Performance Bounds in OFDM Channel Prediction

1
Performance Bounds inOFDM Channel Prediction

• Ian C. Wong and Brian L. Evans
• Wireless Networking and Communications Group
• The University of Texas at Austin

2
Adaptive Orthogonal Frequency Division
Multiplexing (OFDM)

• Adjust transmission based on channel information
• Maximize data rates and/or improve link quality
• Problems
• Feedback delay - significant performance loss
  Souryal Pickholtz, 2001
• Volume of feedback - power and bandwidth overhead

3
Prediction of Wireless Channels

• Use current and previous channel estimates to
  predict future channel response
• Overcome feedback delay
• Adaptation based on predicted channel response
• Lessen amount of feedback
• Predicted channel response may replace direct
  channel feedback

4
Previous Work

• Prediction on each subcarrier Forenza Heath,
  2002
• Each subcarrier treated as a narrowband
  autoregressive WSS process Duel-Hallen et al.,
  2000
• Prediction using pilot subcarriers Sternad
  Aronsson, 2003
• Used unbiased power prediction Ekman, 2002
• Prediction on time-domain taps Schafhuber
  Matz, 2005
• Used adaptive prediction filters
• Applied to predictive equalization

5
Previous Work

• Comparison of prediction approaches using unified
  framework Wong et al, 2004
• Time-domain approach gives best MSE performance
  vs. complexity tradeoff
• Prediction using high-resolution frequency
  estimation Wong Evans, 2005
• Shown to significantly outperform previous
  methods with same order of complexity
• Key idea 2-step 1-dimensional frequency
  estimation

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Summary of Main Contributions

• Simple, closed-form expression for MSE lower
  bound in OFDM channel prediction for any unbiased
  channel estimation/prediction algorithm
• Yields important insight into designing OFDM
  channel predictors without extensive numerical
  simulation
• Simple, closed-form expression for MSE lower
  bound in OFDM channel prediction using
  2-step1-dimensional frequency estimation

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System Model

• OFDM baseband received signal
• Perfect synchronization and inter-symbol
  interference elimination by the cyclic prefix
• Flat passband for transmit and receiver filters
  over used subcarriers
• Deterministic wideband wireless channel model
• Far-field scatterer (plane wave assumption)
• Linear motion with constant velocity
• Small time window (a few wavelengths)

8
Pilot-based Transmission

• Comb pilot pattern
• Least-squares channel estimates

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Prediction as parameter estimation

• Channel is a continuous non-linear function of
  the 4M-length channel parameter vector
• Deterministic channel prediction premise
• Estimate parameters of channel model from the
  least-squares channel estimates
• 2-dimensional sum of complex sinusoids in white
  noise
• Extrapolate the model forward

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Cramer-Rao Lower Bound (CRLB)

• CRLB for narrowband caseBarbarossa Scaglione,
  2001 Teal, 2002
• First-order Taylor approximation
• Expensive numerical evaluations necessary
• Monte-Carlo generation of parameter vector
  realizations
• CRLB for function of parameters Scharf, 1991

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Closed-form asymptotic MSE bound

• Using large-sample limit of CRLB matrix for
  general 2-D complex sinusoidal parameter
  estimation Mitra Stoica, 2002
• Much simpler expression
• Achievable by maximum-likelihood and nonlinear
  least-squares methods
• Monte-Carlo numerical evaluations not necessary

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Insights from the MSE expression
Doppler frequency phase cross covariance
Amplitude phase error variance
Doppler frequency error variance
Time-delay phase cross covariance
Time-delay error variance

• Linear increase with ?2 and M
• Dense multipath channel environments are the
  hardest to predict Teal, 2002
• Quadratic increase in n and k with f and ?
  estimation error variances
• Emphasizes the importance of estimating these
  accurately
• Nt, Nf, Dt and Df should be chosen as large as
  possible to decrease the MSE bound

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High-performance OFDM channel prediction
algorithm Wong Evans, 2005

• In wireless channels, a number of sinusoidal rays
  typically share a common time delay
• Proposed 2-step 1-D estimation
• Lower complexity with minimal performance loss
• Rich literature of 1-D sinusoidal parameter
  estimation
• Allows decoupling of computations between
  receiver and transmitter

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Asymptotic MSE Lower Bound for 2-step estimation
Amplitude phase error variance
Doppler frequency phase cross covariance
Doppler frequency error variance
Time-delay error variance

• Used asymptotic CRLB matrix for 1-D sinusoidal
  parameter estimation Stoica et al., 1997
• Complex amplitude estimation error variance of
  first step used as the noise variance in second
  step
• For large prediction lengths, i.e. large n

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IEEE 802.16 Example
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MSE vs. SNR, n500
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MSE vs. n, SNR10 dB
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Conclusion

• Derived simple, closed-form expressions for
• MSE lower bound for OFDM channel prediction
• Expensive numerical evaluation unnecessary
• Yields valuable insight into design of channel
  predictors
• Block lengths and downsampling factors should be
  made as big as possible
• Estimation of Doppler frequencies/time delays
  very important
• Dense multipath channels may not be predictable
• MSE Lower bound for 2-step OFDM channel
  prediction
• Small penalty compared to above bound
• Basis for a high-performance channel prediction
  algorithm
• Proposed 2-step 1-D prediction algorithm is close
  to the lower bound