1. Performance Bounds in OFDM Channel Prediction
Ian C. Wong and Brian L. Evans
Wireless Networking and Communications Group
The University of Texas at Austin
December 1, 2018

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
Internet
Back haul
Base Station
Doubly-selective
Wireless Channel
Mobile
Feedback channel information
December 1, 2018

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 …
Put description of delta
December 1, 2018

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
December 1, 2018

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
Remove articles
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6. 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-step 1-dimensional frequency estimation
December 1, 2018

7. 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)
Put legend when with equation
December 1, 2018

8. Pilot-based Transmission
Comb pilot pattern
Least-squares channel estimates t f … Dt Df
Get rid of pattern, legend of LS estimates, remind key parameters, Nt nf,…
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9. 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
December 1, 2018

10. Cramer-Rao Lower Bound (CRLB)
CRLB for narrowband case [Barbarossa & 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]
Fix this slide… add legend for notation
December 1, 2018

11. 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
Add box to equation , legend for notation Nf Nt Dt Df, n, k kbar, add bullet lead in to equation
December 1, 2018

12. Insights from the MSE expression
Amplitude & phase error variance
Doppler frequency & phase cross covariance
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
Fix equations, put arrows or animation to explain quadratic increase, say what is new and known, explain some tradeoffs…
December 1, 2018

13. 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
December 1, 2018

14. 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
Put it in dB after 2.5
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15. IEEE Example
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16. MSE vs. SNR, n=500 Legend in order as they appear in plot
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17. MSE vs. n, SNR=10 dB
Same comment as previous,say prediction length in symbols
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18. 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
December 1, 2018