A Factor-Graph Approach to Joint OFDM Channel Estimation and Decoding in Impulsive Noise Channels

1. A Factor-Graph Approach to Joint OFDM Channel Estimation and Decoding in Impulsive Noise Channels Philip Schniter The Ohio State University Marcel Nassar, Brian L. Evans The University of Texas at Austin

2. Outline • Uncoordinated interference in communication systems • Effect of interference on OFDM systems • Prior work on OFDM receivers in uncoordinated interference • Message-passing OFDM receiver design • Simulation results Introduction |Message Passing Receivers | Simulations | Summary

3. Uncoordinated Interference • Typical Scenarios: • Wireless Networks: Ad-hoc Networks, Platform Noise, non-communication sources • Powerline Communication Networks: Non-interoperable standards, electromagnetic emissions • Statistical Models: Interference Model • Two impulsive components: • 7% of time/20dB above background • 3% of time/30dB above background Gaussian Mixture (GM) : #of comp. comp. probability comp. variance Introduction |Message Passing Receivers | Simulations | Summary

4. OFDM Basics System Diagram noise +interference SymbolMapping LDPC Coded DFT Inverse DFT Source + 1+i 1-i -1-i 1+i … 0111 … channel Noise Model Receiver Model • After discarding the cyclic prefix: • After applying DFT: • Subchannels: total noise where background noise interference and GM or GHMM Introduction |Message Passing Receivers | Simulations | Summary

5. OFDM Symbol Structure Coding Data Tones • Added redundancy protects against errors • Symbols carry information • Finite symbol constellation • Adapt to channel conditions Pilot Tones Null Tones • Edge tones (spectral masking) • Guard and low SNR tones • Ignored in decoding • Known symbol (p) • Used to estimate channel pilots → linear channel estimation → symbol detection → decoding But, there is unexploited information and dependencies Introduction |Message Passing Receivers | Simulations | Summary

6. Prior OFDM Designs All don’t consider the non-linear channel estimation, and don’t use code structure Introduction |Message Passing Receivers | Simulations | Summary

7. Joint MAP-Decoding • The MAP decoding rule of LDPC coded OFDM is: • Can be computed as follows: depends on linearly-mixed N noise samples and L channel taps LDPC code non iid & non-Gaussian Very high dimensional integrals and summations !! Introduction |Message Passing Receivers | Simulations | Summary

8. Belief Propagation on Factor Graphs • Graphical representation of pdf-factorization • Two types of nodes: • variable nodes denoted by circles • factor nodes (squares): represent variable “dependence “ • Consider the following pdf: • Corresponding factor graph: Introduction |Message Passing Receivers | Simulations | Summary

9. Belief Propagation on Factor Graphs • Approximates MAP inference by exchanging messages on graph • Factor message = factor’s belief about a variable’s p.d.f. • Variable message = variable’s belief about its own p.d.f. • Variable operation = multiply messages to update p.d.f. • Factor operation = merges beliefs about variable and forwards • Complexity = number of messages = node degrees Introduction |Message Passing Receivers | Simulations | Summary

10. Coded OFDM Factor Graph unknown channel taps Unknown interference samples Symbols Information bits Coding & Interleaving Bit loading & modulation Received Symbols Introduction |Message Passing Receivers | Simulations | Summary

11. BP over OFDM Factor Graph MC Decoding LDPC Decoding via BP [MacKay2003] Node degree=N+L!!! Introduction |Message Passing Receivers | Simulations | Summary

12. Generalized Approximate Message Passing[Donoho2007,Rangan2010] Decoupling via Graphs Estimation with Linear Mixing variables observations coupling • Generally a hard problem due to coupling • Regression, compressed sensing, … • OFDM systems: • If graph is sparse use standard BP • If dense and ”large”→Central Limit Theorem • At factors nodes treat as Normal • Depend only on means and variances of incoming messages • Non-Gaussian output → quad approx. • Similarly for variable nodes • Series of scalar MMSE estimation problems: messages Interference subgraph channel subgraph given given and and 3 types of output channels for each Introduction |Message Passing Receivers | Simulations | Summary

13. Message-Passing Receiver Schedule coded bits to symbols symbols to Run channel GAMP Run noise “equalizer” to symbols Symbols to coded bits Run LDPC decoding Turbo Iteration: GAMP LDPC Dec. GAMP Equalizer Iteration: Run noise GAMP MC Decoding Repeat Initially uniform Introduction |Message Passing Receivers | Simulations | Summary

14. Receiver Design & Complexity Design Freedom • Not all samples required for sparse interference estimation • Receiver can pick the subchannels: • Information provided • Complexity of MMSE estimation • Selectively run subgraphs • Monitor convergence (GAMP variances) • Complexity and resources • GAMP can be parallelized effectively Notation : # tones : # coded bits : # check nodes : set of used tones Introduction |Message Passing Receivers | Simulations | Summary

15. Simulation - Uncoded Performance use LMMSE channel estimate performs well when interference dominates time-domain signal Settings use only known tones, requires matrix inverse 5 Taps GM noise 4-QAM N=256 15 pilots 80 nulls 2.5dB better than SBL within 1dB of MF Bound 15db better than DFT Matched Filter Bound: Send only one symbol at tone k Introduction |Message Passing Receivers | Simulations| Summary

16. Simulation - Coded Performance one turbo iteration gives 9db over DFT Settings 5 turbo iterations gives 13dB over DFT 10 Taps GM noise 16-QAM N=1024 150 pilots Rate ½ L=60k Integrating LDPC-BP into JCNED by passing back bit LLRs gives 1 dB improvement Introduction |Message Passing Receivers | Simulations| Summary

17. Summary • Huge performance gains if receiver account for uncoordinated interference • The proposed solution combines all available information to perform approximate-MAP inference • Asymptotic complexity similar to conventional OFDM receiver • Can be parallelized • Highly flexible framework: performance vs. complexity tradeoff Introduction |Message Passing Receivers | Simulations| Summary

18. Thank you

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20. Interference in Communication Systems Wireless LAN in ISM band Powerline Communication Non-interoperable standards Co-Channelinterference Platform Coexisting Protocols Non-CommunicationSources Electromagnetic emissions Introduction |Message Passing Receivers | Simulations | Robust Receivers| Summary

21. Empirical Modeling Powerline Systems WiFi Platform Interference Gaussian HMM Model 1 2 • [Data provided by Intel] • Partitioned Markov Chain Model [Zimmermann2002] 1 … 1 2 1 5 2 Background Impulsive Introduction |Message Passing Receivers | Simulations | Robust Receivers| Summary

22. Statistical-Physical Modeling Wireless Systems PowerlineSystems WiFi, Ad-hoc [Middleton77, Gulati10] Rural, Industrial, Apartments [Middleton77,Nassar11] Middleton Class-A A Impulsive Index Mean Intensity WiFi Hotspots [Gulati10] Dense Urban, Commercial [Nassar11] Gaussian Mixture (GM) : #of comp. comp. probability comp. variance Introduction |Message Passing Receivers | Simulations | Robust Receivers| Summary

23. Effect of Interference on OFDM Single Carrier (SC) OFDM Single Carrier vs. OFDM (symbol by symbol decoding) DFT • Impulse energy concentrated • Symbol lost with high probability • Symbol errors independent • Min. distance decoding is MAP-optimal • Minimum distance decoding under GM: • Impulse energy spread out • Symbol lost ?? • Symbol errors dependent • Disjoint minimum distance is sub-optimal • Disjoint minimum distance decoding: Impulse energy low → OFDM sym. recovered Impulse energy high → OFDM sym. lost • In theory, with joint MAP decodingOFDM Single Carrier tens of dBs • [Haring2002] Introduction |Message Passing Receivers | Simulations | Robust Receivers| Summary