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 August 10, 2014

2. 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 Doubly-selective Wireless Channel Back haul Internet Mobile Base Station Feedback channel information Adaptive Orthogonal Frequency Division Multiplexing (OFDM) August 10, 2014

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 August 10, 2014

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 August 10, 2014

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 August 10, 2014

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-step1-dimensional frequency estimation August 10, 2014

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) August 10, 2014

8. … f Df t Dt Pilot-based Transmission • Comb pilot pattern • Least-squares channel estimates August 10, 2014

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 August 10, 2014

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] August 10, 2014

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 August 10, 2014

12. Insights from the MSE expression • 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, Dtand Df should be chosen as large as possible to decrease the MSE bound Doppler frequency & phase cross covariance Amplitude & phase error variance Doppler frequency error variance Time-delay & phase cross covariance Time-delay error variance August 10, 2014

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 August 10, 2014

14. Asymptotic MSE Lower Bound for 2-step estimation • 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 Doppler frequency & phase cross covariance Amplitude & phase error variance Doppler frequency error variance Time-delay error variance August 10, 2014

15. IEEE 802.16 Example August 10, 2014

16. MSE vs. SNR, n=500 August 10, 2014

17. MSE vs. n, SNR=10 dB August 10, 2014

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 August 10, 2014