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Limited Feedback Beamforming with Delay: Theory and Practice

Limited Feedback Beamforming with Delay: Theory and Practice. Huang Kaibin Collaborators: Robert Daniels Prof. Robert W. Heath Jr. Prof. Jeffrey G. Andrews Wireless Networking and Communications Group (WNCG) Dept. of Electrical and Computer Engineering

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Limited Feedback Beamforming with Delay: Theory and Practice

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  1. Limited Feedback Beamforming with Delay: Theory and Practice Huang Kaibin Collaborators: Robert Daniels Prof. Robert W. Heath Jr. Prof. Jeffrey G. Andrews Wireless Networking and Communications Group (WNCG) Dept. of Electrical and Computer Engineering The University of Texas at Austin 08/15/2007 TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAA

  2. A new area: MIMO with Limited Feedback • Single-user 2) Multi-user 3) Wireless network talk scope MIMO: a Personal View 1996 Channel capacity (Telatar, Foschini) 1998 Gaussian broadcast Caire & Shamai Vish., Jindal & Goldsmith Viswanath & Tse Yu & Cioffi Space-time codes (Tarokh, Alamouti, Jafarkani) 2000 2002 Multi-user Diversity Knopp & Humblet Viswanath & Tse Sharif & Hassibi Diversity-multiplexing tradeoff (Zheng & Tse, Heath & Paulraj) 2004 IEEE 802.16e (WiMax) 2006 IEEE 802.11n (WiFi) 3GPP-LTE 2008 1

  3. Feedback Enhances Communication In the darkness… ? Here! listener speaker listener speaker no feedback feedback 2

  4. feedback feedback Beamforming Increases Throughput beamforming weights no feedback 3

  5. Wireless Channel Limited Feedback Concept • Adaptive Transmission • Precoder • Beamformer • AMC, etc Receiver Transmiter CSI Finite-Rate Feedback Channel Codebook based quantizer

  6. Limited Feedback Beamforming Increases Throughput quantizer partition index feedback quantizer surface of unit hyper-sphere 4

  7. Prior Work on Limited Feedback Beamforming • Narrow-band block fadingchannels • Research focuses on the codebook design. • Grassmannian line packing [Love & Heath 03] [Mukkavilli et al 03] • Lloyd algorithm [Roh & Rao 06][Xia et al 05] • Broadband channels (MIMO-OFDM) • Sub-channel grouping [Mondal & Heath 05] • Beamformer interpolation [Choi & Heath 04] • Spatially correlated channels • Codebook switching based channel correlation [Mondal & Heath 06] • Temporally correlated channels (considered in this talk) • Delta modulated feedback [Roh & Rao 04] • Drawback: multiple feedback streams • 1-bit feedback based on subspace perturbation [Banister 03] • Drawback: periodic broadcast of matrices

  8. Limited Feedback Beamforming in Industry • Local Area Networks (IEEE 802.11n) • Optional feature for 600 Mbps • IEEE 802.16e (WiMax) • Codebook based precoding/beamforming • 3GPP Long Term Evolution (LTE) • Single- and multi-user limited feedback beamforming • 4G • Lots of discussion

  9. Channel State S1 S2 S3 S4 S1, S2, … are independently distributed. Channel Coherence Time Motivation • Conventional: Block fading channels • (Narula et al 98, Love et al 03, Mukkavilli et al 03, Xia et al 04) • (Pro): Focus on quantizer codebook designs • (Con): Omits temporal correlation in wireless channels • (Con): Analysis of feedback delay and rate is difficult • New: Temporally-correlatedchannels • Feedback rate (vs. channel coherence time) • Feedback compression in time • Effect of feedback delay on throughput Important for designing practical limited feedback systems 6

  10. Outline • Part I: Theory • Channel Markov model • Feedback compression and rate • Feedback delay • Part II: Practice • Experiment setup • Measurement results

  11. System Model CSI {H1, H2, … } is a correlated sequence 7

  12. Proposed Approach: Assumption and Overview • The CSI index Jnvaries as a discrete-time finite-state Markov chain • Accurate for slowly time-varying SISO channel (Wang & Moayeri 95) Temporally Correlated MIMO Channel Markov Chain Feedback rate, compression, delay 8

  13. S2 S1 p13 p33 p63 S3 S6 p64 p43 S4 S5 Proposed Approach: CSI Index Markov Chain • Definition ofMarkov state space • Partition channel space using existing codebook-design techniques • (Love et al 03, Xia et al 05, Rho & Rao 05) • Computation of stationary and transition probabilities • Monte Carlo simulation (next slide) Unit Hyper-Sphere Markov Channel Model 9

  14. S2 S1 p13 p33 p63 S3 S6 p64 p43 S4 S5 Proposed Approach: CSI Index Markov Chain • Computation of stationary and transition probabilities • Generate a long channel sequence • Compute CSI index sequence • Compute stationary probability {pn} • Compute transition probability {pnm} 9

  15. Outline • Part I: Theory • Channel Markov model • Feedback compression and rate • Feedback delay • Part II: Practice • Experiment setup • Measurement results

  16. Overview of Feedback Compression CSI Quantization • Extensively studied • [Love et al 04] [Mukkavilli et al 03] Compression (frequency) Compression (time) Compression (space) • Adaptive Codebooks • [Mondal and Heath 05] • Incremental Feedback • [Roh 04][Banister 03] • Subspace Interpolation • [Choi et al 04] Finite-Rate Feedback

  17. Time Variation of Quantized Channel Feedback? Yes No No Yes No No Temporally Correlated Static (Feedback is unnecessary) Fast fading (Compression is ineffective) Aperiodic Feedback • Motivation:Infrequent channel state changes due to temporal correlation • Proposed: aperiodic feedback triggered by channel state changes • Conventional: periodic feedback per block

  18. Feedback Compression = 2 ! 1 bit Truncation Threshold:  = 0.02 -neighborhood of Channel State 1 Truncation of Channel State Transitions Motivation: Given a current state, the next state belongs to a subset of the state space with high probability

  19. Result 1: Average Feedback Rate Proposition 1: The time-average feedback rate converges with time as where Aperiodic Feedback Transition Truncation

  20. ·  >  Truncation of state transitions Quantization Regions Instantaneous Capacity Result 2: Ergodic Capacity Proposition 2: The average capacity converges as where

  21. Case Study: Beamforming for 2£1 Channel • i.i.d CN(0,1) vector • Clark’s correlation function Partial CSI: Beamformer Partial CSI Codebook lookup • Finite rate • Free of error Grassmanian codebook [Love & Heath 03] [Xia & Giannakis 05]

  22. Compression (colors,  = 1e-6) Reference (black,  = 0) Nt = 2 Compression Ratio > 3 Compression Ratio = 2 Case Study: Beamforming for 2£1 Channel Significant reduction on average feedback rates

  23. Case Study: Beamforming for 2£1 Channel Feedback compression causes no loss on ergodic capacity  = 1e-6

  24. Outline • Part I: Theory • Channel Markov model • Feedback compression and rate • Feedback delay • Part II: Practice • Experiment setup • Measurement results

  25. Recap: System Model • Feedback delay exists due to • Propagation • Signal processing • Protocol 7

  26. S2 S1 t S3 S6 t+1 t+2 S4 S5 How to Model Delay ? CSI Variation at Receiver Feedback Delay Model

  27. Convergence of CSI Index Markov Chain Transition probability matrix Stationary Distribution

  28. Result 1: Ergodic Capacity with Feedback Delay Theorem 1: The ergodic capacity with a feedback delay of D symbols is where Quantization Regions Instantaneous Capacity

  29. Result 2: Feedback Capacity Gain Def: Feedback Capacity Gain Theorem 2: The feedback capacity gain C decreases at least exponentially with the feedback delay D as 2 is the 2nd largest eigenvalue of P

  30. Result 2: Feedback Capacity Gain Remarks: D: Feedback Delay  depends on • Type of System • precoding, beamforming etc. • CSI Quantization Codebook  increases inversely with • Channel Coherence Time

  31. Case Study: Beamforming for 2£1 Channel • i.i.d CN(0,1) vector • Clark’s correlation function Partial CSI: Beamformer Partial CSI Codebook lookup • Feedback delay D • Finite rate • Free of error Grassmanian codebook [Love & Heath 03] [Xia & Giannakis 05]

  32. Nt = 2, Nr = 1, N = 16 Feedback Capacity Gain • Feedback capacity gain decreases exponentially with feedback delay; • Decreasing rate is determined by Doppler • Parameters (WiMax): • Carrier = 2.3 GHz • Symbol rate = 1.5 MHz

  33. Nt = 2, Nr = 1, N = 16 Design Example • Requirement A: • Delay ·0.4 ms • Capacity gain ¸1 bps/Hz • Requirement B: • Speed = 140 km/h • Delay = 0.27 ms Vehicular speed ·43 km/h • Parameters (WiMax): • Carrier = 2.3 GHz • Symbol rate = 1.5 MHz Capacity gain = 0.6 bps/Hz

  34. Summary of Theory • We proposed an analytical framework for designing practical limited feedback beamforming system • Feedback rate • Feedback compression • Feedback delay • Observations • Feedback rate increases (e.g. linearly) with Doppler. • Feedback compression significantly reduces feedback rate. • Feedback capacity gain diminishes at least exponentially with feedback delay.

  35. Motivation for Measurement Results • Validate the analytical model • Channel Markov chain assumption • Shannon capacity gain vs. throughput (QAM, adaptive MCS) • Verify theoretical results • Evaluate the impact of practical factors • Synchronization errors • Channel estimation errors • Frequency offset • Phase noise

  36. Outline • Part I: Theory • Channel Markov model • Feedback compression and rate • Feedback delay • Part II: Practice • Experiment setup • Measurement results

  37. Measurement Setup: Hydra Prototype

  38. IEEE 802.11n Transmitter Extended Training: Non-beamformed training symbols to measure true channel Frame Format Bit Parsing: Unnecessary for our experiment with only 1 spatial stream Transmission Process

  39. IEEE 802.11n Receiver Header Decoding: Any problems with header decoding result in dropped measurements Receiver Header Processing Receiver Data Processsing Equalization: Maximal ratio combining for experiments

  40. Feedback Channel Construction • Wired Feedback Advantages (for measurements): • Low latency (compared to Hydra over-the-air feedback) • High reliability (no dropped feedback packets due to frame synchronization errors) • “Perfect” CSI returned to transmitter (floating point samples)

  41. Measurement Topology Wireless Path: 10 m wireless path between transmitter and receiver obstructed by cubicles and office equipment Usage Scenario: Typical wireless local area network (WLAN) environment

  42. Channel Temporal Statistics (Mobility) Antennas: Mounted on oscillating table fans Oscillation Period: TX Period = 13.75 seconds RX Period = 11.25 seconds

  43. Outline • Part I: Theory • Channel Markov model • Feedback compression and rate • Feedback delay • Part II: Practice • Experiment setup • Measurement results

  44. Measurement Procedure Collecting CSI CDD Sounding LF-BF TX RX • Send a packet with cyclic delay diversity from the uninformed transmitter (baseline case). • Send a sounding packet from the transmitter. • Estimate the MIMO channel using the sounding packet. • Select a beamformer from a codebook and return the index over the wired feedback channel. • Send data packets using beamforming with a desired feedback delay. • Repeat steps 1-5 for 1000 iterations and measure the bit error of each packet.

  45. Measure Throughput Gain IEEE 802.11n Modulation and Coding Schemes (Single Stream) Translation to Throughput: Optimal Adaptation: Measurements taken for each MCS over all SNR

  46. Sample Measurement: • MCS 4 (16-QAM w/ 3/4 coding rate) • 5-bit Grassmannian codebook Results - BER Scatter Plot Throughput Curve Fitting: SNR binning with cubic spline interpolation

  47. Results - Throughput Gain Using adaptive MCS

  48. Results - Transition Probability Matrix

  49. Results - Feedback Delay Best Fit: Least squares mapping of measured data to an exponential decay function Theoretical Upper Bound: Analytically derived (earlier) upper bound using transition probability matrix calculation

  50. Conclusions • We proposed an analytical framework for designing limited feedback beamforming systems • Allocate feedback bandwidth • Compress CSI feedback • Compute allowable mobility range, and signal processing and protocol delay. • Theoretical result on feedback delay is validated using measurement data. • More experiments are being carried for verifying other theoretical results. • The proposed framework can be extended to other types of limited feedback systems e.g. precoding.

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