimate
  and the assumed CFR model
  with respect to Q

is the design CFR correlation matrix is the
design CIR correlation matrix is the design
setting for the WGN variance

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

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Low-complexity CMMSE design-form

• Applying the matrix inversion identities, one can
  show that

• For the equipowered and equispaced pilot
  subcarriers

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What if the parameters are not known ?

• Generally the true CIR correlation matrix
  and the true are not known,
  therefore the optimum CMMSE design (
  , ) is hardly achievable
• 2 practical approaches are possible
• robust mode, when (similar
  to the CLS scheme)
• recursive mode (dynamic estimation of
  and )

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Recursive CMMSE estimator

• is the precision matrix of the CIRnoise
  mixture described as

Substitute with
is an estimate of obtained for the
ith OFDM symbol is an estimate of for
the (i-1)th OFDM symbol
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Recursive CMMSE estimator (cont.)

• Let then

• For the equipowered and equispaced pilot
  subcarriers

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Flow chart of the recursive CMMSE

• Initial settings
• During the initialisation period, until the
  reliable estimate of is obtained,
  estimator operates in the robust mode (as CLS),
  i.e.

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Optimisation of pilots

• To achieve the best CFR estimation accuracy under
  the total transmit power constraint
• -- pilot subcarriers must be equipowered and
  equispaced in the band
• -- pilot-to-data (PDR) power ratio for the CLS
  and CMMSE (worst-case CIR correlation) estimators
  with one-tap equalisation is determined as

Pilot subcarrier Data subcarrier
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Theoretical/simulation results

• System configuration
• (subcarriers), (pilots),
  (CP length), 16QAM
• Average PDR set to optimal calculated for
• Channel model
• (modelled CIR length),
  (modelled Doppler spread)

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MSE BER performance (case 1)

• Channel non-sample-spaced
• 2-path UPDP,

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MSE performance (case 2)

• Channel sample-spaced
• Exponential PDP,

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Impact of the number of pilot subcarriers on the
system performance

• Channel sample-spaced
• Exponential PDP,

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Dependence of SNR gain at equalisers output on
PDR
CMMSE estimator used Channel
non-sample-spaced 2-path UPDP,
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Blind system

• Minimises training overhead to just one pilot
  subcarrier (reference phase acquisition)
• Detection is performed on a portion of
  subcarriers
• (D ? L 1)
• Detected subsymbols are fed forward to the
  channel estimation and interpolation algorithm
  (e.g., CLS, CMMSE) to get CFR
• The optimal data detection involves an exhaustive
  search across the lattice of MD points (M
  modulation constellation size), yielding a vector
  of D detected subsymbols satisfying

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Simulation results

• System configuration
• (total subcarriers),
  (detectable subcarriers),
• (CP length), QPSK, equi-powered
  subcarriers
• CLS channel estimation based on detected
  subsymbols
• Channel model
• 2-path uniform PDP with

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MSE BER performance
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Problems to investigate

• Use a reduced-complexity suboptimal blind
  detection algorithm, e.g. V-BLAST, instead of
  computationally prohibitive exhaustive search
• Optimise D value to allow for fast operation and
  satisfactory performance
• Optimise transmit power distribution between the
  detectable subcarriers and others
• Combine blind algorithm with optional time-domain
  interpolation to improve performance
• Determine whether the blind receiver is more
  efficient than the pilot-assisted one

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Published work

• 1 E. Golovins, and N. Ventura. Comparative
  analysis of low complexity channel estimation
  techniques for the pilot-assisted wireless OFDM
  systems, in Proc. Southern African Telecommun.
  Networks and Applications Conf. (SATNAC), Sep.
  2006.
• 2 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 Proc. Southern African
  Telecommun. Networks and Applications Conf.
  (SATNAC), Sep. 2007.
• 3 E. Golovins, and N. Ventura, Design and
  performance analysis of low-complexity
  pilot-aided OFDM channel estimators, in Proc.
  6th IEEE Intern. Workshop on Multi-Carrier and
  Spread Spectrum (MC-SS), May 2007.
• 4 E. Golovins, and N. Ventura, Modified
  order-recursive least squares estimator for the
  noisy OFDM channels, in Proc. 5th IEEE Commun.
  and Netw. Services Research Conf. (CNSR), May
  2007.
• 5 E. Golovins, and N. Ventura, Low-complexity
  constrained LMMSE estimator for the sparse OFDM
  channels, to appear in Proc. IEEE Africon 2007
  Conf., Sep. 2007.

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Experimental OFDM model in Simulink
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• egolovins_at_crg.ee.uct.ac.za